Finite Group Databasebeta

← C11×#7836 #14585029

Subgroups — C11×#7836 #14585029

Order 2816.

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

normal subgroups only

This group has 378 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×#2806C211yesmaximal, characteristic
2C11×#2100C211yesmaximal, characteristic
3C11×#2095C211yesmaximal, characteristic
4C11×#2095C211yesmaximal, characteristic
5C11×#1272C211yesmaximal, characteristic
6C11×#1272C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×#107—21no—
10C2×C11×#103—21no—
11C2×C11×#103—21no—
12C11×#398—21no—
13C11×#398—21no—
14C11×#395—21no—
15C11×#391—21no—
16C11×#391C2211yescharacteristic
17C11×#391C2211yescharacteristic
18C11×#389—21no—
19C11×#389C2211yescharacteristic
20C11×#387—21no—
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46C11×#107—42no—
47C11×#107—42no—
48C11×#103—42no—
49C11×#103—42no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58#7836C1111yesmaximal, characteristic, direct product factor, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11Q1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4—81no—
101C11×C4⋊C4Q1612yes—
102C42×C11—41no—
103C42×C11—81no—
104#2806C2×C1111yescharacteristic
105#2100C2×C1111yescharacteristic
106#2095C2×C1111yescharacteristic
107#2095C2×C1111yescharacteristic
108#1272C2×C1111yescharacteristic
109#1272C2×C1111yescharacteristic
110#1271C2×C1111yescharacteristic
111C23×C11#12011yescharacteristic
112Q8×C11—42no—
113Q8×C11—42no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
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×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11C2×Q1611yescharacteristic
144C2×C4×C11C2×Q1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C8×C11—42no—
150C8×C11—42no—
151C8×C11—81no—
152C2×#107—21no—
153C2×#107—21no—
154C2×#103—21no—
155C2×#103—21no—
156#398—21no—
157#398—21no—
158#395—21no—
159#391—21no—
160#391C22×C1111yescharacteristic
161#391C22×C1111yescharacteristic
162#389—21no—
163#389C22×C1111yescharacteristic
164#387—21no—
165#384C22×C1111yescharacteristic
166#340—21no—
167#340—21no—
168#336C22×C1111yescharacteristic
169#336C22×C1111yescharacteristic
170#336C22×C1111yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45111yescharacteristic
173C22×C11#45211yescharacteristic
174C22×C11#45311yescharacteristic
175C22×C11#45311yescharacteristic
176C22×C11#45411yescharacteristic
177C22×C11#45811yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—42no—
185C4×C11—42no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—161no—
191C22×Q8D4×C1111yescharacteristic
192C22×Q8D4×C1111yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4D4×C1111yescharacteristic
205C2×C4⋊C4D4×C1111yescharacteristic
206C2×C4⋊C4D4×C1111yescharacteristic
207C2×C4⋊C4D4×C1111yescharacteristic
208C2×C42—21no—
209C2×C42C23×C1111yescharacteristic
210#107—42no—
211#107—42no—
212#103—42no—
213#103—42no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C2×C11#161411yescharacteristic
223C2×C11#161711yescharacteristic
224C2×C11#161811yescharacteristic
225C2×C11#163211yescharacteristic
226C2×C11#163311yescharacteristic
227C2×C11#163611yescharacteristic
228C2×C11#165611yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8C11×Q1612yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4C2×D4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4C11×Q1612yes—
272C42—41no—
273C42—81no—
274C11#783611yescharacteristic, direct product factor, Sylow
275C23C11×#12011yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
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×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×C11×Q1611yescharacteristic
308C2×C4C2×C11×Q1611yescharacteristic
309C2×C4C11×#13511yescharacteristic
310C2×C4C11×#13711yescharacteristic
311C2×C4C11×#13711yescharacteristic
312C2×C4C11×#13711yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C22C11×#45111yescharacteristic
317C22C11×#45111yescharacteristic
318C22C11×#45211yescharacteristic
319C22C11×#45311yescharacteristic
320C22C11×#45311yescharacteristic
321C22C11×#45411yescharacteristic
322C22C11×#45811yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—42no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—81no—
335C4—161no—
336C2C11×#161411yescharacteristic
337C2C11×#161711yescharacteristic
338C2C11×#161811yescharacteristic
339C2C11×#163211yescharacteristic
340C2C11×#163311yescharacteristic
341C2C11×#163611yescharacteristic
342C2C11×#165611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
58. #7836C11direct (N × H)
274. C11#7836direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28062
C11×#21002
C11×#20952
C11×#12722
C11×#12712
#783611