Finite Group Databasebeta

← #29695602

Subgroups — #29695602

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic
2C2×#16839830C211yesmaximal, characteristic, complemented
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446634C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446240C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446129C211yesmaximal, characteristic, complemented
12#21445822C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840419—24no—
20#16840419C418yescomplemented
21C2×#14519764—21no—
22C2×#14519764C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519748—21no—
26C2×#14519748C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32#16839830—24no—
33C2×#14519706C2211yescharacteristic
34#16839769—24no—
35#16839758—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46#16839662—21no—
47#16839656—21no—
48#16839651—21no—
49#16839631C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52#16839613—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—41no—
70C2×Q8×D61—41no—
71C2×Q8×D61C2×C414yes—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—41no—
79C22×#92418—22no—
80C22×#92418—22no—
81C22×#92418—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519764—28no—
85#14519764—22no—
86#14519764C2×C414yes—
87#14519756—22no—
88#14519756—28no—
89#14519756C2×C414yes—
90#14519748—28no—
91#14519748—22no—
92#14519748C2×C414yes—
93Q8×Dic61—22no—
94Q8×Dic61C2×C414yes—
95C4×C22⋊D61—28no—
96C4×C22⋊D61C2×C414yes—
97C4×C22⋊D61D414yes—
98#14519736—22no—
99#14519736—41no—
100#14519735—22no—
101#14519735—41no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196D411yescharacteristic
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519702—22no—
126#14519702—41no—
127#14519701—22no—
128#14519701D414yescomplemented
129#14519700—22no—
130#14519700—41no—
131#14519698—22no—
132#14519698—22no—
133#14519689—22no—
134#14519687—22no—
135#14519684—21no—
136#14519684—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—41no—
141C2×#41×C61—41no—
142C2×#41×C61C2×C414yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—22no—
154#103×C61—22no—
155#102×C61—41no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162#41×C61—28no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61C22×C412yes—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61#4112yes—
172C2×D4×C61—24no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61C22×C412yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—24no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61C22⋊C414yes—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208Q8×D61—28no—
209Q8×D61—44no—
210Q8×D61—44no—
211Q8×D61—44no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—24no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C2×D412yes—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—24no—
227C2×Dic122—42no—
228C2×Dic122—42no—
229C2×Dic122C22×C412yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C22⋊C4×C61—81no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—42no—
246C22⋊Dic61C22⋊C414yes—
247#11758198—42no—
248#11758198—81no—
249#11758198C22⋊C414yes—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—24no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61C22×C412yes—
256C4⋊Dic61C2×D412yes—
257#11758196—24no—
258#11758196—42no—
259#11758196—81no—
260#11758196C22⋊C414yes—
261C4×Dic61—24no—
262C4×Dic61—42no—
263C4×Dic61—42no—
264C4×Dic61—42no—
265C4×Dic61C22×C412yes—
266C4×Dic61C2×D412yes—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—44no—
273C2×#92418C2×D412yes—
274#11758189—44no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C2×C22⋊C412yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61C2×C22⋊C412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61C4×D414yes—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—48no—
304D4×C61—41no—
305D4×C61—41no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—48no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×C22⋊C412yes—
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C22⋊D61—44no—
330C22⋊D61—48no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61C2×C22⋊C412yes—
350C2×Dic61C2×C22⋊C412yes—
351C2×Dic61C2×C22⋊C412yes—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357Dic122—22no—
358Dic122—22no—
359Dic122—48no—
360Dic122—41no—
361Dic122—41no—
362C8×C61—41no—
363C8×C61—41no—
364#92418—22no—
365#92418—41no—
366#22426—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61C22×C22⋊C411yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61#54611yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57511yescharacteristic
386C22×C61#57711yescharacteristic
387C22×C61#57811yescharacteristic
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C4×C61—24no—
396C4×C61—22no—
397C4×C61—81no—
398C4×C61—81no—
399C4×C61C2×C4×D411yescharacteristic
400C4×C61#51811yescharacteristic
401C4×C61D4211yescharacteristic
402C4×C61#54611yescharacteristic
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409Dic61—81no—
410C2×#548—611no—
411C2×#435—611no—
412C2×#419—611no—
413C2×#416—611no—
414#2354—611no—
415#1983—611no—
416#1959—611no—
417#1895—611no—
418#1892—611no—
419#1875—611no—
420#1873—611no—
421#1803—611no—
422#1788D6111yescharacteristic, complemented
423#1787—611no—
424#1763—611no—
425C2×C61—42no—
426C2×C61—82no—
427C2×C61D4×C22⋊C411yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61#289811yescharacteristic
430C2×C61#326911yescharacteristic
431C2×C61#327111yescharacteristic
432C2×C61#331311yescharacteristic
433C2×C61#332111yescharacteristic
434D61—42no—
435C22×#41C2×D6111yescharacteristic
436C23×Q8—611no—
437C22×M16—611no—
438C23×C8—611no—
439#548—618no—
440#548—1224no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×#121—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—611no—
449C2×C4×D4—1221no—
450C2×#117—611no—
451C2×#117—611no—
452#435—1224no—
453C2×C4⋊C8—611no—
454#419—1224no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8C2×D6111yescharacteristic
470C2×#97—611no—
471#390—1221no—
472#388—1221no—
473#388—1221no—
474#384—611no—
475#380—611no—
476#380C2×D6111yescharacteristic
477C4×C4⋊C4—611no—
478C4×C4⋊C4—1221no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483C61#2242611yescharacteristic, complemented, Sylow
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41C4×D6114yes—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—1221no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—2441no—
497C22×Q8—2441no—
498C22×Q8C22×D6111yescharacteristic
499C22×D4—21no—
500C22×D4—611no—
501C22×D4—1221no—
502C22×D4C22×D6111yescharacteristic
503C23×C4—21no—
504C23×C4—611no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×M16—1222no—
508C2×M16—1222no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—1222no—
513C22×C8—1222no—
514C22×C8—2441no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517#124—614no—
518#124—1222no—
519#124—1228no—
520C22⋊Q8—614no—
521C22⋊Q8—1228no—
522C22⋊Q8—1222no—
523#121—614no—
524#121—1222no—
525#121—1228no—
526C4×Q8—614no—
527C4×Q8—1222no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1228no—
531#117—1222no—
532#117—1222no—
533#117—2441no—
534#117—2441no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—611no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C4⋊C8—1222no—
561#103—22no—
562#103—22no—
563#103—614no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—2441no—
568#103—2441no—
569#102—41no—
570#102—41no—
571#102—1222no—
572#102—1222no—
573C22⋊C8—22no—
574C22⋊C8—1222no—
575#97—1222no—
576#95—21no—
577#95—1221no—
578#95—1221no—
579C24—21no—
580C24—611no—
581C24D4×D6111yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—612no—
590C2×Q8—1224no—
591C2×Q8—1221no—
592C2×Q8—1228no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—2442no—
598C2×Q8—2442no—
599C2×Q8—2444no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C2×Q8C2×C4×D6112yes—
603C2×Q8D4×D6112yes—
604C2×Q8#1175822412yes—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—614no—
614C2×D4—1224no—
615C2×D4—2441no—
616C2×D4—2441no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4C2×C4×D6112yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—1224no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4C2×C4×D6112yes—
647C22×C4D4×D6112yes—
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—2444no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—612no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—2444no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—614no—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—1224no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1224no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—4881no—
678C4⋊C4—2442no—
679C22⋊C4—81no—
680C22⋊C4—614no—
681C22⋊C4—614no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—4881no—
687C22⋊C4—2442no—
688C22⋊C4—2442no—
689C42—612no—
690C42—612no—
691C42—1224no—
692C42—2442no—
693C42—2442no—
694C42—2442no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—612no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23C22⋊C4×D6112yes—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—1222no—
721Q8—1222no—
722Q8—2448no—
723Q8—2441no—
724Q8—2441no—
725Q8#1451973714yes—
726D4—22no—
727D4—22no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—2444no—
732D4—2448no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—2448no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22⋊C4×D6112yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×#1175822411yescharacteristic
780C2×C4#1451982211yescharacteristic
781C2×C4#1451982211yescharacteristic
782C8—41no—
783C8—41no—
784C8—1222no—
785C8—2441no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—1222no—
801C22—1222no—
802C22—1222no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22C2×C22⋊C4×D6111yescharacteristic
808C22#1684039411yescharacteristic
809C22#1684039911yescharacteristic
810C22#1684055911yescharacteristic
811C22#1684055911yescharacteristic
812C22#1684057211yescharacteristic
813C22#1684057811yescharacteristic
814C4—22no—
815C4—24no—
816C4—81no—
817C4—81no—
818C4—1222no—
819C4—1222no—
820C4—1222no—
821C4—4881no—
822C4—2442no—
823C4—2442no—
824C4—2442no—
825C4C2×#1451973711yescharacteristic
826C4#1684023511yescharacteristic
827C4#1684039411yescharacteristic
828C4#1684039911yescharacteristic
829C2—42no—
830C2—82no—
831C2—2442no—
832C2#2144863511yescharacteristic
833C2#2145433411yescharacteristic
834C2#2145435011yescharacteristic
835C2#2145736711yescharacteristic
836C2#2145739711yescharacteristic
837C2#2145788911yescharacteristic
838C2#2145800911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22426
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839830C2semidirect
3. C2×#16839769C2semidirect
4. C2×#16839758C2semidirect
5. #21448763C2semidirect
6. #21446750C2semidirect
7. #21446634C2semidirect
8. #21446254C2semidirect
9. #21446240C2semidirect
10. #21446138C2semidirect
11. #21446129C2semidirect
12. #21445822C2semidirect
13. #21445752C2semidirect
14. #21445651C2semidirect
15. C61×#1788C2semidirect
20. #16840419C4semidirect
128. #14519701D4semidirect
422. #1788D61semidirect
483. C61#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×#168398302
C2×#168397692
C2×#168397582
#214487632
#214467502
#214466342
#214462542
#214462402
#214461382
#214461292
#214458222
#214457522
#214456512
C61×#17882
#2242661