Finite Group Databasebeta

← #30610834

Subgroups — #30610834

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462744C211yesmaximal, characteristic, complemented
2C4×#14519864C211yesmaximal, characteristic, complemented
3#21461172C211yesmaximal, characteristic, complemented
4#21461171C211yesmaximal, characteristic, complemented
5#21461164C211yesmaximal, characteristic, complemented
6#21461159C211yesmaximal, characteristic, complemented
7#21461158C211yesmaximal, characteristic, complemented
8#21461154C211yesmaximal, characteristic, complemented
9#21461138C211yesmaximal, characteristic, complemented
10#21461136C211yesmaximal, characteristic, complemented
11#21461135C211yesmaximal, characteristic, complemented
12#21461110C211yesmaximal, characteristic, complemented
13D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
14C2×D4⋊#92420C211yesmaximal, characteristic, complemented
15#21459424C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840794—21no—
19#16840793—21no—
20#16840789—21no—
21#16840784C2211yescharacteristic, complemented
22#16840783C2211yescharacteristic, complemented
23#16840778C2211yescharacteristic, complemented
24#16840765C2211yescharacteristic, complemented
25D61⋊(C4⋊C8)C2211yescharacteristic, complemented
26C2×C4⋊#92420C2211yescharacteristic, complemented
27#16840727—21no—
28#16840726—21no—
29#16840726—21no—
30C4×#11758213C2211yescharacteristic, complemented
31C4×#11758217C2211yescharacteristic, complemented
32C4×#11758217C2211yescharacteristic, complemented
33C4×D61⋊C8C2211yescharacteristic, complemented
34C2×C4×#92420C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52#16840494C411yescharacteristic
53#16840471C411yescharacteristic
54#16840470C411yescharacteristic
55#16840459C411yescharacteristic
56#16840458C411yescharacteristic
57#16840455—21no—
58#16840438—21no—
59#16840435—21no—
60#16840400C411yescharacteristic
61#16840399—21no—
62D4×C22⋊D61C411yescharacteristic
63#16840307C2211yescharacteristic
64#16840298C2211yescharacteristic
65#16840291C2211yescharacteristic
66#16840289—21no—
67#16840272—21no—
68#16840268—21no—
69#41×Dic61C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C2×D4×Dic61C2211yescharacteristic
72C2×#14519737—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic
75#14519864—28no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91C4⋊#92420C2311yescharacteristic
92#14519834—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C4×#92420C2311yescharacteristic
108C2×#11758224—21no—
109C2×#11758224D411yescharacteristic
110C22×C22⋊D61—21no—
111C2×D4×D61C2×C411yescharacteristic
112C23×Dic61—21no—
113C22×C4×D61—21no—
114#14519776C2×C411yescharacteristic
115#14519773C2×C411yescharacteristic
116#14519772—21no—
117#14519772—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769C2×C411yescharacteristic
121#14519768C2×C411yescharacteristic
122#14519767—21no—
123#14519766C2×C411yescharacteristic
124#14519763—21no—
125#14519763—21no—
126#14519761—21no—
127#14519761—21no—
128#14519760—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519757—21no—
134#14519756—21no—
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519753C2×C411yescharacteristic
139#14519751C2×C411yescharacteristic
140#14519751C2×C411yescharacteristic
141#14519749—21no—
142#14519749—21no—
143#14519749—21no—
144#14519749—21no—
145#14519748—21no—
146#14519748C2×C411yescharacteristic
147#14519746—21no—
148#14519745—21no—
149#14519745—21no—
150Q8×Dic61C2×C411yescharacteristic
151Q8×Dic61C2311yescharacteristic
152C4×Dic122C2×C411yescharacteristic
153#14519742D411yescharacteristic
154C4×D244C2×C411yescharacteristic
155D4×Dic61—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158D4×Dic61—21no—
159D4×Dic61C2×C411yescharacteristic
160D4×Dic61C2×C411yescharacteristic
161D4×Dic61C2×C411yescharacteristic
162D4×Dic61D411yescharacteristic
163D4×Dic61C2311yescharacteristic
164D4×Dic61C2311yescharacteristic
165#14519739C2311yescharacteristic
166C4×C22⋊D61—21no—
167C4×C22⋊D61C2×C411yescharacteristic
168C4×C22⋊D61C2×C411yescharacteristic
169#14519737—21no—
170#14519737—21no—
171#14519737—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736—21no—
180#14519736C2×C411yescharacteristic
181#14519735—21no—
182#14519735D411yescharacteristic
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×#11758196—21no—
188C4⋊C4×D61C2×C411yescharacteristic
189C2×C22⋊Dic61—21no—
190C2×#11758198—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C2×C22⋊C4×C61—21no—
207C24×C61—21no—
208C23×D61—21no—
209#41×C61—22no—
210#41×C61—41no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—22no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—41no—
217C2×D4×C61C22⋊C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—81no—
240C22×Dic61—81no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245#11758224—24no—
246#11758224—81no—
247#11758224—81no—
248D4×D61—22no—
249D4×D61—41no—
250C2×D244C22×C411yescharacteristic
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—81no—
255C2×C4×D61—81no—
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22⋊C411yescharacteristic
261#11758217—24no—
262#11758217—24no—
263#11758217—81no—
264C2×#92420—24no—
265C2×#92420—24no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—81no—
275#11758213—24no—
276D61⋊C8—24no—
277D61⋊C8—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C42×C61C22×C411yescharacteristic
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61C22⋊C411yescharacteristic
297C22⋊Dic61C22⋊C411yescharacteristic
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61C22×C411yescharacteristic
329C4×Dic61C22×C411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2411yescharacteristic
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—81no—
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C2×C22⋊C411yescharacteristic
344C22×D61—21no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—81no—
348C22×D61C2×C22⋊C411yescharacteristic
349Q8×C61—21no—
350Q8×C61—21no—
351D4×C61—22no—
352D4×C61—21no—
353D4×C61—21no—
354D4×C61—21no—
355D4×C61—42no—
356D4×C61—42no—
357D4×C61—81no—
358D4×C61#13112yescomplemented
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—42no—
366C2×C4×C61—81no—
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C23×C411yescharacteristic
372C22⋊D61—22no—
373C22⋊D61—42no—
374C22⋊D61—42no—
375C22⋊D61—42no—
376C22⋊D61—42no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61#10414yes—
380C2×Dic61—22no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—22no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—42no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404D244—21no—
405D244—21no—
406C4×D61—22no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—81no—
414C4×D61—81no—
415Dic122—22no—
416Dic122—81no—
417#92420—22no—
418#92420—22no—
419#92420—22no—
420#92420—22no—
421#92420—41no—
422#92420—41no—
423#92420—41no—
424#92420—41no—
425#17517—611nomaximal, Sylow
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—22no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—84no—
438C22×C61C2×#10412yes—
439C22×C61C22×C22⋊C411yescharacteristic
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—84no—
446C2×D61C2×#10412yes—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—41no—
452C4×C61—41no—
453C4×C61C2×#13111yescharacteristic
454C4×C61#56811yescharacteristic
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—41no—
461Dic61—41no—
462Dic61—41no—
463Dic61C2×#10412yes—
464Dic61#57611yescharacteristic
465Dic61#57711yescharacteristic
466#3481—611no—
467#2990—611no—
468C4×#131—611no—
469#1494—611no—
470#1494—611no—
471#1492—611no—
472#1490—611no—
473#1490—611no—
474#1489—611no—
475#1484—611no—
476#1483—611no—
477#1483—611no—
478#1476—611no—
479C2×D4⋊C8—611no—
480C2×D4⋊C8—611no—
481C2×C61—22no—
482C2×C61—42no—
483C2×C61—41no—
484C2×C61—81no—
485C2×C61#288011yescharacteristic
486C2×C61#289711yescharacteristic
487C2×C61C22×#10411yescharacteristic
488D61—22no—
489D61—81no—
490C2×#131—1221no—
491#559—611no—
492#554—611no—
493#554—611no—
494#553—611no—
495#553—611no—
496#553—1221no—
497#551—1221no—
498#551—1221no—
499#546—611no—
500#546—1221no—
501#546#692311yescharacteristic
502D42—611no—
503#532—611no—
504#529—611no—
505#529—611no—
506#529—1221no—
507#525—1221no—
508#525—1221no—
509C4×#41—611no—
510C4×#41—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×C4×D4—1221no—
514#446—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#432—611no—
520#431—611no—
521#423—611no—
522C2×C4⋊C8—611no—
523C2×C4⋊C8—611no—
524#405—1221no—
525#405—1221no—
526#405—1221no—
527C4×M16—611no—
528C4×M16—611no—
529C4×M16—611no—
530C2×C4×C8—611no—
531C2×C4×C8—611no—
532C2×C4×C8—611no—
533Q8⋊C8—611no—
534Q8⋊C8—611no—
535Q8⋊C8—611no—
536Q8⋊C8—611no—
537D4⋊C8—611no—
538D4⋊C8—611no—
539D4⋊C8—611no—
540D4⋊C8—611no—
541D4⋊C8—611no—
542D4⋊C8—611no—
543D4⋊C8—611no—
544D4⋊C8—611no—
545D4⋊C8—611no—
546D4⋊C8—611no—
547D4⋊C8—611no—
548D4⋊C8—611no—
549C61#1751711yescharacteristic, complemented, Sylow
550C2×#41—611no—
551C2×#41—1221no—
552C2×#41C2×#692311yescharacteristic
553C22×D4—611no—
554C22×D4—1221no—
555C22×D4C2×#692311yescharacteristic
556C23×C4—1221no—
557C23×C4—1221no—
558#131—1228no—
559C2×M16—1221no—
560C2×M16—1221no—
561C2×M16—1221no—
562C2×M16—1221no—
563C22×C8—1221no—
564C22×C8—1221no—
565C22×C8—1221no—
566C22×C8—1221no—
567C22×C8—1221no—
568C4⋊Q8—611no—
569#127—611no—
570#126—1221no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#125—611no—
575#125—611no—
576#125—1221no—
577#124—611no—
578#124—1221no—
579#124—1221no—
580#124C2×#692311yescharacteristic
581#123—21no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8C2×#692311yescharacteristic
596#121—21no—
597#121—611no—
598#121—611no—
599#121—611no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121C2×#692311yescharacteristic
606#120—21no—
607#120—1221no—
608#120—1221no—
609#120—1221no—
610C4×Q8—611no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×Q8—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4C2×#692311yescharacteristic
640C4×D4C2×#692311yescharacteristic
641#117—611no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—1221no—
646#117—1221no—
647#117—1221no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—1221no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C42—611no—
656C2×C42—611no—
657C2×C42—611no—
658C2×C42—1221no—
659C4⋊C8—611no—
660C4⋊C8—611no—
661C4⋊C8—611no—
662C4⋊C8—611no—
663C4⋊C8—1221no—
664C4⋊C8—1221no—
665C4⋊C8—1221no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669#97—1221no—
670#97—1221no—
671#97—1221no—
672#97—1221no—
673#97—1221no—
674C4×C8—611no—
675C4×C8—611no—
676C4×C8—611no—
677C4×C8—611no—
678C4×C8—1221no—
679C4×C8—1221no—
680C4×C8—1221no—
681C4×C8—1221no—
682C24—21no—
683C24—1221no—
684#41—22no—
685#41—41no—
686#41—1224no—
687#41—4881no—
688#41—4881no—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8C22×#692311yescharacteristic
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—41no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1222no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—2441no—
708C2×D4—2444no—
709C2×D4C22⋊#692311yescharacteristic
710C2×D4C22×#692311yescharacteristic
711C2×D4C22×#692311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—4881no—
731C22×C4—4881no—
732C22×C4—4881no—
733C22×C4—4881no—
734C22×C4C22×#692311yescharacteristic
735C22×C4C22×#692311yescharacteristic
736M16—1224no—
737M16—1224no—
738M16—1224no—
739M16—4881no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1224no—
745C2×C8—1224no—
746C2×C8—1224no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—4881no—
752C2×C8—4881no—
753C4⋊C4—21no—
754C4⋊C4—611no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4C22⋊#692311yescharacteristic
773C4⋊C4C22×#692311yescharacteristic
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
798C22⋊C4C22⋊#692311yescharacteristic
799C42—611no—
800C42—611no—
801C42—611no—
802C42—611no—
803C42—611no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—1221no—
809C42—1221no—
810C42—1221no—
811C42C22×#692311yescharacteristic
812C23—21no—
813C23—21no—
814C23—42no—
815C23—42no—
816C23—81no—
817C23—611no—
818C23—1221no—
819C23—4881no—
820C23—2442no—
821C23—2442no—
822C23C2×C22⋊#692311yescharacteristic
823C23C2×C22⋊#692311yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—1222no—
827Q8—4881no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—42no—
833D4—42no—
834D4—81no—
835D4—614no—
836D4—1222no—
837D4—1221no—
838D4—1221no—
839D4—4881no—
840D4—4881no—
841D4—2442no—
842D4—2442no—
843D4—2442no—
844D4—2442no—
845D4#1451986412yescomplemented
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—42no—
853C2×C4—81no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1222no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4881no—
879C2×C4—4881no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2442no—
887C2×C4C2×C22⋊#692311yescharacteristic
888C2×C4C2×C22⋊#692311yescharacteristic
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C2×C22⋊#692311yescharacteristic
891C2×C4C23×#692311yescharacteristic
892C8—1222no—
893C8—1222no—
894C8—1222no—
895C8—1222no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—22no—
904C22—21no—
905C22—21no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—84no—
912C22—612no—
913C22—1221no—
914C22—1221no—
915C22—4884no—
916C22—2441no—
917C22—2441no—
918C22—2441no—
919C22D61⋊#10412yes—
920C22C22×C22⋊#692311yescharacteristic
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—41no—
926C4—41no—
927C4—611no—
928C4—611no—
929C4—612no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—1221no—
935C4—2441no—
936C4—2441no—
937C4—2441no—
938C4C2×#1451986411yescharacteristic
939C4#1684084011yescharacteristic
940C2—22no—
941C2—41no—
942C2—42no—
943C2—81no—
944C2—1222no—
945C2—4881no—
946C2#2146240711yescharacteristic
947C2#2146244011yescharacteristic
948C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459424C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17517
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. C4×#14519864C2semidirect
3. #21461172C2semidirect
4. #21461171C2semidirect
5. #21461164C2semidirect
6. #21461159C2semidirect
7. #21461158C2semidirect
8. #21461154C2semidirect
9. #21461138C2semidirect
10. #21461136C2semidirect
11. #21461135C2semidirect
12. #21461110C2semidirect
13. D61⋊(D4⋊C8)C2semidirect
14. C2×D4⋊#92420C2semidirect
21. #16840784C22semidirect
22. #16840783C22semidirect
23. #16840778C22semidirect
24. #16840765C22semidirect
25. D61⋊(C4⋊C8)C22semidirect
26. C2×C4⋊#92420C22semidirect
30. C4×#11758213C22semidirect
31. C4×#11758217C22semidirect
32. C4×#11758217C22semidirect
33. C4×D61⋊C8C22semidirect
34. C2×C4×#92420C22semidirect
35. C2×C4×#92420C22semidirect
36. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
358. D4×C61#131semidirect
549. C61#17517semidirect
845. D4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214627442
C4×#145198642
#214611722
#214611712
#214611642
#214611592
#214611582
#214611542
#214611382
#214611362
#214611352
#214611102
D61⋊(D4⋊C8)2
C2×D4⋊#924202
#214594242
#1751761