Finite Group Databasebeta

← #14674389

Subgroups — #14674389

Order 2816.

182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070934C211yesmaximal, characteristic
2#13070503C211yesmaximal, characteristic
3#13066821C211yesmaximal, characteristic, complemented
4#13066809C211yesmaximal, characteristic, complemented
5#13066802C211yesmaximal, characteristic
6#13066752C211yesmaximal, characteristic, complemented
7C11×#2176C211yesmaximal, characteristic, complemented
8C2×C11×Q32C2211yescharacteristic
9C4×C11×Q16—21no—
10#10622517C2211yescharacteristic
11#10622313—21no—
12C11×#367C2211yescharacteristic
13C11×#358—21no—
14C11×#346C2211yescharacteristic
15#10622160C412yescomplemented
16#10622159C412yescomplemented
17#10622148—21no—
18#10622144C2211yescharacteristic
19#10622137C2211yescharacteristic
20#10622137C2211yescharacteristic
21C2×C11×Q16—21no—
22C4×Q8×C11—41no—
23#66957—21no—
24#66954—41no—
25C11×Q32—21no—
26C11×Q32C2×C412yes—
27C2×C11×C16D411yescharacteristic
28C2×C11×C16C2311yescharacteristic
29C11×#107—21no—
30C11×#103—41no—
31C4×C8×C11D411yescharacteristic
32#66883—21no—
33#66869—41no—
34Dic88C2×C411yescharacteristic
35#66864—21no—
36D176C2×C411yescharacteristic
37C11⋊C32—21no—
38C11⋊C32C2×C412yes—
39#13657—111nomaximal, Sylow
40C2×Q8×C11—41no—
41#4339—41no—
42C11×Q16—22no—
43C11×Q16—41no—
44C2×C8×C11D811yescharacteristic
45C2×C8×C11C2×D411yescharacteristic
46C11×C4⋊C4—41no—
47C11×C4⋊C4—81no—
48C42×C11—81no—
49C42×C11D811yescharacteristic
50#4318—41no—
51Dic44—21no—
52D88—21no—
53#4314—41no—
54#4313—81no—
55C8×D11—81no—
56C11×C16—21no—
57C11×C16C22×C411yescharacteristic
58C11×C16#4111yescharacteristic
59#2264—111no—
60#2179—111no—
61#2176D1111yescharacteristic, complemented
62#1426—111no—
63#1420—111no—
64#1418—111no—
65#1398—111no—
66Q8×C11—42no—
67Q8×C11—81no—
68C2×C4×C11—21no—
69C2×C4×C11—81no—
70C2×C4×C11—81no—
71C2×C4×C11C2×D811yescharacteristic
72C22⋊D11—81no—
73D44—41no—
74C4×D11—81no—
75Dic22—41no—
76C8×C11—21no—
77C8×C11C4×D411yescharacteristic
78C8×C11#13511yescharacteristic
79C11⋊C8—81no—
80#508—111no—
81C2×Q32C2×D1111yescharacteristic
82#443—221no—
83C4×Q16—21no—
84Q64—112no—
85SD64—112no—
86M64—111no—
87M64—111no—
88#368—111no—
89#367C2×D1111yescharacteristic
90#359—221no—
91#358—21no—
92#346C2×D1111yescharacteristic
93C22×C11#50911yescharacteristic
94C2×D11—81no—
95C4×C11—41no—
96C4×C11—82no—
97C4×C11—161no—
98C4×C11C4×D811yescharacteristic
99C4×C11#50911yescharacteristic
100Dic11—81no—
101#135—221no—
102C2×Q16—21no—
103#131—441no—
104C4×Q8—41no—
105Q32—21no—
106Q32—111no—
107Q32C4×D1112yes—
108SD32—221no—
109D16—111no—
110C2×C16C22⋊D1111yescharacteristic
111C2×C16C22×D1111yescharacteristic
112#108—221no—
113#107—21no—
114#104—441no—
115#103—41no—
116C4×C8C22⋊D1111yescharacteristic
117C32—112no—
118C32—221no—
119C2×C11—21no—
120C2×C11#217711yescharacteristic
121D11—161no—
122#41—441no—
123C2×Q8—41no—
124Q16—22no—
125Q16—41no—
126Q16—221no—
127SD16—441no—
128D8—221no—
129M16—441no—
130M16—881no—
131C2×C8—881no—
132C2×C8#432311yescharacteristic
133C2×C8C2×C22⋊D1111yescharacteristic
134C4⋊C4—41no—
135C4⋊C4—81no—
136C42—81no—
137C42#432311yescharacteristic
138C16—21no—
139C16C2×C4×D1111yescharacteristic
140C16#433911yescharacteristic
141C11#1365711yescharacteristic, complemented, Sylow
142Q8—42no—
143Q8—81no—
144Q8—441no—
145D4—441no—
146D4—881no—
147C2×C4—21no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—881no—
151C2×C4C2×#432311yescharacteristic
152C8—21no—
153C8—881no—
154C8C4×C22⋊D1111yescharacteristic
155C8#6700311yescharacteristic
156C22—881no—
157C22#1062276011yescharacteristic
158C4—41no—
159C4—82no—
160C4—161no—
161C4—881no—
162C4C4×#432311yescharacteristic
163C4#1062280611yescharacteristic
164C2—21no—
165C2—1761no—
166C2#1307049011yescharacteristic
subgroupG/H
centerC2#13070490
commutatorC11×C16C22×C4
FrattiniC2×C16C22×D11
FittingC11×#2176C2
socleC2×C11#2177
prime radical#10622517C22
cosocleC2×C11×C16C23
hypercenter#2176D11
hypocenterC11#13657
LCSG ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #346 ◁ #2176

Complements

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

NH ≅ G/Ntype
3. #13066821C2semidirect
4. #13066809C2semidirect
6. #13066752C2semidirect
7. C11×#2176C2semidirect
15. #10622160C4semidirect
16. #10622159C4semidirect
61. #2176D11semidirect
141. C11#13657semidirect

Maximal subgroups

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

subgroupindex
#130709342
#130705032
#130668212
#130668092
#130668022
#130667522
C11×#21762
#1365711