Finite Group Databasebeta

← #30616721

Subgroups — #30616721

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462379C211yesmaximal, characteristic, complemented
2#21462297C211yesmaximal, characteristic, complemented
3#21462003C211yesmaximal, characteristic, complemented
4#21462000C211yesmaximal, characteristic, complemented
5#21461949C211yesmaximal, characteristic, complemented
6#21461948C211yesmaximal, characteristic, complemented
7#21461835C211yesmaximal, characteristic
8#21461834C211yesmaximal, characteristic, complemented
9#21461833C211yesmaximal, characteristic
10#21461832C211yesmaximal, characteristic, complemented
11#21461591C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13C4×#14519840C211yesmaximal, characteristic, complemented
14C4×#14519839C211yesmaximal, characteristic, complemented
15#542×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26#16840727—21no—
27#16840727—21no—
28#16840726—21no—
29#16840726—21no—
30#16840721C2211yescharacteristic
31#16840721C2211yescharacteristic
32C4×D61⋊C8C2211yescharacteristic
33C4×D61⋊C8C2211yescharacteristic
34#16840712—21no—
35#16840712—21no—
36#16840711—21no—
37#16840711—21no—
38#16840708C2211yescharacteristic
39#16840706C2211yescharacteristic
40#16840704C2211yescharacteristic
41#16840704C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840386C411yescharacteristic, complemented
53#16840385C411yescharacteristic, complemented
54#16840384C411yescharacteristic, complemented
55#16840383C411yescharacteristic, complemented
56#16840382—21no—
57#16840381C411yescharacteristic, complemented
58#16840380—21no—
59#16840379C411yescharacteristic, complemented
60#16840378—21no—
61#16840377C411yescharacteristic, complemented
62#16840376—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#126×D61—21no—
65#124×D61—21no—
66#124×D61C2211yescharacteristic
67#123×D61—21no—
68C22⋊Q8×D61—21no—
69C22⋊Q8×D61C2211yescharacteristic
70#121×D61C2211yescharacteristic
71C4×Q8×D61C2211yescharacteristic
72C4×D4×D61C2211yescharacteristic
73#117×D61C2211yescharacteristic
74C61×#542C411yescharacteristic, complemented
75C2×#11758213—21no—
76D61⋊M16—22no—
77D61⋊M16—22no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—22no—
82C2×D61⋊C8C2311yescharacteristic
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C22×#92420—21no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—21no—
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97#14519840—22no—
98#14519840—22no—
99#14519840—22no—
100#14519840—22no—
101#14519839—22no—
102#14519839—22no—
103#14519839—22no—
104#14519839—22no—
105#14519832—21no—
106#14519832—21no—
107#14519832—21no—
108#14519832—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C4×#92420—21no—
112C4×#92420—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×Q8×D61—21no—
120C2×Q8×D61C2311yescharacteristic
121C2×D4×D61—21no—
122C2×D4×D61C2311yescharacteristic
123C22×C4×D61—21no—
124C22×C4×D61C2311yescharacteristic
125#14519777C2×C411yescharacteristic
126#14519776—21no—
127#14519776C2×C411yescharacteristic
128#14519776C2×C411yescharacteristic
129#14519775—21no—
130#14519772—21no—
131#14519772—21no—
132#14519772—21no—
133#14519771—21no—
134#14519770—21no—
135#14519770—21no—
136#14519770—21no—
137#14519766—21no—
138#14519766C2×C411yescharacteristic
139#14519765—21no—
140#14519765C2×C411yescharacteristic
141#14519764—21no—
142#14519764C2×C411yescharacteristic
143#14519763—21no—
144#14519763—21no—
145#14519763—21no—
146#14519763—21no—
147#14519763—21no—
148#14519763—21no—
149#14519762—21no—
150#14519762—21no—
151#14519761—21no—
152#14519760—21no—
153#14519759—21no—
154#14519759—21no—
155#14519758—21no—
156#14519757—21no—
157#14519757C2×C411yescharacteristic
158#14519756—21no—
159#14519756C2×C411yescharacteristic
160#14519755—21no—
161#14519755—21no—
162#14519755—21no—
163#14519754—21no—
164#14519754—21no—
165#14519754—21no—
166#14519753—21no—
167#14519753C2×C411yescharacteristic
168#14519752C2×C411yescharacteristic
169#14519751C2×C411yescharacteristic
170#14519750—21no—
171#14519749—21no—
172#14519748C2×C411yescharacteristic
173Q8×Dic61C2×C411yescharacteristic
174C4×Dic122—21no—
175C4×Dic122C2×C411yescharacteristic
176#14519742—21no—
177#14519742C2×C411yescharacteristic
178C4×D244C2×C411yescharacteristic
179D4×Dic61C2×C411yescharacteristic
180#14519739C2×C411yescharacteristic
181C4×C22⋊D61—21no—
182#14519737—21no—
183#14519736C2×C411yescharacteristic
184#14519735D411yescharacteristic
185#14519735D411yescharacteristic
186#14519734C2×C411yescharacteristic
187#14519734C2×C411yescharacteristic
188#14519733D411yescharacteristic
189#14519733D411yescharacteristic
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61D411yescharacteristic
194C4⋊C4×D61D411yescharacteristic
195C4⋊C4×D61C2311yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61D411yescharacteristic
203C22⋊C4×D61D411yescharacteristic
204C42×D61—21no—
205C42×D61C2311yescharacteristic
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic
208#126×C61—21no—
209#124×C61—21no—
210#124×C61C2×C411yescharacteristic
211#123×C61—21no—
212C22⋊Q8×C61—21no—
213C22⋊Q8×C61C2×C411yescharacteristic
214#121×C61C2×C411yescharacteristic
215C4×Q8×C61C2×C411yescharacteristic
216C4×D4×C61C2×C411yescharacteristic
217#117×C61C2×C411yescharacteristic
218C23×D61—21no—
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61C22×C411yescharacteristic
226C2×D4×C61—21no—
227C2×D4×C61C22×C411yescharacteristic
228C22×C4×C61—21no—
229C22×C4×C61C22×C411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C22×Dic61—21no—
234C22×Dic61C2×D411yescharacteristic
235Q8×D61—21no—
236Q8×D61—21no—
237Q8×D61—21no—
238Q8×D61—21no—
239Q8×D61—81no—
240Q8×D61—81no—
241D4×D61—21no—
242D4×D61—21no—
243D4×D61—21no—
244D4×D61—21no—
245D4×D61—81no—
246D4×D61—81no—
247C2×D244—21no—
248C2×D244C22×C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—81no—
259C2×C4×D61—81no—
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2411yescharacteristic
268C2×Dic122—21no—
269C2×Dic122—21no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122C22×C411yescharacteristic
273C22⋊#6923—81no—
274C22⋊#6923—81no—
275#11758217—24no—
276C2×#92420—24no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—21no—
288C4⋊#6923—21no—
289C4⋊#6923—81no—
290C4⋊#6923—81no—
291C4×#6923—81no—
292C4×#6923—81no—
293#11758213—24no—
294D61⋊C8—24no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8#4112yes—
300D61⋊C8#4112yes—
301D61⋊C8#4112yes—
302D61⋊C8#4112yes—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61C22⋊C411yescharacteristic
307C4⋊C4×C61C22⋊C411yescharacteristic
308C4⋊C4×C61C22×C411yescharacteristic
309C4⋊C4×C61C22×C411yescharacteristic
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61C22⋊C411yescharacteristic
316C22⋊C4×C61C22⋊C411yescharacteristic
317C42×C61—21no—
318C42×C61C22×C411yescharacteristic
319C42×C61C22×C411yescharacteristic
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61C22⋊C411yescharacteristic
326C22⋊Dic61C22⋊C411yescharacteristic
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198C22⋊C411yescharacteristic
338#11758198C22⋊C411yescharacteristic
339#11758198C22⋊C411yescharacteristic
340#11758198C22⋊C411yescharacteristic
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61C22⋊C411yescharacteristic
345C4⋊Dic61C22⋊C411yescharacteristic
346C4⋊Dic61C22×C411yescharacteristic
347C4⋊Dic61C22×C411yescharacteristic
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196C22⋊C411yescharacteristic
357#11758196C22⋊C411yescharacteristic
358#11758196C22⋊C411yescharacteristic
359#11758196C22⋊C411yescharacteristic
360C4×Dic61—21no—
361C4×Dic61—21no—
362C4×Dic61—21no—
363C4×Dic61C22×C411yescharacteristic
364C4×Dic61C22×C411yescharacteristic
365C4×Dic61C2×D411yescharacteristic
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C23×C61—21no—
370C23×C61C2×C22⋊C411yescharacteristic
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C22×D411yescharacteristic
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398Q8×C61—21no—
399Q8×C61—21no—
400Q8×C61—81no—
401D4×C61—21no—
402D4×C61—21no—
403D4×C61—81no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—81no—
410C2×C4×C61C2×C22⋊C411yescharacteristic
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C23×C411yescharacteristic
416C22⋊D61—41no—
417C22⋊D61—41no—
418C22⋊D61—81no—
419C22⋊D61—81no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—81no—
426C2×Dic61C2×C22⋊C411yescharacteristic
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C22×D411yescharacteristic
432D244—21no—
433D244—21no—
434D244—81no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—41no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—81no—
456C4×D61—81no—
457C4×D61C2×#4111yescharacteristic
458C4×D61C2×#4111yescharacteristic
459C4×D61C2×#4111yescharacteristic
460C4×D61C2×#4111yescharacteristic
461Dic122—21no—
462Dic122—21no—
463Dic122—41no—
464Dic122—41no—
465Dic122—81no—
466Dic122—81no—
467Dic122—81no—
468#92420—22no—
469#92420—22no—
470#92420—22no—
471#92420—22no—
472#21412—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61C22×C22⋊C411yescharacteristic
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—41no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—81no—
491C2×D61—81no—
492C2×D61—81no—
493C2×D61—81no—
494C2×D61#53211yescharacteristic
495C2×D61#53211yescharacteristic
496C2×D61#57611yescharacteristic
497C2×D61#57711yescharacteristic
498C2×D61#57711yescharacteristic
499C2×D61#57811yescharacteristic
500#6923—81no—
501#6923—81no—
502#6923—81no—
503#6923—81no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61C4×#4111yescharacteristic
513C4×C61C4×#4111yescharacteristic
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—21no—
518Dic61—21no—
519Dic61—41no—
520Dic61—41no—
521Dic61—41no—
522Dic61#52511yescharacteristic
523Dic61#52511yescharacteristic
524C2×#542—611no—
525C2×#405—611no—
526#2314—611no—
527#1993—611no—
528#1990—611no—
529#1959—611no—
530#1958—611no—
531#1895—611no—
532#1894—611no—
533#1893—611no—
534#1892—611no—
535#1763—611no—
536#1762—611no—
537C4×#103—611no—
538C4×#102—611no—
539C2×C61—41no—
540C2×C61—81no—
541C2×C61#229711yescharacteristic
542C2×C61#289711yescharacteristic
543C2×C61#289811yescharacteristic
544D61—41no—
545D61—81no—
546D61#317311yescharacteristic
547D61#317511yescharacteristic
548D61#317811yescharacteristic
549D61#317911yescharacteristic
550C22×M16—611no—
551C23×C8—611no—
552#542—611no—
553#542—611no—
554#542—611no—
555#542—611no—
556#542—611no—
557#542—611no—
558#542—611no—
559#542—1221no—
560#542—1221no—
561#542—1221no—
562#542—1221no—
563#542#692311yescharacteristic, complemented
564C2×C4⋊Q8—611no—
565C2×#126—1221no—
566C2×#124—611no—
567C2×#124—1221no—
568C2×#123—1221no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8—1221no—
571C2×#121—611no—
572C2×C4×Q8—611no—
573C2×C4×D4—611no—
574C2×#117—611no—
575C2×#103—611no—
576C2×#103—611no—
577C2×#103—611no—
578C2×#103—611no—
579C2×#102—611no—
580C2×#102—611no—
581C2×#102—611no—
582C2×#102—611no—
583#405—1221no—
584#405—1221no—
585#405—1221no—
586#405—1221no—
587C2×#97—611no—
588C2×#97—611no—
589C2×C4×C8—611no—
590C2×C4×C8—611no—
591#388—1221no—
592#388—1221no—
593#387—1221no—
594#387—1221no—
595#384—611no—
596#382—611no—
597#380—611no—
598#380—611no—
599C4×C4⋊C4—611no—
600C4×C4⋊C4—611no—
601#340—611no—
602#340—611no—
603#340—611no—
604#340—611no—
605#340—611no—
606#340—611no—
607#340—611no—
608#340—611no—
609C61#2141211yescharacteristic, complemented, Sylow
610C22×Q8—611no—
611C22×Q8—1221no—
612C22×D4—611no—
613C22×D4—1221no—
614C23×C4—611no—
615C23×C4—1221no—
616C2×M16—1222no—
617C2×M16—1222no—
618C2×M16—1221no—
619C2×M16—1221no—
620C22×C8—611no—
621C22×C8—611no—
622C22×C8—611no—
623C22×C8—611no—
624C22×C8—1222no—
625C22×C8—1222no—
626C22×C8—1221no—
627C22×C8—1221no—
628C4⋊Q8—611no—
629C4⋊Q8—611no—
630C4⋊Q8—611no—
631C4⋊Q8—1221no—
632C4⋊Q8—1221no—
633C4⋊Q8C2×#692311yescharacteristic
634#126—21no—
635#126—1221no—
636#126—1221no—
637#126—1221no—
638#126—1221no—
639#126—1221no—
640#126—1221no—
641#126—1221no—
642#124—21no—
643#124—611no—
644#124—611no—
645#124—611no—
646#124—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
650#124—1221no—
651#124—1221no—
652#124—1221no—
653#124—1221no—
654#124—1221no—
655#124C2×#692311yescharacteristic
656#123—21no—
657#123—1221no—
658#123—1221no—
659#123—1221no—
660#123—1221no—
661#123—1221no—
662#123—1221no—
663#123—1221no—
664C22⋊Q8—21no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—611no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8C2×#692311yescharacteristic
678#121—611no—
679#121—611no—
680#121—611no—
681#121—1221no—
682#121—1221no—
683#121C2×#692311yescharacteristic
684C4×Q8—611no—
685C4×Q8—611no—
686C4×Q8—611no—
687C4×Q8—1221no—
688C4×Q8—1221no—
689C4×Q8C2×#692311yescharacteristic
690C4×D4—611no—
691C4×D4—611no—
692C4×D4—611no—
693C4×D4—1221no—
694C4×D4—1221no—
695C4×D4C2×#692311yescharacteristic
696#117—611no—
697#117—611no—
698#117—611no—
699#117—611no—
700#117—611no—
701#117—611no—
702#117—611no—
703#117C2×#692311yescharacteristic
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—1221no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C22⋊C4—611no—
718C2×C22⋊C4—611no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C22⋊C4—1221no—
725C2×C22⋊C4—1221no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—1221no—
729C2×C42—1221no—
730C2×C42—1221no—
731#103—1222no—
732#103—1222no—
733#103—1222no—
734#103—1222no—
735#102—1222no—
736#102—1222no—
737#102—1222no—
738#102—1222no—
739#97—1221no—
740#97—1221no—
741#97—1221no—
742#97—1221no—
743C4×C8—1221no—
744C4×C8—1221no—
745C4×C8—1221no—
746C4×C8—1221no—
747#95—1221no—
748#95—1221no—
749#95—1221no—
750#95—1221no—
751#95—1221no—
752#95—1221no—
753C24—611no—
754C24—1221no—
755C2×Q8—21no—
756C2×Q8—611no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—4881no—
766C2×Q8—4881no—
767C2×Q8C22×#692311yescharacteristic
768C2×D4—21no—
769C2×D4—611no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—1221no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—4881no—
779C2×D4—4881no—
780C2×D4C22×#692311yescharacteristic
781C22×C4—21no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—4881no—
806C22×C4—4881no—
807C22×C4C22×#692311yescharacteristic
808M16—1224no—
809M16—1224no—
810C2×C8—612no—
811C2×C8—612no—
812C2×C8—612no—
813C2×C8—612no—
814C2×C8—1221no—
815C2×C8—1221no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—1221no—
821C2×C8—1221no—
822C2×C8—1224no—
823C2×C8—1224no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—611no—
828C4⋊C4—611no—
829C4⋊C4—611no—
830C4⋊C4—611no—
831C4⋊C4—611no—
832C4⋊C4—611no—
833C4⋊C4—611no—
834C4⋊C4—611no—
835C4⋊C4—1221no—
836C4⋊C4—1221no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—4881no—
855C4⋊C4—4881no—
856C4⋊C4C22⋊#692311yescharacteristic
857C4⋊C4C22⋊#692311yescharacteristic
858C4⋊C4C22×#692311yescharacteristic
859C4⋊C4C22×#692311yescharacteristic
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—611no—
866C22⋊C4—611no—
867C22⋊C4—611no—
868C22⋊C4—611no—
869C22⋊C4—611no—
870C22⋊C4—611no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—1221no—
886C22⋊C4—4881no—
887C22⋊C4—4881no—
888C22⋊C4C22⋊#692311yescharacteristic
889C22⋊C4C22⋊#692311yescharacteristic
890C42—21no—
891C42—611no—
892C42—611no—
893C42—611no—
894C42—611no—
895C42—611no—
896C42—611no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—4881no—
901C42—4881no—
902C42C22×#692311yescharacteristic
903C42C22×#692311yescharacteristic
904C23—21no—
905C23—611no—
906C23—611no—
907C23—1221no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23C2×C22⋊#692311yescharacteristic
921Q8—21no—
922Q8—21no—
923Q8—81no—
924Q8—1221no—
925Q8—1221no—
926Q8—4881no—
927Q8—4881no—
928Q8—4881no—
929Q8—2441no—
930Q8—2441no—
931D4—21no—
932D4—21no—
933D4—81no—
934D4—1221no—
935D4—1221no—
936D4—4881no—
937D4—4881no—
938D4—4881no—
939D4—2441no—
940D4—2441no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—81no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—611no—
950C2×C4—611no—
951C2×C4—611no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—611no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—4881no—
977C2×C4—4881no—
978C2×C4—4881no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4C2×C22⋊#692311yescharacteristic
998C2×C4C2×C22⋊#692311yescharacteristic
999C2×C4C2×C22⋊#692311yescharacteristic
1000C2×C4C2×C22⋊#692311yescharacteristic
1001C2×C4C2×C22⋊#692311yescharacteristic
1002C2×C4C23×#692311yescharacteristic
1003C8—1222no—
1004C8—1222no—
1005C8—1222no—
1006C8—1222no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—611no—
1014C22—611no—
1015C22—611no—
1016C22—611no—
1017C22—611no—
1018C22—611no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—4881no—
1023C22—4881no—
1024C22—4881no—
1025C22—4881no—
1026C22—2441no—
1027C22—2441no—
1028C22—2441no—
1029C22—2441no—
1030C22—2441no—
1031C22—2441no—
1032C22—2441no—
1033C22C22×C22⋊#692311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—611no—
1043C4—611no—
1044C4—1221no—
1045C4—1221no—
1046C4—1221no—
1047C4—1221no—
1048C4—1221no—
1049C4—4881no—
1050C4—4881no—
1051C4—4881no—
1052C4—4881no—
1053C4—2441no—
1054C4—2441no—
1055C4—2441no—
1056C4#41×#692311yescharacteristic
1057C4#41×#692311yescharacteristic
1058C2—41no—
1059C2—81no—
1060C2—611no—
1061C2—611no—
1062C2—611no—
1063C2—611no—
1064C2—4881no—
1065C2—2441no—
1066C2#2146228011yescharacteristic
1067C2#2146244011yescharacteristic
1068C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#542#6923
hypocenterC61#21412
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #21462379C2semidirect
2. #21462297C2semidirect
3. #21462003C2semidirect
4. #21462000C2semidirect
5. #21461949C2semidirect
6. #21461948C2semidirect
8. #21461834C2semidirect
10. #21461832C2semidirect
11. #21461591C2semidirect
12. #21461589C2semidirect
13. C4×#14519840C2semidirect
14. C4×#14519839C2semidirect
52. #16840386C4semidirect
53. #16840385C4semidirect
54. #16840384C4semidirect
55. #16840383C4semidirect
57. #16840381C4semidirect
59. #16840379C4semidirect
61. #16840377C4semidirect
74. C61×#542C4semidirect
563. #542#6923semidirect
609. C61#21412semidirect

Maximal subgroups

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

subgroupindex
#214623792
#214622972
#214620032
#214620002
#214619492
#214619482
#214618352
#214618342
#214618332
#214618322
#214615912
#214615892
C4×#145198402
C4×#145198392
#542×D612
#2141261