Finite Group Databasebeta

← #29589894

Subgroups — #29589894

Order 15616.

352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C8×#11758226C211yesmaximal, characteristic
2#21447616C211yesmaximal, characteristic, complemented
3#21447573C211yesmaximal, characteristic, complemented
4Q8⋊#11758185C211yesmaximal, characteristic, complemented
5#21443775C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8C4×#11758226C411yescharacteristic
9C2×#14519716—21no—
10Q8×#92418C411yescharacteristic
11C8×D244—21no—
12C8×D244C2211yescharacteristic
13#16839827—21no—
14#16839827C411yescharacteristic
15#16839814—21no—
16#16839814C411yescharacteristic
17C4×C8×D61—21no—
18C4×C8×D61C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic
20#16839580—21no—
21#16839580—21no—
22#16839541—21no—
23C4×#11758185C2211yescharacteristic
24C8×Q8×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C4×C16×C61C2211yescharacteristic
27C2×#11758226C811yescharacteristic
28C2×C8×D61—21no—
29C2×C8×D61—21no—
30C2×C8×D61D411yescharacteristic
31C2×C8×D61D411yescharacteristic
32Q8×Dic61C811yescharacteristic
33C4×D244—21no—
34C4×D244C2×C411yescharacteristic
35#14519739—21no—
36#14519739C811yescharacteristic
37#14519735—21no—
38#14519735C811yescharacteristic
39C42×D61—21no—
40C42×D61C2×C411yescharacteristic
41#14519716—42no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44C4⋊#92418—21no—
45C4⋊#92418C2×C411yescharacteristic
46#14519689—21no—
47#14519689—21no—
48#14519689—21no—
49C4×#92418—21no—
50C4×#92418C2×C411yescharacteristic
51C8×Dic61—21no—
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C4×Q8×C61C2×C411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61C2×C411yescharacteristic
59C4×C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61C2×C811yescharacteristic
62#11758226—22no—
63#11758226—22no—
64C2×D244—21no—
65C2×D244C2×C811yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61C22⋊C411yescharacteristic
70C2×C4×D61C2×C811yescharacteristic
71C2×C4×D61M1611yescharacteristic
72C2×C8×C61—21no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2×C811yescharacteristic
77C42×C61—21no—
78C42×C61C22×C411yescharacteristic
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61C2×C811yescharacteristic
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61C22⋊C411yescharacteristic
87C4×Dic61C2×C811yescharacteristic
88C4×Dic61M1611yescharacteristic
89C2×#92418—21no—
90C2×#92418C22⋊C411yescharacteristic
91C2×#92418C22⋊C411yescharacteristic
92C8×D61—21no—
93C8×D61—21no—
94C8×D61—41no—
95C8×D61—42no—
96C8×D61—41no—
97C8×D61—41no—
98C16×C61—41no—
99C16×C61—41no—
100#11758185—41no—
101#11758185—41no—
102C22×D61—21no—
103C22×D61C22⋊C811yescharacteristic
104Q8×C61—21no—
105Q8×C61M3212yescomplemented
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61C22×C811yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×Dic61—21no—
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C2×Dic61C22⋊C811yescharacteristic
115D244—24no—
116D244—21no—
117D244M3212yescomplemented
118C4×D61—24no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—21no—
122C4×D61—21no—
123C4×D61—22no—
124C4×D61—41no—
125C4×D61—41no—
126C4×D61—42no—
127C8×C61—21no—
128C8×C61—41no—
129C8×C61AGL(1,ℤ/8)11yescharacteristic
130C8×C61#13711yescharacteristic
131#92418—21no—
132#92418—21no—
133#92418—41no—
134#11623—611nomaximal, Sylow
135C22×C61C2×C22⋊C811yescharacteristic
136C2×D61—21no—
137C2×D61—22no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—41no—
142C4×C61—22no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61#41711yescharacteristic
146C4×C61#42111yescharacteristic
147C4×C61C2×M3211yescharacteristic
148C4×C61C2×M3211yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61#35012yes—
153C8×#41—611no—
154#2162—611no—
155#2150—611no—
156Q8⋊C16—611no—
157Q8⋊C16D6111yescharacteristic, complemented
158D4⋊C16—611no—
159D4⋊C16—611no—
160C2×C61#147711yescharacteristic
161C2×C61#211211yescharacteristic
162C2×C61C2×#35011yescharacteristic
163D61—41no—
164D61—42no—
165C4×#41—611no—
166C2×M32—1221no—
167C8×Q8—611no—
168C8×Q8C2×D6111yescharacteristic
169C8×D4—611no—
170C8×D4—611no—
171C8×D4—1221no—
172C8×D4—1221no—
173#431—611no—
174#431—1221no—
175C2×C4×C8—611no—
176C2×C4×C8—1221no—
177C4⋊C16—611no—
178C4⋊C16—1221no—
179C4⋊C16—1221no—
180C4⋊C16C2×D6111yescharacteristic
181C22⋊C16—1221no—
182C4×C16—611no—
183C4×C16C2×D6111yescharacteristic
184C61#1162311yescharacteristic, complemented, Sylow
185C2×#41—611no—
186C22×C8—611no—
187C22×C8—611no—
188C22×C8—1221no—
189C22×C8—1221no—
190C4×Q8—611no—
191C4×Q8C4×D6111yescharacteristic
192C4×D4—611no—
193C4×D4—611no—
194C4×D4—1221no—
195C4×D4—1221no—
196#117—611no—
197#117—1221no—
198C2×C42—611no—
199C2×C42—1221no—
200M32—2442no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—1221no—
204C2×C16—1221no—
205C4⋊C8—21no—
206C4⋊C8—611no—
207C4⋊C8—1221no—
208C4⋊C8C4×D6111yescharacteristic
209C22⋊C8—1221no—
210C22⋊C8—1221no—
211C22⋊C8—1221no—
212C4×C8—21no—
213C4×C8—611no—
214C4×C8—611no—
215C4×C8—611no—
216C4×C8—1221no—
217C4×C8—1221no—
218C4×C8C22×D6111yescharacteristic
219#41—1222no—
220#41—1222no—
221C2×Q8C8×D6111yescharacteristic
222C2×D4—611no—
223C2×D4—1221no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C2×C8—21no—
231C2×C8—611no—
232C2×C8—611no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—1221no—
236C2×C8—2441no—
237C2×C8—2442no—
238C2×C8—2441no—
239C2×C8—2441no—
240C2×C8D4×D6111yescharacteristic
241C2×C8D4×D6111yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—611no—
244C4⋊C4—1221no—
245C4⋊C4C8×D6111yescharacteristic
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C42—21no—
250C42—611no—
251C42—611no—
252C42—611no—
253C42—1221no—
254C42—1221no—
255C42C2×C4×D6111yescharacteristic
256C16—41no—
257C16—41no—
258C16—2441no—
259C16—2441no—
260C23—611no—
261C23—1221no—
262Q8—21no—
263Q8#1451971612yescomplemented
264D4—612no—
265D4—1224no—
266D4—1221no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1222no—
273C2×C4—1224no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—2442no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4C22⋊C4×D6111yescharacteristic
283C2×C4C2×C8×D6111yescharacteristic
284C2×C4M16×D6111yescharacteristic
285C8—21no—
286C8—41no—
287C8—1221no—
288C8—1221no—
289C8—2441no—
290C8#1451980411yescharacteristic
291C8#1451980911yescharacteristic
292C22—1222no—
293C22—1221no—
294C22—1221no—
295C22—1221no—
296C22—2441no—
297C22—2441no—
298C22C22⋊C8×D6111yescharacteristic
299C4—22no—
300C4—21no—
301C4—41no—
302C4—612no—
303C4—1221no—
304C4—1221no—
305C4—2441no—
306C4#1683976211yescharacteristic
307C4#1683977711yescharacteristic
308C4M32×D6111yescharacteristic
309C4C2×#1451971611yescharacteristic
310C2—2441no—
311C2—2442no—
312C2#2144420511yescharacteristic
313C2#2144742811yescharacteristic
314C2#350×D6111yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758226C8
cosocleC4×C8×C61C23
hypercenterQ8⋊C16D61
hypocenterC61#11623
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
2. #21447616C2semidirect
3. #21447573C2semidirect
4. Q8⋊#11758185C2semidirect
5. #21443775C2semidirect
6. #21443773C2semidirect
7. C61×Q8⋊C16C2semidirect
105. Q8×C61M32semidirect
117. D244M32semidirect
157. Q8⋊C16D61semidirect
184. C61#11623semidirect
263. Q8#14519716semidirect

Maximal subgroups

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

subgroupindex
C8×#117582262
#214476162
#214475732
Q8⋊#117581852
#214437752
#214437732
C61×Q8⋊C162
#1162361