Finite Group Databasebeta

← #14640985

Subgroups — #14640985

Order 2816.

402 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#66898C212yesmaximal
2C11×#1955C211yesmaximal, characteristic
3C2×C4×D4×C11C2211yescharacteristic
4C2×C11×C4⋊C8C411yescharacteristic, complemented
5C2×C11×C22⋊C8—22no—
6C2×C11×#97C411yescharacteristic, complemented
7C2×#66898—22no—
8C4×C22⋊Dic11—22no—
9#10622164C414yescomplemented
10C22×D4×C11D411yescharacteristic
11C23×C4×C11D412yes—
12C22×C8×C11—21no—
13C22×C8×C11—21no—
14C4×D4×C11—41no—
15C4×D4×C11—41no—
16C2×C11×C4⋊C4Q811yescharacteristic
17C2×C11×C22⋊C4C2×C412yes—
18C2×C42×C11C2×C411yescharacteristic
19C2×C22⋊Dic11—24no—
20C2×C4×Dic11—42no—
21C11×C4⋊C8—41no—
22C11×C22⋊C8—44no—
23C11×#97—41no—
24#66898—28no—
25C11⋊#95—42no—
26#7283—111nomaximal, Sylow
27C24×C11C22⋊C412yes—
28C2×D4×C11—24no—
29C2×D4×C11—41no—
30C22×C4×C11—22no—
31C22×C4×C11—22no—
32C22×C4×C11—42no—
33C22×C4×C11—42no—
34C22×C4×C11C4211yescharacteristic
35C22×C4×C11C22⋊C411yescharacteristic
36C22×C4×C11C4⋊C411yescharacteristic
37C22×C4×C11C4⋊C412yes—
38C22×Dic11—44no—
39C2×C8×C11—22no—
40C2×C8×C11—41no—
41C2×C8×C11—42no—
42C2×C8×C11—41no—
43C2×C8×C11—41no—
44C11×C4⋊C4—41no—
45C11×C22⋊C4—42no—
46C42×C11—21no—
47C42×C11—21no—
48C22⋊Dic11—28no—
49C22⋊Dic11—44no—
50C4×Dic11—82no—
51C4×Dic11—82no—
52#1955D1111yescharacteristic
53C4×#99—112no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—42no—
57C23×C11—42no—
58C23×C11#9511yescharacteristic
59C23×C11#10414yes—
60D4×C11—44no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—22no—
67C2×C4×C11—42no—
68C2×C4×C11—42no—
69C2×C4×C11—42no—
70C2×C4×C11—41no—
71C2×C4×C11—82no—
72C2×C4×C11#9911yescharacteristic
73C2×C4×C11#9911yescharacteristic
74C2×Dic11—48no—
75C2×Dic11—84no—
76C2×Dic11—84no—
77C8×C11—42no—
78C8×C11—81no—
79C2×C4×D4C2×D1111yescharacteristic
80C2×C4⋊C8Dic1111yescharacteristic, complemented
81C2×#99—222no—
82C2×C22⋊C8—22no—
83C2×#97Dic1111yescharacteristic, complemented
84C4×C22⋊C4—222no—
85#342—114no—
86C22×C11—21no—
87C22×C11—21no—
88C22×C11—24no—
89C22×C11—44no—
90C22×C11—42no—
91C22×C11—42no—
92C22×C11—82no—
93C22×C11#33912yes—
94C22×C11#34211yescharacteristic
95C4×C11—21no—
96C4×C11—41no—
97C4×C11—41no—
98C4×C11—42no—
99C4×C11#35311yescharacteristic
100C4×C11#35411yescharacteristic
101Dic11—88no—
102C22×D4D4411yescharacteristic
103C23×C4C22⋊D1112yes—
104C22×C8—21no—
105C22×C8—21no—
106C4×D4—41no—
107C4×D4—41no—
108C2×C4⋊C4Dic2211yescharacteristic
109C2×C22⋊C4—224no—
110C2×C22⋊C4C4×D1112yes—
111C2×C42—442no—
112C2×C42C2×Dic1111yescharacteristic
113C4⋊C8—41no—
114#99—228no—
115C22⋊C8—44no—
116#97—41no—
117#95—442no—
118C2×C11—22no—
119C2×C11—44no—
120C2×C11#129711yescharacteristic
121C2×C11#139111yescharacteristic
122C2×C11#139311yescharacteristic
123C24(C2×D11)⋊C412yes—
124C2×D4—24no—
125C2×D4—41no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—444no—
131C22×C4C4×Dic1111yescharacteristic
132C22×C4Dic11⋊C412yes—
133C22×C4C4⋊Dic1111yescharacteristic
134C22×C4C22⋊Dic1111yescharacteristic
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—42no—
139C2×C8—41no—
140C4⋊C4—41no—
141C22⋊C4—42no—
142C22⋊C4—228no—
143C22⋊C4—444no—
144C42—21no—
145C42—21no—
146C42—882no—
147C42—882no—
148C11#728311yescharacteristic, complemented, Sylow
149C23—22no—
150C23—22no—
151C23—42no—
152C23—42no—
153C23#6688914yes—
154C23C11⋊#9511yescharacteristic
155D4—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—82no—
167C2×C4—448no—
168C2×C4—884no—
169C2×C4—884no—
170C2×C4#6689811yescharacteristic
171C2×C4#6689811yescharacteristic
172C8—42no—
173C8—81no—
174C22—21no—
175C22—21no—
176C22—24no—
177C22—44no—
178C22—42no—
179C22—42no—
180C22—82no—
181C22#1062216411yescharacteristic
182C22#1062219312yes—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—888no—
188C4#1062217911yescharacteristic
189C4#1062218311yescharacteristic
190C2—22no—
191C2—44no—
192C2#1306650111yescharacteristic
193C2#1306673711yescharacteristic
194C2#1306674111yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC22×C4×C11C42
FrattiniC2×C4×D4C2×D11
FittingC11×#1955C2
socleC22×C11#342
prime radicalC22×D4×C11D4
cosocleC2×C4×D4×C11C22
hypercenter#1955D11
hypocenterC11#7283
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1955

Complements

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

NH ≅ G/Ntype
4. C2×C11×C4⋊C8C4semidirect
6. C2×C11×#97C4semidirect
9. #10622164C4semidirect
80. C2×C4⋊C8Dic11semidirect
83. C2×#97Dic11semidirect
148. C11#7283semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
C11×#19552
#728311