Finite Group Databasebeta

← #33951113

Subgroups — #33951113

Order 18688.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D73C211yesmaximal, characteristic
2#22619102C212yesmaximal, complemented
3#22619095C212yesmaximal, complemented
4#22619094C211yesmaximal, characteristic, complemented
5#22619092C211yesmaximal, characteristic, complemented
6#22619090C211yesmaximal, characteristic, complemented
7#22619086C211yesmaximal, characteristic, complemented
8#22619082C211yesmaximal, characteristic, complemented
9#22619080C211yesmaximal, characteristic, complemented
10#22619076C211yesmaximal, characteristic, complemented
11#22619068C212yesmaximal, complemented
12#22619065C212yesmaximal, complemented
13#22618883C211yesmaximal, characteristic, complemented
14Q8×#11924011C211yesmaximal, characteristic, complemented
15#22618667C211yesmaximal, characteristic, complemented
16#22618667C212yesmaximal, complemented
17#22618664C212yesmaximal, complemented
18D4×#11924011C211yesmaximal, characteristic, complemented
19#22618565C212yesmaximal, complemented
20#22618559C211yesmaximal, characteristic, complemented
21#22618492C212yesmaximal, complemented
22#423×D73C211yesmaximal, characteristic, complemented
23C73×#2993C211yesmaximal, characteristic, complemented
24C22×#11924011C2212yes—
25C2×M16×D73C2212yes—
26C2×M16×D73C2212yes—
27#17989124C2211yescharacteristic
28#17989123C411yescharacteristic
29#17989122C411yescharacteristic
30#17989121C2211yescharacteristic
31#17989120C412yes—
32#17989119C2211yescharacteristic
33#17989118C411yescharacteristic
34#17989117C2212yes—
35#17989116C411yescharacteristic
36#17989115C2212yes—
37#17989114C412yes—
38#126×D73C412yes—
39#125×D73C411yescharacteristic
40#124×D73C411yescharacteristic
41#123×D73C412yes—
42C22⋊Q8×D73C411yescharacteristic
43#121×D73C411yescharacteristic
44C4×Q8×D73C2211yescharacteristic
45C4×D4×D73C2211yescharacteristic
46C4×D4×D73C2212yes—
47#117×D73C2212yes—
48C2×C42×D73C2211yescharacteristic
49#17988718C2211yescharacteristic, complemented
50#17988717C2212yescomplemented
51#17988717C2211yescharacteristic, complemented
52#17988716C2212yescomplemented
53#17988715C2212yescomplemented
54#17988714C2212yescomplemented
55#17988714C2211yescharacteristic, complemented
56Q8×#10596831C2211yescharacteristic, complemented
57C8×Dic146C2211yescharacteristic, complemented
58#17988711C2211yescharacteristic, complemented
59#17988666C2211yescharacteristic, complemented
60#17988665C2211yescharacteristic, complemented
61#17988665C2212yescomplemented
62#17988664C2211yescharacteristic, complemented
63#17988663C2212yescomplemented
64#17988662C2212yescomplemented
65#17988661C2212yescomplemented
66#17988661C2212yescomplemented
67#17988661C2212yescomplemented
68#17988660C2212yescomplemented
69#17988659C2212yescomplemented
70#17988658C2212yescomplemented
71#17988657C2212yescomplemented
72#17988656C2212yescomplemented
73#17988656C2212yescomplemented
74#17988656C2212yescomplemented
75#17988655C2212yescomplemented
76C8×D292C2212yescomplemented
77C8×D292C2211yescharacteristic, complemented
78D4×#10596831C2211yescharacteristic, complemented
79#17988652C2212yescomplemented
80#17988652C2211yescharacteristic, complemented
81C8×C22⋊D73C2212yescomplemented
82#17988650C2212yescomplemented
83#17988649C2212yescomplemented
84#17988648C2212yescomplemented
85#17988647C2212yescomplemented
86#17988647C2212yescomplemented
87#17988646C2212yescomplemented
88#17988645C2212yescomplemented
89#17988645C2212yescomplemented
90#17988643C2211yescharacteristic, complemented
91#17988643C2211yescharacteristic, complemented
92#17988641C2211yescharacteristic, complemented
93#17988641C2211yescharacteristic, complemented
94#17988640C2211yescharacteristic, complemented
95#17988638C2211yescharacteristic, complemented
96#17988638C2211yescharacteristic, complemented
97#17988615C2212yescomplemented
98#17988614C2212yescomplemented
99#17988613C2212yescomplemented
100#17988612C2212yescomplemented
101#17988612C2212yescomplemented
102#17988612C2212yescomplemented
103#17988612C2212yescomplemented
104#17988611C2211yescharacteristic, complemented
105#17988610C2212yescomplemented
106#17988609C2212yes—
107#17988609C2211yescharacteristic
108#17988609C2211yescharacteristic
109#17988609C2212yes—
110#17988609C2212yes—
111#17988609C2211yescharacteristic
112#17988609C2211yescharacteristic
113C4⋊C8×D73C2212yescomplemented
114C4⋊C8×D73C2211yescharacteristic, complemented
115C4⋊C8×D73C2211yescharacteristic, complemented
116#17988549C2212yes—
117#17988549C2211yescharacteristic
118#17988549C2212yes—
119#17988549C2211yescharacteristic
120#17988539C2212yes—
121C4×#11924011C2211yescharacteristic
122C4×#11924011C2212yes—
123C4×#11924011C2211yescharacteristic
124#529×C73C2211yescharacteristic
125#446×C73C2211yescharacteristic, complemented
126C8×Q8×C73C2211yescharacteristic, complemented
127#436×C73C2211yescharacteristic, complemented
128#436×C73C2212yescomplemented
129#435×C73C2212yescomplemented
130C8×D4×C73C2211yescharacteristic, complemented
131#433×C73C2212yescomplemented
132#431×C73C2211yescharacteristic, complemented
133#424×C73C2212yescomplemented
134#423×C73C2211yescharacteristic, complemented
135C2×Q8×D73C2×C411yescharacteristic
136C2×D4×D73C2×C412yes—
137C2×D4×D73C2×C411yescharacteristic
138C22×C4×D73C2×C411yescharacteristic
139C22×C4×D73C2×C411yescharacteristic
140C22×C4×D73C2311yescharacteristic
141C22×C4×D73C2312yes—
142C2×#11924012C2312yes—
143C2×#11924012C2312yes—
144C2×#11924011—44no—
145C2×#11924011C2312yes—
146C2×#11924011C2311yescharacteristic
147C2×#11924011C2311yescharacteristic
148C2×#11924011C2312yes—
149C2×#11924011C2311yescharacteristic
150C2×#11924011C2311yescharacteristic
151C2×#11924011C2312yes—
152C2×#11924011C2312yes—
153M16×D73—44no—
154M16×D73—44no—
155C22×#10596831C2312yes—
156C2×C8×D73C2312yes—
157C2×C8×D73C2312yes—
158C2×C8×D73C2312yes—
159C2×C8×D73C2312yes—
160#14556586C2×C412yes—
161#14556586C2×C412yes—
162#14556586C2×C412yes—
163#14556585C2×C412yes—
164#14556584C2×C412yes—
165#14556584C2×C412yes—
166#14556584C2×C412yes—
167#14556583C2×C411yescharacteristic
168#14556582C2×C411yescharacteristic
169#14556582C2×C411yescharacteristic
170#14556581C2×C412yes—
171#14556581C2×C412yes—
172#14556580C2×C411yescharacteristic
173#14556579C2×C411yescharacteristic
174#14556578C2×C411yescharacteristic
175#14556577C2×C412yes—
176#14556577C2×C412yes—
177#14556576C2×C412yes—
178#14556576C2×C412yes—
179#14556575C2×C412yes—
180#14556574C2×C412yes—
181#14556573C2×C412yes—
182#14556573C2×C412yes—
183#14556572C2×C412yes—
184#14556571C2×C411yescharacteristic
185#14556570C2×C411yescharacteristic
186#14556569C2×C412yes—
187#14556568C2×C412yes—
188#14556567C2×C411yescharacteristic
189#14556566C2×C411yescharacteristic
190#14556565C2×C411yescharacteristic
191#14556564C2×C412yes—
192#14556563C2×C412yes—
193#14556562C2×C411yescharacteristic
194Q8×Dic73C2×C411yescharacteristic
195C4×Dic146C2311yescharacteristic
196C4×Dic146C2312yes—
197#14556556C2×C412yes—
198#14556556C2×C411yescharacteristic
199C4×D292C2311yescharacteristic
200C4×D292C2312yes—
201D4×Dic73C2×C412yes—
202D4×Dic73C2×C411yescharacteristic
203#14556553C2×C412yes—
204#14556553C2×C411yescharacteristic
205C4×C22⋊D73C2312yes—
206C4×C22⋊D73C2312yes—
207C4×C22⋊D73C2312yes—
208#14556551C2×C412yes—
209#14556551C2×C412yes—
210#14556551C2×C412yes—
211#14556550C2312yes—
212#14556549C2×C412yes—
213#14556549C2×C412yes—
214#14556548C2312yes—
215#14556548C2312yes—
216#14556547C2×C412yes—
217#14556547C2×C412yes—
218C4⋊C4×D73C2×C412yes—
219C4⋊C4×D73C2×C412yes—
220C4⋊C4×D73C2×C411yescharacteristic
221C4⋊C4×D73C2×C412yes—
222C4⋊C4×D73C2×C411yescharacteristic
223C4⋊C4×D73C2×C412yes—
224C22⋊C4×D73C2×C412yes—
225C22⋊C4×D73C2×C412yes—
226C22⋊C4×D73C2×C412yes—
227C22⋊C4×D73C2×C412yes—
228C22⋊C4×D73C2×C412yes—
229C2×C4×Dic73C2×C411yescharacteristic
230C2×C4×Dic73C2×C411yescharacteristic
231C2×C4×Dic73C2311yescharacteristic
232C42×D73C2×C411yescharacteristic
233C42×D73C2×C411yescharacteristic
234C42×D73C2×C411yescharacteristic
235C42×D73C2×C411yescharacteristic
236C42×D73C2311yescharacteristic
237C42×D73C2311yescharacteristic
238C42×D73C2312yes—
239C42×D73C2311yescharacteristic
240C42×D73C2311yescharacteristic
241C4⋊#10596831C2312yes—
242C4⋊#10596831C2311yescharacteristic
243C4⋊#10596831C2311yescharacteristic
244C4⋊#10596831C2311yescharacteristic
245C4⋊#10596831C2312yes—
246C4⋊#10596831C2312yes—
247C4⋊#10596831C2311yescharacteristic
248#14556520C2312yes—
249#14556520C2312yes—
250#14556520C2312yes—
251#14556520C2312yes—
252#14556520C2311yescharacteristic
253#14556520C2311yescharacteristic
254#14556520C2312yes—
255#14556520C2312yes—
256#14556520C2312yes—
257#14556520C2312yes—
258#14556520C2311yescharacteristic
259#14556520C2311yescharacteristic
260C22⋊#10596831C2311yescharacteristic
261C22⋊#10596831C2311yescharacteristic
262C22⋊#10596831C2312yes—
263C22⋊#10596831C2312yes—
264#14556503C2311yescharacteristic
265#14556503C2311yescharacteristic
266#14556503C2311yescharacteristic
267#14556503C2311yescharacteristic
268#14556503C2312yes—
269#14556503C2312yes—
270#14556503C2312yes—
271#14556503C2312yes—
272#14556502C2312yes—
273#14556501C2311yescharacteristic
274#14556501C2311yescharacteristic
275#14556501C2311yescharacteristic
276#14556501C2311yescharacteristic
277#14556501C2312yes—
278#14556501C2312yes—
279C4×#10596831C2311yescharacteristic
280C4×#10596831C2311yescharacteristic
281C4×#10596831C2312yes—
282C8×Dic73C2312yes—
283C8×Dic73C2312yes—
284C2×M16×C73C2312yes—
285C2×M16×C73C2312yes—
286C22×C8×C73C2312yes—
287#126×C73C2×C412yes—
288#125×C73C2×C411yescharacteristic
289#124×C73C2×C411yescharacteristic
290#123×C73C2×C412yes—
291C22⋊Q8×C73C2×C411yescharacteristic
292#121×C73C2×C411yescharacteristic
293C4×Q8×C73C2311yescharacteristic
294C4×D4×C73C2311yescharacteristic
295C4×D4×C73C2312yes—
296#117×C73C2312yes—
297C2×C42×C73C2311yescharacteristic
298C4⋊C8×C73C2311yescharacteristic
299C4⋊C8×C73C2312yes—
300C4⋊C8×C73C2312yes—
301C4⋊C8×C73C2312yes—
302C4⋊C8×C73C2311yescharacteristic
303C4⋊C8×C73C2311yescharacteristic
304C4⋊C8×C73C2311yescharacteristic
305C22⋊C8×C73C2311yescharacteristic
306C22⋊C8×C73C2311yescharacteristic
307C22⋊C8×C73C2312yes—
308C22⋊C8×C73C2312yes—
309#97×C73C2312yes—
310C4×C8×C73C2311yescharacteristic
311C4×C8×C73C2311yescharacteristic
312C4×C8×C73C2312yes—
313C23×D73C22×C411yescharacteristic
314C23×D73C22×C412yes—
315C2×Dic146C22×C411yescharacteristic
316C2×Dic146C22×C412yes—
317Q8×D73—42no—
318C2×D292C22×C412yes—
319C2×D292C22×C411yescharacteristic
320C2×C22⋊D73C22×C412yes—
321C2×C22⋊D73C22×C412yes—
322C2×C22⋊D73C22×C412yes—
323D4×D73—42no—
324D4×D73—44no—
325C22×Dic73C22×C411yescharacteristic
326C22×Dic73C22×C412yes—
327C22×Dic73C22×C411yescharacteristic
328C22×Dic73C22×C411yescharacteristic
329C2×C4×D73—22no—
330C2×C4×D73—24no—
331C2×C4×D73—22no—
332C2×C4×D73—24no—
333C2×C4×D73—42no—
334C2×C4×D73—42no—
335C2×C4×D73C22×C411yescharacteristic
336C2×C4×D73C22×C411yescharacteristic
337C2×C4×D73C22×C411yescharacteristic
338C2×C4×D73C22×C411yescharacteristic
339C2×C4×D73C22×C411yescharacteristic
340C2×C4×D73C22×C411yescharacteristic
341C2×C4×D73C22×C412yes—
342C2×C4×D73C22×C412yes—
343C2×C4×D73C22×C411yescharacteristic
344C2×C4×D73C22×C411yescharacteristic
345C2×C4×D73C22×C411yescharacteristic
346C2×C4×D73C22×C411yescharacteristic
347C2×C4×D73C22×C412yes—
348C2×C4×D73C22×C412yes—
349C2×C4×D73C2411yescharacteristic
350C2×C4×D73C2412yes—
351C2×C4×D73C2411yescharacteristic
352#11924012—42no—
353#11924012—42no—
354#11924011—22no—
355#11924011—24no—
356#11924011—24no—
357#11924011—22no—
358#11924011—22no—
359#11924011—22no—
360#11924011—42no—
361#11924011—42no—
362C2×#10596831—42no—
363C2×#10596831C2411yescharacteristic
364C2×#10596831C2412yes—
365C2×#10596831C2411yescharacteristic
366C2×#10596831C2411yescharacteristic
367C2×#10596831C2412yes—
368C2×#10596831C2411yescharacteristic
369C8×D73—42no—
370C8×D73—42no—
371C8×D73—42no—
372C8×D73—42no—
373C4⋊Dic73C22×C412yes—
374C4⋊Dic73C22×C412yes—
375C4⋊Dic73C22×C411yescharacteristic
376C4⋊Dic73C22×C412yes—
377C4⋊Dic73C22×C411yescharacteristic
378C4⋊Dic73C22×C412yes—
379#11924007C22×C412yes—
380#11924007C22×C412yes—
381#11924007C22×C412yes—
382#11924007C22×C412yes—
383#11924007C22×C412yes—
384#11924007C22×C412yes—
385#11924007C22×C412yes—
386#11924007C22×C412yes—
387#11924007C22×C412yes—
388#11924007C22×C412yes—
389C22⋊Dic73C22×C412yes—
390C22⋊Dic73C22×C412yes—
391C22⋊Dic73C22×C412yes—
392C22⋊Dic73C22×C412yes—
393C22⋊Dic73C22×C412yes—
394#11924005C22×C412yes—
395#11924005C22×C412yes—
396#11924005C22×C412yes—
397#11924005C22×C412yes—
398#11924005C22×C412yes—
399#11924005C22×C412yes—
400#11924005C22×C412yes—
401#11924005C22×C412yes—
402#11924005C22×C412yes—
403#11924005C22×C412yes—
404C4×Dic73C22×C411yescharacteristic
405C4×Dic73C22×C411yescharacteristic
406C4×Dic73C22×C411yescharacteristic
407C4×Dic73C22×C411yescharacteristic
408C4×Dic73C22×C411yescharacteristic
409C4×Dic73C22×C411yescharacteristic
410C4×Dic73C22×C411yescharacteristic
411C4×Dic73C22×C411yescharacteristic
412C4×Dic73C22×C411yescharacteristic
413C4×Dic73C22×C411yescharacteristic
414C4×Dic73C22×C412yes—
415C4×Dic73C22×C412yes—
416C4×Dic73C2412yes—
417C4×Dic73C2411yescharacteristic
418C4×Dic73C2411yescharacteristic
419C2×Q8×C73C22×C411yescharacteristic
420C2×D4×C73C22×C411yescharacteristic
421C2×D4×C73C22×C412yes—
422C22×C4×C73C22×C411yescharacteristic
423C22×C4×C73C22×C411yescharacteristic
424C22×C4×C73C2411yescharacteristic
425C22×C4×C73C2412yes—
426M16×C73—42no—
427M16×C73—42no—
428C2×C8×C73—42no—
429C2×C8×C73C2411yescharacteristic
430C2×C8×C73C2411yescharacteristic
431C2×C8×C73C2411yescharacteristic
432C2×C8×C73C2411yescharacteristic
433C2×C8×C73C2412yes—
434C2×C8×C73C2412yes—
435C4⋊C4×C73C22×C412yes—
436C4⋊C4×C73C22×C412yes—
437C4⋊C4×C73C22×C411yescharacteristic
438C4⋊C4×C73C22×C412yes—
439C4⋊C4×C73C22×C411yescharacteristic
440C4⋊C4×C73C22×C412yes—
441C22⋊C4×C73C22×C412yes—
442C22⋊C4×C73C22×C412yes—
443C22⋊C4×C73C22×C412yes—
444C22⋊C4×C73C22×C412yes—
445C22⋊C4×C73C22×C412yes—
446C42×C73C22×C411yescharacteristic
447C42×C73C22×C411yescharacteristic
448C42×C73C2411yescharacteristic
449C42×C73C2412yes—
450C42×C73C2411yescharacteristic
451C23×C73C23×C412yes—
452C23×C73C23×C411yescharacteristic
453C22×D73—22no—
454C22×D73—22no—
455C22×D73—24no—
456C22×D73—41no—
457C22×D73—42no—
458C22×D73—42no—
459C22×D73C23×C412yes—
460C22×D73C23×C411yescharacteristic
461C22×D73C23×C411yescharacteristic
462Q8×C73—22no—
463D4×C73—22no—
464D4×C73—42no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—21no—
468C2×C4×C73—21no—
469C2×C4×C73—22no—
470C2×C4×C73—41no—
471C2×C4×C73C23×C411yescharacteristic
472C2×C4×C73C23×C411yescharacteristic
473C2×C4×C73C23×C411yescharacteristic
474C2×C4×C73C23×C411yescharacteristic
475C2×C4×C73C23×C412yes—
476C2×C4×C73C23×C412yes—
477C2×C4×C73C23×C412yes—
478C2×C4×C73C23×C411yescharacteristic
479C2×C4×C73C2511yescharacteristic
480C22⋊D73—24no—
481C22⋊D73—42no—
482C22⋊D73—42no—
483C2×Dic73—22no—
484C2×Dic73—24no—
485C2×Dic73—41no—
486C2×Dic73—41no—
487C2×Dic73C23×C411yescharacteristic
488C2×Dic73C23×C411yescharacteristic
489C2×Dic73C23×C411yescharacteristic
490C2×Dic73C23×C411yescharacteristic
491C2×Dic73C23×C411yescharacteristic
492C2×Dic73C23×C412yes—
493C2×Dic73C23×C412yes—
494C2×Dic73C23×C412yes—
495C2×Dic73C23×C411yescharacteristic
496D292—24no—
497D292—22no—
498C4×D73—22no—
499C4×D73—24no—
500C4×D73—22no—
501C4×D73—22no—
502C4×D73—22no—
503C4×D73—22no—
504C4×D73—21no—
505C4×D73—22no—
506C4×D73—21no—
507C4×D73—22no—
508C4×D73—22no—
509C4×D73—24no—
510C4×D73—41no—
511C4×D73—41no—
512C4×D73—41no—
513C4×D73—41no—
514C4×D73—42no—
515C4×D73—42no—
516C4×D73H(5,𝔽2)12yes—
517C4×D732−1+412yes—
518Dic146—22no—
519Dic146—42no—
520C8×C73—21no—
521C8×C73—22no—
522C8×C73—21no—
523C8×C73—22no—
524C8×C73—21no—
525C8×C73—21no—
526#10596831—22no—
527#10596831—21no—
528#10596831—22no—
529#10596831—21no—
530#10596831—21no—
531#10596831—21no—
532C22×C73—21no—
533C22×C73—22no—
534C22×C73—21no—
535C22×C73—21no—
536C22×C73—22no—
537C22×C73—22no—
538C22×C73C24×C411yescharacteristic
539C2×D73—21no—
540C2×D73—21no—
541C2×D73—21no—
542C2×D73—21no—
543C2×D73—22no—
544C2×D73—22no—
545C2×D73—22no—
546C2×D73—44no—
547C2×D73—84no—
548C2×D73#52012yes—
549C2×D73#56812yes—
550C4×C73—22no—
551C4×C73—21no—
552C4×C73—22no—
553C4×C73—21no—
554C4×C73—21no—
555C4×C73—21no—
556C4×C73—22no—
557C4×C73#56812yes—
558C4×C73C2×H(5,𝔽2)11yescharacteristic
559C4×C73C2×2−1+411yescharacteristic
560Dic73—21no—
561Dic73—22no—
562Dic73—22no—
563Dic73—21no—
564Dic73—21no—
565Dic73—21no—
566Dic73—21no—
567Dic73—22no—
568Dic73#52012yes—
569#60264—731nomaximal, Sylow
570C2×C73—41no—
571C2×C73—42no—
572C2×C73C2×#52011yescharacteristic
573C2×C73C2×#56811yescharacteristic
574C2×C73C2×#56811yescharacteristic
575D73—22no—
576D73—22no—
577D73—42no—
578C2×#529—731no—
579#2995—732no—
580#2995—732no—
581#2994—731no—
582#2994—731no—
583#2994—731no—
584#2994—731no—
585#2993—731no—
586#2993—731no—
587#2993—731no—
588#2993D7311yescharacteristic, complemented
589#2992—732no—
590#2992—732no—
591Q8×M16—731no—
592Q8×M16—731no—
593D4×M16—732no—
594D4×M16—731no—
595D4×M16—732no—
596D4×M16—731no—
597#2921—732no—
598#2920—731no—
599#2905—732no—
600C2×#423—731no—
601C73#6026411yescharacteristic, complemented, Sylow
602C22×M16—732no—
603C22×M16—732no—
604C22×M16—732no—
605#529—732no—
606#529—731no—
607#529—731no—
608#529—732no—
609#529—731no—
610#529—731no—
611#529—731no—
612#529—731no—
613#529—732no—
614#529—732no—
615#529—731no—
616#529C2×D7311yescharacteristic
617C2×#126—732no—
618C2×#125—731no—
619C2×#124—731no—
620C2×#123—732no—
621C2×C22⋊Q8—731no—
622C2×#121—731no—
623C2×C4×Q8—731no—
624C2×C4×D4—732no—
625C2×C4×D4—731no—
626C2×#117—732no—
627C22×C42—731no—
628#446—731no—
629#446—732no—
630#446—731no—
631#446—732no—
632#446—732no—
633#446—732no—
634#446—731no—
635#446C2×D7311yescharacteristic, complemented
636C8×Q8—731no—
637C8×Q8—731no—
638C8×Q8—731no—
639C8×Q8C2×D7311yescharacteristic, complemented
640#436—732no—
641#436—731no—
642#436—732no—
643#436—731no—
644#436—732no—
645#436—731no—
646#436C2×D7311yescharacteristic, complemented
647#436C2×D7312yescomplemented
648#435—732no—
649#435—732no—
650#435—732no—
651#435—732no—
652#435—732no—
653#435—732no—
654#435—732no—
655#435—732no—
656#435—732no—
657#435—732no—
658#435—732no—
659#435C2×D7312yescomplemented
660C8×D4—732no—
661C8×D4—731no—
662C8×D4—732no—
663C8×D4—731no—
664C8×D4—732no—
665C8×D4—732no—
666C8×D4—731no—
667C8×D4C2×D7311yescharacteristic, complemented
668#433—732no—
669#433—732no—
670#433—732no—
671#433—732no—
672#433—732no—
673#433—732no—
674#433—732no—
675#433C2×D7312yescomplemented
676#432—731no—
677#432—731no—
678#432—731no—
679#432—731no—
680#431—731no—
681#431—731no—
682#431—731no—
683#431C2×D7311yescharacteristic, complemented
684#424—732no—
685#424—732no—
686#424—732no—
687#424—732no—
688#424—732no—
689#424—732no—
690#424—732no—
691#424C2×D7312yescomplemented
692#423—732no—
693#423—731no—
694#423—732no—
695#423—731no—
696#423—731no—
697#423—731no—
698#423—732no—
699#423—732no—
700#423—731no—
701#423C2×D7311yescharacteristic, complemented
702C2×C4⋊C8—732no—
703C2×C4⋊C8—731no—
704C2×C4⋊C8—731no—
705#407—731no—
706#407—731no—
707#407—732no—
708#407—732no—
709C4×M16—732no—
710C4×M16—731no—
711C4×M16—731no—
712C4×M16—732no—
713C22×Q8—731no—
714C22×D4—732no—
715C22×D4—731no—
716C23×C4—731no—
717C23×C4—731no—
718C23×C4—732no—
719C23×C4—731no—
720C2×M16—2924no—
721C2×M16—2924no—
722C2×M16—2924no—
723C2×M16—732no—
724C2×M16—732no—
725C2×M16—732no—
726C2×M16—732no—
727C2×M16—732no—
728C2×M16—732no—
729C2×M16—731no—
730C2×M16—731no—
731C2×M16—731no—
732C2×M16—731no—
733C2×M16C22×D7312yes—
734C2×M16C22×D7312yes—
735C22×C8—732no—
736C22×C8—732no—
737C22×C8—732no—
738C22×C8—732no—
739C22×C8—732no—
740C22×C8C22×D7312yes—
741#126—732no—
742#126—732no—
743#126—732no—
744#126—732no—
745#126—732no—
746#126—732no—
747#126—732no—
748#126C4×D7312yes—
749#125—732no—
750#125—732no—
751#125—731no—
752#125—731no—
753#125—731no—
754#125C4×D7311yescharacteristic
755#124—731no—
756#124—731no—
757#124—732no—
758#124—732no—
759#124—731no—
760#124C4×D7311yescharacteristic
761#123—732no—
762#123—732no—
763#123—732no—
764#123—732no—
765#123—732no—
766#123—732no—
767#123—732no—
768#123C4×D7312yes—
769C22⋊Q8—731no—
770C22⋊Q8—731no—
771C22⋊Q8—732no—
772C22⋊Q8—731no—
773C22⋊Q8—732no—
774C22⋊Q8C4×D7311yescharacteristic
775#121—731no—
776#121—732no—
777#121—731no—
778#121—731no—
779#121—732no—
780#121C4×D7311yescharacteristic
781C4×Q8—731no—
782C4×Q8—732no—
783C4×Q8—731no—
784C4×Q8—731no—
785C4×Q8—732no—
786C4×Q8C22×D7311yescharacteristic
787C4×D4—731no—
788C4×D4—732no—
789C4×D4—732no—
790C4×D4—732no—
791C4×D4—732no—
792C4×D4—731no—
793C4×D4—732no—
794C4×D4—732no—
795C4×D4—732no—
796C4×D4—732no—
797C4×D4—732no—
798C4×D4—731no—
799C4×D4C22×D7311yescharacteristic
800C4×D4C22×D7312yes—
801#117—732no—
802#117—732no—
803#117—732no—
804#117—732no—
805#117—732no—
806#117—732no—
807#117—732no—
808#117C22×D7312yes—
809C2×C4⋊C4—732no—
810C2×C4⋊C4—732no—
811C2×C4⋊C4—731no—
812C2×C4⋊C4—732no—
813C2×C4⋊C4—731no—
814C2×C4⋊C4—732no—
815C2×C22⋊C4—732no—
816C2×C22⋊C4—732no—
817C2×C22⋊C4—732no—
818C2×C22⋊C4—732no—
819C2×C22⋊C4—732no—
820C2×C42—731no—
821C2×C42—731no—
822C2×C42—731no—
823C2×C42—731no—
824C2×C42—731no—
825C2×C42—731no—
826C2×C42—731no—
827C2×C42—731no—
828C2×C42—732no—
829C2×C42—731no—
830C2×C42—731no—
831C2×C42—731no—
832C2×C42C22×D7311yescharacteristic
833C4⋊C8—732no—
834C4⋊C8—732no—
835C4⋊C8—732no—
836C4⋊C8—732no—
837C4⋊C8—731no—
838C4⋊C8—731no—
839C4⋊C8—732no—
840C4⋊C8—732no—
841C4⋊C8—732no—
842C4⋊C8—732no—
843C4⋊C8—731no—
844C4⋊C8—731no—
845C4⋊C8—732no—
846C4⋊C8—731no—
847C4⋊C8—731no—
848C4⋊C8—731no—
849C4⋊C8—732no—
850C4⋊C8—732no—
851C4⋊C8—731no—
852C4⋊C8C22×D7312yes—
853C4⋊C8C22×D7311yescharacteristic
854C4⋊C8C22×D7311yescharacteristic
855C4⋊C8C22×D7311yescharacteristic
856C4⋊C8C22×D7312yes—
857C4⋊C8C22×D7312yes—
858C4⋊C8C22×D7311yescharacteristic
859C22⋊C8—731no—
860C22⋊C8—731no—
861C22⋊C8—732no—
862C22⋊C8—732no—
863C22⋊C8—731no—
864C22⋊C8—731no—
865C22⋊C8—731no—
866C22⋊C8—731no—
867C22⋊C8—732no—
868C22⋊C8—732no—
869C22⋊C8—732no—
870C22⋊C8—732no—
871C22⋊C8C22×D7311yescharacteristic
872C22⋊C8C22×D7311yescharacteristic
873C22⋊C8C22×D7312yes—
874C22⋊C8C22×D7312yes—
875#97—731no—
876#97—731no—
877#97—731no—
878#97—731no—
879#97—732no—
880#97—732no—
881#97—732no—
882#97C22×D7312yes—
883C4×C8—732no—
884C4×C8—732no—
885C4×C8—731no—
886C4×C8—731no—
887C4×C8—732no—
888C4×C8C22×D7311yescharacteristic
889C4×C8C22×D7311yescharacteristic
890C4×C8C22×D7312yes—
891C24—732no—
892C24—731no—
893C2×Q8—2922no—
894C2×Q8—732no—
895C2×Q8—731no—
896C2×Q8C2×C4×D7311yescharacteristic
897C2×D4—2924no—
898C2×D4—2922no—
899C2×D4—732no—
900C2×D4—732no—
901C2×D4—732no—
902C2×D4—732no—
903C2×D4—731no—
904C2×D4C2×C4×D7311yescharacteristic
905C2×D4C2×C4×D7312yes—
906C22×C4—2922no—
907C22×C4—2922no—
908C22×C4—731no—
909C22×C4—731no—
910C22×C4—731no—
911C22×C4—731no—
912C22×C4—731no—
913C22×C4—731no—
914C22×C4—732no—
915C22×C4—732no—
916C22×C4—731no—
917C22×C4—731no—
918C22×C4—732no—
919C22×C4—731no—
920C22×C4—731no—
921C22×C4—731no—
922C22×C4—731no—
923C22×C4—731no—
924C22×C4—731no—
925C22×C4—732no—
926C22×C4—732no—
927C22×C4—731no—
928C22×C4—732no—
929C22×C4—1464no—
930C22×C4—1462no—
931C22×C4—1462no—
932C22×C4—1464no—
933C22×C4C2×C4×D7311yescharacteristic
934C22×C4C2×C4×D7311yescharacteristic
935C22×C4C23×D7311yescharacteristic
936C22×C4C23×D7312yes—
937M16—42no—
938M16—42no—
939M16—2922no—
940M16—2922no—
941M16—2922no—
942M16—2922no—
943M16—1462no—
944M16—1464no—
945M16—1464no—
946M16—1462no—
947M16—1462no—
948M16—1462no—
949C2×C8—42no—
950C2×C8—2922no—
951C2×C8—2922no—
952C2×C8—2922no—
953C2×C8—2922no—
954C2×C8—2922no—
955C2×C8—731no—
956C2×C8—731no—
957C2×C8—732no—
958C2×C8—731no—
959C2×C8—732no—
960C2×C8—731no—
961C2×C8C23×D7311yescharacteristic
962C2×C8C23×D7312yes—
963C2×C8C23×D7311yescharacteristic
964C2×C8C23×D7311yescharacteristic
965C2×C8C23×D7312yes—
966C2×C8C23×D7311yescharacteristic
967C4⋊C4—732no—
968C4⋊C4—732no—
969C4⋊C4—732no—
970C4⋊C4—732no—
971C4⋊C4—732no—
972C4⋊C4—732no—
973C4⋊C4—732no—
974C4⋊C4—732no—
975C4⋊C4—732no—
976C4⋊C4—732no—
977C4⋊C4—732no—
978C4⋊C4—732no—
979C4⋊C4—731no—
980C4⋊C4—732no—
981C4⋊C4—731no—
982C4⋊C4—732no—
983C4⋊C4C2×C4×D7312yes—
984C4⋊C4C2×C4×D7312yes—
985C4⋊C4C2×C4×D7311yescharacteristic
986C4⋊C4C2×C4×D7312yes—
987C4⋊C4C2×C4×D7311yescharacteristic
988C4⋊C4C2×C4×D7312yes—
989C22⋊C4—732no—
990C22⋊C4—732no—
991C22⋊C4—732no—
992C22⋊C4—732no—
993C22⋊C4—732no—
994C22⋊C4—732no—
995C22⋊C4—732no—
996C22⋊C4—732no—
997C22⋊C4—732no—
998C22⋊C4—732no—
999C22⋊C4—732no—
1000C22⋊C4—732no—
1001C22⋊C4—732no—
1002C22⋊C4—732no—
1003C22⋊C4—732no—
1004C22⋊C4C2×C4×D7312yes—
1005C22⋊C4C2×C4×D7312yes—
1006C22⋊C4C2×C4×D7312yes—
1007C22⋊C4C2×C4×D7312yes—
1008C22⋊C4C2×C4×D7312yes—
1009C42—731no—
1010C42—731no—
1011C42—731no—
1012C42—731no—
1013C42—731no—
1014C42—731no—
1015C42—731no—
1016C42—731no—
1017C42—731no—
1018C42—731no—
1019C42—732no—
1020C42—732no—
1021C42—732no—
1022C42—731no—
1023C42—731no—
1024C42C2×C4×D7311yescharacteristic
1025C42C2×C4×D7311yescharacteristic
1026C42C23×D7311yescharacteristic
1027C42C23×D7312yes—
1028C42C23×D7311yescharacteristic
1029C23—2921no—
1030C23—2922no—
1031C23—2922no—
1032C23—731no—
1033C23—731no—
1034C23—732no—
1035C23—1462no—
1036C23—1462no—
1037C23—1464no—
1038C23C22×C4×D7312yes—
1039C23C22×C4×D7311yescharacteristic
1040Q8—22no—
1041Q8—2922no—
1042Q8—1462no—
1043D4—22no—
1044D4—42no—
1045D4—2922no—
1046D4—2922no—
1047D4—1464no—
1048D4—1464no—
1049D4—1462no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—41no—
1056C2×C4—2921no—
1057C2×C4—2921no—
1058C2×C4—2921no—
1059C2×C4—2921no—
1060C2×C4—2922no—
1061C2×C4—2922no—
1062C2×C4—2921no—
1063C2×C4—2921no—
1064C2×C4—731no—
1065C2×C4—732no—
1066C2×C4—732no—
1067C2×C4—731no—
1068C2×C4—731no—
1069C2×C4—731no—
1070C2×C4—731no—
1071C2×C4—731no—
1072C2×C4—732no—
1073C2×C4—732no—
1074C2×C4—732no—
1075C2×C4—1464no—
1076C2×C4—1462no—
1077C2×C4—1462no—
1078C2×C4—1462no—
1079C2×C4—1462no—
1080C2×C4—1464no—
1081C2×C4—1462no—
1082C2×C4—1464no—
1083C2×C4—1461no—
1084C2×C4—1462no—
1085C2×C4—1462no—
1086C2×C4—1461no—
1087C2×C4—1462no—
1088C2×C4—1462no—
1089C2×C4C22×C4×D7311yescharacteristic
1090C2×C4C22×C4×D7311yescharacteristic
1091C2×C4C22×C4×D7311yescharacteristic
1092C2×C4C22×C4×D7311yescharacteristic
1093C2×C4C22×C4×D7312yes—
1094C2×C4C22×C4×D7312yes—
1095C2×C4C22×C4×D7312yes—
1096C2×C4C22×C4×D7311yescharacteristic
1097C2×C4C24×D7311yescharacteristic
1098C8—21no—
1099C8—22no—
1100C8—22no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—1462no—
1105C8—1461no—
1106C8—1462no—
1107C8—1461no—
1108C8—1461no—
1109C8—1461no—
1110C22—21no—
1111C22—22no—
1112C22—21no—
1113C22—22no—
1114C22—21no—
1115C22—22no—
1116C22—2924no—
1117C22—5844no—
1118C22—732no—
1119C22—732no—
1120C22—1462no—
1121C22—1462no—
1122C22—1462no—
1123C22—1461no—
1124C22—1461no—
1125C22—1461no—
1126C22—1461no—
1127C22C23×C4×D7311yescharacteristic
1128C4—21no—
1129C4—21no—
1130C4—22no—
1131C4—21no—
1132C4—22no—
1133C4—22no—
1134C4—21no—
1135C4—732no—
1136C4—1461no—
1137C4—1461no—
1138C4—1462no—
1139C4—1461no—
1140C4—1461no—
1141C4—1462no—
1142C4—1461no—
1143C4—1462no—
1144C4#1798935212yes—
1145C4H(5,𝔽2)×D7311yescharacteristic
1146C42−1+4×D7311yescharacteristic
1147C2—41no—
1148C2—42no—
1149C2—2922no—
1150C2—1462no—
1151C2—1462no—
1152C2#520×D7311yescharacteristic
1153C2#568×D7311yescharacteristic
1154C2C2×#1798935211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2993C2
prime radical#121×D73C4
cosocleC2×C4×C73C25
hypercenter#2993D73
hypocenterC73#60264
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #22619102C2semidirect
3. #22619095C2semidirect
4. #22619094C2semidirect
5. #22619092C2semidirect
6. #22619090C2semidirect
7. #22619086C2semidirect
8. #22619082C2semidirect
9. #22619080C2semidirect
10. #22619076C2semidirect
11. #22619068C2semidirect
12. #22619065C2semidirect
13. #22618883C2semidirect
14. Q8×#11924011C2semidirect
15. #22618667C2semidirect
16. #22618667C2semidirect
17. #22618664C2semidirect
18. D4×#11924011C2semidirect
19. #22618565C2semidirect
20. #22618559C2semidirect
21. #22618492C2semidirect
22. #423×D73C2semidirect
23. C73×#2993C2semidirect
49. #17988718C22semidirect
50. #17988717C22semidirect
51. #17988717C22semidirect
52. #17988716C22semidirect
53. #17988715C22semidirect
54. #17988714C22semidirect
55. #17988714C22semidirect
56. Q8×#10596831C22semidirect
57. C8×Dic146C22semidirect
58. #17988711C22semidirect
59. #17988666C22semidirect
60. #17988665C22semidirect
61. #17988665C22semidirect
62. #17988664C22semidirect
63. #17988663C22semidirect
64. #17988662C22semidirect
65. #17988661C22semidirect
66. #17988661C22semidirect
67. #17988661C22semidirect
68. #17988660C22semidirect
69. #17988659C22semidirect
70. #17988658C22semidirect
71. #17988657C22semidirect
72. #17988656C22semidirect
73. #17988656C22semidirect
74. #17988656C22semidirect
75. #17988655C22semidirect
76. C8×D292C22semidirect
77. C8×D292C22semidirect
78. D4×#10596831C22semidirect
79. #17988652C22semidirect
80. #17988652C22semidirect
81. C8×C22⋊D73C22semidirect
82. #17988650C22semidirect
83. #17988649C22semidirect
84. #17988648C22semidirect
85. #17988647C22semidirect
86. #17988647C22semidirect
87. #17988646C22semidirect
88. #17988645C22semidirect
89. #17988645C22semidirect
90. #17988643C22semidirect
91. #17988643C22semidirect
92. #17988641C22semidirect
93. #17988641C22semidirect
94. #17988640C22semidirect
95. #17988638C22semidirect
96. #17988638C22semidirect
97. #17988615C22semidirect
98. #17988614C22semidirect
99. #17988613C22semidirect
100. #17988612C22semidirect
101. #17988612C22semidirect
102. #17988612C22semidirect
103. #17988612C22semidirect
104. #17988611C22semidirect
105. #17988610C22semidirect
113. C4⋊C8×D73C22semidirect
114. C4⋊C8×D73C22semidirect
115. C4⋊C8×D73C22semidirect
125. #446×C73C22semidirect
126. C8×Q8×C73C22semidirect
127. #436×C73C22semidirect
128. #436×C73C22semidirect
129. #435×C73C22semidirect
130. C8×D4×C73C22semidirect
131. #433×C73C22semidirect
132. #431×C73C22semidirect
133. #424×C73C22semidirect
134. #423×C73C22semidirect
588. #2993D73semidirect
601. C73#60264semidirect
635. #446C2×D73semidirect
639. C8×Q8C2×D73semidirect
646. #436C2×D73semidirect
647. #436C2×D73semidirect
659. #435C2×D73semidirect
667. C8×D4C2×D73semidirect
675. #433C2×D73semidirect
683. #431C2×D73semidirect
691. #424C2×D73semidirect
701. #423C2×D73semidirect

Maximal subgroups

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

subgroupindex
#529×D732
#226191022
#226190952
#226190942
#226190922
#226190902
#226190862
#226190822
#226190802
#226190762
#226190682
#226190652
#226188832
Q8×#119240112
#226186672
#226186642
D4×#119240112
#226185652
#226185592
#226184922
#423×D732
C73×#29932
#6026473