Finite Group Databasebeta

← #11785969

Subgroups — #11785969

Order 1152.

398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C42×#157C211yesmaximal, characteristic
2#10590331C212yesmaximal
3#10590044C214yesmaximal
4C2×C4×#157C412yes—
5C2×C4×#157C411yescharacteristic
6C2×C4×#157C411yescharacteristic
7C2×C4×#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C2×#3710C2214yes—
10C3×C4⋊(C3⋊C8)—22no—
11#63572—22no—
12D3×C4⋊C8—62no—
13C22×#157C2×C412yes—
14C22×#157C2×C412yes—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3C2311yescharacteristic
18C4×#157—24no—
19C4×#157—22no—
20C4×#157—24no—
21C4×#157C814yescomplemented
22C32×C42D411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C4×C3⋊Dic3Q811yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C2×C3×C3⋊C8—24no—
27#3710—28no—
28#1831—91nomaximal, Sylow
29C2×D3×C8—64no—
30C42×D3—62no—
31C3×C4⋊C8—62no—
32Dic3⋊C8—64no—
33C4⋊(C3⋊C8)—22no—
34C22×C3⋊D3C22×C411yescharacteristic
35C2×#157—22no—
36C2×#157—22no—
37C2×#157—22no—
38C2×#157—22no—
39C2×#157C2×C814yes—
40C2×#157M1614yes—
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C2×Q811yescharacteristic
47C4×C3⋊D3—22no—
48C4×C3⋊D3C2×C812yes—
49C4×C3⋊D3M1612yes—
50C4×C3⋊D3#4114yes—
51C3×C3⋊C8—44no—
52C2×C4⋊C8—92no—
53C43—91no—
54#336—94no—
55C2×C4×D3—62no—
56C2×C4×D3—62no—
57C2×C4×D3—62no—
58C2×C3×C8—64no—
59C3×C42—22no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C2×C3⋊C8—24no—
64D3×C8—128no—
65C22×C32C2×C4⋊C411yescharacteristic
66C2×C3⋊D3#11712yes—
67C2×C3⋊D3C22×C811yescharacteristic
68C2×C3⋊D3C2×M1612yes—
69C2×C3⋊D3C2×M1611yescharacteristic
70#157—24no—
71#157—24no—
72C32×C4—21no—
73C32×C4C4⋊C812yes—
74C32×C4#12412yes—
75C3⋊Dic3—21no—
76C3⋊Dic3C4⋊C812yes—
77C3⋊Dic3#12512yes—
78C22×C8—94no—
79C2×C42—91no—
80C2×C42—91no—
81C2×C42—91no—
82C2×C42—92no—
83C2×C42—92no—
84C4⋊C8—62no—
85C4⋊C8—182no—
86C22×D3—62no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×Dic3—62no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C4×D3—64no—
94C4×D3—64no—
95C4×D3—64no—
96C4×D3—64no—
97C4×D3—124no—
98C3×C8—124no—
99C3⋊C8—44no—
100C2×C32#38211yescharacteristic
101C2×C32C2×C4⋊C811yescharacteristic
102C2×C32#42311yescharacteristic
103C3⋊D3#43112yes—
104C3⋊D3#43212yes—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—92no—
108C22×C4—92no—
109C22×C4—91no—
110C2×C8—64no—
111C2×C8—188no—
112C42—94no—
113C42—91no—
114C42—91no—
115C42—91no—
116C42—184no—
117C42—182no—
118C42—184no—
119C42GO+(4,𝔽2)11yescharacteristic
120C22×C3—22no—
121C2×D3—64no—
122C2×D3—62no—
123C2×D3—62no—
124C2×D3—64no—
125C3×C4—22no—
126C3×C4—22no—
127C3×C4—24no—
128C3×C4—42no—
129Dic3—64no—
130Dic3—64no—
131Dic3—122no—
132C32#183111yescharacteristic, complemented, Sylow
133C23—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—94no—
137C2×C4—92no—
138C2×C4—92no—
139C2×C4—94no—
140C2×C4—94no—
141C2×C4—91no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4—182no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4#377311yescharacteristic
148C2×C4#377311yescharacteristic
149C2×C4C2×GO+(4,𝔽2)11yescharacteristic
150C8—124no—
151C2×C3—22no—
152C2×C3—22no—
153C2×C3—22no—
154D3—64no—
155D3—64no—
156C22—91no—
157C22—91no—
158C22—92no—
159C22—92no—
160C22C2×#377311yescharacteristic
161C4—21no—
162C4—92no—
163C4—92no—
164C4—184no—
165C4—184no—
166C4—181no—
167C4#6373212yes—
168C4#6422112yes—
169C3—22no—
170C2—92no—
171C2—92no—
172C2C2×#6373211yescharacteristic
173C2#1059332811yescharacteristic
174C2#1059334411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1831
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
21. C4×#157C8semidirect
132. C32#1831semidirect

Maximal subgroups

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

subgroupindex
C42×#1572
#105903312
#105900442
#18319