Finite Group Databasebeta

← C11×#11810 #14589003

Subgroups — C11×#11810 #14589003

Order 2816.

402 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C11×#2396C211yesmaximal, characteristic
2C11×#1820C211yesmaximal, characteristic
3C11×#1464C211yesmaximal, characteristic
4C11×#1352C212yesmaximal
5C11×#1351C212yesmaximal
6C2×C4×Q8×C11C411yescharacteristic, complemented
7C2×C11×#117C2211yescharacteristic
8C11×#432—21no—
9C11×#400C411yescharacteristic, complemented
10C11×#399C2211yescharacteristic
11C11×#398—21no—
12C11×#396—21no—
13C11×#395C411yescharacteristic, complemented
14C11×#393C2211yescharacteristic
15C11×#381—21no—
16C4×C11×C4⋊C4—21no—
17C4×C11×C4⋊C4C411yescharacteristic, complemented
18C4×C11×C22⋊C4—21no—
19C11×#342—21no—
20C11×#342C2212yes—
21C11×#324—21no—
22C11×#323C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C11×C4⋊C8—41no—
46C11×C22⋊C8—22no—
47C11×#97—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—41no—
53C11×#95—41no—
54C11×#95C2×C411yescharacteristic
55C11×#95C2×C411yescharacteristic
56#11810C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11C2×D411yescharacteristic
58C2×Q8×C11—42no—
59C2×Q8×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—42no—
94C42×C11—41no—
95C42×C11—41no—
96#2396C2×C1111yescharacteristic
97#1820C2×C1111yescharacteristic
98#1464C2×C1111yescharacteristic
99#1352C2×C1112yes—
100#1351C2×C1112yes—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11#13712yes—
107Q8×C11—42no—
108Q8×C11—42no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11#9911yescharacteristic
141C8×C11—82no—
142C2×C4×Q8C4×C1111yescharacteristic, complemented
143C2×#117C22×C1111yescharacteristic
144#432—21no—
145#400C4×C1111yescharacteristic, complemented
146#399C22×C1111yescharacteristic
147#398—21no—
148#396—21no—
149#395C4×C1111yescharacteristic, complemented
150#393C22×C1111yescharacteristic
151#381—21no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4C4×C1111yescharacteristic, complemented
154C4×C22⋊C4—21no—
155#342—21no—
156#342C22×C1112yes—
157#324—21no—
158#323C22×C1112yes—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—42no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—42no—
172C4×C11—41no—
173C4×C11—42no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—162no—
181C22×Q8C2×C4×C1111yescharacteristic
182C23×C4D4×C1111yescharacteristic
183C4×Q8—41no—
184C4×Q8—41no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C1111yescharacteristic
192C2×C4⋊C4C2×C4×C1111yescharacteristic
193C2×C4⋊C4D4×C1111yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4D4×C1111yescharacteristic
198C2×C22⋊C4C23×C1111yescharacteristic
199C2×C42—21no—
200C2×C42—21no—
201C2×C42C2×C4×C1111yescharacteristic
202C2×C42D4×C1111yescharacteristic
203C4⋊C8—41no—
204C22⋊C8—22no—
205#97—41no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—41no—
211#95—41no—
212#95C2×C4×C1111yescharacteristic
213#95C2×C4×C1111yescharacteristic
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—42no—
217C2×C11#151111yescharacteristic
218C2×C11#212011yescharacteristic
219C2×C11#212611yescharacteristic
220C24C2×D4×C1111yescharacteristic
221C2×Q8—42no—
222C2×Q8—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—42no—
232C22×C4C11×C22⋊C411yescharacteristic
233C22×C4C11×C22⋊C411yescharacteristic
234C22×C4C11×C22⋊C411yescharacteristic
235C22×C4C11×C22⋊C411yescharacteristic
236C22×C4C22×C4×C1111yescharacteristic
237C22×C4C2×D4×C1111yescharacteristic
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—42no—
257C42—41no—
258C42—41no—
259C11#1181011yescharacteristic, direct product factor, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×C11×C22⋊C411yescharacteristic
265C23C11×#13712yes—
266Q8—42no—
267Q8—42no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4C11×#9911yescharacteristic
299C2×C4C11×#9911yescharacteristic
300C8—82no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×C11×#9911yescharacteristic
309C22C11×#41911yescharacteristic
310C22C11×#42111yescharacteristic
311C4—21no—
312C4—21no—
313C4—42no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—42no—
318C4—41no—
319C4—41no—
320C4—81no—
321C4—81no—
322C4—162no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2C11×#151111yescharacteristic
327C2C11×#212011yescharacteristic
328C2C11×#212611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C11C4semidirect
9. C11×#400C4semidirect
13. C11×#395C4semidirect
17. C4×C11×C4⋊C4C4semidirect
56. #11810C11direct (N × H)
142. C2×C4×Q8C4×C11semidirect
145. #400C4×C11semidirect
149. #395C4×C11semidirect
153. C4×C4⋊C4C4×C11semidirect
259. C11#11810direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23962
C11×#18202
C11×#14642
C11×#13522
C11×#13512
#1181011