Finite Group Databasebeta

← #30611404

Subgroups — #30611404

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461247C211yesmaximal, characteristic, complemented
4#21461246C211yesmaximal, characteristic, complemented
5#21461241C211yesmaximal, characteristic, complemented
6#21461240C211yesmaximal, characteristic, complemented
7#21461237C211yesmaximal, characteristic, complemented
8#21461236C211yesmaximal, characteristic, complemented
9#21461212C211yesmaximal, characteristic, complemented
10#21461210C211yesmaximal, characteristic, complemented
11#21461207C211yesmaximal, characteristic, complemented
12#21461206C211yesmaximal, characteristic, complemented
13#21461197C211yesmaximal, characteristic, complemented
14#21461196C211yesmaximal, characteristic, complemented
15#21459672C211yesmaximal, 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#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840614C2211yescharacteristic
49#16840614C2211yescharacteristic
50#16840614C2211yescharacteristic
51#16840614C2211yescharacteristic
52#16840497—21no—
53#16840494—21no—
54#16840486C411yescharacteristic, complemented
55#16840475C411yescharacteristic, complemented
56#16840475C411yescharacteristic, complemented
57#16840463—21no—
58#16840463—21no—
59#16840434C411yescharacteristic, complemented
60#16840433C411yescharacteristic, complemented
61#16840414C411yescharacteristic, complemented
62#16840414C411yescharacteristic, complemented
63#16840351—21no—
64#16840351—21no—
65#16840330—21no—
66#16840316C2211yescharacteristic
67#16840313C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840275C2211yescharacteristic
70#16840274C2211yescharacteristic
71#16840274C2211yescharacteristic
72#16840244—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#556C411yescharacteristic, 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×#11758226—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758226C2×C411yescharacteristic, complemented
110C2×#11758222C2×C411yescharacteristic
111C2×#11758222C2×C411yescharacteristic, complemented
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519776C2×C411yescharacteristic, complemented
116#14519775C2×C411yescharacteristic, complemented
117#14519774—21no—
118#14519774C2×C411yescharacteristic, complemented
119#14519773—21no—
120#14519772—21no—
121#14519772—21no—
122#14519767—21no—
123#14519766—21no—
124#14519766—21no—
125#14519765—21no—
126#14519765—21no—
127#14519763—21no—
128#14519763—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519761—21no—
134#14519761—21no—
135#14519759—21no—
136#14519759—21no—
137#14519757C2×C411yescharacteristic
138#14519757C2×C411yescharacteristic, complemented
139#14519757C2311yescharacteristic
140#14519755—21no—
141#14519753C2311yescharacteristic
142#14519752—21no—
143#14519752—21no—
144#14519752—21no—
145#14519752C2×C411yescharacteristic
146#14519752C2×C411yescharacteristic, complemented
147#14519752C2311yescharacteristic
148#14519752C2311yescharacteristic
149#14519751C2×C411yescharacteristic
150#14519751C2×C411yescharacteristic, complemented
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519750—21no—
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160#14519747—21no—
161Q8×Dic61—21no—
162C4×Dic122—21no—
163C4×Dic122C2×C411yescharacteristic, complemented
164C4×D244—21no—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244—21no—
168C4×D244—21no—
169C4×D244C2×C411yescharacteristic
170D4×Dic61D411yescharacteristic
171#14519739—21no—
172#14519739—21no—
173#14519739—21no—
174#14519739—21no—
175#14519739C2×C411yescharacteristic, complemented
176#14519739C2×C411yescharacteristic, complemented
177#14519739D411yescharacteristic
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737—21no—
181#14519737—21no—
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519735C2×C411yescharacteristic
185#14519735C2×C411yescharacteristic, complemented
186#14519734—21no—
187#14519734—21no—
188#14519734—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic, complemented
196#126×C61—21no—
197#126×C61—21no—
198#124×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201C4×Q8×C61—21no—
202C4×Q8×C61C2×C411yescharacteristic, complemented
203C4×D4×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic, complemented
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×C61C22×C411yescharacteristic
217C2×D4×C61C22⋊C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758226—42no—
229#11758226—42no—
230#11758226—81no—
231#11758226—81no—
232D4×D61—41no—
233D4×D61—41no—
234#11758222—81no—
235#11758222—81no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244C22⋊C411yescharacteristic
245C2×D244C22×C411yescharacteristic
246C2×D244C22×C411yescharacteristic
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2411yescharacteristic
264C2×Dic122—21no—
265C2×Dic122C22×C411yescharacteristic
266C22⋊#6923—42no—
267C22⋊#6923—42no—
268C22⋊#6923—81no—
269#11758217—81no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—81no—
275C4⋊#6923—81no—
276C4×#6923—42no—
277C4×#6923—81no—
278#11758213—81no—
279D61⋊C8—81no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61C22⋊C411yescharacteristic
293C22⋊C4×C61C22⋊C411yescharacteristic
294C42×C61—21no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61C22×C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299C22⋊Dic61C22⋊C411yescharacteristic
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61C22⋊C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C2×C22⋊C411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C22×D411yescharacteristic
351C2×#6923—22no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—84no—
364Q8×C61—42no—
365Q8×C61—41no—
366D4×C61—41no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C23×C411yescharacteristic
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C22×D411yescharacteristic
393D244—41no—
394D244—41no—
395D244—41no—
396D244—42no—
397D244—41no—
398D244—41no—
399D244—41no—
400D244—41no—
401D244—81no—
402D244—81no—
403D244—81no—
404D244—81no—
405D244—81no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—42no—
417C4×D61—42no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421C4×D61—81no—
422Dic122—41no—
423Dic122—81no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17629—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61C22×C22⋊C411yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61#57511yescharacteristic
455C2×D61#57511yescharacteristic
456#6923—42no—
457#6923—81no—
458#6923—81no—
459#6923—81no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—41no—
475Dic61—41no—
476#3506—611no—
477#2973—611no—
478#2353—611no—
479#1516—611no—
480#1516—611no—
481#1515—611no—
482#1514—611no—
483#1513—611no—
484#1513—611no—
485#1506—611no—
486#1505—611no—
487#1504—611no—
488#1504—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—41no—
492C2×C61—41no—
493C2×C61#288311yescharacteristic
494C2×C61#289611yescharacteristic
495C2×C61#290111yescharacteristic
496D61—21no—
497D61—21no—
498D61—41no—
499D61—41no—
500D61—81no—
501D61—81no—
502#559—1221no—
503#559—1221no—
504#556—611no—
505#556#692311yescharacteristic, complemented
506#555—611no—
507#555—611no—
508#553—1221no—
509#553—1221no—
510#550—611no—
511#550—611no—
512#547—611no—
513#547—611no—
514#538—1221no—
515#538—1221no—
516#535—1221no—
517#533—611no—
518#532—611no—
519#525—611no—
520#525—611no—
521#525—611no—
522#525—611no—
523#520—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#388—1221no—
536#387—1221no—
537#386—1221no—
538#383—611no—
539#381—611no—
540#380—611no—
541C4×C22⋊C4—611no—
542C4×C22⋊C4—1221no—
543#376—611no—
544C2×#95—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561C61#1762911yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—611no—
565C2×#41—611no—
566C2×#41—1221no—
567C22×D4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—1221no—
571C2×M16—1221no—
572C2×M16—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C4⋊Q8—611no—
576C4⋊Q8—611no—
577C4⋊Q8C2×#692311yescharacteristic, complemented
578#127—611no—
579#127—1221no—
580#127—1221no—
581#126—21no—
582#126—21no—
583#126—1221no—
584#126—1221no—
585#125—1221no—
586#124—21no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124—1221no—
591#124—1221no—
592#124—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—1221no—
606C22⋊Q8C2×#692311yescharacteristic
607C22⋊Q8C2×#692311yescharacteristic, complemented
608#121—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627C4×Q8—21no—
628C4×Q8—611no—
629C4×Q8—1221no—
630C4×Q8—1221no—
631C4×Q8C2×#692311yescharacteristic, complemented
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4C2×#692311yescharacteristic
653#117—611no—
654#117—611no—
655#117—1221no—
656#117—1221no—
657#117—1221no—
658#117C2×#692311yescharacteristic
659#117C2×#692311yescharacteristic, complemented
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C4⋊C4—1221no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4—611no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C42—611no—
670C2×C42—1221no—
671C2×C42—1221no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682#97—1221no—
683#97—1221no—
684#95—611no—
685#95—611no—
686#95—611no—
687#95—611no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693C24—611no—
694C24—611no—
695#41—4881no—
696#41—4881no—
697#41—4881no—
698#41—4881no—
699#41—2442no—
700#41—2442no—
701C2×Q8—21no—
702C2×Q8—611no—
703C2×Q8—1221no—
704C2×Q8C22×#692311yescharacteristic
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—2441no—
723C2×D4—2441no—
724C2×D4C22⋊#692311yescharacteristic
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—4881no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4C22×#692311yescharacteristic
752C22×C4C22×#692311yescharacteristic
753M16—4881no—
754M16—4881no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—4881no—
760C2×C8—4881no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—4881no—
778C4⋊C4C22⋊#692311yescharacteristic
779C4⋊C4C22×#692311yescharacteristic
780C4⋊C4C22×#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
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—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—4881no—
807C22⋊C4—2442no—
808C22⋊C4—2442no—
809C22⋊C4C22⋊#692311yescharacteristic
810C22⋊C4C22⋊#692311yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—611no—
824C23—611no—
825C23—611no—
826C23—1221no—
827C23—1221no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23C2×C22⋊#692311yescharacteristic
837C23C2×C22⋊#692311yescharacteristic
838Q8—41no—
839Q8—42no—
840Q8—4881no—
841Q8—2441no—
842D4—41no—
843D4—4881no—
844D4—4881no—
845D4—4881no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2442no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—4881no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4884no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2442no—
892C2×C4—2442no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C23×#692311yescharacteristic
911C8—2441no—
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—611no—
922C22—611no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—4881no—
932C22—4881no—
933C22—2442no—
934C22—2442no—
935C22—2441no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—4881no—
957C4—4881no—
958C4—4881no—
959C4—2442no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—1221no—
965C2—1221no—
966C2—4881no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241911yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radical#21459672C2
cosocleC2×C4×D61C24
hypercenter#556#6923
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461247C2semidirect
4. #21461246C2semidirect
5. #21461241C2semidirect
6. #21461240C2semidirect
7. #21461237C2semidirect
8. #21461236C2semidirect
9. #21461212C2semidirect
10. #21461210C2semidirect
11. #21461207C2semidirect
12. #21461206C2semidirect
13. #21461197C2semidirect
14. #21461196C2semidirect
54. #16840486C4semidirect
55. #16840475C4semidirect
56. #16840475C4semidirect
59. #16840434C4semidirect
60. #16840433C4semidirect
61. #16840414C4semidirect
62. #16840414C4semidirect
74. C61×#556C4semidirect
109. C2×#11758226C2×C4semidirect
111. C2×#11758222C2×C4semidirect
115. #14519776C2×C4semidirect
116. #14519775C2×C4semidirect
118. #14519774C2×C4semidirect
138. #14519757C2×C4semidirect
146. #14519752C2×C4semidirect
150. #14519751C2×C4semidirect
163. C4×Dic122C2×C4semidirect
175. #14519739C2×C4semidirect
176. #14519739C2×C4semidirect
185. #14519735C2×C4semidirect
195. C4⋊Q8×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
202. C4×Q8×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
505. #556#6923semidirect
561. C61#17629semidirect
577. C4⋊Q8C2×#6923semidirect
607. C22⋊Q8C2×#6923semidirect
631. C4×Q8C2×#6923semidirect
659. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612472
#214612462
#214612412
#214612402
#214612372
#214612362
#214612122
#214612102
#214612072
#214612062
#214611972
#214611962
#214596722
#1762961