Finite Group Databasebeta

← #14663280

Subgroups — #14663280

Order 2816.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#13077549C211yesmaximal, characteristic
2#13070429C212yesmaximal
3#13066569C211yesmaximal, characteristic
4#13066566C212yesmaximal
5C11×#1328C211yesmaximal, characteristic
6#10623048C411yescharacteristic
7C11×#424C2211yescharacteristic
8#10622735C2211yescharacteristic
9#10622731C2211yescharacteristic
10#10622715C411yescharacteristic
11C2×C8×Dic11C411yescharacteristic
12#10622610C411yescharacteristic
13#10622443—22no—
14#10622441—22no—
15C11×#349C2212yes—
16#10622191C2212yes—
17#10622150—22no—
18#10622149—22no—
19C2×C11×M16C2311yescharacteristic
20C22×C8×C11C2×C411yescharacteristic
21C11×#117C2×C411yescharacteristic
22#66979C2×C411yescharacteristic
23C2×C4×Dic11C2×C411yescharacteristic
24C2×#4318C2×C411yescharacteristic
25C22×C11⋊C8C2×C411yescharacteristic
26#66943—21no—
27#66941—21no—
28#66931—22no—
29C4×Dic22—22no—
30C11×M32—22no—
31C11×C4⋊C8—22no—
32#66879D412yes—
33Dic11⋊C8—22no—
34Dic11⋊C8—22no—
35C8×Dic11—21no—
36C8×Dic11—21no—
37C8×Dic11D412yes—
38#66876—22no—
39#66867—21no—
40C4×C11⋊C8—21no—
41#11539—111nomaximal, Sylow
42C22×C4×C11C22×C411yescharacteristic
43C22×Dic11—21no—
44C2×Dic22—22no—
45C11×M16—41no—
46C2×C8×C11—21no—
47C2×C8×C11—41no—
48C2×C8×C11C2×D412yes—
49C11×C4⋊C4—21no—
50C11×C22⋊C4M1612yes—
51C42×C11—21no—
52C22⋊Dic11—21no—
53C4⋊Dic11—22no—
54C4⋊Dic11—21no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57C4×Dic11—21no—
58C4×Dic11C22⋊C412yes—
59C4×Dic11M1611yescharacteristic
60C4×Dic11M1611yescharacteristic
61#4318—41no—
62C2×C11⋊C8—22no—
63C2×C11⋊C8—21no—
64C2×C11⋊C8C22⋊C411yescharacteristic
65C2×C11⋊C8C22⋊C411yescharacteristic
66C11×C16—42no—
67C11⋊C16—42no—
68#2960—111no—
69#2166—112no—
70#1328—111no—
71#1328D1111yescharacteristic
72#1327—112no—
73C23×C11C2×M1611yescharacteristic
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11C2×C22⋊C411yescharacteristic
78C2×C4×C11C2×M1611yescharacteristic
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—22no—
82C2×Dic11—42no—
83Dic22—44no—
84C8×C11—22no—
85C8×C11—41no—
86C11⋊C8—21no—
87C11⋊C8—41no—
88C11⋊C8#10112yes—
89#533—111no—
90#446—222no—
91C8×Q8—222no—
92#424—111no—
93#424C2×D1111yescharacteristic
94#423—111no—
95#405—111no—
96#405—111no—
97C2×C4×C8—111no—
98#364—222no—
99#349—112no—
100#349C2×D1112yes—
101#347—222no—
102C22×C11—21no—
103C22×C11—41no—
104C22×C11#40711yescharacteristic
105C4×C11—21no—
106C4×C11—42no—
107C4×C11#41011yescharacteristic
108C4×C11C2×#10111yescharacteristic
109Dic11—22no—
110Dic11—42no—
111Dic11—41no—
112C2×M16—111no—
113C2×M16C22×D1111yescharacteristic
114C22×C8—111no—
115C22×C8C4×D1111yescharacteristic
116C4⋊Q8—221no—
117#125—221no—
118C22⋊Q8—222no—
119C4×Q8—222no—
120#117—111no—
121#117C4×D1111yescharacteristic
122C2×C42—111no—
123M32—22no—
124M32—222no—
125C4⋊C8—22no—
126C4⋊C8—222no—
127C4⋊C8—222no—
128#97—112no—
129#97—221no—
130C4×C8—112no—
131C4×C8—221no—
132C4×C8—221no—
133C4×C8—221no—
134C2×C11—21no—
135C2×C11—41no—
136C2×C11#146711yescharacteristic
137C2×Q8—222no—
138C22×C4—221no—
139C22×C4C2×C4×D1111yescharacteristic
140M16—41no—
141M16—441no—
142C2×C8—21no—
143C2×C8—41no—
144C2×C8—111no—
145C2×C8—111no—
146C2×C8—222no—
147C2×C8—221no—
148C2×C8D4×D1112yes—
149C4⋊C4—21no—
150C4⋊C4—222no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—221no—
154C22⋊C4—221no—
155C22⋊C4#431312yes—
156C42—21no—
157C42—112no—
158C42—111no—
159C42—111no—
160C42—221no—
161C16—42no—
162C16—442no—
163C11#1153911yescharacteristic, complemented, Sylow
164C23C2×#431311yescharacteristic
165Q8—444no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—221no—
170C2×C4—221no—
171C2×C4—222no—
172C2×C4—442no—
173C2×C4C22⋊C4×D1111yescharacteristic
174C2×C4M16×D1111yescharacteristic
175C8—22no—
176C8—41no—
177C8—112no—
178C8—221no—
179C8—441no—
180C22—21no—
181C22—41no—
182C22#1062233911yescharacteristic
183C4—21no—
184C4—42no—
185C4—222no—
186C4—441no—
187C4—442no—
188C4#1062235311yescharacteristic
189C4D11×#10111yescharacteristic
190C2—21no—
191C2—41no—
192C2#1306695811yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1328C2
socleC2×C11#1467
prime radicalC23×C11C2×M16
cosocleC2×C11×M16C23
hypercenter#1328D11
hypocenterC11#11539
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
163. C11#11539semidirect

Maximal subgroups

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

subgroupindex
#130775492
#130704292
#130665692
#130665662
C11×#13282
#1153911