Finite Group Databasebeta

← C11×#10379 #14587572

Subgroups — C11×#10379 #14587572

Order 2816.

360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2605C211yesmaximal, characteristic
2C11×#1986C211yesmaximal, characteristic
3C11×#1515C211yesmaximal, characteristic
4C11×#1506C211yesmaximal, characteristic
5C11×#1300C211yesmaximal, characteristic
6C11×#1288C211yesmaximal, characteristic
7C11×#1285C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#400—21no—
13C11×#395—21no—
14C11×#391—21no—
15C11×#391—21no—
16C11×#387—21no—
17C11×#387—21no—
18C11×#383C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C11×#376C2211yescharacteristic
21C11×#339—21no—
22C11×#339—21no—
23C11×#328—21no—
24C11×#328—21no—
25C11×#328—21no—
26C11×#328—21no—
27C22×Q8×C11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8Q811yescharacteristic, complemented
30C11×C4⋊Q8Q811yescharacteristic, complemented
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97—21no—
52C4×C8×C11—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#10379C1111yesmaximal, characteristic, direct product factor, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—81no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C11×M16—22no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—81no—
95C11×C22⋊C4—41no—
96C42×C11—42no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×Q811yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104#2605C2×C1111yescharacteristic
105#1986C2×C1111yescharacteristic
106#1515C2×C1111yescharacteristic
107#1506C2×C1111yescharacteristic
108#1300C2×C1111yescharacteristic
109#1288C2×C1111yescharacteristic
110#1285C2×C1111yescharacteristic
111C23×C11#12011yescharacteristic
112Q8×C11—81no—
113Q8×C11—81no—
114Q8×C11—84no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
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—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11C22⋊Q811yescharacteristic
140C2×C4×C11C22⋊Q811yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11#12411yescharacteristic
145C8×C11—42no—
146C8×C11—81no—
147C8×C11—81no—
148#533C22×C1111yescharacteristic
149#432C22×C1111yescharacteristic
150#432C22×C1111yescharacteristic
151C4×M16C22×C1111yescharacteristic
152#400—21no—
153#395—21no—
154#391—21no—
155#391—21no—
156#387—21no—
157#387—21no—
158#383C22×C1111yescharacteristic
159C4×C4⋊C4C22×C1111yescharacteristic
160#376C22×C1111yescharacteristic
161#339—21no—
162#339—21no—
163#328—21no—
164#328—21no—
165#328—21no—
166#328—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39311yescharacteristic
170C22×C11#45511yescharacteristic
171C22×C11#45611yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—42no—
179C4×C11—42no—
180C4×C11—81no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C22×Q8—21no—
187C2×M16—21no—
188C4⋊Q8Q8×C1111yescharacteristic, complemented
189C4⋊Q8Q8×C1111yescharacteristic, complemented
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C42—21no—
201C2×C42D4×C1111yescharacteristic
202C2×C42D4×C1111yescharacteristic
203C2×C42C23×C1111yescharacteristic
204C4⋊C8—21no—
205C4⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208#97—21no—
209#97—21no—
210#97—21no—
211C4×C8—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95D4×C1111yescharacteristic
221#95D4×C1111yescharacteristic
222#95D4×C1111yescharacteristic
223#95D4×C1111yescharacteristic
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#202811yescharacteristic
227C2×C11#203111yescharacteristic
228C2×C11#203111yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—81no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1111yescharacteristic
242C22×C4C2×D4×C1111yescharacteristic
243M16—22no—
244M16—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C22⋊C4—41no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—41no—
263C42C2×Q8×C1111yescharacteristic
264C42C11×#4111yescharacteristic
265C42C11×#4111yescharacteristic
266C42C11×#4111yescharacteristic
267C11#1037911yescharacteristic, direct product factor, Sylow
268C23C11×#12011yescharacteristic
269Q8—81no—
270Q8—81no—
271Q8—84no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
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—41no—
296C2×C4C11×C22⋊Q811yescharacteristic
297C2×C4C11×C22⋊Q811yescharacteristic
298C2×C4C11×C22⋊Q811yescharacteristic
299C2×C4C11×#12411yescharacteristic
300C2×C4C11×#12411yescharacteristic
301C2×C4C11×#12411yescharacteristic
302C8—42no—
303C8—81no—
304C8—81no—
305C22—21no—
306C22—21no—
307C22C11×#39311yescharacteristic
308C22C11×#45511yescharacteristic
309C22C11×#45611yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C2—21no—
325C2—21no—
326C2C11×#202811yescharacteristic
327C2C11×#203111yescharacteristic
328C2C11×#203111yescharacteristic
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
29. C11×C4⋊Q8Q8semidirect
30. C11×C4⋊Q8Q8semidirect
65. #10379C11direct (N × H)
188. C4⋊Q8Q8×C11semidirect
189. C4⋊Q8Q8×C11semidirect
267. C11#10379direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26052
C11×#19862
C11×#15152
C11×#15062
C11×#13002
C11×#12882
C11×#12852
#1037911