Finite Group Databasebeta

← #30611259

Subgroups — #30611259

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462679C211yesmaximal, characteristic, complemented
2#21462301C211yesmaximal, characteristic, complemented
3#21461262C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461249C211yesmaximal, characteristic, complemented
6#21461247C211yesmaximal, characteristic, complemented
7#21461238C211yesmaximal, characteristic, complemented
8#21461236C211yesmaximal, characteristic, complemented
9#21461233C211yesmaximal, characteristic, complemented
10#21461225C211yesmaximal, characteristic, complemented
11#21461216C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13#21461195C211yesmaximal, characteristic, complemented
14C2×#16840614C211yesmaximal, characteristic, complemented
15#21459844C211yesmaximal, characteristic
16#16840796—21no—
17#16840791—21no—
18#16840791—21no—
19D4×#92420—21no—
20#16840784C2211yescharacteristic, complemented
21#16840781C2211yescharacteristic, complemented
22#16840733C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840709—21no—
30#16840707C2211yescharacteristic, complemented
31#16840706C2211yescharacteristic, complemented
32#16840705C2211yescharacteristic, complemented
33#16840704C2211yescharacteristic, complemented
34C4×C22⋊#6923C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840475C411yescharacteristic, complemented
53#16840467C411yescharacteristic, complemented
54#16840465C411yescharacteristic, complemented
55#16840463—21no—
56#16840430C411yescharacteristic, complemented
57#16840408—21no—
58#16840408C411yescharacteristic, complemented
59#16840407C411yescharacteristic, complemented
60#16840404—21no—
61#16840396—21no—
62#16840396C411yescharacteristic, complemented
63#16840364—21no—
64#16840351—21no—
65#16840349—21no—
66#16840309C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C4⋊#92420—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—
97C4×#92420—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×#11758222—21no—
108C2×#11758222C2×C411yescharacteristic, complemented
109C2×#11758224C2×C411yescharacteristic
110C22×D244—21no—
111C22×D244C2×C411yescharacteristic
112C2×D4×D61—21no—
113C2×D4×D61—21no—
114C2×D4×D61C2×C411yescharacteristic, complemented
115C2×D4×D61D411yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118#14519776C2×C411yescharacteristic, complemented
119#14519773—21no—
120#14519773C2×C411yescharacteristic, complemented
121#14519772—21no—
122#14519772—21no—
123#14519767—21no—
124#14519765—21no—
125#14519765C2×C411yescharacteristic, complemented
126#14519763—21no—
127#14519763—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519761—21no—
132#14519761—21no—
133#14519759—21no—
134#14519757C2×C411yescharacteristic, complemented
135#14519757C2311yescharacteristic
136#14519756—21no—
137#14519756C2×C411yescharacteristic
138#14519755—21no—
139#14519752—21no—
140#14519752—21no—
141#14519752—21no—
142#14519752C2×C411yescharacteristic
143#14519752C2×C411yescharacteristic
144#14519752C2×C411yescharacteristic, complemented
145#14519752C2311yescharacteristic
146#14519752C2311yescharacteristic
147#14519751—21no—
148#14519751C2×C411yescharacteristic, complemented
149#14519750—21no—
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519749—21no—
156#14519749—21no—
157#14519748C2311yescharacteristic
158#14519747—21no—
159#14519747—21no—
160#14519747—21no—
161#14519745—21no—
162#14519745—21no—
163#14519745—21no—
164#14519742C2×C411yescharacteristic, complemented
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2×C411yescharacteristic
168C4×D244C2×C411yescharacteristic, complemented
169D4×Dic61—21no—
170D4×Dic61D411yescharacteristic
171#14519739—21no—
172#14519739—21no—
173#14519739C2×C411yescharacteristic, complemented
174#14519739D411yescharacteristic
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#14519735—21no—
184#14519735C2×C411yescharacteristic
185#14519734—21no—
186C4⋊C4×D61C2×C411yescharacteristic, complemented
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195#126×C61—21no—
196#125×C61C2×C411yescharacteristic, complemented
197#123×C61—21no—
198#121×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic, complemented
201C4×D4×C61—21no—
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic, complemented
204#117×C61C2×C411yescharacteristic, complemented
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—42no—
215C22×#6923—81no—
216C22×#6923—81no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61C22⋊C411yescharacteristic
220C2×D4×C61C22×C411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237#11758224—81no—
238D4×D61—42no—
239D4×D61—44no—
240D4×D61—81no—
241D4×D61—81no—
242D4×D61—81no—
243#11758222—81no—
244#11758222—81no—
245#11758222—81no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—81no—
253C2×D244—81no—
254C2×D244—81no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22×C411yescharacteristic
257C2×D244C22×C411yescharacteristic
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—81no—
263C2×C4×D61—81no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2411yescharacteristic
273C2×Dic122—21no—
274C2×Dic122C22×C411yescharacteristic
275C22⋊#6923—42no—
276C22⋊#6923—81no—
277C22⋊#6923—81no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—81no—
283C2×#92420—81no—
284C4⋊#6923—81no—
285C4⋊#6923—81no—
286C4×#6923—81no—
287#11758213—81no—
288#11758213—81no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61C22⋊C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C4⋊C4×C61C22×C411yescharacteristic
295C4⋊C4×C61C22×C411yescharacteristic
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61C22⋊C411yescharacteristic
301C22⋊C4×C61C22⋊C411yescharacteristic
302C42×C61—21no—
303C42×C61C22×C411yescharacteristic
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61C22⋊C411yescharacteristic
307C22⋊Dic61C22⋊C411yescharacteristic
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198C22⋊C411yescharacteristic
322#11758198C22⋊C411yescharacteristic
323#11758198C22⋊C411yescharacteristic
324#11758198C22⋊C411yescharacteristic
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61C22⋊C411yescharacteristic
328C4⋊Dic61C22×C411yescharacteristic
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C22×D61—22no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C22×D411yescharacteristic
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—84no—
375D4×C61—22no—
376D4×C61—41no—
377D4×C61—42no—
378D4×C61—81no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C23×C411yescharacteristic
391C22⋊D61—22no—
392C22⋊D61—41no—
393C22⋊D61—42no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—81no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—81no—
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C22×D411yescharacteristic
411D244—41no—
412D244—41no—
413D244—41no—
414D244—42no—
415D244—41no—
416D244—41no—
417D244—41no—
418D244—41no—
419D244—81no—
420D244—81no—
421D244—81no—
422C4×D61—21no—
423C4×D61—21no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—42no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436Dic122—41no—
437Dic122—81no—
438#92420—41no—
439#92420—41no—
440#92420—41no—
441#92420—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61#42112yes—
452C22×C61C22×C22⋊C411yescharacteristic
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—42no—
462C2×D61—42no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—162no—
472C2×D61—162no—
473C2×D61#57611yescharacteristic
474C2×D61#57711yescharacteristic
475#6923—81no—
476#6923—81no—
477#6923—81no—
478#6923—81no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—41no—
493Dic61—41no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—22no—
510C2×C61—41no—
511C2×C61—81no—
512C2×C61#288311yescharacteristic
513C2×C61#289711yescharacteristic
514C2×C61C2×#42111yescharacteristic
515D61—21no—
516D61—21no—
517D61—41no—
518D61—41no—
519D61—81no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—1221no—
525#553#692311yescharacteristic, complemented
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—1221no—
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8—611no—
598#127—611no—
599#127—1221no—
600#126—21no—
601#126—1221no—
602#126—1221no—
603#125—1221no—
604#125C2×#692311yescharacteristic, complemented
605#124—611no—
606#124—1221no—
607#124—1221no—
608#124—1221no—
609#123—21no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—21no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—1221no—
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#121—1221no—
639#121—1221no—
640#121—1221no—
641#121C2×#692311yescharacteristic
642#121C2×#692311yescharacteristic, complemented
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—21no—
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—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4C2×#692311yescharacteristic
670C4×D4C2×#692311yescharacteristic, complemented
671#117—611no—
672#117—1221no—
673#117—1221no—
674#117C2×#692311yescharacteristic, complemented
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4C2×#692311yescharacteristic
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702C4×C8—1221no—
703#95—611no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712C24—611no—
713C24—611no—
714C24—1221no—
715C24—1221no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—611no—
721C2×Q8—1221no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—611no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—2442no—
749C2×D4—2444no—
750C2×D4C22⋊#692311yescharacteristic
751C2×D4C22×#692311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—4881no—
778C22×C4—2442no—
779C22×C4C22×#692311yescharacteristic
780C22×C4C22×#692311yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—4881no—
803C4⋊C4—4881no—
804C4⋊C4C22⋊#692311yescharacteristic
805C4⋊C4C22×#692311yescharacteristic
806C4⋊C4C22×#692311yescharacteristic
807C4⋊C4C22×#692311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—4881no—
834C22⋊C4—4881no—
835C22⋊C4—2442no—
836C22⋊C4C22⋊#692311yescharacteristic
837C22⋊C4C22⋊#692311yescharacteristic
838C42—21no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—1221no—
843C42—1221no—
844C42—4881no—
845C42C22×#692311yescharacteristic
846C23—21no—
847C23—611no—
848C23—611no—
849C23—611no—
850C23—1221no—
851C23—1221no—
852C23—1221no—
853C23—1221no—
854C23—1222no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23—2442no—
865C23—2442no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—4881no—
869Q8—2441no—
870D4—22no—
871D4—41no—
872D4—42no—
873D4—81no—
874D4—1222no—
875D4—4881no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—2441no—
884D4—2441no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2441no—
892D4—2442no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4881no—
915C2×C4—4884no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2442no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4C2×C22⋊#692311yescharacteristic
940C2×C4C2×C22⋊#692311yescharacteristic
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4C23×#692311yescharacteristic
944C8—2441no—
945C8—2441no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—611no—
957C22—611no—
958C22—1221no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—9762no—
967C22—9762no—
968C22—4881no—
969C22—4881no—
970C22—2442no—
971C22—2442no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22#1684075912yes—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—4881no—
994C4—4881no—
995C4—4881no—
996C4—4881no—
997C4—2441no—
998C4—2441no—
999C2—22no—
1000C2—41no—
1001C2—81no—
1002C2—1221no—
1003C2—1221no—
1004C2—4881no—
1005C2—4881no—
1006C2—2441no—
1007C2—2441no—
1008C2#2146241911yescharacteristic
1009C2#2146244011yescharacteristic
1010C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459844C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462679C2semidirect
2. #21462301C2semidirect
3. #21461262C2semidirect
4. #21461254C2semidirect
5. #21461249C2semidirect
6. #21461247C2semidirect
7. #21461238C2semidirect
8. #21461236C2semidirect
9. #21461233C2semidirect
10. #21461225C2semidirect
11. #21461216C2semidirect
12. #21461204C2semidirect
13. #21461195C2semidirect
14. C2×#16840614C2semidirect
20. #16840784C22semidirect
21. #16840781C22semidirect
22. #16840733C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. C2×#14519834C22semidirect
30. #16840707C22semidirect
31. #16840706C22semidirect
32. #16840705C22semidirect
33. #16840704C22semidirect
34. C4×C22⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840475C4semidirect
53. #16840467C4semidirect
54. #16840465C4semidirect
56. #16840430C4semidirect
58. #16840408C4semidirect
59. #16840407C4semidirect
62. #16840396C4semidirect
74. C61×#553C4semidirect
108. C2×#11758222C2×C4semidirect
114. C2×D4×D61C2×C4semidirect
118. #14519776C2×C4semidirect
120. #14519773C2×C4semidirect
125. #14519765C2×C4semidirect
134. #14519757C2×C4semidirect
144. #14519752C2×C4semidirect
148. #14519751C2×C4semidirect
164. #14519742C2×C4semidirect
168. C4×D244C2×C4semidirect
173. #14519739C2×C4semidirect
186. C4⋊C4×D61C2×C4semidirect
196. #125×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
203. C4×D4×C61C2×C4semidirect
204. #117×C61C2×C4semidirect
525. #553#6923semidirect
580. C61#17597semidirect
604. #125C2×#6923semidirect
642. #121C2×#6923semidirect
670. C4×D4C2×#6923semidirect
674. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626792
#214623012
#214612622
#214612542
#214612492
#214612472
#214612382
#214612362
#214612332
#214612252
#214612162
#214612042
#214611952
C2×#168406142
#214598442
#1759761