Finite Group Databasebeta

← #29592113

Subgroups — #29592113

Order 15616.

476 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456590C211yesmaximal, characteristic, complemented
2#21447748C211yesmaximal, characteristic, complemented
3#21446814C211yesmaximal, characteristic
4#21443832C211yesmaximal, characteristic, complemented
5#21443831C211yesmaximal, characteristic, complemented
6#21443742C211yesmaximal, characteristic, complemented
7C61×#2187C211yesmaximal, characteristic, complemented
8C22⋊Q8×D61—21no—
9C2×#14519748—21no—
10C2×#14519721—21no—
11#16840099—21no—
12#16840096—21no—
13#16840003C2211yescharacteristic
14#16840001—21no—
15#16839919—21no—
16#16839916—21no—
17C2×#14519698—21no—
18C2×#14519689C2211yescharacteristic
19#16839563—21no—
20C22⋊#11758185C2211yescharacteristic
21#16839525C2211yescharacteristic
22C22×D8×C61C2211yescharacteristic
23C2×SD32×C61—21no—
24C61×#467C2211yescharacteristic
25C61×#357—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×Q8×D61—21no—
28C22×C22⋊D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×Dic244D411yescharacteristic, complemented
31C2×#11758202—21no—
32C22×#92418D411yescharacteristic
33#14519757—21no—
34#14519756—21no—
35#14519755—41no—
36#14519754—41no—
37#14519753—21no—
38#14519748—42no—
39#14519748—42no—
40C2×C4⋊Dic61—21no—
41C4⋊C4×D61—21no—
42C4⋊C4×D61—41no—
43C2×C22⋊Dic61—41no—
44C22⋊C4×D61—41no—
45#14519721—42no—
46C2×#11758185—21no—
47#14519711D411yescharacteristic, complemented
48#14519710—21no—
49#14519702—21no—
50#14519701—21no—
51#14519700—21no—
52#14519698—42no—
53#14519689—21no—
54#14519689—21no—
55C22×D4×C61—21no—
56C2×Q16×C61D411yescharacteristic, complemented
57C2×D8×C61—21no—
58C2×D8×C61—21no—
59C2×D8×C61—42no—
60C22×C8×C61C2311yescharacteristic
61C22⋊Q8×C61—21no—
62SD32×C61—42no—
63C2×C16×C61—21no—
64#107×C61D411yescharacteristic, complemented
65#103×C61—21no—
66C24×C61—41no—
67C23×D61D811yescharacteristic
68C2×Q8×C61—21no—
69C2×D4×C61—22no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—44no—
77C2×C22⋊D61—82no—
78C2×C22⋊D61—82no—
79C22×Dic61—41no—
80C22×Dic61D811yescharacteristic
81Q8×D61—81no—
82Q8×D61—81no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91Q16×C61—41no—
92D8×C61—22no—
93D8×C61—22no—
94D8×C61—41no—
95D8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊Dic61—44no—
103C22⋊Dic61—41no—
104#11758202—81no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—22no—
108C4⋊Dic61—21no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114C2×#92418—21no—
115C2×#92418—41no—
116Dic244—41no—
117C16×C61—41no—
118#11758185—41no—
119C23×C61—42no—
120C23×C61—81no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61—81no—
126C23×C61C2×D811yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61SD3212yescomplemented
132Q8×C61—41no—
133Q8×C61—41no—
134D4×C61—42no—
135D4×C61—42no—
136D4×C61—81no—
137D4×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C22⋊D61—88no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—81no—
155C4×D61—82no—
156C4×D61—82no—
157Dic122—41no—
158Dic122—41no—
159Dic122—82no—
160C8×C61—21no—
161C8×C61—21no—
162#92418—41no—
163#12103—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—82no—
167C22×C61—82no—
168C22×C61—82no—
169C22×C61—161no—
170C22×C61—161no—
171C22×C61—161no—
172C22×C61—161no—
173C22×C61#44711yescharacteristic
174C22×C61C2×SD3211yescharacteristic
175C22×C61#51011yescharacteristic
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—42no—
180C2×D61—81no—
181C4×C61—21no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61#45311yescharacteristic
185C4×C61B(4,𝔽2)11yescharacteristic
186Dic61—41no—
187Dic61—82no—
188Dic61—81no—
189Dic61—81no—
190#3189—611no—
191#2187—611no—
192#2187D6111yescharacteristic, complemented
193#1999—611no—
194#1348—611no—
195#1348—611no—
196#1314—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—162no—
200C2×C61#159511yescharacteristic
201C2×C61#218511yescharacteristic
202C2×C61#219011yescharacteristic
203D61—42no—
204C22×D8C2×D6111yescharacteristic
205C2×C22⋊Q8—1221no—
206C2×#121—1221no—
207C2×SD32—21no—
208C2×SD32—1221no—
209#484—1221no—
210#484—1221no—
211#467—611no—
212#467—1221no—
213#467C2×D6111yescharacteristic
214#451—1221no—
215#451—1221no—
216C2×#102—1221no—
217C2×C22⋊C8—611no—
218#357—21no—
219#357—1221no—
220C22⋊C16—611no—
221C22⋊C16C2×D6111yescharacteristic
222#340—611no—
223C61#1210311yescharacteristic, complemented, Sylow
224C22×Q8—1221no—
225C22×D4—21no—
226C22×D4—2441no—
227C23×C4—611no—
228C2×Q16—611no—
229C2×Q16—1221no—
230C2×Q16C22⋊D6111yescharacteristic, complemented
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—42no—
234C22×C8—611no—
235C22×C8C22×D6111yescharacteristic
236C22⋊Q8—21no—
237C22⋊Q8—1221no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8—2441no—
241C22⋊Q8—2441no—
242#121—2442no—
243#121—2442no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—2441no—
247C2×C22⋊C4—2441no—
248C2×C22⋊C4—2441no—
249SD32—42no—
250SD32—2442no—
251C2×C16—21no—
252C2×C16—1221no—
253#107—611no—
254#107—1221no—
255#107C22⋊D6111yescharacteristic, complemented
256#103—21no—
257#103—1221no—
258#103—1221no—
259#103—1221no—
260#102—2442no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263C24—41no—
264C24—611no—
265C2×Q8—21no—
266C2×Q8—1221no—
267C2×Q8—4881no—
268C2×Q8—4881no—
269C2×Q8—2441no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—4882no—
277C2×D4—4882no—
278C2×D4—2444no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4D4×D6111yescharacteristic
288Q16—41no—
289Q16—4881no—
290Q16—2441no—
291D8—22no—
292D8—22no—
293D8—41no—
294D8—41no—
295C2×C8—41no—
296C2×C8—1221no—
297C2×C8—2441no—
298C2×C8D4×D6111yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—1222no—
303C4⋊C4—1221no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C22⋊C4—41no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2444no—
313C22⋊C4—2441no—
314C16—41no—
315C16—2441no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—2441no—
327C23—2441no—
328C23D8×D6111yescharacteristic
329Q8—41no—
330Q8—41no—
331Q8—4882no—
332Q8—2441no—
333Q8—2441no—
334D4—42no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—4888no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—1221no—
344C2×C4—4881no—
345C2×C4—4882no—
346C2×C4—4882no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4#1451974511yescharacteristic
356C2×C4#1451980111yescharacteristic
357C8—21no—
358C8—21no—
359C8—2441no—
360C22—21no—
361C22—21no—
362C22—82no—
363C22—82no—
364C22—82no—
365C22—161no—
366C22—161no—
367C22—161no—
368C22—161no—
369C22—1222no—
370C22—4881no—
371C22—2442no—
372C22—2441no—
373C22—2441no—
374C22#1683989411yescharacteristic
375C22SD32×D6111yescharacteristic
376C22#1684020111yescharacteristic
377C4—21no—
378C4—81no—
379C4—81no—
380C4—4882no—
381C4—4881no—
382C4—4881no—
383C4—2441no—
384C4#1683992811yescharacteristic
385C4#1683994811yescharacteristic
386C2—21no—
387C2—21no—
388C2—162no—
389C2—2442no—
390C2#2144473511yescharacteristic
391C2#2144773411yescharacteristic
392C2#2144776311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2187C2
socleC22×C61#447
prime radical#21446814C2
hypercenter#2187D61
hypocenterC61#12103
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #21456590C2semidirect
2. #21447748C2semidirect
4. #21443832C2semidirect
5. #21443831C2semidirect
6. #21443742C2semidirect
7. C61×#2187C2semidirect
30. C2×Dic244D4semidirect
47. #14519711D4semidirect
56. C2×Q16×C61D4semidirect
64. #107×C61D4semidirect
131. C22×D61SD32semidirect
192. #2187D61semidirect
223. C61#12103semidirect
230. C2×Q16C22⋊D61semidirect
255. #107C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214565902
#214477482
#214468142
#214438322
#214438312
#214437422
C61×#21872
#1210361