Finite Group Databasebeta

← C11×#11210 #14588403

Subgroups — C11×#11210 #14588403

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2316C211yesmaximal, characteristic
2C2×C11×#384C211yesmaximal, characteristic
3C2×C11×#343C211yesmaximal, characteristic
4C11×#1736C212yesmaximal
5C2×C11×#339C212yesmaximal
6C22×C11×M16C2212yes—
7C2×C11×#117C2212yes—
8C22×C11×C4⋊C4—22no—
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C11×#389—24no—
13C11×#384—22no—
14C11×#384C414yescomplemented
15C11×#380—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—28no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—48no—
42C2×C11×C4⋊C4C2×C412yes—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C4⋊C4D414yes—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C22⋊C4—22no—
47C2×C42×C11—21no—
48C2×C42×C11—21no—
49C2×C42×C11—21no—
50C2×C42×C11—22no—
51C2×C42×C11C2×C412yes—
52C2×C42×C11D412yes—
53C2×C42×C11Q812yes—
54C11×#95—24no—
55#11210C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11C2×D411yescharacteristic
57C22×C4×C11—24no—
58C22×C4×C11—24no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—44no—
67C22×C4×C11—44no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11C22⋊C414yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q811yescharacteristic
76C22×C4×C11C2×Q812yes—
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4112yes—
80C22×C4×C11#4112yes—
81C11×M16—24no—
82C11×M16—24no—
83C11×M16—42no—
84C11×M16—42no—
85C2×C8×C11—24no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—416no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—84no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C42×C11—22no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11—42no—
102C42×C11—42no—
103C42×C11C4⋊C414yescomplemented
104#2316C2×C1111yescharacteristic
105C2×#384C2×C1111yescharacteristic
106C2×#343C2×C1111yescharacteristic
107#1736C2×C1112yes—
108C2×#339C2×C1112yes—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11#12011yescharacteristic
113C23×C11#12111yescharacteristic
114C23×C11C22⋊Q811yescharacteristic
115C23×C11#12311yescharacteristic
116C23×C11#12411yescharacteristic
117C23×C11C4⋊Q811yescharacteristic
118C2×C4×C11—24no—
119C2×C4×C11—28no—
120C2×C4×C11—24no—
121C2×C4×C11—28no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—44no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11—82no—
134C2×C4×C11C2×C4⋊C411yescharacteristic
135C2×C4×C11#11711yescharacteristic
136C2×C4×C11C4×D412yes—
137C2×C4×C11C4×Q812yes—
138C2×C4×C11#12112yes—
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12112yes—
141C2×C4×C11C22⋊Q812yes—
142C2×C4×C11C22⋊Q812yes—
143C2×C4×C11C22⋊Q812yes—
144C2×C4×C11C22⋊Q811yescharacteristic
145C2×C4×C11#12312yes—
146C2×C4×C11#12512yes—
147C2×C4×C11#12512yes—
148C2×C4×C11#12612yes—
149C2×C4×C11C4⋊Q812yes—
150C8×C11—44no—
151C22×M16C22×C1112yes—
152C2×#117C22×C1112yes—
153C22×C4⋊C4—22no—
154C22×C4⋊C4C22×C1111yescharacteristic
155C22×C4⋊C4C22×C1111yescharacteristic
156C22×C42C22×C1111yescharacteristic
157#389—24no—
158#384—22no—
159#384C4×C1114yescomplemented
160#380—22no—
161#343—22no—
162#340—24no—
163#339—24no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11#38011yescharacteristic
173C22×C11#38611yescharacteristic
174C22×C11#39111yescharacteristic
175C22×C11#39411yescharacteristic
176C22×C11#39511yescharacteristic
177C22×C11#39811yescharacteristic
178C22×C11#40011yescharacteristic
179C22×C11#45312yes—
180C22×C11#45612yes—
181C4×C11—28no—
182C4×C11—44no—
183C4×C11—82no—
184C4×C11—84no—
185C4×C11#38712yes—
186C4×C11#38912yes—
187C4×C11#39612yes—
188C4×C11#39812yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4D4×C1112yes—
192C23×C4C23×C1111yescharacteristic
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16Q8×C1114yes—
199C22×C8—22no—
200#117—22no—
201#117—22no—
202#117—22no—
203#117—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—28no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—48no—
212C2×C4⋊C4C2×C4×C1112yes—
213C2×C4⋊C4C2×C4×C1112yes—
214C2×C4⋊C4D4×C1114yes—
215C2×C4⋊C4D4×C1112yes—
216C2×C22⋊C4—22no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—22no—
221C2×C42C2×C4×C1112yes—
222C2×C42D4×C1112yes—
223C2×C42Q8×C1112yes—
224#95—24no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11#144111yescharacteristic
230C2×C11#188611yescharacteristic
231C2×C11#188711yescharacteristic
232C2×C11#203912yes—
233C2×C11#206012yes—
234C24C2×D4×C1111yescharacteristic
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C11×C22⋊C414yes—
249C22×C4C22×C4×C1111yescharacteristic
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1112yes—
252C22×C4C2×D4×C1111yescharacteristic
253C22×C4C2×Q8×C1111yescharacteristic
254C22×C4C2×Q8×C1112yes—
255C22×C4C11×#4111yescharacteristic
256C22×C4C11×#4111yescharacteristic
257C22×C4C11×#4112yes—
258C22×C4C11×#4112yes—
259M16—24no—
260M16—24no—
261M16—42no—
262M16—42no—
263C2×C8—24no—
264C2×C8—42no—
265C2×C8—42no—
266C4⋊C4—24no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—416no—
272C4⋊C4—42no—
273C4⋊C4—84no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—42no—
280C42—42no—
281C42C11×C4⋊C414yescomplemented
282C11#1121011yescharacteristic, direct product factor, Sylow
283C23—22no—
284C23—22no—
285C23C2×C11×C22⋊C411yescharacteristic
286C23C11×#12011yescharacteristic
287C23C11×#12111yescharacteristic
288C23C11×C22⋊Q811yescharacteristic
289C23C11×#12311yescharacteristic
290C23C11×#12411yescharacteristic
291C23C11×C4⋊Q811yescharacteristic
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4C2×C11×C4⋊C411yescharacteristic
309C2×C4C11×#11711yescharacteristic
310C2×C4C4×D4×C1112yes—
311C2×C4C4×Q8×C1112yes—
312C2×C4C11×#12112yes—
313C2×C4C11×#12111yescharacteristic
314C2×C4C11×#12112yes—
315C2×C4C11×C22⋊Q812yes—
316C2×C4C11×C22⋊Q812yes—
317C2×C4C11×C22⋊Q812yes—
318C2×C4C11×C22⋊Q811yescharacteristic
319C2×C4C11×#12312yes—
320C2×C4C11×#12512yes—
321C2×C4C11×#12512yes—
322C2×C4C11×#12612yes—
323C2×C4C11×C4⋊Q812yes—
324C8—44no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22C11×#38011yescharacteristic
334C22C11×#38611yescharacteristic
335C22C11×#39111yescharacteristic
336C22C11×#39411yescharacteristic
337C22C11×#39511yescharacteristic
338C22C11×#39811yescharacteristic
339C22C11×#40011yescharacteristic
340C22C11×#45312yes—
341C22C11×#45612yes—
342C4—28no—
343C4—44no—
344C4—82no—
345C4—84no—
346C4C11×#38712yes—
347C4C11×#38912yes—
348C4C11×#39612yes—
349C4C11×#39812yes—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2C11×#144111yescharacteristic
355C2C11×#188611yescharacteristic
356C2C11×#188711yescharacteristic
357C2C11×#203912yes—
358C2C11×#206012yes—
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
14. C11×#384C4semidirect
55. #11210C11direct (N × H)
103. C42×C11C4⋊C4semidirect
159. #384C4×C11semidirect
281. C42C11×C4⋊C4semidirect
282. C11#11210direct (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×#3842
C2×C11×#3432
C11×#17362
C2×C11×#3392
#1121011