Finite Group Databasebeta

← #33254638

Subgroups — #33254638

Order 18688.

2938 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989093C211yesmaximal, characteristic, complemented
2C2×#41×Dic73C211yesmaximal, characteristic, complemented
3#22614129C211yesmaximal, characteristic, complemented
4#22614114C211yesmaximal, characteristic, complemented
5#22614039C211yesmaximal, characteristic, complemented
6#22614024C211yesmaximal, characteristic, complemented
7#22613945C211yesmaximal, characteristic, complemented
8#22613930C211yesmaximal, characteristic, complemented
9#22613846C211yesmaximal, characteristic, complemented
10#22613831C211yesmaximal, characteristic, complemented
11#22613761C211yesmaximal, characteristic, complemented
12#22613679C211yesmaximal, characteristic, complemented
13#22613609C211yesmaximal, characteristic, complemented
14#22613535C211yesmaximal, characteristic, complemented
15#22613471C211yesmaximal, characteristic, complemented
16#22613389C211yesmaximal, characteristic, complemented
17#22613316C211yesmaximal, characteristic, complemented
18#22613213C211yesmaximal, characteristic, complemented
19#22613198C211yesmaximal, characteristic, complemented
20#22613166C211yesmaximal, characteristic, complemented
21#22613143C211yesmaximal, characteristic, complemented
22#22612456C211yesmaximal, characteristic, complemented
23#22612448C211yesmaximal, characteristic, complemented
24#22612441C211yesmaximal, characteristic, complemented
25#22612441C211yesmaximal, characteristic, complemented
26#120×Dic73C211yesmaximal, characteristic, complemented
27#22612416C211yesmaximal, characteristic, complemented
28#22612371C211yesmaximal, characteristic, complemented
29#22612371C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2404C211yesmaximal, characteristic, complemented
32C22×#11924027C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34#17989093—28no—
35C2×#14556575C2211yescharacteristic
36C2×#14556574C2211yescharacteristic
37C2×#14556572C2211yescharacteristic
38C2×#14556572C2211yescharacteristic
39C2×#14556568C2211yescharacteristic
40C2×#14556568C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556563C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556563C2211yescharacteristic
45C2×#14556560C2211yescharacteristic
46#41×Dic73—28no—
47C2×Q8×Dic73C2211yescharacteristic, complemented
48C2×Q8×Dic73C2211yescharacteristic, complemented
49C2×D4×Dic73C2211yescharacteristic
50C2×D4×Dic73C2211yescharacteristic
51C2×D4×Dic73C2211yescharacteristic
52C2×D4×Dic73C2211yescharacteristic
53C2×D4×Dic73C2211yescharacteristic
54C2×D4×Dic73C2211yescharacteristic
55C2×D4×Dic73C2211yescharacteristic
56C2×D4×Dic73C2211yescharacteristic, complemented
57C2×D4×Dic73C2211yescharacteristic, complemented
58C2×#14556551C2211yescharacteristic
59C2×#14556551C2211yescharacteristic
60C2×#14556551C2211yescharacteristic, complemented
61C2×#14556550C2211yescharacteristic
62C2×#14556550C2211yescharacteristic, complemented
63C2×#14556550C2211yescharacteristic, complemented
64C2×#14556547C2211yescharacteristic
65C2×#14556547C2211yescharacteristic, complemented
66C22×C22⋊Dic73C2211yescharacteristic
67C22×C4×Dic73C2211yescharacteristic
68C22×C4×Dic73C2211yescharacteristic
69C22×C4×Dic73C2211yescharacteristic, complemented
70C22×C4×Dic73C2211yescharacteristic, complemented
71#17988529C2211yescharacteristic, complemented
72#17988529C2211yescharacteristic, complemented
73#17988527C2211yescharacteristic, complemented
74#17988523C2211yescharacteristic
75#17988521C2211yescharacteristic, complemented
76#17988521C2211yescharacteristic, complemented
77#17988519C2211yescharacteristic, complemented
78#17988514C2211yescharacteristic, complemented
79#17988512C2211yescharacteristic
80#17988512C2211yescharacteristic, complemented
81#17988510C2211yescharacteristic
82#17988510C2211yescharacteristic
83#17988510C2211yescharacteristic
84#17988510C2211yescharacteristic, complemented
85#17988508C2211yescharacteristic, complemented
86#17988506C2211yescharacteristic, complemented
87#17988503C2211yescharacteristic
88#17988503C2211yescharacteristic
89#17988503C2211yescharacteristic
90#17988503C2211yescharacteristic, complemented
91#17988501C2211yescharacteristic
92#17988501C2211yescharacteristic
93#17988501C2211yescharacteristic
94#17988501C2211yescharacteristic, complemented
95#17988499C2211yescharacteristic, complemented
96#17988498C2211yescharacteristic, complemented
97#17988495C2211yescharacteristic
98#17988495C2211yescharacteristic, complemented
99#17988491C2211yescharacteristic, complemented
100#17988491C2211yescharacteristic, complemented
101#17988487C2211yescharacteristic
102#17988487C2211yescharacteristic
103#17988487C2211yescharacteristic
104#17988487C2211yescharacteristic, complemented
105#17988484C2211yescharacteristic, complemented
106#17988484C2211yescharacteristic, complemented
107#17988481C2211yescharacteristic
108#17988481C2211yescharacteristic
109#17988481C2211yescharacteristic
110#17988481C2211yescharacteristic, complemented
111#17988479C2211yescharacteristic, complemented
112#17988479C2211yescharacteristic, complemented
113#17988476C2211yescharacteristic, complemented
114#17988476C2211yescharacteristic, complemented
115#17988475C2211yescharacteristic
116#17988475C2211yescharacteristic
117#17988475C2211yescharacteristic, complemented
118#17988475C2211yescharacteristic, complemented
119#17988474C2211yescharacteristic, complemented
120#17988474C2211yescharacteristic, complemented
121#17988472C2211yescharacteristic, complemented
122#17988472C2211yescharacteristic, complemented
123#17988470C2211yescharacteristic, complemented
124#17988470C2211yescharacteristic, complemented
125#17988469C2211yescharacteristic, complemented
126#17988469C2211yescharacteristic, complemented
127#17988467C2211yescharacteristic
128#17988467C2211yescharacteristic
129#17988467C2211yescharacteristic
130#17988467C2211yescharacteristic
131#17988467C2211yescharacteristic
132#17988467C2211yescharacteristic
133#17988466C2211yescharacteristic
134#17988466C2211yescharacteristic, complemented
135#17988466C2211yescharacteristic, complemented
136#17988464C2211yescharacteristic
137#17988464C2211yescharacteristic, complemented
138#17988462C2211yescharacteristic
139#17988462C2211yescharacteristic
140#17988462C2211yescharacteristic
141#17988460C2211yescharacteristic
142#17988460C2211yescharacteristic, complemented
143#17988460C2211yescharacteristic, complemented
144#17988459C2211yescharacteristic
145#17988459C2211yescharacteristic
146#17988459C2211yescharacteristic, complemented
147#17988448C2211yescharacteristic, complemented
148#17988445C2211yescharacteristic
149#17988445C2211yescharacteristic, complemented
150#17988443C2211yescharacteristic
151#17988438C2211yescharacteristic, complemented
152#17988438C2211yescharacteristic, 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
161C22⋊C4×Dic73C2211yescharacteristic
162C22⋊C4×Dic73C2211yescharacteristic
163C22⋊C4×Dic73C2211yescharacteristic
164C22⋊C4×Dic73C2211yescharacteristic
165C22⋊C4×Dic73C2211yescharacteristic
166C22⋊C4×Dic73C2211yescharacteristic, complemented
167C22⋊C4×Dic73C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic
173C2×#14556498C2211yescharacteristic
174C22×#41×C73C2211yescharacteristic
175C2×#120×C73C2211yescharacteristic
176C2×#120×C73C2211yescharacteristic
177C22×C22⋊C4×C73C2211yescharacteristic
178#393×C73C2211yescharacteristic
179#393×C73C2211yescharacteristic
180#392×C73C2211yescharacteristic
181#392×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#386×C73C2211yescharacteristic
187#386×C73C2211yescharacteristic
188#381×C73C2211yescharacteristic
189C2×#11924027—24no—
190C2×#11924027—24no—
191C2×#11924027—42no—
192C22×Dic146C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C23×Dic73—24no—
199C23×Dic73—24no—
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
213C22×C4×D73C2311yescharacteristic
214#14556575—24no—
215#14556574—24no—
216#14556572—24no—
217#14556572—24no—
218#14556568—24no—
219#14556568—24no—
220#14556563—24no—
221#14556563—24no—
222#14556563—24no—
223#14556563—24no—
224#14556560—24no—
225Q8×Dic73—24no—
226Q8×Dic73—24no—
227D4×Dic73—24no—
228D4×Dic73—24no—
229D4×Dic73—24no—
230D4×Dic73—24no—
231D4×Dic73—24no—
232D4×Dic73—24no—
233D4×Dic73—24no—
234D4×Dic73—42no—
235D4×Dic73D418yescomplemented
236#14556551—24no—
237#14556551—24no—
238#14556551—42no—
239#14556550—24no—
240#14556550—24no—
241#14556550—24no—
242#14556547—24no—
243#14556547—42no—
244C2×C4⋊Dic73C2311yescharacteristic
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×C4⋊Dic73C2311yescharacteristic
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×#11924007C2311yescharacteristic
268C2×C22⋊Dic73—24no—
269C2×C22⋊Dic73C2311yescharacteristic
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×C22⋊Dic73C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×C4×Dic73—24no—
302C2×C4×Dic73—24no—
303C2×C4×Dic73—24no—
304C2×C4×Dic73—42no—
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
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
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
351C2×#41×C73—24no—
352C2×#41×C73—24no—
353C2×#41×C73—24no—
354C22×Q8×C73C2311yescharacteristic
355C22×D4×C73C2311yescharacteristic
356C22×D4×C73C2311yescharacteristic
357C22×D4×C73C2311yescharacteristic
358C22×D4×C73C2311yescharacteristic
359C22×D4×C73C2311yescharacteristic
360C22×D4×C73C2311yescharacteristic
361C22×D4×C73C2311yescharacteristic
362C23×C4×C73C2311yescharacteristic
363C23×C4×C73C2311yescharacteristic
364C23×C4×C73C2311yescharacteristic
365C23×C4×C73C2311yescharacteristic
366#120×C73—24no—
367#120×C73—24no—
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
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385#95×C73C2311yescharacteristic
386#95×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389#95×C73C2311yescharacteristic
390#95×C73C2311yescharacteristic
391C23×D73C2411yescharacteristic
392#11924027—416no—
393C2×Dic146—22no—
394C2×Dic146—22no—
395C2×Dic146—41no—
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—22no—
407C2×C22⋊D73—41no—
408C2×C22⋊D73—41no—
409C2×C22⋊D73—41no—
410C2×C22⋊D73—41no—
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—41no—
438C22×Dic73—41no—
439C22×Dic73—41no—
440C22×Dic73—41no—
441C22×Dic73—41no—
442C22×Dic73—41no—
443C22×Dic73—41no—
444C22×Dic73—416no—
445C22×Dic73C2×D414yes—
446C22×Dic73C2×D414yes—
447C22×Dic73#4114yescomplemented
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C22×Dic73C2411yescharacteristic
451C22×Dic73C2411yescharacteristic
452C22×Dic73C2411yescharacteristic
453C22×Dic73C2411yescharacteristic
454C22×Dic73C2411yescharacteristic
455C22×Dic73C2411yescharacteristic
456C22×Dic73C2411yescharacteristic
457C22×Dic73C2411yescharacteristic
458C22×Dic73C2411yescharacteristic
459C22×Dic73C2411yescharacteristic
460C22×Dic73C2411yescharacteristic
461C22×Dic73C2411yescharacteristic
462C22×Dic73C2411yescharacteristic
463C2×C4×D73—22no—
464C2×C4×D73—22no—
465C2×C4×D73—22no—
466C4⋊Dic73—22no—
467C4⋊Dic73—22no—
468C4⋊Dic73—22no—
469C4⋊Dic73—22no—
470C4⋊Dic73—22no—
471C4⋊Dic73—22no—
472C4⋊Dic73—22no—
473C4⋊Dic73—41no—
474C4⋊Dic73C2×D414yes—
475#11924007—22no—
476#11924007—22no—
477#11924007—22no—
478#11924007—22no—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007—41no—
486#11924007—41no—
487#11924007—41no—
488#11924007—41no—
489#11924007—41no—
490C22⋊Dic73—22no—
491C22⋊Dic73—22no—
492C22⋊Dic73—22no—
493C22⋊Dic73—22no—
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—41no—
507C22⋊Dic73—41no—
508C22⋊Dic73—41no—
509C22⋊Dic73—41no—
510C22⋊Dic73C2×D414yes—
511C22⋊Dic73C2×D414yes—
512C22⋊Dic73#4114yescomplemented
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—41no—
520#11924005—41no—
521#11924005—41no—
522C4×Dic73—22no—
523C4×Dic73—22no—
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—41no—
545C24×C73—41no—
546C24×C73C2411yescharacteristic
547C24×C73C2411yescharacteristic
548C24×C73C2411yescharacteristic
549C24×C73C2411yescharacteristic
550C24×C73C2411yescharacteristic
551#41×C73—232no—
552C2×Q8×C73—22no—
553C2×Q8×C73—22no—
554C2×Q8×C73—22no—
555C2×D4×C73—22no—
556C2×D4×C73—22no—
557C2×D4×C73—22no—
558C2×D4×C73—22no—
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×C73—22no—
570C2×D4×C73—41no—
571C2×D4×C73—41no—
572C2×D4×C73—41no—
573C2×D4×C73—41no—
574C2×D4×C73C2×D414yes—
575C2×D4×C73#4114yescomplemented
576C22×C4×C73—22no—
577C22×C4×C73—22no—
578C22×C4×C73—22no—
579C22×C4×C73—22no—
580C22×C4×C73—22no—
581C22×C4×C73—22no—
582C22×C4×C73—22no—
583C22×C4×C73—22no—
584C22×C4×C73—22no—
585C22×C4×C73—41no—
586C22×C4×C73—41no—
587C22×C4×C73#4114yescomplemented
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C22×C4×C73C2411yescharacteristic
591C22×C4×C73C2411yescharacteristic
592C22×C4×C73C2411yescharacteristic
593C22×C4×C73C2411yescharacteristic
594C22×C4×C73C2411yescharacteristic
595C22×C4×C73C2411yescharacteristic
596C22×C4×C73C2411yescharacteristic
597C22×C4×C73C2411yescharacteristic
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—22no—
607C22⋊C4×C73—22no—
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—28no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—21no—
621C23×C73—21no—
622C23×C73—21no—
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×C73C22×D412yes—
648C23×C73C22×D412yes—
649C23×C73C2×#4112yes—
650C23×C73C2×#4112yes—
651C23×C73C2×#4112yes—
652C23×C73C2×#4112yes—
653C23×C73C2×#4112yes—
654C23×C73C2511yescharacteristic
655C22×D73—21no—
656C22×D73—21no—
657C22×D73—21no—
658C22×D73—21no—
659C22×D73—21no—
660C22×D73—21no—
661C22×D73—21no—
662Q8×C73—28no—
663D4×C73—28no—
664D4×C73—28no—
665D4×C73—28no—
666D4×C73—44no—
667D4×C73—44no—
668D4×C73—44no—
669D4×C73—44no—
670C2×C4×C73—28no—
671C2×C4×C73—28no—
672C2×C4×C73—28no—
673C2×C4×C73—21no—
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—44no—
700C2×C4×C73C22×D412yes—
701C2×C4×C73C2×#4112yes—
702C2×C4×C73C2×#4112yes—
703C2×C4×C73C2×#4112yes—
704C22⋊D73—44no—
705C22⋊D73—44no—
706C22⋊D73—44no—
707C22⋊D73—44no—
708C22⋊D73—44no—
709C2×Dic73—21no—
710C2×Dic73—21no—
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—28no—
722C2×Dic73—28no—
723C2×Dic73—28no—
724C2×Dic73—21no—
725C2×Dic73—21no—
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—44no—
749C2×Dic73—44no—
750C2×Dic73—44no—
751C2×Dic73—44no—
752C2×Dic73—44no—
753C2×Dic73—44no—
754C2×Dic73—44no—
755C2×Dic73—44no—
756C2×Dic73—44no—
757C2×Dic73C22×D412yes—
758C2×Dic73C22×D412yes—
759C2×Dic73C22×D412yes—
760C2×Dic73C22×D412yes—
761C2×Dic73C2×#4112yes—
762C2×Dic73C2×#4112yes—
763C2×Dic73C2×#4112yes—
764C2×Dic73C2×#4112yes—
765C2×Dic73H(5,𝔽2)12yes—
766C4×D73—44no—
767Dic146—44no—
768C22×C73—22no—
769C22×C73—22no—
770C22×C73—22no—
771C22×C73—22no—
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—416no—
787C22×C73—41no—
788C22×C73—41no—
789C22×C73—41no—
790C22×C73—41no—
791C22×C73—41no—
792C22×C73—41no—
793C22×C73—41no—
794C22×C73—41no—
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#52514yes—
804C22×C73C23×D411yescharacteristic
805C22×C73C22×#4111yescharacteristic
806C22×C73C22×#4111yescharacteristic
807C22×C73C22×#4111yescharacteristic
808C22×C73C22×#4111yescharacteristic
809C22×C73C2×H(5,𝔽2)11yescharacteristic
810C22×C73#58511yescharacteristic
811C2×D73—41no—
812C2×D73—41no—
813C2×D73—41no—
814C2×D73—41no—
815C2×D73—41no—
816C2×D73—41no—
817C2×D73—41no—
818C4×C73—22no—
819C4×C73—22no—
820C4×C73—22no—
821C4×C73—22no—
822C4×C73—41no—
823C4×C73—41no—
824C4×C73—41no—
825C4×C73—41no—
826C4×C73—41no—
827C4×C73—41no—
828Dic73—22no—
829Dic73—22no—
830Dic73—22no—
831Dic73—22no—
832Dic73—22no—
833Dic73—22no—
834Dic73—41no—
835Dic73—41no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840Dic73—41no—
841Dic73—41no—
842Dic73#54614yes—
843#34732—731nomaximal, Sylow
844C2×C73—24no—
845C2×C73—42no—
846C2×C73—42no—
847C2×C73—42no—
848C2×C73—42no—
849C2×C73C2×#52511yescharacteristic
850C2×C73#344411yescharacteristic
851C2×C73#346011yescharacteristic
852C2×C73C2×#54611yescharacteristic
853C2×C73D4×#4111yescharacteristic
854C2×C73#347511yescharacteristic
855C2×C73#348111yescharacteristic
856D73—81no—
857C2×#525—731no—
858C2×C4×#41—731no—
859#2477—731no—
860#2476—731no—
861#2471—731no—
862#2470—731no—
863#2465—731no—
864#2464—731no—
865#2458—731no—
866#2457—731no—
867#2450—731no—
868#2444—731no—
869#2438—731no—
870#2430—731no—
871#2424—731no—
872#2418—731no—
873#2411—731no—
874#2404D7311yescharacteristic, complemented
875#2398—731no—
876#2396—731no—
877#2392—731no—
878#2388—731no—
879C4×#123—731no—
880C4×#123—731no—
881C4×#121—731no—
882C4×#121—731no—
883C4×#120—731no—
884#2297—731no—
885#2290—731no—
886#2290—731no—
887C2×C4×C22⋊C4—731no—
888C73#3473211yescharacteristic, complemented, Sylow
889C22×#41—731no—
890C22×#41C2×D7311yescharacteristic
891C24×C4—731no—
892#525—1468no—
893C2×#123—731no—
894C2×#123—731no—
895C2×#123—731no—
896C2×#123—731no—
897C2×C22⋊Q8—731no—
898C2×C22⋊Q8—731no—
899C2×#121—731no—
900C2×#121—731no—
901C2×#121—731no—
902C2×#121—731no—
903C2×#120—731no—
904C2×#120C2×D7311yescharacteristic
905C2×#120C2×D7311yescharacteristic
906C4×#41—1468no—
907C2×C4×Q8—731no—
908C2×C4×Q8—731no—
909C2×C4×D4—731no—
910C2×C4×D4—731no—
911C2×C4×D4—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×#117—731no—
922C2×#117—731no—
923C2×#117—731no—
924C2×#117—731no—
925C2×#117—731no—
926C22×C22⋊C4—731no—
927C22×C22⋊C4C2×D7311yescharacteristic
928C22×C42—731no—
929C22×C42—731no—
930C22×C42—731no—
931C22×C42—731no—
932#400—731no—
933#400—731no—
934#400—731no—
935#399—731no—
936#398—731no—
937#398—731no—
938#398—731no—
939#397—731no—
940#397—731no—
941#397—731no—
942#396—731no—
943#396—731no—
944#396—731no—
945#396—731no—
946#395—731no—
947#395—731no—
948#394—731no—
949#394—731no—
950#394—731no—
951#394—731no—
952#394—731no—
953#394—731no—
954#394—731no—
955#394—731no—
956#393—731no—
957#393—731no—
958#393C2×D7311yescharacteristic
959#393C2×D7311yescharacteristic
960#392—731no—
961#392—731no—
962#392C2×D7311yescharacteristic
963#392C2×D7311yescharacteristic
964#391—731no—
965#391—731no—
966#390—731no—
967#390—731no—
968#390—731no—
969#390—731no—
970#389—731no—
971#389—731no—
972#388—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#388—731no—
982#388—731no—
983#388—731no—
984#387—731no—
985#387—731no—
986#387—731no—
987#387—731no—
988#387—731no—
989#387—731no—
990#387—731no—
991#387—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#386—731no—
1001#386—731no—
1002#386—731no—
1003#386C2×D7311yescharacteristic
1004#386C2×D7311yescharacteristic
1005#386C2×D7311yescharacteristic
1006#386C2×D7311yescharacteristic
1007#386C2×D7311yescharacteristic
1008#386C2×D7311yescharacteristic
1009#385—731no—
1010#385—731no—
1011#385—731no—
1012#385—731no—
1013#385—731no—
1014#385—731no—
1015#385—731no—
1016#385—731no—
1017#385—731no—
1018#381—731no—
1019#381C2×D7311yescharacteristic
1020#380—731no—
1021#380—731no—
1022#379—731no—
1023C4×C4⋊C4—731no—
1024C4×C4⋊C4—731no—
1025C4×C4⋊C4—731no—
1026C4×C4⋊C4—731no—
1027C4×C22⋊C4—731no—
1028C4×C22⋊C4—731no—
1029C4×C22⋊C4—731no—
1030C4×C22⋊C4—731no—
1031C4×C22⋊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—
1043#376—731no—
1044C2×#95—731no—
1045C2×#95—731no—
1046C25C22×D7311yescharacteristic
1047C2×#41—24no—
1048C2×#41—24no—
1049C2×#41—24no—
1050C2×#41—2922no—
1051C2×#41—1464no—
1052C2×#41—1464no—
1053C22×Q8—731no—
1054C22×Q8C22×D7311yescharacteristic
1055C22×D4—731no—
1056C22×D4—731no—
1057C22×D4—731no—
1058C22×D4—731no—
1059C22×D4—731no—
1060C22×D4C22×D7311yescharacteristic
1061C22×D4C22×D7311yescharacteristic
1062C22×D4C22×D7311yescharacteristic
1063C22×D4C22×D7311yescharacteristic
1064C22×D4C22×D7311yescharacteristic
1065C22×D4C22×D7311yescharacteristic
1066C22×D4C22×D7311yescharacteristic
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—1464no—
1082C23×C4—1464no—
1083C23×C4C22×D7311yescharacteristic
1084C23×C4C22×D7311yescharacteristic
1085C23×C4C22×D7311yescharacteristic
1086C23×C4C22×D7311yescharacteristic
1087#123—1464no—
1088#123—1464no—
1089#123—1464no—
1090#123—1464no—
1091C22⋊Q8—1464no—
1092C22⋊Q8—1464no—
1093#121—1464no—
1094#121—1464no—
1095#121—1464no—
1096#121—1464no—
1097#120—24no—
1098#120—24no—
1099#120—1464no—
1100C4×Q8—1464no—
1101C4×Q8—1464no—
1102C4×D4—2922no—
1103C4×D4—2922no—
1104C4×D4—738no—
1105C4×D4—1464no—
1106C4×D4—1464no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4—1464no—
1112C4×D4—1464no—
1113C4×D4—1464no—
1114#117—2922no—
1115#117—1464no—
1116#117—1464no—
1117#117—1464no—
1118#117—1464no—
1119C2×C4⋊C4—731no—
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—731no—
1143C2×C22⋊C4—24no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
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—1464no—
1177C2×C22⋊C4C22×D7311yescharacteristic
1178C2×C22⋊C4C22×D7311yescharacteristic
1179C2×C22⋊C4C22×D7311yescharacteristic
1180C2×C22⋊C4C22×D7311yescharacteristic
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×C42—2922no—
1192C2×C42—731no—
1193C2×C42—731no—
1194C2×C42—731no—
1195C2×C42—731no—
1196C2×C42—731no—
1197C2×C42—731no—
1198C2×C42—731no—
1199C2×C42—731no—
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—1464no—
1210C2×C42—1464no—
1211C2×C42—1464no—
1212#95—731no—
1213#95—731no—
1214#95—731no—
1215#95—731no—
1216#95—731no—
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#95C22×D7311yescharacteristic
1241#95C22×D7311yescharacteristic
1242#95C22×D7311yescharacteristic
1243#95C22×D7311yescharacteristic
1244#95C22×D7311yescharacteristic
1245#95C22×D7311yescharacteristic
1246#95C22×D7311yescharacteristic
1247#95C22×D7311yescharacteristic
1248C24—22no—
1249C24—22no—
1250C24—22no—
1251C24—22no—
1252C24—22no—
1253C24—41no—
1254C24—41no—
1255C24—731no—
1256C24C23×D7311yescharacteristic
1257C24C23×D7311yescharacteristic
1258C24C23×D7311yescharacteristic
1259C24C23×D7311yescharacteristic
1260C24C23×D7311yescharacteristic
1261#41—232no—
1262#41—29216no—
1263C2×Q8—22no—
1264C2×Q8—22no—
1265C2×Q8—22no—
1266C2×Q8—2921no—
1267C2×Q8—1462no—
1268C2×Q8—1462no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—41no—
1285C2×D4—41no—
1286C2×D4—41no—
1287C2×D4—41no—
1288C2×D4—2921no—
1289C2×D4—2921no—
1290C2×D4—2921no—
1291C2×D4—2921no—
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×D4—1462no—
1303C2×D4D4×D7314yes—
1304C2×D4#1192402714yescomplemented
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—41no—
1315C22×C4—41no—
1316C22×C4—2921no—
1317C22×C4—2921no—
1318C22×C4—2921no—
1319C22×C4—2921no—
1320C22×C4—2921no—
1321C22×C4—2921no—
1322C22×C4—2921no—
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#1192402714yescomplemented
1372C22×C4C23×D7311yescharacteristic
1373C22×C4C23×D7311yescharacteristic
1374C22×C4C23×D7311yescharacteristic
1375C22×C4C23×D7311yescharacteristic
1376C22×C4C23×D7311yescharacteristic
1377C22×C4C23×D7311yescharacteristic
1378C22×C4C23×D7311yescharacteristic
1379C22×C4C23×D7311yescharacteristic
1380C22×C4C23×D7311yescharacteristic
1381C22×C4C23×D7311yescharacteristic
1382C4⋊C4—2921no—
1383C4⋊C4—2921no—
1384C4⋊C4—2921no—
1385C4⋊C4—2921no—
1386C4⋊C4—2921no—
1387C4⋊C4—2921no—
1388C4⋊C4—734no—
1389C4⋊C4—1462no—
1390C4⋊C4—1462no—
1391C4⋊C4—1462no—
1392C4⋊C4—1462no—
1393C4⋊C4—1462no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
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—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—41no—
1417C22⋊C4—41no—
1418C22⋊C4—41no—
1419C22⋊C4—41no—
1420C22⋊C4—2921no—
1421C22⋊C4—2921no—
1422C22⋊C4—2921no—
1423C22⋊C4—2921no—
1424C22⋊C4—2921no—
1425C22⋊C4—2921no—
1426C22⋊C4—2921no—
1427C22⋊C4—734no—
1428C22⋊C4—734no—
1429C22⋊C4—734no—
1430C22⋊C4—1462no—
1431C22⋊C4—1462no—
1432C22⋊C4—1462no—
1433C22⋊C4—1462no—
1434C22⋊C4—1462no—
1435C22⋊C4—1462no—
1436C22⋊C4—1462no—
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—
1452C42—2921no—
1453C42—2921no—
1454C42—734no—
1455C42—1462no—
1456C42—1462no—
1457C42—1462no—
1458C42—1462no—
1459C42—1462no—
1460C42—1462no—
1461C42—1462no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C42—1462no—
1466C42—1462no—
1467C42—1462no—
1468C42—1462no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—28no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
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—44no—
1499C23—44no—
1500C23—44no—
1501C23—44no—
1502C23—44no—
1503C23—44no—
1504C23—1461no—
1505C23—1461no—
1506C23—1461no—
1507C23—1461no—
1508C23—1461no—
1509C23—1461no—
1510C23—1461no—
1511C23C2×D4×D7312yes—
1512C23C2×D4×D7312yes—
1513C23#41×D7312yes—
1514C23#41×D7312yes—
1515C23C2×#1192402712yes—
1516C23C2×#1192402712yes—
1517C23C2×#1192402712yes—
1518C23C24×D7311yescharacteristic
1519Q8—28no—
1520Q8—2924no—
1521D4—28no—
1522D4—28no—
1523D4—28no—
1524D4—44no—
1525D4—44no—
1526D4—44no—
1527D4—44no—
1528D4—2924no—
1529D4—2924no—
1530D4—2924no—
1531D4—2924no—
1532D4—2924no—
1533C2×C4—28no—
1534C2×C4—28no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—28no—
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—44no—
1563C2×C4—2924no—
1564C2×C4—2924no—
1565C2×C4—2924no—
1566C2×C4—2924no—
1567C2×C4—2924no—
1568C2×C4—2924no—
1569C2×C4—2924no—
1570C2×C4—2924no—
1571C2×C4—2924no—
1572C2×C4—2924no—
1573C2×C4—732no—
1574C2×C4—732no—
1575C2×C4—732no—
1576C2×C4—732no—
1577C2×C4—732no—
1578C2×C4—732no—
1579C2×C4—732no—
1580C2×C4—732no—
1581C2×C4—732no—
1582C2×C4—1461no—
1583C2×C4—1461no—
1584C2×C4—1461no—
1585C2×C4—1461no—
1586C2×C4—1461no—
1587C2×C4—1461no—
1588C2×C4—1461no—
1589C2×C4—1461no—
1590C2×C4—1461no—
1591C2×C4—1461no—
1592C2×C4—1461no—
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—1468no—
1607C2×C4—1468no—
1608C2×C4—1468no—
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—1461no—
1618C2×C4—1461no—
1619C2×C4—1461no—
1620C2×C4—1461no—
1621C2×C4C2×D4×D7312yes—
1622C2×C4C2×#1192402712yes—
1623C2×C4C2×#1192402712yes—
1624C2×C4C2×#1192402712yes—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—416no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—2921no—
1661C22—2921no—
1662C22—2921no—
1663C22—2921no—
1664C22—2921no—
1665C22—2921no—
1666C22—2921no—
1667C22#1798909314yes—
1668C22C22×D4×D7311yescharacteristic
1669C22C2×#41×D7311yescharacteristic
1670C22C2×#41×D7311yescharacteristic
1671C22C22×#1192402711yescharacteristic
1672C22C22×#1192402711yescharacteristic
1673C22H(5,𝔽2)×D7311yescharacteristic
1674C22#1798942211yescharacteristic
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—22no—
1679C4—41no—
1680C4—41no—
1681C4—41no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—2921no—
1686C4—2921no—
1687C4—2921no—
1688C4—2921no—
1689C4—2921no—
1690C4—2921no—
1691C4—2921no—
1692C4—2921no—
1693C4—734no—
1694C4—1462no—
1695C4—1462no—
1696C4—1462no—
1697C4—1462no—
1698C4—1462no—
1699C4—1462no—
1700C2—24no—
1701C2—42no—
1702C2—42no—
1703C2—42no—
1704C2—42no—
1705C2—5841no—
1706C2C2×#1798909311yescharacteristic
1707C2#2262322311yescharacteristic
1708C2#2262334411yescharacteristic
1709C2#546×D7311yescharacteristic
1710C2#2262341511yescharacteristic
1711C2#2262348211yescharacteristic
1712C2#2262353611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2404C2
hypercenter#2404D73
hypocenterC73#34732
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#17989093C2semidirect
2. C2×#41×Dic73C2semidirect
3. #22614129C2semidirect
4. #22614114C2semidirect
5. #22614039C2semidirect
6. #22614024C2semidirect
7. #22613945C2semidirect
8. #22613930C2semidirect
9. #22613846C2semidirect
10. #22613831C2semidirect
11. #22613761C2semidirect
12. #22613679C2semidirect
13. #22613609C2semidirect
14. #22613535C2semidirect
15. #22613471C2semidirect
16. #22613389C2semidirect
17. #22613316C2semidirect
18. #22613213C2semidirect
19. #22613198C2semidirect
20. #22613166C2semidirect
21. #22613143C2semidirect
22. #22612456C2semidirect
23. #22612448C2semidirect
24. #22612441C2semidirect
25. #22612441C2semidirect
26. #120×Dic73C2semidirect
27. #22612416C2semidirect
28. #22612371C2semidirect
29. #22612371C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
31. C73×#2404C2semidirect
47. C2×Q8×Dic73C22semidirect
48. C2×Q8×Dic73C22semidirect
56. C2×D4×Dic73C22semidirect
57. C2×D4×Dic73C22semidirect
60. C2×#14556551C22semidirect
62. C2×#14556550C22semidirect
63. C2×#14556550C22semidirect
65. C2×#14556547C22semidirect
69. C22×C4×Dic73C22semidirect
70. C22×C4×Dic73C22semidirect
71. #17988529C22semidirect
72. #17988529C22semidirect
73. #17988527C22semidirect
75. #17988521C22semidirect
76. #17988521C22semidirect
77. #17988519C22semidirect
78. #17988514C22semidirect
80. #17988512C22semidirect
84. #17988510C22semidirect
85. #17988508C22semidirect
86. #17988506C22semidirect
90. #17988503C22semidirect
94. #17988501C22semidirect
95. #17988499C22semidirect
96. #17988498C22semidirect
98. #17988495C22semidirect
99. #17988491C22semidirect
100. #17988491C22semidirect
104. #17988487C22semidirect
105. #17988484C22semidirect
106. #17988484C22semidirect
110. #17988481C22semidirect
111. #17988479C22semidirect
112. #17988479C22semidirect
113. #17988476C22semidirect
114. #17988476C22semidirect
117. #17988475C22semidirect
118. #17988475C22semidirect
119. #17988474C22semidirect
120. #17988474C22semidirect
121. #17988472C22semidirect
122. #17988472C22semidirect
123. #17988470C22semidirect
124. #17988470C22semidirect
125. #17988469C22semidirect
126. #17988469C22semidirect
134. #17988466C22semidirect
135. #17988466C22semidirect
137. #17988464C22semidirect
142. #17988460C22semidirect
143. #17988460C22semidirect
146. #17988459C22semidirect
147. #17988448C22semidirect
149. #17988445C22semidirect
151. #17988438C22semidirect
152. #17988438C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
166. C22⋊C4×Dic73C22semidirect
167. C22⋊C4×Dic73C22semidirect
168. #17988434C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
171. #17988432C22semidirect
235. D4×Dic73D4semidirect
447. C22×Dic73#41semidirect
512. C22⋊Dic73#41semidirect
575. C2×D4×C73#41semidirect
587. C22×C4×C73#41semidirect
874. #2404D73semidirect
888. C73#34732semidirect
1304. C2×D4#11924027semidirect
1371. C22×C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179890932
C2×#41×Dic732
#226141292
#226141142
#226140392
#226140242
#226139452
#226139302
#226138462
#226138312
#226137612
#226136792
#226136092
#226135352
#226134712
#226133892
#226133162
#226132132
#226131982
#226131662
#226131432
#226124562
#226124482
#226124412
#120×Dic732
#226124162
#226123712
C2×C22⋊C4×Dic732
C73×#24042
#3473273