Finite Group Databasebeta

← C11×#21311 #14598504

Subgroups — C11×#21311 #14598504

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C4×C11×#117C211yesmaximal, characteristic
4C11×#1989C214yesmaximal, complemented
5C11×#1988C212yesmaximal, complemented
6C11×#1987C212yesmaximal, complemented
7C11×#1735C214yesmaximal
8C23×C8×C11C2212yes—
9C11×#533—24no—
10C11×#533C418yescomplemented
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#125C2212yes—
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C11×#117C2212yes—
19C2×C11×#117C2212yes—
20C22×C42×C11C2211yescharacteristic
21C2×C11×C4⋊C8—24no—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×C4⋊C8C2212yes—
24C4×C11×C4⋊C4C2212yes—
25C4×C11×C4⋊C4C2212yes—
26C4×C11×C22⋊C4—21no—
27C4×C11×C22⋊C4—21no—
28C11×#376—21no—
29C43×C11—21no—
30C11×#340C2218yes—
31C11×#340C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—24no—
38C22×C8×C11—28no—
39C22×C8×C11C2314yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8C2×C414yes—
43C11×C4⋊Q8C2×C414yes—
44C11×#125—24no—
45C11×#125C2×C418yes—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8—28no—
48C4×Q8×C11—28no—
49C4×Q8×C11—28no—
50C11×#117—24no—
51C11×#117—24no—
52C11×#117C2×C418yes—
53C11×#117Q818yescomplemented
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11C2×C414yes—
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D414yes—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C11×C4⋊C8—24no—
74C11×C4⋊C8—24no—
75C11×#95—22no—
76C11×#95—22no—
77#21311C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—24no—
80C2×Q8×C11—24no—
81C2×Q8×C11—44no—
82C2×Q8×C11—44no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C414yes—
89C22×C4×C11C22⋊C414yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×Q814yes—
98C22×C4×C11#4114yes—
99C22×C4×C11C2411yescharacteristic
100C2×C8×C11—24no—
101C2×C8×C11—28no—
102C2×C8×C11—48no—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4C22×C414yes—
111C11×C4⋊C4C22×C414yes—
112C11×C4⋊C4C2×Q818yes—
113C11×C22⋊C4—28no—
114C11×C22⋊C4—28no—
115C42×C11—28no—
116C42×C11—28no—
117C42×C11—44no—
118C42×C11—44no—
119C42×C11C22⋊C414yes—
120C42×C11C22⋊C414yes—
121C42×C11C22×C412yes—
122C42×C11C22×C412yes—
123C42×C11C2×D412yes—
124C42×C11C2×D412yes—
125C2×#533C2×C1111yescharacteristic
126C22×C4⋊C8C2×C1111yescharacteristic
127C4×#117C2×C1111yescharacteristic
128#1989C2×C1114yescomplemented
129#1988C2×C1112yescomplemented
130#1987C2×C1112yescomplemented
131#1735C2×C1114yes—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11C2×C22⋊C412yes—
135C23×C11C22⋊Q814yes—
136C23×C11C22×D411yescharacteristic
137Q8×C11—48no—
138Q8×C11—48no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—28no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11C2×C22⋊C412yes—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C4×Q818yes—
157C2×C4×C11C22⋊Q814yes—
158C2×C4×C11#12414yes—
159C2×C4×C11C4⋊Q814yes—
160C2×C4×C11#13514yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×Q812yes—
164C2×C4×C11C2×#4112yes—
165C8×C11—44no—
166C23×C8C22×C1112yes—
167#533—24no—
168#533C4×C1118yescomplemented
169C2×C4⋊Q8C22×C1111yescharacteristic
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×#125C22×C1112yes—
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8—21no—
176C2×#117C22×C1112yes—
177C2×#117C22×C1112yes—
178C22×C42C22×C1111yescharacteristic
179C2×C4⋊C8—24no—
180C2×C4⋊C8C22×C1112yes—
181C2×C4⋊C8C22×C1112yes—
182C4×C4⋊C4C22×C1112yes—
183C4×C4⋊C4C22×C1112yes—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186#376—21no—
187C43—21no—
188#340C22×C1118yes—
189#340C22×C1118yes—
190C22×C11—28no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11#39114yes—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11C2×C22⋊Q812yes—
196C22×C11C2×#13512yes—
197C22×C11#57512yes—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—48no—
202C4×C11—44no—
203C4×C11—44no—
204C4×C11#39114yes—
205C4×C11#41614yes—
206C4×C11C2×C4×Q812yes—
207C4×C11C2×#12411yescharacteristic
208C4×C11C2×C4⋊Q811yescharacteristic
209C22×Q8—21no—
210C22×Q8—21no—
211C23×C4D4×C1111yescharacteristic
212C23×C4D4×C1111yescharacteristic
213C23×C4C23×C1111yescharacteristic
214C22×C8—24no—
215C22×C8—28no—
216C22×C8C23×C1114yes—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C4⋊Q8C2×C4×C1114yes—
220C4⋊Q8C2×C4×C1114yes—
221#125—24no—
222#125C2×C4×C1118yes—
223C22⋊Q8—28no—
224C22⋊Q8—28no—
225C4×Q8—28no—
226C4×Q8—28no—
227#117—24no—
228#117—24no—
229#117C2×C4×C1118yes—
230#117Q8×C1118yescomplemented
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C23×C1112yes—
236C2×C4⋊C4C23×C1112yes—
237C2×C4⋊C4C23×C1114yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42C2×C4×C1114yes—
245C2×C42D4×C1111yescharacteristic
246C2×C42D4×C1111yescharacteristic
247C2×C42D4×C1114yes—
248C2×C42C23×C1111yescharacteristic
249C2×C42C23×C1111yescharacteristic
250C4⋊C8—24no—
251C4⋊C8—24no—
252#95—22no—
253#95—22no—
254C2×C11—24no—
255C2×C11C2×#39111yescharacteristic
256C2×C11C2×#41611yescharacteristic
257C2×C11#289611yescharacteristic
258C2×C11#307614yes—
259C24C2×D4×C1111yescharacteristic
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—44no—
263C2×Q8—44no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4C11×C22⋊C414yes—
270C22×C4C11×C22⋊C414yes—
271C22×C4C22×C4×C1112yes—
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C2×D4×C1112yes—
278C22×C4C2×Q8×C1114yes—
279C22×C4C11×#4114yes—
280C22×C4C24×C1111yescharacteristic
281C2×C8—24no—
282C2×C8—28no—
283C2×C8—48no—
284C4⋊C4—28no—
285C4⋊C4—28no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—24no—
291C4⋊C4C22×C4×C1114yes—
292C4⋊C4C22×C4×C1114yes—
293C4⋊C4C2×Q8×C1118yes—
294C22⋊C4—28no—
295C22⋊C4—28no—
296C42—28no—
297C42—28no—
298C42—44no—
299C42—44no—
300C42C11×C22⋊C414yes—
301C42C11×C22⋊C414yes—
302C42C22×C4×C1112yes—
303C42C22×C4×C1112yes—
304C42C2×D4×C1112yes—
305C42C2×D4×C1112yes—
306C11#2131111yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—22no—
309C23C2×C11×C22⋊C412yes—
310C23C11×C22⋊Q814yes—
311C23C22×D4×C1111yescharacteristic
312Q8—48no—
313Q8—48no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—28no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4C2×C11×C22⋊C412yes—
327C2×C4C2×C11×C22⋊C412yes—
328C2×C4C2×C11×C22⋊C412yes—
329C2×C4C2×C11×C22⋊C412yes—
330C2×C4C2×C11×C22⋊C412yes—
331C2×C4C4×Q8×C1118yes—
332C2×C4C11×C22⋊Q814yes—
333C2×C4C11×#12414yes—
334C2×C4C11×C4⋊Q814yes—
335C2×C4C11×#13514yes—
336C2×C4C23×C4×C1111yescharacteristic
337C2×C4C22×D4×C1111yescharacteristic
338C2×C4C22×Q8×C1112yes—
339C2×C4C2×C11×#4112yes—
340C8—44no—
341C22—22no—
342C22—22no—
343C22—28no—
344C22C11×#39114yes—
345C22C22×C11×C22⋊C411yescharacteristic
346C22C2×C11×C22⋊Q812yes—
347C22C2×C11×#13512yes—
348C22C11×#57512yes—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—44no—
353C4—44no—
354C4—48no—
355C4C11×#39114yes—
356C4C11×#41614yes—
357C4C2×C4×Q8×C1112yes—
358C4C2×C11×#12411yescharacteristic
359C4C2×C11×C4⋊Q811yescharacteristic
360C2—24no—
361C2C2×C11×#39111yescharacteristic
362C2C2×C11×#41611yescharacteristic
363C2C11×#289611yescharacteristic
364C2C11×#307614yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1989C2semidirect
5. C11×#1988C2semidirect
6. C11×#1987C2semidirect
10. C11×#533C4semidirect
53. C11×#117Q8semidirect
77. #21311C11direct (N × H)
128. #1989C2×C11semidirect
129. #1988C2×C11semidirect
130. #1987C2×C11semidirect
168. #533C4×C11semidirect
230. #117Q8×C11semidirect
306. C11#21311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C22×C11×C4⋊C82
C4×C11×#1172
C11×#19892
C11×#19882
C11×#19872
C11×#17352
#2131111