Finite Group Databasebeta

← C2×#22622023 #33962634

Subgroups — C2×#22622023 #33962634

Order 18688.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989276C211yesmaximal, characteristic, complemented
2C2×#17989236C211yesmaximal, characteristic
3#22622023C2116yesmaximal, direct product factor
4C2×#17988954C211yesmaximal, characteristic, complemented
5C2×#17988921C211yesmaximal, characteristic, complemented
6C2×#17988928C211yesmaximal, characteristic, complemented
7C2×#17988885C211yesmaximal, characteristic, complemented
8C2×#17988844C211yesmaximal, characteristic, complemented
9C2×#17988828C211yesmaximal, characteristic, complemented
10C2×#17988796C211yesmaximal, characteristic, complemented
11C2×#17988750C211yesmaximal, characteristic, complemented
12C2×#17988749C211yesmaximal, characteristic, complemented
13C2×#17988684C211yesmaximal, characteristic, complemented
14C2×#17988658C211yesmaximal, characteristic, complemented
15C2×#17988585C211yesmaximal, characteristic, complemented
16C2×#416×C73C211yesmaximal, characteristic, complemented
17C22×#11924027C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22#17989276—24no—
23#17989276C2218yescomplemented
24#17989236—24no—
25#17989236C2218yes—
26C2×#14556589C2211yescharacteristic
27C2×#14556584—21no—
28C2×#14556583—21no—
29C2×#14556582C2211yescharacteristic
30C2×#14556574—21no—
31C2×#14556573—21no—
32C2×#14556572—21no—
33C2×#14556571C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556570C2211yescharacteristic
36C2×#14556567C2211yescharacteristic
37C2×#14556563—21no—
38C2×#14556556C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×C4×C22⋊D73C2211yescharacteristic
41C2×#14556548—21no—
42C22×#11924007—21no—
43C2×C4⋊C4×D73C2211yescharacteristic
44#17988954C2218yescomplemented
45#17988928C2218yescomplemented
46#17988921C2218yescomplemented
47#17988885C2218yescomplemented
48#17988844C2218yescomplemented
49#17988828C2218yescomplemented
50#17988796C2218yescomplemented
51#17988750C2218yescomplemented
52#17988749C2218yescomplemented
53#17988684C2218yescomplemented
54#17988658C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59#17988585C2218yescomplemented
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×#117×C73C2211yescharacteristic
72#416×C73C2218yescomplemented
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—22no—
78C2×#11924027—24no—
79C2×#11924027—42no—
80C2×#11924027C2314yes—
81C22×Dic146C2311yescharacteristic
82C22×Dic146C2311yescharacteristic
83C22×C22⋊D73—21no—
84C22×C22⋊D73D411yescharacteristic
85C23×Dic73—21no—
86C23×Dic73—21no—
87C22×C4×D73—21no—
88C22×C4×D73C2311yescharacteristic
89C2×Dic292—42no—
90C2×Dic292C2314yes—
91C2×#11924018—42no—
92C2×#11924018C2314yes—
93C2×#11924016—24no—
94C2×#11924016C2314yes—
95C2×#11924011—42no—
96C2×#11924011C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99#14556589—22no—
100#14556589C2314yes—
101#14556584—28no—
102#14556583—28no—
103#14556582—22no—
104#14556582C2314yes—
105#14556574—28no—
106#14556573—28no—
107#14556572—28no—
108#14556571—22no—
109#14556571C2314yes—
110#14556570—22no—
111#14556570—22no—
112#14556570C2314yes—
113#14556570C2314yes—
114#14556567—22no—
115#14556567C2314yes—
116#14556563—28no—
117#14556556—22no—
118#14556556C2314yes—
119D4×Dic73—22no—
120D4×Dic73C2314yes—
121C4×C22⋊D73D414yes—
122C4×C22⋊D73C2314yes—
123#14556548—28no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—28no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C4⋊C4×D73—22no—
139C4⋊C4×D73C2314yes—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73—21no—
143C2×C22⋊Dic73D411yescharacteristic
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005D411yescharacteristic
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556525C2314yes—
150#14556524C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556515C2314yes—
156#14556514C2314yes—
157#14556514C2314yes—
158#14556512C2314yes—
159C22⋊#10596831C2314yes—
160#14556503C2314yes—
161#14556501C2314yes—
162C2×#41×C73—22no—
163C2×#41×C73—24no—
164C2×#41×C73—42no—
165C2×#41×C73C2314yes—
166C22×Q8×C73C2311yescharacteristic
167C22×D4×C73—21no—
168C22×D4×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73C2311yescharacteristic
171C22×C8×C73—42no—
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2314yes—
175#117×C73—22no—
176#117×C73C2314yes—
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C22⋊C4×C73—21no—
180C2×C42×C73—21no—
181#103×C73C2314yes—
182#103×C73C2314yes—
183#102×C73C2314yes—
184#102×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186#11924027—28no—
187#11924027—44no—
188#11924027—48no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—21no—
194C2×Dic146—21no—
195C2×Dic146C2412yes—
196C2×Dic146C2412yes—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—42no—
199C2×C22⋊D73—44no—
200C2×C22⋊D73C2×D414yes—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—24no—
206C22×Dic73—24no—
207C22×Dic73—44no—
208C22×Dic73—44no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C2×C4×D73—22no—
213C2×C4×D73—22no—
214C2×C4×D73—24no—
215C2×C4×D73—44no—
216C2×C4×D73C2×D412yes—
217C2×C4×D73C2412yes—
218Dic292—44no—
219#11924018—44no—
220#11924016—28no—
221#11924011—44no—
222C2×#10596831—22no—
223C2×#10596831—22no—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73—24no—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924007—24no—
239#11924007—24no—
240#11924007C2×D414yes—
241C22⋊Dic73—24no—
242C22⋊Dic73—24no—
243C22⋊Dic73—24no—
244C22⋊Dic73C2×D414yes—
245#11924005—24no—
246#11924005—24no—
247#11924005C2×D414yes—
248C4×Dic73—24no—
249C4×Dic73C2×D412yes—
250C4×Dic73C2412yes—
251C24×C73—21no—
252C24×C73C2×D411yescharacteristic
253#41×C73—28no—
254#41×C73—44no—
255#41×C73—48no—
256C2×Q8×C73—21no—
257C2×Q8×C73—22no—
258C2×Q8×C73—22no—
259C2×Q8×C73C2412yes—
260C2×D4×C73—24no—
261C2×D4×C73—21no—
262C2×D4×C73—22no—
263C2×D4×C73—44no—
264C2×D4×C73#4114yes—
265C2×D4×C73C2412yes—
266C22×C4×C73—22no—
267C22×C4×C73—22no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—24no—
272C22×C4×C73—44no—
273C22×C4×C73C2×D411yescharacteristic
274C22×C4×C73C2×D412yes—
275C22×C4×C73C2412yes—
276C22×C4×C73C2411yescharacteristic
277C2×C8×C73—22no—
278C2×C8×C73—22no—
279C2×C8×C73—44no—
280C2×C8×C73C2412yes—
281C2×C8×C73C2412yes—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73C2412yes—
285C4⋊C4×C73C2412yes—
286C22⋊C4×C73—24no—
287C42×C73—24no—
288C23×C73—22no—
289C23×C73—24no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—42no—
294C23×C73—42no—
295C23×C73C22×D412yes—
296C23×C73C22×D411yescharacteristic
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—22no—
300C22×D73C22×D412yes—
301Q8×C73—22no—
302Q8×C73—22no—
303Q8×C73—42no—
304D4×C73—24no—
305D4×C73—22no—
306D4×C73—48no—
307D4×C73C2×#4114yes—
308C2×C4×C73—22no—
309C2×C4×C73—24no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—48no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—42no—
319C2×C4×C73C22×D412yes—
320C2×C4×C73C22×D411yescharacteristic
321C2×C4×C73C2×#4112yes—
322C2×C4×C73H(5,𝔽2)12yes—
323C2×C4×C73C2511yescharacteristic
324C22⋊D73—44no—
325C22⋊D73—48no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—48no—
334C2×Dic73—48no—
335C2×Dic73—42no—
336C2×Dic73—42no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73C22×D412yes—
340C2×Dic73C22×D412yes—
341C2×Dic73C22×D412yes—
342C4×D73—24no—
343C4×D73—22no—
344C4×D73—22no—
345C4×D73—48no—
346Dic146—22no—
347Dic146—22no—
348Dic146—22no—
349Dic146—22no—
350Dic146—42no—
351Dic146—42no—
352C8×C73—22no—
353C8×C73—22no—
354#10596831—22no—
355#10596831—22no—
356C22×C73—24no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—44no—
361C22×C73—48no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73#54612yes—
365C22×C73#57512yes—
366C22×C73#57812yes—
367C22×C73C23×D411yescharacteristic
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—44no—
372C4×C73—22no—
373C4×C73—42no—
374C4×C73—42no—
375C4×C73—42no—
376C4×C73#54612yes—
377C4×C73C22×#4111yescharacteristic
378C4×C73C2×H(5,𝔽2)11yescharacteristic
379Dic73—22no—
380Dic73—22no—
381Dic73—22no—
382Dic73—42no—
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386C2×#3315—731nomaximal, Sylow
387C2×C73—42no—
388C2×C73—44no—
389C2×C73#331514yescomplemented
390C2×C73C2×#54611yescharacteristic
391C2×C73C2×#57511yescharacteristic
392C2×C73C2×#57811yescharacteristic
393D73—42no—
394C2×#552—731no—
395C2×#547—731no—
396#3315—7316no—
397C2×#491—731no—
398C2×#484—731no—
399C2×#485—731no—
400C2×#478—731no—
401C2×#470—731no—
402C2×#467—731no—
403C2×#462—731no—
404C2×#452—731no—
405C2×#452—731no—
406C2×#440—731no—
407C2×#435—731no—
408C2×#417—731no—
409C2×#416D7311yescharacteristic, complemented
410C73C2×#331511yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C22×#41C2×D7311yescharacteristic
413C22×Q16—731no—
414C22×Q16—731no—
415C22×SD16—731no—
416C22×M16—731no—
417C23×C8C2×D7311yescharacteristic
418#552—738no—
419#552—1464no—
420#547—738no—
421#547—1464no—
422C2×C4⋊Q8—731no—
423C2×#126—1461no—
424C2×#125—731no—
425C2×#125—1461no—
426C2×#123—1461no—
427C2×#123—1461no—
428C2×#123—1461no—
429C2×C22⋊Q8—731no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—731no—
433C2×#121—1461no—
434C2×C4×Q8—731no—
435C2×C4×D4—731no—
436C2×C4×D4—731no—
437C2×#117—1461no—
438C2×#117C2×D7311yescharacteristic
439C22×C4⋊C4—731no—
440C22×C4⋊C4—1461no—
441#491—738no—
442#485—738no—
443#484—738no—
444#478—738no—
445#470—738no—
446#467—738no—
447#462—738no—
448#452—738no—
449#452—738no—
450#440—738no—
451#435—738no—
452C2×#107—731no—
453C2×#107—731no—
454C2×#106—731no—
455C2×C4⋊C8—731no—
456#417—738no—
457#416C2×D7318yescomplemented
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103C2×D7311yescharacteristic
464C2×#103C2×D7311yescharacteristic
465C2×#102—731no—
466C2×#102C2×D7311yescharacteristic
467C2×#102C2×D7311yescharacteristic
468C2×C22⋊C8—731no—
469C2×C22⋊C8—731no—
470C2×#97—731no—
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41—2922no—
475C2×#41—734no—
476C2×#41—1464no—
477C2×#41—1462no—
478C2×#41C22×D7314yes—
479C22×Q8—731no—
480C22×Q8—731no—
481C22×Q8C22×D7311yescharacteristic
482C22×D4—21no—
483C22×D4—731no—
484C22×D4—1461no—
485C22×D4C22×D7311yescharacteristic
486C23×C4—21no—
487C23×C4—731no—
488C23×C4—1461no—
489C23×C4—1461no—
490C23×C4—1461no—
491C23×C4C22×D7311yescharacteristic
492C2×Q16—2922no—
493C2×Q16—2922no—
494C2×Q16—734no—
495C2×Q16—734no—
496C2×SD16—734no—
497C2×SD16—1464no—
498C2×M16—2922no—
499C2×M16—734no—
500C22×C8—42no—
501C22×C8—731no—
502C22×C8—731no—
503C22×C8C22×D7311yescharacteristic
504C22×C8C22×D7311yescharacteristic
505C22×C8C22×D7314yes—
506C4⋊Q8—734no—
507C4⋊Q8—1462no—
508#126—1468no—
509#125—734no—
510#125—1468no—
511#125—1462no—
512#123—1468no—
513#123—1468no—
514#123—1468no—
515C22⋊Q8—734no—
516C22⋊Q8—734no—
517C22⋊Q8—734no—
518C22⋊Q8—734no—
519C22⋊Q8—1462no—
520C22⋊Q8—1462no—
521C22⋊Q8—1462no—
522C22⋊Q8—1462no—
523#121—1468no—
524C4×Q8—734no—
525C4×Q8—1462no—
526C4×D4—734no—
527C4×D4—734no—
528C4×D4—734no—
529C4×D4—1462no—
530#117—22no—
531#117—1468no—
532#117C22×D7314yes—
533C2×C4⋊C4—731no—
534C2×C4⋊C4—731no—
535C2×C4⋊C4—731no—
536C2×C4⋊C4—734no—
537C2×C4⋊C4—1462no—
538C2×C4⋊C4—1468no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4—1461no—
548C2×C4⋊C4—1461no—
549C2×C4⋊C4C22×D7311yescharacteristic
550C2×C4⋊C4C22×D7311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—731no—
553C2×C22⋊C4—731no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C22⋊C4—1461no—
557C2×C22⋊C4—1461no—
558C2×C22⋊C4—1461no—
559C2×C42—21no—
560C2×C42—731no—
561C2×C42—1461no—
562#107—734no—
563#107—734no—
564#106—734no—
565C4⋊C8—734no—
566#103—734no—
567#103—734no—
568#103—734no—
569#103—734no—
570#103—734no—
571#103C22×D7314yes—
572#103C22×D7314yes—
573#102—734no—
574#102C22×D7314yes—
575#102C22×D7314yes—
576C22⋊C8—734no—
577C22⋊C8—734no—
578#97—734no—
579C24—21no—
580C24—731no—
581C24D4×D7311yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585#41—2928no—
586#41—2924no—
587#41—1468no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—732no—
592C2×Q8—732no—
593C2×Q8—1462no—
594C2×Q8—1462no—
595C2×Q8—1462no—
596C2×Q8—1462no—
597C2×Q8—1461no—
598C2×Q8—1461no—
599C2×Q8C23×D7312yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—2924no—
605C2×D4—2922no—
606C2×D4—734no—
607C2×D4—1464no—
608C2×D4#1192402814yes—
609C2×D4C23×D7312yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—2924no—
618C22×C4—2924no—
619C22×C4—2924no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—732no—
624C22×C4—732no—
625C22×C4—1464no—
626C22×C4—1464no—
627C22×C4—1464no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1462no—
633C22×C4—1462no—
634C22×C4D4×D7312yes—
635C22×C4D4×D7311yescharacteristic
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638Q16—2924no—
639Q16—2924no—
640SD16—1468no—
641M16—2924no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—732no—
646C2×C8—732no—
647C2×C8—1462no—
648C2×C8—1462no—
649C2×C8C23×D7312yes—
650C2×C8C23×D7312yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—734no—
654C4⋊C4—732no—
655C4⋊C4—732no—
656C4⋊C4—1464no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1464no—
663C4⋊C4—1464no—
664C4⋊C4—1464no—
665C4⋊C4—1464no—
666C4⋊C4—1461no—
667C4⋊C4—1461no—
668C4⋊C4C23×D7312yes—
669C4⋊C4C23×D7312yes—
670C22⋊C4—24no—
671C22⋊C4—734no—
672C22⋊C4—734no—
673C22⋊C4—1464no—
674C22⋊C4—1464no—
675C22⋊C4—1464no—
676C22⋊C4—1464no—
677C22⋊C4—1464no—
678C42—24no—
679C42—732no—
680C42—732no—
681C42—1464no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—42no—
688C23—42no—
689C23—732no—
690C23—1462no—
691C23—1462no—
692C23—1462no—
693C23C2×D4×D7312yes—
694C23C2×D4×D7311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—2922no—
699Q8—2922no—
700Q8—1462no—
701Q8—1462no—
702Q8—1462no—
703Q8—1462no—
704D4—22no—
705D4—24no—
706D4—48no—
707D4—2928no—
708D4—2924no—
709D4C2×#1192402814yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—2928no—
722C2×C4—2922no—
723C2×C4—2922no—
724C2×C4—2922no—
725C2×C4—2922no—
726C2×C4—2928no—
727C2×C4—2928no—
728C2×C4—732no—
729C2×C4—732no—
730C2×C4—732no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1464no—
741C2×C4C2×D4×D7312yes—
742C2×C4C2×D4×D7311yescharacteristic
743C2×C4C2×#1192402812yes—
744C2×C4#1455663612yes—
745C2×C4C24×D7311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1462no—
749C8—1462no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—48no—
756C22—42no—
757C22—42no—
758C22—2924no—
759C22—1462no—
760C22—1462no—
761C22—1462no—
762C22#1798922712yes—
763C22#1798938412yes—
764C22#1798940112yes—
765C22C22×D4×D7311yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—2922no—
771C4—2922no—
772C4—2922no—
773C4—2922no—
774C4—1462no—
775C4—1462no—
776C4—1462no—
777C4#1798922712yes—
778C4C22×#1192402811yescharacteristic
779C4C2×#1455663611yescharacteristic
780C2—42no—
781C2—44no—
782C2—2922no—
783C2#2262202314yesdirect product factor
784C2C2×#1798922711yescharacteristic
785C2C2×#1798938411yescharacteristic
786C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#416×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989236C2
hypercenterC2×#416D73
hypocenterC73C2×#3315
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#17989276C2semidirect
3. #22622023C2direct (N × H)
4. C2×#17988954C2semidirect
5. C2×#17988921C2semidirect
6. C2×#17988928C2semidirect
7. C2×#17988885C2semidirect
8. C2×#17988844C2semidirect
9. C2×#17988828C2semidirect
10. C2×#17988796C2semidirect
11. C2×#17988750C2semidirect
12. C2×#17988749C2semidirect
13. C2×#17988684C2semidirect
14. C2×#17988658C2semidirect
15. C2×#17988585C2semidirect
16. C2×#416×C73C2semidirect
23. #17989276C22semidirect
44. #17988954C22semidirect
45. #17988928C22semidirect
46. #17988921C22semidirect
47. #17988885C22semidirect
48. #17988844C22semidirect
49. #17988828C22semidirect
50. #17988796C22semidirect
51. #17988750C22semidirect
52. #17988749C22semidirect
53. #17988684C22semidirect
54. #17988658C22semidirect
59. #17988585C22semidirect
72. #416×C73C22semidirect
389. C2×C73#3315semidirect
409. C2×#416D73semidirect
410. C73C2×#3315semidirect
457. #416C2×D73semidirect
783. C2#22622023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892762
C2×#179892362
#226220232
C2×#179889542
C2×#179889212
C2×#179889282
C2×#179888852
C2×#179888442
C2×#179888282
C2×#179887962
C2×#179887502
C2×#179887492
C2×#179886842
C2×#179886582
C2×#179885852
C2×#416×C732
C2×#331573