Finite Group Databasebeta

← #30615214

Subgroups — #30615214

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C211yesmaximal, characteristic, complemented
2#21462268C211yesmaximal, characteristic, complemented
3#21461724C212yesmaximal, complemented
4#21461688C212yesmaximal, complemented
5#21461687C212yesmaximal, complemented
6#21461659C212yesmaximal
7C4×#14519840C212yesmaximal, complemented
8C4×#14519839C212yesmaximal, complemented
9C4×#41×D61C211yesmaximal, characteristic
10C2×#14519856—21no—
11#16840781—21no—
12#16840780—21no—
13#16840779—21no—
14#16840778—21no—
15D61⋊(C4⋊C8)C2212yes—
16C2×#14519840C2214yes—
17C2×#14519839C2214yes—
18D61⋊(C22⋊C8)C2212yes—
19C4×D61⋊C8C2212yes—
20#16840708C2212yes—
21#16840706—21no—
22#16840704—21no—
23#16840704C2212yes—
24C4×C4⋊#6923—21no—
25C4×C4⋊#6923C2212yes—
26#16840635C2214yes—
27#16840635C2214yes—
28C2×#41×D61C2211yescharacteristic
29#41×Dic61C411yescharacteristic, complemented
30C4×#11758226C411yescharacteristic, complemented
31C4×#11758226C411yescharacteristic, complemented
32C4×#11758222—21no—
33C4×#11758222C411yescharacteristic, complemented
34#16840230—21no—
35#16840230C411yescharacteristic, complemented
36C4×#11758224—21no—
37C4×#11758224—21no—
38C4×#11758224C411yescharacteristic, complemented
39C4×#11758224C411yescharacteristic, complemented
40C4×Q8×D61C2211yescharacteristic
41C4×Q8×D61C2211yescharacteristic
42C4×D4×D61—21no—
43C4×D4×D61—21no—
44C4×D4×D61C2211yescharacteristic
45C4×D4×D61C2211yescharacteristic
46#117×D61—21no—
47#117×D61C2211yescharacteristic
48C2×C42×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C4×#41×C61C411yescharacteristic, complemented
51C2×D61⋊C8C2314yes—
52#14519856—44no—
53C2×C4⋊#6923—22no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923C2314yes—
56C2×C22⋊#6923—22no—
57C2×C4×#6923—22no—
58#14519844—22no—
59C4⋊#92420—22no—
60#14519840—28no—
61#14519839—28no—
62#14519834—22no—
63C22⋊#92420—22no—
64C4×#92420—22no—
65C4×#92420—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68C2×#11758226C2×C411yescharacteristic
69C2×#11758222—21no—
70C2×#11758222C2×C411yescharacteristic
71C2×#11758224—21no—
72C2×#11758224C2×C411yescharacteristic
73#41×D61—24no—
74#41×D61—24no—
75C2×Q8×D61C2311yescharacteristic
76C2×D4×D61—21no—
77C2×D4×D61C2311yescharacteristic
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85Q8×Dic61C2×C411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122C2×C411yescharacteristic
89C4×Dic122C2×C411yescharacteristic
90#14519742—21no—
91#14519742—21no—
92#14519742C2×C411yescharacteristic
93#14519742C2×C411yescharacteristic
94C4×D244—21no—
95C4×D244—21no—
96C4×D244C2×C411yescharacteristic
97C4×D244C2×C411yescharacteristic
98D4×Dic61—21no—
99D4×Dic61—21no—
100D4×Dic61C2×C411yescharacteristic
101D4×Dic61C2×C411yescharacteristic
102#14519739—21no—
103#14519739—21no—
104#14519739C2×C411yescharacteristic
105#14519739C2×C411yescharacteristic
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111C4×C22⋊D61—21no—
112#14519737—21no—
113#14519737—21no—
114#14519737—21no—
115#14519737—21no—
116#14519737—21no—
117#14519737—21no—
118#14519736—21no—
119#14519736C2×C411yescharacteristic
120#14519735—21no—
121#14519735—21no—
122#14519735C2×C411yescharacteristic
123#14519735C2×C411yescharacteristic
124#14519734—21no—
125#14519734—21no—
126#14519734—21no—
127#14519733—21no—
128#14519733—21no—
129#14519733—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61—21no—
147C42×D61—21no—
148C42×D61—21no—
149C42×D61—21no—
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61C2311yescharacteristic
157C42×D61C2311yescharacteristic
158C2×#41×C61C2×C411yescharacteristic
159C4×Q8×C61C2×C411yescharacteristic
160C4×Q8×C61C2×C411yescharacteristic
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61C2×C411yescharacteristic
164C4×D4×C61C2×C411yescharacteristic
165#117×C61—21no—
166#117×C61C2×C411yescharacteristic
167C2×C42×C61—21no—
168C2×C42×C61C2×C411yescharacteristic
169C23×D61—21no—
170C23×D61C2×D411yescharacteristic
171C22×#6923—24no—
172#41×C61—22no—
173#41×C61—22no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22⋊C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C22⋊C411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758226—22no—
193#11758226—22no—
194Q8×D61—22no—
195Q8×D61#4114yes—
196#11758224—28no—
197#11758224—22no—
198#11758224—22no—
199D4×D61—28no—
200D4×D61—22no—
201D4×D61#4114yes—
202#11758222—28no—
203#11758222—22no—
204#11758222—22no—
205C2×D244—21no—
206C2×D244C22×C411yescharacteristic
207C2×C4×D61—28no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—24no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—44no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122C22×C411yescharacteristic
239C22⋊#6923—44no—
240C2×#92420—24no—
241C4⋊#6923—24no—
242C4⋊#6923—24no—
243C4⋊#6923—44no—
244C4⋊#6923—44no—
245C4×#6923—44no—
246D61⋊C8—24no—
247D61⋊C8—24no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C22×C411yescharacteristic
251C4⋊C4×C61C22×C411yescharacteristic
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61C22⋊C411yescharacteristic
259C42×C61C22⋊C411yescharacteristic
260C42×C61C22×C411yescharacteristic
261C42×C61C22×C411yescharacteristic
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61C22×C411yescharacteristic
274C4⋊Dic61C22×C411yescharacteristic
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22⋊C411yescharacteristic
293C4×Dic61C22⋊C411yescharacteristic
294C4×Dic61C22⋊C411yescharacteristic
295C4×Dic61C22⋊C411yescharacteristic
296C4×Dic61C22×C411yescharacteristic
297C4×Dic61C22×C411yescharacteristic
298C4×Dic61C2×D411yescharacteristic
299C4×Dic61C2×D411yescharacteristic
300C4×Dic61C2×D411yescharacteristic
301C4×Dic61C2×D411yescharacteristic
302C23×C61—21no—
303C23×C61C2×C22⋊C411yescharacteristic
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—24no—
307C22×D61—22no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—42no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C2×C22⋊C411yescharacteristic
314C22×D61C22×D411yescharacteristic
315C2×#6923—44no—
316C2×#6923—44no—
317C2×#6923—44no—
318Q8×C61—21no—
319Q8×C61#11712yescomplemented
320D4×C61—24no—
321D4×C61—21no—
322D4×C61#11712yescomplemented
323C2×C4×C61—24no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C23×C411yescharacteristic
339C22⋊D61—24no—
340C22⋊D61—24no—
341C22⋊D61—24no—
342C2×Dic61—24no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C22×D411yescharacteristic
357D244—24no—
358D244—21no—
359D244#11712yescomplemented
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—22no—
363C4×D61—24no—
364C4×D61—22no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—42no—
375C4×D61—41no—
376C4×D61—41no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—42no—
380C4×D61—42no—
381C4×D61#13514yes—
382C4×D61AGL(1,ℤ/8)12yes—
383C4×D61#13712yes—
384C4×D61C2×#4112yes—
385C4×D61C2×#4112yes—
386Dic122—21no—
387Dic122—24no—
388Dic122#11712yescomplemented
389#92420—44no—
390#20737—611nomaximal, Sylow
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—22no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61C22×C22⋊C411yescharacteristic
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—22no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—42no—
405C2×D61—44no—
406C2×D61—42no—
407C2×D61—44no—
408C2×D61#52512yes—
409C2×D61C2×#13512yes—
410C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
411C2×D61C2×#13711yescharacteristic
412#6923—84no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—22no—
416C4×C61—21no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61#41612yes—
420C4×C61#41712yes—
421C4×C61C2×#11711yescharacteristic
422C4×C61C2×#11711yescharacteristic
423Dic61—21no—
424Dic61—21no—
425Dic61—22no—
426Dic61—21no—
427Dic61—41no—
428Dic61—41no—
429Dic61#41612yes—
430Dic61#41712yes—
431Dic61#52512yes—
432C2×C4×#41—611no—
433C2×#431—611no—
434#2285—611no—
435#1825—612no—
436#1803—612no—
437#1802—612no—
438#1788—612no—
439C4×#103—612no—
440C4×#102—612no—
441C2×C61—41no—
442C2×C61—42no—
443C2×C61#228011yescharacteristic
444C2×C61C2×#41611yescharacteristic
445C2×C61C2×#41711yescharacteristic
446D61—41no—
447D61—42no—
448D61#310612yes—
449D61#310712yes—
450C22×#41—611no—
451C4×#41—611no—
452C4×#41—611no—
453C4×#41—611no—
454C4×#41—611no—
455C4×#41—611no—
456C4×#41—611no—
457C4×#41—611no—
458C4×#41—1221no—
459C4×#41—1221no—
460C4×#41—1221no—
461C4×#41—1221no—
462C4×#41#692311yescharacteristic, complemented
463C2×C4×Q8—611no—
464C2×C4×Q8—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×C4×D4—1221no—
468C2×C4×D4—1221no—
469C2×#117—611no—
470C2×#117—1221no—
471C2×#117—1221no—
472C22×C42—611no—
473C22×C42—1221no—
474#431—1221no—
475#431—1221no—
476#431—1221no—
477#431—1221no—
478C2×C4⋊C8—612no—
479C2×#103—614no—
480C2×#102—614no—
481C2×C22⋊C8—612no—
482C2×C4×C8—612no—
483#384—612no—
484#382—1221no—
485#380—612no—
486#380—1221no—
487C4×C4⋊C4—612no—
488C4×C4⋊C4—1221no—
489#340—614no—
490#340—614no—
491C61#2073711yescharacteristic, complemented, Sylow
492C2×#41—611no—
493C2×#41—611no—
494C2×#41—611no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1224no—
498C2×#41—1224no—
499C2×#41C2×#692311yescharacteristic
500C22×Q8—611no—
501C22×D4—611no—
502C22×D4—1221no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C22×C8—614no—
510C4×Q8—611no—
511C4×Q8—611no—
512C4×Q8—611no—
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—611no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8—1221no—
519C4×Q8—1221no—
520C4×Q8C2×#692311yescharacteristic
521C4×Q8C2×#692311yescharacteristic
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—611no—
525C4×D4—611no—
526C4×D4—611no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—611no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4C2×#692311yescharacteristic
549C4×D4C2×#692311yescharacteristic
550#117—21no—
551#117—611no—
552#117—611no—
553#117—611no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—2444no—
564#117C2×#692311yescharacteristic
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—614no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1222no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1222no—
576C2×C42—21no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—1221no—
589C2×C42—1221no—
590C2×C42—1221no—
591C2×C42—1221no—
592C2×C42—1221no—
593C2×C42—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42—1221no—
597C2×C42—1221no—
598C2×C42—1222no—
599C2×C42C2×#692311yescharacteristic
600C4⋊C8—1222no—
601C4⋊C8—1222no—
602#103—1228no—
603#102—1228no—
604C22⋊C8—1222no—
605C22⋊C8—1222no—
606C4×C8—1222no—
607C4×C8—1222no—
608#95—1222no—
609#95—1222no—
610C24—611no—
611C24—1221no—
612#41—22no—
613#41—22no—
614#41—1222no—
615#41—1222no—
616#41—1228no—
617#41—1222no—
618#41—1228no—
619#41—1222no—
620#41—1222no—
621#41—1222no—
622C2×Q8—614no—
623C2×Q8—611no—
624C2×Q8—1221no—
625C2×Q8—1222no—
626C2×Q8C22×#692311yescharacteristic
627C2×D4—21no—
628C2×D4—614no—
629C2×D4—611no—
630C2×D4—1221no—
631C2×D4—1222no—
632C2×D4—1221no—
633C2×D4—1228no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4C22×#692311yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—1221no—
656C22×C4—1222no—
657C22×C4—1224no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1228no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—2444no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4C22⋊#692311yescharacteristic
678C22×C4C22⋊#692311yescharacteristic
679C22×C4C22×#692311yescharacteristic
680C2×C8—1224no—
681C2×C8—1224no—
682C2×C8—1224no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—2444no—
698C4⋊C4—2444no—
699C4⋊C4C22×#692311yescharacteristic
700C4⋊C4C22×#692311yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C22⋊C4—1221no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—2444no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—611no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—1221no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42—1221no—
738C42—2444no—
739C42C22⋊#692311yescharacteristic
740C42C22⋊#692311yescharacteristic
741C42C22×#692311yescharacteristic
742C42C22×#692311yescharacteristic
743C23—21no—
744C23—611no—
745C23—611no—
746C23—1221no—
747C23—1224no—
748C23—1222no—
749C23—1222no—
750C23—1221no—
751C23—1221no—
752C23—2442no—
753C23—2441no—
754C23—2441no—
755C23C2×C22⋊#692311yescharacteristic
756Q8—21no—
757Q8—612no—
758Q8—1224no—
759Q8—1221no—
760Q8#1451985612yescomplemented
761D4—24no—
762D4—21no—
763D4—612no—
764D4—1224no—
765D4—1224no—
766D4—1224no—
767D4—1224no—
768D4—1221no—
769D4#1451985612yescomplemented
770C2×C4—24no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—614no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—611no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—1222no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1224no—
799C2×C4—1224no—
800C2×C4—1224no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1224no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—2442no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2444no—
820C2×C4—2444no—
821C2×C4—2444no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4C2×C22⋊#692311yescharacteristic
825C2×C4C2×C22⋊#692311yescharacteristic
826C2×C4C2×C22⋊#692311yescharacteristic
827C2×C4C2×C22⋊#692311yescharacteristic
828C2×C4C2×C22⋊#692311yescharacteristic
829C2×C4C23×#692311yescharacteristic
830C8—2444no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—612no—
838C22—611no—
839C22—611no—
840C22—612no—
841C22—1221no—
842C22—1221no—
843C22—1222no—
844C22—1221no—
845C22—2442no—
846C22—2442no—
847C22—2444no—
848C22—2444no—
849C22—2441no—
850C22—2441no—
851C22C22×C22⋊#692311yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—612no—
859C4—612no—
860C4—612no—
861C4—1221no—
862C4—1221no—
863C4—1221no—
864C4—1222no—
865C4—4884no—
866C4—2441no—
867C4—2441no—
868C4#1684075212yes—
869C4#1684075312yes—
870C4C2×#1451985611yescharacteristic
871C4C2×#1451985611yescharacteristic
872C2—41no—
873C2—42no—
874C2—612no—
875C2—612no—
876C2—2441no—
877C2—2442no—
878C2#2146226311yescharacteristic
879C2C2×#1684075211yescharacteristic
880C2C2×#1684075311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61#20737
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. #21462268C2semidirect
3. #21461724C2semidirect
4. #21461688C2semidirect
5. #21461687C2semidirect
7. C4×#14519840C2semidirect
8. C4×#14519839C2semidirect
29. #41×Dic61C4semidirect
30. C4×#11758226C4semidirect
31. C4×#11758226C4semidirect
33. C4×#11758222C4semidirect
35. #16840230C4semidirect
38. C4×#11758224C4semidirect
39. C4×#11758224C4semidirect
50. C4×#41×C61C4semidirect
319. Q8×C61#117semidirect
322. D4×C61#117semidirect
359. D244#117semidirect
388. Dic122#117semidirect
462. C4×#41#6923semidirect
491. C61#20737semidirect
760. Q8#14519856semidirect
769. D4#14519856semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
#214622682
#214617242
#214616882
#214616872
#214616592
C4×#145198402
C4×#145198392
C4×#41×D612
#2073761