Finite Group Databasebeta

← #30611376

Subgroups — #30611376

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic
2#21462336C211yesmaximal, characteristic
3#21461259C211yesmaximal, characteristic, complemented
4#21461257C211yesmaximal, characteristic, complemented
5#21461243C211yesmaximal, characteristic, complemented
6#21461241C211yesmaximal, characteristic, complemented
7#21461229C211yesmaximal, characteristic, complemented
8#21461228C211yesmaximal, characteristic, complemented
9#21461219C211yesmaximal, characteristic, complemented
10#21461217C211yesmaximal, characteristic, complemented
11#21461213C211yesmaximal, characteristic, complemented
12#21461212C211yesmaximal, characteristic, complemented
13C2×#16840616C211yesmaximal, characteristic, complemented
14D61⋊#328C211yesmaximal, characteristic, complemented
15#21459614C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic
21#16840784C2211yescharacteristic
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic
30#16840705C2211yescharacteristic
31#16840704C2211yescharacteristic
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic
34#16840698C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840616C2211yescharacteristic
41#16840616C2211yescharacteristic
42#16840616C2211yescharacteristic
43#16840616C2211yescharacteristic
44#16840616C2211yescharacteristic
45#16840616C2211yescharacteristic
46#16840616C2211yescharacteristic
47#16840616C2211yescharacteristic
48#16840615C2211yescharacteristic
49#16840615C2211yescharacteristic
50#16840615C2211yescharacteristic
51#16840615C2211yescharacteristic
52#16840473—21no—
53#16840472C411yescharacteristic, complemented
54#16840471—21no—
55#16840470C411yescharacteristic, complemented
56#16840470C411yescharacteristic, complemented
57#16840469C411yescharacteristic, complemented
58#16840466—21no—
59#16840466—21no—
60#16840427C411yescharacteristic, complemented
61Q8×C22⋊D61C411yescharacteristic, complemented
62Q8×C22⋊D61C411yescharacteristic, complemented
63#16840389—21no—
64#16840387—21no—
65#16840387—21no—
66#16840317C2211yescharacteristic
67#16840316C2211yescharacteristic
68C2×#14519753C2211yescharacteristic
69C2×#14519753C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74D4×Q8×C61C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×Q8×D61C2×C411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic, complemented
109C2×D4×D61D411yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112#14519777C2×C411yescharacteristic, complemented
113#14519776—21no—
114#14519776C2×C411yescharacteristic, complemented
115#14519775—21no—
116#14519775—21no—
117#14519775C2×C411yescharacteristic, complemented
118#14519769—21no—
119#14519768—21no—
120#14519768—21no—
121#14519767—21no—
122#14519767—21no—
123#14519767—21no—
124#14519757—21no—
125#14519757—21no—
126#14519757—21no—
127#14519757C2311yescharacteristic
128#14519756—21no—
129#14519756—21no—
130#14519756C2×C411yescharacteristic
131#14519756C2×C411yescharacteristic, complemented
132#14519755—21no—
133#14519755—21no—
134#14519755—21no—
135#14519755—21no—
136#14519755—21no—
137#14519755—21no—
138#14519755—21no—
139#14519754—21no—
140#14519754—21no—
141#14519754—21no—
142#14519754—21no—
143#14519754—21no—
144#14519754—21no—
145#14519753—21no—
146#14519753—21no—
147#14519753—21no—
148#14519753—21no—
149#14519753—21no—
150#14519753—21no—
151#14519753C2×C411yescharacteristic
152#14519753C2×C411yescharacteristic
153#14519753C2×C411yescharacteristic, complemented
154#14519753C2×C411yescharacteristic, complemented
155#14519753C2311yescharacteristic
156#14519753C2311yescharacteristic
157#14519753C2311yescharacteristic
158Q8×Dic61C2×C411yescharacteristic, complemented
159Q8×Dic61C2×C411yescharacteristic, complemented
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic, complemented
162#14519742—21no—
163C4×D244—21no—
164C4×D244C2×C411yescharacteristic
165D4×Dic61—21no—
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61C2×C411yescharacteristic
172C4×C22⋊D61C2×C411yescharacteristic
173#14519737—21no—
174#14519737—21no—
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519735—21no—
178#14519734—21no—
179C2×C4⋊Dic61C2×C411yescharacteristic
180C2×C4⋊Dic61C2×C411yescharacteristic, complemented
181C2×#11758196—21no—
182C2×#11758196—21no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61C2×C411yescharacteristic
186C4⋊C4×D61C2×C411yescharacteristic, complemented
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C22×Q8×C61C2×C411yescharacteristic
196C22×Q8×C61C2×C411yescharacteristic, complemented
197C4⋊Q8×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic, complemented
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202C22⋊Q8×C61C2×C411yescharacteristic, complemented
203C4×Q8×C61C2×C411yescharacteristic, complemented
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—42no—
213C22×#6923—42no—
214C22×#6923—81no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—81no—
218C2×Q8×C61—81no—
219C2×Q8×C61C22×C411yescharacteristic
220C2×Q8×C61C22×C411yescharacteristic
221C2×Q8×C61C22×C411yescharacteristic
222C2×D4×C61C22⋊C411yescharacteristic
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C2×C22⋊D61C22⋊C411yescharacteristic
228C2×C22⋊D61C22⋊C411yescharacteristic
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233Q8×D61—81no—
234Q8×D61—81no—
235D4×D61—22no—
236D4×D61—22no—
237C2×D244C22⋊C411yescharacteristic
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—81no—
243C2×C4×D61—81no—
244C2×C4×D61C22×C411yescharacteristic
245C2×C4×D61C22×C411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2411yescharacteristic
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122C22×C411yescharacteristic
258C22⋊#6923—42no—
259C22⋊#6923—42no—
260C22⋊#6923—81no—
261#11758217—81no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—81no—
267C4⋊#6923—81no—
268C4×#6923—42no—
269C4×#6923—81no—
270#11758213—81no—
271D61⋊C8—81no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C22⋊C411yescharacteristic
278C4⋊C4×C61C22×C411yescharacteristic
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61C22⋊C411yescharacteristic
282C22⋊C4×C61C22⋊C411yescharacteristic
283C42×C61—21no—
284C42×C61C22×C411yescharacteristic
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61C2×C22⋊C411yescharacteristic
343C22×D61C2×C22⋊C411yescharacteristic
344C22×D61#13712yes—
345C22×D61#13712yes—
346C22×D61C22×D411yescharacteristic
347C2×#6923—22no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—84no—
360Q8×C61—41no—
361Q8×C61—41no—
362Q8×C61—41no—
363Q8×C61—81no—
364Q8×C61—81no—
365D4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—81no—
373C2×C4×C61—81no—
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C22⋊D61—22no—
380C22⋊D61—22no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—81no—
388C2×Dic61—81no—
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C22×D411yescharacteristic
394D244—22no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—41no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—81no—
406C4×D61—81no—
407C4×D61—81no—
408C4×D61—81no—
409Dic122—41no—
410Dic122—81no—
411Dic122—81no—
412Dic122—81no—
413Dic122—81no—
414#92420—41no—
415#92420—41no—
416#92420—41no—
417#92420—41no—
418#17621—611nomaximal, Sylow
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61#41912yes—
425C22×C61C22×C22⋊C411yescharacteristic
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—81no—
436C2×D61—81no—
437C2×D61#41912yes—
438C2×D61C2×#13711yescharacteristic
439C2×D61C2×#13711yescharacteristic
440#6923—42no—
441#6923—81no—
442#6923—81no—
443#6923—81no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61—41no—
452C4×C61—41no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—41no—
459Dic61—41no—
460Dic61—41no—
461Dic61—41no—
462#3501—611no—
463#2973—611no—
464#2353—611no—
465#1520—611no—
466#1520—611no—
467#1515—611no—
468#1515—611no—
469#1511—611no—
470#1511—611no—
471#1508—611no—
472#1508—611no—
473#1506—611no—
474#1506—611no—
475C2×#328—611no—
476C2×#328—611no—
477C2×C61—22no—
478C2×C61—41no—
479C2×C61#288311yescharacteristic
480C2×C61C2×#41911yescharacteristic
481C2×C61#290111yescharacteristic
482D61—21no—
483D61—21no—
484D61—22no—
485D61—41no—
486#554—611no—
487#554—611no—
488#554—611no—
489#554—611no—
490#554—1221no—
491#554—1221no—
492#554—1221no—
493#554—1221no—
494D4×Q8—611no—
495D4×Q8—611no—
496D4×Q8—611no—
497D4×Q8#692311yescharacteristic, complemented
498#544—1221no—
499#543—1221no—
500#543—1221no—
501#533—611no—
502#533—611no—
503C2×C22⋊Q8—611no—
504C2×C22⋊Q8—611no—
505C2×C22⋊Q8—611no—
506C2×C22⋊Q8—611no—
507#518—1221no—
508C2×C4×D4—611no—
509#435—1221no—
510#435—1221no—
511#435—1221no—
512#435—1221no—
513#432—611no—
514#432—611no—
515#407—611no—
516#407—611no—
517C2×C22⋊C8—611no—
518C2×C22⋊C8—611no—
519#388—1221no—
520#387—1221no—
521#386—1221no—
522#383—611no—
523#381—611no—
524#380—611no—
525C4×C22⋊C4—611no—
526C4×C22⋊C4—1221no—
527#376—611no—
528C2×#95—611no—
529#328—611no—
530#328—611no—
531#328—611no—
532#328—611no—
533#328—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#328—611no—
538#328—611no—
539#328—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328—611no—
545C61#1762111yescharacteristic, complemented, Sylow
546C22×Q8—611no—
547C22×Q8—611no—
548C22×Q8C2×#692311yescharacteristic
549C22×Q8C2×#692311yescharacteristic, complemented
550C22×D4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—1221no—
554C2×M16—1221no—
555C2×M16—1221no—
556C22×C8—1221no—
557C22×C8—1221no—
558C4⋊Q8—21no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—611no—
562C4⋊Q8—1221no—
563C4⋊Q8—1221no—
564C4⋊Q8—1221no—
565C4⋊Q8C2×#692311yescharacteristic, complemented
566#125—1221no—
567#125—1221no—
568#125—1221no—
569#125—1221no—
570#125—1221no—
571#125—1221no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—611no—
575C22⋊Q8—611no—
576C22⋊Q8—611no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—611no—
580C22⋊Q8—611no—
581C22⋊Q8—611no—
582C22⋊Q8—611no—
583C22⋊Q8—611no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586C22⋊Q8—1221no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8C2×#692311yescharacteristic
609C22⋊Q8C2×#692311yescharacteristic, complemented
610C4×Q8—611no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×Q8—1221no—
614C4×Q8—1221no—
615C4×Q8C2×#692311yescharacteristic, complemented
616C4×D4—21no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4C2×#692311yescharacteristic
632#117—1221no—
633#117—1221no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—611no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C4⋊C4—1221no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C22⋊C4—611no—
645C2×C22⋊C4—611no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C42—611no—
654C2×C42—1221no—
655C2×C42—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C22⋊C8—611no—
659C22⋊C8—611no—
660C22⋊C8—611no—
661C22⋊C8—611no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C22⋊C8—1221no—
665C22⋊C8—1221no—
666#97—1221no—
667#97—1221no—
668#95—611no—
669#95—611no—
670#95—611no—
671#95—611no—
672#95—1221no—
673#95—1221no—
674#95—1221no—
675#95—1221no—
676#95—1221no—
677C24—611no—
678C24—611no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—81no—
682C2×Q8—81no—
683C2×Q8—611no—
684C2×Q8—1221no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—4881no—
689C2×Q8—4881no—
690C2×Q8C22×#692311yescharacteristic
691C2×Q8C22×#692311yescharacteristic
692C2×Q8C22×#692311yescharacteristic
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4C22⋊#692311yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—4881no—
723C22×C4—4881no—
724C22×C4—4881no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4C22×#692311yescharacteristic
728C22×C4C22×#692311yescharacteristic
729M16—4881no—
730M16—4881no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—4881no—
736C2×C8—4881no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—4881no—
770C4⋊C4C22⋊#692311yescharacteristic
771C4⋊C4C22×#692311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—611no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—4881no—
791C22⋊C4—2442no—
792C22⋊C4—2442no—
793C22⋊C4C22⋊#692311yescharacteristic
794C22⋊C4C22⋊#692311yescharacteristic
795C42—21no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—1221no—
800C42—1221no—
801C42—1221no—
802C42—4881no—
803C42—2442no—
804C42C22×#692311yescharacteristic
805C23—611no—
806C23—611no—
807C23—612no—
808C23—612no—
809C23—611no—
810C23—1221no—
811C23—1221no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23C2×C22⋊#692311yescharacteristic
817C23C2×C22⋊#692311yescharacteristic
818Q8—41no—
819Q8—41no—
820Q8—41no—
821Q8—81no—
822Q8—81no—
823Q8—4881no—
824Q8—4881no—
825Q8—4881no—
826Q8—4881no—
827Q8—2441no—
828D4—22no—
829D4—1222no—
830D4—1222no—
831D4—1222no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1222no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—4881no—
853C2×C4—4881no—
854C2×C4—4881no—
855C2×C4—4881no—
856C2×C4—4884no—
857C2×C4—4881no—
858C2×C4—4881no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4C2×C22⋊#692311yescharacteristic
881C2×C4C2×C22⋊#692311yescharacteristic
882C2×C4C2×C22⋊#692311yescharacteristic
883C2×C4C2×C22⋊#692311yescharacteristic
884C2×C4C23×#692311yescharacteristic
885C8—2441no—
886C8—2441no—
887C8—2441no—
888C8—2441no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—611no—
895C22—611no—
896C22—612no—
897C22—1221no—
898C22—1221no—
899C22—1221no—
900C22—1221no—
901C22—1221no—
902C22—1221no—
903C22—1221no—
904C22—4881no—
905C22—4881no—
906C22—2442no—
907C22—2442no—
908C22#1684075512yes—
909C22C22×C22⋊#692311yescharacteristic
910C4—21no—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4—1221no—
920C4—1221no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—4881no—
925C4—4881no—
926C4—4881no—
927C4—2442no—
928C4—2441no—
929C4—2441no—
930C4—2441no—
931C4—2441no—
932C2—22no—
933C2—41no—
934C2—1221no—
935C2—1221no—
936C2—1222no—
937C2—2441no—
938C2#2146241811yescharacteristic
939C2C2×#1684075511yescharacteristic
940C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenterD4×Q8#6923
hypocenterC61#17621
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461259C2semidirect
4. #21461257C2semidirect
5. #21461243C2semidirect
6. #21461241C2semidirect
7. #21461229C2semidirect
8. #21461228C2semidirect
9. #21461219C2semidirect
10. #21461217C2semidirect
11. #21461213C2semidirect
12. #21461212C2semidirect
13. C2×#16840616C2semidirect
14. D61⋊#328C2semidirect
53. #16840472C4semidirect
55. #16840470C4semidirect
56. #16840470C4semidirect
57. #16840469C4semidirect
60. #16840427C4semidirect
61. Q8×C22⋊D61C4semidirect
62. Q8×C22⋊D61C4semidirect
74. D4×Q8×C61C4semidirect
108. C2×Q8×D61C2×C4semidirect
112. #14519777C2×C4semidirect
114. #14519776C2×C4semidirect
117. #14519775C2×C4semidirect
131. #14519756C2×C4semidirect
153. #14519753C2×C4semidirect
154. #14519753C2×C4semidirect
158. Q8×Dic61C2×C4semidirect
159. Q8×Dic61C2×C4semidirect
161. C4×Dic122C2×C4semidirect
180. C2×C4⋊Dic61C2×C4semidirect
186. C4⋊C4×D61C2×C4semidirect
196. C22×Q8×C61C2×C4semidirect
198. C4⋊Q8×C61C2×C4semidirect
202. C22⋊Q8×C61C2×C4semidirect
203. C4×Q8×C61C2×C4semidirect
497. D4×Q8#6923semidirect
545. C61#17621semidirect
549. C22×Q8C2×#6923semidirect
565. C4⋊Q8C2×#6923semidirect
609. C22⋊Q8C2×#6923semidirect
615. C4×Q8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612592
#214612572
#214612432
#214612412
#214612292
#214612282
#214612192
#214612172
#214612132
#214612122
C2×#168406162
D61⋊#3282
#214596142
#1762161