Finite Group Databasebeta

← #30610208

Subgroups — #30610208

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic
2D61⋊#432C211yesmaximal, characteristic
3#21461099C212yesmaximal
4#21461097C212yesmaximal
5#21461091C214yesmaximal, complemented
6#21461081C214yesmaximal, complemented
7C2×#16840316C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840784—21no—
11#16840783C2212yes—
12#16840783C2212yes—
13#16840782C2212yes—
14#16840781—21no—
15#16840778C2212yes—
16#16840766—21no—
17D61⋊(C4⋊C8)—21no—
18#16840733C2212yes—
19D61⋊(C22⋊C8)C2212yes—
20C4×#11758213—21no—
21#16840721—21no—
22#16840608C2218yes—
23#16840607C2218yes—
24#16840316—21no—
25#16840316—21no—
26#16840316—21no—
27#16840316—21no—
28#16840316—21no—
29#16840316—21no—
30#16840316—21no—
31#16840316—21no—
32C2×#14519776C411yescharacteristic
33C2×#14519775C411yescharacteristic
34C2×#14519767C2212yes—
35C2×#14519757C2211yescharacteristic
36C2×#14519755C412yes—
37C2×#14519753C2211yescharacteristic
38C2×C4×Dic122C411yescharacteristic
39C2×C4×Dic122C2212yes—
40C2×#14519734C412yes—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×D61⋊C8—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50#14519834—22no—
51C22⋊#92420C2314yes—
52C22⋊#92420C2314yes—
53#14519832—22no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C22×Dic122C2×C411yescharacteristic
58C22×Dic122C2×C412yes—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62#14519776—21no—
63#14519776—21no—
64#14519776—21no—
65#14519776—21no—
66#14519775—21no—
67#14519775—21no—
68#14519775—21no—
69#14519775—21no—
70#14519767—22no—
71#14519767—22no—
72#14519767—22no—
73#14519767—22no—
74#14519757—21no—
75#14519757—21no—
76#14519757—21no—
77#14519757—21no—
78#14519755—22no—
79#14519755—22no—
80#14519755—22no—
81#14519755—22no—
82#14519753—21no—
83#14519753—21no—
84#14519753—21no—
85#14519753—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92C4×Dic122—22no—
93C4×Dic122—22no—
94#14519734—22no—
95#14519734—22no—
96#14519734—22no—
97#14519734—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2312yes—
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2×C412yes—
103C2×#11758196C2×C412yes—
104C2×#11758196C2312yes—
105C2×#11758198C2×C412yes—
106C2×#11758198C2×C412yes—
107C2×C4×Dic61C2×C412yes—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C22×Q8×C61C2×C411yescharacteristic
120C4×Q8×C61—21no—
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C2×C4⋊C4×C61C2×C412yes—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C42×C61C2×C412yes—
127C2×C42×C61C2×C411yescharacteristic
128C23×D61C22×C411yescharacteristic
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—42no—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C412yes—
137C22×Dic61C22×C412yes—
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C412yes—
141C22×Dic61C2411yescharacteristic
142C2×C4×D61—24no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×C4×D61C22⋊C411yescharacteristic
146C2×C4×D61C22⋊C411yescharacteristic
147C2×C4×D61C22⋊C411yescharacteristic
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—22no—
160C2×Dic122—22no—
161C2×Dic122—44no—
162C2×Dic122—42no—
163C2×#92420—24no—
164C2×#92420—24no—
165#11758213—44no—
166D61⋊C8—44no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C42×C61—22no—
172C42×C61—22no—
173C42×C61C22⋊C411yescharacteristic
174C42×C61C22⋊C411yescharacteristic
175C42×C61C22⋊C411yescharacteristic
176C42×C61C22⋊C411yescharacteristic
177#11758198—22no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195C4×Dic61—22no—
196C4×Dic61—22no—
197C4×Dic61C22⋊C411yescharacteristic
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C23×C61C23×C411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—41no—
213C22×D61C2×C22⋊C411yescharacteristic
214C22×D61C2×C22⋊C411yescharacteristic
215Q8×C61—42no—
216Q8×C61—42no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—42no—
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—24no—
235C2×Dic61—41no—
236C2×Dic61—42no—
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61C2×C22⋊C411yescharacteristic
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C22×D411yescharacteristic
242C2×Dic61C22×D411yescharacteristic
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61#10114yes—
255Dic122—44no—
256Dic122—44no—
257Dic122—42no—
258Dic122—42no—
259#92420—44no—
260#92420—44no—
261#17404—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61C22×C22⋊C411yescharacteristic
265C22×C61#56812yes—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—44no—
272C2×D61C2×#10112yes—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—42no—
278C4×C61—42no—
279C4×C61#41012yes—
280C4×C61C2×#10112yes—
281Dic61—21no—
282Dic61—21no—
283Dic61—21no—
284Dic61—21no—
285Dic61—21no—
286Dic61—42no—
287Dic61—42no—
288Dic61C2×#10112yes—
289C2×#533—611no—
290#2920—611no—
291C2×#432—611no—
292#1472—612no—
293#1472—612no—
294#1470—614no—
295#1467—614no—
296C2×C61—22no—
297C2×C61#287911yescharacteristic
298C2×C61C2×#41011yescharacteristic
299C2×C61C22×#10111yescharacteristic
300D61—22no—
301D61—41no—
302#533—1221no—
303#533—1221no—
304#533—1221no—
305#533—1221no—
306#533—1221no—
307#533—1221no—
308#533—1221no—
309#533—1221no—
310C2×C4⋊Q8—611no—
311C2×C4⋊Q8—611no—
312C2×#125—612no—
313C2×C22⋊Q8—611no—
314C2×C22⋊Q8—612no—
315C2×C22⋊Q8—611no—
316C2×C4×Q8—612no—
317C2×C4×Q8—611no—
318C2×C4×Q8#692311yescharacteristic
319C2×#117—612no—
320C22×C42—611no—
321#432—612no—
322#432—612no—
323#432—612no—
324#432—1221no—
325#432—1221no—
326#432—1221no—
327#431—612no—
328#431—1221no—
329#423—1221no—
330C2×C4⋊C8—1221no—
331#407—612no—
332C2×C22⋊C8—612no—
333C4×M16—1221no—
334C2×#97—1221no—
335#324—618no—
336#324—618no—
337C61#1740411yescharacteristic, complemented, Sylow
338C22×Q8—612no—
339C22×Q8—611no—
340C22×Q8C2×#692311yescharacteristic
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C2×M16—1222no—
345C22×C8—1222no—
346C4⋊Q8—1221no—
347C4⋊Q8—1221no—
348C4⋊Q8—1221no—
349C4⋊Q8—1221no—
350C4⋊Q8—1221no—
351C4⋊Q8—1221no—
352C4⋊Q8—1221no—
353C4⋊Q8—1221no—
354#125—1222no—
355#125—1222no—
356#125—1222no—
357#125—1222no—
358C22⋊Q8—1222no—
359C22⋊Q8—1222no—
360C22⋊Q8—1222no—
361C22⋊Q8—1222no—
362C22⋊Q8—1221no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C22⋊Q8—1221no—
368C22⋊Q8—1221no—
369C22⋊Q8—1221no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—1222no—
375C4×Q8—1222no—
376C4×Q8—1222no—
377C4×Q8—1222no—
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382#117—1222no—
383#117—1222no—
384#117—1222no—
385#117—1222no—
386C2×C4⋊C4—612no—
387C2×C4⋊C4—612no—
388C2×C4⋊C4—612no—
389C2×C4⋊C4—612no—
390C2×C4⋊C4—612no—
391C2×C4⋊C4—612no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4C2×#692312yes—
394C2×C4⋊C4C2×#692311yescharacteristic
395C2×C22⋊C4—612no—
396C2×C22⋊C4—612no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—612no—
409C2×C42C2×#692312yes—
410C2×C42C2×#692311yescharacteristic
411C4⋊C8—1222no—
412C4⋊C8—1222no—
413C4⋊C8—1222no—
414C4⋊C8—1222no—
415C22⋊C8—614no—
416C22⋊C8—614no—
417C22⋊C8—1222no—
418C22⋊C8—1222no—
419#97—1222no—
420#97—1222no—
421#97—1222no—
422C4×C8—1222no—
423C24—611no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—1222no—
428C2×Q8—1222no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—2444no—
432C2×Q8—2442no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—1224no—
451C22×C4—2442no—
452C22×C4—2442no—
453C22×C4C22×#692312yes—
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692312yes—
458M16—2444no—
459C2×C8—1224no—
460C2×C8—1224no—
461C2×C8—2444no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C22⋊C4—1222no—
481C22⋊C4—1222no—
482C22⋊C4—1222no—
483C22⋊C4—1222no—
484C42—22no—
485C42—22no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—1222no—
499C42—1222no—
500C42C22⋊#692311yescharacteristic
501C42C22⋊#692311yescharacteristic
502C42C22⋊#692311yescharacteristic
503C42C22⋊#692311yescharacteristic
504C23—611no—
505C23—611no—
506C23—1222no—
507C23—1222no—
508C23—2441no—
509C23C23×#692311yescharacteristic
510Q8—42no—
511Q8—42no—
512Q8—2442no—
513Q8—2444no—
514Q8—2444no—
515Q8—2442no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—611no—
524C2×C4—614no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1224no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2442no—
548C2×C4C2×C22⋊#692311yescharacteristic
549C2×C4C2×C22⋊#692311yescharacteristic
550C2×C4C2×C22⋊#692311yescharacteristic
551C2×C4C2×C22⋊#692311yescharacteristic
552C2×C4C2×C22⋊#692311yescharacteristic
553C2×C4C2×C22⋊#692311yescharacteristic
554C8—2444no—
555C8—2444no—
556C22—21no—
557C22—21no—
558C22—612no—
559C22—1221no—
560C22—1221no—
561C22—1221no—
562C22—1221no—
563C22—1221no—
564C22—2444no—
565C22C22×C22⋊#692311yescharacteristic
566C22#1684084112yes—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—42no—
572C4—42no—
573C4—612no—
574C4—1221no—
575C4—1221no—
576C4—1221no—
577C4—1221no—
578C4—1221no—
579C4—2442no—
580C4—2442no—
581C4#1684074112yes—
582C4D61⋊#10112yes—
583C2—22no—
584C2—1222no—
585C2—2441no—
586C2#2146240411yescharacteristic
587C2C2×#1684074111yescharacteristic
588C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17404
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
5. #21461091C2semidirect
6. #21461081C2semidirect
337. C61#17404semidirect

Maximal subgroups

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

subgroupindex
#214624962
D61⋊#4322
#214610992
#214610972
#214610912
#214610812
C2×#168403162
#1740461