Finite Group Databasebeta

← C11×#7831 #14585024

Subgroups — C11×#7831 #14585024

Order 2816.

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

normal subgroups only

This group has 350 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×#2809C211yesmaximal, characteristic
2C11×#2100C212yesmaximal
3C11×#2095C211yesmaximal, characteristic
4C11×#1272C211yesmaximal, characteristic
5C11×#1271C212yesmaximal
6C2×C11×#107—21no—
7C2×C11×#103—21no—
8C11×#400—21no—
9C11×#398—22no—
10C11×#391—21no—
11C11×#391C2211yescharacteristic
12C11×#389C2212yes—
13C11×#387—22no—
14C11×#384C2211yescharacteristic
15C11×#340—22no—
16C11×#340—22no—
17C11×#336C2211yescharacteristic
18C11×#336C2212yes—
19C22×Q8×C11D411yescharacteristic
20C22×C8×C11—21no—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D412yes—
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C11×#107—42no—
33C11×#103—42no—
34C11×#95—21no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95—22no—
38C11×#95—22no—
39#7831C1111yesmaximal, characteristic, direct product factor, Sylow
40C2×Q8×C11—21no—
41C2×Q8×C11—41no—
42C2×Q8×C11—41no—
43C2×Q8×C11Q1612yes—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C2×C8×C11—22no—
52C2×C8×C11—41no—
53C2×C8×C11—42no—
54C2×C8×C11—42no—
55C2×C8×C11—42no—
56C2×C8×C11—41no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—44no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—81no—
67C11×C4⋊C4—81no—
68C42×C11—41no—
69C42×C11—81no—
70#2809C2×C1111yescharacteristic
71#2100C2×C1112yes—
72#2095C2×C1111yescharacteristic
73#1272C2×C1111yescharacteristic
74#1271C2×C1112yes—
75C23×C11#12011yescharacteristic
76Q8×C11—42no—
77Q8×C11—81no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—81no—
94C2×C4×C11—82no—
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13512yes—
97C2×C4×C11#13711yescharacteristic
98C2×C4×C11#13712yes—
99C8×C11—42no—
100C8×C11—82no—
101C2×#107—21no—
102C2×#103—21no—
103#400—21no—
104#398—22no—
105#391—21no—
106#391C22×C1111yescharacteristic
107#389C22×C1112yes—
108#387—22no—
109#384C22×C1111yescharacteristic
110#340—22no—
111#340—22no—
112#336C22×C1111yescharacteristic
113#336C22×C1112yes—
114C22×C11#45111yescharacteristic
115C22×C11#45212yes—
116C22×C11#45311yescharacteristic
117C22×C11#45412yes—
118C22×C11#45811yescharacteristic
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—22no—
122C4×C11—22no—
123C4×C11—42no—
124C4×C11—82no—
125C4×C11—82no—
126C4×C11—81no—
127C4×C11—161no—
128C22×Q8D4×C1111yescharacteristic
129C22×C8—21no—
130C22×C8—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4D4×C1112yes—
137C2×C4⋊C4D4×C1112yes—
138C2×C4⋊C4D4×C1111yescharacteristic
139C2×C42—21no—
140C2×C42C23×C1111yescharacteristic
141#107—42no—
142#103—42no—
143#95—21no—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148C2×C11#161411yescharacteristic
149C2×C11#161512yes—
150C2×C11#163411yescharacteristic
151C2×C11#163612yes—
152C2×C11#165711yescharacteristic
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8C11×Q1612yes—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—41no—
162C22×C4C2×D4×C1111yescharacteristic
163C22×C4C2×D4×C1112yes—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C42—41no—
182C42—81no—
183C11#783111yescharacteristic, direct product factor, Sylow
184C23C11×#12011yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—82no—
204C2×C4C2×C11×Q1611yescharacteristic
205C2×C4C11×#13512yes—
206C2×C4C11×#13711yescharacteristic
207C2×C4C11×#13712yes—
208C8—42no—
209C8—82no—
210C22C11×#45111yescharacteristic
211C22C11×#45212yes—
212C22C11×#45311yescharacteristic
213C22C11×#45412yes—
214C22C11×#45811yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—82no—
222C4—81no—
223C4—161no—
224C2C11×#161411yescharacteristic
225C2C11×#161512yes—
226C2C11×#163411yescharacteristic
227C2C11×#163612yes—
228C2C11×#165711yescharacteristic
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
39. #7831C11direct (N × H)
183. C11#7831direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28092
C11×#21002
C11×#20952
C11×#12722
C11×#12712
#783111