Finite Group Databasebeta

← C11×#10133 #14587326

Subgroups — C11×#10133 #14587326

Order 2816.

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

normal subgroups only

This group has 536 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×#3230C211yesmaximal, characteristic, complemented
2C11×#3215C211yesmaximal, characteristic
3C2×C11×#497C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1531C211yesmaximal, characteristic, complemented
6C11×#1469C211yesmaximal, characteristic
7C11×#1302C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C22×C11×SD16—21no—
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#124C2211yescharacteristic
13C11×#500—21no—
14C11×#497—22no—
15C11×#497—21no—
16C11×#497—22no—
17C11×#489—21no—
18C11×#487—21no—
19C11×#484—22no—
20C11×#477—22no—
21C11×#464—22no—
22C11×#451—21no—
23C11×#450—21no—
24C11×#432C2211yescharacteristic
25C11×#432C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#332—22no—
29C11×#330—22no—
30C11×#323—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×C11×Q16—24no—
35C2×C11×Q16—22no—
36C2×C11×Q16—44no—
37C2×C11×SD16—24no—
38C2×C11×SD16—22no—
39C2×C11×SD16—44no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D411yescharacteristic
45C11×C4⋊Q8D411yescharacteristic
46C11×C4⋊Q8D412yes—
47C11×#125—21no—
48C11×#124—21no—
49C11×#124—21no—
50C11×#124—21no—
51C11×#124—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C11×#117—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#107—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—22no—
67C11×#103—24no—
68C11×#102—22no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C11×#97—21no—
73C11×#97—21no—
74C11×#97—21no—
75C11×#97D412yes—
76C4×C8×C11—21no—
77#10133C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11—42no—
87C2×Q8×C11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C11×Q16—48no—
97C11×Q16—82no—
98C11×SD16—48no—
99C11×SD16—82no—
100C2×C8×C11—24no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125#3230C2×C1111yescharacteristic, complemented
126#3215C2×C1111yescharacteristic
127C2×#497C2×C1111yescharacteristic
128#1556C2×C1111yescharacteristic, complemented
129#1531C2×C1111yescharacteristic, complemented
130#1469C2×C1111yescharacteristic
131#1302C2×C1111yescharacteristic, complemented
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—82no—
144D4×C11—42no—
145D4×C11—42no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C8×C11—24no—
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—81no—
165C22×Q16—21no—
166C22×SD16—21no—
167#533C22×C1111yescharacteristic
168C2×C4⋊Q8C22×C1111yescharacteristic
169C2×#124C22×C1111yescharacteristic
170#500—21no—
171#497—22no—
172#497—21no—
173#497—22no—
174#489—21no—
175#487—21no—
176#484—22no—
177#477—22no—
178#464—22no—
179#451—21no—
180#450—21no—
181#432C22×C1111yescharacteristic
182#432C22×C1111yescharacteristic
183#431C22×C1111yescharacteristic
184C2×#97C22×C1111yescharacteristic
185#332—22no—
186#330—22no—
187#323—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—162no—
194C22×C11#39211yescharacteristic
195C22×C11#47312yes—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11#45312yes—
206C22×Q8—21no—
207C22×Q8D4×C1111yescharacteristic
208C22×D4D4×C1111yescharacteristic
209C2×Q16—24no—
210C2×Q16—22no—
211C2×Q16—44no—
212C2×SD16—24no—
213C2×SD16—22no—
214C2×SD16—44no—
215C22×C8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8D4×C1112yes—
220C4⋊Q8D4×C1111yescharacteristic
221C4⋊Q8D4×C1111yescharacteristic
222#125—21no—
223#124—21no—
224#124—21no—
225#124—21no—
226#124—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42C23×C1111yescharacteristic
237#107—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1112yes—
241#103—22no—
242#103—24no—
243#102—22no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8D4×C1112yes—
247#97—21no—
248#97—21no—
249#97—21no—
250#97D4×C1112yes—
251C4×C8—21no—
252C2×C11—22no—
253C2×C11—161no—
254C2×C11#200211yescharacteristic
255C2×C11#200911yescharacteristic
256C2×C11#202011yescharacteristic
257C24—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—41no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—42no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C11×#4111yescharacteristic
275Q16—48no—
276Q16—82no—
277SD16—48no—
278SD16—82no—
279C2×C8—24no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42—41no—
300C42C2×D4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C2×D4×C1111yescharacteristic
303C42C2×D4×C1111yescharacteristic
304C11#1013311yescharacteristic, direct product factor, Sylow
305C23—41no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23C11×#12111yescharacteristic
310Q8—42no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—42no—
315Q8—42no—
316Q8—82no—
317D4—42no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—81no—
328C2×C4C11×#12011yescharacteristic
329C2×C4C11×#12011yescharacteristic
330C2×C4C11×#12011yescharacteristic
331C2×C4C11×#12111yescharacteristic
332C2×C4C11×#12111yescharacteristic
333C2×C4C11×#12711yescharacteristic
334C8—24no—
335C8—42no—
336C8—42no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—162no—
344C22C11×#39211yescharacteristic
345C22C11×#47312yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4C11×#45312yes—
356C2—22no—
357C2—161no—
358C2C11×#200211yescharacteristic
359C2C11×#200911yescharacteristic
360C2C11×#202011yescharacteristic
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×#3230C2semidirect
4. C11×#1556C2semidirect
5. C11×#1531C2semidirect
7. C11×#1302C2semidirect
77. #10133C11direct (N × H)
125. #3230C2×C11semidirect
128. #1556C2×C11semidirect
129. #1531C2×C11semidirect
131. #1302C2×C11semidirect
304. C11#10133direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#32152
C2×C11×#4972
C11×#15562
C11×#15312
C11×#14692
C11×#13022
#1013311