Finite Group Databasebeta

← #30620360

Subgroups — #30620360

Order 15616.

1130 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
1D61⋊#435C211yesmaximal, characteristic
2#21462335C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic, complemented
4#21461997C211yesmaximal, characteristic, complemented
5#21461834C211yesmaximal, characteristic, complemented
6#21461832C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461804C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461724C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461508C211yesmaximal, characteristic, complemented
14#21461504C211yesmaximal, characteristic, complemented
15#556×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31#16840721C2211yescharacteristic
32#16840712—21no—
33#16840711—21no—
34#16840710—21no—
35#16840706C2211yescharacteristic
36#16840704C2211yescharacteristic
37#16840704C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C22⋊C4×#6923—21no—
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840486C411yescharacteristic, complemented
53#16840485C411yescharacteristic, complemented
54#16840484—21no—
55#16840483C411yescharacteristic, complemented
56#16840483C411yescharacteristic, complemented
57#16840482C411yescharacteristic, complemented
58#16840481—21no—
59#16840480C411yescharacteristic, complemented
60#16840480C411yescharacteristic, complemented
61#16840479—21no—
62#16840479—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#126×D61—21no—
65#126×D61—21no—
66#124×D61—21no—
67C22⋊Q8×D61C2211yescharacteristic
68C22⋊Q8×D61C2211yescharacteristic
69C4×Q8×D61—21no—
70C4×Q8×D61C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72#117×D61C2211yescharacteristic
73#117×D61C2211yescharacteristic
74C61×#556C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77D61⋊M16—22no—
78D61⋊M16—41no—
79C2×#11758217—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—21no—
82C2×D61⋊C8—41no—
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C22×#92420—21no—
88#14519856—22no—
89#14519856—41no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—41no—
93C2×C4⋊#6923C2311yescharacteristic
94C2×C4⋊#6923C2311yescharacteristic
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519840—22no—
105#14519840—22no—
106#14519840—41no—
107#14519840—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112#14519832—21no—
113#14519832—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×D61D411yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124#14519777C2×C411yescharacteristic, complemented
125#14519776—21no—
126#14519776C2×C411yescharacteristic, complemented
127#14519776C2×C411yescharacteristic, complemented
128#14519775—21no—
129#14519772—21no—
130#14519772—21no—
131#14519772—21no—
132#14519772—21no—
133#14519772—21no—
134#14519772—21no—
135#14519771—21no—
136#14519771—21no—
137#14519770—21no—
138#14519770—21no—
139#14519770—21no—
140#14519770—21no—
141#14519770—21no—
142#14519770—21no—
143#14519766—21no—
144#14519765—21no—
145#14519764—21no—
146#14519763—21no—
147#14519763—21no—
148#14519763—21no—
149#14519763—21no—
150#14519757C2×C411yescharacteristic
151#14519757C2×C411yescharacteristic, complemented
152#14519756C2×C411yescharacteristic
153#14519756C2×C411yescharacteristic, complemented
154#14519755—21no—
155#14519755—21no—
156#14519754—21no—
157#14519754—21no—
158#14519753C2×C411yescharacteristic
159#14519753C2×C411yescharacteristic, complemented
160Q8×Dic61—21no—
161Q8×Dic61C2×C411yescharacteristic, complemented
162C4×Dic122—21no—
163C4×Dic122—21no—
164C4×Dic122—21no—
165C4×Dic122—21no—
166C4×Dic122C2×C411yescharacteristic, complemented
167#14519742—21no—
168#14519742—21no—
169#14519742—21no—
170#14519742—21no—
171#14519742C2×C411yescharacteristic, complemented
172C4×D244C2×C411yescharacteristic
173D4×Dic61D411yescharacteristic
174#14519739D411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736C2×C411yescharacteristic
180#14519736C2×C411yescharacteristic, complemented
181#14519735C2×C411yescharacteristic
182#14519735C2×C411yescharacteristic
183#14519735C2×C411yescharacteristic, complemented
184#14519735C2×C411yescharacteristic, complemented
185#14519734—21no—
186#14519734—21no—
187#14519733—21no—
188#14519733—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61D411yescharacteristic
194C4⋊C4×D61C2311yescharacteristic
195C4⋊C4×D61C2311yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61D411yescharacteristic
202C22⋊C4×D61D411yescharacteristic
203C42×D61—21no—
204C42×D61—21no—
205C42×D61—21no—
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic, complemented
208#126×C61—21no—
209#126×C61—21no—
210#124×C61—21no—
211C22⋊Q8×C61C2×C411yescharacteristic
212C22⋊Q8×C61C2×C411yescharacteristic, complemented
213C4×Q8×C61—21no—
214C4×Q8×C61C2×C411yescharacteristic, complemented
215C4×D4×C61C2×C411yescharacteristic
216#117×C61C2×C411yescharacteristic
217#117×C61C2×C411yescharacteristic, complemented
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—42no—
225C22×#6923—42no—
226C22×#6923—81no—
227C2×Q8×C61—21no—
228C2×Q8×C61C22×C411yescharacteristic
229C2×D4×C61C22⋊C411yescharacteristic
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C22×C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236Q8×D61—21no—
237Q8×D61—21no—
238Q8×D61—21no—
239Q8×D61—21no—
240Q8×D61—42no—
241Q8×D61—42no—
242D4×D61—41no—
243D4×D61—41no—
244C2×D244C22⋊C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
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×D61C22×C411yescharacteristic
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×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—21no—
270C2×Dic122C22×C411yescharacteristic
271C22⋊#6923—42no—
272C22⋊#6923—42no—
273C22⋊#6923—81no—
274#11758217—42no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—42no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—42no—
288C4⋊#6923#4112yes—
289C4×#6923—42no—
290C4×#6923—81no—
291#11758213—42no—
292D61⋊C8—21no—
293D61⋊C8—21no—
294D61⋊C8—21no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—42no—
300D61⋊C8#4112yes—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61C22⋊C411yescharacteristic
306C4⋊C4×C61C22×C411yescharacteristic
307C4⋊C4×C61C22×C411yescharacteristic
308C4⋊C4×C61C22×C411yescharacteristic
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61C22⋊C411yescharacteristic
314C22⋊C4×C61C22⋊C411yescharacteristic
315C42×C61—21no—
316C42×C61—21no—
317C42×C61—21no—
318C42×C61C22×C411yescharacteristic
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61C22⋊C411yescharacteristic
324C22⋊Dic61C22⋊C411yescharacteristic
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198C22⋊C411yescharacteristic
334#11758198C22⋊C411yescharacteristic
335#11758198C22⋊C411yescharacteristic
336#11758198C22⋊C411yescharacteristic
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61C22⋊C411yescharacteristic
342C4⋊Dic61C22×C411yescharacteristic
343C4⋊Dic61C22×C411yescharacteristic
344C4⋊Dic61C22×C411yescharacteristic
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
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
358C4×Dic61—21no—
359C4×Dic61—21no—
360C4×Dic61—21no—
361C4×Dic61—21no—
362C4×Dic61—21no—
363C4×Dic61—21no—
364C4×Dic61—21no—
365C4×Dic61—21no—
366C4×Dic61—21no—
367C4×Dic61C22×C411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C23×C61C2×C22⋊C411yescharacteristic
371C23×C61C2×C22⋊C411yescharacteristic
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C22×D411yescharacteristic
387C2×#6923—22no—
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—
398C2×#6923—41no—
399C2×#6923—84no—
400Q8×C61—21no—
401Q8×C61—21no—
402Q8×C61—42no—
403D4×C61—41no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C23×C411yescharacteristic
417C22⋊D61—41no—
418C22⋊D61—41no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C22×D411yescharacteristic
432D244—41no—
433C4×D61—21no—
434C4×D61—21no—
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—41no—
456C4×D61—41no—
457C4×D61C2×#4111yescharacteristic
458C4×D61C2×#4111yescharacteristic
459C4×D61H(5,𝔽2)11yescharacteristic
460C4×D612−1+411yescharacteristic
461Dic122—21no—
462Dic122—21no—
463Dic122—42no—
464Dic122—42no—
465Dic122—42no—
466Dic122—41no—
467Dic122—41no—
468#92420—22no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#22494—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61C22×C22⋊C411yescharacteristic
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—41no—
492C2×D61—41no—
493C2×D61—41no—
494C2×D61#54611yescharacteristic
495C2×D61#54711yescharacteristic
496C2×D61#57511yescharacteristic
497C2×D61#57511yescharacteristic
498C2×D61#57711yescharacteristic
499C2×D61#57811yescharacteristic
500#6923—42no—
501#6923—81no—
502#6923—81no—
503#6923—81no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61C4×#4111yescharacteristic
513C4×C61#52011yescharacteristic
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—21no—
518Dic61—41no—
519Dic61—41no—
520Dic61—41no—
521Dic61—41no—
522Dic61#54611yescharacteristic
523Dic61#54711yescharacteristic
524C2×#556—611no—
525C2×#435—611no—
526#2352—611no—
527#1993—611no—
528#1987—611no—
529#1894—611no—
530#1892—611no—
531#1873—611no—
532#1872—611no—
533#1825—611no—
534#1825—611no—
535#1805—611no—
536#1763—611no—
537#1736—611no—
538#1735—611no—
539C2×C61—41no—
540C2×C61—41no—
541C2×C61#233911yescharacteristic
542C2×C61#289611yescharacteristic
543C2×C61#289811yescharacteristic
544D61—41no—
545D61—41no—
546D61#331111yescharacteristic
547D61#331311yescharacteristic
548D61#334911yescharacteristic
549D61#335011yescharacteristic
550C22×M16—611no—
551C23×C8—611no—
552#556—611no—
553#556—611no—
554#556—611no—
555#556—611no—
556#556—611no—
557#556—611no—
558#556—611no—
559#556—1221no—
560#556—1221no—
561#556—1221no—
562#556—1221no—
563#556#692311yescharacteristic, complemented
564C2×C4⋊Q8—611no—
565C2×#126—1221no—
566C2×#126—1221no—
567C2×#124—1221no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C4×Q8—611no—
571C2×C4×Q8—1221no—
572C2×C4×D4—611no—
573C2×#117—611no—
574C2×#117—611no—
575C2×#117—611no—
576C22×C4⋊C4—611no—
577#435—1221no—
578#435—1221no—
579#435—1221no—
580#435—1221no—
581C2×C4⋊C8—611no—
582C2×#103—611no—
583C2×#103—611no—
584C2×#103—611no—
585C2×#103—611no—
586C2×C22⋊C8—611no—
587C2×C22⋊C8—611no—
588C2×#97—611no—
589#388—1221no—
590#387—1221no—
591#386—1221no—
592#382—611no—
593#380—611no—
594#380—611no—
595C4×C4⋊C4—611no—
596C4×C22⋊C4—1221no—
597#340—611no—
598#340—611no—
599#340—611no—
600#340—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#2249411yescharacteristic, complemented, Sylow
610C22×Q8—611no—
611C22×Q8—1221no—
612C22×D4—611no—
613C23×C4—611no—
614C23×C4—611no—
615C23×C4—1221no—
616C2×M16—1222no—
617C2×M16—1221no—
618C2×M16—1221no—
619C2×M16—2441no—
620C22×C8—611no—
621C22×C8—611no—
622C22×C8—611no—
623C22×C8—611no—
624C22×C8—1222no—
625C22×C8—1221no—
626C22×C8—1221no—
627C22×C8—2441no—
628C4⋊Q8—611no—
629C4⋊Q8—611no—
630C4⋊Q8—611no—
631C4⋊Q8—1221no—
632C4⋊Q8—1221no—
633C4⋊Q8C2×#692311yescharacteristic, complemented
634#126—21no—
635#126—21no—
636#126—1221no—
637#126—1221no—
638#126—1221no—
639#126—1221no—
640#126—1221no—
641#126—1221no—
642#126—1221no—
643#126—1221no—
644#126—1221no—
645#126—1221no—
646#126—1221no—
647#126—1221no—
648#126—1221no—
649#126—1221no—
650#124—21no—
651#124—1221no—
652#124—1221no—
653#124—1221no—
654#124—1221no—
655#124—1221no—
656#124—1221no—
657#124—1221no—
658C22⋊Q8—611no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—1221no—
665C22⋊Q8—1221no—
666C22⋊Q8—1221no—
667C22⋊Q8—1221no—
668C22⋊Q8C2×#692311yescharacteristic
669C22⋊Q8C2×#692311yescharacteristic, complemented
670C4×Q8—21no—
671C4×Q8—611no—
672C4×Q8—611no—
673C4×Q8—611no—
674C4×Q8—1221no—
675C4×Q8—1221no—
676C4×Q8—1221no—
677C4×Q8—1221no—
678C4×Q8—1221no—
679C4×Q8—1221no—
680C4×Q8—1221no—
681C4×Q8—1221no—
682C4×Q8—1221no—
683C4×Q8C2×#692311yescharacteristic, complemented
684C4×D4—611no—
685C4×D4—611no—
686C4×D4—611no—
687C4×D4—611no—
688C4×D4—611no—
689C4×D4—611no—
690C4×D4—611no—
691C4×D4C2×#692311yescharacteristic
692#117—611no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—611no—
697#117—611no—
698#117—1221no—
699#117—1221no—
700#117—1221no—
701#117—1221no—
702#117—1222no—
703#117—2441no—
704#117C2×#692311yescharacteristic
705#117C2×#692311yescharacteristic, complemented
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—611no—
713C2×C4⋊C4—611no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1222no—
719C2×C4⋊C4—1221no—
720C2×C4⋊C4—2441no—
721C2×C22⋊C4—611no—
722C2×C22⋊C4—611no—
723C2×C22⋊C4—1221no—
724C2×C22⋊C4—1221no—
725C2×C22⋊C4—1221no—
726C2×C22⋊C4—1221no—
727C2×C22⋊C4—1221no—
728C2×C22⋊C4—1221no—
729C2×C22⋊C4—1221no—
730C2×C42—611no—
731C2×C42—1221no—
732C2×C42—1221no—
733C2×C42—1221no—
734C2×C42—1221no—
735C2×C42—1221no—
736C4⋊C8—1221no—
737C4⋊C8—1221no—
738#103—1222no—
739#103—1222no—
740#103—2441no—
741#103—2441no—
742C22⋊C8—1221no—
743C22⋊C8—1221no—
744C22⋊C8—1221no—
745C22⋊C8—1221no—
746#97—1221no—
747#97—1221no—
748#95—1221no—
749#95—1221no—
750#95—1221no—
751#95—1221no—
752#95—1221no—
753C24—611no—
754C24—611no—
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—2442no—
766C2×Q8—2442no—
767C2×Q8C22×#692311yescharacteristic
768C2×D4—611no—
769C2×D4—611no—
770C2×D4—611no—
771C2×D4—2441no—
772C2×D4—2441no—
773C2×D4C22⋊#692311yescharacteristic
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
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—4881no—
802C22×C4—2442no—
803C22×C4—2442no—
804C22×C4C22×#692311yescharacteristic
805C22×C4C22×#692311yescharacteristic
806M16—2442no—
807M16—2442no—
808C2×C8—612no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—1221no—
813C2×C8—1221no—
814C2×C8—1221no—
815C2×C8—1221no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—2442no—
821C2×C8—2442no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—611no—
827C4⋊C4—611no—
828C4⋊C4—611no—
829C4⋊C4—612no—
830C4⋊C4—611no—
831C4⋊C4—611no—
832C4⋊C4—611no—
833C4⋊C4—1221no—
834C4⋊C4—1221no—
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—1221no—
855C4⋊C4—2442no—
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—611no—
865C22⋊C4—611no—
866C22⋊C4—611no—
867C22⋊C4—611no—
868C22⋊C4—611no—
869C22⋊C4—611no—
870C22⋊C4—1221no—
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—4881no—
883C22⋊C4—2442no—
884C22⋊C4—2442no—
885C22⋊C4C22⋊#692311yescharacteristic
886C22⋊C4C22⋊#692311yescharacteristic
887C42—21no—
888C42—21no—
889C42—21no—
890C42—611no—
891C42—611no—
892C42—611no—
893C42—1221no—
894C42—1221no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—1221no—
901C42—1221no—
902C42—4881no—
903C42—2442no—
904C42C22×#692311yescharacteristic
905C23—611no—
906C23—611no—
907C23—611no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—1221no—
915C23—1221no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23—1221no—
920C23C2×C22⋊#692311yescharacteristic
921C23C2×C22⋊#692311yescharacteristic
922Q8—21no—
923Q8—21no—
924Q8—42no—
925Q8—1221no—
926Q8—1221no—
927Q8—2442no—
928Q8—2441no—
929Q8—2441no—
930Q8—2442no—
931Q8—2442no—
932D4—41no—
933D4—2441no—
934D4—2441no—
935D4—2441no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—611no—
950C2×C4—611no—
951C2×C4—611no—
952C2×C4—611no—
953C2×C4—1221no—
954C2×C4—1221no—
955C2×C4—1221no—
956C2×C4—1221no—
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—1222no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—4884no—
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×C4—2441no—
998C2×C4C2×C22⋊#692311yescharacteristic
999C2×C4C2×C22⋊#692311yescharacteristic
1000C2×C4C2×C22⋊#692311yescharacteristic
1001C2×C4C2×C22⋊#692311yescharacteristic
1002C2×C4C23×#692311yescharacteristic
1003C8—1222no—
1004C8—2441no—
1005C8—2441no—
1006C8—2441no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—611no—
1014C22—611no—
1015C22—611no—
1016C22—611no—
1017C22—611no—
1018C22—611no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—2441no—
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—41no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—611no—
1043C4—611no—
1044C4—1221no—
1045C4—1221no—
1046C4—1221no—
1047C4—1221no—
1048C4—4881no—
1049C4—4881no—
1050C4—4881no—
1051C4—2442no—
1052C4—2441no—
1053C4—2441no—
1054C4—2441no—
1055C4—2441no—
1056C4#41×#692311yescharacteristic
1057C4#1684083111yescharacteristic
1058C2—41no—
1059C2—41no—
1060C2—611no—
1061C2—611no—
1062C2—611no—
1063C2—611no—
1064C2—2441no—
1065C2—2441no—
1066C2#2146232211yescharacteristic
1067C2#2146243911yescharacteristic
1068C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenter#556#6923
hypocenterC61#22494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
3. #21462003C2semidirect
4. #21461997C2semidirect
5. #21461834C2semidirect
6. #21461832C2semidirect
7. #21461805C2semidirect
8. #21461804C2semidirect
9. #21461724C2semidirect
10. #21461724C2semidirect
11. #21461690C2semidirect
12. #21461591C2semidirect
13. #21461508C2semidirect
14. #21461504C2semidirect
52. #16840486C4semidirect
53. #16840485C4semidirect
55. #16840483C4semidirect
56. #16840483C4semidirect
57. #16840482C4semidirect
59. #16840480C4semidirect
60. #16840480C4semidirect
74. C61×#556C4semidirect
124. #14519777C2×C4semidirect
126. #14519776C2×C4semidirect
127. #14519776C2×C4semidirect
151. #14519757C2×C4semidirect
153. #14519756C2×C4semidirect
159. #14519753C2×C4semidirect
161. Q8×Dic61C2×C4semidirect
166. C4×Dic122C2×C4semidirect
171. #14519742C2×C4semidirect
180. #14519736C2×C4semidirect
183. #14519735C2×C4semidirect
184. #14519735C2×C4semidirect
207. C4⋊Q8×C61C2×C4semidirect
212. C22⋊Q8×C61C2×C4semidirect
214. C4×Q8×C61C2×C4semidirect
217. #117×C61C2×C4semidirect
563. #556#6923semidirect
609. C61#22494semidirect
633. C4⋊Q8C2×#6923semidirect
669. C22⋊Q8C2×#6923semidirect
683. C4×Q8C2×#6923semidirect
705. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
#214623352
#214620032
#214619972
#214618342
#214618322
#214618052
#214618042
#214617242
#214616902
#214615912
#214615082
#214615042
#556×D612
#2249461