Finite Group Databasebeta

← #14658837

Subgroups — #14658837

Order 2816.

410 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 147 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
1#13069578C212yesmaximal
2#13068776C211yesmaximal, characteristic
3#13068743C212yesmaximal
4C11⋊#1273C211yesmaximal, characteristic
5C11×#1956C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#103—22no—
8C2×C4×C8×C11C2211yescharacteristic
9C11×#384C2211yescharacteristic
10C2×#66882—22no—
11#10622548C2212yes—
12C2×C4×C11⋊C8C2212yes—
13#10622167—24no—
14#10622167—24no—
15C22×Q8×C11—21no—
16C22×C8×C11D412yes—
17C11×C4⋊Q8—22no—
18C11×C4⋊Q8—21no—
19C11×C4⋊Q8Q812yes—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—22no—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—22no—
27C22×C11⋊C8D414yes—
28C11×#103—44no—
29C4×C8×C11—22no—
30#66882—44no—
31C4×C11⋊C8—22no—
32C4×C11⋊C8—22no—
33#10676—111nomaximal, Sylow
34C2×Q8×C11—22no—
35C2×Q8×C11—41no—
36C2×Q8×C11—42no—
37C2×Q8×C11—42no—
38C22×C4×C11—41no—
39C22×C4×C11—41no—
40C22×C4×C11C2×D411yescharacteristic
41C22×C4×C11C2×D412yes—
42C22×Dic11—42no—
43C2×C8×C11—22no—
44C2×C8×C11—22no—
45C2×C8×C11D814yes—
46C11×C4⋊C4—24no—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—44no—
50C42×C11C2×Q811yescharacteristic
51C42×C11#4111yescharacteristic
52C42×C11#4112yes—
53C4⋊Dic11—44no—
54C4⋊Dic11—44no—
55C4⋊Dic11—44no—
56C2×C11⋊C8—24no—
57C2×C11⋊C8—24no—
58C2×C11⋊C8—24no—
59#1990—112no—
60#1956D1111yescharacteristic
61#1845—111no—
62#1834—112no—
63#1273—111no—
64C23×C11#12711yescharacteristic
65Q8×C11—44no—
66Q8×C11—82no—
67C2×C4×C11—42no—
68C2×C4×C11—81no—
69C2×C4×C11—81no—
70C2×C4×C11—81no—
71C2×C4×C11—82no—
72C2×C4×C11C22⋊Q812yes—
73C2×C4×C11C22⋊Q811yescharacteristic
74C2×C4×C11#12312yes—
75C2×C4×C11#12311yescharacteristic
76C2×C4×C11C2×D812yes—
77C2×C4×C11#13514yes—
78C2×C4×C11#13714yes—
79C2×C4×C11#13712yes—
80C2×Dic11—82no—
81C2×Dic11—82no—
82C2×Dic11—82no—
83C8×C11—24no—
84C11⋊C8—44no—
85C2×C4⋊Q8C2×D1111yescharacteristic
86C2×#107—222no—
87C2×#103—22no—
88C2×C4×C8—112no—
89C2×C4×C8C2×D1111yescharacteristic
90#384—112no—
91#384C2×D1111yescharacteristic
92#340—224no—
93#340—224no—
94C22×C11#39911yescharacteristic
95C22×C11#49311yescharacteristic
96C22×C11#49512yes—
97C22×C11#49712yes—
98C22×C11#49711yescharacteristic
99C4×C11—82no—
100C4×C11—161no—
101C4×C11#47412yes—
102C4×C11#47914yes—
103C4×C11#48012yes—
104C4×C11#48514yes—
105Dic11—162no—
106C22×Q8—21no—
107C22×C8—114no—
108C22×C8C22⋊D1112yes—
109C4⋊Q8—21no—
110C4⋊Q8—22no—
111C4⋊Q8Dic2212yes—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—222no—
116C2×C4⋊C4—222no—
117C2×C4⋊C4—222no—
118C2×C42C22×D1111yescharacteristic
119#107—444no—
120#103—44no—
121C4×C8—22no—
122C4×C8—222no—
123C4×C8—222no—
124C2×C11#170911yescharacteristic
125C2×C11#171812yes—
126C2×C11#172211yescharacteristic
127C2×C11#209311yescharacteristic
128C2×C11#209712yes—
129C2×Q8—22no—
130C2×Q8—41no—
131C2×Q8—42no—
132C2×Q8—42no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—442no—
136C22×C4D4×D1112yes—
137C22×C4C2×C22⋊D1111yescharacteristic
138C2×C8—22no—
139C2×C8—22no—
140C2×C8—224no—
141C2×C8—224no—
142C2×C8—224no—
143C2×C8#432314yes—
144C4⋊C4—24no—
145C4⋊C4—42no—
146C4⋊C4—44no—
147C4⋊C4—42no—
148C4⋊C4—444no—
149C4⋊C4—444no—
150C4⋊C4—444no—
151C42C2×Dic2211yescharacteristic
152C42#433911yescharacteristic
153C42#434112yes—
154C11#1067611yescharacteristic, complemented, Sylow
155C23#6699311yescharacteristic
156Q8—44no—
157Q8—82no—
158C2×C4—42no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—82no—
162C2×C4—81no—
163C2×C4—882no—
164C2×C4—882no—
165C2×C4—882no—
166C2×C4#6693112yes—
167C2×C4#6693612yes—
168C2×C4#6696814yes—
169C2×C4#6697214yes—
170C2×C4#6697711yescharacteristic
171C2×C4C2×#432312yes—
172C2×C4#6698811yescharacteristic
173C2×C4#6700412yes—
174C8—24no—
175C8—444no—
176C22#1062256211yescharacteristic
177C22#1062267311yescharacteristic
178C22#1062268611yescharacteristic
179C22#1062278012yes—
180C22#1062280412yes—
181C4—82no—
182C4—161no—
183C4—1762no—
184C4#1062240914yes—
185C4#1062242714yes—
186C4#1062262012yes—
187C4#1062264612yes—
188C2#1306822311yescharacteristic
189C2#1306826512yes—
190C2#1306828511yescharacteristic
191C2#1307014411yescharacteristic
192C2#1307016212yes—
subgroupG/H
centerC23#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1956C2
socle, prime radicalC23×C11#127
hypercenter#1956D11
hypocenterC11#10676
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
154. C11#10676semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130687762
#130687432
C11⋊#12732
C11×#19562
#1067611