Finite Group Databasebeta

← #30610271

Subgroups — #30610271

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462508C212yesmaximal, complemented
2#21461098C212yesmaximal, complemented
3#21461093C212yesmaximal, complemented
4#21461091C212yesmaximal, complemented
5#21461077C211yesmaximal, characteristic
6#21461073C211yesmaximal, characteristic, complemented
7#21461072C211yesmaximal, characteristic, complemented
8#21461057C211yesmaximal, characteristic
9#21461053C211yesmaximal, characteristic, complemented
10#21461052C211yesmaximal, characteristic, complemented
11C2×#16840448C211yesmaximal, 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#16840608C2212yes—
23#16840608C2212yes—
24#16840608C2212yes—
25#16840608C2212yes—
26#16840607C2212yes—
27#16840607C2212yes—
28#16840606C2211yescharacteristic
29#16840606C2211yescharacteristic
30#16840606C2211yescharacteristic
31#16840606C2211yescharacteristic
32#16840448—22no—
33#16840448—22no—
34#16840448—22no—
35#16840448—22no—
36C2×#14519770C411yescharacteristic
37C2×#14519768C2211yescharacteristic
38C2×#14519767C411yescharacteristic
39C2×#14519767C2211yescharacteristic
40C2×#14519759C411yescharacteristic
41C2×#14519759C411yescharacteristic
42C2×#14519755C411yescharacteristic
43C2×#14519754C2211yescharacteristic
44C2×C4×Dic122C411yescharacteristic
45C2×#14519737C2211yescharacteristic
46C2×#14519735C2211yescharacteristic
47C2×#14519734C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C2×C4⋊C4×D61C411yescharacteristic
50C2×#126×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×Dic122C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C23×Dic61C2311yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73#14519770—22no—
74#14519770—22no—
75#14519768—22no—
76#14519768—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519759—22no—
82#14519759—22no—
83#14519759—22no—
84#14519759—22no—
85#14519755—22no—
86#14519755—22no—
87#14519754—22no—
88#14519754—22no—
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122—21no—
92C4×Dic122—21no—
93#14519737—22no—
94#14519737—22no—
95#14519735—22no—
96#14519735—22no—
97#14519734—22no—
98#14519734—22no—
99#14519733D412yes—
100#14519733D412yes—
101#14519733D412yes—
102#14519733D412yes—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×C4⋊Dic61C2×C411yescharacteristic
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2311yescharacteristic
115C2×#11758196C2311yescharacteristic
116C4⋊C4×D61—21no—
117C4⋊C4×D61—21no—
118C4⋊C4×D61—21no—
119C4⋊C4×D61—21no—
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2311yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129#126×C61—22no—
130#126×C61—22no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—41no—
149C22×Dic61—42no—
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C2×D412yes—
157C22×Dic61C2×D412yes—
158C22×Dic61C2411yescharacteristic
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—41no—
168C2×C4×D61—41no—
169C2×C4×D61—42no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—42no—
173#11758217—44no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C2×#92420—22no—
178C2×#92420—44no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61C22⋊C412yes—
186C22⋊C4×C61C22⋊C412yes—
187C42×C61—21no—
188C42×C61—21no—
189C22⋊Dic61—22no—
190C22⋊Dic61C22⋊C412yes—
191C22⋊Dic61C22⋊C412yes—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—22no—
201#11758196—21no—
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196C22⋊C411yescharacteristic
211#11758196C22⋊C411yescharacteristic
212#11758196C22⋊C411yescharacteristic
213#11758196C22⋊C411yescharacteristic
214#11758196C22⋊C412yes—
215#11758196C22⋊C412yes—
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—41no—
227C23×C61—41no—
228C23×C61C2×C22⋊C412yes—
229C23×C61C23×C411yescharacteristic
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61#13112yes—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
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—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C412yes—
250C22⋊D61—44no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—24no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—42no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C412yes—
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C22×D412yes—
272C4×D61—42no—
273C4×D61—42no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278Dic122—42no—
279Dic122—42no—
280#92420—42no—
281#92420—42no—
282#92420—42no—
283#92420—42no—
284#17413—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61C22×C22⋊C411yescharacteristic
293C22×C61C2×#13111yescharacteristic
294C22×C61#56811yescharacteristic
295C2×D61—22no—
296C2×D61—42no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—42no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—22no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—41no—
307Dic61—21no—
308Dic61—21no—
309Dic61—22no—
310Dic61—21no—
311Dic61—22no—
312Dic61—41no—
313Dic61—41no—
314Dic61—41no—
315Dic61#41012yes—
316C2×#552—611no—
317#2924—612no—
318#1472—612no—
319#1470—612no—
320#1470—612no—
321#1465—611no—
322#1464—611no—
323#1464—611no—
324#1459—611no—
325#1458—611no—
326#1458—611no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—42no—
330C2×C61#288011yescharacteristic
331C2×C61C2×#41011yescharacteristic
332C2×C61#288911yescharacteristic
333D61—42no—
334#552—1222no—
335#552—1222no—
336#552—1222no—
337#552—1222no—
338C2×#126—611no—
339C2×#126#692311yescharacteristic
340C2×#125—611no—
341C2×#125—611no—
342C2×#125—611no—
343C2×#123—611no—
344C2×#123—611no—
345C2×C22⋊Q8—611no—
346C2×C22⋊Q8—611no—
347C2×C4×Q8—611no—
348C2×C4×D4—611no—
349C2×#117—611no—
350C2×#117—611no—
351C2×#117—611no—
352C22×C4⋊C4—611no—
353#433—1222no—
354#433—1222no—
355#432—612no—
356#432—612no—
357#431—612no—
358#431—612no—
359#424—1222no—
360#407—612no—
361C2×C22⋊C8—612no—
362#405—1222no—
363#324—612no—
364#324—612no—
365#324—612no—
366#324—612no—
367#324—612no—
368#324—612no—
369#323—611no—
370#323—611no—
371#323—611no—
372#323—611no—
373C61#1741311yescharacteristic, complemented, Sylow
374C22×Q8—611no—
375C22×D4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C2×M16—1222no—
381C22×C8—1222no—
382#126—22no—
383#126—22no—
384#126—1222no—
385#126—1222no—
386#125—1222no—
387#125—1222no—
388#125—1222no—
389#125—1222no—
390#125—1222no—
391#125—1222no—
392#123—1222no—
393#123—1222no—
394#123—1222no—
395#123—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C22⋊Q8—1222no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×D4—1222no—
405C4×D4—1222no—
406#117—612no—
407#117—612no—
408#117—612no—
409#117—612no—
410#117—1222no—
411#117—1222no—
412#117—1222no—
413#117—1222no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
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—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4C2×#692311yescharacteristic
432C2×C4⋊C4C2×#692311yescharacteristic
433C2×C4⋊C4C2×#692311yescharacteristic
434C2×C22⋊C4—611no—
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4C2×#692311yescharacteristic
440C2×C22⋊C4C2×#692311yescharacteristic
441C2×C22⋊C4C2×#692311yescharacteristic
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42C2×#692311yescharacteristic
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C22⋊C8—612no—
452C22⋊C8—612no—
453C22⋊C8—612no—
454C22⋊C8—612no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457#97—1222no—
458#97—1222no—
459C4×C8—1222no—
460C4×C8—1222no—
461C24—611no—
462C24C22×#692311yescharacteristic
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—2442no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—2441no—
469C22×C4—612no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—612no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—2441no—
487C22×C4—2441no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C22×#692311yescharacteristic
491C22×C4C22×#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496M16—2444no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—2444no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—611no—
507C4⋊C4—611no—
508C4⋊C4—611no—
509C4⋊C4—611no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1222no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—612no—
530C22⋊C4—612no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4C22⋊#692312yes—
536C22⋊C4C22⋊#692312yes—
537C42—21no—
538C42—21no—
539C42—612no—
540C42—612no—
541C42—612no—
542C42—612no—
543C42—1221no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—612no—
552C23—1221no—
553C23—1221no—
554C23—2441no—
555C23—2441no—
556C23C2×C22⋊#692312yes—
557C23C23×#692311yescharacteristic
558Q8—2442no—
559Q8—2442no—
560D4—2444no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—612no—
577C2×C4—611no—
578C2×C4—612no—
579C2×C4—1224no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2442no—
599C2×C4—2441no—
600C2×C4C2×C22⋊#692311yescharacteristic
601C2×C4C2×C22⋊#692311yescharacteristic
602C2×C4C2×C22⋊#692312yes—
603C8—2442no—
604C8—2442no—
605C8—2442no—
606C8—2442no—
607C22—21no—
608C22—21no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—81no—
613C22—81no—
614C22—1222no—
615C22—2442no—
616C22—2442no—
617C22—2441no—
618C22—2441no—
619C22C22×C22⋊#692311yescharacteristic
620C22D61⋊#13111yescharacteristic
621C22#1684084111yescharacteristic
622C4—21no—
623C4—21no—
624C4—22no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—612no—
630C4—1221no—
631C4—1221no—
632C4—1222no—
633C4—1221no—
634C4—1222no—
635C4—2441no—
636C4—2441no—
637C4—2441no—
638C2—21no—
639C2—21no—
640C2—42no—
641C2—2442no—
642C2#2146240911yescharacteristic
643C2D61⋊#41011yescharacteristic
644C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#126×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×#126#6923
hypocenterC61#17413
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #21462508C2semidirect
2. #21461098C2semidirect
3. #21461093C2semidirect
4. #21461091C2semidirect
6. #21461073C2semidirect
7. #21461072C2semidirect
9. #21461053C2semidirect
10. #21461052C2semidirect
373. C61#17413semidirect

Maximal subgroups

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

subgroupindex
#214625082
#214610982
#214610932
#214610912
#214610772
#214610732
#214610722
#214610572
#214610532
#214610522
C2×#168404482
#1741361