Finite Group Databasebeta

← C11×#10141 #14587334

Subgroups — C11×#10141 #14587334

Order 2816.

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

normal subgroups only

This group has 472 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×#3229C211yesmaximal, characteristic, complemented
2C11×#3215C211yesmaximal, characteristic
3C2×C11×#489C211yesmaximal, characteristic
4C11×#1558C211yesmaximal, characteristic, complemented
5C11×#1531C211yesmaximal, characteristic, complemented
6C11×#1469C211yesmaximal, characteristic
7C11×#1302C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124C2211yescharacteristic
11C11×#498—21no—
12C11×#497—21no—
13C11×#489—21no—
14C11×#489—22no—
15C11×#489—22no—
16C11×#487—21no—
17C11×#483—22no—
18C11×#475—22no—
19C11×#464—22no—
20C11×#451—21no—
21C11×#450—21no—
22C11×#432C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C2×C11×#103—21no—
26C2×C11×#102—21no—
27C2×C11×#97C2211yescharacteristic
28C11×#333—22no—
29C11×#330—22no—
30C11×#323—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×C11×Q16—22no—
35C2×C11×SD16—22no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×#125—21no—
44C11×#124—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#106—24no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63C11×#103—22no—
64C11×#103—24no—
65C11×#102—24no—
66C11×#102—22no—
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#10141C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C11×Q16—82no—
94C11×SD16—82no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—42no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#3229C2×C1111yescharacteristic, complemented
121#3215C2×C1111yescharacteristic
122C2×#489C2×C1111yescharacteristic
123#1558C2×C1111yescharacteristic, complemented
124#1531C2×C1111yescharacteristic, complemented
125#1469C2×C1111yescharacteristic
126#1302C2×C1111yescharacteristic, complemented
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11#12111yescharacteristic
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—82no—
137Q8×C11—82no—
138D4×C11—42no—
139D4×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—82no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—42no—
158C8×C11—81no—
159#533C22×C1111yescharacteristic
160C2×C4⋊Q8C22×C1111yescharacteristic
161C2×#124C22×C1111yescharacteristic
162#498—21no—
163#497—21no—
164#489—22no—
165#489—21no—
166#489—22no—
167#487—21no—
168#483—22no—
169#475—22no—
170#464—22no—
171#451—21no—
172#450—21no—
173#432C22×C1111yescharacteristic
174#432C22×C1111yescharacteristic
175#431C22×C1111yescharacteristic
176C2×#103—21no—
177C2×#102—21no—
178C2×#97C22×C1111yescharacteristic
179#333—22no—
180#330—22no—
181#323—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39211yescharacteristic
189C22×C11#47112yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11#45512yes—
200C22×Q8—21no—
201C22×Q8D4×C1111yescharacteristic
202C22×D4D4×C1111yescharacteristic
203C2×Q16—22no—
204C2×SD16—22no—
205C22×C8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D4×C1112yes—
210C4⋊Q8D4×C1111yescharacteristic
211C4⋊Q8D4×C1111yescharacteristic
212#125—21no—
213#124—21no—
214#124—21no—
215#124—21no—
216#124—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42C23×C1111yescharacteristic
227#106—24no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8D4×C1112yes—
231#103—24no—
232#103—22no—
233#103—24no—
234#102—24no—
235#102—22no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8D4×C1112yes—
239#97—21no—
240#97—21no—
241#97—21no—
242#97D4×C1112yes—
243C4×C8—21no—
244C2×C11—22no—
245C2×C11—161no—
246C2×C11#200411yescharacteristic
247C2×C11#200911yescharacteristic
248C2×C11#201911yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—42no—
256C2×Q8—41no—
257C2×Q8—82no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—42no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265C22×C4C11×#4111yescharacteristic
266Q16—82no—
267SD16—82no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—41no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42C2×D4×C1111yescharacteristic
290C42C2×D4×C1111yescharacteristic
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C11#1014111yescharacteristic, direct product factor, Sylow
294C23—41no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23C11×#12111yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—42no—
302Q8—42no—
303Q8—82no—
304Q8—82no—
305D4—42no—
306D4—42no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4C11×#12011yescharacteristic
317C2×C4C11×#12011yescharacteristic
318C2×C4C11×#12011yescharacteristic
319C2×C4C11×#12111yescharacteristic
320C2×C4C11×#12111yescharacteristic
321C2×C4C11×#12711yescharacteristic
322C8—42no—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22C11×#39211yescharacteristic
333C22C11×#47112yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—82no—
343C4C11×#45512yes—
344C2—22no—
345C2—161no—
346C2C11×#200411yescharacteristic
347C2C11×#200911yescharacteristic
348C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
1. C11×#3229C2semidirect
4. C11×#1558C2semidirect
5. C11×#1531C2semidirect
7. C11×#1302C2semidirect
75. #10141C11direct (N × H)
120. #3229C2×C11semidirect
123. #1558C2×C11semidirect
124. #1531C2×C11semidirect
126. #1302C2×C11semidirect
293. C11#10141direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#32152
C2×C11×#4892
C11×#15582
C11×#15312
C11×#14692
C11×#13022
#1014111