Finite Group Databasebeta

← C2×#13066562 #14662927

Subgroups — C2×#13066562 #14662927

Order 2816.

598 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#10622166C212yesmaximal
2#13066562C214yesmaximal, direct product factor
3C2×C11×#384C211yesmaximal, characteristic
4C22×C11×C4⋊C4—22no—
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C22×C42×C11C411yescharacteristic
8C11×#384—22no—
9C11×#384C412yes—
10C11×#384C2212yes—
11C2×C22⋊(C11⋊C8)—22no—
12#10622166—22no—
13#10622166C2214yes—
14C23×C4×C11—21no—
15C23×C4×C11—21no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D412yes—
18C2×C11×C4⋊C4—24no—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—24no—
21C2×C11×C4⋊C4—41no—
22C2×C11×C4⋊C4—41no—
23C2×C11×C4⋊C4—41no—
24C2×C11×C4⋊C4—41no—
25C2×C11×C4⋊C4—48no—
26C2×C11×C4⋊C4C2×C412yes—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11—22no—
32C2×C42×C11C814yescomplemented
33C2×C42×C11C2×C412yes—
34C22×C11⋊C8—42no—
35C22⋊(C11⋊C8)—24no—
36C22⋊(C11⋊C8)—42no—
37C2×#1325—111nomaximal, Sylow
38C24×C11C22⋊C411yescharacteristic
39C22×C4×C11—24no—
40C22×C4×C11—24no—
41C22×C4×C11—24no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—44no—
50C22×C4×C11—44no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C2×C812yes—
56C22×C4×C11M1612yes—
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D412yes—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—48no—
63C11×C4⋊C4—48no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C42×C11—24no—
67C42×C11—22no—
68C42×C11C2×C814yescomplemented
69C2×C11⋊C8—44no—
70C2×C11⋊C8—84no—
71C2×#384D1111yescharacteristic
72C2×#324—112no—
73#1325—114no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11C22⋊C812yes—
77C23×C11#9911yescharacteristic
78C23×C11#9911yescharacteristic
79C23×C11#10112yes—
80C23×C11C2×C22⋊C411yescharacteristic
81C2×C4×C11—24no—
82C2×C4×C11—216no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—24no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—44no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—44no—
99C2×C4×C11—42no—
100C2×C4×C11—82no—
101C2×C4×C11—82no—
102C2×C4×C11—82no—
103C2×C4×C11C22⋊C812yes—
104C2×C4×C11C22×C811yescharacteristic
105C2×C4×C11C2×M1611yescharacteristic
106C11⋊C8—84no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4Dic1111yescharacteristic
109C22×C4⋊C4C2×D1111yescharacteristic
110C22×C42Dic1111yescharacteristic
111C2×C22⋊C8—222no—
112#384—22no—
113#384Dic1112yes—
114#384C2×D1112yes—
115#324—114no—
116#324—222no—
117C22×C11—24no—
118C22×C11—24no—
119C22×C11—21no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#32412yes—
124C22×C11#32412yes—
125C22×C11#35312yes—
126C22×C11#35612yes—
127C22×C11C2×C22⋊C811yescharacteristic
128C22×C11C2×#9911yescharacteristic
129C22×C11C2×#10111yescharacteristic
130C4×C11—28no—
131C4×C11—22no—
132C4×C11—21no—
133C4×C11—21no—
134C4×C11—42no—
135C4×C11—42no—
136C4×C11—82no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4C2×Dic1111yescharacteristic
140C23×C4C22⋊D1112yes—
141C22×C8—442no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—48no—
150C2×C4⋊C4C2×Dic1112yes—
151C2×C4⋊C4C2×Dic1111yescharacteristic
152C2×C4⋊C4C22⋊D1112yes—
153C2×C4⋊C4C22×D1111yescharacteristic
154C2×C42—22no—
155C2×C42—21no—
156C2×C42C11⋊C814yescomplemented
157C2×C42C2×Dic1112yes—
158C22⋊C8—224no—
159C22⋊C8—442no—
160C2×C11—21no—
161C2×C11—22no—
162C2×C11—21no—
163C2×C11#132514yescomplemented
164C2×C11C2×#32411yescharacteristic
165C2×C11C2×#35311yescharacteristic
166C2×C11C2×#35611yescharacteristic
167C24C22⋊Dic1111yescharacteristic
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—44no—
179C22×C4—44no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4C2×C11⋊C812yes—
183C22×C4#431812yes—
184C22×C4C22⋊Dic1111yescharacteristic
185C22×C4C22⋊Dic1112yes—
186C22×C4C22×Dic1111yescharacteristic
187C22×C4C2×C22⋊D1112yes—
188C2×C8—444no—
189C2×C8—884no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—48no—
195C4⋊C4—48no—
196C4⋊C4—42no—
197C42—24no—
198C42—22no—
199C42C2×C11⋊C814yescomplemented
200C11C2×#132511yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23C22⋊(C11⋊C8)12yes—
204C23#6689811yescharacteristic
205C23#6689811yescharacteristic
206C23#6690012yes—
207C23C2×C22⋊Dic1111yescharacteristic
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—24no—
211C2×C4—24no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4—82no—
230C2×C4C22⋊(C11⋊C8)12yes—
231C2×C4C22×C11⋊C811yescharacteristic
232C2×C4C2×#431811yescharacteristic
233C8—884no—
234C22—24no—
235C22—24no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—21no—
240C22#1062216612yes—
241C22#1062216612yes—
242C22#1062218312yes—
243C22#1062218612yes—
244C22C2×C22⋊(C11⋊C8)11yescharacteristic
245C22C2×#6689811yescharacteristic
246C22C2×#6690011yescharacteristic
247C4—28no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C2—21no—
255C2—21no—
256C2—22no—
257C2#1306656214yesdirect product factor
258C2C2×#1062216611yescharacteristic
259C2C2×#1062218311yescharacteristic
260C2C2×#1062218611yescharacteristic
subgroupG/H
centerC23#66898
commutatorC2×C4×C11C22×C8
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#384C2
socleC23×C11#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#384D11
hypocenterC11C2×#1325
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. #13066562C2direct (N × H)
32. C2×C42×C11C8semidirect
68. C42×C11C2×C8semidirect
156. C2×C42C11⋊C8semidirect
163. C2×C11#1325semidirect
199. C42C2×C11⋊C8semidirect
200. C11C2×#1325semidirect
257. C2#13066562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221662
#130665622
C2×C11×#3842
C2×#132511