Finite Group Databasebeta

← C11×#11791 #14588984

Subgroups — C11×#11791 #14588984

Order 2816.

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

normal subgroups only

This group has 572 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×#2409C211yesmaximal, characteristic
2C4×C11×#100C211yesmaximal, characteristic
3C11×#1465C211yesmaximal, characteristic
4C11×#1354C214yesmaximal, complemented
5C23×Q8×C11C411yescharacteristic
6C2×C11×C22⋊Q8—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C2×C11×#100—21no—
9C11×#407—21no—
10C4×C11×M16—21no—
11C11×#395C2212yes—
12C11×#393C412yes—
13C11×#391—21no—
14C11×#386—21no—
15C11×#385—21no—
16C11×#380C411yescharacteristic
17C11×#343C2212yes—
18C11×#324C2212yes—
19C11×#323—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11—41no—
22C22×Q8×C11—41no—
23C22×Q8×C11—44no—
24C22×Q8×C11C2×C412yes—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C2×C11×M16—22no—
30C2×C11×M16—41no—
31C11×C22⋊Q8—44no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C11×#100—24no—
43C11×C22⋊C8—22no—
44C11×C22⋊C8—41no—
45C11×#97—41no—
46C4×C8×C11—41no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95C2×C412yes—
50#11791C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22⋊C411yescharacteristic
53C2×Q8×C11—24no—
54C2×Q8×C11—42no—
55C2×Q8×C11—44no—
56C2×Q8×C11—42no—
57C2×Q8×C11—48no—
58C2×Q8×C11—44no—
59C2×Q8×C11—44no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—44no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C11×M16—24no—
81C11×M16—42no—
82C11×M16—82no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—44no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—44no—
91C11×C22⋊C4—42no—
92C42×C11—21no—
93C42×C11—21no—
94#2409C2×C1111yescharacteristic
95C4×#100C2×C1111yescharacteristic
96#1465C2×C1111yescharacteristic
97#1354C2×C1114yescomplemented
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10412yes—
108C23×C11C2×C22⋊C411yescharacteristic
109Q8×C11—44no—
110Q8×C11—44no—
111Q8×C11—44no—
112Q8×C11—44no—
113D4×C11—44no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—48no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#13712yes—
137C8×C11—44no—
138C8×C11—82no—
139C23×Q8C4×C1111yescharacteristic
140C2×C22⋊Q8—21no—
141C2×C4×D4C22×C1111yescharacteristic
142C2×#100—21no—
143#407—21no—
144C4×M16—21no—
145#395C22×C1112yes—
146#393C4×C1112yes—
147#391—21no—
148#386—21no—
149#385—21no—
150#380C4×C1111yescharacteristic
151#343C22×C1112yes—
152#324C22×C1112yes—
153#323—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11C2×#10411yescharacteristic
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—44no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—82no—
176C4×C11AΣL(1,𝔽16)12yes—
177C22×Q8—21no—
178C22×Q8—41no—
179C22×Q8—41no—
180C22×Q8—44no—
181C22×Q8C2×C4×C1112yes—
182C22×D4D4×C1111yescharacteristic
183C23×C4—21no—
184C23×C4C2×C4×C1111yescharacteristic
185C23×C4D4×C1111yescharacteristic
186C2×M16—22no—
187C2×M16—41no—
188C22⋊Q8—44no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C23×C1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C2×C4×C1111yescharacteristic
197C2×C22⋊C4D4×C1111yescharacteristic
198C2×C42D4×C1111yescharacteristic
199#100—24no—
200C22⋊C8—22no—
201C22⋊C8—41no—
202#97—41no—
203C4×C8—41no—
204#95—22no—
205#95—22no—
206#95C2×C4×C1112yes—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—42no—
210C2×C11—81no—
211C2×C11#150811yescharacteristic
212C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C11#213511yescharacteristic
214C24C11×C22⋊C411yescharacteristic
215C24C11×C22⋊C411yescharacteristic
216C2×Q8—24no—
217C2×Q8—44no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—44no—
221C2×Q8—48no—
222C2×Q8—44no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4C11×C22⋊C411yescharacteristic
239C22×C4C11×C22⋊C411yescharacteristic
240C22×C4C22×C4×C1111yescharacteristic
241C22×C4C2×D4×C1111yescharacteristic
242C22×C4C2×D4×C1111yescharacteristic
243M16—24no—
244M16—42no—
245M16—82no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—44no—
254C22⋊C4—42no—
255C42—21no—
256C42—21no—
257C11#1179111yescharacteristic, direct product factor, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C11×#10412yes—
268C23C2×C11×C22⋊C411yescharacteristic
269Q8—44no—
270Q8—44no—
271Q8—44no—
272Q8—44no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4C11×#9911yescharacteristic
295C2×C4C11×#9911yescharacteristic
296C2×C4C11×#13712yes—
297C8—44no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×C11×#9911yescharacteristic
312C22C11×#41911yescharacteristic
313C22C2×C11×#10411yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—44no—
319C4—41no—
320C4—82no—
321C4C11×AΣL(1,𝔽16)12yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2C11×#150811yescharacteristic
327C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
328C2C11×#213511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊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×#1354C2semidirect
50. #11791C11direct (N × H)
97. #1354C2×C11semidirect
257. C11#11791direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24092
C4×C11×#1002
C11×#14652
C11×#13542
#1179111