Finite Group Databasebeta

← #34020581

Subgroups — #34020581

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989561C211yesmaximal, characteristic
2C2×#17989560C211yesmaximal, characteristic
3#22625673C211yesmaximal, characteristic, complemented
4#22625673C211yesmaximal, characteristic, complemented
5#22625672C211yesmaximal, characteristic, complemented
6#22625672C211yesmaximal, characteristic, complemented
7#22625669C211yesmaximal, characteristic, complemented
8#22625668C211yesmaximal, characteristic, complemented
9#22625665C211yesmaximal, characteristic, complemented
10C22⋊C4×#10596833C211yesmaximal, characteristic, complemented
11#22625661C211yesmaximal, characteristic, complemented
12#22625661C211yesmaximal, characteristic, complemented
13#22625657C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596833C211yesmaximal, characteristic, complemented
15#22612416C211yesmaximal, characteristic
16C22×#11924038C2211yescharacteristic
17C22×#11924037C2211yescharacteristic
18C22×#11924036C2211yescharacteristic
19C23×#10596833C2211yescharacteristic
20#17989561C418yescomplemented
21#17989560C418yescomplemented
22C2×#14556648C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×C22⋊#10596833C2211yescharacteristic
25C2×C22⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×#14556646C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C22×#11924027C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C22×C4×Dic73C2211yescharacteristic
49#17988491C411yescharacteristic
50#17988491C411yescharacteristic
51#17988487C411yescharacteristic
52#17988487C411yescharacteristic
53#17988467C411yescharacteristic
54#17988466C411yescharacteristic
55#17988464C411yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57C22⋊C4×Dic73C2211yescharacteristic
58#17988434C2211yescharacteristic
59#17988434C2211yescharacteristic
60#386×C73C411yescharacteristic
61C2×#11924038—41no—
62C2×#11924038—41no—
63C2×#11924038C2×C414yescomplemented
64C2×#11924037—41no—
65C2×#11924037—41no—
66C2×#11924037C2×C414yescomplemented
67C2×#11924036—41no—
68C2×#11924036—41no—
69C2×#11924036C2×C414yescomplemented
70C22×#10596833—41no—
71C22×#10596833—41no—
72C22×#10596833C2×C414yescomplemented
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75C22×#10596833C2311yescharacteristic
76C22×#10596833C2311yescharacteristic
77C22×#10596833C2311yescharacteristic
78C22×#10596833C2311yescharacteristic
79C22×#10596833C2311yescharacteristic
80C22×#10596833C2311yescharacteristic
81#14556648C2×C414yescomplemented
82#14556648C2×C414yescomplemented
83C22⋊#10596833C2×C414yes—
84C22⋊#10596833C2×C414yes—
85C22⋊#10596833C2×C414yes—
86C22⋊#10596833C2×C414yes—
87C22⋊#10596833C2×C414yescomplemented
88C22⋊#10596833C2×C414yescomplemented
89#14556646—41no—
90#14556646—41no—
91#14556646—41no—
92#14556646—41no—
93C4×#10596833—41no—
94C4×#10596833—41no—
95C4×#10596833—41no—
96C4×#10596833—41no—
97C2×#11924027—41no—
98C2×#11924027—41no—
99C2×#11924027—41no—
100C2×#11924027—41no—
101C2×#11924027C2×C414yes—
102C2×#11924027C2×C414yes—
103C22×Dic146C2×C411yescharacteristic
104C22×C22⋊D73C2×C411yescharacteristic
105C22×C22⋊D73C2×C411yescharacteristic
106C23×Dic73C2×C411yescharacteristic
107C23×Dic73C2311yescharacteristic
108C23×Dic73C2311yescharacteristic
109C22×C4×D73C2311yescharacteristic
110#14556547—41no—
111#14556547—41no—
112C2×#11924007C2×C411yescharacteristic
113C2×#11924007C2×C411yescharacteristic
114C2×C22⋊Dic73C2×C411yescharacteristic
115C2×C22⋊Dic73C2×C411yescharacteristic
116C2×C22⋊Dic73C2×C411yescharacteristic
117C2×#11924005C2×C411yescharacteristic
118C2×#11924005C2×C411yescharacteristic
119C2×#11924005C2×C411yescharacteristic
120C2×#11924005C2×C411yescharacteristic
121C2×C4×Dic73—41no—
122C2×C4×Dic73—41no—
123C2×C4×Dic73C2×C411yescharacteristic
124C2×C4×Dic73C2×C411yescharacteristic
125C2×C4×Dic73C2311yescharacteristic
126C2×C4×Dic73C2311yescharacteristic
127C2×C4×Dic73C2311yescharacteristic
128C2×C4×Dic73C2311yescharacteristic
129#14556498C2×C411yescharacteristic
130#14556498C2×C411yescharacteristic
131#14556498C2×C411yescharacteristic
132#14556498C2×C411yescharacteristic
133#14556498C2×C411yescharacteristic
134#14556498C2×C411yescharacteristic
135C22×D4×C73C2×C411yescharacteristic
136C23×C4×C73C2×C411yescharacteristic
137C2×C22⋊C4×C73C2×C411yescharacteristic
138C2×C22⋊C4×C73C2×C411yescharacteristic
139C2×C22⋊C4×C73C2×C411yescharacteristic
140#95×C73C2×C411yescharacteristic
141#95×C73C2×C411yescharacteristic
142#11924038—44no—
143#11924037—44no—
144#11924036—44no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—21no—
156C2×#10596833—21no—
157C2×#10596833—21no—
158C2×#10596833—21no—
159C2×#10596833—21no—
160C2×#10596833—21no—
161C2×#10596833—44no—
162C2×#10596833C22×C412yes—
163C2×#10596833C22×C412yes—
164C2×#10596833C22×C412yes—
165C2×#10596833C22×C412yes—
166C2×#10596833C22×C412yes—
167C2×#10596833C22×C412yes—
168C2×#10596833C22×C412yes—
169C2×#10596833C22×C412yes—
170C23×D73C22×C411yescharacteristic
171#11924027—44no—
172#11924027—44no—
173#11924027—44no—
174#11924027—44no—
175C2×Dic146—41no—
176C2×Dic146—41no—
177C2×Dic146C4214yes—
178C2×C22⋊D73—41no—
179C2×C22⋊D73—41no—
180C2×C22⋊D73—41no—
181C2×C22⋊D73—41no—
182C2×C22⋊D73C4214yes—
183C2×C22⋊D73C4214yes—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—22no—
193C22×Dic73—41no—
194C22×Dic73—41no—
195C22×Dic73C22×C411yescharacteristic
196C22×Dic73C22×C411yescharacteristic
197C22×Dic73C22×C411yescharacteristic
198C22×Dic73C22×C411yescharacteristic
199C22×Dic73C22×C411yescharacteristic
200C22×Dic73C22×C412yes—
201C22×Dic73C22×C412yes—
202C22×Dic73C22×C412yes—
203C22×Dic73C22×C412yes—
204C22×Dic73C22×C411yescharacteristic
205C22×Dic73C2411yescharacteristic
206C2×C4×D73—21no—
207C2×C4×D73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73C22×C412yes—
211C2×C4×D73C22×C412yes—
212#11924007—41no—
213#11924007—41no—
214C22⋊Dic73—22no—
215C22⋊Dic73—41no—
216C22⋊Dic73—41no—
217#11924005—22no—
218#11924005—22no—
219#11924005—41no—
220#11924005—41no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C4×Dic73—21no—
227C4×Dic73—21no—
228C4×Dic73—21no—
229C4×Dic73—41no—
230C4×Dic73—41no—
231C24×C73C22×C411yescharacteristic
232C24×C73C22×C411yescharacteristic
233C2×D4×C73—41no—
234C2×D4×C73—41no—
235C2×D4×C73C4214yes—
236C22×C4×C73—22no—
237C22×C4×C73—41no—
238C22×C4×C73—41no—
239C22×C4×C73C22×C411yescharacteristic
240C22×C4×C73C22×C411yescharacteristic
241C22×C4×C73C22×C411yescharacteristic
242C22×C4×C73C22×C411yescharacteristic
243C22×C4×C73C22×C411yescharacteristic
244C22⋊C4×C73—22no—
245C22⋊C4×C73—41no—
246C22⋊C4×C73—41no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73C2×C4212yes—
260C23×C73C2×C4212yes—
261C23×C73C23×C411yescharacteristic
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73C2×C4212yes—
269D4×C73—44no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—44no—
284C2×C4×C73C2×C4212yes—
285C2×C4×C73#13112yes—
286C22⋊D73—44no—
287C22⋊D73—44no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—44no—
312C2×Dic73C2×C4212yes—
313C2×Dic73C2×C4212yes—
314C2×Dic73#13112yes—
315C2×Dic73C23×C411yescharacteristic
316C2×Dic73C23×C411yescharacteristic
317C2×Dic73H(5,𝔽2)11yescharacteristic
318C2×Dic73H(5,𝔽2)11yescharacteristic
319C2×Dic73H(5,𝔽2)11yescharacteristic
320C2×Dic73H(5,𝔽2)11yescharacteristic
321C4×D73—22no—
322C4×D73—22no—
323C4×D73—22no—
324C4×D73—22no—
325Dic146—44no—
326#10596833—22no—
327#10596833—22no—
328#10596833—22no—
329#10596833—22no—
330#10596833—22no—
331#10596833—22no—
332#10596833—22no—
333#10596833—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73C22×C4211yescharacteristic
349C22×C73#51811yescharacteristic
350C22×C73#51811yescharacteristic
351C22×C73C2×#13111yescharacteristic
352C22×C73C2×#13111yescharacteristic
353C22×C73#56811yescharacteristic
354C22×C73#56811yescharacteristic
355C2×D73—22no—
356C2×D73—22no—
357C2×D73—22no—
358C2×D73—41no—
359C2×D73—41no—
360C2×D73—41no—
361C2×D73—41no—
362C4×C73—22no—
363C4×C73—22no—
364C4×C73—41no—
365C4×C73—41no—
366C4×C73—41no—
367Dic73—22no—
368Dic73—22no—
369Dic73—22no—
370Dic73—41no—
371Dic73—41no—
372Dic73—41no—
373Dic73#51811yescharacteristic
374Dic73#51811yescharacteristic
375Dic73#51811yescharacteristic
376Dic73#51811yescharacteristic
377#20531—731nomaximal, Sylow
378C2×C73—42no—
379C2×C73—42no—
380C2×C73#227311yescharacteristic
381C2×C73C4×#13111yescharacteristic
382C2×C73#287511yescharacteristic
383C2×C73#297611yescharacteristic
384C2×C73#297611yescharacteristic
385C2×C73#298111yescharacteristic
386C2×C73#298111yescharacteristic
387D73—42no—
388C2×#408—731no—
389C2×#408—731no—
390#2297—731no—
391#1753—731no—
392#1753—731no—
393#1753—731no—
394#1753—731no—
395#1752—731no—
396#1752—731no—
397C8×C22⋊C4—731no—
398C8×C22⋊C4—731no—
399#1750—731no—
400#1750—731no—
401#1749—731no—
402C4×C22⋊C8—731no—
403C73#2053111yescharacteristic, complemented, Sylow
404C22×#41—731no—
405C22×M16—731no—
406C22×M16—731no—
407C23×C8—731no—
408C23×C8—731no—
409C2×#117—731no—
410C22×C42—731no—
411#408—738no—
412#408—738no—
413C2×C22⋊C8—731no—
414C2×C22⋊C8—731no—
415C2×C22⋊C8—731no—
416C2×C22⋊C8—731no—
417C2×C22⋊C8—731no—
418C2×C22⋊C8—731no—
419C2×C22⋊C8—731no—
420C2×C22⋊C8—731no—
421C2×#97—731no—
422C2×#97—731no—
423C2×#97—731no—
424C2×#97—731no—
425C2×C4×C8—731no—
426C2×C4×C8—731no—
427C2×C4×C8—731no—
428C2×C4×C8—731no—
429#391—731no—
430#391—731no—
431#390—731no—
432#390—731no—
433#386—731no—
434#386—731no—
435#386—731no—
436#386#6440811yescharacteristic
437C4×C22⋊C4—731no—
438C4×C22⋊C4—731no—
439C4×C22⋊C4—731no—
440C4×C22⋊C4—731no—
441#336—731no—
442#336—731no—
443#336—731no—
444#336—731no—
445#336—731no—
446#336—731no—
447#336—731no—
448#336—731no—
449C2×#41—2921no—
450C2×#41—2921no—
451C2×#41—2921no—
452C2×#41—2921no—
453C2×#41—734no—
454C2×#41—734no—
455C22×Q8—731no—
456C22×D4—731no—
457C22×D4—731no—
458C22×D4C2×#6440811yescharacteristic
459C23×C4—731no—
460C23×C4—731no—
461C23×C4—731no—
462C23×C4—731no—
463C23×C4C2×#6440811yescharacteristic
464C2×M16—2921no—
465C2×M16—2921no—
466C2×M16—2921no—
467C2×M16—2921no—
468C2×M16—734no—
469C2×M16—734no—
470C22×C8—2921no—
471C22×C8—2921no—
472C22×C8—2921no—
473C22×C8—2921no—
474C22×C8—734no—
475C22×C8—734no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8—731no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484#117—2921no—
485#117—2921no—
486C2×C4⋊C4—731no—
487C2×C4⋊C4—731no—
488C2×C22⋊C4—731no—
489C2×C22⋊C4—731no—
490C2×C22⋊C4—731no—
491C2×C22⋊C4—731no—
492C2×C22⋊C4—731no—
493C2×C22⋊C4—731no—
494C2×C22⋊C4—731no—
495C2×C22⋊C4C2×#6440811yescharacteristic
496C2×C22⋊C4C2×#6440811yescharacteristic
497C2×C22⋊C4C2×#6440811yescharacteristic
498C2×C42—2921no—
499C2×C42—2921no—
500C2×C42—731no—
501C2×C42—731no—
502C2×C42—731no—
503C2×C42—731no—
504C2×C42—731no—
505C2×C42—731no—
506C22⋊C8—734no—
507C22⋊C8—734no—
508C22⋊C8—734no—
509C22⋊C8—734no—
510C22⋊C8—734no—
511C22⋊C8—734no—
512C22⋊C8—734no—
513C22⋊C8—734no—
514#97—2921no—
515#97—2921no—
516#97—2921no—
517#97—2921no—
518C4×C8—2921no—
519C4×C8—2921no—
520C4×C8—2921no—
521C4×C8—2921no—
522#95—731no—
523#95—731no—
524#95—731no—
525#95—731no—
526#95—731no—
527#95—731no—
528#95C2×#6440811yescharacteristic
529#95C2×#6440811yescharacteristic
530C24—731no—
531C24C22×#6440811yescharacteristic
532C24C22×#6440811yescharacteristic
533#41—2924no—
534#41—2924no—
535#41—2924no—
536#41—2924no—
537C2×Q8—2921no—
538C2×Q8—2921no—
539C2×Q8—734no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—2921no—
543C2×D4—2921no—
544C2×D4—2921no—
545C2×D4—2921no—
546C2×D4—734no—
547C2×D4—734no—
548C2×D4C4×#6440814yes—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—2921no—
553C22×C4—2921no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—732no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—731no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1462no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4C22×#6440811yescharacteristic
581C22×C4C22×#6440811yescharacteristic
582C22×C4C22×#6440811yescharacteristic
583C22×C4C22×#6440811yescharacteristic
584C22×C4C22×#6440811yescharacteristic
585M16—2924no—
586M16—2924no—
587C2×C8—2924no—
588C2×C8—2924no—
589C2×C8—732no—
590C2×C8—732no—
591C2×C8—732no—
592C2×C8—732no—
593C2×C8—732no—
594C2×C8—732no—
595C2×C8—732no—
596C2×C8—732no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8—1461no—
600C2×C8—1461no—
601C2×C8—1461no—
602C2×C8—1461no—
603C2×C8—1461no—
604C2×C8—1461no—
605C2×C8—1461no—
606C2×C8—1461no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C4⋊C4—2921no—
614C4⋊C4—2921no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—2921no—
619C22⋊C4—2921no—
620C22⋊C4—2921no—
621C22⋊C4—2921no—
622C22⋊C4—1462no—
623C22⋊C4—1462no—
624C22⋊C4—1462no—
625C42—2921no—
626C42—2921no—
627C42—1461no—
628C42—1461no—
629C42—1461no—
630C42—1461no—
631C42—1461no—
632C42—1461no—
633C42—1461no—
634C42—1461no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—732no—
648C23—1461no—
649C23—1461no—
650C23—1461no—
651C23—1461no—
652C23—1461no—
653C23—1461no—
654C23C2×C4×#6440812yes—
655C23C2×C4×#6440812yes—
656C23C23×#6440811yescharacteristic
657Q8—2924no—
658D4—44no—
659D4—2924no—
660D4—2924no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—44no—
675C2×C4—2924no—
676C2×C4—731no—
677C2×C4—731no—
678C2×C4—731no—
679C2×C4—731no—
680C2×C4—731no—
681C2×C4—731no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—732no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1461no—
707C2×C4—1461no—
708C2×C4—1461no—
709C2×C4—1461no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4C2×C4×#6440812yes—
713C2×C4#1455667812yes—
714C8—1462no—
715C8—1462no—
716C8—1462no—
717C8—1462no—
718C8—1462no—
719C8—1462no—
720C8—1462no—
721C8—1462no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—2921no—
737C22—2921no—
738C22—2921no—
739C22—2921no—
740C22—1462no—
741C22—1462no—
742C22—1462no—
743C22C22×C4×#6440811yescharacteristic
744C22#1798965411yescharacteristic
745C22#1798965411yescharacteristic
746C22C2×#1455667811yescharacteristic
747C22D73⋊#13111yescharacteristic
748C22#1798966511yescharacteristic
749C22#1798966611yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—2921no—
756C4—2921no—
757C4—2921no—
758C4—731no—
759C4—731no—
760C4—731no—
761C4—731no—
762C4—1462no—
763C4—1462no—
764C4—1462no—
765C2—42no—
766C2—42no—
767C2—2922no—
768C2#2262636711yescharacteristic
769C2C4×#1455667811yescharacteristic
770C2#2262650211yescharacteristic
771C2#2262679711yescharacteristic
772C2#2262679911yescharacteristic
773C2#2262681911yescharacteristic
774C2#2262682111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
Fitting#386×C73C4
socleC23×C73C23×C4
prime radicalC22×#11924027C22
cosocleC22×Dic73C24
hypercenter#386#64408
hypocenterC73#20531
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #22625673C2semidirect
4. #22625673C2semidirect
5. #22625672C2semidirect
6. #22625672C2semidirect
7. #22625669C2semidirect
8. #22625668C2semidirect
9. #22625665C2semidirect
10. C22⋊C4×#10596833C2semidirect
11. #22625661C2semidirect
12. #22625661C2semidirect
13. #22625657C2semidirect
14. C4×C22⋊#10596833C2semidirect
20. #17989561C4semidirect
21. #17989560C4semidirect
63. C2×#11924038C2×C4semidirect
66. C2×#11924037C2×C4semidirect
69. C2×#11924036C2×C4semidirect
72. C22×#10596833C2×C4semidirect
81. #14556648C2×C4semidirect
82. #14556648C2×C4semidirect
87. C22⋊#10596833C2×C4semidirect
88. C22⋊#10596833C2×C4semidirect
403. C73#20531semidirect

Maximal subgroups

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

subgroupindex
C2×#179895612
C2×#179895602
#226256732
#226256722
#226256692
#226256682
#226256652
C22⋊C4×#105968332
#226256612
#226256572
C4×C22⋊#105968332
#226124162
#2053173