Finite Group Databasebeta

← C2×C11×#2175 #14610641

Subgroups — C2×C11×#2175 #14610641

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×SD32C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2175C218yesmaximal, direct product factor
5C2×C11×#366C211yesmaximal, characteristic, complemented
6C2×C11×#358C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic
8C2×C11×#346C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C22×C11×D8C2211yescharacteristic
11C2×C4×Q8×C11—21no—
12C2×C4×D4×C11—21no—
13C2×C11×SD32C418yescomplemented
14C2×C11×SD32C2214yes—
15C22×C11×C16C2211yescharacteristic
16C22×C11×C16C2211yescharacteristic
17C4×C11×Q16—22no—
18C4×C11×Q16C2214yescomplemented
19C4×C11×D8—22no—
20C4×C11×D8C2214yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103—21no—
24C2×C11×#102—21no—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#366C2214yescomplemented
27C11×#358C2214yescomplemented
28C11×#357C2214yes—
29C11×#346C2214yescomplemented
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C23×C4×C11—41no—
33C2×C11×Q16—21no—
34C2×C11×Q16—22no—
35C2×C11×Q16C2×C414yescomplemented
36C2×C11×Q16C2312yes—
37C2×C11×D8—21no—
38C2×C11×D8—22no—
39C2×C11×D8C2×C414yes—
40C2×C11×D8C2312yes—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C4×Q8×C11—24no—
44C4×Q8×C11—42no—
45C4×D4×C11—24no—
46C4×D4×C11—42no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C22⋊C4—41no—
51C2×C42×C11—41no—
52C2×C42×C11D411yescharacteristic
53C11×SD32C2×C4116yescomplemented
54C2×C11×C16—22no—
55C2×C11×C16C2×C414yescomplemented
56C2×C11×C16C2312yes—
57C2×C11×C16C2312yes—
58C11×#107—21no—
59C11×#107—21no—
60C11×#107C2312yes—
61C11×#107C2312yes—
62C11×#103—24no—
63C11×#102—24no—
64C4×C8×C11D412yes—
65C4×C8×C11C2312yes—
66C2×#2175C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—41no—
68C2×Q8×C11—24no—
69C2×Q8×C11—22no—
70C2×Q8×C11—41no—
71C2×Q8×C11—42no—
72C2×D4×C11—24no—
73C2×D4×C11—22no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—44no—
80C22×C4×C11—84no—
81C22×C4×C11D811yescharacteristic
82C22×C4×C11D811yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C11×Q16—24no—
85C11×Q16—22no—
86C11×Q16C22×C414yescomplemented
87C11×D8—24no—
88C11×D8—22no—
89C11×D8C22×C414yes—
90C2×C8×C11—22no—
91C2×C8×C11C22×C412yes—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11#4112yes—
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—44no—
101C11×C22⋊C4—44no—
102C42×C11—44no—
103C42×C11D812yes—
104C42×C11C2×D412yes—
105C11×C16—22no—
106C11×C16C22×C414yescomplemented
107C22×SD32C2×C1111yescharacteristic
108C2×C4×Q16C2×C1111yescharacteristic, complemented
109C2×C4×D8C2×C1111yescharacteristic
110#2175C2×C1118yesdirect product factor
111C2×#366C2×C1111yescharacteristic, complemented
112C2×#358C2×C1111yescharacteristic, complemented
113C2×#357C2×C1111yescharacteristic
114C2×#346C2×C1111yescharacteristic, complemented
115C23×C11—42no—
116C23×C11—44no—
117C23×C11—82no—
118C23×C11—82no—
119C23×C11C2×D811yescharacteristic
120Q8×C11—24no—
121Q8×C11—42no—
122Q8×C11—44no—
123D4×C11—24no—
124D4×C11—42no—
125D4×C11—44no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—88no—
133C2×C4×C11—82no—
134C2×C4×C11—82no—
135C2×C4×C11C4×D412yes—
136C2×C4×C11C2×D812yes—
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11#13512yes—
140C2×C4×C11C22×D411yescharacteristic
141C8×C11—22no—
142C8×C11C4×D412yes—
143C8×C11C23×C411yescharacteristic
144C8×C11C2×#4111yescharacteristic
145C22×Q16C22×C1111yescharacteristic
146C22×D8C22×C1111yescharacteristic
147C2×C4×Q8—21no—
148C2×C4×D4—21no—
149C2×SD32C4×C1118yescomplemented
150C2×SD32C22×C1114yes—
151C22×C16C22×C1111yescharacteristic
152C22×C16C22×C1111yescharacteristic
153C4×Q16—22no—
154C4×Q16C22×C1114yescomplemented
155C4×D8—22no—
156C4×D8C22×C1114yes—
157C2×#107C22×C1111yescharacteristic
158C2×#107C22×C1111yescharacteristic
159C2×#103—21no—
160C2×#102—21no—
161C2×C4×C8C22×C1111yescharacteristic
162#366C22×C1114yescomplemented
163#358C22×C1114yescomplemented
164#357C22×C1114yes—
165#346C22×C1114yescomplemented
166C22×C11—44no—
167C22×C11—82no—
168C22×C11—82no—
169C22×C11—88no—
170C22×C11C4×D812yes—
171C22×C11#50912yes—
172C22×C11#51012yes—
173C22×C11C22×D811yescharacteristic
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—44no—
177C4×C11—82no—
178C4×C11—82no—
179C4×C11C4×D812yes—
180C4×C11C2×C4×D411yescharacteristic
181C4×C11C2×#13511yescharacteristic
182C22×Q8—21no—
183C22×D4—21no—
184C23×C4—41no—
185C2×Q16—21no—
186C2×Q16—22no—
187C2×Q16C2×C4×C1114yescomplemented
188C2×Q16C23×C1112yes—
189C2×D8—21no—
190C2×D8—22no—
191C2×D8C2×C4×C1114yes—
192C2×D8C23×C1112yes—
193C22×C8D4×C1111yescharacteristic
194C22×C8C23×C1111yescharacteristic
195C4×Q8—24no—
196C4×Q8—42no—
197C4×D4—24no—
198C4×D4—42no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—41no—
202C2×C22⋊C4—41no—
203C2×C42—41no—
204C2×C42D4×C1111yescharacteristic
205SD32C2×C4×C11116yescomplemented
206C2×C16—22no—
207C2×C16C2×C4×C1114yescomplemented
208C2×C16C23×C1112yes—
209C2×C16C23×C1112yes—
210#107—21no—
211#107—21no—
212#107C23×C1112yes—
213#107C23×C1112yes—
214#103—24no—
215#102—24no—
216C4×C8D4×C1112yes—
217C4×C8C23×C1112yes—
218C2×C11—84no—
219C2×C11#217514yesdirect product factor
220C2×C11C2×C4×D811yescharacteristic
221C2×C11C2×#50911yescharacteristic
222C2×C11C2×#51011yescharacteristic
223C24—41no—
224C2×Q8—24no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C2×D4—24no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—44no—
236C22×C4—84no—
237C22×C4C11×D811yescharacteristic
238C22×C4C11×D811yescharacteristic
239C22×C4C2×D4×C1111yescharacteristic
240Q16—24no—
241Q16—22no—
242Q16C22×C4×C1114yescomplemented
243D8—24no—
244D8—22no—
245D8C22×C4×C1114yes—
246C2×C8—22no—
247C2×C8C22×C4×C1112yes—
248C2×C8C2×D4×C1112yes—
249C2×C8C2×D4×C1111yescharacteristic
250C2×C8C11×#4112yes—
251C2×C8C24×C1111yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—44no—
257C22⋊C4—44no—
258C42—44no—
259C42C11×D812yes—
260C42C2×D4×C1112yes—
261C16—22no—
262C16C22×C4×C1114yescomplemented
263C11C2×#217511yescharacteristic, direct product factor, Sylow
264C23—42no—
265C23—44no—
266C23—82no—
267C23—82no—
268C23C2×C11×D811yescharacteristic
269Q8—24no—
270Q8—42no—
271Q8—44no—
272D4—24no—
273D4—42no—
274D4—44no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—88no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4C4×D4×C1112yes—
285C2×C4C2×C11×D812yes—
286C2×C4C2×C11×D812yes—
287C2×C4C2×C11×D811yescharacteristic
288C2×C4C11×#13512yes—
289C2×C4C22×D4×C1111yescharacteristic
290C8—22no—
291C8C4×D4×C1112yes—
292C8C23×C4×C1111yescharacteristic
293C8C2×C11×#4111yescharacteristic
294C22—44no—
295C22—82no—
296C22—82no—
297C22—88no—
298C22C4×C11×D812yes—
299C22C11×#50912yes—
300C22C11×#51012yes—
301C22C22×C11×D811yescharacteristic
302C4—22no—
303C4—22no—
304C4—44no—
305C4—82no—
306C4—82no—
307C4C4×C11×D812yes—
308C4C2×C4×D4×C1111yescharacteristic
309C4C2×C11×#13511yescharacteristic
310C2—84no—
311C2C11×#217514yesdirect product factor
312C2C2×C4×C11×D811yescharacteristic
313C2C2×C11×#50911yescharacteristic
314C2C2×C11×#51011yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutatorC8C23×C4×C11
Frattini, cosocleC2×C8C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×Q16C2semidirect
4. C11×#2175C2direct (N × H)
5. C2×C11×#366C2semidirect
6. C2×C11×#358C2semidirect
8. C2×C11×#346C2semidirect
13. C2×C11×SD32C4semidirect
18. C4×C11×Q16C22semidirect
26. C11×#366C22semidirect
27. C11×#358C22semidirect
29. C11×#346C22semidirect
35. C2×C11×Q16C2×C4semidirect
53. C11×SD32C2×C4semidirect
55. C2×C11×C16C2×C4semidirect
66. C2×#2175C11direct (N × H)
86. C11×Q16C22×C4semidirect
106. C11×C16C22×C4semidirect
108. C2×C4×Q16C2×C11semidirect
110. #2175C2×C11direct (N × H)
111. C2×#366C2×C11semidirect
112. C2×#358C2×C11semidirect
114. C2×#346C2×C11semidirect
149. C2×SD32C4×C11semidirect
154. C4×Q16C22×C11semidirect
162. #366C22×C11semidirect
163. #358C22×C11semidirect
165. #346C22×C11semidirect
187. C2×Q16C2×C4×C11semidirect
205. SD32C2×C4×C11semidirect
207. C2×C16C2×C4×C11semidirect
219. C2×C11#2175direct (N × H)
242. Q16C22×C4×C11semidirect
262. C16C22×C4×C11semidirect
263. C11C2×#2175direct (N × H)
311. C2C11×#2175direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×SD322
C2×C4×C11×Q162
C2×C4×C11×D82
C11×#21752
C2×C11×#3662
C2×C11×#3582
C2×C11×#3572
C2×C11×#3462
C2×#217511