Finite Group Databasebeta

← #30611254

Subgroups — #30611254

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#21462677C211yesmaximal, characteristic, complemented
2#21462301C211yesmaximal, characteristic, complemented
3#21461260C211yesmaximal, characteristic, complemented
4#21461255C211yesmaximal, characteristic, complemented
5#21461249C211yesmaximal, characteristic, complemented
6#21461246C211yesmaximal, characteristic, complemented
7#21461238C211yesmaximal, characteristic, complemented
8#21461237C211yesmaximal, characteristic, complemented
9#21461231C211yesmaximal, characteristic, complemented
10#21461224C211yesmaximal, characteristic, complemented
11#21461214C211yesmaximal, characteristic, complemented
12#21461205C211yesmaximal, characteristic, complemented
13#21461194C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459848C211yesmaximal, characteristic
16#16840797—21no—
17#16840794—21no—
18#16840794—21no—
19#16840790—21no—
20#16840784C2211yescharacteristic, complemented
21#16840781C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840734C2211yescharacteristic, complemented
24D61⋊(C22⋊C8)C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, 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#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic, complemented
41#16840614C2211yescharacteristic, complemented
42#16840614C2211yescharacteristic, complemented
43#16840614C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840476C411yescharacteristic, complemented
53#16840470C411yescharacteristic, complemented
54#16840462C411yescharacteristic, complemented
55#16840458C411yescharacteristic, complemented
56#16840457—21no—
57#16840431C411yescharacteristic, complemented
58#16840409—21no—
59#16840405C411yescharacteristic, complemented
60#16840402—21no—
61D4×C22⋊D61C411yescharacteristic, complemented
62#16840394—21no—
63#16840362—21no—
64#16840348—21no—
65#16840347—21no—
66#16840309C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840235—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—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×#11758226C2×C411yescharacteristic, complemented
108C2×#11758222—21no—
109C22×C22⋊D61—21no—
110C22×C22⋊D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61C2×C411yescharacteristic
113C2×D4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116#14519776C2×C411yescharacteristic, complemented
117#14519773—21no—
118#14519773C2×C411yescharacteristic, complemented
119#14519772—21no—
120#14519770—21no—
121#14519770—21no—
122#14519769C2×C411yescharacteristic, complemented
123#14519767—21no—
124#14519764—21no—
125#14519763—21no—
126#14519763—21no—
127#14519762—21no—
128#14519760—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519757—21no—
134#14519754—21no—
135#14519753C2×C411yescharacteristic
136#14519753C2311yescharacteristic
137#14519752C2311yescharacteristic
138#14519751—21no—
139#14519751C2×C411yescharacteristic
140#14519751C2×C411yescharacteristic, complemented
141#14519750—21no—
142#14519750—21no—
143#14519750—21no—
144#14519750—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2×C411yescharacteristic, complemented
155#14519748C2311yescharacteristic
156#14519748C2311yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519746—21no—
160#14519745—21no—
161#14519745—21no—
162Q8×Dic61C2×C411yescharacteristic, complemented
163C4×D244C2×C411yescharacteristic
164C4×D244C2×C411yescharacteristic, complemented
165D4×Dic61C2×C411yescharacteristic, complemented
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519736C2×C411yescharacteristic
183#14519735C2×C411yescharacteristic, complemented
184#14519733—21no—
185#14519733—21no—
186C2×C4⋊Dic61C2×C411yescharacteristic, complemented
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C2×C22⋊Dic61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic, complemented
197#124×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic, complemented
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
205C2×C22⋊C4×C61—21no—
206C24×C61—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—
217#41×C61—81no—
218C2×Q8×C61C22×C411yescharacteristic
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—81no—
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C22×C411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61—81no—
242C2×C22⋊D61—81no—
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249#11758226—81no—
250D4×D61—42no—
251D4×D61—81no—
252D4×D61—81no—
253D4×D61—81no—
254#11758222—81no—
255#11758222—81no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C22⋊C411yescharacteristic
259C2×D244C22×C411yescharacteristic
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—81no—
264C2×C4×D61—81no—
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2411yescharacteristic
274C2×Dic122—21no—
275C22⋊#6923—42no—
276C22⋊#6923—81no—
277C22⋊#6923—81no—
278#11758217—81no—
279#11758217—81no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—21no—
284C4⋊#6923—81no—
285C4⋊#6923—81no—
286C4×#6923—81no—
287D61⋊C8—81no—
288D61⋊C8—81no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C22⋊C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61C22⋊C411yescharacteristic
298C22⋊C4×C61C22⋊C411yescharacteristic
299C42×C61C22×C411yescharacteristic
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61C22⋊C411yescharacteristic
308C22⋊Dic61C22⋊C411yescharacteristic
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⋊Dic61C22⋊C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324C4⋊Dic61C22×C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—42no—
343C23×C61—81no—
344C23×C61—81no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—22no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—42no—
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—
375Q8×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—81no—
380D4×C61—81no—
381D4×C61—81no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—81no—
387C2×C4×C61—81no—
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C23×C411yescharacteristic
393C22⋊D61—22no—
394C22⋊D61—41no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—42no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—42no—
413C2×Dic61—81no—
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C22×D411yescharacteristic
419D244—22no—
420D244—41no—
421D244—41no—
422D244—41no—
423D244—81no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—81no—
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—21no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—162no—
456C22×C61C22×C22⋊C411yescharacteristic
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—42no—
465C2×D61—42no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—162no—
472C2×D61#42112yes—
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—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—41no—
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—41no—
510C2×C61—41no—
511C2×C61—81no—
512C2×C61—81no—
513C2×C61#288311yescharacteristic
514C2×C61#289711yescharacteristic
515C2×C61C2×#42111yescharacteristic
516D61—21no—
517D61—21no—
518D61—22no—
519D61—41no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—1221no—
529#546—1221no—
530#546#692311yescharacteristic, complemented
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—1221no—
583C2×#41C2×#692311yescharacteristic
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4C2×#692311yescharacteristic, complemented
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—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—1221no—
606#124—1221no—
607#124—1221no—
608#124C2×#692311yescharacteristic, complemented
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—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8C2×#692311yescharacteristic, complemented
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—611no—
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#121—1221no—
642#121C2×#692311yescharacteristic
643#120—21no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—611no—
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—1221no—
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—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—611no—
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—21no—
713C24—611no—
714C24—611no—
715C24—1221no—
716#41—81no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—1221no—
721C2×Q8C22×#692311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—81no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—611no—
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—2442no—
748C2×D4—2444no—
749C2×D4C22⋊#692311yescharacteristic
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—611no—
791C4⋊C4—611no—
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—1221no—
803C4⋊C4—1221no—
804C4⋊C4—4881no—
805C4⋊C4—4881no—
806C4⋊C4C22⋊#692311yescharacteristic
807C4⋊C4C22×#692311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
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—611no—
839C42—611no—
840C42—611no—
841C42—1221no—
842C42—1221no—
843C42—1221no—
844C42—4881no—
845C42C22×#692311yescharacteristic
846C23—21no—
847C23—21no—
848C23—42no—
849C23—81no—
850C23—81no—
851C23—611no—
852C23—611no—
853C23—611no—
854C23—1221no—
855C23—1221no—
856C23—1222no—
857C23—1221no—
858C23—1221no—
859C23—1221no—
860C23—4881no—
861C23—4881no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2442no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—41no—
869Q8—4881no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—81no—
874D4—81no—
875D4—81no—
876D4—1222no—
877D4—1222no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—2441no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2442no—
889D4—2442no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2442no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4884no—
915C2×C4—4881no—
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—2441no—
925C2×C4—2441no—
926C2×C4—2442no—
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—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—162no—
961C22—611no—
962C22—611no—
963C22—612no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—1221no—
970C22—1221no—
971C22—9762no—
972C22—4881no—
973C22—4881no—
974C22—2442no—
975C22—2442no—
976C22—2441no—
977C22—2441no—
978C22—2441no—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—41no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—4881no—
993C4—4881no—
994C4—4881no—
995C4—4881no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—1221no—
1004C2—1221no—
1005C2—1222no—
1006C2—4881no—
1007C2—2441no—
1008C2#2146241811yescharacteristic
1009C2#2146244011yescharacteristic
1010C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459848C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462677C2semidirect
2. #21462301C2semidirect
3. #21461260C2semidirect
4. #21461255C2semidirect
5. #21461249C2semidirect
6. #21461246C2semidirect
7. #21461238C2semidirect
8. #21461237C2semidirect
9. #21461231C2semidirect
10. #21461224C2semidirect
11. #21461214C2semidirect
12. #21461205C2semidirect
13. #21461194C2semidirect
14. D61⋊#327C2semidirect
20. #16840784C22semidirect
21. #16840781C22semidirect
22. #16840734C22semidirect
23. #16840734C22semidirect
24. D61⋊(C22⋊C8)C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
30. #16840707C22semidirect
31. #16840706C22semidirect
32. #16840705C22semidirect
33. #16840704C22semidirect
34. C4×C22⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840476C4semidirect
53. #16840470C4semidirect
54. #16840462C4semidirect
55. #16840458C4semidirect
57. #16840431C4semidirect
59. #16840405C4semidirect
61. D4×C22⋊D61C4semidirect
74. C61×#546C4semidirect
107. C2×#11758226C2×C4semidirect
116. #14519776C2×C4semidirect
118. #14519773C2×C4semidirect
122. #14519769C2×C4semidirect
140. #14519751C2×C4semidirect
153. #14519748C2×C4semidirect
154. #14519748C2×C4semidirect
162. Q8×Dic61C2×C4semidirect
164. C4×D244C2×C4semidirect
165. D4×Dic61C2×C4semidirect
183. #14519735C2×C4semidirect
186. C2×C4⋊Dic61C2×C4semidirect
196. C22×D4×C61C2×C4semidirect
197. #124×C61C2×C4semidirect
199. C22⋊Q8×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
530. #546#6923semidirect
580. C61#17597semidirect
589. C22×D4C2×#6923semidirect
608. #124C2×#6923semidirect
620. C22⋊Q8C2×#6923semidirect
670. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626772
#214623012
#214612602
#214612552
#214612492
#214612462
#214612382
#214612372
#214612312
#214612242
#214612142
#214612052
#214611942
D61⋊#3272
#214598482
#1759761