Finite Group Databasebeta

← C11×#10135 #14587328

Subgroups — C11×#10135 #14587328

Order 2816.

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

normal subgroups only

This group has 434 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×#3236C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic
3C2×C11×#491C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic
5C11×#1531C211yesmaximal, characteristic
6C11×#1470C211yesmaximal, characteristic
7C11×#1302C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—21no—
12C11×#500—21no—
13C11×#491—21no—
14C11×#491—22no—
15C11×#491—22no—
16C11×#487—21no—
17C11×#484—21no—
18C11×#484—22no—
19C11×#483—21no—
20C11×#479—22no—
21C11×#477—22no—
22C11×#432C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C2×C11×#103—21no—
26C2×C11×#103—21no—
27C2×C11×#97C2211yescharacteristic
28C11×#332—22no—
29C11×#330—22no—
30C11×#324—22no—
31C22×Q8×C11—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#107—22no—
58C11×#106—22no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63C11×#103—24no—
64C11×#103—22no—
65C11×#103—22no—
66C11×#103—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8D412yes—
70C11×#97—21no—
71C11×#97—21no—
72C11×#97—21no—
73C11×#97D412yes—
74C4×C8×C11—21no—
75#10135C1111yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—44no—
80C2×Q8×C11—41no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—42no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#3236C2×C1111yescharacteristic
117#3230C2×C1111yescharacteristic
118C2×#491C2×C1111yescharacteristic
119#1556C2×C1111yescharacteristic
120#1531C2×C1111yescharacteristic
121#1470C2×C1111yescharacteristic
122#1302C2×C1111yescharacteristic
123C23×C11#12111yescharacteristic
124Q8×C11—42no—
125Q8×C11—44no—
126Q8×C11—42no—
127Q8×C11—82no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11—81no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C8×C11—42no—
146C8×C11—42no—
147C8×C11—42no—
148C8×C11—81no—
149#533C22×C1111yescharacteristic
150C2×C4⋊Q8C22×C1111yescharacteristic
151C2×#125C22×C1111yescharacteristic
152#501—21no—
153#500—21no—
154#491—22no—
155#491—21no—
156#491—22no—
157#487—21no—
158#484—21no—
159#484—22no—
160#483—21no—
161#479—22no—
162#477—22no—
163#432C22×C1111yescharacteristic
164#432C22×C1111yescharacteristic
165#431C22×C1111yescharacteristic
166C2×#103—21no—
167C2×#103—21no—
168C2×#97C22×C1111yescharacteristic
169#332—22no—
170#330—22no—
171#324—22no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#39211yescharacteristic
175C22×C11#47312yes—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—82no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11#45412yes—
187C22×Q8—21no—
188C22×C8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8D4×C1112yes—
193C4⋊Q8D4×C1111yescharacteristic
194C4⋊Q8D4×C1111yescharacteristic
195#125—21no—
196#125—21no—
197#125—21no—
198#125—21no—
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4D4×C1111yescharacteristic
210C2×C4⋊C4D4×C1111yescharacteristic
211C2×C42C23×C1111yescharacteristic
212#107—24no—
213#107—22no—
214#106—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8D4×C1112yes—
218#103—24no—
219#103—24no—
220#103—24no—
221#103—22no—
222#103—22no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225C22⋊C8D4×C1112yes—
226#97—21no—
227#97—21no—
228#97—21no—
229#97D4×C1112yes—
230C4×C8—21no—
231C2×C11—22no—
232C2×C11#200311yescharacteristic
233C2×C11#200911yescharacteristic
234C2×C11#202011yescharacteristic
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—44no—
239C2×Q8—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4C2×D4×C1111yescharacteristic
244C22×C4C2×D4×C1111yescharacteristic
245C22×C4C11×#4111yescharacteristic
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—42no—
250C2×C8—41no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—41no—
270C42—41no—
271C42C2×D4×C1111yescharacteristic
272C42C2×D4×C1111yescharacteristic
273C42C2×D4×C1111yescharacteristic
274C42C2×D4×C1111yescharacteristic
275C11#1013511yescharacteristic, direct product factor, Sylow
276C23C11×#12111yescharacteristic
277Q8—42no—
278Q8—44no—
279Q8—42no—
280Q8—82no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—82no—
291C2×C4—81no—
292C2×C4C11×#12011yescharacteristic
293C2×C4C11×#12011yescharacteristic
294C2×C4C11×#12011yescharacteristic
295C2×C4C11×#12111yescharacteristic
296C2×C4C11×#12111yescharacteristic
297C2×C4C11×#12711yescharacteristic
298C8—42no—
299C8—42no—
300C8—42no—
301C8—81no—
302C22—21no—
303C22—21no—
304C22C11×#39211yescharacteristic
305C22C11×#47312yes—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—82no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4C11×#45412yes—
317C2—22no—
318C2C11×#200311yescharacteristic
319C2C11×#200911yescharacteristic
320C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
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
75. #10135C11direct (N × H)
275. C11#10135direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32362
C11×#32302
C2×C11×#4912
C11×#15562
C11×#15312
C11×#14702
C11×#13022
#1013511