Finite Group Databasebeta

← #30611378

Subgroups — #30611378

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462332C211yesmaximal, characteristic, complemented
3#21461258C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461236C211yesmaximal, characteristic, complemented
6#21461235C211yesmaximal, characteristic, complemented
7#21461233C211yesmaximal, characteristic, complemented
8#21461230C211yesmaximal, characteristic, complemented
9#21461222C211yesmaximal, characteristic, complemented
10#21461221C211yesmaximal, characteristic, complemented
11#21461207C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13C2×#16840615C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459648C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17#16840794—21no—
18#16840793—21no—
19#16840792—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic, complemented
22#16840784C2211yescharacteristic, complemented
23#16840734C2211yescharacteristic, complemented
24#16840733C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic
26D61⋊(C22⋊C8)C2211yescharacteristic
27#16840713—21no—
28#16840709—21no—
29#16840709—21no—
30#16840706C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32#16840704C2211yescharacteristic, complemented
33C4×C4⋊#6923C2211yescharacteristic, complemented
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464—21no—
53#16840460C411yescharacteristic, complemented
54#16840458—21no—
55#16840451C411yescharacteristic, complemented
56#16840450C411yescharacteristic, complemented
57#16840437—21no—
58#16840435—21no—
59#16840421C411yescharacteristic, complemented
60#16840418C411yescharacteristic, complemented
61#16840409C411yescharacteristic, complemented
62#16840407C411yescharacteristic, complemented
63#16840353—21no—
64#16840348—21no—
65#16840320—21no—
66#16840297C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81D4×#6923—44no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90C4⋊#92420—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100#14519832—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108C2×#11758222C2×C411yescharacteristic, complemented
109C2×#11758224C2×C411yescharacteristic, complemented
110C22×Dic122C2×C411yescharacteristic, complemented
111C2×D4×D61—21no—
112C2×D4×D61C2×C411yescharacteristic, complemented
113C2×D4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519770—21no—
120#14519770—21no—
121#14519769—21no—
122#14519768—21no—
123#14519768C2×C411yescharacteristic, complemented
124#14519765C2×C411yescharacteristic, complemented
125#14519764C2×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#14519759—21no—
135#14519759—21no—
136#14519759—21no—
137#14519757—21no—
138#14519757—21no—
139#14519757C2×C411yescharacteristic, complemented
140#14519757C2×C411yescharacteristic, complemented
141#14519757C2×C411yescharacteristic, complemented
142#14519757C2311yescharacteristic
143#14519757C2311yescharacteristic
144#14519756C2×C411yescharacteristic, complemented
145#14519755—21no—
146#14519754—21no—
147#14519752C2×C411yescharacteristic, complemented
148#14519752C2311yescharacteristic
149#14519751—21no—
150#14519751—21no—
151#14519751C2×C411yescharacteristic, complemented
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519748—21no—
157#14519748C2311yescharacteristic
158#14519747—21no—
159#14519747—21no—
160#14519745—21no—
161#14519745—21no—
162C4×Dic122C2×C411yescharacteristic, complemented
163#14519742C2×C411yescharacteristic, complemented
164C4×D244—21no—
165C4×D244—21no—
166C4×D244C2×C411yescharacteristic
167D4×Dic61—21no—
168D4×Dic61—21no—
169D4×Dic61D411yescharacteristic
170#14519739—21no—
171#14519739C2×C411yescharacteristic, complemented
172#14519739D411yescharacteristic
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736—21no—
182#14519735—21no—
183#14519735—21no—
184#14519735C2×C411yescharacteristic, complemented
185#14519734—21no—
186C2×C4⋊Dic61—21no—
187C4⋊C4×D61C2×C411yescharacteristic, complemented
188C4⋊C4×D61D411yescharacteristic
189C2×#11758198—21no—
190C2×#11758198—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic, complemented
201#121×C61C2×C411yescharacteristic, complemented
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
205#117×C61C2×C411yescharacteristic, complemented
206C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
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—42no—
216C22×#6923—42no—
217C22×#6923—42no—
218C22×#6923—81no—
219C22×#6923—81no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61C22⋊C411yescharacteristic
223C2×D4×C61C22×C411yescharacteristic
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⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758224—81no—
240D4×D61—22no—
241D4×D61—22no—
242D4×D61—42no—
243D4×D61—42no—
244D4×D61—81no—
245#11758222—81no—
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—81no—
266C2×Dic122C22×C411yescharacteristic
267C2×Dic122C22×C411yescharacteristic
268C22⋊#6923—42no—
269C22⋊#6923—42no—
270#11758217—81no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—81no—
276C4⋊#6923—42no—
277C4⋊#6923—42no—
278C4⋊#6923—81no—
279C4⋊#6923—81no—
280C4×#6923—42no—
281#11758213—81no—
282D61⋊C8—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61C22⋊C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C4⋊C4×C61C22×C411yescharacteristic
289C4⋊C4×C61C22×C411yescharacteristic
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61C22⋊C411yescharacteristic
295C22⋊C4×C61C22⋊C411yescharacteristic
296C42×C61—21no—
297C42×C61C22×C411yescharacteristic
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61C22⋊C411yescharacteristic
303C22⋊Dic61C22⋊C411yescharacteristic
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#11758198—21no—
315#11758198—21no—
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61C22⋊C411yescharacteristic
327C4⋊Dic61C22×C411yescharacteristic
328#11758196—21no—
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×Dic61—21no—
338C4×Dic61C22×C411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C23×C61—21no—
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C2×C22⋊C411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—42no—
352C22×D61—81no—
353C22×D61—81no—
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61AGL(1,ℤ/8)12yes—
357C22×D61#13712yes—
358C22×D61C22×D411yescharacteristic
359C2×#6923—22no—
360C2×#6923—41no—
361C2×#6923—41no—
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—84no—
372C2×#6923—84no—
373D4×C61—22no—
374D4×C61—41no—
375D4×C61—42no—
376D4×C61—81no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—81no—
383C2×C4×C61—81no—
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C22⋊D61—22no—
390C22⋊D61—22no—
391C22⋊D61—42no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—81no—
395C22⋊D61—81no—
396C22⋊D61—81no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—81no—
403C2×Dic61—81no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C22×D411yescharacteristic
409D244—22no—
410D244—41no—
411D244—41no—
412D244—41no—
413D244—81no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—42no—
425C4×D61—81no—
426C4×D61—81no—
427Dic122—41no—
428Dic122—41no—
429Dic122—81no—
430#92420—41no—
431#92420—41no—
432#92420—41no—
433#92420—41no—
434#17622—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61#41712yes—
444C22×C61C22×C22⋊C411yescharacteristic
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—162no—
460C2×D61#41712yes—
461C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
462C2×D61C2×#13711yescharacteristic
463#6923—42no—
464#6923—81no—
465#6923—81no—
466#6923—81no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—41no—
473C4×C61—41no—
474C4×C61—41no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—21no—
479Dic61—21no—
480Dic61—41no—
481Dic61—41no—
482Dic61—41no—
483#3505—611no—
484#2973—611no—
485#2349—611no—
486#1520—611no—
487#1519—611no—
488#1513—611no—
489#1513—611no—
490#1512—611no—
491#1512—611no—
492#1509—611no—
493#1509—611no—
494#1504—611no—
495#1504—611no—
496C2×#328—611no—
497C2×#327—611no—
498C2×C61—22no—
499C2×C61—41no—
500C2×C61—81no—
501C2×C61#288311yescharacteristic
502C2×C61C2×#41711yescharacteristic
503C2×C61#290111yescharacteristic
504D61—21no—
505D61—21no—
506D61—22no—
507D61—41no—
508D61—81no—
509#553—611no—
510#553—1221no—
511#553—1221no—
512#553#692311yescharacteristic, complemented
513#552—611no—
514#552—611no—
515#551—1221no—
516#551—1221no—
517#548—611no—
518#548—611no—
519#546—611no—
520#546—611no—
521#539—1221no—
522#538—1221no—
523#534—1221no—
524#529—611no—
525#529—611no—
526#525—611no—
527#525—611no—
528C2×C22⋊Q8—611no—
529C2×#121—611no—
530#518—1221no—
531C2×C4×D4—611no—
532C2×C4×D4—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#435—1221no—
537#432—611no—
538#432—611no—
539#407—611no—
540#407—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543#389—1221no—
544#385—1221no—
545#385—1221no—
546#382—611no—
547#380—611no—
548#380—611no—
549C4×C4⋊C4—611no—
550C2×#95—611no—
551C2×#95—611no—
552#328—611no—
553#328—611no—
554#328—611no—
555#328—611no—
556#328—611no—
557#328—611no—
558#328—611no—
559#328—611no—
560#327—611no—
561#327—611no—
562#327—611no—
563#327—611no—
564#327—611no—
565#327—611no—
566#327—611no—
567#327—611no—
568C61#1762211yescharacteristic, complemented, Sylow
569C2×#41—611no—
570C2×#41—611no—
571C22×Q8—611no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—1221no—
578C23×C4—1221no—
579C2×M16—1221no—
580C2×M16—1221no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—21no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#125—611no—
590#125—1221no—
591#125—1221no—
592#125C2×#692311yescharacteristic, complemented
593#124—611no—
594#124—611no—
595#124—1221no—
596#124—1221no—
597#123—21no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—611no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—611no—
612C22⋊Q8—611no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8—1221no—
617#121—21no—
618#121—611no—
619#121—611no—
620#121—611no—
621#121—611no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121C2×#692311yescharacteristic, complemented
630#121C2×#692311yescharacteristic, complemented
631#120—1221no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635C4×Q8—611no—
636C4×Q8—611no—
637C4×D4—21no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—2444no—
656C4×D4C2×#692311yescharacteristic
657C4×D4C2×#692311yescharacteristic, complemented
658#117—611no—
659#117—1221no—
660#117—1221no—
661#117—1221no—
662#117—1221no—
663#117C2×#692311yescharacteristic, complemented
664C2×C4⋊C4—611no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—1221no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4C2×#692311yescharacteristic, complemented
672C2×C22⋊C4—611no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—1221no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C42—611no—
681C2×C42—1221no—
682C4⋊C8—1221no—
683C4⋊C8—1221no—
684C22⋊C8—611no—
685C22⋊C8—611no—
686C22⋊C8—611no—
687C22⋊C8—611no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8—1221no—
691C22⋊C8—1221no—
692#97—1221no—
693#97—1221no—
694#95—611no—
695#95—611no—
696#95—611no—
697#95—611no—
698#95—1221no—
699#95—1221no—
700#95—1221no—
701C24—611no—
702C24—611no—
703C24—1221no—
704#41—4881no—
705#41—4881no—
706C2×Q8—611no—
707C2×Q8—611no—
708C2×Q8—1221no—
709C2×Q8—4881no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—4881no—
726C2×D4—2442no—
727C2×D4—2442no—
728C2×D4C22⋊#692311yescharacteristic
729C2×D4C22×#692311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—4881no—
753C22×C4—4881no—
754C22×C4—4881no—
755C22×C4—4881no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4C22×#692311yescharacteristic
761C22×C4C22×#692311yescharacteristic
762M16—4881no—
763M16—4881no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—4881no—
769C2×C8—4881no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—611no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—4881no—
789C4⋊C4—4881no—
790C4⋊C4—2442no—
791C4⋊C4—2442no—
792C4⋊C4C22⋊#692311yescharacteristic
793C4⋊C4C22×#692311yescharacteristic
794C4⋊C4C22×#692311yescharacteristic
795C4⋊C4C22×#692311yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—611no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—2442no—
823C22⋊C4—2442no—
824C22⋊C4C22⋊#692311yescharacteristic
825C22⋊C4C22⋊#692311yescharacteristic
826C42—21no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42—2442no—
834C42C22×#692311yescharacteristic
835C23—21no—
836C23—611no—
837C23—611no—
838C23—612no—
839C23—612no—
840C23—611no—
841C23—1221no—
842C23—1221no—
843C23—1221no—
844C23—4881no—
845C23—4881no—
846C23—2441no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2442no—
851C23C2×C22⋊#692311yescharacteristic
852C23C2×C22⋊#692311yescharacteristic
853Q8—4881no—
854Q8—2441no—
855Q8—2441no—
856D4—22no—
857D4—41no—
858D4—42no—
859D4—81no—
860D4—1222no—
861D4—1222no—
862D4—1222no—
863D4—4881no—
864D4—4881no—
865D4—4881no—
866D4—4881no—
867D4—2441no—
868D4—2441no—
869D4—2441no—
870D4—2441no—
871D4—2441no—
872D4—2442no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1222no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4884no—
895C2×C4—4884no—
896C2×C4—4881no—
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—2442no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4C2×C22⋊#692311yescharacteristic
920C2×C4C2×C22⋊#692311yescharacteristic
921C2×C4C2×C22⋊#692311yescharacteristic
922C2×C4C2×C22⋊#692311yescharacteristic
923C2×C4C23×#692311yescharacteristic
924C8—2441no—
925C8—2441no—
926C8—2441no—
927C8—2441no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—611no—
937C22—611no—
938C22—612no—
939C22—1221no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—9762no—
947C22—2442no—
948C22—2442no—
949C22—2442no—
950C22—2442no—
951C22—2441no—
952C22—2441no—
953C22—2441no—
954C22#1684075312yes—
955C22C22×C22⋊#692311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—41no—
962C4—41no—
963C4—41no—
964C4—1221no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—1221no—
969C4—4881no—
970C4—4881no—
971C4—4881no—
972C4—2442no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C2—22no—
977C2—41no—
978C2—81no—
979C2—1221no—
980C2—1222no—
981C2—1221no—
982C2—4881no—
983C2—2441no—
984C2#2146241911yescharacteristic
985C2C2×#1684075311yescharacteristic
986C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459648C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#17622
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. #21462671C2semidirect
2. #21462332C2semidirect
3. #21461258C2semidirect
4. #21461254C2semidirect
5. #21461236C2semidirect
6. #21461235C2semidirect
7. #21461233C2semidirect
8. #21461230C2semidirect
9. #21461222C2semidirect
10. #21461221C2semidirect
11. #21461207C2semidirect
12. #21461204C2semidirect
13. C2×#16840615C2semidirect
14. D61⋊#327C2semidirect
21. #16840785C22semidirect
22. #16840784C22semidirect
23. #16840734C22semidirect
24. #16840733C22semidirect
30. #16840706C22semidirect
32. #16840704C22semidirect
33. C4×C4⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
40. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
53. #16840460C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840421C4semidirect
60. #16840418C4semidirect
61. #16840409C4semidirect
62. #16840407C4semidirect
74. C61×#553C4semidirect
108. C2×#11758222C2×C4semidirect
109. C2×#11758224C2×C4semidirect
110. C22×Dic122C2×C4semidirect
112. C2×D4×D61C2×C4semidirect
123. #14519768C2×C4semidirect
124. #14519765C2×C4semidirect
125. #14519764C2×C4semidirect
139. #14519757C2×C4semidirect
140. #14519757C2×C4semidirect
141. #14519757C2×C4semidirect
144. #14519756C2×C4semidirect
147. #14519752C2×C4semidirect
151. #14519751C2×C4semidirect
162. C4×Dic122C2×C4semidirect
163. #14519742C2×C4semidirect
171. #14519739C2×C4semidirect
184. #14519735C2×C4semidirect
187. C4⋊C4×D61C2×C4semidirect
197. #125×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
201. #121×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
206. C2×C4⋊C4×C61C2×C4semidirect
512. #553#6923semidirect
568. C61#17622semidirect
592. #125C2×#6923semidirect
629. #121C2×#6923semidirect
630. #121C2×#6923semidirect
657. C4×D4C2×#6923semidirect
663. #117C2×#6923semidirect
671. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623322
#214612582
#214612542
#214612362
#214612352
#214612332
#214612302
#214612222
#214612212
#214612072
#214612042
C2×#168406152
D61⋊#3272
#214596482
#1762261