Finite Group Databasebeta

← #14647296

Subgroups — #14647296

Order 2816.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071202C211yesmaximal, characteristic
2#13068540C211yesmaximal, characteristic
3#13066525C214yesmaximal
4C11×#1784C211yesmaximal, characteristic
5C23×Q8×C11C2211yescharacteristic
6C2×#66979C412yes—
7C2×C11×#101—22no—
8C11×#407C2212yes—
9#10622843—22no—
10#10622843—22no—
11C2×#66900—22no—
12#10622824C412yes—
13#10622824C2212yes—
14#10622820C2212yes—
15C22×Q8×C11—24no—
16C22×Q8×C11—44no—
17C22×Q8×C11D412yes—
18C22×Q8×C11D412yes—
19C23×C4×C11C2×C411yescharacteristic
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11C2311yescharacteristic
22C2×C11×M16—22no—
23C2×C22⋊Dic11C2×C414yes—
24#66979—44no—
25C2×C4⋊Dic11—22no—
26C2×C4×Dic11—22no—
27C2×#4318—22no—
28C11×#101—44no—
29C11×C22⋊C8—24no—
30#66900—44no—
31C11⋊#95—24no—
32C11⋊#95—22no—
33C11⋊#95—22no—
34C22⋊(C11⋊C8)—24no—
35#8754—111nomaximal, Sylow
36C24×C11C22×C411yescharacteristic
37C2×Q8×C11—24no—
38C2×Q8×C11—24no—
39C2×Q8×C11—24no—
40C2×Q8×C11—24no—
41C2×Q8×C11—42no—
42C2×Q8×C11—42no—
43C2×Q8×C11—416no—
44C22×C4×C11—22no—
45C22×C4×C11—24no—
46C22×C4×C11—22no—
47C22×C4×C11—42no—
48C22×C4×C11—42no—
49C22×C4×C11C22⋊C412yes—
50C22×C4×C11C22⋊C412yes—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4114yes—
54C22×Dic11—24no—
55C11×M16—44no—
56C2×C8×C11—42no—
57C22⋊Dic11—44no—
58C4⋊Dic11—44no—
59C4×Dic11—44no—
60#4318—44no—
61C2×C11⋊C8—42no—
62#2310—111no—
63#1784—111no—
64#1784D1111yescharacteristic
65#1306—114no—
66C23×C11—22no—
67C23×C11—42no—
68C23×C11C2×C22⋊C411yescharacteristic
69C23×C11#11712yes—
70Q8×C11—48no—
71Q8×C11—48no—
72C2×C4×C11—28no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—44no—
81C2×C4×C11—44no—
82C2×C4×C11#9914yes—
83C2×C4×C11#12312yes—
84C2×C4×C11#12312yes—
85C2×Dic11—48no—
86C2×Dic11—44no—
87C8×C11—82no—
88C11⋊C8—82no—
89C23×Q8C2×D1111yescharacteristic
90C2×#117—112no—
91C2×#101—22no—
92C2×#101—222no—
93#407—112no—
94#407C2×D1112yes—
95#391—222no—
96#391—222no—
97#381—112no—
98#381—112no—
99C22×C11—22no—
100C22×C11—22no—
101C22×C11—24no—
102C22×C11—44no—
103C22×C11#38111yescharacteristic
104C22×C11C2×#9912yes—
105C4×C11—24no—
106C4×C11—22no—
107C4×C11—22no—
108C4×C11—42no—
109Dic11—84no—
110C22×Q8—24no—
111C22×Q8—44no—
112C22×Q8D4412yes—
113C22×Q8C22⋊D1112yes—
114C23×C4C4×D1111yescharacteristic
115C23×C4C4×D1111yescharacteristic
116C23×C4C22×D1111yescharacteristic
117C2×M16—22no—
118C2×M16—222no—
119#117—444no—
120C2×C4⋊C4—222no—
121C2×C22⋊C4—114no—
122C2×C42—222no—
123#101—44no—
124#101—444no—
125C22⋊C8—24no—
126C22⋊C8—224no—
127#95—224no—
128#95—222no—
129#95—222no—
130C2×C11—22no—
131C2×C11—42no—
132C2×C11#181911yescharacteristic
133C2×C11#183012yes—
134C24C2×C4×D1111yescharacteristic
135C2×Q8—24no—
136C2×Q8—24no—
137C2×Q8—24no—
138C2×Q8—24no—
139C2×Q8—42no—
140C2×Q8—42no—
141C2×Q8—416no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—224no—
148C22×C4(C2×D11)⋊C412yes—
149C22×C4(C2×D11)⋊C412yes—
150C22×C4C2×D4411yescharacteristic
151C22×C4#434114yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153M16—44no—
154M16—444no—
155C2×C8—42no—
156C2×C8—442no—
157C4⋊C4—444no—
158C22⋊C4—444no—
159C42—444no—
160C11#875411yescharacteristic, complemented, Sylow
161C23—22no—
162C23—42no—
163C23#6693012yes—
164C23C2×(C2×D11)⋊C411yescharacteristic
165Q8—48no—
166Q8—48no—
167C2×C4—28no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—448no—
178C2×C4—444no—
179C2×C4#6687014yes—
180C2×C4#6693912yes—
181C2×C4#6698812yes—
182C8—82no—
183C8—882no—
184C22—22no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22#1062255611yescharacteristic
189C22C2×#6687012yes—
190C4—22no—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—884no—
195C2—22no—
196C2—42no—
197C2#1306868811yescharacteristic
198C2#1306872812yes—
subgroupG/H
centerC22#10622556
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1784C2
socleC22×C11#381
cosocleC23×C4×C11C23
hypercenter#1784D11
hypocenterC11#8754
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
160. C11#8754semidirect

Maximal subgroups

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

subgroupindex
#130712022
#130685402
#130665252
C11×#17842
#875411