Finite Group Databasebeta

← #30610291

Subgroups — #30610291

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462508C212yesmaximal, complemented
2#21461103C212yesmaximal, complemented
3#21461092C212yesmaximal, complemented
4#21461086C212yesmaximal
5#21461082C211yesmaximal, characteristic, complemented
6#21461073C211yesmaximal, characteristic, complemented
7#21461067C211yesmaximal, characteristic, complemented
8#21461062C211yesmaximal, characteristic, complemented
9#21461053C211yesmaximal, characteristic, complemented
10C2×#16840607C211yesmaximal, characteristic, complemented
11C2×#16840454C211yesmaximal, characteristic
12#16840786—22no—
13#16840786—22no—
14#16840783C2212yes—
15#16840782C2212yes—
16#16840779C2212yes—
17#16840778C2212yes—
18#16840768—22no—
19#16840732C2212yes—
20C2×C22⋊#92420C2212yes—
21#16840726—22no—
22#16840607C2211yescharacteristic
23#16840607C2211yescharacteristic
24#16840607C2212yes—
25#16840607C2211yescharacteristic
26#16840607C2211yescharacteristic
27#16840607C2212yes—
28#16840607C2212yes—
29#16840607C2212yes—
30#16840606C2212yes—
31#16840606C2212yes—
32#16840454—22no—
33#16840454—22no—
34#16840454—22no—
35#16840454—22no—
36C2×#14519772C411yescharacteristic
37C2×#14519772C2211yescharacteristic
38C2×#14519768C411yescharacteristic
39C2×#14519768C411yescharacteristic
40C2×#14519768C2211yescharacteristic
41C2×#14519761C411yescharacteristic
42C2×#14519761C2211yescharacteristic
43C2×#14519753C411yescharacteristic
44C2×Q8×Dic61C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×#14519735C2211yescharacteristic
47C2×#14519733C411yescharacteristic
48C2×#14519733C2211yescharacteristic
49C22×C4⋊Dic61C2211yescharacteristic
50C2×C22⋊Q8×C61C411yescharacteristic
51C2×#11758217—22no—
52C22×#92420—22no—
53#14519844—22no—
54#14519844—22no—
55C4⋊#92420—22no—
56C4⋊#92420—22no—
57C22⋊#92420—22no—
58C22⋊#92420—22no—
59C22⋊#92420C2312yes—
60C22⋊#92420C2312yes—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67C22×C22⋊D61C2×C411yescharacteristic
68C23×Dic61C2×C411yescharacteristic
69C23×Dic61C2311yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71#14519772—22no—
72#14519772—22no—
73#14519772—22no—
74#14519772—22no—
75#14519768—22no—
76#14519768—22no—
77#14519768—22no—
78#14519768—22no—
79#14519768—22no—
80#14519768—22no—
81#14519761—22no—
82#14519761—22no—
83#14519761—22no—
84#14519761—22no—
85#14519753—22no—
86#14519753—22no—
87Q8×Dic61—22no—
88Q8×Dic61—22no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93#14519735—22no—
94#14519735—22no—
95#14519733—21no—
96#14519733—21no—
97#14519733—21no—
98#14519733—21no—
99#14519733D412yes—
100#14519733D412yes—
101#14519733D412yes—
102#14519733D412yes—
103C2×C4⋊Dic61—22no—
104C2×C4⋊Dic61—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2311yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C2×Q8×C61—22no—
141C2×Q8×C61—22no—
142C2×Q8×C61—41no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—41no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—42no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—42no—
159C22×Dic61—42no—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C2×D412yes—
167C22×Dic61C2×D412yes—
168C22×Dic61C2411yescharacteristic
169C2×C4×D61—22no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—41no—
173#11758217—44no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C2×#92420—22no—
178C2×#92420—44no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61C22⋊C412yes—
185C22⋊C4×C61C22⋊C412yes—
186C22⋊Dic61C22⋊C411yescharacteristic
187C22⋊Dic61C22⋊C411yescharacteristic
188C22⋊Dic61C22⋊C411yescharacteristic
189C22⋊Dic61C22⋊C411yescharacteristic
190#11758198—22no—
191#11758198—22no—
192#11758198—21no—
193#11758198—21no—
194#11758198—22no—
195#11758198—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207#11758196—21no—
208#11758196—21no—
209#11758196—21no—
210#11758196C22⋊C412yes—
211#11758196C22⋊C412yes—
212#11758196C22⋊C412yes—
213#11758196C22⋊C412yes—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61C2×D412yes—
221C4×Dic61C2×D412yes—
222C4×Dic61C2×D412yes—
223C4×Dic61C2×D412yes—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—22no—
227C23×C61—41no—
228C23×C61C2×C22⋊C411yescharacteristic
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C23×C411yescharacteristic
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—41no—
235C22×D61—41no—
236Q8×C61—44no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—41no—
252C2×C4×C61C2×C22⋊C412yes—
253C2×C4×C61C2×C22⋊C412yes—
254C2×C4×C61#13112yes—
255C22⋊D61—42no—
256C22⋊D61—42no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—24no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C412yes—
277C2×Dic61C22×D412yes—
278C4×D61—42no—
279C4×D61—42no—
280#92420—42no—
281#92420—42no—
282#92420—42no—
283#92420—42no—
284#17417—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61#41012yes—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C2×#13111yescharacteristic
297C22×C61#56811yescharacteristic
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—81no—
302C2×D61—81no—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—41no—
309Dic61—21no—
310Dic61—21no—
311Dic61—22no—
312Dic61—22no—
313Dic61—21no—
314Dic61—21no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318C2×#552—611no—
319#2924—612no—
320#1473—612no—
321#1470—612no—
322#1468—612no—
323#1467—611no—
324#1464—611no—
325#1463—611no—
326#1461—611no—
327#1458—611no—
328C2×#324—611no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—22no—
332C2×C61—41no—
333C2×C61#288011yescharacteristic
334C2×C61C2×#41011yescharacteristic
335C2×C61#288911yescharacteristic
336D61—81no—
337#552—1222no—
338#552—1222no—
339#552—1222no—
340#552—1222no—
341C2×#126—611no—
342C2×#126—611no—
343C2×#125—611no—
344C2×#125—611no—
345C2×#125—611no—
346C2×#123—611no—
347C2×#123—611no—
348C2×C22⋊Q8—611no—
349C2×C22⋊Q8#692311yescharacteristic
350C2×C4×Q8—611no—
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C2×#117—611no—
355C22×C4⋊C4—611no—
356#433—1222no—
357#433—1222no—
358#432—612no—
359#432—612no—
360#431—612no—
361#431—612no—
362#424—1222no—
363#407—612no—
364C2×C22⋊C8—612no—
365#405—1222no—
366#324—611no—
367#324—611no—
368#324—612no—
369#324—611no—
370#324—611no—
371#324—612no—
372#324—612no—
373#324—612no—
374#323—612no—
375#323—612no—
376C61#1741711yescharacteristic, complemented, Sylow
377C22×Q8C2×#692311yescharacteristic
378C22×D4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4C2×#692311yescharacteristic
383C2×M16—1222no—
384C22×C8—1222no—
385#126—1222no—
386#126—1222no—
387#126—1222no—
388#126—1222no—
389#125—1222no—
390#125—1222no—
391#125—1222no—
392#125—1222no—
393#125—1222no—
394#125—1222no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409#117—612no—
410#117—612no—
411#117—612no—
412#117—612no—
413#117—1222no—
414#117—1222no—
415#117—1221no—
416#117—1221no—
417#117—1221no—
418#117—1221no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4C2×#692311yescharacteristic
435C2×C4⋊C4C2×#692311yescharacteristic
436C2×C4⋊C4C2×#692311yescharacteristic
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C22⋊C4—611no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4C2×#692311yescharacteristic
444C2×C22⋊C4C2×#692311yescharacteristic
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C22⋊C8—612no—
455C22⋊C8—612no—
456C22⋊C8—612no—
457C22⋊C8—612no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460#97—1222no—
461#97—1222no—
462C4×C8—1222no—
463C4×C8—1222no—
464C24—611no—
465C24C22×#692311yescharacteristic
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—41no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—2442no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4—612no—
477C22×C4—611no—
478C22×C4—612no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—2441no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4C22×#692311yescharacteristic
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499M16—2444no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2444no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—612no—
509C4⋊C4—612no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—611no—
529C22⋊C4—611no—
530C22⋊C4—611no—
531C22⋊C4—611no—
532C22⋊C4—1222no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4C22⋊#692312yes—
539C22⋊C4C22⋊#692312yes—
540C42—612no—
541C42—612no—
542C42—612no—
543C42—612no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C23—22no—
551C23—21no—
552C23—21no—
553C23—41no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—2441no—
558C23—2441no—
559C23C2×C22⋊#692311yescharacteristic
560C23C2×C22⋊#692311yescharacteristic
561C23C23×#692311yescharacteristic
562Q8—44no—
563D4—2442no—
564D4—2442no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—612no—
585C2×C4—612no—
586C2×C4—1224no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2442no—
597C2×C4—2441no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4C2×C22⋊#692312yes—
604C2×C4C2×C22⋊#692312yes—
605C2×C4#1451986412yes—
606C8—2442no—
607C8—2442no—
608C8—2442no—
609C8—2442no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—42no—
619C22—4881no—
620C22—4881no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22#1684074312yes—
625C22C22×C22⋊#692311yescharacteristic
626C22C2×#1451986411yescharacteristic
627C22#1684084011yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—1221no—
635C4—1221no—
636C4—1222no—
637C4—1222no—
638C4—1221no—
639C4—1221no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—41no—
647C2—4881no—
648C2#2146240711yescharacteristic
649C2C2×#1684074311yescharacteristic
650C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#17417
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462508C2semidirect
2. #21461103C2semidirect
3. #21461092C2semidirect
5. #21461082C2semidirect
6. #21461073C2semidirect
7. #21461067C2semidirect
8. #21461062C2semidirect
9. #21461053C2semidirect
10. C2×#16840607C2semidirect
376. C61#17417semidirect

Maximal subgroups

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

subgroupindex
#214625082
#214611032
#214610922
#214610862
#214610822
#214610732
#214610672
#214610622
#214610532
C2×#168406072
C2×#168404542
#1741761