Finite Group Databasebeta

← C2×#13066567 #14662958

Subgroups — C2×#13066567 #14662958

Order 2816.

410 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622191C212yesmaximal
2#13066567C214yesmaximal, direct product factor
3C2×C11×#423C211yesmaximal, characteristic
4C22×C11×M16C411yescharacteristic
5C22×C11×M16C2211yescharacteristic
6C22×C42×C11C411yescharacteristic
7C11×#423—22no—
8C11×#423C412yes—
9C11×#423C2212yes—
10C2×C11×C4⋊C8—22no—
11C2×#66876—22no—
12#10622191—22no—
13#10622191C2214yes—
14C23×C4×C11—21no—
15C23×C4×C11C2×C411yescharacteristic
16C2×C11×M16—21no—
17C2×C11×M16—41no—
18C2×C11×M16—41no—
19C2×C11×M16—41no—
20C2×C11×M16—41no—
21C2×C11×M16C2×C412yes—
22C2×C11×M16C2×C411yescharacteristic
23C2×C11×M16D412yes—
24C2×C11×M16C2311yescharacteristic
25C22×C8×C11—21no—
26C22×C8×C11D412yes—
27C2×C42×C11—21no—
28C2×C42×C11—21no—
29C2×C42×C11—21no—
30C2×C42×C11C811yescharacteristic
31C2×C42×C11C812yes—
32C2×C42×C11C811yescharacteristic
33C2×C42×C11C2×C412yes—
34C11×C4⋊C8—24no—
35C11×C4⋊C8—24no—
36#66876—24no—
37#66876—42no—
38C2×C11⋊C16—42no—
39C2×#1327—111nomaximal, Sylow
40C24×C11M1611yescharacteristic
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11—22no—
49C22×C4×C11—44no—
50C22×C4×C11C22⋊C411yescharacteristic
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C2×C811yescharacteristic
53C22×C4×C11C2×C811yescharacteristic
54C22×C4×C11M1611yescharacteristic
55C22×C4×C11C22×C411yescharacteristic
56C11×M16—41no—
57C11×M16—42no—
58C11×M16—41no—
59C11×M16—42no—
60C11×M16—42no—
61C2×C8×C11—22no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C2×C8×C11C22⋊C412yes—
67C2×C8×C11C2×D412yes—
68C42×C11—21no—
69C42×C11—22no—
70C42×C11—21no—
71C42×C11—22no—
72C42×C11C2×C812yes—
73C42×C11C2×C812yes—
74C11⋊C16—44no—
75C2×#423D1111yescharacteristic
76C2×#349—112no—
77#1327—114no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—42no—
81C23×C11C22⋊C811yescharacteristic
82C23×C11C22⋊C811yescharacteristic
83C23×C11C2×M1611yescharacteristic
84C2×C4×C11—24no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—44no—
98C2×C4×C11—44no—
99C2×C4×C11—42no—
100C2×C4×C11C22⋊C811yescharacteristic
101C2×C4×C11C22⋊C811yescharacteristic
102C2×C4×C11#9911yescharacteristic
103C2×C4×C11#9911yescharacteristic
104C2×C4×C11#10111yescharacteristic
105C2×C4×C11#10111yescharacteristic
106C2×C4×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11C22×C811yescharacteristic
108C8×C11—22no—
109C8×C11—22no—
110C8×C11—42no—
111C22×M16Dic1111yescharacteristic
112C22×M16C2×D1111yescharacteristic
113C22×C42Dic1111yescharacteristic
114C2×M32—222no—
115#423—22no—
116#423Dic1112yes—
117#423C2×D1112yes—
118C2×C4⋊C8—22no—
119#349—114no—
120#349—222no—
121C22×C11—22no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11#32411yescharacteristic
129C22×C11#32411yescharacteristic
130C22×C11C2×C22⋊C811yescharacteristic
131C4×C11—24no—
132C4×C11—21no—
133C4×C11—21no—
134C4×C11—42no—
135C4×C11#32411yescharacteristic
136C4×C11#32411yescharacteristic
137C4×C11C2×#9911yescharacteristic
138C4×C11C2×#10111yescharacteristic
139C23×C4—21no—
140C23×C4C2×Dic1111yescharacteristic
141C2×M16—21no—
142C2×M16—41no—
143C2×M16—41no—
144C2×M16—41no—
145C2×M16—41no—
146C2×M16C2×Dic1112yes—
147C2×M16C2×Dic1111yescharacteristic
148C2×M16C22⋊D1112yes—
149C2×M16C22×D1111yescharacteristic
150C22×C8—21no—
151C22×C8C22⋊D1112yes—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42C11⋊C811yescharacteristic
156C2×C42C11⋊C812yes—
157C2×C42C11⋊C811yescharacteristic
158C2×C42C2×Dic1112yes—
159M32—224no—
160M32—442no—
161C2×C16—442no—
162C4⋊C8—24no—
163C4⋊C8—24no—
164C2×C11—21no—
165C2×C11—21no—
166C2×C11—41no—
167C2×C11—41no—
168C2×C11#132712yescomplemented
169C2×C11C2×#32411yescharacteristic
170C24#431811yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—44no—
180C22×C4C2×C11⋊C811yescharacteristic
181C22×C4C2×C11⋊C811yescharacteristic
182C22×C4#431811yescharacteristic
183C22×C4C22⋊Dic1111yescharacteristic
184C22×C4C22⋊Dic1111yescharacteristic
185C22×C4C22×Dic1111yescharacteristic
186M16—41no—
187M16—41no—
188M16—42no—
189M16—42no—
190M16—42no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8C22⋊Dic1112yes—
197C2×C8C2×C22⋊D1112yes—
198C42—21no—
199C42—22no—
200C42—21no—
201C42—22no—
202C42C2×C11⋊C812yes—
203C42C2×C11⋊C812yes—
204C16—444no—
205C11C2×#132711yescharacteristic, complemented, Sylow
206C23—21no—
207C23—21no—
208C23—42no—
209C23C22⋊(C11⋊C8)11yescharacteristic
210C23C22⋊(C11⋊C8)11yescharacteristic
211C23C2×#431811yescharacteristic
212C2×C4—24no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4C22⋊(C11⋊C8)11yescharacteristic
229C2×C4C22⋊(C11⋊C8)11yescharacteristic
230C2×C4#6689811yescharacteristic
231C2×C4#6689811yescharacteristic
232C2×C4#6690011yescharacteristic
233C2×C4#6690011yescharacteristic
234C2×C4C22×C11⋊C811yescharacteristic
235C2×C4C2×C22⋊Dic1111yescharacteristic
236C8—22no—
237C8—22no—
238C8—42no—
239C22—22no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—42no—
246C22#1062216611yescharacteristic
247C22#1062216611yescharacteristic
248C22C2×C22⋊(C11⋊C8)11yescharacteristic
249C4—24no—
250C4—21no—
251C4—21no—
252C4—42no—
253C4#1062216611yescharacteristic
254C4#1062216611yescharacteristic
255C4C2×#6689811yescharacteristic
256C4C2×#6690011yescharacteristic
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2#1306656712yesdirect product factor
262C2C2×#1062216611yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC2×C11×#423C2
socleC22×C11#324
prime radicalC24×C11M16
cosocleC2×C11×M16C23
hypercenterC2×#423D11
hypocenterC11C2×#1327
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
2. #13066567C2direct (N × H)
168. C2×C11#1327semidirect
205. C11C2×#1327semidirect
261. C2#13066567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221912
#130665672
C2×C11×#4232
C2×#132711