Finite Group Databasebeta

← #33256157

Subgroups — #33256157

Order 18688.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989118C211yesmaximal, characteristic, complemented
2C2×#17989093C211yesmaximal, characteristic, complemented
3#22615068C211yesmaximal, characteristic, complemented
4#22615053C211yesmaximal, characteristic, complemented
5#22615038C211yesmaximal, characteristic, complemented
6#22615023C211yesmaximal, characteristic, complemented
7#22615014C211yesmaximal, characteristic, complemented
8#22615004C211yesmaximal, characteristic, complemented
9#22614988C211yesmaximal, characteristic, complemented
10#22614973C211yesmaximal, characteristic, complemented
11#22614944C211yesmaximal, characteristic, complemented
12#22614889C211yesmaximal, characteristic, complemented
13#22614859C211yesmaximal, characteristic, complemented
14#22614818C211yesmaximal, characteristic, complemented
15#22614259C211yesmaximal, characteristic, complemented
16#22614051C211yesmaximal, characteristic, complemented
17#22613476C211yesmaximal, characteristic, complemented
18#22613206C211yesmaximal, characteristic, complemented
19#22613187C211yesmaximal, characteristic, complemented
20#22613174C211yesmaximal, characteristic, complemented
21#22613143C211yesmaximal, characteristic, complemented
22#22612472C211yesmaximal, characteristic, complemented
23#22612450C211yesmaximal, characteristic, complemented
24#121×Dic73C211yesmaximal, characteristic, complemented
25#22612441C211yesmaximal, characteristic, complemented
26#120×Dic73C211yesmaximal, characteristic, complemented
27#22612416C211yesmaximal, characteristic, complemented
28#22612393C211yesmaximal, characteristic, complemented
29C4×D4×Dic73C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2424C211yesmaximal, characteristic, complemented
32C22×#11924027C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34#17989118—28no—
35C2×#14556584C2211yescharacteristic, complemented
36C2×#14556584C2211yescharacteristic, complemented
37C2×#14556582C2211yescharacteristic, complemented
38C2×#14556578C2211yescharacteristic, complemented
39C2×#14556577C2211yescharacteristic
40#17989093—28no—
41C2×#14556575C2211yescharacteristic
42C2×#14556575C2211yescharacteristic
43C2×#14556572C2211yescharacteristic
44C2×#14556572C2211yescharacteristic
45C2×#14556572C2211yescharacteristic
46C2×#14556570C2211yescharacteristic
47C2×#14556568C2211yescharacteristic
48C2×#14556568C2211yescharacteristic
49C2×#14556563C2211yescharacteristic
50C2×#14556563C2211yescharacteristic
51C2×#14556563C2211yescharacteristic
52C2×#14556560C2211yescharacteristic
53C2×#14556556C2211yescharacteristic, complemented
54C2×D4×Dic73C2211yescharacteristic
55C2×D4×Dic73C2211yescharacteristic
56C2×D4×Dic73C2211yescharacteristic
57C2×D4×Dic73C2211yescharacteristic
58C2×D4×Dic73C2211yescharacteristic
59C2×D4×Dic73C2211yescharacteristic
60C2×D4×Dic73C2211yescharacteristic, complemented
61C2×#14556551C2211yescharacteristic
62C2×#14556551C2211yescharacteristic
63C2×#14556551C2211yescharacteristic, complemented
64C2×#14556547C2211yescharacteristic
65C2×#14556547C2211yescharacteristic, complemented
66C2×#14556547C2211yescharacteristic, complemented
67C22×C22⋊Dic73C2211yescharacteristic
68C22×C4×Dic73C2211yescharacteristic
69C22×C4×Dic73C2211yescharacteristic
70C22×C4×Dic73C2211yescharacteristic, complemented
71#17988529C2211yescharacteristic, complemented
72#17988528C2211yescharacteristic, complemented
73#17988523C2211yescharacteristic
74#17988523C2211yescharacteristic
75#17988521C2211yescharacteristic, complemented
76#17988520C2211yescharacteristic, complemented
77#17988520C2211yescharacteristic, complemented
78#17988517C2211yescharacteristic, complemented
79#17988515C2211yescharacteristic
80#17988515C2211yescharacteristic, complemented
81#17988515C2211yescharacteristic, complemented
82#17988512C2211yescharacteristic, complemented
83#17988510C2211yescharacteristic
84#17988510C2211yescharacteristic
85#17988509C2211yescharacteristic, complemented
86#17988508C2211yescharacteristic, complemented
87#17988507C2211yescharacteristic, complemented
88#17988503C2211yescharacteristic
89#17988503C2211yescharacteristic, complemented
90#17988503C2211yescharacteristic, complemented
91#17988502C2211yescharacteristic
92#17988501C2211yescharacteristic
93#17988501C2211yescharacteristic
94#17988499C2211yescharacteristic
95#17988499C2211yescharacteristic, complemented
96#17988495C2211yescharacteristic
97#17988495C2211yescharacteristic
98#17988495C2211yescharacteristic, complemented
99#17988491C2211yescharacteristic, complemented
100#17988491C2211yescharacteristic, complemented
101#17988491C2211yescharacteristic, complemented
102#17988490C2211yescharacteristic
103#17988490C2211yescharacteristic
104#17988487C2211yescharacteristic
105#17988487C2211yescharacteristic
106#17988487C2211yescharacteristic
107#17988487C2211yescharacteristic, complemented
108#17988486C2211yescharacteristic, complemented
109#17988485C2211yescharacteristic, complemented
110#17988484C2211yescharacteristic, complemented
111#17988483C2211yescharacteristic, complemented
112#17988481C2211yescharacteristic
113#17988481C2211yescharacteristic
114#17988481C2211yescharacteristic, complemented
115#17988480C2211yescharacteristic
116#17988480C2211yescharacteristic, complemented
117#17988479C2211yescharacteristic, complemented
118#17988478C2211yescharacteristic, complemented
119#17988477C2211yescharacteristic, complemented
120#17988477C2211yescharacteristic, complemented
121#17988477C2211yescharacteristic, complemented
122#17988475C2211yescharacteristic
123#17988475C2211yescharacteristic, complemented
124#17988475C2211yescharacteristic, complemented
125#17988470C2211yescharacteristic, complemented
126#17988470C2211yescharacteristic, complemented
127#17988467C2211yescharacteristic
128#17988467C2211yescharacteristic
129#17988467C2211yescharacteristic
130#17988467C2211yescharacteristic
131#17988467C2211yescharacteristic
132#17988467C2211yescharacteristic, complemented
133#17988466C2211yescharacteristic
134#17988466C2211yescharacteristic
135#17988466C2211yescharacteristic, complemented
136#17988464C2211yescharacteristic, complemented
137#17988462C2211yescharacteristic
138#17988462C2211yescharacteristic
139#17988462C2211yescharacteristic
140#17988451C2211yescharacteristic, complemented
141#17988448C2211yescharacteristic
142#17988447C2211yescharacteristic, complemented
143#17988445C2211yescharacteristic
144#17988443C2211yescharacteristic
145C4⋊C4×Dic73C2211yescharacteristic, complemented
146C4⋊C4×Dic73C2211yescharacteristic, complemented
147C4⋊C4×Dic73C2211yescharacteristic, complemented
148C4⋊C4×Dic73C2211yescharacteristic, complemented
149C4×C4⋊Dic73C2211yescharacteristic, complemented
150#17988438C2211yescharacteristic, complemented
151C22⋊C4×Dic73C2211yescharacteristic
152C22⋊C4×Dic73C2211yescharacteristic
153C22⋊C4×Dic73C2211yescharacteristic
154C22⋊C4×Dic73C2211yescharacteristic
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, complemented
164C22⋊C4×Dic73C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic, complemented
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic
172C2×#14556498C2211yescharacteristic
173C42×Dic73C2211yescharacteristic, complemented
174C2×#121×C73C2211yescharacteristic
175C2×#121×C73C2211yescharacteristic
176C2×#120×C73C2211yescharacteristic
177C2×#120×C73C2211yescharacteristic
178C2×C4×D4×C73C2211yescharacteristic
179C22×C22⋊C4×C73C2211yescharacteristic
180#396×C73C2211yescharacteristic
181#394×C73C2211yescharacteristic
182#394×C73C2211yescharacteristic
183#392×C73C2211yescharacteristic
184#390×C73C2211yescharacteristic
185#388×C73C2211yescharacteristic
186#386×C73C2211yescharacteristic
187#386×C73C2211yescharacteristic
188#385×C73C2211yescharacteristic
189C2×#11924027—24no—
190C2×#11924027—24no—
191C2×#11924027—42no—
192C22×Dic146C2311yescharacteristic
193C22×Dic146C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C23×Dic73—24no—
200C23×Dic73—24no—
201C23×Dic73—42no—
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#14556584—24no—
215#14556584—24no—
216#14556582—24no—
217#14556578—24no—
218#14556577—24no—
219#14556575—24no—
220#14556575—24no—
221#14556572—24no—
222#14556572—24no—
223#14556572—24no—
224#14556570—24no—
225#14556568—24no—
226#14556568—24no—
227#14556563—24no—
228#14556563—24no—
229#14556563—24no—
230#14556560—24no—
231#14556556—24no—
232D4×Dic73—24no—
233D4×Dic73—24no—
234D4×Dic73—24no—
235D4×Dic73—24no—
236D4×Dic73—24no—
237D4×Dic73—42no—
238D4×Dic73D418yescomplemented
239#14556551—24no—
240#14556551—24no—
241#14556551—42no—
242#14556547—24no—
243#14556547—24no—
244#14556547—24no—
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×C4⋊Dic73C2311yescharacteristic
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⋊Dic73C2311yescharacteristic
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—42no—
303C2×C4×Dic73—42no—
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
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
351C22×D4×C73C2311yescharacteristic
352C22×D4×C73C2311yescharacteristic
353C22×D4×C73C2311yescharacteristic
354C22×D4×C73C2311yescharacteristic
355C22×D4×C73C2311yescharacteristic
356C22×D4×C73C2311yescharacteristic
357C22×D4×C73C2311yescharacteristic
358C23×C4×C73C2311yescharacteristic
359C23×C4×C73C2311yescharacteristic
360C23×C4×C73C2311yescharacteristic
361#121×C73—24no—
362#121×C73—24no—
363#120×C73—24no—
364#120×C73—24no—
365C4×D4×C73—24no—
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C4⋊C4×C73C2311yescharacteristic
368C2×C4⋊C4×C73C2311yescharacteristic
369C2×C4⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73—24no—
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×C42×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—22no—
396C2×Dic146—22no—
397C2×Dic146—41no—
398C2×Dic146—41no—
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—22no—
408C2×C22⋊D73—22no—
409C2×C22⋊D73—41no—
410C2×C22⋊D73—41no—
411C2×C22⋊D73—41no—
412C2×C22⋊D73—41no—
413C2×C22⋊D73—41no—
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—41no—
437C22×Dic73—41no—
438C22×Dic73—41no—
439C22×Dic73—41no—
440C22×Dic73—41no—
441C22×Dic73—41no—
442C22×Dic73—41no—
443C22×Dic73—416no—
444C22×Dic73C2×D414yes—
445C22×Dic73C2×D414yes—
446C22×Dic73#4114yes—
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—22no—
486#11924007—41no—
487#11924007—41no—
488C22⋊Dic73—22no—
489C22⋊Dic73—22no—
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—22no—
507C22⋊Dic73—41no—
508C22⋊Dic73—41no—
509C22⋊Dic73—41no—
510C22⋊Dic73C2×D414yes—
511C22⋊Dic73C2×D414yes—
512#11924005—22no—
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—41no—
520#11924005—41no—
521C4×Dic73—22no—
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—41no—
534C4×Dic73—41no—
535C4×Dic73—41no—
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
551C2×D4×C73—22no—
552C2×D4×C73—22no—
553C2×D4×C73—22no—
554C2×D4×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—41no—
567C2×D4×C73—41no—
568C2×D4×C73—41no—
569C2×D4×C73—41no—
570C2×D4×C73—41no—
571C2×D4×C73C2×D414yes—
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×C73—41no—
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
590C22×C4×C73C2411yescharacteristic
591C4⋊C4×C73—22no—
592C4⋊C4×C73—22no—
593C4⋊C4×C73—22no—
594C4⋊C4×C73—41no—
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—22no—
607C22⋊C4×C73—41no—
608C22⋊C4×C73#4114yescomplemented
609C22⋊C4×C73#4114yescomplemented
610C42×C73—22no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—28no—
616C23×C73—21no—
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×C73C2511yescharacteristic
654C22×D73—21no—
655C22×D73—21no—
656C22×D73—21no—
657C22×D73—21no—
658C22×D73—21no—
659C22×D73—21no—
660C22×D73—21no—
661D4×C73—28no—
662D4×C73—44no—
663D4×C73—44no—
664D4×C73—44no—
665D4×C73—44no—
666D4×C73—44no—
667D4×C73—44no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
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—44no—
694C2×C4×C73—44no—
695C2×C4×C73—44no—
696C2×C4×C73C22×D412yes—
697C2×C4×C73C2×#4112yes—
698C2×C4×C73C2×#4112yes—
699C2×C4×C73C2×#4112yes—
700C2×C4×C73C2×#4112yes—
701C22⋊D73—44no—
702C22⋊D73—44no—
703C22⋊D73—44no—
704C22⋊D73—44no—
705C22⋊D73—44no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
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—28no—
719C2×Dic73—28no—
720C2×Dic73—28no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
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—44no—
746C2×Dic73—44no—
747C2×Dic73—44no—
748C2×Dic73—44no—
749C2×Dic73—44no—
750C2×Dic73—44no—
751C2×Dic73—44no—
752C2×Dic73—44no—
753C2×Dic73C22×D412yes—
754C2×Dic73C22×D412yes—
755C2×Dic73C22×D412yes—
756C2×Dic73C22×D412yes—
757C2×Dic73C2×#4112yes—
758C2×Dic73C2×#4112yes—
759C2×Dic73C2×#4112yes—
760C2×Dic73C2×#4112yes—
761C2×Dic73H(5,𝔽2)12yes—
762C4×D73—44no—
763Dic146—44no—
764Dic146—44no—
765C22×C73—22no—
766C22×C73—22no—
767C22×C73—22no—
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—416no—
781C22×C73—41no—
782C22×C73—41no—
783C22×C73—41no—
784C22×C73—41no—
785C22×C73—41no—
786C22×C73—41no—
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#53214yes—
801C22×C73C23×D411yescharacteristic
802C22×C73C22×#4111yescharacteristic
803C22×C73C22×#4111yescharacteristic
804C22×C73C22×#4111yescharacteristic
805C22×C73C22×#4111yescharacteristic
806C22×C73C2×H(5,𝔽2)11yescharacteristic
807C22×C73#58511yescharacteristic
808C2×D73—41no—
809C2×D73—41no—
810C2×D73—41no—
811C2×D73—41no—
812C2×D73—41no—
813C2×D73—41no—
814C2×D73—41no—
815C4×C73—22no—
816C4×C73—22no—
817C4×C73—22no—
818C4×C73—22no—
819C4×C73—22no—
820C4×C73—41no—
821C4×C73—41no—
822C4×C73—41no—
823C4×C73—41no—
824C4×C73—41no—
825Dic73—22no—
826Dic73—22no—
827Dic73—22no—
828Dic73—22no—
829Dic73—22no—
830Dic73—22no—
831Dic73—41no—
832Dic73—41no—
833Dic73—41no—
834Dic73—41no—
835Dic73—41no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73#54614yes—
840#34829—731nomaximal, Sylow
841C2×C73—24no—
842C2×C73—42no—
843C2×C73—42no—
844C2×C73—42no—
845C2×C73—81no—
846C2×C73C2×#53211yescharacteristic
847C2×C73#344411yescharacteristic
848C2×C73#345911yescharacteristic
849C2×C73C2×#54611yescharacteristic
850C2×C73D4×#4111yescharacteristic
851C2×C73#347511yescharacteristic
852C2×C73#348111yescharacteristic
853D73—81no—
854C2×#529—731no—
855C2×#525—731no—
856#2560—731no—
857#2559—731no—
858#2558—731no—
859#2557—731no—
860#2556—731no—
861#2555—731no—
862#2554—731no—
863#2553—731no—
864#2549—731no—
865#2543—731no—
866#2539—731no—
867#2534—731no—
868#2488—731no—
869#2472—731no—
870#2425—731no—
871#2424D7311yescharacteristic, complemented
872#2396—731no—
873#2395—731no—
874#2392—731no—
875#2388—731no—
876C4×#124—731no—
877C4×#123—731no—
878C4×#121—731no—
879C4×#121—731no—
880C4×#120—731no—
881#2297—731no—
882#2293—731no—
883C42×D4—731no—
884C2×C4×C22⋊C4—731no—
885C73#3482911yescharacteristic, complemented, Sylow
886C22×#41—731no—
887C24×C4—731no—
888#529—1468no—
889C2×#126—731no—
890C2×#126—731no—
891C2×#125—731no—
892C2×#124—731no—
893C2×#124—731no—
894#525—1468no—
895C2×#123—731no—
896C2×#123—731no—
897C2×#123—731no—
898C2×#123—731no—
899C2×#123—731no—
900C2×C22⋊Q8—731no—
901C2×C22⋊Q8—731no—
902C2×C22⋊Q8—731no—
903C2×#121—731no—
904C2×#121—731no—
905C2×#121—731no—
906C2×#121C2×D7311yescharacteristic
907C2×#121C2×D7311yescharacteristic
908C2×#120—731no—
909C2×#120C2×D7311yescharacteristic
910C2×#120C2×D7311yescharacteristic
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×D4C2×D7311yescharacteristic
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—
931#400—731no—
932#400—731no—
933#399—731no—
934#399—731no—
935#398—731no—
936#398—731no—
937#398—731no—
938#398—731no—
939#397—731no—
940#397—731no—
941#397—731no—
942#397—731no—
943#396—731no—
944#396—731no—
945#396—731no—
946#396C2×D7311yescharacteristic
947#395—731no—
948#395—731no—
949#394—731no—
950#394—731no—
951#394—731no—
952#394—731no—
953#394—731no—
954#394—731no—
955#394C2×D7311yescharacteristic
956#394C2×D7311yescharacteristic
957#393—731no—
958#393—731no—
959#392—731no—
960#392—731no—
961#392—731no—
962#392C2×D7311yescharacteristic
963#391—731no—
964#391—731no—
965#391—731no—
966#390—731no—
967#390—731no—
968#390—731no—
969#390—731no—
970#390—731no—
971#390—731no—
972#390C2×D7311yescharacteristic
973#389—731no—
974#389—731no—
975#389—731no—
976#389—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388—731no—
983#388—731no—
984#388—731no—
985#388—731no—
986#388—731no—
987#388—731no—
988#388—731no—
989#388—731no—
990#388C2×D7311yescharacteristic
991#387—731no—
992#387—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#385—731no—
1006#385—731no—
1007#385—731no—
1008#385C2×D7311yescharacteristic
1009#382—731no—
1010#381—731no—
1011#380—731no—
1012#380—731no—
1013#379—731no—
1014C4×C4⋊C4—731no—
1015C4×C4⋊C4—731no—
1016C4×C4⋊C4—731no—
1017C4×C4⋊C4—731no—
1018C4×C4⋊C4—731no—
1019C4×C4⋊C4—731no—
1020C4×C22⋊C4—731no—
1021C4×C22⋊C4—731no—
1022C4×C22⋊C4—731no—
1023C4×C22⋊C4—731no—
1024C4×C22⋊C4—731no—
1025C4×C22⋊C4—731no—
1026C4×C22⋊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—
1040C2×#95—731no—
1041C2×#95—731no—
1042C43—731no—
1043C25C22×D7311yescharacteristic
1044C2×#41—2922no—
1045C2×#41—1464no—
1046C2×#41—1464no—
1047C22×Q8—731no—
1048C22×Q8—731no—
1049C22×D4—731no—
1050C22×D4—731no—
1051C22×D4—731no—
1052C22×D4—731no—
1053C22×D4—731no—
1054C22×D4C22×D7311yescharacteristic
1055C22×D4C22×D7311yescharacteristic
1056C22×D4C22×D7311yescharacteristic
1057C22×D4C22×D7311yescharacteristic
1058C22×D4C22×D7311yescharacteristic
1059C22×D4C22×D7311yescharacteristic
1060C22×D4C22×D7311yescharacteristic
1061C23×C4—2922no—
1062C23×C4—731no—
1063C23×C4—731no—
1064C23×C4—731no—
1065C23×C4—731no—
1066C23×C4—731no—
1067C23×C4—731no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4—731no—
1072C23×C4—731no—
1073C23×C4—731no—
1074C23×C4—1464no—
1075C23×C4—1464no—
1076C23×C4C22×D7311yescharacteristic
1077C23×C4C22×D7311yescharacteristic
1078C23×C4C22×D7311yescharacteristic
1079#126—1464no—
1080#126—1464no—
1081#125—1464no—
1082#124—1464no—
1083#124—1464no—
1084#123—1464no—
1085#123—1464no—
1086#123—1464no—
1087#123—1464no—
1088#123—1464no—
1089C22⋊Q8—1464no—
1090C22⋊Q8—1464no—
1091C22⋊Q8—1464no—
1092#121—24no—
1093#121—24no—
1094#121—1464no—
1095#121—1464no—
1096#121—1464no—
1097#120—24no—
1098#120—24no—
1099#120—1464no—
1100C4×Q8—1464no—
1101C4×D4—24no—
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—
1112#117—1464no—
1113#117—1464no—
1114#117—1464no—
1115C2×C4⋊C4—731no—
1116C2×C4⋊C4—731no—
1117C2×C4⋊C4—731no—
1118C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
1138C2×C4⋊C4C22×D7311yescharacteristic
1139C2×C4⋊C4C22×D7311yescharacteristic
1140C2×C4⋊C4C22×D7311yescharacteristic
1141C2×C22⋊C4—24no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
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—1464no—
1176C2×C22⋊C4C22×D7311yescharacteristic
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—2922no—
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—731no—
1210C2×C42—731no—
1211C2×C42—1464no—
1212C2×C42C22×D7311yescharacteristic
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#95—731no—
1241#95C22×D7311yescharacteristic
1242#95C22×D7311yescharacteristic
1243#95C22×D7311yescharacteristic
1244#95C22×D7311yescharacteristic
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—22no—
1250C24—41no—
1251C24—41no—
1252C24—731no—
1253C24C23×D7311yescharacteristic
1254C24C23×D7311yescharacteristic
1255C24C23×D7311yescharacteristic
1256C24C23×D7311yescharacteristic
1257C24C23×D7311yescharacteristic
1258#41—29216no—
1259C2×Q8—2921no—
1260C2×Q8—2921no—
1261C2×Q8—1462no—
1262C2×Q8—1462no—
1263C2×Q8—1462no—
1264C2×Q8—1462no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
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—41no—
1281C2×D4—41no—
1282C2×D4—41no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—2921no—
1286C2×D4—2921no—
1287C2×D4—2921no—
1288C2×D4—2921no—
1289C2×D4—2921no—
1290C2×D4—1462no—
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×D4D4×D7314yes—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—2921no—
1311C22×C4—2921no—
1312C22×C4—2921no—
1313C22×C4—2921no—
1314C22×C4—2921no—
1315C22×C4—2921no—
1316C22×C4—2921no—
1317C22×C4—29216no—
1318C22×C4—734no—
1319C22×C4—731no—
1320C22×C4—734no—
1321C22×C4—734no—
1322C22×C4—734no—
1323C22×C4—731no—
1324C22×C4—731no—
1325C22×C4—731no—
1326C22×C4—731no—
1327C22×C4—731no—
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—1462no—
1338C22×C4—1462no—
1339C22×C4—1462no—
1340C22×C4—1462no—
1341C22×C4—1462no—
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×C4C23×D7311yescharacteristic
1363C22×C4C23×D7311yescharacteristic
1364C22×C4C23×D7311yescharacteristic
1365C22×C4C23×D7311yescharacteristic
1366C22×C4C23×D7311yescharacteristic
1367C22×C4C23×D7311yescharacteristic
1368C22×C4C23×D7311yescharacteristic
1369C22×C4C23×D7311yescharacteristic
1370C22×C4C23×D7311yescharacteristic
1371C22×C4C23×D7311yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—41no—
1376C4⋊C4—2921no—
1377C4⋊C4—2921no—
1378C4⋊C4—2921no—
1379C4⋊C4—734no—
1380C4⋊C4—1462no—
1381C4⋊C4—1462no—
1382C4⋊C4—1462no—
1383C4⋊C4—1462no—
1384C4⋊C4—1462no—
1385C4⋊C4—1462no—
1386C4⋊C4—1462no—
1387C4⋊C4—1462no—
1388C4⋊C4—1462no—
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—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—41no—
1411C22⋊C4—2921no—
1412C22⋊C4—2921no—
1413C22⋊C4—2921no—
1414C22⋊C4—2921no—
1415C22⋊C4—2921no—
1416C22⋊C4—734no—
1417C22⋊C4—734no—
1418C22⋊C4—1462no—
1419C22⋊C4—1462no—
1420C22⋊C4—1462no—
1421C22⋊C4—1462no—
1422C22⋊C4—1462no—
1423C22⋊C4—1462no—
1424C22⋊C4—1462no—
1425C22⋊C4—1462no—
1426C22⋊C4—1462no—
1427C22⋊C4—1462no—
1428C22⋊C4—1462no—
1429C22⋊C4—1462no—
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#1192402714yescomplemented
1445C22⋊C4#1192402714yescomplemented
1446C42—22no—
1447C42—2921no—
1448C42—2921no—
1449C42—2921no—
1450C42—2921no—
1451C42—2921no—
1452C42—734no—
1453C42—1462no—
1454C42—1462no—
1455C42—1462no—
1456C42—1462no—
1457C42—1462no—
1458C42—1462no—
1459C42—1462no—
1460C42—1462no—
1461C42—1462no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—28no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
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—44no—
1496C23—44no—
1497C23—44no—
1498C23—44no—
1499C23—44no—
1500C23—44no—
1501C23—1461no—
1502C23—1461no—
1503C23—1461no—
1504C23—1461no—
1505C23—1461no—
1506C23—1461no—
1507C23—1461no—
1508C23C2×D4×D7312yes—
1509C23C2×D4×D7312yes—
1510C23#41×D7312yes—
1511C23#41×D7312yes—
1512C23C2×#1192402712yes—
1513C23C2×#1192402712yes—
1514C23C24×D7311yescharacteristic
1515Q8—2924no—
1516Q8—2924no—
1517D4—28no—
1518D4—44no—
1519D4—44no—
1520D4—44no—
1521D4—44no—
1522D4—44no—
1523D4—44no—
1524D4—2924no—
1525D4—2924no—
1526D4—2924no—
1527D4—2924no—
1528D4—2924no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
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—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—44no—
1555C2×C4—44no—
1556C2×C4—44no—
1557C2×C4—2924no—
1558C2×C4—2924no—
1559C2×C4—2924no—
1560C2×C4—2924no—
1561C2×C4—2924no—
1562C2×C4—2924no—
1563C2×C4—2924no—
1564C2×C4—2924no—
1565C2×C4—2924no—
1566C2×C4—732no—
1567C2×C4—732no—
1568C2×C4—732no—
1569C2×C4—732no—
1570C2×C4—732no—
1571C2×C4—732no—
1572C2×C4—732no—
1573C2×C4—732no—
1574C2×C4—732no—
1575C2×C4—1461no—
1576C2×C4—1461no—
1577C2×C4—1461no—
1578C2×C4—1461no—
1579C2×C4—1461no—
1580C2×C4—1461no—
1581C2×C4—1461no—
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—1468no—
1600C2×C4—1468no—
1601C2×C4—1468no—
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×C4C2×D4×D7312yes—
1615C2×C4C2×#1192402712yes—
1616C2×C4C2×#1192402712yes—
1617C2×C4C2×#1192402712yes—
1618C2×C4C2×#1192402712yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—416no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—2921no—
1655C22—2921no—
1656C22—2921no—
1657C22—2921no—
1658C22—2921no—
1659C22—2921no—
1660C22—2921no—
1661C22#1798913214yes—
1662C22C22×D4×D7311yescharacteristic
1663C22C2×#41×D7311yescharacteristic
1664C22C2×#41×D7311yescharacteristic
1665C22C22×#1192402711yescharacteristic
1666C22C22×#1192402711yescharacteristic
1667C22H(5,𝔽2)×D7311yescharacteristic
1668C22#1798942211yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—22no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—2921no—
1680C4—2921no—
1681C4—2921no—
1682C4—2921no—
1683C4—2921no—
1684C4—2921no—
1685C4—2921no—
1686C4—2921no—
1687C4—734no—
1688C4—1462no—
1689C4—1462no—
1690C4—1462no—
1691C4—1462no—
1692C4—1462no—
1693C4—1462no—
1694C2—24no—
1695C2—42no—
1696C2—42no—
1697C2—42no—
1698C2—81no—
1699C2—5841no—
1700C2C2×#1798913211yescharacteristic
1701C2#2262322311yescharacteristic
1702C2#2262334211yescharacteristic
1703C2#546×D7311yescharacteristic
1704C2D4×#1192402711yescharacteristic
1705C2#2262348211yescharacteristic
1706C2#2262353211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2424C2
hypercenter#2424D73
hypocenterC73#34829
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2424

Complements

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

NH ≅ G/Ntype
1. C2×#17989118C2semidirect
2. C2×#17989093C2semidirect
3. #22615068C2semidirect
4. #22615053C2semidirect
5. #22615038C2semidirect
6. #22615023C2semidirect
7. #22615014C2semidirect
8. #22615004C2semidirect
9. #22614988C2semidirect
10. #22614973C2semidirect
11. #22614944C2semidirect
12. #22614889C2semidirect
13. #22614859C2semidirect
14. #22614818C2semidirect
15. #22614259C2semidirect
16. #22614051C2semidirect
17. #22613476C2semidirect
18. #22613206C2semidirect
19. #22613187C2semidirect
20. #22613174C2semidirect
21. #22613143C2semidirect
22. #22612472C2semidirect
23. #22612450C2semidirect
24. #121×Dic73C2semidirect
25. #22612441C2semidirect
26. #120×Dic73C2semidirect
27. #22612416C2semidirect
28. #22612393C2semidirect
29. C4×D4×Dic73C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
31. C73×#2424C2semidirect
35. C2×#14556584C22semidirect
36. C2×#14556584C22semidirect
37. C2×#14556582C22semidirect
38. C2×#14556578C22semidirect
53. C2×#14556556C22semidirect
60. C2×D4×Dic73C22semidirect
63. C2×#14556551C22semidirect
65. C2×#14556547C22semidirect
66. C2×#14556547C22semidirect
70. C22×C4×Dic73C22semidirect
71. #17988529C22semidirect
72. #17988528C22semidirect
75. #17988521C22semidirect
76. #17988520C22semidirect
77. #17988520C22semidirect
78. #17988517C22semidirect
80. #17988515C22semidirect
81. #17988515C22semidirect
82. #17988512C22semidirect
85. #17988509C22semidirect
86. #17988508C22semidirect
87. #17988507C22semidirect
89. #17988503C22semidirect
90. #17988503C22semidirect
95. #17988499C22semidirect
98. #17988495C22semidirect
99. #17988491C22semidirect
100. #17988491C22semidirect
101. #17988491C22semidirect
107. #17988487C22semidirect
108. #17988486C22semidirect
109. #17988485C22semidirect
110. #17988484C22semidirect
111. #17988483C22semidirect
114. #17988481C22semidirect
116. #17988480C22semidirect
117. #17988479C22semidirect
118. #17988478C22semidirect
119. #17988477C22semidirect
120. #17988477C22semidirect
121. #17988477C22semidirect
123. #17988475C22semidirect
124. #17988475C22semidirect
125. #17988470C22semidirect
126. #17988470C22semidirect
132. #17988467C22semidirect
135. #17988466C22semidirect
136. #17988464C22semidirect
140. #17988451C22semidirect
142. #17988447C22semidirect
145. C4⋊C4×Dic73C22semidirect
146. C4⋊C4×Dic73C22semidirect
147. C4⋊C4×Dic73C22semidirect
148. C4⋊C4×Dic73C22semidirect
149. C4×C4⋊Dic73C22semidirect
150. #17988438C22semidirect
163. C22⋊C4×Dic73C22semidirect
164. C22⋊C4×Dic73C22semidirect
165. C22⋊C4×Dic73C22semidirect
167. C4×C22⋊Dic73C22semidirect
168. #17988434C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
173. C42×Dic73C22semidirect
238. D4×Dic73D4semidirect
447. C22×Dic73#41semidirect
608. C22⋊C4×C73#41semidirect
609. C22⋊C4×C73#41semidirect
871. #2424D73semidirect
885. C73#34829semidirect
1444. C22⋊C4#11924027semidirect
1445. C22⋊C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179891182
C2×#179890932
#226150682
#226150532
#226150382
#226150232
#226150142
#226150042
#226149882
#226149732
#226149442
#226148892
#226148592
#226148182
#226142592
#226140512
#226134762
#226132062
#226131872
#226131742
#226131432
#226124722
#226124502
#121×Dic732
#226124412
#120×Dic732
#226124162
#226123932
C4×D4×Dic732
C2×C22⋊C4×Dic732
C73×#24242
#3482973