Finite Group Databasebeta

← #14667156

Subgroups — #14667156

Order 2816.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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#13080010C211yesmaximal, characteristic
2#13070836C212yesmaximal
3#13070191C211yesmaximal, characteristic
4#13066605C212yesmaximal
5C11×#1327C211yesmaximal, characteristic
6#10623001—21no—
7C11×#423C2211yescharacteristic
8#10622750—21no—
9#10622750C2212yes—
10#10622738C2211yescharacteristic
11#10622464—22no—
12#10622462—22no—
13C11×#349C2212yes—
14#10622197—21no—
15#10622195C2211yescharacteristic
16#10622161—21no—
17#10622155—22no—
18#10622151—22no—
19C2×C11×M16D411yescharacteristic
20C2×C11×M16C2311yescharacteristic
21C2×C42×C11D411yescharacteristic
22#66979—21no—
23#66979—41no—
24#66977—22no—
25#66977—41no—
26C2×#4318—21no—
27C2×Dic44—21no—
28C2×Dic44D412yes—
29#66923—41no—
30#66922—21no—
31#66922—21no—
32C4×Dic22—22no—
33C4×Dic22—41no—
34C11×M32—22no—
35C11×C4⋊C8—22no—
36#66883—22no—
37#66881—21no—
38#66881D412yes—
39#66880—22no—
40#66880—22no—
41#12308—111nomaximal, Sylow
42C22×C4×C11—21no—
43C22×C4×C11C2×D411yescharacteristic
44C2×Dic22—22no—
45C2×Dic22—41no—
46C11×M16—41no—
47C11×M16—41no—
48C2×C8×C11—21no—
49C2×C8×C11C2×D412yes—
50C42×C11—21no—
51C42×C11SD1611yescharacteristic
52C42×C11SD1611yescharacteristic
53C22⋊Dic11—42no—
54C22⋊Dic11—41no—
55C4⋊Dic11—22no—
56C4⋊Dic11—41no—
57C4⋊Dic11—41no—
58C4⋊Dic11—41no—
59C4⋊Dic11—41no—
60Dic11⋊C4—42no—
61Dic11⋊C4—42no—
62C4×Dic11—42no—
63C4×Dic11—41no—
64#4318—41no—
65#4318—41no—
66C2×C11⋊C8—41no—
67Dic44—42no—
68Dic44—81no—
69C11×C16—42no—
70#3255—111no—
71#2239—112no—
72#2102—111no—
73#1340—112no—
74#1327D1111yescharacteristic
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11#12011yescharacteristic
82C2×C4×C11C2×SD1611yescharacteristic
83C2×Dic11—42no—
84C2×Dic11—42no—
85C2×Dic11—81no—
86Dic22—42no—
87Dic22—42no—
88Dic22—82no—
89C8×C11—22no—
90C8×C11—41no—
91C11⋊C8—81no—
92#533—221no—
93#475—222no—
94#470—112no—
95#470—221no—
96#462—222no—
97#430—111no—
98#423C2×D1111yescharacteristic
99#365—222no—
100#362—222no—
101#349C2×D1112yes—
102#344—221no—
103#339—221no—
104H(3,ℤ/4)—111no—
105C22×C11—21no—
106C22×C11—41no—
107C22×C11#45011yescharacteristic
108C4×C11—22no—
109C4×C11—21no—
110C4×C11—41no—
111C4×C11#45411yescharacteristic
112C4×C11#45811yescharacteristic
113Dic11—82no—
114Dic11—82no—
115Dic11—161no—
116C2×Q16—112no—
117C2×Q16—221no—
118C2×M16—221no—
119C2×M16D4411yescharacteristic
120C2×M16C22×D1111yescharacteristic
121C4⋊Q8—221no—
122C4⋊Q8—221no—
123#125—441no—
124C22⋊Q8—222no—
125C22⋊Q8—441no—
126C4×Q8—222no—
127C4×Q8—441no—
128#117—221no—
129#117—441no—
130C2×C42D4411yescharacteristic
131M32—22no—
132#108—222no—
133#106—112no—
134#106—221no—
135C4⋊C8—22no—
136#103—222no—
137#103—222no—
138C2×C11—21no—
139C2×C11—41no—
140C2×C11#161611yescharacteristic
141C2×Q8—222no—
142C2×Q8—441no—
143C22×C4—21no—
144C22×C4C2×D4411yescharacteristic
145Q16—442no—
146Q16—881no—
147M16—41no—
148M16—41no—
149M16—441no—
150M16—441no—
151C2×C8—21no—
152C2×C8—441no—
153C2×C8D4×D1112yes—
154C4⋊C4—222no—
155C4⋊C4—441no—
156C4⋊C4—441no—
157C4⋊C4—442no—
158C4⋊C4—441no—
159C4⋊C4—441no—
160C4⋊C4—442no—
161C22⋊C4—442no—
162C22⋊C4—441no—
163C42—21no—
164C42—442no—
165C42—441no—
166C42#431411yescharacteristic
167C42#431411yescharacteristic
168C16—42no—
169C11#1230811yescharacteristic, complemented, Sylow
170C23#6696111yescharacteristic
171Q8—442no—
172Q8—442no—
173Q8—882no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—442no—
180C2×C4—442no—
181C2×C4—881no—
182C2×C4#6693511yescharacteristic
183C2×C4C2×#431411yescharacteristic
184C8—22no—
185C8—41no—
186C8—881no—
187C22—21no—
188C22—41no—
189C22#1062234411yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—882no—
194C4—882no—
195C4—1761no—
196C4#1062235511yescharacteristic
197C4#1062236611yescharacteristic
198C2—21no—
199C2—41no—
200C2#1306765511yescharacteristic
subgroupG/H
centerC2#13067655
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11#1616
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1327D11
hypocenterC11#12308
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
169. C11#12308semidirect

Maximal subgroups

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

subgroupindex
#130800102
#130708362
#130701912
#130666052
C11×#13272
#1230811