Finite Group Databasebeta

← C2×#13066566 #14662957

Subgroups — C2×#13066566 #14662957

Order 2816.

410 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622731C211yesmaximal, characteristic
2C2×#10622191C211yesmaximal, characteristic
3#13066566C214yesmaximal, direct product factor
4C2×C11×#349C211yesmaximal, characteristic
5C22×C11×M16C2211yescharacteristic
6C22×C4×Dic11C411yescharacteristic
7C22×#4318C411yescharacteristic
8C2×C11×M32—21no—
9#10622731—21no—
10#10622731—21no—
11#10622731C412yes—
12#10622731C2212yes—
13C2×Dic11⋊C8—21no—
14C2×Dic11⋊C8—21no—
15C2×#66876—21no—
16C11×#349—21no—
17C11×#349C2212yes—
18#10622191—21no—
19#10622191C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×Dic11—21no—
22C2×C11×M16—41no—
23C2×C11×M16—41no—
24C2×C11×M16C2×C411yescharacteristic
25C2×C11×M16D411yescharacteristic
26C2×C11×M16D411yescharacteristic
27C2×C11×M16C2311yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C2×C4×Dic11—21no—
31C2×C4×Dic11—21no—
32C2×C4×Dic11—21no—
33C2×C4×Dic11C811yescharacteristic
34C2×C4×Dic11C811yescharacteristic
35C2×C4×Dic11C812yes—
36C2×C4×Dic11C2×C412yes—
37C2×#4318—21no—
38C2×#4318—41no—
39C2×#4318—41no—
40C2×#4318C2×C412yes—
41C22×C11⋊C8—21no—
42C11×M32—22no—
43C11×M32—41no—
44C2×C11×C16—41no—
45Dic11⋊C8—22no—
46Dic11⋊C8—22no—
47Dic11⋊C8—22no—
48Dic11⋊C8—22no—
49#66876—22no—
50#66876—41no—
51C2×C11⋊C16—41no—
52C2×#1327—111nomaximal, Sylow
53C24×C11M1611yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C2×C811yescharacteristic
61C22×C4×C11C2×C811yescharacteristic
62C22×C4×C11M1611yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—44no—
69C11×M16—41no—
70C11×M16—41no—
71C11×M16—41no—
72C11×M16—41no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11C22⋊C411yescharacteristic
78C2×C8×C11C22⋊C411yescharacteristic
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C4×Dic11—21no—
82C4×Dic11—21no—
83C4×Dic11—22no—
84C4×Dic11—22no—
85C4×Dic11C2×C812yes—
86C4×Dic11C2×C812yes—
87#4318—42no—
88#4318—42no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92C11×C16—42no—
93C11⋊C16—42no—
94C2×#423—111no—
95C2×#349—111no—
96C2×#349D1111yescharacteristic
97#1327—114no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—42no—
101C23×C11C22⋊C811yescharacteristic
102C23×C11C22⋊C811yescharacteristic
103C23×C11C2×M1611yescharacteristic
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C22⋊C811yescharacteristic
115C2×C4×C11C22⋊C811yescharacteristic
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11#9911yescharacteristic
118C2×C4×C11#10111yescharacteristic
119C2×C4×C11#10111yescharacteristic
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C22×C811yescharacteristic
122C2×Dic11—24no—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—44no—
126C2×Dic11—44no—
127C2×Dic11—42no—
128C8×C11—21no—
129C8×C11—21no—
130C8×C11—21no—
131C8×C11—21no—
132C11⋊C8—42no—
133C22×M16—111no—
134C22×M16C2×D1111yescharacteristic
135C22×C42—111no—
136C2×M32—21no—
137C2×M32—221no—
138#423—112no—
139#423—112no—
140#423—221no—
141#423—221no—
142C2×C4⋊C8—221no—
143C2×C4⋊C8—221no—
144#349—21no—
145#349—112no—
146#349—221no—
147#349C2×D1112yes—
148C22×C11—22no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—42no—
154C22×C11—42no—
155C22×C11#32411yescharacteristic
156C22×C11#32411yescharacteristic
157C22×C11C2×C22⋊C811yescharacteristic
158C4×C11—21no—
159C4×C11—21no—
160C4×C11#32411yescharacteristic
161C4×C11#32411yescharacteristic
162C4×C11C2×#9911yescharacteristic
163C4×C11C2×#10111yescharacteristic
164Dic11—24no—
165Dic11—42no—
166C23×C4—221no—
167C23×C4C4×D1111yescharacteristic
168C2×M16—41no—
169C2×M16—41no—
170C2×M16—112no—
171C2×M16—221no—
172C2×M16—441no—
173C2×M16—441no—
174C2×M16C4×D1111yescharacteristic
175C2×M16D4411yescharacteristic
176C2×M16C22⋊D1111yescharacteristic
177C2×M16C22×D1111yescharacteristic
178C22×C8—221no—
179C22×C8D4411yescharacteristic
180C22×C8C22⋊D1111yescharacteristic
181C2×C42—111no—
182C2×C42—112no—
183C2×C42—111no—
184C2×C42—112no—
185C2×C42—221no—
186C2×C42—221no—
187C2×C42—221no—
188M32—22no—
189M32—41no—
190M32—222no—
191M32—441no—
192C2×C16—41no—
193C2×C16—441no—
194C4⋊C8—222no—
195C4⋊C8—222no—
196C4⋊C8—222no—
197C4⋊C8—222no—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11—41no—
201C2×C11—41no—
202C2×C11#132712yescomplemented
203C2×C11C2×#32411yescharacteristic
204C24#431311yescharacteristic
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—221no—
210C22×C4—222no—
211C22×C4—221no—
212C22×C4—222no—
213C22×C4—444no—
214C22×C4C8×D1111yescharacteristic
215C22×C4C8×D1111yescharacteristic
216C22×C4#431311yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4(C2×D11)⋊C411yescharacteristic
219C22×C4C2×C4×D1111yescharacteristic
220M16—41no—
221M16—41no—
222M16—41no—
223M16—41no—
224M16—442no—
225M16—442no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—222no—
231C2×C8—441no—
232C2×C8—441no—
233C2×C8(C2×D11)⋊C411yescharacteristic
234C2×C8(C2×D11)⋊C411yescharacteristic
235C2×C8C2×D4411yescharacteristic
236C2×C8C2×C22⋊D1111yescharacteristic
237C42—112no—
238C42—112no—
239C42—221no—
240C42—222no—
241C42—221no—
242C42—222no—
243C16—42no—
244C16—442no—
245C11C2×#132711yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—42no—
249C23(C2×D11)⋊C811yescharacteristic
250C23(C2×D11)⋊C811yescharacteristic
251C23C2×#431311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—224no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—444no—
266C2×C4—444no—
267C2×C4—442no—
268C2×C4#6687011yescharacteristic
269C2×C4#6687011yescharacteristic
270C2×C4(C2×D11)⋊C811yescharacteristic
271C2×C4(C2×D11)⋊C811yescharacteristic
272C2×C4#6688811yescharacteristic
273C2×C4#6688811yescharacteristic
274C2×C4C2×C8×D1111yescharacteristic
275C2×C4C2×(C2×D11)⋊C411yescharacteristic
276C8—21no—
277C8—21no—
278C8—21no—
279C8—21no—
280C8—442no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22#1062210711yescharacteristic
289C22#1062210711yescharacteristic
290C22C2×(C2×D11)⋊C811yescharacteristic
291C4—21no—
292C4—21no—
293C4—224no—
294C4—442no—
295C4#1062210711yescharacteristic
296C4#1062210711yescharacteristic
297C4C2×#6687011yescharacteristic
298C4C2×#6688811yescharacteristic
299C2—21no—
300C2—21no—
301C2—41no—
302C2—41no—
303C2#1306656612yesdirect product factor
304C2C2×#1062210711yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC2×C11×#349C2
socleC22×C11#324
prime radicalC24×C11M16
cosocleC2×C11×M16C23
hypercenterC2×#349D11
hypocenterC11C2×#1327
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
3. #13066566C2direct (N × H)
202. C2×C11#1327semidirect
245. C11C2×#1327semidirect
303. C2#13066566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227312
C2×#106221912
#130665662
C2×C11×#3492
C2×#132711