Finite Group Databasebeta

← #30616737

Subgroups — #30616737

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462500C211yesmaximal, characteristic, complemented
2#117×#6923C211yesmaximal, characteristic, complemented
3#21462007C211yesmaximal, characteristic, complemented
4#21462004C211yesmaximal, characteristic, complemented
5#21461956C211yesmaximal, characteristic, complemented
6#21461954C211yesmaximal, characteristic, complemented
7#21461839C211yesmaximal, characteristic, complemented
8#21461838C211yesmaximal, characteristic, complemented
9#21461837C211yesmaximal, characteristic, complemented
10#21461836C211yesmaximal, characteristic, complemented
11#21461583C211yesmaximal, characteristic, complemented
12#21461582C211yesmaximal, characteristic, complemented
13C4×#14519842C211yesmaximal, characteristic, complemented
14C4×#14519841C211yesmaximal, characteristic, complemented
15#21459206C211yesmaximal, characteristic
16C2×#14519856C2211yescharacteristic
17C22×C4×#6923C2211yescharacteristic
18#16840787—21no—
19#16840787—21no—
20#16840786—21no—
21#16840786—21no—
22#16840767C2211yescharacteristic
23#16840766C2211yescharacteristic
24C2×#14519842C2211yescharacteristic
25C2×#14519842C2211yescharacteristic
26C2×#14519842C2211yescharacteristic
27C2×#14519842C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29C2×#14519841C2211yescharacteristic
30C2×#14519841C2211yescharacteristic
31C2×#14519841C2211yescharacteristic
32#16840733C2211yescharacteristic
33#16840733C2211yescharacteristic
34C4×#11758213C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36C4⋊C4×#6923—21no—
37C4⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C22⋊C4×#6923—21no—
40#16840698C2211yescharacteristic
41#16840698C2211yescharacteristic
42C42×#6923C2211yescharacteristic
43C42×#6923C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52#16840386C411yescharacteristic, complemented
53#16840383C411yescharacteristic, complemented
54#16840381C411yescharacteristic, complemented
55#16840372C411yescharacteristic, complemented
56#16840370C411yescharacteristic, complemented
57#16840365C411yescharacteristic, complemented
58#16840363C411yescharacteristic, complemented
59#16840358—21no—
60#16840353—21no—
61#16840348—21no—
62#16840346—21no—
63#16840317C2211yescharacteristic
64#16840311C2211yescharacteristic
65#16840298—21no—
66#16840295—21no—
67#16840291—21no—
68#16840289—21no—
69#16840275C2211yescharacteristic
70#16840272C2211yescharacteristic
71C4×#11758226C2211yescharacteristic
72C4×#11758224C2211yescharacteristic
73#117×D61C2211yescharacteristic
74C61×#542C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×#11758213C2311yescharacteristic
80#14519856—22no—
81#14519856—22no—
82C2×C4⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—22no—
86C2×C4×#6923—22no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923C2311yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94C2×C4×#6923C2311yescharacteristic
95#14519844—21no—
96#14519844—21no—
97C4⋊#92420—21no—
98C4⋊#92420—21no—
99#14519842—22no—
100#14519842—22no—
101#14519842—22no—
102#14519842—22no—
103#14519841—22no—
104#14519841—22no—
105#14519841—22no—
106#14519841—22no—
107#14519834—21no—
108#14519834—21no—
109C22⋊#92420—21no—
110C22⋊#92420—21no—
111#14519832—21no—
112#14519832—21no—
113C4×#92420—21no—
114C4×#92420—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×#11758226C2311yescharacteristic
120C2×#11758224C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122#14519777C2×C411yescharacteristic, complemented
123#14519775C2×C411yescharacteristic, complemented
124#14519773C2×C411yescharacteristic, complemented
125#14519772—21no—
126#14519772—21no—
127#14519772—21no—
128#14519771—21no—
129#14519770—21no—
130#14519770—21no—
131#14519770—21no—
132#14519769—21no—
133#14519768—21no—
134#14519768C2×C411yescharacteristic, complemented
135#14519768C2×C411yescharacteristic, complemented
136#14519767—21no—
137#14519767—21no—
138#14519766—21no—
139#14519765C2×C411yescharacteristic, complemented
140#14519763—21no—
141#14519763—21no—
142#14519762—21no—
143#14519762—21no—
144#14519761—21no—
145#14519761—21no—
146#14519760—21no—
147#14519759—21no—
148#14519759—21no—
149#14519759—21no—
150#14519759—21no—
151#14519757—21no—
152#14519757C2×C411yescharacteristic
153#14519756C2×C411yescharacteristic
154#14519755—21no—
155#14519754—21no—
156#14519753—21no—
157#14519753—21no—
158#14519753C2×C411yescharacteristic
159#14519752C2×C411yescharacteristic
160#14519751—21no—
161#14519751C2×C411yescharacteristic
162#14519750—21no—
163#14519750—21no—
164#14519750—21no—
165#14519749—21no—
166#14519748—21no—
167#14519748C2×C411yescharacteristic
168#14519747—21no—
169#14519745—21no—
170Q8×Dic61—21no—
171Q8×Dic61C2×C411yescharacteristic, complemented
172C4×Dic122C2×C411yescharacteristic, complemented
173#14519742—21no—
174#14519742C2×C411yescharacteristic, complemented
175C4×D244—21no—
176C4×D244C2×C411yescharacteristic, complemented
177D4×Dic61—21no—
178D4×Dic61C2×C411yescharacteristic, complemented
179#14519739—21no—
180#14519739—21no—
181#14519739C2×C411yescharacteristic, complemented
182C4×C22⋊D61—21no—
183#14519737—21no—
184#14519737—21no—
185#14519737—21no—
186#14519737—21no—
187#14519737—21no—
188#14519736C2×C411yescharacteristic
189#14519735—21no—
190#14519735D411yescharacteristic
191#14519735D411yescharacteristic
192#14519735C2311yescharacteristic
193#14519735C2311yescharacteristic
194#14519734C2×C411yescharacteristic
195#14519734C2×C411yescharacteristic
196#14519733—21no—
197#14519733D411yescharacteristic
198#14519733D411yescharacteristic
199C4⋊C4×D61D411yescharacteristic
200C4⋊C4×D61D411yescharacteristic
201C22⋊C4×D61D411yescharacteristic
202C22⋊C4×D61D411yescharacteristic
203C2×C4×Dic61—21no—
204C42×D61—21no—
205C42×D61C2311yescharacteristic
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic, complemented
208#126×C61—21no—
209#124×C61—21no—
210#124×C61C2×C411yescharacteristic, complemented
211#123×C61—21no—
212C22⋊Q8×C61—21no—
213C22⋊Q8×C61C2×C411yescharacteristic
214#121×C61C2×C411yescharacteristic
215C4×Q8×C61C2×C411yescharacteristic, complemented
216C4×D4×C61C2×C411yescharacteristic, complemented
217#117×C61C2×C411yescharacteristic
218C23×D61C2×D411yescharacteristic
219C22×#6923—21no—
220C22×#6923—24no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—42no—
225C22×#6923—42no—
226C2×Q8×C61—21no—
227C2×Q8×C61C22×C411yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61C22×C411yescharacteristic
230C22×C4×C61—21no—
231C22×C4×C61C22×C411yescharacteristic
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240#11758226—21no—
241#11758226—21no—
242#11758226—21no—
243#11758226—21no—
244#11758224—21no—
245#11758224—21no—
246#11758224—21no—
247#11758224—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244C22×C411yescharacteristic
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×D61C22×C411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
268C22⋊#6923—24no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C4⋊#6923—24no—
274C4×#6923—24no—
275C4×#6923—21no—
276C4×#6923—21no—
277C4×#6923—21no—
278C4×#6923—21no—
279C4×#6923—42no—
280C4×#6923—42no—
281C4×#6923—42no—
282C4×#6923—42no—
283C4×#6923#4112yes—
284C4×#6923#4112yes—
285C4×#6923#4112yes—
286C4×#6923#4112yes—
287#11758213—21no—
288#11758213—21no—
289#11758213—21no—
290#11758213—21no—
291#11758213—21no—
292#11758213—21no—
293#11758213—21no—
294#11758213—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61C22⋊C411yescharacteristic
299C4⋊C4×C61C22⋊C411yescharacteristic
300C4⋊C4×C61C22×C411yescharacteristic
301C4⋊C4×C61C22×C411yescharacteristic
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61C22⋊C411yescharacteristic
308C22⋊C4×C61C22⋊C411yescharacteristic
309C42×C61—21no—
310C42×C61C22×C411yescharacteristic
311C42×C61C22×C411yescharacteristic
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61C22⋊C411yescharacteristic
316C22⋊Dic61C22⋊C411yescharacteristic
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198C22⋊C411yescharacteristic
328#11758198C22⋊C411yescharacteristic
329#11758198C22⋊C411yescharacteristic
330#11758198C22⋊C411yescharacteristic
331C4⋊Dic61—21no—
332C4⋊Dic61—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61—21no—
335C4⋊Dic61—21no—
336C4⋊Dic61C22⋊C411yescharacteristic
337C4⋊Dic61C22⋊C411yescharacteristic
338C4⋊Dic61C22×C411yescharacteristic
339C4⋊Dic61C22×C411yescharacteristic
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196C22⋊C411yescharacteristic
349#11758196C22⋊C411yescharacteristic
350#11758196C22⋊C411yescharacteristic
351#11758196C22⋊C411yescharacteristic
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—21no—
356C4×Dic61—21no—
357C4×Dic61C22×C411yescharacteristic
358C4×Dic61C22×C411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C4×Dic61C2×D411yescharacteristic
361C4×Dic61C2×D411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C23×C61—21no—
364C23×C61C2×C22⋊C411yescharacteristic
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61C22×D411yescharacteristic
372C2×#6923—22no—
373C2×#6923—22no—
374C2×#6923—22no—
375C2×#6923—22no—
376C2×#6923—22no—
377C2×#6923—22no—
378C2×#6923—48no—
379C2×#6923—41no—
380C2×#6923—41no—
381C2×#6923—41no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385Q8×C61—21no—
386Q8×C61—21no—
387Q8×C61—81no—
388D4×C61—21no—
389D4×C61—21no—
390D4×C61—81no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—81no—
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C2×C22⋊C411yescharacteristic
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C23×C411yescharacteristic
403C22⋊D61—41no—
404C22⋊D61—41no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C22⋊D61—81no—
408C22⋊D61—81no—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—81no—
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C22×D411yescharacteristic
423D244—21no—
424D244—21no—
425D244—41no—
426D244—41no—
427D244—81no—
428C4×D61—21no—
429C4×D61—21no—
430C4×D61—21no—
431C4×D61—21no—
432C4×D61—21no—
433C4×D61—21no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—81no—
441C4×D61—81no—
442C4×D61C2×#4111yescharacteristic
443C4×D61C2×#4111yescharacteristic
444C4×D61C2×#4111yescharacteristic
445C4×D61C2×#4111yescharacteristic
446Dic122—21no—
447Dic122—21no—
448Dic122—81no—
449#92420—41no—
450#92420—41no—
451#92420—41no—
452#92420—41no—
453#21419—611nomaximal, Sylow
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61C22×C22⋊C411yescharacteristic
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61#52511yescharacteristic
472C2×D61#52511yescharacteristic
473#6923—24no—
474#6923—42no—
475#6923—42no—
476#6923—42no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61C4×#4111yescharacteristic
486C4×C61C4×#4111yescharacteristic
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—41no—
493Dic61—41no—
494Dic61—41no—
495Dic61#53211yescharacteristic
496Dic61#53211yescharacteristic
497#3455—611no—
498#2921—611no—
499C4×#117—611no—
500#1995—611no—
501#1994—611no—
502#1963—611no—
503#1962—611no—
504#1897—611no—
505#1897—611no—
506#1896—611no—
507#1896—611no—
508#1759—611no—
509#1759—611no—
510C4×#104—611no—
511C4×#104—611no—
512C2×C61—41no—
513C2×C61—81no—
514C2×C61#229711yescharacteristic
515C2×C61#290111yescharacteristic
516C2×C61#290111yescharacteristic
517D61—21no—
518D61—21no—
519D61—41no—
520D61—81no—
521#542—611no—
522#542—611no—
523#542—611no—
524#542#692311yescharacteristic, complemented
525#541—611no—
526#541—611no—
527#540—611no—
528#540—611no—
529#539—1221no—
530#539—1221no—
531#538—1221no—
532#538—1221no—
533#533—611no—
534#532—611no—
535#529—1221no—
536#529—1221no—
537#529—1221no—
538#529—1221no—
539#525—611no—
540#525—611no—
541C4×#41—611no—
542C4×#41—611no—
543C2×#117—611no—
544C2×#117—611no—
545C22×C42—611no—
546#433—1221no—
547#433—1221no—
548#433—1221no—
549#433—1221no—
550#423—611no—
551#423—611no—
552C2×#104—611no—
553C2×#104—611no—
554C2×#104—611no—
555C2×#104—611no—
556C2×#104—611no—
557C2×#104—611no—
558C2×#104—611no—
559C2×#104—611no—
560#407—611no—
561#407—611no—
562C4×M16—611no—
563C4×M16—611no—
564C4×C4⋊C4—1221no—
565C4×C4⋊C4—1221no—
566C4×C22⋊C4—1221no—
567C4×C22⋊C4—1221no—
568#376—611no—
569#376—611no—
570C43—611no—
571C43—611no—
572#339—611no—
573#339—611no—
574#339—611no—
575#339—611no—
576#339—611no—
577#339—611no—
578#339—611no—
579#339—611no—
580C61#2141911yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C23×C4—611no—
584C23×C4—1221no—
585C2×M16—611no—
586C2×M16—611no—
587C2×M16—611no—
588C2×M16—611no—
589C4⋊Q8—611no—
590C4⋊Q8—611no—
591C4⋊Q8C2×#692311yescharacteristic, complemented
592#127—611no—
593#126—21no—
594#126—1221no—
595#126—1221no—
596#126—1221no—
597#126—1221no—
598#126—1221no—
599#126—1221no—
600#126—1221no—
601#125—611no—
602#125—611no—
603#125—1221no—
604#125—1221no—
605#125—1221no—
606#125—1221no—
607#124—21no—
608#124—611no—
609#124—1221no—
610#124—1221no—
611#124—1221no—
612#124C2×#692311yescharacteristic, complemented
613#123—21no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623C22⋊Q8—21no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—611no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8C2×#692311yescharacteristic
633#121—611no—
634#121—611no—
635#121—611no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121C2×#692311yescharacteristic
643#120—1221no—
644#120—1221no—
645C4×Q8—611no—
646C4×Q8—611no—
647C4×Q8—611no—
648C4×Q8—1221no—
649C4×Q8—1221no—
650C4×Q8C2×#692311yescharacteristic, complemented
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4C2×#692311yescharacteristic, complemented
665#117—611no—
666#117—611no—
667#117—611no—
668#117—611no—
669#117—611no—
670#117—611no—
671#117—611no—
672#117—611no—
673#117—611no—
674#117—1221no—
675#117—1221no—
676#117—1222no—
677#117—1222no—
678#117C2×#692311yescharacteristic
679C2×C4⋊C4—611no—
680C2×C4⋊C4—611no—
681C2×C4⋊C4—1221no—
682C2×C22⋊C4—611no—
683C2×C22⋊C4—611no—
684C2×C22⋊C4—1221no—
685C2×C42—611no—
686C2×C42—611no—
687C2×C42—611no—
688C2×C42—611no—
689C2×C42—611no—
690C2×C42—611no—
691C2×C42—1221no—
692C2×C42—1221no—
693C2×C42—1222no—
694C2×C42—1222no—
695C2×C42—1221no—
696C2×C42—1221no—
697C2×C42—1221no—
698C2×C42—1221no—
699C2×C42—1221no—
700C4⋊C8—1221no—
701C4⋊C8—1221no—
702C4⋊C8—1221no—
703C4⋊C8—1221no—
704#104—1222no—
705#104—1222no—
706#104—1222no—
707#104—1222no—
708#104—1222no—
709#104—1222no—
710#104—1222no—
711#104—1222no—
712C22⋊C8—1221no—
713C22⋊C8—1221no—
714C22⋊C8—1221no—
715C22⋊C8—1221no—
716#97—1221no—
717#97—1221no—
718C4×C8—1221no—
719C4×C8—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723#95—1221no—
724C24—611no—
725#41—1221no—
726#41—1221no—
727#41—1221no—
728#41—1221no—
729#41—1221no—
730#41—1221no—
731#41—1221no—
732#41—1221no—
733C2×Q8—21no—
734C2×Q8—611no—
735C2×Q8—1221no—
736C2×Q8C22×#692311yescharacteristic
737C2×D4—21no—
738C2×D4—611no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4C22×#692311yescharacteristic
747C22×C4—21no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1224no—
770C22×C4—1221no—
771C22×C4—2442no—
772C22×C4—2442no—
773C22×C4C22×#692311yescharacteristic
774M16—1221no—
775M16—1221no—
776M16—1221no—
777M16—1221no—
778M16—1221no—
779M16—1221no—
780M16—1221no—
781M16—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1224no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4C22⋊#692311yescharacteristic
812C4⋊C4C22⋊#692311yescharacteristic
813C4⋊C4C22×#692311yescharacteristic
814C4⋊C4C22×#692311yescharacteristic
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—611no—
821C22⋊C4—611no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1224no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4C22⋊#692311yescharacteristic
841C22⋊C4C22⋊#692311yescharacteristic
842C42—21no—
843C42—611no—
844C42—611no—
845C42—611no—
846C42—611no—
847C42—611no—
848C42—611no—
849C42—612no—
850C42—612no—
851C42—612no—
852C42—612no—
853C42—1221no—
854C42—1221no—
855C42—1221no—
856C42—1221no—
857C42—1221no—
858C42—1221no—
859C42—1221no—
860C42—1221no—
861C42—1224no—
862C42—1221no—
863C42—2442no—
864C42—2442no—
865C42—2442no—
866C42—2442no—
867C42C22×#692311yescharacteristic
868C42C22×#692311yescharacteristic
869C23—21no—
870C23—611no—
871C23—611no—
872C23—1221no—
873C23—1221no—
874C23—1221no—
875C23—2441no—
876C23—2441no—
877C23C2×C22⋊#692311yescharacteristic
878Q8—21no—
879Q8—21no—
880Q8—81no—
881Q8—1221no—
882Q8—1221no—
883Q8—4881no—
884D4—21no—
885D4—21no—
886D4—81no—
887D4—1221no—
888D4—1221no—
889D4—4881no—
890D4—4881no—
891D4—4881no—
892D4—4881no—
893D4—4881no—
894D4—2441no—
895D4—2441no—
896D4—2441no—
897D4—2441no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—81no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—4881no—
932C2×C4—4881no—
933C2×C4—4881no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2448no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4C2×C22⋊#692311yescharacteristic
950C2×C4C2×C22⋊#692311yescharacteristic
951C2×C4C2×C22⋊#692311yescharacteristic
952C2×C4C2×C22⋊#692311yescharacteristic
953C2×C4C2×C22⋊#692311yescharacteristic
954C2×C4C23×#692311yescharacteristic
955C8—2441no—
956C8—2441no—
957C8—2441no—
958C8—2441no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—611no—
966C22—611no—
967C22—1221no—
968C22—1221no—
969C22—1221no—
970C22—1221no—
971C22—1221no—
972C22—2442no—
973C22—2442no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22C22×C22⋊#692311yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—611no—
987C4—611no—
988C4—1224no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—2442no—
995C4—2442no—
996C4—2442no—
997C4—2441no—
998C4—2441no—
999C4—2441no—
1000C4#41×#692311yescharacteristic
1001C4#41×#692311yescharacteristic
1002C2—41no—
1003C2—81no—
1004C2—1221no—
1005C2—1221no—
1006C2—4881no—
1007C2—2441no—
1008C2#2146228011yescharacteristic
1009C2#2146244911yescharacteristic
1010C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#21459206C2
cosocleC2×C4×D61C24
hypercenter#542#6923
hypocenterC61#21419
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. #21462500C2semidirect
2. #117×#6923C2semidirect
3. #21462007C2semidirect
4. #21462004C2semidirect
5. #21461956C2semidirect
6. #21461954C2semidirect
7. #21461839C2semidirect
8. #21461838C2semidirect
9. #21461837C2semidirect
10. #21461836C2semidirect
11. #21461583C2semidirect
12. #21461582C2semidirect
13. C4×#14519842C2semidirect
14. C4×#14519841C2semidirect
52. #16840386C4semidirect
53. #16840383C4semidirect
54. #16840381C4semidirect
55. #16840372C4semidirect
56. #16840370C4semidirect
57. #16840365C4semidirect
58. #16840363C4semidirect
74. C61×#542C4semidirect
122. #14519777C2×C4semidirect
123. #14519775C2×C4semidirect
124. #14519773C2×C4semidirect
134. #14519768C2×C4semidirect
135. #14519768C2×C4semidirect
139. #14519765C2×C4semidirect
171. Q8×Dic61C2×C4semidirect
172. C4×Dic122C2×C4semidirect
174. #14519742C2×C4semidirect
176. C4×D244C2×C4semidirect
178. D4×Dic61C2×C4semidirect
181. #14519739C2×C4semidirect
207. C4⋊Q8×C61C2×C4semidirect
210. #124×C61C2×C4semidirect
215. C4×Q8×C61C2×C4semidirect
216. C4×D4×C61C2×C4semidirect
524. #542#6923semidirect
580. C61#21419semidirect
591. C4⋊Q8C2×#6923semidirect
612. #124C2×#6923semidirect
650. C4×Q8C2×#6923semidirect
664. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625002
#117×#69232
#214620072
#214620042
#214619562
#214619542
#214618392
#214618382
#214618372
#214618362
#214615832
#214615822
C4×#145198422
C4×#145198412
#214592062
#2141961