Finite Group Databasebeta

← #11771101

Subgroups — #11771101

Order 1152.

504 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593845C211yesmaximal, characteristic
2#10591705C212yesmaximal
3C23×C3⋊Dic3C2211yescharacteristic
4C2×#3792C412yescomplemented
5C2×C3×#217—22no—
6C2×Dic32—22no—
7C22⋊#622—22no—
8#63579C414yescomplemented
9Dic3×C22⋊C4—62no—
10C24×C32D411yescharacteristic
11C22×C3⋊Dic3—42no—
12C22×C3⋊Dic3C2×C411yescharacteristic
13C22×C3⋊Dic3C2×C412yes—
14C22×C3⋊Dic3D412yes—
15C22×C3⋊Dic3Q811yescharacteristic
16C22×C3×Dic3—24no—
17#3792—42no—
18C2×#622—22no—
19C3×#217—28no—
20Dic32—44no—
21#1297—91nomaximal, Sylow
22C23×Dic3—62no—
23C2×C3×C22⋊C4—62no—
24C2×#217—22no—
25C2×C4×Dic3—64no—
26C3⋊#95—64no—
27C23×C32—24no—
28C23×C32—41no—
29C23×C32C22⋊C412yes—
30C23×C32C4⋊C411yescharacteristic
31C2×C3⋊Dic3—24no—
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3—42no—
34C2×C3⋊Dic3—41no—
35C2×C3⋊Dic3C4211yescharacteristic
36C2×C3⋊Dic3C22⋊C411yescharacteristic
37C2×C3⋊Dic3C4⋊C412yes—
38C2×C3×Dic3—28no—
39C2×C3×Dic3—44no—
40C2×C3×Dic3—44no—
41#622—42no—
42#407—91no—
43C4×C22⋊C4—92no—
44C24×C3—22no—
45C22×C3×C4—64no—
46C22×Dic3—24no—
47C22×Dic3—62no—
48C22×Dic3—62no—
49C22×Dic3—62no—
50C22×Dic3—62no—
51C22×Dic3—62no—
52C22×Dic3—62no—
53C22×Dic3—128no—
54C3×C22⋊C4—68no—
55#217—28no—
56C4×Dic3—128no—
57C22×C32—22no—
58C22×C32—22no—
59C22×C32—22no—
60C22×C32—21no—
61C22×C32—44no—
62C22×C32#9511yescharacteristic
63C22×C32#10414yes—
64C3⋊Dic3—22no—
65C3⋊Dic3—21no—
66C3⋊Dic3#9912yes—
67C3×Dic3—48no—
68C23×C4—91no—
69C2×M16—92no—
70C2×C22⋊C4—62no—
71C2×C42—182no—
72C22⋊C8—182no—
73#95—94no—
74C23×C3—24no—
75C23×C3—24no—
76C23×C3—22no—
77C23×C3—22no—
78C23×C3—22no—
79C23×C3—44no—
80C23×C3—44no—
81C2×C3×C4—68no—
82C2×C3×C4—124no—
83C2×C3×C4—124no—
84C2×Dic3—28no—
85C2×Dic3—44no—
86C2×Dic3—44no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—68no—
92C2×Dic3—124no—
93C2×Dic3—124no—
94C2×Dic3—124no—
95C2×Dic3—124no—
96C2×Dic3—124no—
97C2×C32—24no—
98C2×C32—41no—
99C2×C32#33912yes—
100C2×C32#34211yescharacteristic
101C24GO+(4,𝔽2)11yescharacteristic
102C22×C4—64no—
103C22×C4—92no—
104C22×C4—91no—
105C22×C4—92no—
106C22×C4—91no—
107C22×C4—362no—
108M16—362no—
109C2×C8—182no—
110C22⋊C4—68no—
111C42—364no—
112C22×C3—22no—
113C22×C3—24no—
114C22×C3—22no—
115C22×C3—24no—
116C22×C3—22no—
117C22×C3—24no—
118C22×C3—24no—
119C22×C3—42no—
120C22×C3—42no—
121C22×C3—42no—
122C22×C3—42no—
123C22×C3—48no—
124C22×C3—48no—
125C3×C4—128no—
126Dic3—48no—
127Dic3—64no—
128Dic3—64no—
129Dic3—122no—
130Dic3—122no—
131C32#129711yescharacteristic, complemented, Sylow
132C23—24no—
133C23—41no—
134C23D32⋊C412yes—
135C23#377311yescharacteristic
136C2×C4—68no—
137C2×C4—91no—
138C2×C4—92no—
139C2×C4—91no—
140C2×C4—124no—
141C2×C4—124no—
142C2×C4—184no—
143C2×C4—182no—
144C2×C4—361no—
145C2×C4—362no—
146C8—362no—
147C2×C3—24no—
148C2×C3—24no—
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—22no—
152C2×C3—44no—
153C2×C3—44no—
154C22—22no—
155C22—22no—
156C22—22no—
157C22—21no—
158C22—44no—
159C22#6373711yescharacteristic
160C22#6374114yes—
161C4—92no—
162C4—128no—
163C4—182no—
164C4—181no—
165C3—22no—
166C2—24no—
167C2—41no—
168C2#1059007412yes—
169C2#1059007711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC24GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC22×C32#95
cosocleC23×C3⋊Dic3C22
hypocenterC32#1297
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
4. C2×#3792C4semidirect
8. #63579C4semidirect
131. C32#1297semidirect

Maximal subgroups

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

subgroupindex
#105938452
#105917052
#12979