Finite Group Databasebeta

← #30604501

Subgroups — #30604501

Order 15616.

362 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 106 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#21462178C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3#21460786C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5C8×#11758224C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840683—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840657—21no—
11C4×#11758187C2212yes—
12C4×#11758224C411yescharacteristic
13C8×Dic122C411yescharacteristic
14#16839886C2211yescharacteristic
15D4×#92418C2211yescharacteristic
16C8×C22⋊D61—21no—
17#16839825—21no—
18#16839814C411yescharacteristic
19#16839812—21no—
20C2×C8×Dic61—21no—
21C4×C8×D61C2211yescharacteristic
22C8×D4×C61C411yescharacteristic
23D61⋊C16—42no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758224C811yescharacteristic
27C22×#92418—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30C4×Dic122C2×C411yescharacteristic
31#14519742C811yescharacteristic
32D4×Dic61C811yescharacteristic
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735C811yescharacteristic
36#14519733—21no—
37C2×C4×Dic61—21no—
38C42×D61C2×C411yescharacteristic
39C4⋊#92418C2×C411yescharacteristic
40#14519706—21no—
41#14519706—21no—
42C22⋊#92418—21no—
43#14519689—21no—
44C4×#92418C2311yescharacteristic
45C8×Dic61—21no—
46C8×Dic61—21no—
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C22×C8×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61C2×C811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60#11758224—22no—
61#11758224C1614yescomplemented
62C2×C4×D61C22⋊C411yescharacteristic
63C2×C4×D61C2×C811yescharacteristic
64C2×C4×D61M1611yescharacteristic
65C2×Dic122C2×C811yescharacteristic
66C2×C8×C61—21no—
67C2×C8×C61—42no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C4⋊C4×C61C2×C811yescharacteristic
71C22⋊C4×C61—21no—
72C42×C61C22×C411yescharacteristic
73C22⋊Dic61—21no—
74#11758198—21no—
75C4⋊Dic61C2×C811yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61C2×C811yescharacteristic
83C4×Dic61M1611yescharacteristic
84C2×#92418—21no—
85C2×#92418—41no—
86C2×#92418—41no—
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89C8×D61—21no—
90C8×D61—21no—
91C8×D61—41no—
92#11758187—42no—
93#11758187—42no—
94C23×C61—21no—
95C22×D61C22⋊C811yescharacteristic
96D4×C61—21no—
97D4×C61C2×C1612yescomplemented
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61C22×C811yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C22⋊D61—24no—
105C2×Dic61—21no—
106C2×Dic61—24no—
107C2×Dic61—21no—
108C2×Dic61—42no—
109C2×Dic61C22⋊C811yescharacteristic
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—41no—
115C4×D61C2×C1612yes—
116C4×D61M3212yes—
117Dic122—21no—
118Dic122C2×C1612yescomplemented
119C8×C61—21no—
120C8×C61—21no—
121C8×C61—41no—
122#92418—21no—
123#92418—41no—
124#92418AGL(1,ℤ/8)11yescharacteristic
125#92418#13711yescharacteristic
126#11621—611nomaximal, Sylow
127C22×C61—22no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61C2×C22⋊C811yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61C22⋊C1612yes—
134C4×C61—21no—
135C4×C61—41no—
136C4×C61#41711yescharacteristic
137C4×C61#42111yescharacteristic
138C4×C61C22×C1611yescharacteristic
139C4×C61C2×M3211yescharacteristic
140Dic61—22no—
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61C22⋊C1612yes—
145C8×#41—611no—
146#2162—611no—
147C2×C4⋊C16—611no—
148Q8⋊C16—612no—
149D4⋊C16—612no—
150C2×C61—42no—
151C2×C61#147711yescharacteristic
152C2×C61C2×C22⋊C1611yescharacteristic
153C2×C61#211711yescharacteristic
154D61—22no—
155C4×#41—611no—
156C22×C16—1221no—
157C8×Q8—611no—
158C8×Q8—611no—
159C8×D4—611no—
160C8×D4—1221no—
161C8×D4—1221no—
162C8×D4#692311yescharacteristic
163#431—611no—
164#431—1221no—
165C2×C4×C8—611no—
166C2×C4×C8—1221no—
167C4⋊C16—612no—
168C4⋊C16—1221no—
169C4⋊C16—1221no—
170C22⋊C16—1221no—
171C4×C16—612no—
172C61#1162111yescharacteristic, complemented, Sylow
173C2×#41—611no—
174C22×C8—21no—
175C22×C8—611no—
176C22×C8—611no—
177C22×C8—1221no—
178C4×Q8—611no—
179C4×Q8—611no—
180C4×D4—611no—
181C4×D4—1221no—
182C4×D4—1221no—
183C4×D4C2×#692311yescharacteristic
184#117—611no—
185#117—1221no—
186C2×C42—611no—
187C2×C42—1221no—
188C2×C16—1222no—
189C2×C16—1222no—
190C2×C16—2442no—
191C4⋊C8—611no—
192C4⋊C8—1221no—
193C4⋊C8—1221no—
194C4⋊C8C2×#692311yescharacteristic
195C22⋊C8—21no—
196C22⋊C8—1221no—
197C22⋊C8—1221no—
198C4×C8—611no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—1221no—
202C4×C8—1221no—
203C4×C8—1221no—
204C4×C8C2×#692311yescharacteristic
205#41—614no—
206#41—1222no—
207C2×Q8—611no—
208C2×D4—1221no—
209C2×D4D61⋊C811yescharacteristic
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C2×C8—21no—
217C2×C8—42no—
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—1221no—
221C2×C8—1221no—
222C2×C8—1221no—
223C2×C8—2441no—
224C2×C8—2441no—
225C2×C8—2441no—
226C2×C8C22⋊#692311yescharacteristic
227C2×C8C22⋊#692311yescharacteristic
228C4⋊C4—611no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4D61⋊C811yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—1221no—
234C22⋊C4—1221no—
235C42—611no—
236C42—611no—
237C42—611no—
238C42—1221no—
239C42—1221no—
240C42—1221no—
241C42C22×#692311yescharacteristic
242C16—2442no—
243C16—2442no—
244C23—21no—
245C23—611no—
246Q8—612no—
247Q8—1221no—
248D4—21no—
249D4—1224no—
250D4D61⋊C1612yescomplemented
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—611no—
255C2×C4—612no—
256C2×C4—612no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—1224no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—2441no—
265C2×C4—2442no—
266C2×C4C2×C22⋊#692311yescharacteristic
267C2×C4C2×D61⋊C811yescharacteristic
268C2×C4D61⋊M1611yescharacteristic
269C8—21no—
270C8—21no—
271C8—41no—
272C8—611no—
273C8—611no—
274C8—1221no—
275C8—2441no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—612no—
280C22—1221no—
281C22—1221no—
282C22D61⋊(C22⋊C8)11yescharacteristic
283C4—21no—
284C4—41no—
285C4—612no—
286C4—1222no—
287C4—1221no—
288C4—1221no—
289C4—2441no—
290C4#1684075311yescharacteristic
291C4#1684076011yescharacteristic
292C4C2×D61⋊C1611yescharacteristic
293C4D61⋊M3211yescharacteristic
294C2—42no—
295C2—1222no—
296C2#2146111511yescharacteristic
297C2D61⋊(C22⋊C16)11yescharacteristic
298C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C22×C16
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758224C8
cosocleC4×#92418C23
hypercenterC8×D4#6923
hypocenterC61#11621
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. D61⋊(C4⋊C16)C2semidirect
3. #21460786C2semidirect
4. D4⋊#11758187C2semidirect
61. #11758224C16semidirect
97. D4×C61C2×C16semidirect
118. Dic122C2×C16semidirect
172. C61#11621semidirect
250. D4D61⋊C16semidirect

Maximal subgroups

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

subgroupindex
#214621782
D61⋊(C4⋊C16)2
#214607862
D4⋊#117581872
C8×#117582242
#1162161