Finite Group Databasebeta

← #30616726

Subgroups — #30616726

Order 15616.

1430 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C2×C42×#6923C211yesmaximal, characteristic, complemented
3#21462005C212yesmaximal, complemented
4#21461954C212yesmaximal, complemented
5#21461837C212yesmaximal, complemented
6#21461836C212yesmaximal, complemented
7C4×#14519842C212yesmaximal, complemented
8C4×#14519841C212yesmaximal, complemented
9#21459113C211yesmaximal, characteristic
10C22×C4×#6923—21no—
11C22×C4×#6923—21no—
12C22×C4×#6923C2212yes—
13#16840785—21no—
14#16840782—21no—
15#16840780—21no—
16#16840779—21no—
17#16840767C2212yes—
18C2×#14519842C2214yes—
19C2×#14519841C2214yes—
20#16840733C2212yes—
21C4×#11758213C2212yes—
22C42×#6923—21no—
23C42×#6923—21no—
24C42×#6923C2212yes—
25C42×#6923C2212yes—
26#16840632C2214yes—
27#16840632C2214yes—
28#16840318C2211yescharacteristic
29#16840316C411yescharacteristic, complemented
30#16840314C411yescharacteristic, complemented
31#16840311C2211yescharacteristic
32#16840309C411yescharacteristic, complemented
33#16840307C411yescharacteristic, complemented
34#16840297C411yescharacteristic, complemented
35#16840296C411yescharacteristic, complemented
36#16840295—21no—
37#16840295—21no—
38#16840291C411yescharacteristic, complemented
39#16840290—21no—
40#16840289—21no—
41#16840275C2211yescharacteristic
42#16840272C2211yescharacteristic
43#16840271—21no—
44#16840270—21no—
45C4×#11758226C2211yescharacteristic
46#16840230—21no—
47C4×#11758224—21no—
48C4×#11758224C2211yescharacteristic
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C23×#6923—22no—
52C2×#11758213C2314yes—
53C2×C4×#6923—28no—
54C2×C4×#6923—28no—
55C2×C4×#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—28no—
61C2×C4×#6923C2314yes—
62#14519844—22no—
63#14519844—22no—
64#14519842—28no—
65#14519841—28no—
66#14519834—22no—
67C22⋊#92420—22no—
68#14519832—22no—
69C4×#92420—22no—
70C2×#11758226C2311yescharacteristic
71C2×#11758222—21no—
72C2×#11758224—21no—
73C2×#11758224C2311yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519776C2×C411yescharacteristic, complemented
78#14519776C2×C411yescharacteristic, complemented
79#14519775C2×C411yescharacteristic, complemented
80#14519773C2×C411yescharacteristic, complemented
81#14519772—21no—
82#14519771—21no—
83#14519770—21no—
84#14519769C2×C411yescharacteristic, complemented
85#14519767—21no—
86#14519767—21no—
87#14519765C2×C411yescharacteristic, complemented
88#14519763—21no—
89#14519763—21no—
90#14519762—21no—
91#14519762—21no—
92#14519760—21no—
93#14519759—21no—
94#14519759—21no—
95#14519757C2×C411yescharacteristic
96#14519756C2×C411yescharacteristic
97#14519755—21no—
98#14519755—21no—
99#14519755—21no—
100#14519754—21no—
101#14519753C2×C411yescharacteristic
102#14519752C2×C411yescharacteristic
103#14519751C2×C411yescharacteristic
104#14519750—21no—
105#14519750—21no—
106#14519750—21no—
107#14519749—21no—
108#14519748C2×C411yescharacteristic
109#14519747—21no—
110#14519745—21no—
111Q8×Dic61C2×C411yescharacteristic, complemented
112C4×Dic122—21no—
113C4×Dic122C2×C411yescharacteristic, complemented
114#14519742—21no—
115#14519742—21no—
116#14519742—21no—
117#14519742C2×C411yescharacteristic, complemented
118C4×D244—21no—
119C4×D244C2×C411yescharacteristic, complemented
120D4×Dic61—21no—
121D4×Dic61C2×C411yescharacteristic, complemented
122#14519739—21no—
123#14519739—21no—
124#14519739—21no—
125#14519739C2×C411yescharacteristic, complemented
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519735—21no—
137#14519735—21no—
138#14519735C2311yescharacteristic
139#14519735C2311yescharacteristic
140#14519734—21no—
141#14519734—21no—
142#14519733—21no—
143#14519733—21no—
144#14519733—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2×C411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C42×D61—21no—
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61C2311yescharacteristic
157C42×D61C2311yescharacteristic
158#126×C61—21no—
159#125×C61C2×C411yescharacteristic, complemented
160#124×C61C2×C411yescharacteristic, complemented
161#123×C61—21no—
162C22⋊Q8×C61C2×C411yescharacteristic
163#121×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic, complemented
165C4×D4×C61—21no—
166C4×D4×C61C2×C411yescharacteristic, complemented
167#117×C61—21no—
168C2×C42×C61C2×C411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C22×#6923—28no—
171C22×#6923—28no—
172C22×#6923—28no—
173C22×#6923—24no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61—21no—
178C22×C4×C61C22⋊C411yescharacteristic
179C22×C4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61C22⋊C411yescharacteristic
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191#11758226—24no—
192#11758224—24no—
193#11758224—44no—
194#11758222—44no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244C22×C411yescharacteristic
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2411yescharacteristic
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122C22×C411yescharacteristic
219C2×#92420—24no—
220C4×#6923—28no—
221C4×#6923—28no—
222C4×#6923—28no—
223C4×#6923—28no—
224C4×#6923—28no—
225C4×#6923—24no—
226C4×#6923#4118yescomplemented
227#11758213—24no—
228#11758213—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61C22×C411yescharacteristic
234C4⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C42×C61—21no—
241C42×C61C22⋊C411yescharacteristic
242C42×C61C22⋊C411yescharacteristic
243C42×C61C22×C411yescharacteristic
244C42×C61C22×C411yescharacteristic
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22×C411yescharacteristic
261C4⋊Dic61C22×C411yescharacteristic
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22×C411yescharacteristic
284C4×Dic61C22×C411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C23×C61—21no—
290C23×C61C2×C22⋊C411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—21no—
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C22×D411yescharacteristic
297C2×#6923—28no—
298C2×#6923—28no—
299C2×#6923—232no—
300C2×#6923—28no—
301Q8×C61—22no—
302D4×C61—22no—
303D4×C61—42no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—42no—
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C22⋊D61—42no—
318C22⋊D61—42no—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61#10414yescomplemented
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C22×D411yescharacteristic
336D244—22no—
337D244—42no—
338D244—42no—
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—22no—
348C4×D61—22no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61#10414yescomplemented
353C4×D61C2×#4114yes—
354Dic122—22no—
355Dic122—42no—
356Dic122—42no—
357#92420—44no—
358#21415—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—28no—
367C2×D61—21no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61C2×#10412yes—
375C2×D61#52512yes—
376#6923—216no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—41no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61C2×#10412yes—
385C4×C61C4×#4112yes—
386Dic61—21no—
387Dic61—21no—
388Dic61—41no—
389Dic61—41no—
390Dic61—41no—
391Dic61C2×#10412yes—
392Dic61C2×#10412yes—
393Dic61C2×#10412yes—
394Dic61#53212yes—
395#3444—611no—
396#2920—611no—
397C2×C43—611no—
398#1994—612no—
399#1962—612no—
400#1896—612no—
401#1896—612no—
402C4×#104—612no—
403C4×#104—612no—
404C2×C61—22no—
405C2×C61—81no—
406C2×C61#229711yescharacteristic
407C2×C61C22×#10411yescharacteristic
408C2×C61C22×#10411yescharacteristic
409D61—22no—
410D61—22no—
411D61—81no—
412#533—611no—
413#533—611no—
414#533—611no—
415#532—611no—
416#532—611no—
417#532—611no—
418#529—611no—
419#529—611no—
420#529—611no—
421#529—1221no—
422#529—1221no—
423#529—1221no—
424#529—1221no—
425#529#692311yescharacteristic, complemented
426#525—611no—
427#525—611no—
428#525—1221no—
429#525—1221no—
430C4×#41—611no—
431C4×#41—611no—
432C4×#41—1221no—
433C4×#41—1221no—
434C22×C42—611no—
435C22×C42—612no—
436C22×C42—1221no—
437C22×C42—1221no—
438#432—1221no—
439#432—1221no—
440#431—1221no—
441#431—1221no—
442#423—612no—
443C2×#104—614no—
444C2×#104—614no—
445#407—612no—
446C4×M16—612no—
447C43—612no—
448C43—612no—
449C43—1221no—
450C43—1221no—
451#339—614no—
452#339—614no—
453C61#2141511yescharacteristic, complemented, Sylow
454C2×#41—611no—
455C2×#41—611no—
456C2×#41—1221no—
457C2×#41—1221no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—1222no—
462C2×M16—614no—
463C4⋊Q8—611no—
464C4⋊Q8—611no—
465C4⋊Q8—611no—
466#127—611no—
467#126—21no—
468#126—1221no—
469#126—1221no—
470#126—1221no—
471#125—611no—
472#125—1221no—
473#125—1221no—
474#125C2×#692311yescharacteristic, complemented
475#124—611no—
476#124—1221no—
477#124—1221no—
478#124C2×#692311yescharacteristic, complemented
479#123—21no—
480#123—1221no—
481#123—1221no—
482#123—1221no—
483#123—1221no—
484#123—1221no—
485C22⋊Q8—611no—
486C22⋊Q8—611no—
487C22⋊Q8—611no—
488C22⋊Q8—1221no—
489C22⋊Q8—1221no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8C2×#692311yescharacteristic
493#121—611no—
494#121—611no—
495#121—611no—
496#121—1221no—
497#121—1221no—
498#121—1221no—
499#121—1221no—
500#121C2×#692311yescharacteristic
501#120—1221no—
502#120—1221no—
503C4×Q8—611no—
504C4×Q8—611no—
505C4×Q8—611no—
506C4×Q8—1221no—
507C4×Q8—1221no—
508C4×Q8—1221no—
509C4×Q8—1221no—
510C4×Q8C2×#692311yescharacteristic, complemented
511C4×D4—21no—
512C4×D4—611no—
513C4×D4—611no—
514C4×D4—611no—
515C4×D4—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
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×D4C2×#692311yescharacteristic, complemented
531#117—21no—
532#117—611no—
533#117—611no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—614no—
553C2×C42—1221no—
554C2×C42—1221no—
555C2×C42—1228no—
556C2×C42—1222no—
557C2×C42—1222no—
558C2×C42—1222no—
559C2×C42—1222no—
560C2×C42—1222no—
561C2×C42—1228no—
562C2×C42—1228no—
563C2×C42C2×#692311yescharacteristic
564C4⋊C8—1222no—
565C4⋊C8—1222no—
566#104—1228no—
567#104—1228no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570#97—1222no—
571C4×C8—1222no—
572C24—611no—
573#41—1224no—
574#41—1224no—
575#41—2444no—
576#41—2444no—
577C2×Q8—611no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8C22×#692311yescharacteristic
581C2×D4—21no—
582C2×D4—611no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4C22×#692311yescharacteristic
591C22×C4—21no—
592C22×C4—611no—
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—1224no—
608C22×C4—1224no—
609C22×C4—1224no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1224no—
615C22×C4—1228no—
616C22×C4—1228no—
617C22×C4—1228no—
618C22×C4—1221no—
619C22×C4C22⋊#692311yescharacteristic
620C22×C4C22⋊#692311yescharacteristic
621C22×C4C22×#692311yescharacteristic
622M16—1224no—
623M16—1224no—
624C2×C8—1224no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—1221no—
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—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4C22×#692311yescharacteristic
644C4⋊C4C22×#692311yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—1221no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
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—
663C42—21no—
664C42—611no—
665C42—611no—
666C42—611no—
667C42—611no—
668C42—611no—
669C42—611no—
670C42—611no—
671C42—611no—
672C42—611no—
673C42—611no—
674C42—611no—
675C42—611no—
676C42—618no—
677C42—1221no—
678C42—1221no—
679C42—1221no—
680C42—1221no—
681C42—1224no—
682C42—1228no—
683C42—1228no—
684C42—1228no—
685C42—1228no—
686C42—1228no—
687C42—1221no—
688C42C22⋊#692311yescharacteristic
689C42C22⋊#692311yescharacteristic
690C42C22×#692311yescharacteristic
691C42C22×#692311yescharacteristic
692C23—21no—
693C23—611no—
694C23—611no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1221no—
699C23C2×C22⋊#692311yescharacteristic
700Q8—22no—
701Q8—1222no—
702Q8—2442no—
703Q8—2442no—
704D4—22no—
705D4—42no—
706D4—1222no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2442no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—42no—
721C2×C4—614no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—614no—
727C2×C4—614no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1228no—
741C2×C4—1228no—
742C2×C4—1228no—
743C2×C4—12232no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4C2×C22⋊#692311yescharacteristic
755C2×C4C2×C22⋊#692311yescharacteristic
756C2×C4C2×C22⋊#692311yescharacteristic
757C2×C4C2×C22⋊#692311yescharacteristic
758C2×C4C2×C22⋊#692311yescharacteristic
759C2×C4C23×#692311yescharacteristic
760C8—2444no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—612no—
767C22—612no—
768C22—1228no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22D61⋊#10412yes—
777C22C22×C22⋊#692311yescharacteristic
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—612no—
786C4—612no—
787C4—612no—
788C4—612no—
789C4—12216no—
790C4—1221no—
791C4—1221no—
792C4—2441no—
793C4—2441no—
794C4—2441no—
795C4D61⋊#10412yes—
796C4#41×#692312yes—
797C2—22no—
798C2—81no—
799C2—1222no—
800C2—1222no—
801C2—4881no—
802C2#2146228011yescharacteristic
803C2C2×D61⋊#10411yescharacteristic
804C2C2×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#21415
LCSG ▷ C2×C4×C61 ▷ C2×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×C42×#6923C2semidirect
3. #21462005C2semidirect
4. #21461954C2semidirect
5. #21461837C2semidirect
6. #21461836C2semidirect
7. C4×#14519842C2semidirect
8. C4×#14519841C2semidirect
29. #16840316C4semidirect
30. #16840314C4semidirect
32. #16840309C4semidirect
33. #16840307C4semidirect
34. #16840297C4semidirect
35. #16840296C4semidirect
38. #16840291C4semidirect
50. C61×#529C4semidirect
77. #14519776C2×C4semidirect
78. #14519776C2×C4semidirect
79. #14519775C2×C4semidirect
80. #14519773C2×C4semidirect
84. #14519769C2×C4semidirect
87. #14519765C2×C4semidirect
111. Q8×Dic61C2×C4semidirect
113. C4×Dic122C2×C4semidirect
117. #14519742C2×C4semidirect
119. C4×D244C2×C4semidirect
121. D4×Dic61C2×C4semidirect
125. #14519739C2×C4semidirect
159. #125×C61C2×C4semidirect
160. #124×C61C2×C4semidirect
164. C4×Q8×C61C2×C4semidirect
166. C4×D4×C61C2×C4semidirect
226. C4×#6923#41semidirect
329. C2×Dic61#104semidirect
352. C4×D61#104semidirect
425. #529#6923semidirect
453. C61#21415semidirect
474. #125C2×#6923semidirect
478. #124C2×#6923semidirect
510. C4×Q8C2×#6923semidirect
530. 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×C42×#69232
#214620052
#214619542
#214618372
#214618362
C4×#145198422
C4×#145198412
#214591132
#2141561