Finite Group Databasebeta

← #29648415

Subgroups — #29648415

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3#431×D61C211yesmaximal, characteristic
4#21444518C212yesmaximal, complemented
5#21444516C212yesmaximal, complemented
6#21444502C212yesmaximal, complemented
7#21444489C212yesmaximal, complemented
8#21444484C211yesmaximal, characteristic, complemented
9#21444483C211yesmaximal, characteristic, complemented
10#21444483C211yesmaximal, characteristic, complemented
11C61×#1544C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840318C412yes—
14#16840317C2211yescharacteristic
15#16840317C2211yescharacteristic
16#16840316—21no—
17#16840316—21no—
18#16840315C412yes—
19#16840314—21no—
20#16840314—21no—
21C4⋊Q8×D61C2211yescharacteristic
22C4⋊Q8×D61C2211yescharacteristic
23#125×D61C412yes—
24C22⋊Q8×D61—21no—
25C22⋊Q8×D61—21no—
26C4×Q8×D61—21no—
27C4×Q8×D61—21no—
28#117×D61C412yes—
29C2×C42×D61C2211yescharacteristic
30#16839818C2212yes—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839814C2212yes—
35#16839813—21no—
36#16839813—21no—
37#16839812—21no—
38#16839784C2212yes—
39C4⋊C8×D61C2212yes—
40#16839724—21no—
41C22⋊C8×D61—21no—
42C4×#11758189—21no—
43C4×C8×D61—21no—
44#16839509C2212yescomplemented
45#16839509C2212yescomplemented
46#16839508C2212yescomplemented
47#16839508C2212yescomplemented
48#16839507C2212yescomplemented
49#16839507C2212yescomplemented
50C61×#533C2211yescharacteristic
51C61×#431C2211yescharacteristic
52C61×#431C2211yescharacteristic
53C61×#332C2212yescomplemented
54C61×#332C2212yescomplemented
55C2×Q8×D61—21no—
56C2×Q8×D61—21no—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C2×#11758189—22no—
61C2×C8×D61—22no—
62#14519777C2311yescharacteristic
63#14519777C2311yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519776C2×C412yes—
67#14519776C2×C412yes—
68#14519775—21no—
69#14519775—21no—
70#14519769C2×C412yes—
71#14519768C2×C412yes—
72#14519768C2×C412yes—
73#14519767—22no—
74#14519767—22no—
75#14519757—21no—
76#14519757—21no—
77#14519756—21no—
78#14519756—21no—
79#14519755—22no—
80#14519755—22no—
81#14519754—22no—
82#14519754—22no—
83#14519753—21no—
84#14519753—21no—
85Q8×Dic61—21no—
86Q8×Dic61—21no—
87C4×Dic122—21no—
88C4×Dic122—21no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91#14519742—22no—
92#14519742—22no—
93#14519742—21no—
94#14519742—21no—
95#14519736C2×C412yes—
96#14519735C2×C412yes—
97#14519735C2×C412yes—
98#14519734—22no—
99#14519733—22no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61C2×C412yes—
105C4⋊C4×D61C2×C412yes—
106C22⋊C4×D61—22no—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C42×D61—22no—
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119C4⋊#92418C2312yes—
120C4⋊#92418C2312yes—
121#14519706—22no—
122#14519706—22no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519689—22no—
126#14519689—22no—
127#14519687—22no—
128C4×#92418—21no—
129C4×#92418—21no—
130C8×Dic61—22no—
131C4⋊Q8×C61C2311yescharacteristic
132C4⋊Q8×C61C2311yescharacteristic
133#125×C61C2×C412yes—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C4×Q8×C61—21no—
137C4×Q8×C61—21no—
138#117×C61C2×C412yes—
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61C2312yes—
141C4⋊C8×C61C2312yes—
142C22⋊C8×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61—21no—
145C4×C8×C61—21no—
146C23×D61C22⋊C411yescharacteristic
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155Q8×D61—44no—
156Q8×D61—44no—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—42no—
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22×C411yescharacteristic
169C2×C4×D61C22×C411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61C22×C412yes—
185C4⋊C4×C61C22×C412yes—
186C22⋊C4×C61—22no—
187C42×C61—22no—
188C42×C61C22×C411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2411yescharacteristic
192C22⋊Dic61—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61C22×C412yes—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C2×#92418—22no—
225C2×#92418—22no—
226#11758189—44no—
227C8×D61—44no—
228C23×C61C2×C22⋊C411yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—41no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234Q8×C61—42no—
235Q8×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61#10114yes—
271C4×D61#13514yes—
272Dic122—44no—
273Dic122—42no—
274Dic122—42no—
275Dic122—44no—
276C8×C61—42no—
277C8×C61—42no—
278#92418—42no—
279#92418—42no—
280#17715—611nomaximal, Sylow
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61C22×C22⋊C411yescharacteristic
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—44no—
290C2×D61C2×#10112yes—
291C2×D61#41612yes—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61C2×#10112yes—
298C4×C61C2×#13512yes—
299C4×C61#57512yes—
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—42no—
305Dic61—42no—
306Dic61C2×#10112yes—
307Dic61#41612yes—
308C2×#533—611no—
309#2920—611no—
310C2×#431—611no—
311#1552—612no—
312#1552—612no—
313#1549—612no—
314#1546—612no—
315#1544—611no—
316#1544—611no—
317#1544—611no—
318#1544D6111yescharacteristic, complemented
319C2×C61—41no—
320C2×C61C22×#10111yescharacteristic
321C2×C61C2×#41611yescharacteristic
322C2×C61#289611yescharacteristic
323D61—22no—
324D61—22no—
325#533—611no—
326#533—611no—
327#533—612no—
328#533—612no—
329#533—611no—
330#533—1221no—
331#533—1221no—
332#533—1221no—
333#533—1221no—
334#533C2×D6111yescharacteristic
335C2×C4⋊Q8—611no—
336C2×C4⋊Q8—611no—
337C2×#125—612no—
338C2×C22⋊Q8—1221no—
339C2×C22⋊Q8—1221no—
340C2×C4×Q8—1221no—
341C2×C4×Q8—1221no—
342C2×#117—612no—
343C22×C42—611no—
344#432—612no—
345#432—1221no—
346#431—611no—
347#431—611no—
348#431—612no—
349#431—1221no—
350#431—1221no—
351#431—1221no—
352#431C2×D6111yescharacteristic
353#431C2×D6111yescharacteristic
354#423—612no—
355C2×C4⋊C8—612no—
356#407—1221no—
357C2×C22⋊C8—1221no—
358C4×M16—1221no—
359C2×C4×C8—1221no—
360#332—612no—
361#332—612no—
362#332—612no—
363#332—612no—
364#332—612no—
365#332—612no—
366#332C2×D6112yescomplemented
367#332C2×D6112yescomplemented
368C61#1771511yescharacteristic, complemented, Sylow
369C22×Q8—1221no—
370C22×Q8—1221no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C2×M16—1222no—
375C22×C8—1222no—
376C4⋊Q8—612no—
377C4⋊Q8—612no—
378C4⋊Q8—611no—
379C4⋊Q8—611no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383C4⋊Q8—1221no—
384C4⋊Q8C22×D6111yescharacteristic
385C4⋊Q8C22×D6111yescharacteristic
386#125—612no—
387#125—612no—
388#125—612no—
389#125—1222no—
390#125—1222no—
391#125C4×D6112yes—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1221no—
399C22⋊Q8—1221no—
400C22⋊Q8—1221no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1221no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—1222no—
407C4×Q8—1222no—
408C4×Q8—1221no—
409C4×Q8—1221no—
410C4×Q8—1222no—
411C4×Q8—1222no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416#117—612no—
417#117—612no—
418#117—612no—
419#117—1222no—
420#117—1222no—
421#117C4×D6112yes—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1222no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C22⋊C4—1222no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—1222no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—612no—
443C4⋊C8—612no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8C22×D6112yes—
447C4⋊C8C22×D6112yes—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454#97—1222no—
455C4×C8—21no—
456C4×C8—21no—
457C4×C8—1222no—
458C4×C8—1221no—
459C4×C8—1221no—
460C24—611no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—1222no—
464C2×Q8—1222no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—2444no—
468C2×Q8—2444no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—2442no—
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492M16—2444no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—1222no—
496C2×C8—1222no—
497C2×C8—2444no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—612no—
503C4⋊C4—612no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4C2×C4×D6112yes—
517C4⋊C4C2×C4×D6112yes—
518C22⋊C4—22no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C42—22no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C42C2×C4×D6111yescharacteristic
539C42D4×D6111yescharacteristic
540C42D4×D6111yescharacteristic
541C42C23×D6111yescharacteristic
542C23—611no—
543C23—611no—
544C23—1222no—
545C23—1222no—
546C23—2441no—
547C23C22⋊C4×D6111yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—2444no—
551Q8—2444no—
552Q8—2442no—
553Q8—2442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—614no—
562C2×C4—614no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2444no—
582C2×C4—2444no—
583C2×C4—2441no—
584C2×C4C22⋊C4×D6111yescharacteristic
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C22⋊C4×D6111yescharacteristic
587C2×C4C22×C4×D6111yescharacteristic
588C2×C4C2×D4×D6111yescharacteristic
589C2×C4C2×D4×D6111yescharacteristic
590C8—42no—
591C8—42no—
592C8—2442no—
593C8—2442no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—612no—
598C22—612no—
599C22—1221no—
600C22—1221no—
601C22—1221no—
602C22—1221no—
603C22—2444no—
604C22C2×C22⋊C4×D6111yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—612no—
611C4—612no—
612C4—1221no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—2442no—
617C4—2442no—
618C4#101×D6112yes—
619C4#135×D6112yes—
620C4#1684055912yes—
621C2—41no—
622C2—1222no—
623C2—1222no—
624C2C2×#101×D6111yescharacteristic
625C2#416×D6111yescharacteristic
626C2#2145433411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1544C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1544D61
hypocenterC61#17715
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
4. #21444518C2semidirect
5. #21444516C2semidirect
6. #21444502C2semidirect
7. #21444489C2semidirect
8. #21444484C2semidirect
9. #21444483C2semidirect
10. #21444483C2semidirect
11. C61×#1544C2semidirect
44. #16839509C22semidirect
45. #16839509C22semidirect
46. #16839508C22semidirect
47. #16839508C22semidirect
48. #16839507C22semidirect
49. #16839507C22semidirect
53. C61×#332C22semidirect
54. C61×#332C22semidirect
318. #1544D61semidirect
366. #332C2×D61semidirect
367. #332C2×D61semidirect
368. C61#17715semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214544472
#431×D612
#214445182
#214445162
#214445022
#214444892
#214444842
#214444832
C61×#15442
#1771561