Finite Group Databasebeta

← C11×#12166 #14589359

Subgroups — C11×#12166 #14589359

Order 2816.

362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3262C211yesmaximal, characteristic, complemented
2C11×#2187C211yesmaximal, characteristic, complemented
3C11×#2184C211yesmaximal, characteristic
4C11×#2045C211yesmaximal, characteristic, complemented
5C11×#1350C211yesmaximal, characteristic, complemented
6C11×#1349C211yesmaximal, characteristic, complemented
7C11×#1323C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C11×#542—21no—
10C2×C11×SD32—21no—
11C2×C11×D16—21no—
12C11×#477—21no—
13C11×#474—21no—
14C11×#468—21no—
15C11×#467C2211yescharacteristic
16C11×#466C2211yescharacteristic
17C11×#464—21no—
18C11×#463—21no—
19C11×#424C2211yescharacteristic
20C11×#418—21no—
21C2×C11×#100—21no—
22C11×#357—21no—
23C11×#357—21no—
24C11×C22⋊C16C2211yescharacteristic
25C11×C22⋊C16C2211yescharacteristic
26C11×#341C2211yescharacteristic
27C22×D4×C11—21no—
28C2×C11×Q16D411yescharacteristic
29C2×C11×SD16—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—42no—
33C2×C11×D8D411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C11×C4⋊Q8—21no—
38C11×#126—41no—
39C11×#124—21no—
40C11×#124—41no—
41C11×#123—41no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—41no—
44C11×#121—21no—
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C11×#117D411yescharacteristic
48C11×SD32—42no—
49C11×D16—42no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C11×#107—21no—
53C11×#107D411yescharacteristic
54C11×#107D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#103—21no—
58C11×#103—21no—
59C11×#102—21no—
60C11×#102—21no—
61C11×#102—41no—
62C11×#102—41no—
63C11×#100—42no—
64#12166C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—41no—
66C2×Q8×C11—21no—
67C2×Q8×C11—41no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C11×Q16—41no—
79C11×SD16—81no—
80C11×D8—22no—
81C11×D8—22no—
82C11×D8—41no—
83C11×D8—41no—
84C11×D8—41no—
85C11×M16—41no—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—21no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4D811yescharacteristic
99C11×C4⋊C4D811yescharacteristic
100C11×C22⋊C4—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—21no—
107C42×C11—41no—
108C11×C16—41no—
109C11×C16—41no—
110#3262C2×C1111yescharacteristic, complemented
111#2187C2×C1111yescharacteristic, complemented
112#2184C2×C1111yescharacteristic
113#2045C2×C1111yescharacteristic, complemented
114#1350C2×C1111yescharacteristic, complemented
115#1349C2×C1111yescharacteristic, complemented
116#1323C2×C1111yescharacteristic, complemented
117C23×C11—42no—
118C23×C11—41no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11—161no—
122C23×C11—161no—
123C23×C11AGL(1,ℤ/8)11yescharacteristic
124Q8×C11—41no—
125Q8×C11—41no—
126Q8×C11—161no—
127D4×C11—42no—
128D4×C11—41no—
129D4×C11—42no—
130D4×C11—41no—
131D4×C11—81no—
132D4×C11—81no—
133D4×C11—161no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—161no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C8×C11—21no—
145C8×C11—21no—
146C8×C11—41no—
147C8×C11—81no—
148C22×D8C22×C1111yescharacteristic
149#542—21no—
150C2×SD32—21no—
151C2×D16—21no—
152#477—21no—
153#474—21no—
154#468—21no—
155#467C22×C1111yescharacteristic
156#466C22×C1111yescharacteristic
157#464—21no—
158#463—21no—
159#424C22×C1111yescharacteristic
160#418—21no—
161C2×#100—21no—
162#357—21no—
163#357—21no—
164C22⋊C16C22×C1111yescharacteristic
165C22⋊C16C22×C1111yescharacteristic
166#341C22×C1111yescharacteristic
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—82no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—162no—
175C22×C11—162no—
176C22×C11—161no—
177C22×C11—161no—
178C22×C11#44711yescharacteristic
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11#45411yescharacteristic
186C4×C11B(4,𝔽2)11yescharacteristic
187C22×D4—21no—
188C2×Q16D4×C1111yescharacteristic
189C2×SD16—21no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—42no—
193C2×D8D4×C1111yescharacteristic
194C2×M16—21no—
195C2×M16D4×C1111yescharacteristic
196C22×C8C23×C1111yescharacteristic
197C4⋊Q8—21no—
198#126—41no—
199#124—21no—
200#124—41no—
201#123—41no—
202C22⋊Q8—21no—
203C22⋊Q8—41no—
204#121—21no—
205C4×Q8—21no—
206C4×D4—21no—
207#117D4×C1111yescharacteristic
208SD32—42no—
209D16—42no—
210C2×C16—21no—
211C2×C16—21no—
212#107—21no—
213#107D4×C1111yescharacteristic
214#107D4×C1111yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217#103—21no—
218#103—21no—
219#102—21no—
220#102—21no—
221#102—41no—
222#102—41no—
223#100—42no—
224C2×C11—41no—
225C2×C11—161no—
226C2×C11—162no—
227C2×C11#159811yescharacteristic
228C2×C11#219211yescharacteristic
229C2×C11#219311yescharacteristic
230C24—41no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4C2×D4×C1111yescharacteristic
243Q16—41no—
244SD16—81no—
245D8—22no—
246D8—22no—
247D8—41no—
248D8—41no—
249D8—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8C2×D4×C1111yescharacteristic
257C2×C8C2×D4×C1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4C11×D811yescharacteristic
264C4⋊C4C11×D811yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—21no—
272C42—41no—
273C16—41no—
274C16—41no—
275C11#1216611yescharacteristic, direct product factor, Sylow
276C23—42no—
277C23—41no—
278C23—81no—
279C23—81no—
280C23—161no—
281C23—161no—
282C23C11×AGL(1,ℤ/8)11yescharacteristic
283Q8—41no—
284Q8—41no—
285Q8—161no—
286D4—42no—
287D4—41no—
288D4—42no—
289D4—41no—
290D4—81no—
291D4—81no—
292D4—161no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—161no—
301C2×C4C11×#12011yescharacteristic
302C2×C4C2×C11×D811yescharacteristic
303C8—21no—
304C8—21no—
305C8—41no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—81no—
311C22—81no—
312C22—82no—
313C22—81no—
314C22—162no—
315C22—162no—
316C22—161no—
317C22—161no—
318C22C11×#44711yescharacteristic
319C4—21no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4C11×#45411yescharacteristic
326C4C11×B(4,𝔽2)11yescharacteristic
327C2—41no—
328C2—161no—
329C2—162no—
330C2C11×#159811yescharacteristic
331C2C11×#219211yescharacteristic
332C2C11×#219311yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC11×#2184C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#424 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3262C2semidirect
2. C11×#2187C2semidirect
4. C11×#2045C2semidirect
5. C11×#1350C2semidirect
6. C11×#1349C2semidirect
7. C11×#1323C2semidirect
64. #12166C11direct (N × H)
110. #3262C2×C11semidirect
111. #2187C2×C11semidirect
113. #2045C2×C11semidirect
114. #1350C2×C11semidirect
115. #1349C2×C11semidirect
116. #1323C2×C11semidirect
275. C11#12166direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32622
C11×#21872
C11×#21842
C11×#20452
C11×#13502
C11×#13492
C11×#13232
#1216611