Finite Group Databasebeta

← #30611401

Subgroups — #30611401

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#21461246C211yesmaximal, characteristic, complemented
4#21461245C211yesmaximal, characteristic, complemented
5#21461243C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic, complemented
7#21461237C211yesmaximal, characteristic, complemented
8#21461234C211yesmaximal, characteristic, complemented
9#21461213C211yesmaximal, characteristic, complemented
10#21461209C211yesmaximal, characteristic, complemented
11#21461206C211yesmaximal, characteristic, complemented
12#21461205C211yesmaximal, characteristic, complemented
13#21461197C211yesmaximal, characteristic, complemented
14#21461194C211yesmaximal, characteristic, complemented
15#21459669C211yesmaximal, 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#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840496—21no—
53#16840496—21no—
54#16840483C411yescharacteristic, complemented
55#16840483C411yescharacteristic, complemented
56#16840477C411yescharacteristic, complemented
57#16840477C411yescharacteristic, complemented
58#16840460—21no—
59#16840459—21no—
60#16840431C411yescharacteristic, complemented
61#16840431C411yescharacteristic, complemented
62#16840415C411yescharacteristic, complemented
63#16840348—21no—
64#16840348—21no—
65#16840328—21no—
66#16840317C2211yescharacteristic
67#16840309C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840275C2211yescharacteristic
70#16840269C2211yescharacteristic
71#16840269C2211yescharacteristic
72#16840243—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#547C411yescharacteristic, 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×#11758226C2×C411yescharacteristic
108C2×#11758226C2×C411yescharacteristic, complemented
109C2×#11758222—21no—
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519777C2×C411yescharacteristic, complemented
114#14519776C2×C411yescharacteristic, complemented
115#14519773—21no—
116#14519773—21no—
117#14519773C2×C411yescharacteristic, complemented
118#14519772—21no—
119#14519772—21no—
120#14519770—21no—
121#14519770—21no—
122#14519768—21no—
123#14519763—21no—
124#14519763—21no—
125#14519763—21no—
126#14519763—21no—
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519762—21no—
134#14519758—21no—
135#14519758—21no—
136#14519757—21no—
137#14519753C2×C411yescharacteristic
138#14519753C2×C411yescharacteristic, complemented
139#14519753C2311yescharacteristic
140#14519753C2311yescharacteristic
141#14519752—21no—
142#14519752C2311yescharacteristic
143#14519751—21no—
144#14519751—21no—
145#14519751—21no—
146#14519751C2×C411yescharacteristic
147#14519751C2×C411yescharacteristic, complemented
148#14519750—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2311yescharacteristic
155#14519747—21no—
156#14519747—21no—
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic, complemented
160Q8×Dic61C2×C411yescharacteristic, complemented
161#14519742—21no—
162#14519742—21no—
163#14519742—21no—
164C4×D244C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic, complemented
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739—21no—
169#14519739D411yescharacteristic
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61C2×C411yescharacteristic
178C4×C22⋊D61C2×C411yescharacteristic
179#14519737—21no—
180#14519737—21no—
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519736—21no—
184#14519736C2×C411yescharacteristic
185#14519736C2×C411yescharacteristic, complemented
186#14519735—21no—
187#14519735—21no—
188#14519735C2×C411yescharacteristic
189#14519735C2×C411yescharacteristic, complemented
190C4⋊C4×D61—21no—
191C4⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197C4⋊Q8×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic, complemented
202#121×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
205C2×C4⋊C4×C61—21no—
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—
215#41×C61—81no—
216#41×C61—81no—
217C2×Q8×C61C22×C411yescharacteristic
218C2×Q8×C61C22×C411yescharacteristic
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61C22⋊C411yescharacteristic
222C2×D4×C61C22×C411yescharacteristic
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C22×C411yescharacteristic
228C2×C22⋊D61—21no—
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⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758226—81no—
240#11758226—81no—
241D4×D61—41no—
242D4×D61—41no—
243#11758222—42no—
244#11758222—42no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244C22⋊C411yescharacteristic
249C2×D244C22×C411yescharacteristic
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×Dic122—21no—
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
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C42×C61C22×C411yescharacteristic
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299#11758198—21no—
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#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319C4⋊Dic61C22×C411yescharacteristic
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61—21no—
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C411yescharacteristic
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—41no—
365Q8×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—81no—
369D4×C61—81no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61—81no—
377C2×C4×C61—81no—
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C23×C411yescharacteristic
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—42no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C22⋊D61—81no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403D244—41no—
404D244—41no—
405D244—41no—
406D244—41no—
407D244—81no—
408D244—81no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—42no—
420C4×D61—81no—
421C4×D61—81no—
422Dic122—42no—
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×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—42no—
448C2×D61—42no—
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—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—41no—
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—81no—
494C2×C61#288311yescharacteristic
495C2×C61#289611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—21no—
498D61—21no—
499D61—41no—
500D61—41no—
501D61—81no—
502#559—1221no—
503#559—1221no—
504#556—611no—
505#556—611no—
506#555—611no—
507#555—611no—
508#553—1221no—
509#553—1221no—
510#550—611no—
511#550—611no—
512#547—611no—
513#547#692311yescharacteristic, complemented
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—1221no—
565C2×#41C2×#692311yescharacteristic
566C2×#41C2×#692311yescharacteristic, complemented
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—1221no—
582#126—1221no—
583#126—1221no—
584#126—1221no—
585#125—1221no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124—1221no—
591#124—1221no—
592#124—1221no—
593#123—21no—
594#123—21no—
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—21no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—611no—
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—611no—
628C4×Q8—611no—
629C4×Q8—1221no—
630C4×Q8—1221no—
631C4×Q8—1221no—
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—1221no—
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×D4C2×#692311yescharacteristic
652C4×D4C2×#692311yescharacteristic, complemented
653#117—611no—
654#117—611no—
655#117—611no—
656#117—611no—
657#117—1221no—
658#117—1221no—
659#117—1221no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—611no—
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—81no—
696#41—81no—
697#41—4881no—
698#41—4881no—
699#41—2442no—
700#41—2442no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8C22×#692311yescharacteristic
704C2×Q8C22×#692311yescharacteristic
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—611no—
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—2441no—
722C2×D4—2441no—
723C2×D4C22⋊#692311yescharacteristic
724C2×D4C22×#692311yescharacteristic
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
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—611no—
737C22×C4—611no—
738C22×C4—611no—
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—611no—
770C4⋊C4—611no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—4881no—
780C4⋊C4C22⋊#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—1221no—
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—611no—
812C42—611no—
813C42—611no—
814C42—1221no—
815C42—1221no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—611no—
825C23—611no—
826C23—611no—
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—41no—
840Q8—4881no—
841Q8—2442no—
842D4—41no—
843D4—41no—
844D4—81no—
845D4—81no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—4881no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2442no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1222no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4884no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
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—41no—
922C22—41no—
923C22—41no—
924C22—611no—
925C22—611no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—4881no—
935C22—4881no—
936C22—2442no—
937C22—2442no—
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—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—4881no—
956C4—4881no—
957C4—4881no—
958C4—2442no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—1221no—
966C2—1221no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241811yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459669C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461246C2semidirect
4. #21461245C2semidirect
5. #21461243C2semidirect
6. #21461238C2semidirect
7. #21461237C2semidirect
8. #21461234C2semidirect
9. #21461213C2semidirect
10. #21461209C2semidirect
11. #21461206C2semidirect
12. #21461205C2semidirect
13. #21461197C2semidirect
14. #21461194C2semidirect
54. #16840483C4semidirect
55. #16840483C4semidirect
56. #16840477C4semidirect
57. #16840477C4semidirect
60. #16840431C4semidirect
61. #16840431C4semidirect
62. #16840415C4semidirect
74. C61×#547C4semidirect
108. C2×#11758226C2×C4semidirect
113. #14519777C2×C4semidirect
114. #14519776C2×C4semidirect
117. #14519773C2×C4semidirect
138. #14519753C2×C4semidirect
147. #14519751C2×C4semidirect
153. #14519748C2×C4semidirect
159. Q8×Dic61C2×C4semidirect
160. Q8×Dic61C2×C4semidirect
165. C4×D244C2×C4semidirect
185. #14519736C2×C4semidirect
189. #14519735C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
197. C4⋊Q8×C61C2×C4semidirect
201. C22⋊Q8×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
513. #547#6923semidirect
561. C61#17629semidirect
566. C2×#41C2×#6923semidirect
577. C4⋊Q8C2×#6923semidirect
607. C22⋊Q8C2×#6923semidirect
652. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612462
#214612452
#214612432
#214612382
#214612372
#214612342
#214612132
#214612092
#214612062
#214612052
#214611972
#214611942
#214596692
#1762961