Finite Group Databasebeta

← C11×#11788 #14588981

Subgroups — C11×#11788 #14588981

Order 2816.

516 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2542C211yesmaximal, characteristic
2C4×C11×#99C211yesmaximal, characteristic
3C11×#1465C211yesmaximal, characteristic
4C11×#1352C214yesmaximal, complemented
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C11×C22⋊Q8—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C2×C11×#99—21no—
10C11×#407—21no—
11C11×#399C412yescomplemented
12C11×#399C2212yes—
13C11×#390—21no—
14C11×#384—21no—
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C11×#342C2212yes—
18C11×#324—21no—
19C11×#323C2212yes—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C2×C11×M16—41no—
25C11×C4⋊Q8—41no—
26C11×C4⋊Q8—41no—
27C11×C22⋊Q8—44no—
28C11×C22⋊Q8—44no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11—41no—
44C2×C42×C11C2×C411yescharacteristic
45C11×#99—24no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—41no—
48C11×#95—41no—
49C11×#95C2×C412yes—
50#11788C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—41no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C11×M16—82no—
75C2×C8×C11—42no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4—44no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—24no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—44no—
86C11×C22⋊C4—44no—
87C11×C22⋊C4—42no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—42no—
91C42×C11—82no—
92#2542C2×C1111yescharacteristic
93C4×#99C2×C1111yescharacteristic
94#1465C2×C1111yescharacteristic
95#1352C2×C1114yescomplemented
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11#13712yes—
107Q8×C11—82no—
108Q8×C11—82no—
109D4×C11—44no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—24no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#10412yes—
135C8×C11—82no—
136C2×C4⋊Q8C4×C1111yescharacteristic, complemented
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C4×D4C22×C1111yescharacteristic
140C2×#99—21no—
141#407—21no—
142#399C4×C1112yescomplemented
143#399C22×C1112yes—
144#390—21no—
145#384—21no—
146C4×C4⋊C4C4×C1111yescharacteristic, complemented
147C4×C22⋊C4—21no—
148#342C22×C1112yes—
149#324—21no—
150#323C22×C1112yes—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—22no—
154C22×C11—42no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11C2×#9911yescharacteristic
164C22×C11#41911yescharacteristic
165C22×C11C2×#10411yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—84no—
173C4×C11—82no—
174C4×C11#35312yes—
175C22×Q8—21no—
176C22×D4D4×C1111yescharacteristic
177C23×C4D4×C1111yescharacteristic
178C23×C4D4×C1111yescharacteristic
179C2×M16—41no—
180C4⋊Q8—41no—
181C4⋊Q8—41no—
182C22⋊Q8—44no—
183C22⋊Q8—44no—
184C4×D4—41no—
185C4×D4—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4C2×C4×C1112yes—
191C2×C4⋊C4D4×C1111yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4C2×C4×C1111yescharacteristic
196C2×C22⋊C4C23×C1111yescharacteristic
197C2×C42—21no—
198C2×C42—41no—
199C2×C42C2×C4×C1111yescharacteristic
200#99—24no—
201C22⋊C8—22no—
202C22⋊C8—41no—
203#95—41no—
204#95C2×C4×C1112yes—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11—81no—
209C2×C11#150811yescharacteristic
210C2×C11#212311yescharacteristic
211C2×C11C2×#35311yescharacteristic
212C24C11×C22⋊C411yescharacteristic
213C24C2×D4×C1111yescharacteristic
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C11×C22⋊C411yescharacteristic
231C22×C4C11×C22⋊C411yescharacteristic
232C22×C4C11×C22⋊C411yescharacteristic
233C22×C4C22×C4×C1111yescharacteristic
234C22×C4C2×D4×C1111yescharacteristic
235M16—82no—
236C2×C8—42no—
237C4⋊C4—24no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—44no—
241C4⋊C4—44no—
242C4⋊C4—42no—
243C22⋊C4—24no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C42—21no—
250C42—21no—
251C42—42no—
252C42—82no—
253C11#1178811yescharacteristic, direct product factor, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C11×C22⋊C411yescharacteristic
264C23C11×#13712yes—
265Q8—82no—
266Q8—82no—
267D4—44no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C11×#9911yescharacteristic
291C2×C4C11×#9911yescharacteristic
292C2×C4C11×#10412yes—
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22—81no—
306C22C2×C11×#9911yescharacteristic
307C22C11×#41911yescharacteristic
308C22C2×C11×#10411yescharacteristic
309C4—21no—
310C4—22no—
311C4—44no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—84no—
316C4—82no—
317C4C11×#35312yes—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—81no—
322C2C11×#150811yescharacteristic
323C2C11×#212311yescharacteristic
324C2C2×C11×#35311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1352C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
11. C11×#399C4semidirect
15. C4×C11×C4⋊C4C4semidirect
50. #11788C11direct (N × H)
95. #1352C2×C11semidirect
136. C2×C4⋊Q8C4×C11semidirect
142. #399C4×C11semidirect
146. C4×C4⋊C4C4×C11semidirect
253. C11#11788direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25422
C4×C11×#992
C11×#14652
C11×#13522
#1178811