Finite Group Databasebeta

← C11×#11211 #14588404

Subgroups — C11×#11211 #14588404

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2316C211yesmaximal, characteristic
2C2×C11×#382C211yesmaximal, characteristic
3C2×C11×#343C211yesmaximal, characteristic
4C11×#1736C212yesmaximal
5C2×C11×#339C212yesmaximal
6C22×C11×M16C2212yes—
7C2×C11×#117C2212yes—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C11×#389—24no—
12C11×#382—22no—
13C11×#382C414yescomplemented
14C11×#380—22no—
15C2×C11×#95—22no—
16C11×#343—22no—
17C11×#340—24no—
18C11×#339—24no—
19C23×C4×C11—21no—
20C23×C4×C11—21no—
21C23×C4×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C2×C11×M16—22no—
24C2×C11×M16—22no—
25C2×C11×M16—22no—
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16Q814yes—
29C22×C8×C11—22no—
30C11×#117—22no—
31C11×#117—22no—
32C11×#117—22no—
33C11×#117—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C4⋊C4D414yes—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C22⋊C4—22no—
45C2×C42×C11—21no—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C42×C11—22no—
49C2×C42×C11C2×C412yes—
50C2×C42×C11D412yes—
51C2×C42×C11Q812yes—
52C11×#95—24no—
53C11×#95—28no—
54#11211C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11C2×D411yescharacteristic
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—44no—
66C22×C4×C11—44no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C414yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×Q811yescharacteristic
75C22×C4×C11C2×Q812yes—
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4112yes—
79C22×C4×C11#4112yes—
80C11×M16—24no—
81C11×M16—24no—
82C11×M16—42no—
83C11×M16—42no—
84C2×C8×C11—24no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—84no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—42no—
100C42×C11—42no—
101C42×C11C4⋊C414yescomplemented
102#2316C2×C1111yescharacteristic
103C2×#382C2×C1111yescharacteristic
104C2×#343C2×C1111yescharacteristic
105#1736C2×C1112yes—
106C2×#339C2×C1112yes—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#12011yescharacteristic
111C23×C11#12111yescharacteristic
112C23×C11C22⋊Q811yescharacteristic
113C23×C11#12311yescharacteristic
114C23×C11#12411yescharacteristic
115C23×C11C4⋊Q811yescharacteristic
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—82no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11#11711yescharacteristic
134C2×C4×C11C4×D412yes—
135C2×C4×C11C4×Q812yes—
136C2×C4×C11#12112yes—
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11C22⋊Q812yes—
140C2×C4×C11C22⋊Q812yes—
141C2×C4×C11C22⋊Q812yes—
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11#12312yes—
144C2×C4×C11#12512yes—
145C2×C4×C11#12512yes—
146C2×C4×C11#12612yes—
147C2×C4×C11C4⋊Q812yes—
148C8×C11—44no—
149C22×M16C22×C1112yes—
150C2×#117C22×C1112yes—
151C22×C4⋊C4C22×C1111yescharacteristic
152C22×C4⋊C4C22×C1111yescharacteristic
153C22×C42C22×C1111yescharacteristic
154#389—24no—
155#382—22no—
156#382C4×C1114yescomplemented
157#380—22no—
158C2×#95—22no—
159#343—22no—
160#340—24no—
161#339—24no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11#38011yescharacteristic
171C22×C11#38611yescharacteristic
172C22×C11#39111yescharacteristic
173C22×C11#39411yescharacteristic
174C22×C11#39511yescharacteristic
175C22×C11#39811yescharacteristic
176C22×C11#40011yescharacteristic
177C22×C11#45412yes—
178C22×C11#45512yes—
179C4×C11—44no—
180C4×C11—44no—
181C4×C11—82no—
182C4×C11—84no—
183C4×C11#38712yes—
184C4×C11#38912yes—
185C4×C11#39612yes—
186C4×C11#39812yes—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4D4×C1112yes—
190C23×C4C23×C1111yescharacteristic
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16Q8×C1114yes—
197C22×C8—22no—
198#117—22no—
199#117—22no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4C2×C4×C1112yes—
209C2×C4⋊C4C2×C4×C1112yes—
210C2×C4⋊C4D4×C1114yes—
211C2×C4⋊C4D4×C1112yes—
212C2×C22⋊C4—22no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—22no—
217C2×C42C2×C4×C1112yes—
218C2×C42D4×C1112yes—
219C2×C42Q8×C1112yes—
220#95—24no—
221#95—28no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#144111yescharacteristic
227C2×C11#188511yescharacteristic
228C2×C11#188811yescharacteristic
229C2×C11#204012yes—
230C2×C11#206112yes—
231C24C2×D4×C1111yescharacteristic
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C11×C22⋊C414yes—
246C22×C4C22×C4×C1111yescharacteristic
247C22×C4C2×D4×C1111yescharacteristic
248C22×C4C2×D4×C1112yes—
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C2×Q8×C1111yescharacteristic
251C22×C4C2×Q8×C1112yes—
252C22×C4C11×#4111yescharacteristic
253C22×C4C11×#4111yescharacteristic
254C22×C4C11×#4112yes—
255C22×C4C11×#4112yes—
256M16—24no—
257M16—24no—
258M16—42no—
259M16—42no—
260C2×C8—24no—
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—24no—
268C4⋊C4—42no—
269C4⋊C4—84no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C42—22no—
273C42—22no—
274C42—22no—
275C42—42no—
276C42—42no—
277C42C11×C4⋊C414yescomplemented
278C11#1121111yescharacteristic, direct product factor, Sylow
279C23—22no—
280C23—22no—
281C23C2×C11×C22⋊C411yescharacteristic
282C23C11×#12011yescharacteristic
283C23C11×#12111yescharacteristic
284C23C11×C22⋊Q811yescharacteristic
285C23C11×#12311yescharacteristic
286C23C11×#12411yescharacteristic
287C23C11×C4⋊Q811yescharacteristic
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4C2×C11×C4⋊C411yescharacteristic
305C2×C4C11×#11711yescharacteristic
306C2×C4C4×D4×C1112yes—
307C2×C4C4×Q8×C1112yes—
308C2×C4C11×#12112yes—
309C2×C4C11×#12111yescharacteristic
310C2×C4C11×#12112yes—
311C2×C4C11×C22⋊Q812yes—
312C2×C4C11×C22⋊Q812yes—
313C2×C4C11×C22⋊Q812yes—
314C2×C4C11×C22⋊Q811yescharacteristic
315C2×C4C11×#12312yes—
316C2×C4C11×#12512yes—
317C2×C4C11×#12512yes—
318C2×C4C11×#12612yes—
319C2×C4C11×C4⋊Q812yes—
320C8—44no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22C11×#38011yescharacteristic
330C22C11×#38611yescharacteristic
331C22C11×#39111yescharacteristic
332C22C11×#39411yescharacteristic
333C22C11×#39511yescharacteristic
334C22C11×#39811yescharacteristic
335C22C11×#40011yescharacteristic
336C22C11×#45412yes—
337C22C11×#45512yes—
338C4—44no—
339C4—44no—
340C4—82no—
341C4—84no—
342C4C11×#38712yes—
343C4C11×#38912yes—
344C4C11×#39612yes—
345C4C11×#39812yes—
346C2—21no—
347C2—21no—
348C2—21no—
349C2—21no—
350C2C11×#144111yescharacteristic
351C2C11×#188511yescharacteristic
352C2C11×#188811yescharacteristic
353C2C11×#204012yes—
354C2C11×#206112yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
13. C11×#382C4semidirect
54. #11211C11direct (N × H)
101. C42×C11C4⋊C4semidirect
156. #382C4×C11semidirect
277. C42C11×C4⋊C4semidirect
278. C11#11211direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23162
C2×C11×#3822
C2×C11×#3432
C11×#17362
C2×C11×#3392
#1121111