Finite Group Databasebeta

← C2×C11×#1657 #14596175

Subgroups — C2×C11×#1657 #14596175

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic, complemented
2C2×C11×#496C211yesmaximal, characteristic
3C2×C11×#490C212yesmaximal, complemented
4C11×#1657C218yesmaximal, direct product factor
5C2×C11×#330C212yesmaximal, complemented
6C2×C11×#329C211yesmaximal, characteristic, complemented
7C22×C11×SD16—21no—
8C22×C11×D8—21no—
9C11×#563—24no—
10C11×#563—22no—
11C11×#563C2214yescomplemented
12C2×C11×C4⋊Q8—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#126—22no—
15C2×C11×#125C2212yes—
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—22no—
19C11×#496—22no—
20C11×#496C2214yes—
21C11×#490—24no—
22C11×#490C2218yescomplemented
23C2×C11×#102—22no—
24C2×C11×#102—22no—
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2212yes—
27C11×#330C2218yescomplemented
28C11×#329C2214yescomplemented
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—22no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×SD16—24no—
36C2×C11×SD16—44no—
37C2×C11×D8—24no—
38C2×C11×D8—44no—
39C22×C8×C11—21no—
40C22×C8×C11—22no—
41C11×C4⋊Q8—24no—
42C11×C4⋊Q8—24no—
43C11×#127—22no—
44C11×#127—21no—
45C11×#127C2312yes—
46C11×#126—28no—
47C11×#126—28no—
48C11×#125—22no—
49C11×#125—22no—
50C11×#125D414yes—
51C11×#125C2314yes—
52C11×#124—22no—
53C11×#124D412yes—
54C11×#124C2312yes—
55C11×#123—24no—
56C11×#123—24no—
57C11×C22⋊Q8—28no—
58C11×C22⋊Q8—28no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C11×#102—28no—
70C11×#102—28no—
71C11×#97—22no—
72C11×#97—21no—
73C11×#97C2314yes—
74C11×#97C2312yes—
75C2×#1657C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C24×C11—41no—
78C2×Q8×C11—24no—
79C2×Q8×C11—21no—
80C2×Q8×C11—42no—
81C2×Q8×C11—82no—
82C2×Q8×C11C2×D412yes—
83C2×D4×C11—21no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—48no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11C2×D412yes—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C11×SD16—48no—
101C11×D8—48no—
102C2×C8×C11—24no—
103C2×C8×C11—22no—
104C2×C8×C11—24no—
105C2×C8×C11—44no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4C2×D414yes—
114C11×C4⋊C4C2×D414yes—
115C11×C22⋊C4—28no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C42×C11—24no—
120C42×C11C2×D412yes—
121C42×C11C2×D411yescharacteristic
122C42×C11C2411yescharacteristic
123C2×#563C2×C1111yescharacteristic, complemented
124C2×#496C2×C1111yescharacteristic
125C2×#490C2×C1112yescomplemented
126#1657C2×C1118yesdirect product factor
127C2×#330C2×C1112yescomplemented
128C2×#329C2×C1111yescharacteristic, complemented
129C23×C11—22no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11—42no—
133C23×C11—82no—
134C23×C11—84no—
135C23×C11#12011yescharacteristic
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—84no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—48no—
143D4×C11—81no—
144D4×C11—82no—
145D4×C11—84no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—84no—
155C2×C4×C11#12012yes—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11C22×D412yes—
158C2×C4×C11C22×D411yescharacteristic
159C8×C11—24no—
160C8×C11—44no—
161C22×SD16—21no—
162C22×D8—21no—
163#563—24no—
164#563—22no—
165#563C22×C1114yescomplemented
166C2×C4⋊Q8—21no—
167C2×#127C22×C1111yescharacteristic
168C2×#126—22no—
169C2×#125C22×C1112yes—
170C2×#124C22×C1111yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8—22no—
173#496—22no—
174#496C22×C1114yes—
175#490—24no—
176#490C22×C1118yescomplemented
177C2×#102—22no—
178C2×#102—22no—
179C2×#97C22×C1112yes—
180C2×#97C22×C1111yescharacteristic
181#330C22×C1118yescomplemented
182#329C22×C1114yescomplemented
183C22×C11—42no—
184C22×C11—44no—
185C22×C11—84no—
186C22×C11—82no—
187C22×C11—84no—
188C22×C11—164no—
189C22×C11#45312yes—
190C22×C11#45414yes—
191C22×C11C2×#12011yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—44no—
197C4×C11—42no—
198C4×C11—44no—
199C22×Q8—21no—
200C22×Q8D4×C1111yescharacteristic
201C22×D4—21no—
202C22×D4—22no—
203C22×D4D4×C1111yescharacteristic
204C23×C4—21no—
205C2×SD16—24no—
206C2×SD16—44no—
207C2×D8—24no—
208C2×D8—44no—
209C22×C8—21no—
210C22×C8—22no—
211C4⋊Q8—24no—
212C4⋊Q8—24no—
213#127—22no—
214#127—21no—
215#127C23×C1112yes—
216#126—28no—
217#126—28no—
218#125—22no—
219#125—22no—
220#125D4×C1114yes—
221#125C23×C1114yes—
222#124—22no—
223#124D4×C1112yes—
224#124C23×C1112yes—
225#123—24no—
226#123—24no—
227C22⋊Q8—28no—
228C22⋊Q8—28no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4D4×C1112yes—
233C2×C4⋊C4D4×C1112yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C42—21no—
238C2×C42C23×C1111yescharacteristic
239#102—28no—
240#102—28no—
241#97—22no—
242#97—21no—
243#97C23×C1114yes—
244#97C23×C1112yes—
245C2×C11—82no—
246C2×C11—162no—
247C2×C11#165714yesdirect product factor
248C2×C11C2×#45311yescharacteristic
249C2×C11C2×#45412yes—
250C24—21no—
251C24—41no—
252C2×Q8—24no—
253C2×Q8—21no—
254C2×Q8—42no—
255C2×Q8—82no—
256C2×Q8C2×D4×C1112yes—
257C2×D4—21no—
258C2×D4—24no—
259C2×D4—22no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—48no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4C2×D4×C1112yes—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—82no—
272C22×C4C2×D4×C1112yes—
273C22×C4C2×D4×C1111yescharacteristic
274SD16—48no—
275D8—48no—
276C2×C8—24no—
277C2×C8—22no—
278C2×C8—24no—
279C2×C8—44no—
280C4⋊C4—28no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4C2×D4×C1114yes—
288C4⋊C4C2×D4×C1114yes—
289C22⋊C4—28no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—24no—
293C42—24no—
294C42C2×D4×C1112yes—
295C42C2×D4×C1111yescharacteristic
296C42C24×C1111yescharacteristic
297C11C2×#165711yescharacteristic, direct product factor, Sylow
298C23—22no—
299C23—42no—
300C23—44no—
301C23—42no—
302C23—82no—
303C23—84no—
304C23C11×#12011yescharacteristic
305Q8—42no—
306Q8—81no—
307Q8—84no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—48no—
312D4—81no—
313D4—82no—
314D4—84no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—84no—
324C2×C4C11×#12012yes—
325C2×C4C11×#12011yescharacteristic
326C2×C4C22×D4×C1112yes—
327C2×C4C22×D4×C1111yescharacteristic
328C8—24no—
329C8—44no—
330C22—42no—
331C22—44no—
332C22—84no—
333C22—82no—
334C22—84no—
335C22—164no—
336C22C11×#45312yes—
337C22C11×#45414yes—
338C22C2×C11×#12011yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—44no—
344C4—42no—
345C4—44no—
346C2—82no—
347C2—162no—
348C2C11×#165714yesdirect product factor
349C2C2×C11×#45311yescharacteristic
350C2C2×C11×#45412yes—
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#496C2
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×#563C2semidirect
3. C2×C11×#490C2semidirect
4. C11×#1657C2direct (N × H)
5. C2×C11×#330C2semidirect
6. C2×C11×#329C2semidirect
11. C11×#563C22semidirect
22. C11×#490C22semidirect
27. C11×#330C22semidirect
28. C11×#329C22semidirect
75. C2×#1657C11direct (N × H)
123. C2×#563C2×C11semidirect
125. C2×#490C2×C11semidirect
126. #1657C2×C11direct (N × H)
127. C2×#330C2×C11semidirect
128. C2×#329C2×C11semidirect
165. #563C22×C11semidirect
176. #490C22×C11semidirect
181. #330C22×C11semidirect
182. #329C22×C11semidirect
247. C2×C11#1657direct (N × H)
297. C11C2×#1657direct (N × H)
348. C2C11×#1657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5632
C2×C11×#4962
C2×C11×#4902
C11×#16572
C2×C11×#3302
C2×C11×#3292
C2×#165711