Finite Group Databasebeta

← #33253746

Subgroups — #33253746

Order 18688.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989114C211yesmaximal, characteristic, complemented
2C22×D4×Dic73C211yesmaximal, characteristic, complemented
3#22614189C211yesmaximal, characteristic, complemented
4#22614174C211yesmaximal, characteristic, complemented
5#22614069C211yesmaximal, characteristic, complemented
6#22614054C211yesmaximal, characteristic, complemented
7#22613975C211yesmaximal, characteristic, complemented
8#22613960C211yesmaximal, characteristic, complemented
9#22613876C211yesmaximal, characteristic, complemented
10#22613861C211yesmaximal, characteristic, complemented
11#22613761C211yesmaximal, characteristic, complemented
12#22613679C211yesmaximal, characteristic, complemented
13#22613597C211yesmaximal, characteristic, complemented
14#22613486C211yesmaximal, characteristic, complemented
15#22613404C211yesmaximal, characteristic, complemented
16#22613327C211yesmaximal, characteristic, complemented
17#22613305C211yesmaximal, characteristic
18#22613219C211yesmaximal, characteristic, complemented
19#22613187C211yesmaximal, characteristic, complemented
20#22613174C211yesmaximal, characteristic, complemented
21#22613170C211yesmaximal, characteristic, complemented
22#22612463C211yesmaximal, characteristic, complemented
23#123×Dic73C211yesmaximal, characteristic, complemented
24#22612441C211yesmaximal, characteristic, complemented
25#22612430C211yesmaximal, characteristic, complemented
26#22612430C211yesmaximal, characteristic, complemented
27#22612371C211yesmaximal, characteristic, complemented
28#22612367C211yesmaximal, characteristic, complemented
29#22612309C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2405C211yesmaximal, characteristic, complemented
32C24×Dic73C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34#17989114—28no—
35C2×#14556586C2211yescharacteristic, complemented
36C2×#14556584C2211yescharacteristic, complemented
37C2×#14556581C2211yescharacteristic, complemented
38C2×#14556577C2211yescharacteristic, complemented
39C2×#14556574C2211yescharacteristic, complemented
40C2×#14556568C2211yescharacteristic
41C2×#14556568C2211yescharacteristic, complemented
42C2×#14556563C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556560C2211yescharacteristic
45C2×#14556560C2211yescharacteristic
46C2×#14556556C2211yescharacteristic, complemented
47C2×D4×Dic73—28no—
48C2×D4×Dic73C2211yescharacteristic
49C2×D4×Dic73C2211yescharacteristic
50C2×D4×Dic73C2211yescharacteristic
51C2×D4×Dic73C2211yescharacteristic
52C2×D4×Dic73C2211yescharacteristic
53C2×D4×Dic73C2211yescharacteristic
54C2×D4×Dic73C2211yescharacteristic
55C2×D4×Dic73C2211yescharacteristic
56C2×#14556551C2211yescharacteristic
57C2×#14556551C2211yescharacteristic, complemented
58C2×#14556551C2211yescharacteristic, complemented
59C2×#14556551C2211yescharacteristic, complemented
60C2×#14556551C2211yescharacteristic, complemented
61C2×#14556549C2211yescharacteristic, complemented
62C2×#14556547C2211yescharacteristic, complemented
63C2×#14556547C2211yescharacteristic, complemented
64C22×C4⋊Dic73C2211yescharacteristic
65C22×C22⋊Dic73C2211yescharacteristic
66C22×C22⋊Dic73C2211yescharacteristic
67C22×C22⋊Dic73C2211yescharacteristic
68C22×C4×Dic73C2211yescharacteristic
69C22×C4×Dic73C2211yescharacteristic, complemented
70C22×C4×Dic73C2211yescharacteristic, complemented
71#17988529C2211yescharacteristic, complemented
72#17988527C2211yescharacteristic, complemented
73#17988526C2211yescharacteristic, complemented
74#17988523C2211yescharacteristic, complemented
75#17988521C2211yescharacteristic, complemented
76#17988520C2211yescharacteristic, complemented
77#17988517C2211yescharacteristic, complemented
78#17988515C2211yescharacteristic, complemented
79#17988515C2211yescharacteristic, complemented
80#17988515C2211yescharacteristic, complemented
81#17988515C2211yescharacteristic, complemented
82#17988515C2211yescharacteristic, complemented
83#17988514C2211yescharacteristic, complemented
84#17988512C2211yescharacteristic, complemented
85#17988510C2211yescharacteristic, complemented
86#17988510C2211yescharacteristic, complemented
87#17988510C2211yescharacteristic, complemented
88#17988509C2211yescharacteristic, complemented
89#17988503C2211yescharacteristic, complemented
90#17988502C2211yescharacteristic, complemented
91#17988502C2211yescharacteristic, complemented
92#17988502C2211yescharacteristic, complemented
93#17988501C2211yescharacteristic
94#17988501C2211yescharacteristic
95#17988499C2211yescharacteristic, complemented
96#17988499C2211yescharacteristic, complemented
97#17988495C2211yescharacteristic
98#17988495C2211yescharacteristic
99#17988491C2211yescharacteristic, complemented
100#17988487C2211yescharacteristic, complemented
101#17988484C2211yescharacteristic, complemented
102#17988482C2211yescharacteristic, complemented
103#17988481C2211yescharacteristic, complemented
104#17988480C2211yescharacteristic, complemented
105#17988480C2211yescharacteristic, complemented
106#17988479C2211yescharacteristic, complemented
107#17988479C2211yescharacteristic, complemented
108#17988477C2211yescharacteristic, complemented
109#17988475C2211yescharacteristic, complemented
110#17988475C2211yescharacteristic, complemented
111#17988474C2211yescharacteristic, complemented
112#17988473C2211yescharacteristic, complemented
113#17988473C2211yescharacteristic, complemented
114#17988472C2211yescharacteristic, complemented
115#17988472C2211yescharacteristic, complemented
116#17988470C2211yescharacteristic, complemented
117#17988468C2211yescharacteristic, complemented
118#17988468C2211yescharacteristic, complemented
119#17988467C2211yescharacteristic
120#17988467C2211yescharacteristic
121#17988466C2211yescharacteristic
122#17988466C2211yescharacteristic, complemented
123#17988464C2211yescharacteristic
124#17988464C2211yescharacteristic
125#17988464C2211yescharacteristic
126#17988464C2211yescharacteristic, complemented
127#17988464C2211yescharacteristic, complemented
128#17988464C2211yescharacteristic, complemented
129#17988464C2211yescharacteristic, complemented
130#17988462C2211yescharacteristic
131#17988462C2211yescharacteristic, complemented
132#17988460C2211yescharacteristic
133#17988460C2211yescharacteristic, complemented
134#17988459C2211yescharacteristic
135#17988459C2211yescharacteristic
136#17988459C2211yescharacteristic, complemented
137#17988459C2211yescharacteristic, complemented
138#17988459C2211yescharacteristic, complemented
139#17988459C2211yescharacteristic, complemented
140#17988459C2211yescharacteristic, complemented
141#17988450C2211yescharacteristic, complemented
142#17988448C2211yescharacteristic, complemented
143#17988448C2211yescharacteristic, complemented
144#17988445C2211yescharacteristic
145#17988445C2211yescharacteristic
146#17988445C2211yescharacteristic
147#17988445C2211yescharacteristic, complemented
148#17988445C2211yescharacteristic, complemented
149#17988445C2211yescharacteristic, complemented
150#17988443C2211yescharacteristic
151C4⋊C4×Dic73C2211yescharacteristic, complemented
152C4⋊C4×Dic73C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic, complemented
161C22⋊C4×Dic73C2211yescharacteristic, complemented
162C22⋊C4×Dic73C2211yescharacteristic, complemented
163C22⋊C4×Dic73C2211yescharacteristic, complemented
164C22⋊C4×Dic73C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic, complemented
166C22⋊C4×Dic73C2211yescharacteristic, complemented
167C22⋊C4×Dic73C2211yescharacteristic, complemented
168C22⋊C4×Dic73C2211yescharacteristic, complemented
169C22⋊C4×Dic73C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic, complemented
173C2×#14556498C2211yescharacteristic, complemented
174C23×D4×C73C2211yescharacteristic
175C2×#123×C73C2211yescharacteristic
176C2×#123×C73C2211yescharacteristic
177C22×C22⋊C4×C73C2211yescharacteristic
178#394×C73C2211yescharacteristic
179#394×C73C2211yescharacteristic
180#394×C73C2211yescharacteristic
181#394×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#385×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186#379×C73C2211yescharacteristic
187#379×C73C2211yescharacteristic
188#379×C73C2211yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C23×Dic73—24no—
196C23×Dic73—24no—
197C23×Dic73—24no—
198C23×Dic73—24no—
199C23×Dic73—42no—
200C23×Dic73—42no—
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C23×Dic73C2311yescharacteristic
208C23×Dic73C2311yescharacteristic
209C23×Dic73C2311yescharacteristic
210C23×Dic73C2311yescharacteristic
211C23×Dic73C2311yescharacteristic
212C23×Dic73C2311yescharacteristic
213C23×Dic73C2311yescharacteristic
214C23×Dic73C2311yescharacteristic
215C22×C4×D73C2311yescharacteristic
216#14556586—24no—
217#14556584—24no—
218#14556581—24no—
219#14556577—24no—
220#14556574—24no—
221#14556568—24no—
222#14556568—24no—
223#14556563—24no—
224#14556563—24no—
225#14556560—24no—
226#14556560—24no—
227#14556556—24no—
228D4×Dic73—24no—
229D4×Dic73—24no—
230D4×Dic73—24no—
231D4×Dic73—24no—
232D4×Dic73—24no—
233D4×Dic73—24no—
234D4×Dic73—24no—
235D4×Dic73D418yescomplemented
236#14556551—24no—
237#14556551—24no—
238#14556551—24no—
239#14556551—42no—
240#14556551—42no—
241#14556549—24no—
242#14556547—24no—
243#14556547—42no—
244C2×C4⋊Dic73—24no—
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×C22⋊Dic73—24no—
268C2×C22⋊Dic73—24no—
269C2×C22⋊Dic73—24no—
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×C22⋊Dic73C2311yescharacteristic
289C2×C22⋊Dic73C2311yescharacteristic
290C2×C22⋊Dic73C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×C4×Dic73—24no—
301C2×C4×Dic73—24no—
302C2×C4×Dic73—42no—
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308C2×C4×Dic73C2311yescharacteristic
309C2×C4×Dic73C2311yescharacteristic
310C2×C4×Dic73C2311yescharacteristic
311C2×C4×Dic73C2311yescharacteristic
312C2×C4×Dic73C2311yescharacteristic
313C2×C4×Dic73C2311yescharacteristic
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348#14556498C2311yescharacteristic
349#14556498C2311yescharacteristic
350C25×C73C2311yescharacteristic
351C25×C73C2311yescharacteristic
352C22×D4×C73—24no—
353C22×D4×C73—24no—
354C22×D4×C73—24no—
355C22×D4×C73C2311yescharacteristic
356C22×D4×C73C2311yescharacteristic
357C22×D4×C73C2311yescharacteristic
358C22×D4×C73C2311yescharacteristic
359C23×C4×C73C2311yescharacteristic
360C23×C4×C73C2311yescharacteristic
361C23×C4×C73C2311yescharacteristic
362#123×C73—24no—
363#123×C73—24no—
364C2×C4⋊C4×C73C2311yescharacteristic
365C2×C4⋊C4×C73C2311yescharacteristic
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C4⋊C4×C73C2311yescharacteristic
368C2×C22⋊C4×C73—24no—
369C2×C22⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73C2311yescharacteristic
372C2×C22⋊C4×C73C2311yescharacteristic
373C2×C22⋊C4×C73C2311yescharacteristic
374C2×C22⋊C4×C73C2311yescharacteristic
375C2×C22⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73C2311yescharacteristic
377C2×C22⋊C4×C73C2311yescharacteristic
378C2×C22⋊C4×C73C2311yescharacteristic
379C2×C22⋊C4×C73C2311yescharacteristic
380C2×C22⋊C4×C73C2311yescharacteristic
381C2×C22⋊C4×C73C2311yescharacteristic
382C2×C22⋊C4×C73C2311yescharacteristic
383C2×C22⋊C4×C73C2311yescharacteristic
384C2×C22⋊C4×C73C2311yescharacteristic
385C2×C22⋊C4×C73C2311yescharacteristic
386C2×C22⋊C4×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389#95×C73C2311yescharacteristic
390#95×C73C2311yescharacteristic
391C23×D73C2411yescharacteristic
392C2×Dic146—22no—
393C2×Dic146—22no—
394C2×Dic146—41no—
395C2×C22⋊D73—22no—
396C2×C22⋊D73—22no—
397C2×C22⋊D73—22no—
398C2×C22⋊D73—22no—
399C2×C22⋊D73—22no—
400C2×C22⋊D73—22no—
401C2×C22⋊D73—22no—
402C2×C22⋊D73—22no—
403C2×C22⋊D73—22no—
404C2×C22⋊D73—22no—
405C2×C22⋊D73—22no—
406C2×C22⋊D73—41no—
407C2×C22⋊D73—41no—
408C2×C22⋊D73—41no—
409C2×C22⋊D73—41no—
410C22×Dic73—22no—
411C22×Dic73—22no—
412C22×Dic73—22no—
413C22×Dic73—22no—
414C22×Dic73—22no—
415C22×Dic73—22no—
416C22×Dic73—22no—
417C22×Dic73—22no—
418C22×Dic73—22no—
419C22×Dic73—22no—
420C22×Dic73—22no—
421C22×Dic73—22no—
422C22×Dic73—22no—
423C22×Dic73—22no—
424C22×Dic73—22no—
425C22×Dic73—22no—
426C22×Dic73—22no—
427C22×Dic73—22no—
428C22×Dic73—22no—
429C22×Dic73—22no—
430C22×Dic73—22no—
431C22×Dic73—22no—
432C22×Dic73—22no—
433C22×Dic73—22no—
434C22×Dic73—22no—
435C22×Dic73—22no—
436C22×Dic73—22no—
437C22×Dic73—22no—
438C22×Dic73—22no—
439C22×Dic73—22no—
440C22×Dic73—41no—
441C22×Dic73—41no—
442C22×Dic73—41no—
443C22×Dic73—41no—
444C22×Dic73—41no—
445C22×Dic73—41no—
446C22×Dic73—41no—
447C22×Dic73—41no—
448C22×Dic73—41no—
449C22×Dic73—416no—
450C22×Dic73—416no—
451C22×Dic73C2×D414yes—
452C22×Dic73C2×D414yes—
453C22×Dic73#4114yes—
454C22×Dic73C2411yescharacteristic
455C22×Dic73C2411yescharacteristic
456C22×Dic73C2411yescharacteristic
457C22×Dic73C2411yescharacteristic
458C22×Dic73C2411yescharacteristic
459C22×Dic73C2411yescharacteristic
460C22×Dic73C2411yescharacteristic
461C22×Dic73C2411yescharacteristic
462C22×Dic73C2411yescharacteristic
463C22×Dic73C2411yescharacteristic
464C22×Dic73C2411yescharacteristic
465C22×Dic73C2411yescharacteristic
466C22×Dic73C2411yescharacteristic
467C22×Dic73C2411yescharacteristic
468C22×Dic73C2411yescharacteristic
469C2×C4×D73—22no—
470C2×C4×D73—22no—
471C2×C4×D73—22no—
472C4⋊Dic73—22no—
473C4⋊Dic73—22no—
474C4⋊Dic73—22no—
475C4⋊Dic73—22no—
476C4⋊Dic73—22no—
477C4⋊Dic73—41no—
478C4⋊Dic73C2×D414yes—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007—22no—
486#11924007—22no—
487#11924007—22no—
488#11924007—22no—
489#11924007—41no—
490#11924007—41no—
491#11924007—41no—
492#11924007—41no—
493#11924007—41no—
494C22⋊Dic73—22no—
495C22⋊Dic73—22no—
496C22⋊Dic73—22no—
497C22⋊Dic73—22no—
498C22⋊Dic73—22no—
499C22⋊Dic73—22no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—22no—
503C22⋊Dic73—22no—
504C22⋊Dic73—22no—
505C22⋊Dic73—22no—
506C22⋊Dic73—22no—
507C22⋊Dic73—22no—
508C22⋊Dic73—22no—
509C22⋊Dic73—22no—
510C22⋊Dic73—41no—
511C22⋊Dic73—41no—
512C22⋊Dic73C2×D414yes—
513C22⋊Dic73C2×D414yes—
514C22⋊Dic73#4114yes—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—41no—
522#11924005—41no—
523#11924005—41no—
524C4×Dic73—22no—
525C4×Dic73—22no—
526C4×Dic73—22no—
527C4×Dic73—22no—
528C4×Dic73—22no—
529C4×Dic73—22no—
530C4×Dic73—22no—
531C4×Dic73—22no—
532C4×Dic73—22no—
533C4×Dic73—22no—
534C4×Dic73—22no—
535C4×Dic73—22no—
536C4×Dic73—41no—
537C4×Dic73—41no—
538C4×Dic73C2×D414yes—
539C24×C73—22no—
540C24×C73—22no—
541C24×C73—22no—
542C24×C73—22no—
543C24×C73—22no—
544C24×C73—22no—
545C24×C73—22no—
546C24×C73—22no—
547C24×C73—22no—
548C24×C73—41no—
549C24×C73—41no—
550C24×C73—41no—
551C24×C73—41no—
552C24×C73#4114yes—
553C24×C73C2411yescharacteristic
554C24×C73C2411yescharacteristic
555C24×C73C2411yescharacteristic
556C24×C73C2411yescharacteristic
557C24×C73C2411yescharacteristic
558C2×D4×C73—232no—
559C2×D4×C73—22no—
560C2×D4×C73—22no—
561C2×D4×C73—22no—
562C2×D4×C73—22no—
563C2×D4×C73—22no—
564C2×D4×C73—22no—
565C2×D4×C73—22no—
566C2×D4×C73—22no—
567C2×D4×C73—22no—
568C2×D4×C73—22no—
569C2×D4×C73C2×D414yes—
570C2×D4×C73#4114yes—
571C22×C4×C73—22no—
572C22×C4×C73—22no—
573C22×C4×C73—22no—
574C22×C4×C73—22no—
575C22×C4×C73—22no—
576C22×C4×C73—22no—
577C22×C4×C73—22no—
578C22×C4×C73—41no—
579C22×C4×C73—41no—
580C22×C4×C73C2411yescharacteristic
581C22×C4×C73C2411yescharacteristic
582C22×C4×C73C2411yescharacteristic
583C22×C4×C73C2411yescharacteristic
584C22×C4×C73C2411yescharacteristic
585C22×C4×C73C2411yescharacteristic
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C4⋊C4×C73—22no—
591C4⋊C4×C73—22no—
592C4⋊C4×C73—22no—
593C4⋊C4×C73—22no—
594C22⋊C4×C73—22no—
595C22⋊C4×C73—22no—
596C22⋊C4×C73—22no—
597C22⋊C4×C73—22no—
598C22⋊C4×C73—22no—
599C22⋊C4×C73—22no—
600C22⋊C4×C73—22no—
601C22⋊C4×C73—22no—
602C22⋊C4×C73—22no—
603C22⋊C4×C73—22no—
604C22⋊C4×C73—22no—
605C22⋊C4×C73—22no—
606C22⋊C4×C73—41no—
607C22⋊C4×C73—41no—
608C22⋊C4×C73—41no—
609C22⋊C4×C73—41no—
610C22⋊C4×C73—41no—
611C22⋊C4×C73—41no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—28no—
621C23×C73—28no—
622C23×C73—28no—
623C23×C73—21no—
624C23×C73—21no—
625C23×C73—21no—
626C23×C73—21no—
627C23×C73—21no—
628C23×C73—21no—
629C23×C73—21no—
630C23×C73—21no—
631C23×C73—21no—
632C23×C73—21no—
633C23×C73—21no—
634C23×C73—21no—
635C23×C73—21no—
636C23×C73—21no—
637C23×C73—21no—
638C23×C73—21no—
639C23×C73—21no—
640C23×C73—21no—
641C23×C73—44no—
642C23×C73—44no—
643C23×C73—44no—
644C23×C73—44no—
645C23×C73—44no—
646C23×C73—44no—
647C23×C73—44no—
648C23×C73—44no—
649C23×C73—44no—
650C23×C73—44no—
651C23×C73—44no—
652C23×C73C22×D412yes—
653C23×C73C22×D412yes—
654C23×C73C2×#4112yes—
655C23×C73C2×#4112yes—
656C23×C73C2×#4112yes—
657C23×C73C2×#4112yes—
658C23×C73C2×#4112yes—
659C23×C73C2×#4112yes—
660C23×C73C2×#4112yes—
661C23×C73C2511yescharacteristic
662C22×D73—21no—
663C22×D73—21no—
664C22×D73—21no—
665C22×D73—21no—
666C22×D73—21no—
667C22×D73—21no—
668C22×D73—21no—
669D4×C73—28no—
670D4×C73—28no—
671D4×C73—28no—
672D4×C73—28no—
673C2×C4×C73—28no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—21no—
696C2×C4×C73—21no—
697C2×C4×C73—21no—
698C2×C4×C73—21no—
699C2×C4×C73—21no—
700C2×C4×C73—21no—
701C2×C4×C73—21no—
702C2×C4×C73—44no—
703C2×C4×C73—44no—
704C2×C4×C73C22×D412yes—
705C2×C4×C73C2×#4112yes—
706C22⋊D73—44no—
707C22⋊D73—44no—
708C22⋊D73—44no—
709C22⋊D73—44no—
710C22⋊D73—44no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—28no—
724C2×Dic73—28no—
725C2×Dic73—28no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—21no—
731C2×Dic73—21no—
732C2×Dic73—21no—
733C2×Dic73—21no—
734C2×Dic73—21no—
735C2×Dic73—21no—
736C2×Dic73—21no—
737C2×Dic73—21no—
738C2×Dic73—21no—
739C2×Dic73—21no—
740C2×Dic73—21no—
741C2×Dic73—21no—
742C2×Dic73—21no—
743C2×Dic73—21no—
744C2×Dic73—21no—
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—21no—
750C2×Dic73—44no—
751C2×Dic73—44no—
752C2×Dic73—44no—
753C2×Dic73—44no—
754C2×Dic73—44no—
755C2×Dic73—44no—
756C2×Dic73—44no—
757C2×Dic73—44no—
758C2×Dic73—44no—
759C2×Dic73—44no—
760C2×Dic73—44no—
761C2×Dic73C22×D412yes—
762C2×Dic73C22×D412yes—
763C2×Dic73C22×D412yes—
764C2×Dic73C22×D412yes—
765C2×Dic73C2×#4112yes—
766C2×Dic73C2×#4112yes—
767C2×Dic73C2×#4112yes—
768C2×Dic73C2×#4112yes—
769C2×Dic73H(5,𝔽2)12yes—
770C4×D73—44no—
771Dic146—44no—
772C22×C73—22no—
773C22×C73—22no—
774C22×C73—22no—
775C22×C73—22no—
776C22×C73—22no—
777C22×C73—22no—
778C22×C73—22no—
779C22×C73—22no—
780C22×C73—22no—
781C22×C73—22no—
782C22×C73—22no—
783C22×C73—22no—
784C22×C73—22no—
785C22×C73—22no—
786C22×C73—22no—
787C22×C73—22no—
788C22×C73—22no—
789C22×C73—22no—
790C22×C73—22no—
791C22×C73—22no—
792C22×C73—22no—
793C22×C73—416no—
794C22×C73—416no—
795C22×C73—41no—
796C22×C73—41no—
797C22×C73—41no—
798C22×C73—41no—
799C22×C73—41no—
800C22×C73—41no—
801C22×C73—41no—
802C22×C73—41no—
803C22×C73—41no—
804C22×C73—41no—
805C22×C73—41no—
806C22×C73—41no—
807C22×C73#52514yes—
808C22×C73#52914yescomplemented
809C22×C73C23×D411yescharacteristic
810C22×C73C22×#4111yescharacteristic
811C22×C73C22×#4111yescharacteristic
812C22×C73C22×#4111yescharacteristic
813C22×C73C22×#4111yescharacteristic
814C22×C73C2×H(5,𝔽2)11yescharacteristic
815C22×C73#58511yescharacteristic
816C2×D73—41no—
817C2×D73—41no—
818C2×D73—41no—
819C2×D73—41no—
820C2×D73—41no—
821C2×D73—41no—
822C2×D73—41no—
823C4×C73—22no—
824C4×C73—22no—
825C4×C73—41no—
826C4×C73—41no—
827C4×C73—41no—
828C4×C73—41no—
829C4×C73—41no—
830C4×C73—41no—
831C4×C73—41no—
832C4×C73—41no—
833Dic73—22no—
834Dic73—22no—
835Dic73—22no—
836Dic73—22no—
837Dic73—22no—
838Dic73—22no—
839Dic73—41no—
840Dic73—41no—
841Dic73—41no—
842Dic73—41no—
843Dic73—41no—
844Dic73—41no—
845Dic73—41no—
846Dic73—41no—
847Dic73#54614yes—
848#34670—731nomaximal, Sylow
849C2×C73—24no—
850C2×C73—24no—
851C2×C73—42no—
852C2×C73—42no—
853C2×C73—42no—
854C2×C73C2×#52511yescharacteristic
855C2×C73C2×#52911yescharacteristic
856C2×C73#345911yescharacteristic
857C2×C73C2×#54611yescharacteristic
858C2×C73D4×#4111yescharacteristic
859C2×C73#347511yescharacteristic
860C2×C73#348111yescharacteristic
861D73—81no—
862C2×#529—731no—
863C22×C4×D4—731no—
864#2481—731no—
865#2480—731no—
866#2473—731no—
867#2472—731no—
868#2467—731no—
869#2466—731no—
870#2460—731no—
871#2459—731no—
872#2450—731no—
873#2444—731no—
874#2437—731no—
875#2425—731no—
876#2419—731no—
877#2412—731no—
878#2410—731no—
879#2405D7311yescharacteristic, complemented
880#2398—731no—
881#2395—731no—
882#2392—731no—
883#2392—731no—
884C4×C22⋊Q8—731no—
885C4×#123—731no—
886C4×#121—731no—
887C4×#120—731no—
888C4×#120—731no—
889#2290—731no—
890#2290—731no—
891#2280—731no—
892C2×C4×C22⋊C4—731no—
893C73#3467011yescharacteristic, complemented, Sylow
894C23×D4C2×D7311yescharacteristic
895C24×C4—731no—
896C24×C4—731no—
897#529—1468no—
898C2×#126—731no—
899C2×#126—731no—
900C2×#125—731no—
901C2×#124—731no—
902C2×#123—731no—
903C2×#123C2×D7311yescharacteristic
904C2×#123C2×D7311yescharacteristic
905C2×C22⋊Q8—731no—
906C2×C22⋊Q8—731no—
907C2×#121—731no—
908C2×#121—731no—
909C2×#120—731no—
910C2×#120—731no—
911C2×C4×Q8—731no—
912C2×C4×D4—731no—
913C2×C4×D4—731no—
914C2×C4×D4—731no—
915C2×C4×D4—731no—
916C2×C4×D4—731no—
917C2×C4×D4—731no—
918C2×C4×D4—731no—
919C2×C4×D4—731no—
920C2×C4×D4—731no—
921C2×C4×D4—731no—
922C2×C4×D4—731no—
923C2×C4×D4—731no—
924C2×C4×D4—731no—
925C2×C4×D4—1468no—
926C2×#117—731no—
927C2×#117—731no—
928C2×#117—731no—
929C22×C4⋊C4—731no—
930C22×C22⋊C4—731no—
931C22×C22⋊C4—731no—
932C22×C22⋊C4—731no—
933C22×C22⋊C4C2×D7311yescharacteristic
934C22×C42—731no—
935C22×C42—731no—
936C22×C42—731no—
937#400—731no—
938#400—731no—
939#400—731no—
940#399—731no—
941#398—731no—
942#398—731no—
943#398—731no—
944#397—731no—
945#397—731no—
946#397—731no—
947#397—731no—
948#397—731no—
949#397—731no—
950#397—731no—
951#396—731no—
952#396—731no—
953#396—731no—
954#396—731no—
955#394—731no—
956#394—731no—
957#394—731no—
958#394—731no—
959#394—731no—
960#394—731no—
961#394C2×D7311yescharacteristic
962#394C2×D7311yescharacteristic
963#394C2×D7311yescharacteristic
964#394C2×D7311yescharacteristic
965#393—731no—
966#393—731no—
967#392—731no—
968#392—731no—
969#391—731no—
970#390—731no—
971#389—731no—
972#389—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#387—731no—
982#387—731no—
983#387—731no—
984#387—731no—
985#387—731no—
986#387—731no—
987#387—731no—
988#387—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#386—731no—
1000#386C2×D7311yescharacteristic
1001#386C2×D7311yescharacteristic
1002#385—731no—
1003#385—731no—
1004#385—731no—
1005#385—731no—
1006#385—731no—
1007#385—731no—
1008#385—731no—
1009#385—731no—
1010#385—731no—
1011#385—731no—
1012#385—731no—
1013#385C2×D7311yescharacteristic
1014#385C2×D7311yescharacteristic
1015#381—731no—
1016#381—731no—
1017#381—731no—
1018#380—731no—
1019#380—731no—
1020#380—731no—
1021#380—731no—
1022#380—731no—
1023#380—731no—
1024#379—731no—
1025#379C2×D7311yescharacteristic
1026#379C2×D7311yescharacteristic
1027#379C2×D7311yescharacteristic
1028C4×C4⋊C4—731no—
1029C4×C4⋊C4—731no—
1030C4×C4⋊C4—731no—
1031C4×C4⋊C4—731no—
1032C4×C22⋊C4—731no—
1033C4×C22⋊C4—731no—
1034C4×C22⋊C4—731no—
1035C4×C22⋊C4—731no—
1036C4×C22⋊C4—731no—
1037C4×C22⋊C4—731no—
1038C4×C22⋊C4—731no—
1039C4×C22⋊C4—731no—
1040C4×C22⋊C4—731no—
1041C4×C22⋊C4—731no—
1042C4×C22⋊C4—731no—
1043C4×C22⋊C4—731no—
1044C4×C22⋊C4—731no—
1045C4×C22⋊C4—731no—
1046C4×C22⋊C4—731no—
1047C4×C22⋊C4—731no—
1048#376—731no—
1049C2×#95—731no—
1050C2×#95—731no—
1051C25C22×D7311yescharacteristic
1052C25C22×D7311yescharacteristic
1053C22×Q8—731no—
1054C22×D4—24no—
1055C22×D4—24no—
1056C22×D4—24no—
1057C22×D4—731no—
1058C22×D4—731no—
1059C22×D4—731no—
1060C22×D4—731no—
1061C22×D4—731no—
1062C22×D4C22×D7311yescharacteristic
1063C22×D4C22×D7311yescharacteristic
1064C22×D4C22×D7311yescharacteristic
1065C22×D4C22×D7311yescharacteristic
1066C23×C4—2922no—
1067C23×C4—2922no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4—731no—
1072C23×C4—731no—
1073C23×C4—731no—
1074C23×C4—731no—
1075C23×C4—731no—
1076C23×C4—731no—
1077C23×C4—731no—
1078C23×C4—731no—
1079C23×C4—731no—
1080C23×C4—731no—
1081C23×C4—731no—
1082C23×C4—731no—
1083C23×C4—1464no—
1084C23×C4—1464no—
1085C23×C4—1464no—
1086C23×C4—1464no—
1087C23×C4C22×D7311yescharacteristic
1088C23×C4C22×D7311yescharacteristic
1089C23×C4C22×D7311yescharacteristic
1090#126—1464no—
1091#126—1464no—
1092#125—1464no—
1093#124—1464no—
1094#123—24no—
1095#123—24no—
1096#123—1464no—
1097C22⋊Q8—1464no—
1098C22⋊Q8—1464no—
1099#121—1464no—
1100#121—1464no—
1101#120—1464no—
1102#120—1464no—
1103C4×Q8—1464no—
1104C4×D4—2922no—
1105C4×D4—2922no—
1106C4×D4—738no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4—1464no—
1112C4×D4—1464no—
1113C4×D4—1464no—
1114C4×D4—1464no—
1115C4×D4—1464no—
1116C4×D4—1464no—
1117#117—2922no—
1118#117—1464no—
1119#117—1464no—
1120C2×C4⋊C4—731no—
1121C2×C4⋊C4—731no—
1122C2×C4⋊C4—731no—
1123C2×C4⋊C4—731no—
1124C2×C4⋊C4—731no—
1125C2×C4⋊C4—731no—
1126C2×C4⋊C4—731no—
1127C2×C4⋊C4—731no—
1128C2×C4⋊C4—731no—
1129C2×C4⋊C4—731no—
1130C2×C4⋊C4—731no—
1131C2×C4⋊C4—731no—
1132C2×C4⋊C4—731no—
1133C2×C4⋊C4—731no—
1134C2×C4⋊C4—731no—
1135C2×C4⋊C4—731no—
1136C2×C4⋊C4—731no—
1137C2×C4⋊C4—731no—
1138C2×C4⋊C4—731no—
1139C2×C4⋊C4—731no—
1140C2×C4⋊C4—731no—
1141C2×C4⋊C4—731no—
1142C2×C4⋊C4—1464no—
1143C2×C4⋊C4C22×D7311yescharacteristic
1144C2×C4⋊C4C22×D7311yescharacteristic
1145C2×C4⋊C4C22×D7311yescharacteristic
1146C2×C4⋊C4C22×D7311yescharacteristic
1147C2×C22⋊C4—24no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4—731no—
1171C2×C22⋊C4—731no—
1172C2×C22⋊C4—731no—
1173C2×C22⋊C4—731no—
1174C2×C22⋊C4—731no—
1175C2×C22⋊C4—731no—
1176C2×C22⋊C4—731no—
1177C2×C22⋊C4—731no—
1178C2×C22⋊C4—1464no—
1179C2×C22⋊C4—1464no—
1180C2×C22⋊C4—1464no—
1181C2×C22⋊C4C22×D7311yescharacteristic
1182C2×C22⋊C4C22×D7311yescharacteristic
1183C2×C22⋊C4C22×D7311yescharacteristic
1184C2×C22⋊C4C22×D7311yescharacteristic
1185C2×C22⋊C4C22×D7311yescharacteristic
1186C2×C22⋊C4C22×D7311yescharacteristic
1187C2×C22⋊C4C22×D7311yescharacteristic
1188C2×C22⋊C4C22×D7311yescharacteristic
1189C2×C22⋊C4C22×D7311yescharacteristic
1190C2×C22⋊C4C22×D7311yescharacteristic
1191C2×C22⋊C4C22×D7311yescharacteristic
1192C2×C22⋊C4C22×D7311yescharacteristic
1193C2×C22⋊C4C22×D7311yescharacteristic
1194C2×C22⋊C4C22×D7311yescharacteristic
1195C2×C22⋊C4C22×D7311yescharacteristic
1196C2×C22⋊C4C22×D7311yescharacteristic
1197C2×C22⋊C4C22×D7311yescharacteristic
1198C2×C22⋊C4C22×D7311yescharacteristic
1199C2×C42—2922no—
1200C2×C42—731no—
1201C2×C42—731no—
1202C2×C42—731no—
1203C2×C42—731no—
1204C2×C42—731no—
1205C2×C42—731no—
1206C2×C42—731no—
1207C2×C42—731no—
1208C2×C42—731no—
1209C2×C42—731no—
1210C2×C42—731no—
1211C2×C42—731no—
1212C2×C42—731no—
1213C2×C42—731no—
1214C2×C42—731no—
1215C2×C42—1464no—
1216C2×C42—1464no—
1217#95—731no—
1218#95—731no—
1219#95—731no—
1220#95—731no—
1221#95—731no—
1222#95—731no—
1223#95—731no—
1224#95—731no—
1225#95—731no—
1226#95—731no—
1227#95—731no—
1228#95—731no—
1229#95—731no—
1230#95—731no—
1231#95—731no—
1232#95—731no—
1233#95—731no—
1234#95—731no—
1235#95—731no—
1236#95—731no—
1237#95—731no—
1238#95—731no—
1239#95—731no—
1240#95—731no—
1241#95—731no—
1242#95—731no—
1243#95—731no—
1244#95—731no—
1245#95—731no—
1246#95—731no—
1247#95—731no—
1248#95—731no—
1249#95C22×D7311yescharacteristic
1250#95C22×D7311yescharacteristic
1251#95C22×D7311yescharacteristic
1252#95C22×D7311yescharacteristic
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—22no—
1258C24—22no—
1259C24—22no—
1260C24—22no—
1261C24—22no—
1262C24—41no—
1263C24—41no—
1264C24—41no—
1265C24—41no—
1266C24—731no—
1267C24#1192402714yes—
1268C24C23×D7311yescharacteristic
1269C24C23×D7311yescharacteristic
1270C24C23×D7311yescharacteristic
1271C24C23×D7311yescharacteristic
1272C24C23×D7311yescharacteristic
1273C2×Q8—2921no—
1274C2×Q8—1462no—
1275C2×Q8—1462no—
1276C2×D4—232no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—22no—
1287C2×D4—2921no—
1288C2×D4—2921no—
1289C2×D4—2921no—
1290C2×D4—2921no—
1291C2×D4—1462no—
1292C2×D4—1462no—
1293C2×D4—1462no—
1294C2×D4—1462no—
1295C2×D4—1462no—
1296C2×D4—1462no—
1297C2×D4—1462no—
1298C2×D4—1462no—
1299C2×D4—1462no—
1300C2×D4—1462no—
1301C2×D4—1462no—
1302C2×D4D4×D7314yes—
1303C2×D4#1192402714yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—2921no—
1314C22×C4—2921no—
1315C22×C4—2921no—
1316C22×C4—2921no—
1317C22×C4—2921no—
1318C22×C4—2921no—
1319C22×C4—2921no—
1320C22×C4—2921no—
1321C22×C4—2921no—
1322C22×C4—29216no—
1323C22×C4—29216no—
1324C22×C4—731no—
1325C22×C4—734no—
1326C22×C4—734no—
1327C22×C4—734no—
1328C22×C4—731no—
1329C22×C4—731no—
1330C22×C4—731no—
1331C22×C4—731no—
1332C22×C4—731no—
1333C22×C4—731no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—731no—
1337C22×C4—731no—
1338C22×C4—731no—
1339C22×C4—731no—
1340C22×C4—731no—
1341C22×C4—731no—
1342C22×C4—1462no—
1343C22×C4—1462no—
1344C22×C4—1462no—
1345C22×C4—1462no—
1346C22×C4—1462no—
1347C22×C4—1462no—
1348C22×C4—1462no—
1349C22×C4—1462no—
1350C22×C4—1462no—
1351C22×C4—1462no—
1352C22×C4—1462no—
1353C22×C4—1462no—
1354C22×C4—1462no—
1355C22×C4—1462no—
1356C22×C4—1462no—
1357C22×C4—1462no—
1358C22×C4—1462no—
1359C22×C4—1462no—
1360C22×C4—1462no—
1361C22×C4—1462no—
1362C22×C4—1462no—
1363C22×C4—1462no—
1364C22×C4—1462no—
1365C22×C4—1462no—
1366C22×C4—1462no—
1367C22×C4—1462no—
1368C22×C4—1462no—
1369C22×C4—1462no—
1370C22×C4—1462no—
1371C22×C4—1462no—
1372C22×C4—1462no—
1373C22×C4—1462no—
1374C22×C4—1462no—
1375C22×C4C23×D7311yescharacteristic
1376C22×C4C23×D7311yescharacteristic
1377C22×C4C23×D7311yescharacteristic
1378C22×C4C23×D7311yescharacteristic
1379C22×C4C23×D7311yescharacteristic
1380C22×C4C23×D7311yescharacteristic
1381C22×C4C23×D7311yescharacteristic
1382C22×C4C23×D7311yescharacteristic
1383C22×C4C23×D7311yescharacteristic
1384C22×C4C23×D7311yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—2921no—
1390C4⋊C4—2921no—
1391C4⋊C4—2921no—
1392C4⋊C4—2921no—
1393C4⋊C4—2921no—
1394C4⋊C4—2921no—
1395C4⋊C4—734no—
1396C4⋊C4—1462no—
1397C4⋊C4—1462no—
1398C4⋊C4—1462no—
1399C4⋊C4—1462no—
1400C4⋊C4—1462no—
1401C4⋊C4—1462no—
1402C4⋊C4—1462no—
1403C4⋊C4—1462no—
1404C4⋊C4—1462no—
1405C4⋊C4—1462no—
1406C4⋊C4—1462no—
1407C4⋊C4—1462no—
1408C4⋊C4—1462no—
1409C4⋊C4—1462no—
1410C4⋊C4—1462no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—22no—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—2921no—
1430C22⋊C4—2921no—
1431C22⋊C4—2921no—
1432C22⋊C4—2921no—
1433C22⋊C4—2921no—
1434C22⋊C4—734no—
1435C22⋊C4—734no—
1436C22⋊C4—734no—
1437C22⋊C4—1462no—
1438C22⋊C4—1462no—
1439C22⋊C4—1462no—
1440C22⋊C4—1462no—
1441C22⋊C4—1462no—
1442C22⋊C4—1462no—
1443C22⋊C4—1462no—
1444C22⋊C4—1462no—
1445C22⋊C4—1462no—
1446C22⋊C4—1462no—
1447C22⋊C4—1462no—
1448C22⋊C4—1462no—
1449C22⋊C4—1462no—
1450C22⋊C4—1462no—
1451C22⋊C4—1462no—
1452C22⋊C4—1462no—
1453C22⋊C4—1462no—
1454C22⋊C4—1462no—
1455C22⋊C4—1462no—
1456C22⋊C4—1462no—
1457C22⋊C4—1462no—
1458C22⋊C4—1462no—
1459C42—2921no—
1460C42—2921no—
1461C42—734no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C42—1462no—
1466C42—1462no—
1467C42—1462no—
1468C42—1462no—
1469C42—1462no—
1470C42—1462no—
1471C42—1462no—
1472C42—1462no—
1473C42—1462no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—28no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—28no—
1502C23—28no—
1503C23—44no—
1504C23—44no—
1505C23—44no—
1506C23—44no—
1507C23—44no—
1508C23—44no—
1509C23—44no—
1510C23—44no—
1511C23—44no—
1512C23—44no—
1513C23—44no—
1514C23—1461no—
1515C23—1461no—
1516C23—1461no—
1517C23—1461no—
1518C23—1461no—
1519C23—1461no—
1520C23—1461no—
1521C23C2×D4×D7312yes—
1522C23C2×D4×D7312yes—
1523C23#41×D7312yes—
1524C23#41×D7312yes—
1525C23C2×#1192402712yes—
1526C23C2×#1192402712yes—
1527C23C2×#1192402712yes—
1528C23C2×#1192402712yes—
1529C23C2×#1192402712yes—
1530C23C24×D7311yescharacteristic
1531Q8—2924no—
1532D4—28no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—2924no—
1537D4—2924no—
1538D4—2924no—
1539D4—2924no—
1540D4—2924no—
1541C2×C4—28no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—44no—
1571C2×C4—44no—
1572C2×C4—2924no—
1573C2×C4—2924no—
1574C2×C4—2924no—
1575C2×C4—2924no—
1576C2×C4—2924no—
1577C2×C4—2924no—
1578C2×C4—2924no—
1579C2×C4—2924no—
1580C2×C4—2924no—
1581C2×C4—2924no—
1582C2×C4—2924no—
1583C2×C4—2924no—
1584C2×C4—732no—
1585C2×C4—732no—
1586C2×C4—732no—
1587C2×C4—732no—
1588C2×C4—732no—
1589C2×C4—732no—
1590C2×C4—732no—
1591C2×C4—732no—
1592C2×C4—732no—
1593C2×C4—1461no—
1594C2×C4—1461no—
1595C2×C4—1461no—
1596C2×C4—1461no—
1597C2×C4—1461no—
1598C2×C4—1461no—
1599C2×C4—1461no—
1600C2×C4—1461no—
1601C2×C4—1461no—
1602C2×C4—1461no—
1603C2×C4—1461no—
1604C2×C4—1461no—
1605C2×C4—1461no—
1606C2×C4—1461no—
1607C2×C4—1461no—
1608C2×C4—1461no—
1609C2×C4—1461no—
1610C2×C4—1461no—
1611C2×C4—1461no—
1612C2×C4—1461no—
1613C2×C4—1461no—
1614C2×C4—1461no—
1615C2×C4—1461no—
1616C2×C4—1461no—
1617C2×C4—1468no—
1618C2×C4—1468no—
1619C2×C4—1468no—
1620C2×C4—1461no—
1621C2×C4—1461no—
1622C2×C4—1461no—
1623C2×C4—1461no—
1624C2×C4—1461no—
1625C2×C4—1461no—
1626C2×C4—1461no—
1627C2×C4—1461no—
1628C2×C4—1461no—
1629C2×C4—1461no—
1630C2×C4—1461no—
1631C2×C4—1461no—
1632C2×C4C2×D4×D7312yes—
1633C2×C4C2×#1192402712yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—416no—
1656C22—416no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—2921no—
1670C22—2921no—
1671C22—2921no—
1672C22—2921no—
1673C22—2921no—
1674C22—2921no—
1675C22—2921no—
1676C22#1798909314yes—
1677C22#1798911414yescomplemented
1678C22C22×D4×D7311yescharacteristic
1679C22C2×#41×D7311yescharacteristic
1680C22C2×#41×D7311yescharacteristic
1681C22C22×#1192402711yescharacteristic
1682C22C22×#1192402711yescharacteristic
1683C22H(5,𝔽2)×D7311yescharacteristic
1684C22#1798942211yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—2921no—
1696C4—2921no—
1697C4—2921no—
1698C4—2921no—
1699C4—2921no—
1700C4—2921no—
1701C4—2921no—
1702C4—2921no—
1703C4—734no—
1704C4—1462no—
1705C4—1462no—
1706C4—1462no—
1707C4—1462no—
1708C4—1462no—
1709C4—1462no—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—42no—
1714C2—42no—
1715C2—5841no—
1716C2C2×#1798909311yescharacteristic
1717C2C2×#1798911411yescharacteristic
1718C2#2262333711yescharacteristic
1719C2#546×D7311yescharacteristic
1720C2#2262341511yescharacteristic
1721C2#2262348211yescharacteristic
1722C2#2262353611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2405C2
prime radical#22613305C2
hypercenter#2405D73
hypocenterC73#34670
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2405

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989114C2semidirect
2. C22×D4×Dic73C2semidirect
3. #22614189C2semidirect
4. #22614174C2semidirect
5. #22614069C2semidirect
6. #22614054C2semidirect
7. #22613975C2semidirect
8. #22613960C2semidirect
9. #22613876C2semidirect
10. #22613861C2semidirect
11. #22613761C2semidirect
12. #22613679C2semidirect
13. #22613597C2semidirect
14. #22613486C2semidirect
15. #22613404C2semidirect
16. #22613327C2semidirect
18. #22613219C2semidirect
19. #22613187C2semidirect
20. #22613174C2semidirect
21. #22613170C2semidirect
22. #22612463C2semidirect
23. #123×Dic73C2semidirect
24. #22612441C2semidirect
25. #22612430C2semidirect
26. #22612430C2semidirect
27. #22612371C2semidirect
28. #22612367C2semidirect
29. #22612309C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
31. C73×#2405C2semidirect
35. C2×#14556586C22semidirect
36. C2×#14556584C22semidirect
37. C2×#14556581C22semidirect
38. C2×#14556577C22semidirect
39. C2×#14556574C22semidirect
41. C2×#14556568C22semidirect
46. C2×#14556556C22semidirect
57. C2×#14556551C22semidirect
58. C2×#14556551C22semidirect
59. C2×#14556551C22semidirect
60. C2×#14556551C22semidirect
61. C2×#14556549C22semidirect
62. C2×#14556547C22semidirect
63. C2×#14556547C22semidirect
69. C22×C4×Dic73C22semidirect
70. C22×C4×Dic73C22semidirect
71. #17988529C22semidirect
72. #17988527C22semidirect
73. #17988526C22semidirect
74. #17988523C22semidirect
75. #17988521C22semidirect
76. #17988520C22semidirect
77. #17988517C22semidirect
78. #17988515C22semidirect
79. #17988515C22semidirect
80. #17988515C22semidirect
81. #17988515C22semidirect
82. #17988515C22semidirect
83. #17988514C22semidirect
84. #17988512C22semidirect
85. #17988510C22semidirect
86. #17988510C22semidirect
87. #17988510C22semidirect
88. #17988509C22semidirect
89. #17988503C22semidirect
90. #17988502C22semidirect
91. #17988502C22semidirect
92. #17988502C22semidirect
95. #17988499C22semidirect
96. #17988499C22semidirect
99. #17988491C22semidirect
100. #17988487C22semidirect
101. #17988484C22semidirect
102. #17988482C22semidirect
103. #17988481C22semidirect
104. #17988480C22semidirect
105. #17988480C22semidirect
106. #17988479C22semidirect
107. #17988479C22semidirect
108. #17988477C22semidirect
109. #17988475C22semidirect
110. #17988475C22semidirect
111. #17988474C22semidirect
112. #17988473C22semidirect
113. #17988473C22semidirect
114. #17988472C22semidirect
115. #17988472C22semidirect
116. #17988470C22semidirect
117. #17988468C22semidirect
118. #17988468C22semidirect
122. #17988466C22semidirect
126. #17988464C22semidirect
127. #17988464C22semidirect
128. #17988464C22semidirect
129. #17988464C22semidirect
131. #17988462C22semidirect
133. #17988460C22semidirect
136. #17988459C22semidirect
137. #17988459C22semidirect
138. #17988459C22semidirect
139. #17988459C22semidirect
140. #17988459C22semidirect
141. #17988450C22semidirect
142. #17988448C22semidirect
143. #17988448C22semidirect
147. #17988445C22semidirect
148. #17988445C22semidirect
149. #17988445C22semidirect
151. C4⋊C4×Dic73C22semidirect
152. C4⋊C4×Dic73C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
160. C22⋊C4×Dic73C22semidirect
161. C22⋊C4×Dic73C22semidirect
162. C22⋊C4×Dic73C22semidirect
163. C22⋊C4×Dic73C22semidirect
164. C22⋊C4×Dic73C22semidirect
165. C22⋊C4×Dic73C22semidirect
166. C22⋊C4×Dic73C22semidirect
167. C22⋊C4×Dic73C22semidirect
168. C22⋊C4×Dic73C22semidirect
169. C22⋊C4×Dic73C22semidirect
170. #17988434C22semidirect
171. #17988432C22semidirect
172. C2×#14556498C22semidirect
173. C2×#14556498C22semidirect
235. D4×Dic73D4semidirect
808. C22×C73#529semidirect
879. #2405D73semidirect
893. C73#34670semidirect
1677. C22#17989114semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891142
C22×D4×Dic732
#226141892
#226141742
#226140692
#226140542
#226139752
#226139602
#226138762
#226138612
#226137612
#226136792
#226135972
#226134862
#226134042
#226133272
#226133052
#226132192
#226131872
#226131742
#226131702
#226124632
#123×Dic732
#226124412
#226124302
#226123712
#226123672
#226123092
C2×C22⋊C4×Dic732
C73×#24052
#3467073