Finite Group Databasebeta

← C2×#11763838 #14545489

Subgroups — C2×#11763838 #14545489

Order 2176.

564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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
1C22×#63243C211yesmaximal, characteristic, complemented
2C23×#3624C211yesmaximal, characteristic, complemented
3#11763838C218yesmaximal, direct product factor
4C2×C4⋊#3624C211yesmaximal, characteristic, complemented
5C2×#10587543C211yesmaximal, characteristic, complemented
6C2×C22⋊#3624C211yesmaximal, characteristic, complemented
7C2×#10587542C211yesmaximal, characteristic, complemented
8C2×#10587567C211yesmaximal, characteristic
9C22×C22⋊D17C411yescharacteristic
10C23×Dic17C2211yescharacteristic
11C22×C4×D17C2211yescharacteristic
12C22×#3624—24no—
13C22×#3624C2211yescharacteristic
14C22×#3624C2211yescharacteristic
15C22×#3624C2211yescharacteristic
16C22×#3624C2211yescharacteristic
17C22×#3624C2214yescomplemented
18C2×#63243—24no—
19C2×#63243C2214yescomplemented
20C2×C22⋊C4×C17C411yescharacteristic
21C2×#63227C411yescharacteristic
22C2×#63225C411yescharacteristic
23C2×C4×Dic17C2211yescharacteristic
24#10587567C414yes—
25#10587567C2214yes—
26C22⋊#3624C2214yescomplemented
27#10587543C2214yescomplemented
28#10587542C2214yescomplemented
29C4⋊#3624C2214yescomplemented
30C24×C17C2×C411yescharacteristic
31C23×D17C2×C411yescharacteristic
32C22×C4×C17C2×C411yescharacteristic
33C22×C4×C17C2×C411yescharacteristic
34C2×C22⋊D17—24no—
35C2×C22⋊D17C2×C414yes—
36C22×Dic17—22no—
37C22×Dic17—22no—
38C22×Dic17C2×C412yes—
39C22×Dic17C2×C411yescharacteristic
40C22×Dic17C2×C411yescharacteristic
41C22×Dic17C2312yes—
42C22×Dic17C2311yescharacteristic
43C2×C4×D17—22no—
44C2×C4×D17—22no—
45C2×C4×D17C2×C412yes—
46C2×C4×D17C2312yes—
47C2×#3624—22no—
48C2×#3624—22no—
49C2×#3624—22no—
50C2×#3624—28no—
51C2×#3624D414yescomplemented
52C2×#3624C2312yes—
53C2×#3624C2312yes—
54C2×#3624C2312yes—
55C2×#3624C2312yes—
56#63243—28no—
57C22⋊C4×C17C2×C414yes—
58#63227C2×C414yes—
59#63225C2×C414yes—
60C4×Dic17C2×C412yes—
61C4×Dic17C2312yes—
62C23×C17—22no—
63C23×C17—22no—
64C23×C17M1614yescomplemented
65C23×C17C22×C412yes—
66C23×C17C22×C411yescharacteristic
67C22×D17—22no—
68C22×D17—22no—
69C22×D17—22no—
70C22×D17C22×C412yes—
71C2×C4×C17—22no—
72C2×C4×C17—22no—
73C2×C4×C17C22×C412yes—
74C2×C4×C17C22×C412yes—
75C22⋊D17—28no—
76C2×Dic17—22no—
77C2×Dic17—22no—
78C2×Dic17—24no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17C22×C412yes—
82C2×Dic17C22×C412yes—
83C2×Dic17C22×C411yescharacteristic
84C2×Dic17C2×D412yes—
85C2×Dic17#4112yes—
86C2×Dic17C2411yescharacteristic
87C4×D17—24no—
88C4×D17—22no—
89C4×D17—22no—
90#3624—22no—
91#3624—22no—
92#3624—22no—
93#3624C2×D414yescomplemented
94C2×#435—171nomaximal, Sylow
95C22×C17—22no—
96C22×C17—22no—
97C22×C17—28no—
98C22×C17C4×D412yes—
99C22×C17C2×M1612yes—
100C22×C17C2×M1614yescomplemented
101C22×C17#13112yes—
102C22×C17C23×C411yescharacteristic
103C2×D17—22no—
104C2×D17—22no—
105C2×D17—22no—
106C2×D17—44no—
107C4×C17—22no—
108C4×C17—22no—
109Dic17—22no—
110Dic17—22no—
111Dic17C4×D412yes—
112Dic17C22×D411yescharacteristic
113Dic17C2×#4111yescharacteristic
114C22×M16—171no—
115C23×C8—171no—
116C2×C4×D4—171no—
117#435—178no—
118C2×C4⋊C8—171no—
119C2×C22⋊C8—171no—
120C2×C22⋊C8—171no—
121C2×#97—171no—
122C2×C17—24no—
123C2×C17#43514yescomplemented
124C2×C17C2×C4×D411yescharacteristic
125C2×C17C22×M1611yescharacteristic
126C2×C17C2×#13111yescharacteristic
127D17—42no—
128C22×D4—171no—
129C23×C4—171no—
130C23×C4—171no—
131C2×M16—174no—
132C2×M16—344no—
133C22×C8—171no—
134C22×C8—171no—
135C22×C8—171no—
136C22×C8—171no—
137C22×C8—174no—
138C22×C8—344no—
139C4×D4—174no—
140C4×D4—174no—
141C2×C4⋊C4—171no—
142C2×C22⋊C4—171no—
143C2×C22⋊C4#59511yescharacteristic
144C2×C42—171no—
145C4⋊C8—174no—
146C22⋊C8—174no—
147C22⋊C8—174no—
148#97—174no—
149C17C2×#43511yescharacteristic, complemented, Sylow
150C24—171no—
151C24C2×#59511yescharacteristic
152C2×D4—174no—
153C2×D4—344no—
154C22×C4—171no—
155C22×C4—172no—
156C22×C4—172no—
157C22×C4—171no—
158C22×C4—171no—
159C22×C4—172no—
160C22×C4—172no—
161C22×C4—342no—
162C22×C4—342no—
163C22×C4—342no—
164C22×C4—342no—
165C22×C4C2×#59511yescharacteristic
166C22×C4C2×#59511yescharacteristic
167M16—348no—
168C2×C8—174no—
169C2×C8—172no—
170C2×C8—172no—
171C2×C8—172no—
172C2×C8—172no—
173C2×C8—348no—
174C2×C8—342no—
175C2×C8—342no—
176C2×C8—342no—
177C4⋊C4—174no—
178C22⋊C4—174no—
179C22⋊C4C2×#59514yes—
180C42—172no—
181C42—172no—
182C23—22no—
183C23—22no—
184C23—172no—
185C23—342no—
186C23—342no—
187C23—342no—
188C23#6324314yescomplemented
189C23C22×#59512yes—
190C23C22×#59511yescharacteristic
191D4—348no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—172no—
195C2×C4—172no—
196C2×C4—171no—
197C2×C4—171no—
198C2×C4—172no—
199C2×C4—172no—
200C2×C4—342no—
201C2×C4—342no—
202C2×C4—344no—
203C2×C4—342no—
204C2×C4—342no—
205C2×C4—344no—
206C2×C4—342no—
207C2×C4—342no—
208C2×C4C22×#59512yes—
209C2×C4C22×#59512yes—
210C8—174no—
211C8—342no—
212C8—342no—
213C8—342no—
214C22—28no—
215C22—22no—
216C22—22no—
217C22—342no—
218C22—342no—
219C22—342no—
220C22—684no—
221C22C2×#6324312yes—
222C22C2×#6324314yescomplemented
223C22#1058767812yes—
224C22D4×#59512yes—
225C22C23×#59511yescharacteristic
226C4—22no—
227C4—22no—
228C4—171no—
229C4—171no—
230C4—172no—
231C4—342no—
232C4—342no—
233C2—24no—
234C2—682no—
235C2#1176383814yesdirect product factor
236C2C2×D4×#59511yescharacteristic
237C2C22×#6324311yescharacteristic
238C2C2×#1058767811yescharacteristic
subgroupG/H
centerC23C22×#595
commutatorC22×C17C23×C4
FrattiniC22C23×#595
FittingC2×C22⋊C4×C17C4
socleC23×C17C22×C4
prime radicalC22×C22⋊D17C4
cosocleC2×Dic17C24
hypercenterC2×C22⋊C4#595
hypocenterC17C2×#435
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#63243C2semidirect
2. C23×#3624C2semidirect
3. #11763838C2direct (N × H)
4. C2×C4⋊#3624C2semidirect
5. C2×#10587543C2semidirect
6. C2×C22⋊#3624C2semidirect
7. C2×#10587542C2semidirect
17. C22×#3624C22semidirect
19. C2×#63243C22semidirect
26. C22⋊#3624C22semidirect
27. #10587543C22semidirect
28. #10587542C22semidirect
29. C4⋊#3624C22semidirect
51. C2×#3624D4semidirect
64. C23×C17M16semidirect
93. #3624C2×D4semidirect
100. C22×C17C2×M16semidirect
123. C2×C17#435semidirect
149. C17C2×#435semidirect
188. C23#63243semidirect
222. C22C2×#63243semidirect
235. C2#11763838direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#632432
C23×#36242
#117638382
C2×C4⋊#36242
C2×#105875432
C2×C22⋊#36242
C2×#105875422
C2×#105875672
C2×#43517