Finite Group Databasebeta

← C11×#10101 #14587294

Subgroups — C11×#10101 #14587294

Order 2816.

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

normal subgroups only

This group has 474 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×#3165C211yesmaximal, characteristic
3C11×#2660C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic
5C11×#1528C211yesmaximal, characteristic
6C11×#1506C211yesmaximal, characteristic
7C11×#1300C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—21no—
12C11×#501—22no—
13C11×#500—21no—
14C11×#498—21no—
15C11×#491—21no—
16C11×#484—21no—
17C11×#483—21no—
18C11×#479—22no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#428—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#398—22no—
24C11×#395—22no—
25C11×#384—21no—
26C11×#382—21no—
27C11×#376C2211yescharacteristic
28C11×#332—22no—
29C11×#330—22no—
30C11×#328—22no—
31C22×Q8×C11—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
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—24no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—24no—
59C11×#107—22no—
60C11×#106—24no—
61C11×#106—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#103—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×#97—21no—
69C11×#97—21no—
70C11×#97D412yes—
71C4×C8×C11—21no—
72C11×#95—24no—
73C11×#95—21no—
74C11×#95D412yes—
75#10101C1111yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C11×M16—24no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
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—21no—
100C11×C4⋊C4—22no—
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×C4⋊C4—84no—
111C11×C22⋊C4—41no—
112C42×C11—24no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118#3236C2×C1111yescharacteristic
119#3165C2×C1111yescharacteristic
120#2660C2×C1111yescharacteristic
121#1556C2×C1111yescharacteristic
122#1528C2×C1111yescharacteristic
123#1506C2×C1111yescharacteristic
124#1300C2×C1111yescharacteristic
125C23×C11#12011yescharacteristic
126Q8×C11—42no—
127Q8×C11—81no—
128Q8×C11—82no—
129Q8×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—44no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C8×C11—24no—
151C8×C11—42no—
152C8×C11—81no—
153#533C22×C1111yescharacteristic
154C2×C4⋊Q8C22×C1111yescharacteristic
155C2×#125C22×C1111yescharacteristic
156#501—21no—
157#501—22no—
158#500—21no—
159#498—21no—
160#491—21no—
161#484—21no—
162#483—21no—
163#479—22no—
164#432C22×C1111yescharacteristic
165#432C22×C1111yescharacteristic
166#428—22no—
167C4×M16C22×C1111yescharacteristic
168#398—22no—
169#395—22no—
170#384—21no—
171#382—21no—
172#376C22×C1111yescharacteristic
173#332—22no—
174#330—22no—
175#328—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#45612yes—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—44no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11#45612yes—
192C22×Q8—21no—
193C2×M16—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8D4×C1111yescharacteristic
199C4⋊Q8D4×C1111yescharacteristic
200#125—21no—
201#125—21no—
202#125—21no—
203#125—21no—
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4D4×C1111yescharacteristic
215C2×C4⋊C4D4×C1111yescharacteristic
216C2×C4⋊C4D4×C1112yes—
217C2×C42—21no—
218C2×C42C23×C1111yescharacteristic
219#107—24no—
220#107—22no—
221#106—24no—
222#106—22no—
223C4⋊C8—21no—
224C4⋊C8D4×C1112yes—
225#103—22no—
226#103—22no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229#97—21no—
230#97—21no—
231#97D4×C1112yes—
232C4×C8—21no—
233#95—24no—
234#95—21no—
235#95D4×C1112yes—
236C2×C11—22no—
237C2×C11#200511yescharacteristic
238C2×C11#200511yescharacteristic
239C2×C11#200811yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—82no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1111yescharacteristic
252M16—24no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—84no—
275C22⋊C4—41no—
276C42—24no—
277C42—41no—
278C42C2×D4×C1111yescharacteristic
279C42C2×D4×C1111yescharacteristic
280C42C2×D4×C1111yescharacteristic
281C42C11×#4111yescharacteristic
282C11#1010111yescharacteristic, direct product factor, Sylow
283C23C11×#12011yescharacteristic
284Q8—42no—
285Q8—81no—
286Q8—82no—
287Q8—82no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4C11×#12011yescharacteristic
303C2×C4C11×#12011yescharacteristic
304C2×C4C11×#12111yescharacteristic
305C2×C4C11×#12111yescharacteristic
306C2×C4C11×#12111yescharacteristic
307C2×C4C11×#12711yescharacteristic
308C8—24no—
309C8—42no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22C11×#39211yescharacteristic
314C22C11×#45612yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—81no—
322C4—81no—
323C4—82no—
324C4—81no—
325C4—81no—
326C4C11×#45612yes—
327C2—22no—
328C2C11×#200511yescharacteristic
329C2C11×#200511yescharacteristic
330C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
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
75. #10101C11direct (N × H)
282. C11#10101direct (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×#31652
C11×#26602
C11×#15562
C11×#15282
C11×#15062
C11×#13002
#1010111