Finite Group Databasebeta

← C11×#7821 #14585014

Subgroups — C11×#7821 #14585014

Order 2816.

422 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C11×#2093C211yesmaximal, characteristic
3C11×#2072C212yesmaximal, complemented
4C11×#1272C212yesmaximal, complemented
5C11×#1270C211yesmaximal, characteristic
6C2×C11×#107—21no—
7C2×C11×#103—22no—
8C2×C11×#102—21no—
9C11×#400—21no—
10C11×#393—22no—
11C11×#391C2212yes—
12C11×#390C2211yescharacteristic
13C11×#386—21no—
14C11×#385—22no—
15C11×#384C2211yescharacteristic
16C11×#340—22no—
17C11×#336C2212yes—
18C11×#336C2211yescharacteristic
19C22×Q8×C11D412yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C22×C8×C11—21no—
23C22×C8×C11—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D412yes—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C11×#107—42no—
34C11×#103—44no—
35C11×#102—42no—
36C11×#95—22no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95—22no—
40#7821C1111yesmaximal, characteristic, direct product factor, Sylow
41C24×C11—21no—
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C2×Q8×C11—42no—
45C2×Q8×C11—42no—
46C2×D4×C11—21no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11Q1612yes—
50C22×C4×C11—22no—
51C22×C4×C11—21no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11—81no—
55C22×C4×C11—82no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D412yes—
58C2×C8×C11—22no—
59C2×C8×C11—41no—
60C2×C8×C11—42no—
61C2×C8×C11—42no—
62C2×C8×C11—42no—
63C2×C8×C11—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—81no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—82no—
74C11×C22⋊C4—81no—
75C42×C11—41no—
76#2804C2×C1111yescharacteristic
77#2093C2×C1111yescharacteristic
78#2072C2×C1112yescomplemented
79#1272C2×C1112yescomplemented
80#1270C2×C1111yescharacteristic
81C23×C11—22no—
82C23×C11—42no—
83C23×C11—41no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11#12011yescharacteristic
87Q8×C11—44no—
88Q8×C11—82no—
89D4×C11—42no—
90D4×C11—81no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—84no—
104C2×C4×C11—82no—
105C2×C4×C11—81no—
106C2×C4×C11C2×Q1611yescharacteristic
107C2×C4×C11#13512yes—
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×C4×C11#13711yescharacteristic
110C8×C11—42no—
111C8×C11—82no—
112C2×#107—21no—
113C2×#103—22no—
114C2×#102—21no—
115#400—21no—
116#393—22no—
117#391C22×C1112yes—
118#390C22×C1111yescharacteristic
119#386—21no—
120#385—22no—
121#384C22×C1111yescharacteristic
122#340—22no—
123#336C22×C1112yes—
124#336C22×C1111yescharacteristic
125C22×C11—42no—
126C22×C11—44no—
127C22×C11—82no—
128C22×C11—81no—
129C22×C11—81no—
130C22×C11#44912yes—
131C22×C11#45111yescharacteristic
132C22×C11#45311yescharacteristic
133C22×C11#45512yes—
134C22×C11#45811yescharacteristic
135C4×C11—22no—
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—82no—
140C4×C11—81no—
141C4×C11—82no—
142C4×C11—161no—
143C22×Q8D4×C1112yes—
144C22×D4D4×C1111yescharacteristic
145C23×C4—21no—
146C22×C8—21no—
147C22×C8—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4D4×C1112yes—
152C2×C4⋊C4D4×C1111yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—21no—
156C2×C42C23×C1111yescharacteristic
157#107—42no—
158#103—44no—
159#102—42no—
160#95—22no—
161#95—21no—
162#95—22no—
163#95—22no—
164C2×C11—82no—
165C2×C11#161212yes—
166C2×C11#161411yescharacteristic
167C2×C11#162011yescharacteristic
168C2×C11#164412yes—
169C2×C11#165911yescharacteristic
170C24—21no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4C11×Q1612yes—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4—81no—
184C22×C4—82no—
185C22×C4C2×D4×C1111yescharacteristic
186C22×C4C2×D4×C1112yes—
187C2×C8—22no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—82no—
203C22⋊C4—81no—
204C42—41no—
205C11#782111yescharacteristic, direct product factor, Sylow
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23C11×#12011yescharacteristic
212Q8—44no—
213Q8—82no—
214D4—42no—
215D4—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—82no—
230C2×C4—81no—
231C2×C4C2×C11×Q1611yescharacteristic
232C2×C4C11×#13512yes—
233C2×C4C11×AGL(1,ℤ/8)12yes—
234C2×C4C11×#13711yescharacteristic
235C8—42no—
236C8—82no—
237C22—42no—
238C22—44no—
239C22—82no—
240C22—81no—
241C22—81no—
242C22C11×#44912yes—
243C22C11×#45111yescharacteristic
244C22C11×#45311yescharacteristic
245C22C11×#45512yes—
246C22C11×#45811yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—82no—
252C4—81no—
253C4—82no—
254C4—161no—
255C2—82no—
256C2C11×#161212yes—
257C2C11×#161411yescharacteristic
258C2C11×#162011yescharacteristic
259C2C11×#164412yes—
260C2C11×#165911yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
3. C11×#2072C2semidirect
4. C11×#1272C2semidirect
40. #7821C11direct (N × H)
78. #2072C2×C11semidirect
79. #1272C2×C11semidirect
205. C11#7821direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28042
C11×#20932
C11×#20722
C11×#12722
C11×#12702
#782111