Finite Group Databasebeta

← #14670247

Subgroups — #14670247

Order 2816.

374 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 131 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#13081719C211yesmaximal, characteristic
2#13070374C212yesmaximal, complemented
3#13068416C211yesmaximal, characteristic
4#13066703C212yesmaximal, complemented
5C11×#2113C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C22×C11×C16C2211yescharacteristic
9#10622853C411yescharacteristic
10#10622850C411yescharacteristic
11#10622753—24no—
12#10622714C2212yes—
13C2×#66876—22no—
14C2×#66876C2212yes—
15C11×C22⋊C16—22no—
16#10622194C412yes—
17Dic11⋊C16—24no—
18C2×C11×#41C2×C411yescharacteristic
19C11×#131—22no—
20C11×#131—22no—
21C2×C11×M16C2×C411yescharacteristic
22C2×C11×M16Q812yes—
23C22×C8×C11D412yes—
24C22×C8×C11C2311yescharacteristic
25#66979C2×C412yes—
26C2×#4318C2×C412yes—
27C11×M32—22no—
28C2×C11×C16—21no—
29C2×C11×C16—22no—
30C2×C11×C16—21no—
31#66900—21no—
32#66898C814yes—
33#66897—21no—
34#66879—22no—
35C8×Dic11—22no—
36#66876—24no—
37#66876—22no—
38#66876—22no—
39C2×C11⋊C16—24no—
40C2×C11⋊C16D414yes—
41#12915—111nomaximal, Sylow
42C11×#41—22no—
43C11×#41—22no—
44C2×Q8×C11M1611yescharacteristic
45C2×D4×C11C2×C812yes—
46C2×D4×C11M1611yescharacteristic
47C22×C4×C11C4⋊C412yes—
48C22×C4×C11C22×C411yescharacteristic
49C11×M16—24no—
50C11×M16—22no—
51C2×C8×C11—22no—
52C2×C8×C11—22no—
53C2×C8×C11C4⋊C412yes—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11C2×D412yes—
56C2×C8×C11C2×Q811yescharacteristic
57C2×C8×C11#4112yes—
58C22⋊Dic11C2×C814yes—
59C4⋊Dic11—22no—
60C4×Dic11—22no—
61#4318—22no—
62#4318—22no—
63C2×C11⋊C8—22no—
64C11×C16—41no—
65C11×C16—41no—
66C11⋊C16—24no—
67#3407—111no—
68#2151—112no—
69#2113D1111yescharacteristic
70#1757—111no—
71#1378—112no—
72C23×C11C4⋊C812yes—
73C23×C11C22×C811yescharacteristic
74Q8×C11—22no—
75D4×C11—24no—
76D4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11C4⋊C812yes—
80C2×C4×C11C2×C4⋊C411yescharacteristic
81C2×C4×C11C4×D412yes—
82C2×C4×C11C2×M1611yescharacteristic
83C2×C4×C11#13112yes—
84C2×Dic11—24no—
85C8×C11—22no—
86C8×C11#12011yescharacteristic
87C8×C11C22⋊Q812yes—
88C8×C11#12311yescharacteristic
89C11⋊C8—42no—
90C2×#131C2×D1111yescharacteristic
91#504—224no—
92C2×M32—112no—
93C2×M32—222no—
94C2×M32C2×D1111yescharacteristic
95C22×C16C2×D1111yescharacteristic
96#413—111no—
97#410—111no—
98#405—112no—
99C4⋊C16—224no—
100C22⋊C16—22no—
101#344—112no—
102C22×C11—22no—
103C22×C11—41no—
104C22×C11—42no—
105C22×C11C2×C4⋊C811yescharacteristic
106C22×C11C8×D412yes—
107C4×C11—22no—
108C4×C11#38511yescharacteristic
109C4×C11#42411yescharacteristic
110C4×C11#43512yes—
111Dic11—44no—
112C2×#41C4×D1111yescharacteristic
113#131—22no—
114#131—22no—
115C2×M16—112no—
116C2×M16Dic2212yes—
117C2×M16C4×D1111yescharacteristic
118C22×C8C22⋊D1112yes—
119C22×C8C22×D1111yescharacteristic
120#117—112no—
121M32—22no—
122M32—224no—
123M32—222no—
124M32—222no—
125C2×C16—22no—
126C2×C16—21no—
127C2×C16—21no—
128C2×C16—114no—
129C2×C16—224no—
130#101—221no—
131#100—221no—
132#99—114no—
133#97—222no—
134C4×C8—222no—
135C2×C11—22no—
136C2×C11—21no—
137C2×C11—42no—
138C2×C11#185011yescharacteristic
139#41—22no—
140#41—22no—
141C2×Q8#431311yescharacteristic
142C2×D4C8×D1112yes—
143C2×D4#431311yescharacteristic
144C22×C4Dic11⋊C412yes—
145C22×C4C2×C4×D1111yescharacteristic
146M16—22no—
147M16—24no—
148M16—222no—
149M16—222no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—222no—
153C2×C8Dic11⋊C412yes—
154C2×C8C2×Dic2211yescharacteristic
155C2×C8D4×D1112yes—
156C2×C8#434112yes—
157C2×C8C2×C22⋊D1111yescharacteristic
158C4⋊C4—222no—
159C22⋊C4—114no—
160C42—222no—
161C16—41no—
162C16—41no—
163C16—224no—
164C11#1291511yescharacteristic, complemented, Sylow
165C23Dic11⋊C812yes—
166C23C2×C8×D1111yescharacteristic
167Q8—22no—
168D4—24no—
169D4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—224no—
173C2×C4Dic11⋊C812yes—
174C2×C4(C22⋊D11)⋊C412yes—
175C2×C4C2×#431311yescharacteristic
176C2×C4#6696012yes—
177C2×C4C2×Dic11⋊C411yescharacteristic
178C8—22no—
179C8—442no—
180C8#6693112yes—
181C8#6698811yescharacteristic
182C8#6699011yescharacteristic
183C22—22no—
184C22—41no—
185C22—42no—
186C22(C22⋊D11)⋊C812yes—
187C22C2×Dic11⋊C811yescharacteristic
188C4—22no—
189C4—444no—
190C4#1062234312yes—
191C4#1062255911yescharacteristic
192C4#1062273211yescharacteristic
193C2—22no—
194C2—21no—
195C2—42no—
196C2#1306879311yescharacteristic
subgroupG/H
centerC8#66990
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2113C2
socleC2×C11#1850
prime radicalC2×C11×#41C2×C4
cosocleC22×C8×C11C23
hypercenter#2113D11
hypocenterC11#12915
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. #13070374C2semidirect
4. #13066703C2semidirect
164. C11#12915semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130703742
#130684162
#130667032
C11×#21132
#1291511