Finite Group Databasebeta

← C2×C11×#1656 #14596173

Subgroups — C2×C11×#1656 #14596173

Order 2816.

1138 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 238 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×C11×#562C211yesmaximal, characteristic, complemented
2C2×C11×#496C212yesmaximal, complemented
3C2×C11×#490C211yesmaximal, characteristic, complemented
4C11×#1656C218yesmaximal, direct product factor
5C2×C11×#330C211yesmaximal, characteristic, complemented
6C2×C11×#329C212yesmaximal, complemented
7C22×C11×SD16—22no—
8C22×C11×D8—22no—
9C11×#562—22no—
10C11×#562—24no—
11C11×#562C2214yescomplemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#123—22no—
16C2×C11×C22⋊Q8—22no—
17C2×C11×#121—22no—
18C11×#496—24no—
19C11×#496C2218yescomplemented
20C11×#490—22no—
21C11×#490C2214yescomplemented
22C2×C11×#102—22no—
23C2×C11×#97C2212yes—
24C2×C11×#97C2211yescharacteristic
25C11×#330C2214yescomplemented
26C11×#329C2218yescomplemented
27C22×Q8×C11D412yes—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11D412yes—
32C23×C4×C11—22no—
33C2×C11×SD16—28no—
34C2×C11×SD16—48no—
35C2×C11×D8—28no—
36C2×C11×D8—48no—
37C22×C8×C11—22no—
38C22×C8×C11—21no—
39C11×#127—21no—
40C11×#127—22no—
41C11×#127C2312yes—
42C11×#125—22no—
43C11×#125D412yes—
44C11×#125C2312yes—
45C11×#124—22no—
46C11×#124—22no—
47C11×#124D414yes—
48C11×#124C2314yes—
49C11×#123—28no—
50C11×#123—28no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—28no—
53C11×#121—28no—
54C11×#121—28no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C42×C11C2311yescharacteristic
62C11×#102—28no—
63C11×#97—21no—
64C11×#97—22no—
65C11×#97C2312yes—
66C11×#97C2314yes—
67C2×#1656C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—22no—
69C24×C11—41no—
70C2×Q8×C11—22no—
71C2×Q8×C11—44no—
72C2×Q8×C11C2×D414yes—
73C2×D4×C11—28no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—24no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—42no—
83C2×D4×C11—84no—
84C2×D4×C11C2×D414yes—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—28no—
88C22×C4×C11—84no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C11×SD16—416no—
92C11×D8—416no—
93C2×C8×C11—28no—
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4C2×D414yes—
102C11×C22⋊C4—28no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—24no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D412yes—
109C42×C11C2411yescharacteristic
110C2×#562C2×C1111yescharacteristic, complemented
111C2×#496C2×C1112yescomplemented
112C2×#490C2×C1111yescharacteristic, complemented
113#1656C2×C1118yesdirect product factor
114C2×#330C2×C1111yescharacteristic, complemented
115C2×#329C2×C1112yescomplemented
116C23×C11—24no—
117C23×C11—44no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11—42no—
121C23×C11—84no—
122C23×C11—82no—
123C23×C11#12011yescharacteristic
124Q8×C11—44no—
125Q8×C11—82no—
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—82no—
131D4×C11—84no—
132D4×C11—82no—
133D4×C11—88no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—88no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12012yes—
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C22×D412yes—
145C8×C11—28no—
146C8×C11—42no—
147C22×SD16—22no—
148C22×D8—22no—
149#562—22no—
150#562—24no—
151#562C22×C1114yescomplemented
152C2×#127C22×C1111yescharacteristic
153C2×#125C22×C1111yescharacteristic
154C2×#124C22×C1112yes—
155C2×#123—22no—
156C2×C22⋊Q8—22no—
157C2×#121—22no—
158#496—24no—
159#496C22×C1118yescomplemented
160#490—22no—
161#490C22×C1114yescomplemented
162C2×#102—22no—
163C2×#97C22×C1111yescharacteristic
164C2×#97C22×C1112yes—
165#330C22×C1114yescomplemented
166#329C22×C1118yescomplemented
167C22×C11—44no—
168C22×C11—44no—
169C22×C11—44no—
170C22×C11—88no—
171C22×C11—84no—
172C22×C11—82no—
173C22×C11—164no—
174C22×C11#45314yes—
175C22×C11#45412yes—
176C22×C11C2×#12011yescharacteristic
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—44no—
182C4×C11—44no—
183C22×Q8D4×C1112yes—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—21no—
187C22×D4D4×C1112yes—
188C23×C4—22no—
189C2×SD16—28no—
190C2×SD16—48no—
191C2×D8—28no—
192C2×D8—48no—
193C22×C8—22no—
194C22×C8—21no—
195#127—21no—
196#127—22no—
197#127C23×C1112yes—
198#125—22no—
199#125D4×C1112yes—
200#125C23×C1112yes—
201#124—22no—
202#124—22no—
203#124D4×C1114yes—
204#124C23×C1114yes—
205#123—28no—
206#123—28no—
207C22⋊Q8—28no—
208C22⋊Q8—28no—
209#121—28no—
210#121—28no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4D4×C1112yes—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C42C23×C1111yescharacteristic
218#102—28no—
219#97—21no—
220#97—22no—
221#97C23×C1112yes—
222#97C23×C1114yes—
223C2×C11—84no—
224C2×C11—162no—
225C2×C11#165614yesdirect product factor
226C2×C11C2×#45312yes—
227C2×C11C2×#45411yescharacteristic
228C24—22no—
229C24—41no—
230C2×Q8—22no—
231C2×Q8—44no—
232C2×Q8C2×D4×C1114yes—
233C2×D4—28no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—24no—
237C2×D4—44no—
238C2×D4—44no—
239C2×D4—44no—
240C2×D4—44no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—84no—
244C2×D4C2×D4×C1114yes—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—28no—
248C22×C4—84no—
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C2×D4×C1112yes—
251SD16—416no—
252D8—416no—
253C2×C8—28no—
254C2×C8—24no—
255C2×C8—22no—
256C2×C8—42no—
257C4⋊C4—28no—
258C4⋊C4—24no—
259C4⋊C4—22no—
260C4⋊C4—24no—
261C4⋊C4C2×D4×C1114yes—
262C22⋊C4—28no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C42C2×D4×C1111yescharacteristic
268C42C2×D4×C1112yes—
269C42C24×C1111yescharacteristic
270C11C2×#165611yescharacteristic, direct product factor, Sylow
271C23—24no—
272C23—44no—
273C23—44no—
274C23—44no—
275C23—42no—
276C23—84no—
277C23—82no—
278C23C11×#12011yescharacteristic
279Q8—44no—
280Q8—82no—
281D4—44no—
282D4—44no—
283D4—44no—
284D4—44no—
285D4—82no—
286D4—84no—
287D4—82no—
288D4—88no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—88no—
296C2×C4C11×#12011yescharacteristic
297C2×C4C11×#12012yes—
298C2×C4C22×D4×C1111yescharacteristic
299C2×C4C22×D4×C1112yes—
300C8—28no—
301C8—42no—
302C22—44no—
303C22—44no—
304C22—44no—
305C22—88no—
306C22—84no—
307C22—82no—
308C22—164no—
309C22C11×#45314yes—
310C22C11×#45412yes—
311C22C2×C11×#12011yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—44no—
318C2—84no—
319C2—162no—
320C2C11×#165614yesdirect product factor
321C2C2×C11×#45312yes—
322C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#562C2semidirect
2. C2×C11×#496C2semidirect
3. C2×C11×#490C2semidirect
4. C11×#1656C2direct (N × H)
5. C2×C11×#330C2semidirect
6. C2×C11×#329C2semidirect
11. C11×#562C22semidirect
19. C11×#496C22semidirect
21. C11×#490C22semidirect
25. C11×#330C22semidirect
26. C11×#329C22semidirect
67. C2×#1656C11direct (N × H)
110. C2×#562C2×C11semidirect
111. C2×#496C2×C11semidirect
112. C2×#490C2×C11semidirect
113. #1656C2×C11direct (N × H)
114. C2×#330C2×C11semidirect
115. C2×#329C2×C11semidirect
151. #562C22×C11semidirect
159. #496C22×C11semidirect
161. #490C22×C11semidirect
165. #330C22×C11semidirect
166. #329C22×C11semidirect
225. C2×C11#1656direct (N × H)
270. C11C2×#1656direct (N × H)
320. C2C11×#1656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5622
C2×C11×#4962
C2×C11×#4902
C11×#16562
C2×C11×#3302
C2×C11×#3292
C2×#165611