Finite Group Databasebeta

← #14910145

Subgroups — #14910145

Order 2816.

484 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 151 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#13079202C212yesmaximal
2#13070759C214yesmaximal, complemented
3#13070724C214yesmaximal
4#13070667C214yesmaximal, complemented
5C11×#2150C211yesmaximal, characteristic
6#10623001—22no—
7C2×C11×M32C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622729—22no—
10#10622729C2214yes—
11C2×Dic88C2214yes—
12#10622312C2212yes—
13C4×Dic44—22no—
14C4×Dic44C2214yes—
15#10622295C2212yes—
16#10622294—22no—
17C11×C4⋊C16C2214yes—
18#10622143C2214yes—
19#10622141C2218yes—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66979—42no—
24#66977—24no—
25#66977—42no—
26C2×Dic44—22no—
27C2×Dic44C2314yes—
28#66923—42no—
29#66922—22no—
30#66922—22no—
31C4×Dic22—24no—
32C4×Dic22—42no—
33C11×M32—42no—
34C2×C11×C16C2314yes—
35C4×C8×C11D412yes—
36C4×C8×C11C2312yes—
37#66882—22no—
38#66882C2314yes—
39#66880—24no—
40#66880—24no—
41Dic88—44no—
42#33821—111nomaximal, Sylow
43C22×C4×C11D812yes—
44C22×C4×C11C2×D411yescharacteristic
45C2×Dic22—24no—
46C2×Dic22—42no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11—41no—
50C2×C8×C11C2×D411yescharacteristic
51C2×C8×C11C2×D412yes—
52C2×C8×C11C2411yescharacteristic
53C42×C11D811yescharacteristic
54C42×C11D811yescharacteristic
55C42×C11C2×D412yes—
56C22⋊Dic11—44no—
57C4⋊Dic11—24no—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61Dic11⋊C4—44no—
62Dic11⋊C4—44no—
63C4×Dic11—44no—
64Dic44—24no—
65Dic44—24no—
66Dic44—44no—
67C11×C16—24no—
68#3170—112no—
69#2225—114no—
70#2219—114no—
71#2209—114no—
72#2150D1111yescharacteristic
73C23×C11C2×D811yescharacteristic
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—24no—
77C2×C4×C11C2×D811yescharacteristic
78C2×C4×C11C2×D812yes—
79C2×C4×C11C2×D812yes—
80C2×C4×C11C22×D411yescharacteristic
81C2×Dic11—44no—
82C2×Dic11—44no—
83Dic22—44no—
84Dic22—44no—
85Dic22—84no—
86C8×C11—21no—
87C8×C11—22no—
88C8×C11H(5,𝔽2)11yescharacteristic
89C8×C112−1+411yescharacteristic
90#533—222no—
91C2×Q32—114no—
92C2×M32C2×D1112yes—
93#500—112no—
94#494—112no—
95#487—222no—
96#467—114no—
97#467—222no—
98C4×Q16—114no—
99C4×Q16—222no—
100C2×C4×C8C2×D1111yescharacteristic
101#367—114no—
102C4⋊C16C2×D1114yes—
103#358—118no—
104C22×C11—22no—
105C22×C11—21no—
106C22×C11C22×D811yescharacteristic
107C4×C11—22no—
108C4×C11—21no—
109C4×C11#51014yes—
110C4×C11#53711yescharacteristic
111C4×C11#57511yescharacteristic
112Dic11—84no—
113Dic11—84no—
114C2×Q16—114no—
115C2×Q16—222no—
116C22×C8D4411yescharacteristic
117C22×C8C22×D1111yescharacteristic
118C4⋊Q8—222no—
119C4⋊Q8—222no—
120#125—442no—
121C22⋊Q8—224no—
122C22⋊Q8—442no—
123C4×Q8—224no—
124C4×Q8—442no—
125#117—442no—
126C2×C42D4411yescharacteristic
127Q32—444no—
128M32—42no—
129C2×C16C22×D1114yes—
130#107—114no—
131#107—222no—
132#103—224no—
133#103—224no—
134C4×C8D4412yes—
135C4×C8C22×D1112yes—
136C2×C11—41no—
137C2×C11#324511yescharacteristic
138C2×C11C2×#51012yes—
139C2×Q8—224no—
140C2×Q8—442no—
141C22×C4D8812yes—
142C22×C4C2×D4411yescharacteristic
143Q16—224no—
144Q16—224no—
145Q16—444no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8C2×D4412yes—
150C2×C8C2×D4411yescharacteristic
151C2×C8C23×D1111yescharacteristic
152C4⋊C4—224no—
153C4⋊C4—442no—
154C4⋊C4—442no—
155C4⋊C4—444no—
156C4⋊C4—444no—
157C4⋊C4—442no—
158C22⋊C4—444no—
159C42—444no—
160C42D8811yescharacteristic
161C42D8811yescharacteristic
162C42C2×D4412yes—
163C16—24no—
164C11#3382111yescharacteristic, complemented, Sylow
165C23C2×D8811yescharacteristic
166Q8—444no—
167Q8—444no—
168Q8—884no—
169C2×C4—21no—
170C2×C4—24no—
171C2×C4—21no—
172C2×C4—444no—
173C2×C4—444no—
174C2×C4C2×D8811yescharacteristic
175C2×C4C2×D8812yes—
176C2×C4C2×D8812yes—
177C2×C4C22×D4411yescharacteristic
178C8—22no—
179C8—21no—
180C8#6703711yescharacteristic
181C8#6704011yescharacteristic
182C22—21no—
183C22—22no—
184C22C22×D8811yescharacteristic
185C4—21no—
186C4—22no—
187C4—884no—
188C4—884no—
189C4#1062252214yes—
190C4#1062304111yescharacteristic
191C4#1062327911yescharacteristic
192C2—41no—
193C2#1307992611yescharacteristic
194C2C2×#1062252212yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2150C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2150D11
hypocenterC11#33821
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2150

Complements

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

NH ≅ G/Ntype
2. #13070759C2semidirect
4. #13070667C2semidirect
164. C11#33821semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130707592
#130707242
#130706672
C11×#21502
#3382111