Finite Group Databasebeta

← #33101556

Subgroups — #33101556

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×#17988597C211yesmaximal, characteristic, complemented
3C22×#14556516C211yesmaximal, characteristic, complemented
4#22612860C211yesmaximal, characteristic
5#22610853C211yesmaximal, characteristic, complemented
6#22610751C211yesmaximal, characteristic, complemented
7#22610364C211yesmaximal, characteristic, complemented
8#22610354C211yesmaximal, characteristic, complemented
9#22610241C211yesmaximal, characteristic, complemented
10#22610236C211yesmaximal, characteristic, complemented
11#22609947C211yesmaximal, characteristic, complemented
12#22609867C211yesmaximal, characteristic, complemented
13#22609867C211yesmaximal, characteristic, complemented
14#22609762C211yesmaximal, characteristic, complemented
15C2×#435×C73C211yesmaximal, characteristic
16C23×Dic146C2211yescharacteristic
17C23×Dic146C2211yescharacteristic
18D4×Dic146—24no—
19D4×Dic146C418yescomplemented
20C2×#14556591C2211yescharacteristic
21C2×#14556590—21no—
22C2×#14556570C2211yescharacteristic
23C2×#14556570C2211yescharacteristic
24C2×#14556568—21no—
25C2×#14556568—21no—
26C2×C4×Dic146C2211yescharacteristic
27C2×D4×Dic73—21no—
28C2×#14556550C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30#17988597—24no—
31C2×#14556516—24no—
32C2×#14556516C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556516C2211yescharacteristic
36C2×#14556516C2211yescharacteristic
37C2×#14556516C2211yescharacteristic
38C2×#14556516C2211yescharacteristic
39C2×#14556516C2211yescharacteristic
40C2×#14556516C2211yescharacteristic
41C2×#14556516C2211yescharacteristic
42C2×#14556516C2211yescharacteristic
43C2×#14556516C2211yescharacteristic
44#17988480—21no—
45#17988473—21no—
46#17988467—21no—
47#17988453C2211yescharacteristic
48#17988447C2211yescharacteristic
49#17988447C2211yescharacteristic
50C4×C4⋊Dic73C2211yescharacteristic
51C22⋊C4×Dic73—21no—
52#17988350C2211yescharacteristic
53#17988350C2211yescharacteristic
54#17988350C2211yescharacteristic
55#17988350C2211yescharacteristic
56C22×M16×C73C2211yescharacteristic
57C23×C8×C73C2211yescharacteristic
58C2×C4×D4×C73C2211yescharacteristic
59#435×C73—24no—
60C2×C4⋊C8×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C2×C22⋊C8×C73C2211yescharacteristic
63C2×#97×C73C2211yescharacteristic
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—
83C23×Dic73—21no—
84#14556591—22no—
85#14556591C2×C414yescomplemented
86#14556590—28no—
87#14556570—22no—
88#14556570—22no—
89#14556570C2×C414yes—
90#14556570C2×C414yescomplemented
91#14556568—28no—
92#14556568—28no—
93C4×Dic146—22no—
94C4×Dic146C2×C414yescomplemented
95D4×Dic73—28no—
96#14556550—22no—
97#14556550—41no—
98C2×C4⋊Dic73—22no—
99C2×C4⋊Dic73—21no—
100C2×C4⋊Dic73—21no—
101C2×C4⋊Dic73—21no—
102C2×C4⋊Dic73—41no—
103C2×C4⋊Dic73C2311yescharacteristic
104C2×C4⋊Dic73C2311yescharacteristic
105C2×C4⋊Dic73C2311yescharacteristic
106C2×C4⋊Dic73C2311yescharacteristic
107C2×C4⋊Dic73C2311yescharacteristic
108C2×#11924007—21no—
109C2×#11924007—21no—
110C2×#11924007—21no—
111C2×C22⋊Dic73—21no—
112C2×C22⋊Dic73—21no—
113C2×C22⋊Dic73—21no—
114C2×C22⋊Dic73—21no—
115C2×C22⋊Dic73—21no—
116C2×C4×Dic73—21no—
117C2×C4×Dic73—21no—
118C2×C4×Dic73—21no—
119#14556516—22no—
120#14556516—22no—
121#14556516—22no—
122#14556516—22no—
123#14556516—22no—
124#14556516—22no—
125#14556516—22no—
126#14556516—41no—
127#14556516—41no—
128#14556516—41no—
129#14556516—41no—
130#14556516D414yescomplemented
131#14556498—21no—
132#14556498—21no—
133#14556498—21no—
134#14556498—21no—
135#14556498—21no—
136C22×D4×C73D411yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C2×M16×C73—22no—
140C2×M16×C73—22no—
141C2×M16×C73—41no—
142C22×C8×C73—22no—
143C22×C8×C73—22no—
144C22×C8×C73—41no—
145C22×C8×C73C2311yescharacteristic
146C22×C8×C73C2311yescharacteristic
147C22×C8×C73C2311yescharacteristic
148C22×C8×C73C2311yescharacteristic
149C4×D4×C73C2×C414yes—
150C4×D4×C73D414yes—
151C2×C4⋊C4×C73D411yescharacteristic
152C2×C22⋊C4×C73D411yescharacteristic
153C2×C22⋊C4×C73D411yescharacteristic
154C2×C42×C73C2311yescharacteristic
155C4⋊C8×C73—22no—
156C22⋊C8×C73—22no—
157C22⋊C8×C73—22no—
158#97×C73—22no—
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—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—42no—
202C22×Dic73—42no—
203C22×Dic73—42no—
204C22×Dic73—42no—
205C22×Dic73—42no—
206C22×Dic73—42no—
207C22×Dic73—81no—
208C4⋊Dic73—24no—
209C4⋊Dic73—24no—
210C4⋊Dic73—21no—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—42no—
219C4⋊Dic73C22×C412yes—
220C4⋊Dic73C2×D412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224C22⋊Dic73—24no—
225C22⋊Dic73—24no—
226C22⋊Dic73—42no—
227C22⋊Dic73—42no—
228C22⋊Dic73—81no—
229C4×Dic73—24no—
230C4×Dic73—42no—
231C4×Dic73—81no—
232C24×C73C2×D411yescharacteristic
233C24×C73C2×D411yescharacteristic
234C2×D4×C73—22no—
235C2×D4×C73—22no—
236C2×D4×C73C22⋊C414yes—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73C22×C412yes—
246C22×C4×C73C22×C412yes—
247C22×C4×C73C2×D412yes—
248C22×C4×C73C2×D412yes—
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2411yescharacteristic
254M16×C73—44no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—44no—
267C2×C8×C73C2×D412yes—
268C4⋊C4×C73C22⋊C414yes—
269C22⋊C4×C73C22⋊C414yes—
270C22⋊C4×C73C22⋊C414yes—
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×C73C2×C22⋊C412yes—
306C2×C4×C73C2×C22⋊C412yes—
307C2×C4×C73C2×C22⋊C412yes—
308C2×C4×C73C2×C22⋊C412yes—
309C2×C4×C73C23×C411yescharacteristic
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C2×#4111yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—48no—
323C2×Dic73—48no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—41no—
329C2×Dic73—41no—
330C2×Dic73—41no—
331C2×Dic73—41no—
332C2×Dic73—41no—
333C2×Dic73—41no—
334C2×Dic73—41no—
335C2×Dic73—41no—
336C2×Dic73—41no—
337C2×Dic73—41no—
338C2×Dic73—41no—
339C2×Dic73—41no—
340C2×Dic73—41no—
341C2×Dic73—84no—
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—
356C8×C73—22no—
357C8×C73—41no—
358C8×C73—41no—
359C8×C73—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×C73C2×C4×D411yescharacteristic
386C4×C73#51811yescharacteristic
387C4×C73D4211yescharacteristic
388C4×C73#54611yescharacteristic
389Dic73—24no—
390Dic73—42no—
391Dic73—42no—
392Dic73—42no—
393Dic73—42no—
394Dic73—81no—
395Dic73—81no—
396Dic73—81no—
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×#435D7311yescharacteristic
409C2×#419—731no—
410C22×#103—731no—
411#2352—731no—
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×M16C2×D7311yescharacteristic
426C23×C8C2×D7311yescharacteristic
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×#117—731no—
439C22×C4⋊C4—731no—
440#435—24no—
441C2×C4⋊C8C2×D7311yescharacteristic
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⋊C8C2×D7311yescharacteristic
457C2×C22⋊C8C2×D7311yescharacteristic
458C2×#97C2×D7311yescharacteristic
459#388—1461no—
460#387—1461no—
461#386—1461no—
462#382—731no—
463#380—731no—
464#380—731no—
465C4×C4⋊C4—731no—
466C4×C22⋊C4—1461no—
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—1462no—
485C22×Q8—1462no—
486C22×Q8—1461no—
487C22×Q8—1461no—
488C22×D4D29211yescharacteristic
489C23×C4—1461no—
490C23×C4—1461no—
491C23×C4—1461no—
492C23×C4C22×D7311yescharacteristic
493C23×C4C22×D7311yescharacteristic
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—41no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—41no—
500C22×C8C22×D7311yescharacteristic
501C22×C8C22×D7311yescharacteristic
502C22×C8C22×D7311yescharacteristic
503C22×C8C22×D7311yescharacteristic
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×D4C22⋊D7314yes—
518#117—2921no—
519#117—1462no—
520C2×C4⋊C4—2921no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—731no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1462no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4—1461no—
533C2×C4⋊C4D29211yescharacteristic
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4D29211yescharacteristic
540C2×C22⋊C4D29211yescharacteristic
541C2×C42—1461no—
542C2×C42—1461no—
543C2×C42—1461no—
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—22no—
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—22no—
559C22⋊C8—22no—
560#97—22no—
561#95—1461no—
562#95—1461no—
563#95—1461no—
564#95—1461no—
565#95—1461no—
566C24C2×D29211yescharacteristic
567C24C2×D29211yescharacteristic
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—2922no—
612C22×C4—2922no—
613C22×C4—2922no—
614C22×C4—2922no—
615C22×C4—2922no—
616C22×C4—2922no—
617C22×C4—5841no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1464no—
622C22×C4—1464no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4C2×C4×D7312yes—
629C22×C4C2×C4×D7312yes—
630C22×C4C2×C22⋊D7312yes—
631C22×C4C2×C22⋊D7312yes—
632C22×C4C2×D29211yescharacteristic
633C22×C4C2×D29211yescharacteristic
634C22×C4C2×D29211yescharacteristic
635C22×C4C2×D29211yescharacteristic
636C22×C4C23×D7311yescharacteristic
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C2×C8D4×D7312yes—
651C4⋊C4—2922no—
652C4⋊C4—732no—
653C4⋊C4—732no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4—1461no—
658C4⋊C4—1461no—
659C4⋊C4—1461no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1464no—
663C4⋊C4—1464no—
664C4⋊C4—1464no—
665C4⋊C4—1461no—
666C4⋊C4—1461no—
667C4⋊C4#1192400514yes—
668C22⋊C4—2922no—
669C22⋊C4—2922no—
670C22⋊C4—5841no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4#1192400514yes—
674C22⋊C4#1192400514yes—
675C42—2922no—
676C42—5841no—
677C42—1464no—
678C42C2×C4×D7312yes—
679C42C2×C22⋊D7312yes—
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#1455662412yes—
693C23#1455662412yes—
694C23C22×D29211yescharacteristic
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—2921no—
727C2×C4—2921no—
728C2×C4—2921no—
729C2×C4—2921no—
730C2×C4—2921no—
731C2×C4—2921no—
732C2×C4—2921no—
733C2×C4—2921no—
734C2×C4—2928no—
735C2×C4—2928no—
736C2×C4—2921no—
737C2×C4—2921no—
738C2×C4—2921no—
739C2×C4—2921no—
740C2×C4—2921no—
741C2×C4—2921no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—5844no—
746C2×C4—1462no—
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×C22⋊D7311yescharacteristic
760C2×C4#41×D7311yescharacteristic
761C2×C4#1455663611yescharacteristic
762C2×C4#1455663711yescharacteristic
763C8—22no—
764C8—41no—
765C8—41no—
766C8—41no—
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#1798859714yescomplemented
781C22C22×#1192400511yescharacteristic
782C22D4×D29211yescharacteristic
783C22#1798923211yescharacteristic
784C22C2×#1455662411yescharacteristic
785C22C2×#1455662411yescharacteristic
786C22#1798939911yescharacteristic
787C22#1798940411yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—2922no—
793C4—2922no—
794C4—2922no—
795C4—2922no—
796C4—5841no—
797C4—5841no—
798C4—5841no—
799C4—1464no—
800C4C4×D4×D7311yescharacteristic
801C4#1798905911yescharacteristic
802C4D4×C22⋊D7311yescharacteristic
803C4#1798922511yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#1192400511yescharacteristic
807C2C2×#1798859711yescharacteristic
808C2#2261846511yescharacteristic
809C2#2262144611yescharacteristic
810C2#2262150611yescharacteristic
811C2#2262198411yescharacteristic
812C2#2262210411yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#435×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
cosocleC22×C4×C73C24
hypercenterC2×#435D73
hypocenterC73#22425
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#17988597C2semidirect
3. C22×#14556516C2semidirect
5. #22610853C2semidirect
6. #22610751C2semidirect
7. #22610364C2semidirect
8. #22610354C2semidirect
9. #22610241C2semidirect
10. #22610236C2semidirect
11. #22609947C2semidirect
12. #22609867C2semidirect
13. #22609867C2semidirect
14. #22609762C2semidirect
19. D4×Dic146C4semidirect
77. C22×Dic146C2×C4semidirect
85. #14556591C2×C4semidirect
90. #14556570C2×C4semidirect
94. C4×Dic146C2×C4semidirect
130. #14556516D4semidirect
373. C22×C73#419semidirect
422. C73#22425semidirect
780. C22#17988597semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1462
C2×#179885972
C22×#145565162
#226128602
#226108532
#226107512
#226103642
#226103542
#226102412
#226102362
#226099472
#226098672
#226097622
C2×#435×C732
#2242573