Finite Group Databasebeta

← #30610793

Subgroups — #30610793

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462629C211yesmaximal, characteristic, complemented
2#21462514C211yesmaximal, characteristic, complemented
3#21461179C211yesmaximal, characteristic, complemented
4#21461178C211yesmaximal, characteristic, complemented
5#21461164C211yesmaximal, characteristic, complemented
6#21461159C211yesmaximal, characteristic, complemented
7#21461158C211yesmaximal, characteristic, complemented
8#21461144C211yesmaximal, characteristic, complemented
9#21461139C211yesmaximal, characteristic, complemented
10#21461138C211yesmaximal, characteristic, complemented
11#21461124C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461118C211yesmaximal, characteristic, complemented
14C2×D4⋊#92420C211yesmaximal, characteristic, complemented
15D4×#11758224C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic, complemented
23#16840783C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic, complemented
25#16840780C2211yescharacteristic, complemented
26#16840779C2211yescharacteristic, complemented
27#16840778C2211yescharacteristic, complemented
28#16840778C2211yescharacteristic, complemented
29#16840765C2211yescharacteristic, complemented
30C2×C4⋊#92420C2211yescharacteristic, complemented
31#16840735—21no—
32#16840726—21no—
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36#16840610C2211yescharacteristic, complemented
37#16840610C2211yescharacteristic, complemented
38#16840610C2211yescharacteristic, complemented
39#16840610C2211yescharacteristic, complemented
40D4⋊#92420C2211yescharacteristic
41D4⋊#92420C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic, complemented
45D4⋊#92420C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52C22×#11758224—21no—
53#16840432C411yescharacteristic
54D4×Dic122C411yescharacteristic
55#16840418—21no—
56#16840416C411yescharacteristic
57#16840412C411yescharacteristic
58#16840412C411yescharacteristic
59#16840406—21no—
60#16840399—21no—
61#16840399—21no—
62D4×C22⋊D61C411yescharacteristic
63D4×C22⋊D61C411yescharacteristic
64#16840310C2211yescharacteristic
65#16840307C2211yescharacteristic
66#16840307C2211yescharacteristic
67#16840272—21no—
68#16840268—21no—
69#16840268—21no—
70C4×#11758224C2211yescharacteristic
71C2×D4×Dic61C2211yescharacteristic
72C2×D4×Dic61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74D42×C61C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758224—21no—
108C2×#11758224—21no—
109C2×#11758224—21no—
110C2×#11758224—21no—
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—44no—
115C2×#11758224—44no—
116C2×#11758224D411yescharacteristic
117C22×Dic122—21no—
118C22×C22⋊D61—21no—
119C22×C22⋊D61—21no—
120C2×D4×D61C2×C411yescharacteristic
121C23×Dic61—21no—
122C23×Dic61—21no—
123C22×C4×D61—21no—
124#14519777C2×C411yescharacteristic
125#14519776C2×C411yescharacteristic
126#14519776C2×C411yescharacteristic
127#14519773C2×C411yescharacteristic
128#14519773C2×C411yescharacteristic
129#14519764—21no—
130#14519763—21no—
131#14519763—21no—
132#14519761—21no—
133#14519761—21no—
134#14519759—21no—
135#14519759—21no—
136#14519758—21no—
137#14519758—21no—
138#14519757—21no—
139#14519756—21no—
140#14519754—21no—
141#14519754—21no—
142#14519754—21no—
143#14519754—21no—
144#14519751C2×C411yescharacteristic
145#14519751C2×C411yescharacteristic
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519749—21no—
150#14519749—21no—
151#14519749—21no—
152#14519748—21no—
153#14519748—21no—
154#14519748C2×C411yescharacteristic
155#14519748C2×C411yescharacteristic
156#14519746—21no—
157#14519746—21no—
158#14519745—21no—
159#14519745—21no—
160C4×Dic122C2×C411yescharacteristic
161#14519742D411yescharacteristic
162C4×D244C2×C411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61—21no—
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61C2×C411yescharacteristic
170D4×Dic61C2×C411yescharacteristic
171D4×Dic61C2×C411yescharacteristic
172D4×Dic61D411yescharacteristic
173D4×Dic61C2311yescharacteristic
174D4×Dic61C2311yescharacteristic
175D4×Dic61C2311yescharacteristic
176#14519739C2311yescharacteristic
177C4×C22⋊D61—21no—
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737—21no—
181#14519737—21no—
182#14519737—21no—
183#14519737D411yescharacteristic
184#14519737D411yescharacteristic
185#14519735D411yescharacteristic
186#14519733D411yescharacteristic
187#14519733D411yescharacteristic
188C2×C4⋊Dic61C2×C411yescharacteristic
189C2×C4⋊Dic61C2×C411yescharacteristic
190C4⋊C4×D61C2×C411yescharacteristic
191C2×C22⋊Dic61—21no—
192C2×C22⋊Dic61—21no—
193C22⋊C4×D61—21no—
194C2×C4×Dic61C2311yescharacteristic
195C2×C4×Dic61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C22×D4×C61—21no—
198C22×D4×C61C2×C411yescharacteristic
199C22×D4×C61C2×C411yescharacteristic
200#127×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic
204#120×C61—21no—
205#120×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207C4×D4×C61C2×C411yescharacteristic
208C24×C61—21no—
209C24×C61—21no—
210C23×D61—21no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—41no—
220C2×D4×C61—41no—
221C2×D4×C61—44no—
222C2×D4×C61C22⋊C411yescharacteristic
223C2×D4×C61C22×C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—44no—
239C2×C22⋊D61—44no—
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—42no—
252C22×Dic61—42no—
253C22×Dic61—42no—
254C22×Dic61—42no—
255C22×Dic61C2×D411yescharacteristic
256C22×Dic61C2×D411yescharacteristic
257C22×Dic61C2×D411yescharacteristic
258C22×Dic61C2×D411yescharacteristic
259#11758224—22no—
260#11758224—22no—
261#11758224—44no—
262#11758224—42no—
263#11758224—42no—
264#11758224—42no—
265#11758224—42no—
266#11758224—44no—
267#11758224—44no—
268#11758224—44no—
269#11758224—42no—
270#11758224—42no—
271D4×D61—22no—
272D4×D61—41no—
273C2×D244C22×C411yescharacteristic
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—42no—
278C2×C4×D61—42no—
279C2×C4×D61C22×C411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D411yescharacteristic
282C2×Dic122—21no—
283C2×Dic122—21no—
284C2×Dic122—21no—
285C2×Dic122—44no—
286C2×Dic122C22⋊C411yescharacteristic
287#11758217—42no—
288#11758217—42no—
289C2×#92420—21no—
290C2×#92420—21no—
291C2×#92420—21no—
292C2×#92420—21no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—21no—
297C2×#92420—42no—
298C2×#92420—42no—
299#11758213—42no—
300C4⋊C4×C61C22⋊C411yescharacteristic
301C4⋊C4×C61C22×C411yescharacteristic
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61C22⋊C411yescharacteristic
306C22⋊C4×C61C22⋊C411yescharacteristic
307C42×C61C22×C411yescharacteristic
308C22⋊Dic61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61C22⋊C411yescharacteristic
318C22⋊Dic61C22⋊C411yescharacteristic
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198C22⋊C411yescharacteristic
324#11758198C22⋊C411yescharacteristic
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61C22⋊C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196C22⋊C411yescharacteristic
336#11758196C22⋊C411yescharacteristic
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339C4×Dic61C22×C411yescharacteristic
340C4×Dic61C22×C411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C4×Dic61C2×D411yescharacteristic
346C4×Dic61C2×D411yescharacteristic
347C4×Dic61C2411yescharacteristic
348C23×C61—21no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—42no—
354C23×C61—42no—
355C23×C61—81no—
356C23×C61—81no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C22×D61—21no—
360C22×D61—42no—
361C22×D61—42no—
362C22×D61—81no—
363C22×D61C2×C22⋊C411yescharacteristic
364D4×C61—22no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—21no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—42no—
375D4×C61—81no—
376D4×C61#13112yes—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—42no—
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C23×C411yescharacteristic
388C22⋊D61—22no—
389C22⋊D61—22no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—42no—
409C2×Dic61—42no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—42no—
417C2×Dic61—42no—
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61AGL(1,ℤ/8)12yes—
424C2×Dic61AGL(1,ℤ/8)12yes—
425C2×Dic61C22×D411yescharacteristic
426C2×Dic61C22×D411yescharacteristic
427D244—21no—
428D244—21no—
429C4×D61—21no—
430C4×D61—21no—
431C4×D61—21no—
432C4×D61—21no—
433C4×D61—41no—
434C4×D61—42no—
435C4×D61—42no—
436C4×D61—41no—
437C4×D61—41no—
438Dic122—22no—
439Dic122—42no—
440Dic122—42no—
441Dic122—42no—
442#92420—22no—
443#92420—41no—
444#92420—41no—
445#92420—41no—
446#92420—41no—
447#92420—41no—
448#92420—41no—
449#92420—41no—
450#17511—611nomaximal, Sylow
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—22no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—84no—
466C22×C61—84no—
467C22×C61#41812yes—
468C22×C61C22×C22⋊C411yescharacteristic
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—41no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—84no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—41no—
481C4×C61C2×#13111yescharacteristic
482C4×C61#56811yescharacteristic
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—41no—
489Dic61—41no—
490Dic61—41no—
491Dic61#41812yes—
492Dic61C2×AGL(1,ℤ/8)11yescharacteristic
493Dic61C2×AGL(1,ℤ/8)11yescharacteristic
494D4×#41—611no—
495#2965—611no—
496#2925—611no—
497#1496—611no—
498#1496—611no—
499#1492—611no—
500#1490—611no—
501#1490—611no—
502#1486—611no—
503#1484—611no—
504#1484—611no—
505#1480—611no—
506#1478—611no—
507#1478—611no—
508C2×D4⋊C8—611no—
509C2×C61—22no—
510C2×C61—42no—
511C2×C61—41no—
512C2×C61—81no—
513C2×C61—81no—
514C2×C61#288011yescharacteristic
515C2×C61C2×#41811yescharacteristic
516C2×C61#290111yescharacteristic
517D61—41no—
518D61—81no—
519C22×#41—1221no—
520#550—611no—
521D4×Q8—611no—
522#548—1221no—
523#547—611no—
524#547—611no—
525#547—611no—
526#546—1221no—
527#546—1221no—
528#546—1221no—
529D42—611no—
530D42—611no—
531D42#692311yescharacteristic
532#532—611no—
533#532—611no—
534#532—611no—
535#525—1221no—
536#525—1221no—
537#525—1221no—
538C4×#41—611no—
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—611no—
542#446—1221no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546#433—1221no—
547#433—1221no—
548#432—611no—
549#432—611no—
550#431—611no—
551#431—611no—
552#431—611no—
553#431—611no—
554#431—611no—
555#423—611no—
556C2×C4⋊C8—611no—
557#408—1221no—
558#405—1221no—
559C4×M16—611no—
560C4×M16—611no—
561C2×C4×C8—611no—
562D4⋊C8—611no—
563D4⋊C8—611no—
564D4⋊C8—611no—
565D4⋊C8—611no—
566D4⋊C8—611no—
567D4⋊C8—611no—
568D4⋊C8—611no—
569D4⋊C8—611no—
570D4⋊C8—611no—
571D4⋊C8—611no—
572D4⋊C8—611no—
573D4⋊C8—611no—
574D4⋊C8—611no—
575D4⋊C8—611no—
576D4⋊C8—611no—
577D4⋊C8—611no—
578C61#1751111yescharacteristic, complemented, Sylow
579C2×#41—611no—
580C2×#41—1221no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1221no—
585C2×#41—1221no—
586C2×#41—1221no—
587C2×#41—2444no—
588C2×#41—2444no—
589C22×Q8—1221no—
590C22×D4—21no—
591C22×D4—611no—
592C22×D4—1221no—
593C22×D4—1221no—
594C22×D4C2×#692311yescharacteristic
595C22×D4C2×#692311yescharacteristic
596C23×C4—1221no—
597C23×C4—1221no—
598C23×C4—1221no—
599C2×M16—1221no—
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605C4⋊Q8—611no—
606C4⋊Q8—611no—
607#127—611no—
608#127—611no—
609#127C2×#692311yescharacteristic
610#124—1221no—
611#124—1221no—
612#124—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625#121—21no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—611no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121C2×#692311yescharacteristic
639#121C2×#692311yescharacteristic
640#120—21no—
641#120—21no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646C4×Q8—611no—
647C4×Q8—611no—
648C4×D4—611no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4C2×#692311yescharacteristic
672C4×D4C2×#692311yescharacteristic
673#117—611no—
674#117—611no—
675#117—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C42—611no—
683C2×C42—611no—
684C2×C42—611no—
685C4⋊C8—611no—
686C4⋊C8—611no—
687C4⋊C8—611no—
688C4⋊C8—611no—
689C4⋊C8—1221no—
690C4⋊C8—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C4⋊C8—1221no—
694C22⋊C8—1221no—
695C22⋊C8—1221no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702#97—1221no—
703#97—1221no—
704#97—1221no—
705C4×C8—611no—
706C4×C8—611no—
707C4×C8—611no—
708C4×C8—611no—
709C4×C8—1221no—
710C4×C8—1221no—
711C4×C8—1221no—
712C24—21no—
713C24—21no—
714C24—1221no—
715#41—1222no—
716#41—1222no—
717#41—2442no—
718#41—2442no—
719#41—2442no—
720#41—2442no—
721#41—2442no—
722#41—2442no—
723#41—2444no—
724#41—2444no—
725#41—2444no—
726#41—2444no—
727C2×Q8—611no—
728C2×Q8—1221no—
729C2×Q8—1221no—
730C2×Q8—1221no—
731C2×Q8—2444no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—44no—
743C2×D4—611no—
744C2×D4—611no—
745C2×D4—611no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1222no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—2441no—
757C2×D4—2444no—
758C2×D4—2444no—
759C2×D4C22⋊#692311yescharacteristic
760C2×D4C22×#692311yescharacteristic
761C2×D4C22×#692311yescharacteristic
762C2×D4C22×#692311yescharacteristic
763C22×C4—21no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4—2442no—
789C22×C4C22×#692311yescharacteristic
790C22×C4C22×#692311yescharacteristic
791M16—2442no—
792M16—2442no—
793M16—2442no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—1221no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—2442no—
803C2×C8—2442no—
804C4⋊C4—611no—
805C4⋊C4—611no—
806C4⋊C4—611no—
807C4⋊C4—611no—
808C4⋊C4—611no—
809C4⋊C4—611no—
810C4⋊C4—611no—
811C4⋊C4—611no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4C22⋊#692311yescharacteristic
819C4⋊C4C22×#692311yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4C22⋊#692311yescharacteristic
841C22⋊C4C22⋊#692311yescharacteristic
842C42—611no—
843C42—611no—
844C42—611no—
845C42—611no—
846C42—611no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—611no—
851C42C22×#692311yescharacteristic
852C23—21no—
853C23—21no—
854C23—21no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—611no—
862C23—1221no—
863C23—4881no—
864C23—2442no—
865C23—2442no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—1222no—
869Q8—2442no—
870Q8—2442no—
871Q8—2442no—
872D4—22no—
873D4—21no—
874D4—21no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—42no—
879D4—42no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—81no—
884D4—1222no—
885D4—1222no—
886D4—1221no—
887D4—1221no—
888D4—4881no—
889D4—4881no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4#1451986412yes—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—42no—
904C2×C4—612no—
905C2×C4—612no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—2441no—
923C2×C4—2442no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2442no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2442no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2442no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2442no—
938C2×C4—2442no—
939C2×C4—2442no—
940C2×C4—2442no—
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4C2×C22⋊#692311yescharacteristic
944C2×C4C2×C22⋊#692311yescharacteristic
945C2×C4C23×#692311yescharacteristic
946C8—1222no—
947C8—2441no—
948C8—2441no—
949C8—2441no—
950C8—2441no—
951C8—2441no—
952C8—2441no—
953C8—2441no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—22no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—84no—
969C22—84no—
970C22—1221no—
971C22—1221no—
972C22—1221no—
973C22—4884no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22#1684075412yes—
978C22C22×C22⋊#692311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—611no—
985C4—611no—
986C4—612no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—2441no—
993C4—2441no—
994C4—2441no—
995C4C2×#1451986411yescharacteristic
996C4#1684084011yescharacteristic
997C2—22no—
998C2—41no—
999C2—42no—
1000C2—81no—
1001C2—81no—
1002C2—4881no—
1003C2—2441no—
1004C2#2146240711yescharacteristic
1005C2C2×#1684075411yescharacteristic
1006C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radicalD4×#11758224C2
cosocleC4×Dic61C24
hypercenterD42#6923
hypocenterC61#17511
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462629C2semidirect
2. #21462514C2semidirect
3. #21461179C2semidirect
4. #21461178C2semidirect
5. #21461164C2semidirect
6. #21461159C2semidirect
7. #21461158C2semidirect
8. #21461144C2semidirect
9. #21461139C2semidirect
10. #21461138C2semidirect
11. #21461124C2semidirect
12. #21461119C2semidirect
13. #21461118C2semidirect
14. C2×D4⋊#92420C2semidirect
22. #16840784C22semidirect
23. #16840783C22semidirect
24. #16840781C22semidirect
25. #16840780C22semidirect
26. #16840779C22semidirect
27. #16840778C22semidirect
28. #16840778C22semidirect
29. #16840765C22semidirect
30. C2×C4⋊#92420C22semidirect
33. C4×#11758213C22semidirect
34. C4×#11758217C22semidirect
35. C2×C4×#92420C22semidirect
36. #16840610C22semidirect
37. #16840610C22semidirect
38. #16840610C22semidirect
39. #16840610C22semidirect
44. D4⋊#92420C22semidirect
45. D4⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
578. C61#17511semidirect

Maximal subgroups

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

subgroupindex
#214626292
#214625142
#214611792
#214611782
#214611642
#214611592
#214611582
#214611442
#214611392
#214611382
#214611242
#214611192
#214611182
C2×D4⋊#924202
D4×#117582242
#1751161