Finite Group Databasebeta

← #11784451

Subgroups — #11784451

Order 1152.

474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×C4×#622C211yesmaximal, characteristic
2C2×#63742C212yesmaximal
3#10591257C212yesmaximal
4#10590075C212yesmaximal
5C22×#622C2211yescharacteristic
6C22×#622C2211yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×#3724C2214yes—
9C2×Dic32—22no—
10C4×#622C414yescomplemented
11#63742C418yescomplemented
12C3×C3⋊#95—22no—
13#4649—62no—
14C22×C32×C4D411yescharacteristic
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3⋊Dic3C2311yescharacteristic
17C22×C3×Dic3—24no—
18C2×#622—22no—
19C2×#622C2×C412yes—
20C2×#622C2×C412yes—
21C2×#622C2×C414yes—
22C4×C3⋊Dic3C2×C412yes—
23C4×C3⋊Dic3Q812yes—
24#3724—24no—
25#3724C2×C418yes—
26Dic32—44no—
27C4×#106—91nomaximal, Sylow
28C2×Dic3⋊C4—64no—
29C2×C4×Dic3—62no—
30C2×C4×Dic3—64no—
31C3×#95—62no—
32C3⋊#95—22no—
33C23×C32C2×D411yescharacteristic
34C2×C32×C4—22no—
35C2×C32×C4C4⋊C412yes—
36C2×C3⋊Dic3C4⋊C412yes—
37C2×C3⋊Dic3SD1614yes—
38C2×C3⋊Dic3C22×C411yescharacteristic
39C2×C3⋊Dic3C22×C412yes—
40C2×C3⋊Dic3C2×Q811yescharacteristic
41C2×C3⋊Dic3#4112yes—
42C2×C3×Dic3—28no—
43C2×C3×Dic3—44no—
44C2×C3×Dic3—44no—
45#622—22no—
46#622C4214yescomplemented
47C2×#106—92no—
48C2×C4×C8—91no—
49C4×C4⋊C4—92no—
50#340—92no—
51C22×C3×C4—22no—
52C22×C3×C4—64no—
53C22×Dic3—24no—
54C22×Dic3—62no—
55C22×Dic3—62no—
56Dic3⋊C4—68no—
57Dic3⋊C4—68no—
58C4×Dic3—64no—
59C4×Dic3—64no—
60C4×Dic3—128no—
61C22×C32C2×C4⋊C411yescharacteristic
62C22×C32C4×D412yes—
63C22×C32C2×SD1612yes—
64C22×C32#13512yes—
65C32×C4—22no—
66C3⋊Dic3#10614yescomplemented
67C3⋊Dic3C2×C4211yescharacteristic
68C3⋊Dic3#11711yescharacteristic
69C3⋊Dic3C4×Q812yes—
70C3×Dic3—48no—
71C22×C8—91no—
72C22×C8—91no—
73C2×C4⋊C4—94no—
74C2×C42—91no—
75C2×C42—182no—
76#106—98no—
77C4×C8—94no—
78#95—62no—
79C23×C3—22no—
80C2×C3×C4—24no—
81C2×C3×C4—44no—
82C2×C3×C4—68no—
83C2×C3×C4—124no—
84C2×C3×C4—124no—
85C2×Dic3—28no—
86C2×Dic3—44no—
87C2×Dic3—44no—
88C2×Dic3—64no—
89C2×Dic3—64no—
90C2×Dic3—64no—
91C2×Dic3—62no—
92C2×Dic3—64no—
93C2×Dic3—62no—
94C2×Dic3—64no—
95C2×C32C4×C4⋊C411yescharacteristic
96C2×C32C2×#10611yescharacteristic
97C2×C32#42711yescharacteristic
98C2×C32C4×SD1614yes—
99C22×C4—64no—
100C22×C4—91no—
101C22×C4—91no—
102C22×C4GO+(4,𝔽2)11yescharacteristic
103C2×C8—92no—
104C2×C8—94no—
105C2×C8—92no—
106C2×C8—182no—
107C4⋊C4—98no—
108C4⋊C4—184no—
109C42—92no—
110C42—92no—
111C42—364no—
112C22×C3—22no—
113C22×C3—22no—
114C22×C3—24no—
115C22×C3—22no—
116C22×C3—24no—
117C3×C4—44no—
118C3×C4—128no—
119Dic3—48no—
120Dic3—68no—
121Dic3—62no—
122Dic3—62no—
123Dic3—64no—
124C32C4×#10611yescharacteristic, complemented, Sylow
125C23C2×GO+(4,𝔽2)11yescharacteristic
126C2×C4—22no—
127C2×C4—68no—
128C2×C4—94no—
129C2×C4—92no—
130C2×C4—92no—
131C2×C4—91no—
132C2×C4—92no—
133C2×C4—91no—
134C2×C4—124no—
135C2×C4—124no—
136C2×C4#377312yes—
137C8—94no—
138C8—182no—
139C2×C3—22no—
140C2×C3—22no—
141C2×C3—24no—
142C2×C3—24no—
143C2×C3—22no—
144C22#6422712yes—
145C22C4×GO+(4,𝔽2)12yes—
146C22C2×#377311yescharacteristic
147C22#6423712yes—
148C4—22no—
149C4—94no—
150C4—91no—
151C4—91no—
152C4—92no—
153C4—128no—
154C3—22no—
155C2#1059338711yescharacteristic
156C2C4×#377311yescharacteristic
157C2#1059343314yes—
158C2#1059351111yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4×#106
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. C4×#622C4semidirect
11. #63742C4semidirect
46. #622C42semidirect
66. C3⋊Dic3#106semidirect
124. C32C4×#106semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
C2×#637422
#105912572
#105900752
C4×#1069