Finite Group Databasebeta

← #14667181

Subgroups — #14667181

Order 2816.

356 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070697C212yesmaximal, complemented
2#13068232C211yesmaximal, characteristic, complemented
3#13066655C211yesmaximal, characteristic, complemented
4#13066589C212yesmaximal, complemented
5C11×#3293C211yesmaximal, characteristic
6C11×#578—22no—
7C11×#494C2211yescharacteristic
8C11×#473—22no—
9C11×#456—22no—
10C11×#443C2212yes—
11#10622808—22no—
12#10622691—22no—
13#10622312C2211yescharacteristic
14#10622134—22no—
15#10622101C2212yes—
16C8×C11⋊C8C2211yescharacteristic
17C11×2−1+4—22no—
18C11×#137—24no—
19C11×#137—44no—
20C11×#135—42no—
21C11×#135D412yes—
22C2×C11×Q16—22no—
23C2×C11×Q16—42no—
24C11×#131—22no—
25C11×C4⋊Q8D412yes—
26C2×Dic44—22no—
27#66922—21no—
28C11×#108D412yes—
29C11×#104—22no—
30C11×#101—22no—
31C4×C8×C11C2311yescharacteristic
32#66893—42no—
33#66891—42no—
34#66876—22no—
35#66871—44no—
36C4×C11⋊C8—21no—
37#12313—111nomaximal, Sylow
38C11×#41—22no—
39C11×#41—44no—
40C11×#41—82no—
41C2×Q8×C11—22no—
42C2×Q8×C11—44no—
43C2×Dic22—41no—
44C11×Q16—44no—
45C11×Q16—42no—
46C11×Q16—42no—
47C11×Q16D812yes—
48C11×SD16—22no—
49C11×SD16—44no—
50C11×D8D812yes—
51C11×M16—22no—
52C11×M16—42no—
53C2×C8×C11—42no—
54C2×C8×C11C2×D412yes—
55C11×C4⋊C4—42no—
56C42×C11C2×D411yescharacteristic
57C4⋊Dic11—42no—
58C2×C11⋊C8—22no—
59Dic44—42no—
60Dic44—42no—
61C11⋊C16—42no—
62#3293D1111yescharacteristic
63#2214—112no—
64#1713—111no—
65#1358—111no—
66#1335—112no—
67Q8×C11—22no—
68Q8×C11—44no—
69Q8×C11—82no—
70D4×C11—22no—
71D4×C11—42no—
72D4×C11—82no—
73C2×C4×C11—21no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—84no—
77C2×C4×C11#12011yescharacteristic
78C2×Dic11—81no—
79Dic22—82no—
80C8×C11—42no—
81C8×C11C2×D812yes—
82C8×C11AGL(1,ℤ/8)12yes—
83C11⋊C8—24no—
84#578—22no—
85#510—222no—
86#500—222no—
87#494—111no—
88#494C2×D1111yescharacteristic
89#473—22no—
90#456—22no—
91#443C2×D1112yes—
92#364—112no—
93#362—222no—
94C82—111no—
95C22×C11—42no—
96C22×C11#45311yescharacteristic
97C4×C11—22no—
98C4×C11—42no—
99C4×C11—82no—
100C4×C11#44712yes—
101Dic11—161no—
1022−1+4—22no—
103#137—24no—
104#137—44no—
105#135—42no—
106#135C22⋊D1112yes—
107C2×Q16—22no—
108C2×Q16—42no—
109C2×Q16—222no—
110#131—22no—
111C4⋊Q8—221no—
112C4⋊Q8C22⋊D1112yes—
113Q32—442no—
114SD32—442no—
115M32—222no—
116#108C22⋊D1112yes—
117#107—444no—
118#104—22no—
119#101—22no—
120C4×C8—221no—
121C4×C8C22×D1111yescharacteristic
122C2×C11—21no—
123C2×C11—82no—
124C2×C11#161911yescharacteristic
125#41—22no—
126#41—44no—
127#41—82no—
128C2×Q8—22no—
129C2×Q8—44no—
130C2×Q8—441no—
131Q16—44no—
132Q16—42no—
133Q16—42no—
134Q16—442no—
135Q16—442no—
136Q16#432312yes—
137SD16—22no—
138SD16—44no—
139D8#432312yes—
140M16—22no—
141M16—42no—
142C2×C8—42no—
143C2×C8—222no—
144C2×C8C2×C22⋊D1112yes—
145C4⋊C4—42no—
146C4⋊C4—442no—
147C42C2×C22⋊D1111yescharacteristic
148C16—442no—
149C11#1231311yescharacteristic, complemented, Sylow
150Q8—22no—
151Q8—44no—
152Q8—82no—
153Q8—882no—
154D4—22no—
155D4—42no—
156D4—82no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—84no—
161C2×C4—881no—
162C2×C4#6700611yescharacteristic
163C8—42no—
164C8—224no—
165C8C2×#432312yes—
166C8#6698512yes—
167C22—42no—
168C22#1062285411yescharacteristic
169C4—22no—
170C4—42no—
171C4—82no—
172C4—1761no—
173C4#1062283012yes—
174C2—21no—
175C2—82no—
176C2#1306767011yescharacteristic
subgroupG/H
centerC2#13067670
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#3293C2
socleC2×C11#1619
hypercenter#3293D11
hypocenterC11#12313
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #13070697C2semidirect
2. #13068232C2semidirect
3. #13066655C2semidirect
4. #13066589C2semidirect
149. C11#12313semidirect

Maximal subgroups

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

subgroupindex
#130706972
#130682322
#130666552
#130665892
C11×#32932
#1231311