Finite Group Databasebeta

← C11×#11778 #14588971

Subgroups — C11×#11778 #14588971

Order 2816.

446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2536C211yesmaximal, characteristic
2C4×C11×#101C211yesmaximal, characteristic, complemented
3C11×#1467C211yesmaximal, characteristic, complemented
4C11×#1346C212yesmaximal, complemented
5C11×#1345C212yesmaximal
6C2×C11×C22⋊Q8—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8C2×C4×D4×C11C411yescharacteristic
9C11×#432—21no—
10C2×C11×#101—21no—
11C4×C11×M16—21no—
12C11×#398C411yescharacteristic
13C11×#398C2211yescharacteristic
14C11×#394C411yescharacteristic
15C11×#394C2211yescharacteristic
16C11×#388—21no—
17C11×#388—21no—
18C11×#382C411yescharacteristic
19C11×#380—21no—
20C11×#343C2212yes—
21C11×#324—21no—
22C11×#324C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C2×C11×M16—22no—
27C11×C22⋊Q8—44no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4C2311yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C11×C4⋊C8—41no—
48C11×#101—24no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C11×#97—41no—
52C4×C8×C11—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11×#95C2×C411yescharacteristic
58#11778C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—42no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C11×M16—24no—
79C11×M16—42no—
80C2×C8×C11—42no—
81C2×C8×C11—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—42no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—21no—
101#2536C2×C1111yescharacteristic
102C4×#101C2×C1111yescharacteristic, complemented
103#1467C2×C1111yescharacteristic, complemented
104#1346C2×C1112yescomplemented
105#1345C2×C1112yes—
106C23×C11—22no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11C2×C22⋊C411yescharacteristic
114Q8×C11—44no—
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
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—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—84no—
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#10412yes—
144C2×C4×C11AGL(1,ℤ/8)12yes—
145C8×C11—44no—
146C8×C11—82no—
147C2×C22⋊Q8—21no—
148C2×C4×Q8C22×C1111yescharacteristic
149C2×C4×D4C4×C1111yescharacteristic
150#432—21no—
151C2×#101—21no—
152C4×M16—21no—
153#398C4×C1111yescharacteristic
154#398C22×C1111yescharacteristic
155#394C4×C1111yescharacteristic
156#394C22×C1111yescharacteristic
157#388—21no—
158#388—21no—
159#382C4×C1111yescharacteristic
160#380—21no—
161#343C22×C1112yes—
162#324—21no—
163#324C22×C1112yes—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—81no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11C2×#9911yescharacteristic
174C22×C11#41811yescharacteristic
175C22×C11C2×#10411yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C22×Q8D4×C1111yescharacteristic
188C22×D4C2×C4×C1111yescharacteristic
189C23×C4—21no—
190C2×M16—22no—
191C22⋊Q8—44no—
192C4×Q8—41no—
193C4×Q8—41no—
194C4×D4—41no—
195C4×D4—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×C4×C1111yescharacteristic
200C2×C4⋊C4C2×C4×C1111yescharacteristic
201C2×C4⋊C4D4×C1111yescharacteristic
202C2×C4⋊C4C23×C1111yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42C2×C4×C1111yescharacteristic
209C2×C42D4×C1111yescharacteristic
210C2×C42D4×C1111yescharacteristic
211C4⋊C8—41no—
212#101—24no—
213C22⋊C8—22no—
214#97—41no—
215#97—41no—
216C4×C8—41no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×C4×C1111yescharacteristic
221#95C2×C4×C1111yescharacteristic
222C2×C11—21no—
223C2×C11—21no—
224C2×C11—82no—
225C2×C11#150711yescharacteristic
226C2×C11#212011yescharacteristic
227C2×C11#213311yescharacteristic
228C24—21no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×D4—41no—
233C2×D4—42no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C11×C22⋊C411yescharacteristic
241C22×C4C11×C22⋊C411yescharacteristic
242C22×C4C11×C22⋊C411yescharacteristic
243C22×C4C11×C22⋊C411yescharacteristic
244C22×C4C22×C4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247M16—24no—
248M16—42no—
249C2×C8—42no—
250C2×C8—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C11#1177811yescharacteristic, direct product factor, Sylow
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C11×C22⋊C411yescharacteristic
279Q8—44no—
280D4—42no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—84no—
306C2×C4C11×#9911yescharacteristic
307C2×C4C11×#9911yescharacteristic
308C2×C4C11×#10412yes—
309C2×C4C11×AGL(1,ℤ/8)12yes—
310C8—44no—
311C8—82no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C2×C11×#9911yescharacteristic
322C22C11×#41811yescharacteristic
323C22C2×C11×#10411yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2C11×#150711yescharacteristic
339C2C11×#212011yescharacteristic
340C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#101C2semidirect
3. C11×#1467C2semidirect
4. C11×#1346C2semidirect
58. #11778C11direct (N × H)
102. C4×#101C2×C11semidirect
103. #1467C2×C11semidirect
104. #1346C2×C11semidirect
270. C11#11778direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25362
C4×C11×#1012
C11×#14672
C11×#13462
C11×#13452
#1177811