Finite Group Databasebeta

← #30610985

Subgroups — #30610985

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21461222C212yesmaximal, complemented
4#21461220C212yesmaximal, complemented
5#21461206C212yesmaximal, complemented
6#21461204C212yesmaximal, complemented
7#21461201C212yesmaximal, complemented
8#21461198C212yesmaximal, complemented
9#21459113C211yesmaximal, characteristic
10C22×C4⋊#6923—21no—
11C22×C4×#6923—21no—
12#16840785C2212yes—
13#16840782—21no—
14#16840780C2212yes—
15#16840779—21no—
16#16840767—21no—
17#16840733C2212yes—
18C4×#11758213—21no—
19C4×C4⋊#6923—21no—
20C4×C4⋊#6923—21no—
21C4×C4⋊#6923C2212yes—
22C4×C4⋊#6923C2212yes—
23C2×(C2×#6923)⋊C4C2212yes—
24#16840616C2214yes—
25#16840615C2214yes—
26#16840614C2214yes—
27#16840613C2214yes—
28#16840318C411yescharacteristic, complemented
29#16840316C2211yescharacteristic
30#16840314C411yescharacteristic, complemented
31#16840311C411yescharacteristic, complemented
32#16840309C2211yescharacteristic
33#16840307C411yescharacteristic, complemented
34#16840297C2211yescharacteristic
35#16840296C411yescharacteristic, complemented
36#16840295—21no—
37#16840295—21no—
38#16840291C2211yescharacteristic
39#16840290—21no—
40#16840289—21no—
41#16840275C2211yescharacteristic
42#16840272C2211yescharacteristic
43#16840271—21no—
44#16840270—21no—
45C4×#11758226C411yescharacteristic, complemented
46#16840230—21no—
47C4×#11758224—21no—
48C4×#11758224C411yescharacteristic, complemented
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C23×#6923—22no—
52C2×#11758213—22no—
53C2×C4⋊#6923—28no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—44no—
59#14519844—22no—
60#14519844—22no—
61#14519834C2314yes—
62C22⋊#92420—22no—
63#14519832—22no—
64C4×#92420—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4C2314yes—
67C2×#11758226C2×C411yescharacteristic
68C2×#11758222—21no—
69C2×#11758224—21no—
70C2×#11758224C2×C411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74#14519776C2×C411yescharacteristic, complemented
75#14519776C2×C411yescharacteristic, complemented
76#14519775C2×C411yescharacteristic, complemented
77#14519773C2×C411yescharacteristic, complemented
78#14519772—21no—
79#14519771—21no—
80#14519770—21no—
81#14519769C2×C411yescharacteristic, complemented
82#14519767—21no—
83#14519767—21no—
84#14519765C2×C411yescharacteristic, complemented
85#14519763—21no—
86#14519763—21no—
87#14519762—21no—
88#14519762—21no—
89#14519760—21no—
90#14519759—21no—
91#14519759—21no—
92#14519757C2311yescharacteristic
93#14519756C2×C411yescharacteristic
94#14519755—21no—
95#14519755—21no—
96#14519755—21no—
97#14519754—21no—
98#14519753C2311yescharacteristic
99#14519752C2311yescharacteristic
100#14519751C2×C411yescharacteristic
101#14519750—21no—
102#14519750—21no—
103#14519750—21no—
104#14519749—21no—
105#14519748C2311yescharacteristic
106#14519747—21no—
107#14519745—21no—
108Q8×Dic61C2×C411yescharacteristic, complemented
109C4×Dic122—21no—
110C4×Dic122C2×C411yescharacteristic, complemented
111#14519742—21no—
112#14519742—21no—
113#14519742—21no—
114#14519742C2×C411yescharacteristic, complemented
115C4×D244—21no—
116C4×D244C2×C411yescharacteristic, complemented
117D4×Dic61—21no—
118D4×Dic61C2×C411yescharacteristic, complemented
119#14519739—21no—
120#14519739—21no—
121#14519739—21no—
122#14519739C2×C411yescharacteristic, complemented
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519735—21no—
134#14519735—21no—
135#14519735C2×C411yescharacteristic
136#14519735C2×C411yescharacteristic
137#14519734—21no—
138#14519734—21no—
139#14519733—21no—
140#14519733—21no—
141#14519733—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C42×D61—21no—
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61C2311yescharacteristic
154C42×D61C2311yescharacteristic
155#126×C61—21no—
156#125×C61C2×C411yescharacteristic, complemented
157#124×C61C2×C411yescharacteristic, complemented
158#123×C61—21no—
159C22⋊Q8×C61C2×C411yescharacteristic
160#121×C61C2×C411yescharacteristic
161C4×Q8×C61C2×C411yescharacteristic, complemented
162C4×D4×C61—21no—
163C4×D4×C61C2×C411yescharacteristic, complemented
164#117×C61—21no—
165C2×C42×C61C2×C411yescharacteristic
166C23×D61C2×D411yescharacteristic
167C22×#6923—28no—
168C22×#6923—24no—
169C22×#6923—44no—
170C22×#6923—44no—
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22⋊C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188#11758226—42no—
189#11758224—42no—
190#11758224—44no—
191#11758222—42no—
192#11758222—42no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C411yescharacteristic
196C2×C4×D61—24no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—42no—
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22×C411yescharacteristic
218C2×#92420—24no—
219C4⋊#6923—28no—
220C4⋊#6923—28no—
221C4×#6923—44no—
222C4×#6923—44no—
223#11758213—44no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61C22×C411yescharacteristic
229C4⋊C4×C61C22×C411yescharacteristic
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C42×C61—21no—
236C42×C61C22⋊C411yescharacteristic
237C42×C61C22⋊C411yescharacteristic
238C42×C61C22×C411yescharacteristic
239C42×C61C22×C411yescharacteristic
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61C22×C411yescharacteristic
256C4⋊Dic61C22×C411yescharacteristic
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61C22⋊C411yescharacteristic
273C4×Dic61C22⋊C411yescharacteristic
274C4×Dic61C22⋊C411yescharacteristic
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22×C411yescharacteristic
279C4×Dic61C22×C411yescharacteristic
280C4×Dic61C2×D411yescharacteristic
281C4×Dic61C2×D411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C23×C61—21no—
285C23×C61C2×C22⋊C411yescharacteristic
286C22×D61—22no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—22no—
290C22×D61—21no—
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C22×D411yescharacteristic
293C2×#6923—28no—
294C2×#6923—416no—
295C2×#6923—44no—
296C2×#6923—44no—
297Q8×C61—41no—
298D4×C61—41no—
299D4×C61—42no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C22⋊D61—42no—
314C22⋊D61—41no—
315C22⋊D61—41no—
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—42no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61#10414yes—
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C22×D411yescharacteristic
333D244—41no—
334D244—41no—
335D244—41no—
336D244—42no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61AGL(1,ℤ/8)12yes—
353C4×D61#13712yes—
354Dic122—42no—
355Dic122—42no—
356Dic122—41no—
357#92420—44no—
358#17546—611nomaximal, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61C2×#10412yes—
365C22×C61C22×C22⋊C411yescharacteristic
366C2×D61—24no—
367C2×D61—24no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61#41012yes—
376C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
377C2×D61C2×#13711yescharacteristic
378#6923—48no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61#41712yes—
388Dic61—21no—
389Dic61—21no—
390Dic61—21no—
391Dic61—41no—
392Dic61—41no—
393Dic61—41no—
394Dic61#41712yes—
395Dic61C2×#10412yes—
396Dic61C2×#10412yes—
397#3444—611no—
398#2920—611no—
399C2×C4×C4⋊C4—611no—
400#1509—612no—
401#1509—612no—
402#1504—612no—
403#1504—612no—
404#1503—612no—
405#1502—612no—
406C2×C61—22no—
407C2×C61—81no—
408C2×C61C2×#41011yescharacteristic
409C2×C61C2×#41711yescharacteristic
410C2×C61C22×#10411yescharacteristic
411D61—21no—
412D61—21no—
413D61—22no—
414D61—81no—
415#533—611no—
416#533—611no—
417#533—611no—
418#532—611no—
419#532—611no—
420#532—611no—
421#529—611no—
422#529—611no—
423#529—611no—
424#529—1221no—
425#529—1221no—
426#529—1221no—
427#529—1221no—
428#529#692311yescharacteristic, complemented
429#525—611no—
430#525—611no—
431#525—1221no—
432#525—1221no—
433C4×#41—611no—
434C4×#41—611no—
435C4×#41—1221no—
436C4×#41—1221no—
437C22×C4⋊C4—1221no—
438C22×C42—611no—
439C22×C42—1221no—
440#432—612no—
441#432—1221no—
442#431—612no—
443#431—1221no—
444#423—1221no—
445#407—612no—
446C4×M16—1221no—
447C4×C4⋊C4—612no—
448C4×C4⋊C4—612no—
449C4×C4⋊C4—1221no—
450C4×C4⋊C4—1221no—
451C2×#95—612no—
452#328—614no—
453#328—614no—
454#327—614no—
455#327—614no—
456C61#1754611yescharacteristic, complemented, Sylow
457C2×#41—611no—
458C2×#41—611no—
459C2×#41—1221no—
460C2×#41—1221no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—1222no—
465C2×M16—1222no—
466C4⋊Q8—611no—
467C4⋊Q8—611no—
468C4⋊Q8—611no—
469#127—611no—
470#126—21no—
471#126—1221no—
472#126—1221no—
473#126—1221no—
474#125—611no—
475#125—1221no—
476#125—1221no—
477#125C2×#692311yescharacteristic, complemented
478#124—611no—
479#124—1221no—
480#124—1221no—
481#124C2×#692311yescharacteristic, complemented
482#123—21no—
483#123—1221no—
484#123—1221no—
485#123—1221no—
486#123—1221no—
487#123—1221no—
488C22⋊Q8—611no—
489C22⋊Q8—611no—
490C22⋊Q8—611no—
491C22⋊Q8—1221no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494C22⋊Q8—1221no—
495C22⋊Q8C2×#692311yescharacteristic
496#121—611no—
497#121—611no—
498#121—611no—
499#121—1221no—
500#121—1221no—
501#121—1221no—
502#121—1221no—
503#121C2×#692311yescharacteristic
504#120—1221no—
505#120—1221no—
506C4×Q8—611no—
507C4×Q8—611no—
508C4×Q8—611no—
509C4×Q8—1221no—
510C4×Q8—1221no—
511C4×Q8—1221no—
512C4×Q8—1221no—
513C4×Q8C2×#692311yescharacteristic, complemented
514C4×D4—21no—
515C4×D4—611no—
516C4×D4—611no—
517C4×D4—611no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4C2×#692311yescharacteristic, complemented
534#117—21no—
535#117—611no—
536#117—611no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1228no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1222no—
561C2×C42—1222no—
562C2×C42—2444no—
563C2×C42C2×#692311yescharacteristic
564C4⋊C8—1222no—
565C4⋊C8—1222no—
566C22⋊C8—614no—
567C22⋊C8—1222no—
568#97—1222no—
569C4×C8—1222no—
570#95—614no—
571#95—1222no—
572C24—611no—
573#41—2442no—
574#41—2442no—
575#41—2444no—
576#41—2442no—
577#41—2442no—
578C2×Q8—611no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8C22×#692311yescharacteristic
582C2×D4—21no—
583C2×D4—611no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4C22×#692311yescharacteristic
592C22×C4—21no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—1222no—
609C22×C4—1224no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1224no—
616C22×C4—1228no—
617C22×C4—1221no—
618C22×C4—2442no—
619C22×C4—2444no—
620C22×C4—2444no—
621C22×C4C22⋊#692311yescharacteristic
622C22×C4C22⋊#692311yescharacteristic
623C22×C4C22×#692311yescharacteristic
624M16—2444no—
625C2×C8—1224no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1228no—
641C4⋊C4—1228no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4C22×#692311yescharacteristic
647C4⋊C4C22×#692311yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
659C22⋊C4—1221no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C42—21no—
667C42—611no—
668C42—611no—
669C42—611no—
670C42—611no—
671C42—611no—
672C42—611no—
673C42—611no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—1221no—
680C42—1221no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—2444no—
685C42—2444no—
686C42C22⋊#692311yescharacteristic
687C42C22⋊#692311yescharacteristic
688C42C22×#692311yescharacteristic
689C42C22×#692311yescharacteristic
690C23—21no—
691C23—611no—
692C23—611no—
693C23—1221no—
694C23—1221no—
695C23—1222no—
696C23—1222no—
697C23—1221no—
698C23C2×C22⋊#692311yescharacteristic
699Q8—41no—
700Q8—2441no—
701Q8—2442no—
702Q8—2442no—
703D4—41no—
704D4—42no—
705D4—2441no—
706D4—2442no—
707D4—2441no—
708D4—2441no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2441no—
713D4—2441no—
714D4—2442no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—614no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1228no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2444no—
754C2×C4—24416no—
755C2×C4—2444no—
756C2×C4—2442no—
757C2×C4C2×C22⋊#692311yescharacteristic
758C2×C4C2×C22⋊#692311yescharacteristic
759C2×C4C2×C22⋊#692311yescharacteristic
760C2×C4C2×C22⋊#692311yescharacteristic
761C2×C4C2×C22⋊#692311yescharacteristic
762C2×C4C23×#692311yescharacteristic
763C8—2444no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—612no—
770C22—611no—
771C22—611no—
772C22—1224no—
773C22—1224no—
774C22—1221no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22D61⋊#10412yes—
782C22C22×C22⋊#692311yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—612no—
792C4—612no—
793C4—612no—
794C4—1221no—
795C4—1221no—
796C4—1221no—
797C4—2448no—
798C4—2441no—
799C4—2441no—
800C4—2441no—
801C4#1684075312yes—
802C2—22no—
803C2—81no—
804C2—1221no—
805C2—1222no—
806C2—1221no—
807C2—4881no—
808C2D61⋊#41011yescharacteristic
809C2C2×#1684075311yescharacteristic
810C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#529C4
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC2×C4×D61C24
hypercenter#529#6923
hypocenterC61#17546
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. C2×C4×C4⋊#6923C2semidirect
3. #21461222C2semidirect
4. #21461220C2semidirect
5. #21461206C2semidirect
6. #21461204C2semidirect
7. #21461201C2semidirect
8. #21461198C2semidirect
28. #16840318C4semidirect
30. #16840314C4semidirect
31. #16840311C4semidirect
33. #16840307C4semidirect
35. #16840296C4semidirect
45. C4×#11758226C4semidirect
48. C4×#11758224C4semidirect
50. C61×#529C4semidirect
74. #14519776C2×C4semidirect
75. #14519776C2×C4semidirect
76. #14519775C2×C4semidirect
77. #14519773C2×C4semidirect
81. #14519769C2×C4semidirect
84. #14519765C2×C4semidirect
108. Q8×Dic61C2×C4semidirect
110. C4×Dic122C2×C4semidirect
114. #14519742C2×C4semidirect
116. C4×D244C2×C4semidirect
118. D4×Dic61C2×C4semidirect
122. #14519739C2×C4semidirect
156. #125×C61C2×C4semidirect
157. #124×C61C2×C4semidirect
161. C4×Q8×C61C2×C4semidirect
163. C4×D4×C61C2×C4semidirect
428. #529#6923semidirect
456. C61#17546semidirect
477. #125C2×#6923semidirect
481. #124C2×#6923semidirect
513. C4×Q8C2×#6923semidirect
533. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624982
C2×C4×C4⋊#69232
#214612222
#214612202
#214612062
#214612042
#214612012
#214611982
#214591132
#1754661