Finite Group Databasebeta

← #33101548

Subgroups — #33101548

Order 18688.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic146C211yesmaximal, characteristic
2C2×#17988659C211yesmaximal, characteristic
3C2×#17988595C211yesmaximal, characteristic, complemented
4C22×#14556514C211yesmaximal, characteristic, complemented
5#22610854C211yesmaximal, characteristic, complemented
6#22610750C211yesmaximal, characteristic, complemented
7#22610362C211yesmaximal, characteristic, complemented
8#22610352C211yesmaximal, characteristic, complemented
9#22610243C211yesmaximal, characteristic, complemented
10#22610238C211yesmaximal, characteristic, complemented
11#22609943C211yesmaximal, characteristic, complemented
12#22609865C211yesmaximal, characteristic, complemented
13#22609865C211yesmaximal, characteristic, complemented
14#22609764C211yesmaximal, characteristic, complemented
15C73×#2352C211yesmaximal, characteristic
16C23×Dic146C2211yescharacteristic
17C23×Dic146C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20D4×Dic146—24no—
21D4×Dic146C418yescomplemented
22C2×#14556591C2211yescharacteristic
23C2×#14556590—21no—
24C2×#14556570C2211yescharacteristic
25C2×#14556570C2211yescharacteristic
26C2×#14556568—21no—
27C2×#14556568—21no—
28C2×C4×Dic146C2211yescharacteristic
29C2×D4×Dic73—21no—
30#17988659—24no—
31C2×C4⋊#10596831C2211yescharacteristic
32#17988595—24no—
33C2×#14556514—24no—
34C2×#14556514C2211yescharacteristic
35C2×#14556514C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556514C2211yescharacteristic
39C2×#14556514C2211yescharacteristic
40C2×#14556514C2211yescharacteristic
41C2×#14556514C2211yescharacteristic
42C2×#14556514C2211yescharacteristic
43C2×#14556514C2211yescharacteristic
44C2×#14556514C2211yescharacteristic
45C2×#14556514C2211yescharacteristic
46C2×C22⋊#10596831C2211yescharacteristic
47C2×C22⋊#10596831C2211yescharacteristic
48C2×#14556502C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×#117×C73C2211yescharacteristic
55C22×C4⋊C4×C73C2211yescharacteristic
56#388×C73—21no—
57#387×C73—21no—
58#386×C73—21no—
59#382×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61#380×C73C2211yescharacteristic
62C4×C4⋊C4×C73C2211yescharacteristic
63C4×C22⋊C4×C73—21no—
64C22×Dic146—22no—
65C22×Dic146—22no—
66C22×Dic146—22no—
67C22×Dic146—22no—
68C22×Dic146—21no—
69C22×Dic146—21no—
70C22×Dic146—22no—
71C22×Dic146—22no—
72C22×Dic146—41no—
73C22×Dic146—41no—
74C22×Dic146—41no—
75C22×Dic146—41no—
76C22×Dic146C2×C414yes—
77C22×Dic146C2×C414yescomplemented
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C23×Dic73—21no—
82C23×Dic73—21no—
83C2×#11924012—22no—
84C2×#11924012—22no—
85C2×#11924012—41no—
86C22×#10596831—22no—
87C22×#10596831—22no—
88C22×#10596831—41no—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93#14556591—22no—
94#14556591C2×C414yescomplemented
95#14556590—28no—
96#14556570—22no—
97#14556570—22no—
98#14556570C2×C414yes—
99#14556570C2×C414yescomplemented
100#14556568—28no—
101#14556568—28no—
102C4×Dic146—22no—
103C4×Dic146C2×C414yescomplemented
104D4×Dic73—28no—
105C2×C4⋊Dic73—21no—
106C2×C4⋊Dic73—21no—
107C2×C4⋊Dic73C2311yescharacteristic
108C2×#11924007—21no—
109C2×#11924007—21no—
110C2×#11924007—21no—
111C2×C22⋊Dic73—21no—
112C2×C22⋊Dic73—21no—
113C2×C4×Dic73—21no—
114C4⋊#10596831—22no—
115#14556514—22no—
116#14556514—22no—
117#14556514—22no—
118#14556514—22no—
119#14556514—22no—
120#14556514—22no—
121#14556514—22no—
122#14556514—41no—
123#14556514—41no—
124#14556514—41no—
125#14556514—41no—
126#14556514D414yescomplemented
127C22⋊#10596831—22no—
128C22⋊#10596831—22no—
129#14556502—22no—
130C22×D4×C73D411yescharacteristic
131C23×C4×C73—21no—
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C4×D4×C73C2×C414yes—
135C4×D4×C73D414yes—
136#117×C73—22no—
137#117×C73—41no—
138C2×C4⋊C4×C73—22no—
139C2×C4⋊C4×C73—21no—
140C2×C4⋊C4×C73—41no—
141C2×C4⋊C4×C73D411yescharacteristic
142C2×C4⋊C4×C73C2311yescharacteristic
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C22⋊C4×C73—21no—
147C2×C22⋊C4×C73—21no—
148C2×C22⋊C4×C73—21no—
149C2×C22⋊C4×C73D411yescharacteristic
150C2×C22⋊C4×C73D411yescharacteristic
151C2×C42×C73—21no—
152C2×C42×C73—21no—
153C2×C42×C73C2311yescharacteristic
154#95×C73—21no—
155#95×C73—21no—
156#95×C73—21no—
157#95×C73—21no—
158#95×C73—21no—
159C2×Dic146—21no—
160C2×Dic146—21no—
161C2×Dic146—21no—
162C2×Dic146—21no—
163C2×Dic146—21no—
164C2×Dic146—21no—
165C2×Dic146—21no—
166C2×Dic146—21no—
167C2×Dic146—21no—
168C2×Dic146—21no—
169C2×Dic146—21no—
170C2×Dic146—28no—
171C2×Dic146—28no—
172C2×Dic146—24no—
173C2×Dic146—24no—
174C2×Dic146—21no—
175C2×Dic146—21no—
176C2×Dic146—44no—
177C2×Dic146—44no—
178C2×Dic146—44no—
179C2×Dic146—44no—
180C2×Dic146—44no—
181C2×Dic146—44no—
182C2×Dic146—42no—
183C2×Dic146—42no—
184C2×Dic146—42no—
185C2×Dic146—42no—
186C2×Dic146C22×C412yes—
187C2×Dic146C22×C412yes—
188C2×Dic146C22×C412yes—
189C2×Dic146C2×D412yes—
190C2×Dic146#4112yes—
191C22×Dic73—21no—
192C22×Dic73—24no—
193C22×Dic73—24no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—42no—
198C22×Dic73—42no—
199C22×Dic73—42no—
200C22×Dic73—42no—
201#11924012—44no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—21no—
210C2×#10596831—21no—
211C2×#10596831—21no—
212C2×#10596831—21no—
213C2×#10596831—44no—
214C2×#10596831C2×D412yes—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73—21no—
218C4⋊Dic73C22×C412yes—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222C22⋊Dic73—24no—
223C22⋊Dic73—24no—
224C4×Dic73—24no—
225C24×C73C2×D411yescharacteristic
226C24×C73C2×D411yescharacteristic
227C2×D4×C73—22no—
228C2×D4×C73—22no—
229C2×D4×C73C22⋊C414yes—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—42no—
243C22×C4×C73—42no—
244C22×C4×C73—81no—
245C22×C4×C73C22×C412yes—
246C22×C4×C73C22×C412yes—
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D412yes—
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2411yescharacteristic
254C4⋊C4×C73—21no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—21no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—42no—
262C4⋊C4×C73C22⋊C414yes—
263C4⋊C4×C73C2×D412yes—
264C22⋊C4×C73—42no—
265C22⋊C4×C73—42no—
266C22⋊C4×C73—81no—
267C22⋊C4×C73C22⋊C414yes—
268C22⋊C4×C73C22⋊C414yes—
269C42×C73—42no—
270C42×C73—81no—
271C42×C73C22×C412yes—
272C42×C73C2×D412yes—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73C2×C22⋊C412yes—
284C23×C73C2×C22⋊C412yes—
285C23×C73#13712yes—
286C23×C73#13712yes—
287C23×C73C22×D411yescharacteristic
288D4×C73—28no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—84no—
318C2×C4×C73C2×C22⋊C412yes—
319C2×C4×C73C2×C22⋊C412yes—
320C2×C4×C73C2×C22⋊C412yes—
321C2×C4×C73C2×C22⋊C412yes—
322C2×C4×C73C23×C411yescharacteristic
323C2×C4×C73C22×D411yescharacteristic
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C2×#4111yescharacteristic
326C2×C4×C73H(5,𝔽2)11yescharacteristic
327C2×C4×C73H(5,𝔽2)11yescharacteristic
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—48no—
335C2×Dic73—48no—
336C2×Dic73—41no—
337C2×Dic73—41no—
338C2×Dic73—41no—
339C2×Dic73—41no—
340C2×Dic73—41no—
341C2×Dic73—41no—
342Dic146—22no—
343Dic146—22no—
344Dic146—22no—
345Dic146—22no—
346Dic146—22no—
347Dic146—22no—
348Dic146—22no—
349Dic146—48no—
350Dic146—48no—
351Dic146—41no—
352Dic146—41no—
353Dic146—41no—
354Dic146—41no—
355Dic146C4×D414yes—
356#10596831—22no—
357#10596831—41no—
358#10596831—41no—
359#10596831—41no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—22no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73#41914yescomplemented
374C22×C73C22×C22⋊C411yescharacteristic
375C22×C73D4211yescharacteristic
376C22×C73#54611yescharacteristic
377C22×C73C2×#13711yescharacteristic
378C22×C73C2×#13711yescharacteristic
379C22×C73#57711yescharacteristic
380C22×C73#57811yescharacteristic
381C4×C73—22no—
382C4×C73—22no—
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—42no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73—81no—
389C4×C73C2×C4×D411yescharacteristic
390C4×C73#51811yescharacteristic
391C4×C73D4211yescharacteristic
392C4×C73#54611yescharacteristic
393Dic73—24no—
394Dic73—42no—
395Dic73—42no—
396Dic73—42no—
397#22425—731nomaximal, Sylow
398C2×C73—24no—
399C2×C73—42no—
400C2×C73D4×C22⋊C411yescharacteristic
401C2×C73C2×#41911yescharacteristic
402C2×C73#289811yescharacteristic
403C2×C73#326611yescharacteristic
404C2×C73#327011yescharacteristic
405C2×C73#331211yescharacteristic
406C2×C73#332011yescharacteristic
407C2×D4×Q8—731no—
408C2×#435—731no—
409C2×#419—731no—
410C22×#103—731no—
411#2352D7311yescharacteristic
412#1981—731no—
413#1960—731no—
414#1894—731no—
415#1892—731no—
416#1873—731no—
417#1872—731no—
418#1805—731no—
419#1787—731no—
420#1787—731no—
421#1763—731no—
422C73#2242511yescharacteristic, complemented, Sylow
423C23×Q8—731no—
424C23×Q8—731no—
425C22×M16—731no—
426C23×C8—731no—
427D4×Q8—738no—
428D4×Q8—1464no—
429C2×C4⋊Q8—731no—
430C2×C4⋊Q8—1461no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—731no—
433C2×C22⋊Q8—1461no—
434C2×C22⋊Q8—1461no—
435C2×C4×Q8—731no—
436C2×C4×D4—1461no—
437C2×C4×D4C2×D7311yescharacteristic
438C2×#117C2×D7311yescharacteristic
439C22×C4⋊C4C2×D7311yescharacteristic
440#435—1464no—
441C2×C4⋊C8—731no—
442#419—1464no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#103—731no—
446C2×#103—731no—
447C2×#103—731no—
448C2×#103—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—1464no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×#97—731no—
459#388—21no—
460#387—21no—
461#386—21no—
462#382C2×D7311yescharacteristic
463#380C2×D7311yescharacteristic
464#380C2×D7311yescharacteristic
465C4×C4⋊C4C2×D7311yescharacteristic
466C4×C22⋊C4—21no—
467#340—731no—
468#340—731no—
469#340—731no—
470#340—731no—
471C22×Q8—2921no—
472C22×Q8—2921no—
473C22×Q8—2921no—
474C22×Q8—2921no—
475C22×Q8—734no—
476C22×Q8—734no—
477C22×Q8—731no—
478C22×Q8—731no—
479C22×Q8—731no—
480C22×Q8—1462no—
481C22×Q8—1462no—
482C22×Q8—1462no—
483C22×Q8—1462no—
484C22×Q8—1461no—
485C22×Q8—1461no—
486C22×Q8—1462no—
487C22×Q8—1462no—
488C22×D4C22⋊D7311yescharacteristic
489C23×C4—21no—
490C23×C4—1461no—
491C23×C4—1461no—
492C23×C4C22×D7311yescharacteristic
493C23×C4C22×D7311yescharacteristic
494C2×M16—2921no—
495C2×M16—1462no—
496C2×M16—1462no—
497C22×C8—2921no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8—731no—
501C22×C8—731no—
502C22×C8—1462no—
503C22×C8—1462no—
504C4⋊Q8—734no—
505C4⋊Q8—1468no—
506C4⋊Q8—1462no—
507C22⋊Q8—734no—
508C22⋊Q8—734no—
509C22⋊Q8—1462no—
510C22⋊Q8—1462no—
511C22⋊Q8—1468no—
512C22⋊Q8—1468no—
513C4×Q8—734no—
514C4×Q8—1462no—
515C4×D4—1468no—
516C4×D4C4×D7314yes—
517C4×D4D29214yes—
518#117—22no—
519#117—41no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4C22⋊D7311yescharacteristic
530C2×C4⋊C4C22×D7311yescharacteristic
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4C22⋊D7311yescharacteristic
540C2×C22⋊C4C22⋊D7311yescharacteristic
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—1461no—
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—1462no—
546#103—2921no—
547#103—2921no—
548#103—2921no—
549#103—2921no—
550#103—734no—
551#103—1462no—
552#103—1462no—
553#103—1462no—
554#103—1462no—
555#103—1462no—
556#103—1462no—
557#103—1462no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560#97—1462no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24C2×C22⋊D7311yescharacteristic
567C24C2×C22⋊D7311yescharacteristic
568C2×Q8—2924no—
569C2×Q8—2924no—
570C2×Q8—2924no—
571C2×Q8—2924no—
572C2×Q8—2924no—
573C2×Q8—2924no—
574C2×Q8—2922no—
575C2×Q8—2922no—
576C2×Q8—2922no—
577C2×Q8—2922no—
578C2×Q8—732no—
579C2×Q8—732no—
580C2×Q8—732no—
581C2×Q8—732no—
582C2×Q8—732no—
583C2×Q8—1468no—
584C2×Q8—1468no—
585C2×Q8—1461no—
586C2×Q8—1461no—
587C2×Q8—1461no—
588C2×Q8—1461no—
589C2×Q8—1461no—
590C2×Q8—1461no—
591C2×Q8—1461no—
592C2×Q8—1461no—
593C2×Q8—1464no—
594C2×Q8—1464no—
595C2×Q8—1461no—
596C2×Q8—1461no—
597C2×Q8—1461no—
598C2×Q8—1461no—
599C2×Q8—1461no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4#1192400514yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—2922no—
619C22×C4—2922no—
620C22×C4—2922no—
621C22×C4—2922no—
622C22×C4—1464no—
623C22×C4—1464no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4C2×C4×D7312yes—
629C22×C4C2×C4×D7312yes—
630C22×C4C2×C22⋊D7311yescharacteristic
631C22×C4C2×C22⋊D7311yescharacteristic
632C22×C4C2×C22⋊D7311yescharacteristic
633C22×C4C2×C22⋊D7311yescharacteristic
634C22×C4C2×D29212yes—
635C22×C4C2×D29212yes—
636C22×C4C23×D7311yescharacteristic
637M16—2924no—
638C2×C8—2924no—
639C2×C8—732no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8—1461no—
645C2×C8—1461no—
646C2×C8—1461no—
647C2×C8—1461no—
648C2×C8—1461no—
649C2×C8—1461no—
650C2×C8—1461no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—732no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1464no—
663C4⋊C4—1464no—
664C4⋊C4—1464no—
665C4⋊C4—1461no—
666C4⋊C4#1192400514yes—
667C4⋊C4D4×D7312yes—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—81no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4#1192400514yes—
674C22⋊C4#1192400514yes—
675C42—42no—
676C42—81no—
677C42—1464no—
678C42C2×C4×D7312yes—
679C42C2×D29212yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×#1192400512yes—
691C23C2×#1192400512yes—
692C23#1455662112yes—
693C23#1455662112yes—
694C23C22×C22⋊D7311yescharacteristic
695Q8—2928no—
696Q8—2928no—
697Q8—2921no—
698Q8—2921no—
699Q8—2921no—
700Q8—2921no—
701Q8—734no—
702Q8—1462no—
703Q8—1462no—
704Q8—1462no—
705Q8—1462no—
706Q8—1462no—
707Q8—1462no—
708Q8—1462no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—2921no—
740C2×C4—2921no—
741C2×C4—2921no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—2928no—
746C2×C4—2928no—
747C2×C4—1462no—
748C2×C4—1462no—
749C2×C4—1462no—
750C2×C4—1462no—
751C2×C4—1462no—
752C2×C4—1462no—
753C2×C4C2×#1192400512yes—
754C2×C4C2×#1192400512yes—
755C2×C4C2×#1192400512yes—
756C2×C4C2×#1192400512yes—
757C2×C4C22×C4×D7311yescharacteristic
758C2×C4C2×D4×D7311yescharacteristic
759C2×C4C22×D29211yescharacteristic
760C2×C4#41×D7311yescharacteristic
761C2×C4#1455663611yescharacteristic
762C2×C4#1455663711yescharacteristic
763C8—2921no—
764C8—2921no—
765C8—2921no—
766C8—1462no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1798859514yescomplemented
781C22C22×#1192400511yescharacteristic
782C22D4×C22⋊D7311yescharacteristic
783C22#1798922511yescharacteristic
784C22C2×#1455662111yescharacteristic
785C22C2×#1455662111yescharacteristic
786C22#1798939811yescharacteristic
787C22#1798940211yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—2922no—
797C4—2922no—
798C4—2922no—
799C4—1464no—
800C4C4×D4×D7311yescharacteristic
801C4#1798905911yescharacteristic
802C4D4×D29211yescharacteristic
803C4#1798923211yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#1192400511yescharacteristic
807C2C2×#1798859511yescharacteristic
808C2#2261846111yescharacteristic
809C2#2262143711yescharacteristic
810C2#2262149711yescharacteristic
811C2#2262197611yescharacteristic
812C2#2262209611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2352C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
cosocleC22×C4×C73C24
hypercenter#2352D73
hypocenterC73#22425
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#17988595C2semidirect
4. C22×#14556514C2semidirect
5. #22610854C2semidirect
6. #22610750C2semidirect
7. #22610362C2semidirect
8. #22610352C2semidirect
9. #22610243C2semidirect
10. #22610238C2semidirect
11. #22609943C2semidirect
12. #22609865C2semidirect
13. #22609865C2semidirect
14. #22609764C2semidirect
21. D4×Dic146C4semidirect
77. C22×Dic146C2×C4semidirect
94. #14556591C2×C4semidirect
99. #14556570C2×C4semidirect
103. C4×Dic146C2×C4semidirect
126. #14556514D4semidirect
373. C22×C73#419semidirect
422. C73#22425semidirect
780. C22#17988595semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1462
C2×#179886592
C2×#179885952
C22×#145565142
#226108542
#226107502
#226103622
#226103522
#226102432
#226102382
#226099432
#226098652
#226097642
C73×#23522
#2242573