Finite Group Databasebeta

← #14668103

Subgroups — #14668103

Order 2816.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070891C211yesmaximal, characteristic, complemented
2#13068015C212yesmaximal
3#13066688C211yesmaximal, characteristic, complemented
4#13066673C212yesmaximal, complemented
5D4×C11×C16C211yesmaximal, characteristic
6C22×C11×C16—21no—
7C8×D4×C11C2211yescharacteristic
8#10622621—22no—
9#10622295C2212yes—
10C11×C4⋊C16C2211yescharacteristic
11C11×C22⋊C16—21no—
12C4×C11×C16C2211yescharacteristic
13#10622142—21no—
14#10622142—21no—
15#10622119—22no—
16#10622096C2212yes—
17C22×C8×C11—21no—
18C4×D4×C11D411yescharacteristic
19#66922—22no—
20C2×C11×C16—21no—
21C2×C11×C16—42no—
22C2×C11×C16D411yescharacteristic
23C2×C11×C16D411yescharacteristic
24C11×C4⋊C8D411yescharacteristic
25C11×C22⋊C8—21no—
26C4×C8×C11C2311yescharacteristic
27#66896—42no—
28#66882—22no—
29#66882—22no—
30#66872—42no—
31C4⋊(C11⋊C8)—22no—
32#12452—111nomaximal, Sylow
33C2×D4×C11D811yescharacteristic
34C22×C4×C11—21no—
35C2×Dic22—42no—
36C2×C8×C11—21no—
37C2×C8×C11—41no—
38C2×C8×C11—41no—
39C2×C8×C11C2×D411yescharacteristic
40C2×C8×C11#4111yescharacteristic
41C11×C4⋊C4D811yescharacteristic
42C11×C22⋊C4—21no—
43C42×C11C2×D411yescharacteristic
44C4⋊Dic11—42no—
45C4⋊Dic11—42no—
46C2×C11⋊C8—42no—
47C11×C16—21no—
48C11×C16—41no—
49C11×C16SD1612yes—
50#2252—111no—
51D4×C16D1111yescharacteristic
52#1675—112no—
53#1371—111no—
54#1365—112no—
55C23×C11—21no—
56D4×C11—21no—
57D4×C11Q3212yes—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11#12111yescharacteristic
62C2×C4×C11C2×D811yescharacteristic
63C2×C4×C11#13511yescharacteristic
64C2×Dic11—82no—
65Dic22—162no—
66C8×C11—21no—
67C8×C11—41no—
68C8×C11C2×SD1611yescharacteristic
69C8×C11#13711yescharacteristic
70C11⋊C8—82no—
71C22×C16—21no—
72#500—112no—
73#476—222no—
74C8×D4C2×D1111yescharacteristic
75#366—221no—
76#366—221no—
77C4⋊C16C2×D1111yescharacteristic
78C22⋊C16—21no—
79C4×C16C2×D1111yescharacteristic
80#335—112no—
81#333—222no—
82C22×C11—22no—
83C22×C11—41no—
84C22×C11—41no—
85C22×C11#46611yescharacteristic
86C4×C11—21no—
87C4×C11—41no—
88C4×C11#46111yescharacteristic
89C4×C11#47311yescharacteristic
90C4×C11C2×Q3211yescharacteristic
91C4×C11#50811yescharacteristic
92Dic11—162no—
93C22×C8—21no—
94C4⋊Q8—222no—
95C4×D4D4411yescharacteristic
96C2×C16—21no—
97C2×C16—42no—
98C2×C16C22⋊D1111yescharacteristic
99C2×C16C22⋊D1111yescharacteristic
100#107—222no—
101#107—222no—
102#106—442no—
103C4⋊C8—222no—
104C4⋊C8D4411yescharacteristic
105#102—442no—
106C22⋊C8—21no—
107C4×C8C22×D1111yescharacteristic
108C2×C11—42no—
109C2×C11#167311yescharacteristic
110C2×C11#221611yescharacteristic
111C2×C11#222111yescharacteristic
112C2×Q8—442no—
113C2×D4D8811yescharacteristic
114C22×C4—21no—
115C2×C8—21no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—442no—
119C2×C8#433911yescharacteristic
120C2×C8C2×C22⋊D1111yescharacteristic
121C4⋊C4—442no—
122C4⋊C4—442no—
123C4⋊C4D8811yescharacteristic
124C22⋊C4—21no—
125C42C2×D4411yescharacteristic
126C16—21no—
127C16—41no—
128C16#432412yes—
129C11#1245211yescharacteristic, complemented, Sylow
130C23—21no—
131Q8—1762no—
132D4—21no—
133D4Dic8812yes—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—882no—
138C2×C4C2×D8811yescharacteristic
139C2×C4#6695711yescharacteristic
140C2×C4#6698311yescharacteristic
141C8—21no—
142C8—41no—
143C8—882no—
144C8C2×#432411yescharacteristic
145C8#6700411yescharacteristic
146C22—22no—
147C22—41no—
148C22—41no—
149C22#1062272811yescharacteristic
150C4—21no—
151C4—41no—
152C4—1762no—
153C4#1062251711yescharacteristic
154C4C2×Dic8811yescharacteristic
155C4#1062263211yescharacteristic
156C4#1062275611yescharacteristic
157C2—42no—
158C2#1306800511yescharacteristic
159C2#1307070711yescharacteristic
160C2#1307073611yescharacteristic
subgroupG/H
centerC22#10622728
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingD4×C11×C16C2
socleC22×C11#466
prime radicalC2×D4×C11D8
hypercenterD4×C16D11
hypocenterC11#12452
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13070891C2semidirect
3. #13066688C2semidirect
4. #13066673C2semidirect
129. C11#12452semidirect

Maximal subgroups

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

subgroupindex
#130708912
#130680152
#130666882
#130666732
D4×C11×C162
#1245211