Finite Group Databasebeta

← #11784207

Subgroups — #11784207

Order 1152.

438 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 107 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
2C2×#63732C212yesmaximal
3#10590322C212yesmaximal
4#10590044C212yesmaximal
5C2×C4×#157C412yes—
6C2×C4×#157C412yes—
7C2×C4×#157C2211yescharacteristic
8C2×C4×#157C2211yescharacteristic
9C42×C3⋊D3C2211yescharacteristic
10C2×#3710C2214yes—
11#63732C418yescomplemented
12C3×#803—22no—
13#63555—22no—
14D3×#97—62no—
15C22×#157C2×C411yescharacteristic
16C22×#157C2×C412yes—
17C22×#157C2×C411yescharacteristic
18C2×C4×C3⋊D3C2×C412yes—
19C2×C4×C3⋊D3C2311yescharacteristic
20C4×#157—24no—
21C4×#157—24no—
22C4×#157—22no—
23C4×#157C2×C414yes—
24C32×C42D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q812yes—
27C2×C3×C3⋊C8—24no—
28#3710—24no—
29#3710C2×C418yes—
30#1767—91nomaximal, Sylow
31C2×D3×C8—64no—
32C42×D3—62no—
33C3×#97—62no—
34#815—64no—
35#803—22no—
36C22×C3⋊D3C22×C411yescharacteristic
37C2×#157—22no—
38C2×#157—22no—
39C2×#157—22no—
40C2×#157C4212yes—
41C2×#157C4212yes—
42C2×#157M1614yes—
43C2×#157M1614yes—
44C2×C32×C4C4⋊C412yes—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3C4⋊C412yes—
47C2×C3⋊Dic3C2×Q811yescharacteristic
48C4×C3⋊D3—22no—
49C4×C3⋊D3—22no—
50C4×C3⋊D3C22×C412yes—
51C4×C3⋊D3#4112yes—
52C3×C3⋊C8—28no—
53C2×C4⋊C8—92no—
54C2×#97—92no—
55C43—91no—
56#336—92no—
57C2×C4×D3—62no—
58C2×C4×D3—64no—
59C2×C3×C8—64no—
60C3×C42—22no—
61C4×Dic3—62no—
62C4×Dic3—64no—
63C2×C3⋊C8—24no—
64D3×C8—68no—
65D3×C8—68no—
66C22×C32C2×C4⋊C411yescharacteristic
67C2×C3⋊D3C2×C4211yescharacteristic
68C2×C3⋊D3#11711yescharacteristic
69C2×C3⋊D3C2×M1612yes—
70C2×C3⋊D3C2×M1612yes—
71#157—22no—
72#157—24no—
73#157#9714yescomplemented
74C32×C4—22no—
75C32×C4C4×D412yes—
76C3⋊Dic3—22no—
77C3⋊Dic3C4×Q812yes—
78C22×C8—94no—
79C2×C42—91no—
80C2×C42—91no—
81C2×C42—92no—
82C2×C42—92no—
83C2×C42—91no—
84C4⋊C8—98no—
85#97—62no—
86#97—182no—
87C22×D3—62no—
88C2×C3×C4—22no—
89C2×C3×C4—24no—
90C2×Dic3—62no—
91C2×Dic3—64no—
92C4×D3—64no—
93C4×D3—64no—
94C4×D3—124no—
95C4×D3—124no—
96C3×C8—68no—
97C3⋊C8—28no—
98C2×C32C4×C4⋊C411yescharacteristic
99C2×C32#42312yes—
100C3⋊D3C2×#9711yescharacteristic
101C3⋊D3C4×M1611yescharacteristic
102C3⋊D3#43212yes—
103C22×C4—91no—
104C22×C4—91no—
105C22×C4—91no—
106C22×C4—92no—
107C22×C4—92no—
108C2×C8—64no—
109C2×C8—98no—
110C2×C8—184no—
111C42—94no—
112C42—91no—
113C42—92no—
114C42—184no—
115C42—182no—
116C42—184no—
117C42GO+(4,𝔽2)11yescharacteristic
118C22×C3—22no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—64no—
122C2×D3—64no—
123C3×C4—24no—
124C3×C4—44no—
125Dic3—64no—
126Dic3—124no—
127C32#176711yescharacteristic, complemented, Sylow
128C23—91no—
129C2×C4—92no—
130C2×C4—94no—
131C2×C4—91no—
132C2×C4—92no—
133C2×C4—92no—
134C2×C4—92no—
135C2×C4—94no—
136C2×C4—92no—
137C2×C4—182no—
138C2×C4—182no—
139C2×C4—182no—
140C2×C4—182no—
141C2×C4—182no—
142C2×C4#377312yes—
143C2×C4C2×GO+(4,𝔽2)11yescharacteristic
144C8—68no—
145C2×C3—24no—
146C2×C3—22no—
147D3—62no—
148D3—62no—
149D3—64no—
150C22—92no—
151C22—92no—
152C22—91no—
153C22—91no—
154C22C2×#377311yescharacteristic
155C4—22no—
156C4—94no—
157C4—92no—
158C4—182no—
159C4—184no—
160C4—182no—
161C4C4×GO+(4,𝔽2)12yes—
162C3—22no—
163C2—91no—
164C2—91no—
165C2—92no—
166C2#1059332812yes—
167C2C4×#377311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1767
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #63732C4semidirect
73. #157#97semidirect
127. C32#1767semidirect

Maximal subgroups

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

subgroupindex
C42×#1572
C2×#637322
#105903222
#105900442
#17679