Finite Group Databasebeta

← C11×#10626 #14587819

Subgroups — C11×#10626 #14587819

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#1984C211yesmaximal, characteristic
2C11×#1834C211yesmaximal, characteristic
3C11×#1803C211yesmaximal, characteristic
4C11×#1803C211yesmaximal, characteristic
5C11×#1296C211yesmaximal, characteristic
6C11×#1296C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C2×C11×#103—21no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C11×#340—21no—
18C11×#340—21no—
19C11×#340—21no—
20C11×#340—21no—
21C11×#336—21no—
22C11×#336—21no—
23C22×Q8×C11D411yescharacteristic
24C22×C8×C11—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—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×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×#103—42no—
50C11×#103—42no—
51C4×C8×C11—21no—
52C4×C8×C11—21no—
53#10626C1111yesmaximal, characteristic, direct product factor, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—21no—
56C2×Q8×C11—21no—
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11SD1612yes—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
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—81no—
95C11×C4⋊C4—81no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102#1984C2×C1111yescharacteristic
103#1834C2×C1111yescharacteristic
104#1803C2×C1111yescharacteristic
105#1803C2×C1111yescharacteristic
106#1296C2×C1111yescharacteristic
107#1296C2×C1111yescharacteristic
108#1277C2×C1111yescharacteristic
109C23×C11#12111yescharacteristic
110Q8×C11—22no—
111Q8×C11—22no—
112Q8×C11—41no—
113Q8×C11—41no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12611yescharacteristic
133C2×C4×C11#12611yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C8×C11—41no—
143C8×C11—41no—
144C8×C11—81no—
145C8×C11—81no—
146C8×C11—81no—
147C2×C4×Q8C22×C1111yescharacteristic
148C2×C4⋊C8C22×C1111yescharacteristic
149C2×C4⋊C8C22×C1111yescharacteristic
150C2×C4⋊C8C22×C1111yescharacteristic
151C2×#103—21no—
152C2×#103—21no—
153C2×C4×C8C22×C1111yescharacteristic
154#384C22×C1111yescharacteristic
155#384C22×C1111yescharacteristic
156#340—21no—
157#340—21no—
158#340—21no—
159#340—21no—
160#336—21no—
161#336—21no—
162C22×C11#39711yescharacteristic
163C22×C11#46411yescharacteristic
164C22×C11#46411yescharacteristic
165C22×C11#46511yescharacteristic
166C22×C11#46811yescharacteristic
167C22×C11#47211yescharacteristic
168C22×C11#47311yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—42no—
172C4×C11—81no—
173C4×C11—161no—
174C4×C11—161no—
175C4×C11#48111yescharacteristic
176C4×C11#48211yescharacteristic
177C4×C11#48311yescharacteristic
178C4×C11#48511yescharacteristic
179C4×C11#48511yescharacteristic
180C4×C11#48511yescharacteristic
181C4×C11#48811yescharacteristic
182C4×C11#49111yescharacteristic
183C22×Q8D4×C1111yescharacteristic
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8D4×C1111yescharacteristic
188C22×C8D4×C1111yescharacteristic
189C4×Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4D4×C1111yescharacteristic
201C2×C42—21no—
202C2×C42C23×C1111yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209#103—42no—
210#103—42no—
211C4×C8—21no—
212C4×C8—21no—
213C2×C11#167811yescharacteristic
214C2×C11#168011yescharacteristic
215C2×C11#169811yescharacteristic
216C2×C11#170011yescharacteristic
217C2×C11#207411yescharacteristic
218C2×C11#207711yescharacteristic
219C2×C11#207811yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8C11×SD1612yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C2×D4×C1111yescharacteristic
232C22×C4C11×#4111yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C42—41no—
263C42—41no—
264C42C11×#4111yescharacteristic
265C42C11×#4111yescharacteristic
266C42C11×#4111yescharacteristic
267C42C11×#4111yescharacteristic
268C11#1062611yescharacteristic, direct product factor, Sylow
269C23C11×#12111yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4C11×#12311yescharacteristic
289C2×C4C11×#12311yescharacteristic
290C2×C4C11×#12311yescharacteristic
291C2×C4C11×#12411yescharacteristic
292C2×C4C11×#12611yescharacteristic
293C2×C4C11×#12611yescharacteristic
294C2×C4C2×C11×SD1611yescharacteristic
295C2×C4C11×#13511yescharacteristic
296C2×C4C11×#13511yescharacteristic
297C2×C4C11×#13511yescharacteristic
298C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
299C2×C4C11×#13711yescharacteristic
300C2×C4C11×#13711yescharacteristic
301C2×C4C11×#13711yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—81no—
307C22C11×#39711yescharacteristic
308C22C11×#46411yescharacteristic
309C22C11×#46411yescharacteristic
310C22C11×#46511yescharacteristic
311C22C11×#46811yescharacteristic
312C22C11×#47211yescharacteristic
313C22C11×#47311yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—161no—
320C4C11×#48111yescharacteristic
321C4C11×#48211yescharacteristic
322C4C11×#48311yescharacteristic
323C4C11×#48511yescharacteristic
324C4C11×#48511yescharacteristic
325C4C11×#48511yescharacteristic
326C4C11×#48811yescharacteristic
327C4C11×#49111yescharacteristic
328C2C11×#167811yescharacteristic
329C2C11×#168011yescharacteristic
330C2C11×#169811yescharacteristic
331C2C11×#170011yescharacteristic
332C2C11×#207411yescharacteristic
333C2C11×#207711yescharacteristic
334C2C11×#207811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
53. #10626C11direct (N × H)
268. C11#10626direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#19842
C11×#18342
C11×#18032
C11×#12962
C11×#12772
#1062611