Finite Group Databasebeta

← C11×#7833 #14585026

Subgroups — C11×#7833 #14585026

Order 2816.

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

normal subgroups only

This group has 438 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×#2095C212yesmaximal, complemented
3C11×#2094C211yesmaximal, characteristic
4C11×#1272C212yesmaximal, complemented
5C11×#1270C211yesmaximal, characteristic
6C2×C11×#107—22no—
7C2×C11×#106—21no—
8C2×C11×#103—22no—
9C2×C11×#102—21no—
10C11×#400—21no—
11C11×#393—22no—
12C11×#391C2212yes—
13C11×#390C2211yescharacteristic
14C11×#386—21no—
15C11×#385—22no—
16C11×#384C2211yescharacteristic
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—21no—
25C2×C11×C4⋊C4—22no—
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—44no—
34C11×#106—42no—
35C11×#103—44no—
36C11×#102—42no—
37C11×#95—22no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—22no—
41#7833C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11—21no—
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11—42no—
46C2×Q8×C11—42no—
47C2×D4×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11Q1612yes—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—41no—
55C22×C4×C11—82no—
56C22×C4×C11—81no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D412yes—
59C2×C8×C11—22no—
60C2×C8×C11—24no—
61C2×C8×C11—41no—
62C2×C8×C11—42no—
63C2×C8×C11—42no—
64C2×C8×C11—41no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—81no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—82no—
75C11×C22⋊C4—81no—
76C42×C11—41no—
77#2804C2×C1111yescharacteristic
78#2095C2×C1112yescomplemented
79#2094C2×C1111yescharacteristic
80#1272C2×C1112yescomplemented
81#1270C2×C1111yescharacteristic
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11—41no—
87C23×C11#12011yescharacteristic
88Q8×C11—44no—
89Q8×C11—82no—
90D4×C11—42no—
91D4×C11—81no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—84no—
105C2×C4×C11—81no—
106C2×C4×C11—82no—
107C2×C4×C11C2×Q1611yescharacteristic
108C2×C4×C11#13512yes—
109C2×C4×C11#13711yescharacteristic
110C2×C4×C11#13712yes—
111C8×C11—42no—
112C8×C11—44no—
113C2×#107—22no—
114C2×#106—21no—
115C2×#103—22no—
116C2×#102—21no—
117#400—21no—
118#393—22no—
119#391C22×C1112yes—
120#390C22×C1111yescharacteristic
121#386—21no—
122#385—22no—
123#384C22×C1111yescharacteristic
124#336C22×C1111yescharacteristic
125#336C22×C1112yes—
126C22×C11—42no—
127C22×C11—44no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#45111yescharacteristic
132C22×C11#45212yes—
133C22×C11#45311yescharacteristic
134C22×C11#45312yes—
135C22×C11#45811yescharacteristic
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11—82no—
143C4×C11—161no—
144C22×Q8D4×C1112yes—
145C22×D4D4×C1111yescharacteristic
146C23×C4—21no—
147C22×C8—21no—
148C22×C8—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4D4×C1112yes—
153C2×C4⋊C4D4×C1111yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C42C23×C1111yescharacteristic
158#107—44no—
159#106—42no—
160#103—44no—
161#102—42no—
162#95—22no—
163#95—21no—
164#95—22no—
165#95—22no—
166C2×C11—82no—
167C2×C11#161411yescharacteristic
168C2×C11#161812yes—
169C2×C11#163011yescharacteristic
170C2×C11#163212yes—
171C2×C11#165511yescharacteristic
172C24—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4C11×Q1612yes—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—41no—
185C22×C4—82no—
186C22×C4—81no—
187C22×C4C2×D4×C1111yescharacteristic
188C22×C4C2×D4×C1112yes—
189C2×C8—22no—
190C2×C8—24no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—81no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—82no—
205C22⋊C4—81no—
206C42—41no—
207C11#783311yescharacteristic, direct product factor, Sylow
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23C11×#12011yescharacteristic
214Q8—44no—
215Q8—82no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4C2×C11×Q1611yescharacteristic
234C2×C4C11×#13512yes—
235C2×C4C11×#13711yescharacteristic
236C2×C4C11×#13712yes—
237C8—42no—
238C8—44no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C11×#45111yescharacteristic
245C22C11×#45212yes—
246C22C11×#45311yescharacteristic
247C22C11×#45312yes—
248C22C11×#45811yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C11×#161411yescharacteristic
259C2C11×#161812yes—
260C2C11×#163011yescharacteristic
261C2C11×#163212yes—
262C2C11×#165511yescharacteristic
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
2. C11×#2095C2semidirect
4. C11×#1272C2semidirect
41. #7833C11direct (N × H)
78. #2095C2×C11semidirect
80. #1272C2×C11semidirect
207. C11#7833direct (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×#20952
C11×#20942
C11×#12722
C11×#12702
#783311