Finite Group Databasebeta

← #30622471

Subgroups — #30622471

Order 15616.

846 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462350C211yesmaximal, characteristic
2#21462339C211yesmaximal, characteristic, complemented
3#21461969C211yesmaximal, characteristic
4#21461967C211yesmaximal, characteristic, complemented
5#21461948C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic
11#21461616C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic
14C4×#14519840C211yesmaximal, characteristic, complemented
15#464×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×#14519831C2211yescharacteristic
28C4×D61⋊C8C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31(C2×#6923)⋊Q8C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840711—21no—
37#16840709—21no—
38#16840707—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C22⋊C4×#6923—21no—
45#16840698—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×Q16×D61C2211yescharacteristic
53C2×SD16×D61C2211yescharacteristic
54#124×D61C2211yescharacteristic
55C4×Q8×D61C2211yescharacteristic
56#16839987C411yescharacteristic, complemented
57#16839986C411yescharacteristic, complemented
58#16839985C411yescharacteristic, complemented
59#16839984C411yescharacteristic, complemented
60#16839983C411yescharacteristic, complemented
61#16839982C411yescharacteristic, complemented
62#16839981C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#464C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72D4×#6923—22no—
73D4×#6923—41no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923D411yescharacteristic
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923C2311yescharacteristic
89C2×C4×#6923C2311yescharacteristic
90#14519846—41no—
91#14519845—41no—
92#14519840—22no—
93#14519840—22no—
94#14519840—22no—
95#14519840—41no—
96#14519839—22no—
97#14519839—41no—
98#14519831—41no—
99#14519831—41no—
100C4×#92420—21no—
101C4×#92420—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×D4×D61C2311yescharacteristic
118C2×Dic244C2×C411yescharacteristic, complemented
119C2×#11758202C2×C411yescharacteristic, complemented
120C2×#11758202C2×C411yescharacteristic, complemented
121Q16×D61—41no—
122Q16×D61—41no—
123C2×#11758190C2×C411yescharacteristic
124C2×#11758200C2×C411yescharacteristic
125C2×#11758201C2×C411yescharacteristic
126SD16×D61—41no—
127SD16×D61—41no—
128C2×C8×D61C2311yescharacteristic
129C2×C8×D61C2311yescharacteristic
130#14519766C2×C411yescharacteristic
131#14519765C2×C411yescharacteristic
132#14519764C2×C411yescharacteristic
133#14519763—21no—
134#14519763—21no—
135Q8×Dic61C2×C411yescharacteristic, complemented
136C4×Dic122—21no—
137C4×Dic122C2×C411yescharacteristic, complemented
138#14519742—21no—
139#14519742C2×C411yescharacteristic, complemented
140C4⋊C4×D61—21no—
141C4⋊C4×D61C2311yescharacteristic
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C42×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic, complemented
147#14519706C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519701C2×C411yescharacteristic, complemented
151#14519700C2×C411yescharacteristic, complemented
152#14519699C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×Q16×C61C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic
157#124×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic, complemented
159C4⋊C8×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—42no—
168C22×#6923—42no—
169C22×#6923—81no—
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C2×Q8×C61C22×C411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C2×D4×C61C22×C411yescharacteristic
177C2×C22⋊D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190C2×D244C22×C411yescharacteristic
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2411yescharacteristic
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122C22×C411yescharacteristic
200C2×Dic122C22×C411yescharacteristic
201C22⋊#6923—42no—
202C22⋊#6923—42no—
203C22⋊#6923—81no—
204C2×#92420—21no—
205C2×#92420—21no—
206C4⋊#6923—21no—
207C4⋊#6923—21no—
208C4⋊#6923—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—41no—
214C4⋊#6923—41no—
215C4⋊#6923—42no—
216C4⋊#6923#4112yes—
217C4×#6923—21no—
218C4×#6923—21no—
219C4×#6923—21no—
220C4×#6923—21no—
221C4×#6923—42no—
222C4×#6923—42no—
223C4×#6923—42no—
224C4×#6923—81no—
225D61⋊C8—21no—
226D61⋊C8—21no—
227D61⋊C8—21no—
228D61⋊C8#4112yes—
229Q16×C61—41no—
230SD16×C61—41no—
231C2×C8×C61C22×C411yescharacteristic
232C2×C8×C61C22×C411yescharacteristic
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—21no—
238C42×C61C22×C411yescharacteristic
239C22⋊Dic61—21no—
240C22⋊Dic61—21no—
241#11758202—41no—
242#11758202—41no—
243#11758201—41no—
244#11758200—41no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61C22×C411yescharacteristic
251#11758196—21no—
252#11758196—21no—
253#11758196—21no—
254C4×Dic61—21no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C4×Dic61C22×C411yescharacteristic
258C4×Dic61#4111yescharacteristic
259C4×Dic61#4111yescharacteristic
260C2×#92418C22×C411yescharacteristic
261C2×#92418C22×C411yescharacteristic
262Dic244—41no—
263#11758190—41no—
264C8×D61—21no—
265C8×D61—21no—
266C8×D61—21no—
267C8×D61—21no—
268C23×C61—21no—
269C22×D61—21no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61C22×D411yescharacteristic
277C2×#6923—21no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—22no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—41no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—84no—
302Q8×C61—21no—
303Q8×C61—21no—
304Q8×C61—21no—
305Q8×C61—21no—
306D4×C61—21no—
307D4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61C23×C411yescharacteristic
314C22⋊D61—41no—
315C22⋊D61—41no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61C4×D411yescharacteristic
320C2×Dic61C4×D411yescharacteristic
321C2×Dic61C2×#4111yescharacteristic
322D244—21no—
323D244—21no—
324C4×D61—21no—
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61C2×#4111yescharacteristic
335C4×D61C2×#4111yescharacteristic
336C4×D61H(5,𝔽2)11yescharacteristic
337C4×D61H(5,𝔽2)11yescharacteristic
338Dic122—21no—
339Dic122—21no—
340Dic122—21no—
341Dic122—21no—
342Dic122—41no—
343Dic122—41no—
344Dic122—41no—
345Dic122—41no—
346#92420—22no—
347#92420—41no—
348C8×C61—21no—
349C8×C61—21no—
350#92418—21no—
351#92418—21no—
352#23103—611nomaximal, Sylow
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61C2×C4×D411yescharacteristic
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61#54611yescharacteristic
365C2×D61#55011yescharacteristic
366C2×D61#57511yescharacteristic
367C2×D61#57511yescharacteristic
368C2×D61#57711yescharacteristic
369C2×D61#57811yescharacteristic
370#6923—41no—
371#6923—41no—
372#6923—42no—
373#6923—41no—
374#6923—41no—
375#6923—81no—
376#6923—81no—
377#6923—81no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—41no—
383C4×C61C4×#4111yescharacteristic
384C4×C61#51811yescharacteristic
385Dic61—21no—
386Dic61—21no—
387Dic61—41no—
388Dic61—41no—
389Dic61—41no—
390Dic61#55311yescharacteristic
391Dic61#55511yescharacteristic
392C2×#464—611no—
393#2367—611no—
394#2356—611no—
395#1973—611no—
396#1971—611no—
397#1958—611no—
398#1949—611no—
399#1928—611no—
400#1926—611no—
401#1878—611no—
402#1877—611no—
403#1770—611no—
404#1763—611no—
405#1762—611no—
406C4×#103—611no—
407C2×C61—81no—
408C2×C61#236311yescharacteristic
409C2×C61#294311yescharacteristic
410C2×C61#294711yescharacteristic
411D61—81no—
412D61#332311yescharacteristic
413D61#332711yescharacteristic
414D61#340111yescharacteristic
415D61#340211yescharacteristic
416C22×Q16—611no—
417C22×SD16—611no—
418C2×#124—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×D4—611no—
422#464—611no—
423#464—611no—
424#464—611no—
425#464—611no—
426#464—611no—
427#464—611no—
428#464—611no—
429#464#692311yescharacteristic, complemented
430C2×#107—611no—
431C2×#106—611no—
432C2×C4⋊C8—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#97—611no—
442C2×#97—611no—
443C2×C4×C8—611no—
444#391—611no—
445#391—611no—
446#391—611no—
447#390—611no—
448#388—1221no—
449#388—1221no—
450#387—1221no—
451#387—1221no—
452#385—1221no—
453#383—1221no—
454#382—611no—
455C4×C4⋊C4—611no—
456C4×C4⋊C4—611no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—611no—
459C4×C22⋊C4—1221no—
460#376—1221no—
461#340—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465#336—611no—
466#336—611no—
467C61#2310311yescharacteristic, complemented, Sylow
468C22×Q8—611no—
469C22×Q8—611no—
470C22×D4—611no—
471C23×C4—1221no—
472C2×Q16—611no—
473C2×Q16—611no—
474C2×Q16—611no—
475C2×Q16—2441no—
476C2×Q16—2441no—
477C2×Q16C2×#692311yescharacteristic, complemented
478C2×SD16—611no—
479C2×SD16—611no—
480C2×SD16—611no—
481C2×SD16—2441no—
482C2×SD16—2441no—
483C2×SD16C2×#692311yescharacteristic
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488#124—611no—
489#124—611no—
490#124—611no—
491#124—1221no—
492#124—1221no—
493#124C2×#692311yescharacteristic
494C4×Q8—611no—
495C4×Q8—611no—
496C4×Q8—611no—
497C4×Q8—1221no—
498C4×Q8—1221no—
499C4×Q8—1222no—
500C4×Q8—2441no—
501C4×Q8C2×#692311yescharacteristic, complemented
502C4×D4—1222no—
503C4×D4—2441no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1221no—
525C2×C42—1221no—
526#107—2441no—
527#106—2441no—
528C4⋊C8—611no—
529C4⋊C8—611no—
530C4⋊C8—611no—
531C4⋊C8C2×#692311yescharacteristic, complemented
532#103—611no—
533#103—611no—
534#103—611no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#103—2441no—
539#103C2×#692311yescharacteristic, complemented
540#102—611no—
541#102—611no—
542#102—611no—
543#102—1222no—
544#102—2441no—
545#102C2×#692311yescharacteristic
546#97—2441no—
547#97—2441no—
548C4×C8—1221no—
549C4×C8—1221no—
550#95—611no—
551#95—611no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563C24—1221no—
564C2×Q8—611no—
565C2×Q8—611no—
566C2×Q8—1221no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8C22×#692311yescharacteristic
577C2×Q8C22×#692311yescharacteristic
578C2×D4—611no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4C22×#692311yescharacteristic
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—4881no—
600C22×C4—2442no—
601C22×C4—2442no—
602Q16—41no—
603Q16—2441no—
604Q16—2441no—
605Q16—2441no—
606SD16—41no—
607SD16—2441no—
608SD16—2441no—
609SD16—2441no—
610C2×C8—612no—
611C2×C8—611no—
612C2×C8—611no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8C22×#692311yescharacteristic
623C2×C8C22×#692311yescharacteristic
624C4⋊C4—21no—
625C4⋊C4—612no—
626C4⋊C4—611no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—2441no—
639C4⋊C4—2441no—
640C4⋊C4—2442no—
641C4⋊C4C22×#692311yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—4881no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C42—21no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—1221no—
664C42—4881no—
665C42—2442no—
666C42—2442no—
667C42—2442no—
668C42C22×#692311yescharacteristic
669C23—21no—
670C23—611no—
671C23—1221no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—1221no—
683Q8—1221no—
684Q8—1221no—
685Q8—1221no—
686Q8—2441no—
687Q8—2441no—
688Q8—2441no—
689Q8—2441no—
690D4—21no—
691D4—21no—
692D4—1221no—
693D4—1221no—
694D4—2441no—
695D4—2441no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—4884no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4D4×#692311yescharacteristic
745C2×C4D4×#692311yescharacteristic
746C2×C4C23×#692311yescharacteristic
747C8—21no—
748C8—21no—
749C8—1222no—
750C8—1221no—
751C8—1221no—
752C8—2441no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—611no—
757C22—611no—
758C22—611no—
759C22—611no—
760C22—611no—
761C22—611no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22C2×D4×#692311yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—611no—
776C4—611no—
777C4—1221no—
778C4—1221no—
779C4—4881no—
780C4—4881no—
781C4—4881no—
782C4—2441no—
783C4—2441no—
784C4—2441no—
785C4—2441no—
786C4—2442no—
787C4—2441no—
788C4—2441no—
789C4—2441no—
790C4#41×#692311yescharacteristic
791C4#1684082911yescharacteristic
792C2—81no—
793C2—611no—
794C2—611no—
795C2—611no—
796C2—611no—
797C2—4881no—
798C2#2146234611yescharacteristic
799C2#2146257311yescharacteristic
800C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#464C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#464#6923
hypocenterC61#23103
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #21462339C2semidirect
4. #21461967C2semidirect
6. #21461932C2semidirect
7. #21461899C2semidirect
9. #21461813C2semidirect
11. #21461616C2semidirect
12. #21461592C2semidirect
14. C4×#14519840C2semidirect
56. #16839987C4semidirect
57. #16839986C4semidirect
58. #16839985C4semidirect
59. #16839984C4semidirect
60. #16839983C4semidirect
61. #16839982C4semidirect
62. #16839981C4semidirect
66. C61×#464C4semidirect
118. C2×Dic244C2×C4semidirect
119. C2×#11758202C2×C4semidirect
120. C2×#11758202C2×C4semidirect
135. Q8×Dic61C2×C4semidirect
137. C4×Dic122C2×C4semidirect
139. #14519742C2×C4semidirect
146. C4⋊#92418C2×C4semidirect
147. #14519706C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519701C2×C4semidirect
151. #14519700C2×C4semidirect
155. C2×Q16×C61C2×C4semidirect
158. C4×Q8×C61C2×C4semidirect
159. C4⋊C8×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
429. #464#6923semidirect
467. C61#23103semidirect
477. C2×Q16C2×#6923semidirect
501. C4×Q8C2×#6923semidirect
531. C4⋊C8C2×#6923semidirect
539. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623502
#214623392
#214619692
#214619672
#214619482
#214619322
#214618992
#214618972
#214618132
#214618122
#214616162
#214615922
#214615902
C4×#145198402
#464×D612
#2310361