Finite Group Databasebeta

← #30616706

Subgroups — #30616706

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#433C211yesmaximal, characteristic, complemented
2#21462256C211yesmaximal, characteristic, complemented
3#21461998C211yesmaximal, characteristic, complemented
4#21461997C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic, complemented
6#21461987C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic
8#21461806C211yesmaximal, characteristic
9#21461805C211yesmaximal, characteristic, complemented
10#21461804C211yesmaximal, characteristic, complemented
11#21461591C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13C4×#14519840C211yesmaximal, characteristic, complemented
14C4×#14519839C211yesmaximal, characteristic, complemented
15#542×D61C211yesmaximal, characteristic
16C2×#14519856C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18#16840787—21no—
19#16840787—21no—
20#16840786—21no—
21#16840786—21no—
22D61⋊(C4⋊C8)C2211yescharacteristic
23D61⋊(C4⋊C8)C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32D61⋊(C22⋊C8)C2211yescharacteristic
33D61⋊(C22⋊C8)C2211yescharacteristic
34#16840721C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36C4⋊C4×#6923—21no—
37C4⋊C4×#6923—21no—
38C4×C4⋊#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40C4×C4⋊#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42C22⋊C4×#6923—21no—
43C22⋊C4×#6923—21no—
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
75C23×#6923—21no—
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C2×D61⋊C8C2311yescharacteristic
80#14519856—22no—
81#14519856—22no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—22no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95#14519844—21no—
96#14519844—21no—
97C4⋊#92420—21no—
98C4⋊#92420—21no—
99#14519840—22no—
100#14519840—22no—
101#14519840—22no—
102#14519840—22no—
103#14519839—22no—
104#14519839—22no—
105#14519839—22no—
106#14519839—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×Q8×D61—21no—
120C2×Q8×D61C2311yescharacteristic
121C2×D4×D61—21no—
122C2×D4×D61C2311yescharacteristic
123C22×C4×D61—21no—
124C22×C4×D61C2311yescharacteristic
125#14519777C2×C411yescharacteristic, complemented
126#14519776—21no—
127#14519776C2×C411yescharacteristic, complemented
128#14519776C2×C411yescharacteristic, complemented
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, complemented
139#14519765—21no—
140#14519765C2×C411yescharacteristic, complemented
141#14519764—21no—
142#14519764C2×C411yescharacteristic, complemented
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, complemented
174C4×Dic122—21no—
175C4×Dic122C2×C411yescharacteristic, complemented
176#14519742—21no—
177#14519742C2×C411yescharacteristic, complemented
178C4×D244C2×C411yescharacteristic, complemented
179D4×Dic61C2×C411yescharacteristic, complemented
180#14519739C2×C411yescharacteristic, complemented
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, 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×D61—21no—
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—24no—
225C22×#6923—81no—
226C22×#6923—81no—
227C2×Q8×C61—21no—
228C2×Q8×C61C22×C411yescharacteristic
229C2×D4×C61—21no—
230C2×D4×C61C22×C411yescharacteristic
231C22×C4×C61—21no—
232C22×C4×C61C22×C411yescharacteristic
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C22×Dic61—21no—
237C22×Dic61C2×D411yescharacteristic
238Q8×D61—21no—
239Q8×D61—21no—
240Q8×D61—21no—
241Q8×D61—21no—
242Q8×D61—81no—
243Q8×D61—81no—
244D4×D61—21no—
245D4×D61—21no—
246D4×D61—21no—
247D4×D61—21no—
248D4×D61—81no—
249D4×D61—81no—
250C2×D244—21no—
251C2×D244C22×C411yescharacteristic
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—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—81no—
262C2×C4×D61—81no—
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2411yescharacteristic
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122C22×C411yescharacteristic
276C22⋊#6923—24no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C4⋊#6923—24no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923#4112yes—
287C4⋊#6923#4112yes—
288C4⋊#6923#4112yes—
289C4⋊#6923#4112yes—
290C4×#6923—24no—
291C4×#6923—81no—
292C4×#6923—81no—
293C4×#6923—81no—
294C4×#6923—81no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—21no—
300D61⋊C8—21no—
301D61⋊C8—21no—
302D61⋊C8—21no—
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—22no—
387C2×#6923—22no—
388C2×#6923—22no—
389C2×#6923—22no—
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—84no—
399Q8×C61—21no—
400Q8×C61—21no—
401Q8×C61—81no—
402D4×C61—21no—
403D4×C61—21no—
404D4×C61—81no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—81no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
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—
419C22⋊D61—81no—
420C22⋊D61—81no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—81no—
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C22×D411yescharacteristic
433D244—21no—
434D244—21no—
435D244—81no—
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—21no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—81no—
457C4×D61—81no—
458C4×D61C2×#4111yescharacteristic
459C4×D61C2×#4111yescharacteristic
460C4×D61C2×#4111yescharacteristic
461C4×D61C2×#4111yescharacteristic
462Dic122—21no—
463Dic122—21no—
464Dic122—41no—
465Dic122—41no—
466Dic122—81no—
467Dic122—81no—
468Dic122—81no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#92420—41no—
473#21397—611nomaximal, Sylow
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61C22×C22⋊C411yescharacteristic
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—81no—
492C2×D61—81no—
493C2×D61—81no—
494C2×D61—81no—
495C2×D61#52511yescharacteristic
496C2×D61#52511yescharacteristic
497C2×D61#57611yescharacteristic
498C2×D61#57711yescharacteristic
499C2×D61#57711yescharacteristic
500C2×D61#57811yescharacteristic
501#6923—42no—
502#6923—42no—
503#6923—42no—
504#6923—42no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61—41no—
513C4×C61C4×#4111yescharacteristic
514C4×C61C4×#4111yescharacteristic
515Dic61—21no—
516Dic61—21no—
517Dic61—21no—
518Dic61—21no—
519Dic61—21no—
520Dic61—41no—
521Dic61—41no—
522Dic61—41no—
523Dic61#53211yescharacteristic
524Dic61#53211yescharacteristic
525C2×#542—611no—
526C2×#433—611no—
527#2274—611no—
528#1988—611no—
529#1987—611no—
530#1983—611no—
531#1983—611no—
532#1875—611no—
533#1874—611no—
534#1873—611no—
535#1872—611no—
536#1763—611no—
537#1762—611no—
538C4×#103—611no—
539C4×#102—611no—
540C2×C61—41no—
541C2×C61—81no—
542C2×C61#229711yescharacteristic
543C2×C61#289711yescharacteristic
544C2×C61#289811yescharacteristic
545D61—41no—
546D61—81no—
547D61#311811yescharacteristic
548D61#312111yescharacteristic
549D61#312411yescharacteristic
550D61#312511yescharacteristic
551#542—611no—
552#542—611no—
553#542—611no—
554#542—611no—
555#542—611no—
556#542—611no—
557#542—611no—
558#542—1221no—
559#542—1221no—
560#542—1221no—
561#542—1221no—
562#542#692311yescharacteristic, complemented
563C2×C4⋊Q8—611no—
564C2×#126—1221no—
565C2×#124—611no—
566C2×#124—1221no—
567C2×#123—1221no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—1221no—
570C2×#121—611no—
571C2×C4×Q8—611no—
572C2×C4×D4—611no—
573C2×#117—611no—
574C2×#117—611no—
575C22×C4⋊C4—611no—
576#433—1221no—
577#433—1221no—
578#433—1221no—
579#433—1221no—
580C2×C4⋊C8—611no—
581C2×C4⋊C8—611no—
582C2×#103—611no—
583C2×#103—611no—
584C2×#103—611no—
585C2×#103—611no—
586C2×#102—611no—
587C2×#102—611no—
588C2×#102—611no—
589C2×#102—611no—
590C2×C22⋊C8—611no—
591C2×C22⋊C8—611no—
592C2×#97—611no—
593C2×C4×C8—611no—
594C4×C4⋊C4—611no—
595C4×C4⋊C4—611no—
596C4×C4⋊C4—611no—
597C4×C4⋊C4—611no—
598C4×C4⋊C4—1221no—
599C4×C4⋊C4—1221no—
600C4×C22⋊C4—1221no—
601C4×C22⋊C4—1221no—
602#340—611no—
603#340—611no—
604#340—611no—
605#340—611no—
606#340—611no—
607#340—611no—
608#340—611no—
609#340—611no—
610C61#2139711yescharacteristic, complemented, Sylow
611C22×Q8—611no—
612C22×Q8—1221no—
613C22×D4—611no—
614C22×D4—1221no—
615C23×C4—611no—
616C23×C4—1221no—
617C23×C4—1221no—
618C22×C8—611no—
619C22×C8—611no—
620C22×C8—611no—
621C22×C8—611no—
622C4⋊Q8—611no—
623C4⋊Q8—611no—
624C4⋊Q8—611no—
625C4⋊Q8—1221no—
626C4⋊Q8—1221no—
627C4⋊Q8C2×#692311yescharacteristic, complemented
628#126—21no—
629#126—1221no—
630#126—1221no—
631#126—1221no—
632#126—1221no—
633#126—1221no—
634#126—1221no—
635#126—1221no—
636#124—21no—
637#124—611no—
638#124—611no—
639#124—611no—
640#124—1221no—
641#124—1221no—
642#124—1221no—
643#124—1221no—
644#124—1221no—
645#124—1221no—
646#124—1221no—
647#124—1221no—
648#124—1221no—
649#124C2×#692311yescharacteristic, complemented
650#123—21no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658C22⋊Q8—21no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—1221no—
663C22⋊Q8—1221no—
664C22⋊Q8—1221no—
665C22⋊Q8—1221no—
666C22⋊Q8—1221no—
667C22⋊Q8—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8C2×#692311yescharacteristic
672#121—611no—
673#121—611no—
674#121—611no—
675#121—1221no—
676#121—1221no—
677#121C2×#692311yescharacteristic
678C4×Q8—611no—
679C4×Q8—611no—
680C4×Q8—611no—
681C4×Q8—1221no—
682C4×Q8—1221no—
683C4×Q8C2×#692311yescharacteristic, complemented
684C4×D4—611no—
685C4×D4—611no—
686C4×D4—611no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4C2×#692311yescharacteristic, complemented
690#117—611no—
691#117—611no—
692#117—611no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—611no—
697#117—1222no—
698#117—1222no—
699#117C2×#692311yescharacteristic
700C2×C4⋊C4—611no—
701C2×C4⋊C4—611no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—1221no—
709C2×C4⋊C4—1221no—
710C2×C4⋊C4—1221no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1221no—
714C2×C22⋊C4—611no—
715C2×C22⋊C4—611no—
716C2×C22⋊C4—1221no—
717C2×C22⋊C4—1221no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—1221no—
725C2×C42—1221no—
726C2×C42—1221no—
727C2×C42—1221no—
728C2×C42—1221no—
729C2×C42—1221no—
730C4⋊C8—1221no—
731C4⋊C8—1221no—
732C4⋊C8—1221no—
733C4⋊C8—1221no—
734#103—1222no—
735#103—1222no—
736#103—1222no—
737#103—1222no—
738#102—1222no—
739#102—1222no—
740#102—1222no—
741#102—1222no—
742C22⋊C8—1221no—
743C22⋊C8—1221no—
744C22⋊C8—1221no—
745C22⋊C8—1221no—
746#97—1221no—
747#97—1221no—
748C4×C8—1221no—
749C4×C8—1221no—
750#95—1221no—
751#95—1221no—
752#95—1221no—
753#95—1221no—
754C24—611no—
755C24—1221no—
756C2×Q8—21no—
757C2×Q8—611no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—4881no—
767C2×Q8—4881no—
768C2×Q8C22×#692311yescharacteristic
769C2×D4—21no—
770C2×D4—611no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—1221no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—1221no—
779C2×D4—4881no—
780C2×D4—4881no—
781C2×D4C22×#692311yescharacteristic
782C22×C4—21no—
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—611no—
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—1224no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—4881no—
808C22×C4—4881no—
809C22×C4—4881no—
810C22×C4—4881no—
811C22×C4C22×#692311yescharacteristic
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—1221no—
821C2×C8—1221no—
822C2×C8—1221no—
823C2×C8—1221no—
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—612no—
834C4⋊C4—612no—
835C4⋊C4—612no—
836C4⋊C4—612no—
837C4⋊C4—611no—
838C4⋊C4—611no—
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—1224no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4C22⋊#692311yescharacteristic
856C4⋊C4C22⋊#692311yescharacteristic
857C4⋊C4C22×#692311yescharacteristic
858C4⋊C4C22×#692311yescharacteristic
859C22⋊C4—21no—
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—1224no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—1221no—
886C22⋊C4C22⋊#692311yescharacteristic
887C22⋊C4C22⋊#692311yescharacteristic
888C42—21no—
889C42—611no—
890C42—611no—
891C42—611no—
892C42—611no—
893C42—611no—
894C42—611no—
895C42—1221no—
896C42—1221no—
897C42—1224no—
898C42—1221no—
899C42—4881no—
900C42—4881no—
901C42—4881no—
902C42—4881no—
903C42C22×#692311yescharacteristic
904C42C22×#692311yescharacteristic
905C23—21no—
906C23—611no—
907C23—611no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—1221no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23—2441no—
921C23C2×C22⋊#692311yescharacteristic
922Q8—21no—
923Q8—21no—
924Q8—81no—
925Q8—1221no—
926Q8—1221no—
927Q8—4881no—
928Q8—4881no—
929Q8—4881no—
930Q8—2441no—
931Q8—2441no—
932D4—21no—
933D4—21no—
934D4—81no—
935D4—1221no—
936D4—1221no—
937D4—4881no—
938D4—4881no—
939D4—4881no—
940D4—2441no—
941D4—2441no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—81no—
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—611no—
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—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—4881no—
982C2×C4—4881no—
983C2×C4—4881no—
984C2×C4—4884no—
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×C4—2441no—
999C2×C4C2×C22⋊#692311yescharacteristic
1000C2×C4C2×C22⋊#692311yescharacteristic
1001C2×C4C2×C22⋊#692311yescharacteristic
1002C2×C4C2×C22⋊#692311yescharacteristic
1003C2×C4C2×C22⋊#692311yescharacteristic
1004C2×C4C23×#692311yescharacteristic
1005C8—2441no—
1006C8—2441no—
1007C8—2441no—
1008C8—2441no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—611no—
1016C22—611no—
1017C22—611no—
1018C22—611no—
1019C22—611no—
1020C22—611no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—4881no—
1025C22—4881no—
1026C22—4881no—
1027C22—4881no—
1028C22—2441no—
1029C22—2441no—
1030C22—2441no—
1031C22—2441no—
1032C22—2441no—
1033C22—2441no—
1034C22—2441no—
1035C22C22×C22⋊#692311yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—611no—
1045C4—611no—
1046C4—1221no—
1047C4—1221no—
1048C4—1221no—
1049C4—1221no—
1050C4—1221no—
1051C4—2442no—
1052C4—2442no—
1053C4—2442no—
1054C4—2442no—
1055C4—2441no—
1056C4—2441no—
1057C4—2441no—
1058C4#41×#692311yescharacteristic
1059C4#41×#692311yescharacteristic
1060C2—41no—
1061C2—81no—
1062C2—611no—
1063C2—611no—
1064C2—611no—
1065C2—611no—
1066C2—4881no—
1067C2—2441no—
1068C2#2146228011yescharacteristic
1069C2#2146244011yescharacteristic
1070C2#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#21397
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. D61⋊#433C2semidirect
2. #21462256C2semidirect
3. #21461998C2semidirect
4. #21461997C2semidirect
5. #21461987C2semidirect
6. #21461987C2semidirect
9. #21461805C2semidirect
10. #21461804C2semidirect
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
125. #14519777C2×C4semidirect
127. #14519776C2×C4semidirect
128. #14519776C2×C4semidirect
138. #14519766C2×C4semidirect
140. #14519765C2×C4semidirect
142. #14519764C2×C4semidirect
173. Q8×Dic61C2×C4semidirect
175. C4×Dic122C2×C4semidirect
177. #14519742C2×C4semidirect
178. C4×D244C2×C4semidirect
179. D4×Dic61C2×C4semidirect
180. #14519739C2×C4semidirect
207. C4⋊Q8×C61C2×C4semidirect
210. #124×C61C2×C4semidirect
215. C4×Q8×C61C2×C4semidirect
216. C4×D4×C61C2×C4semidirect
562. #542#6923semidirect
610. C61#21397semidirect
627. C4⋊Q8C2×#6923semidirect
649. #124C2×#6923semidirect
683. C4×Q8C2×#6923semidirect
689. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4332
#214622562
#214619982
#214619972
#214619872
#214618072
#214618062
#214618052
#214618042
#214615912
#214615892
C4×#145198402
C4×#145198392
#542×D612
#2139761