Finite Group Databasebeta

← #11770770

Subgroups — #11770770

Order 1152.

290 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C4×#3788C211yesmaximal, characteristic
2C4×#3787C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4C2×#3788C412yes—
5C2×#3787—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63777—21no—
8C4×#622—21no—
9C4×#622—21no—
10C4×#622C412yes—
11C32×C4⋊C8C411yescharacteristic
12#63647—21no—
13C8×C3⋊Dic3—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
15#4833—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21#3788—22no—
22#3788C814yescomplemented
23#3787—22no—
24#3787—22no—
25C2×C32×C8—21no—
26C32×C42C2×C411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C2×C3⋊(C3⋊C8)—21no—
31#1278—91nomaximal, Sylow
32C42×D3—62no—
33C3×C4⋊C8—22no—
34(C2×D3)⋊C8—64no—
35C8×Dic3—64no—
36C4⋊(C3⋊C8)—62no—
37C22×C3⋊D3C4⋊C411yescharacteristic
38C2×C32×C4C4211yescharacteristic
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46C4×C3⋊D3—22no—
47C4×C3⋊D3C2×C812yes—
48C4×C3⋊D3M1612yes—
49#622—24no—
50#622—24no—
51C32×C8—41no—
52C3⋊(C3⋊C8)—41no—
53#431—91no—
54C4×M16—91no—
55C2×C4×C8—91no—
56C2×C4×D3—62no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C3×C8—24no—
60C3×C42—22no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C2×C3⋊C8—64no—
65C22×C32#9511yescharacteristic
66C2×C3⋊D3—21no—
67C2×C3⋊D3—21no—
68C2×C3⋊D3C4⋊C812yes—
69C32×C4—21no—
70C32×C4C4×C811yescharacteristic
71C32×C4#9711yescharacteristic
72C32×C4#10411yescharacteristic
73C32×C4#10411yescharacteristic
74C3⋊Dic3—21no—
75C3⋊Dic3C22⋊C812yes—
76C3⋊Dic3#10812yes—
77C2×M16—92no—
78C22×C8—181no—
79C2×C42—91no—
80C4⋊C8—91no—
81C4⋊C8#15711yescharacteristic
82C22⋊C8—181no—
83#97—181no—
84C4×C8—92no—
85C4×C8—181no—
86C4×C8—181no—
87C4×C8—181no—
88C22×D3—62no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C4×D3—64no—
96C4×D3—64no—
97C4×D3—124no—
98C4×D3—122no—
99C4×D3—122no—
100C3×C8—44no—
101C3⋊C8—124no—
102C2×C32#33611yescharacteristic
103C2×C32#33911yescharacteristic
104C2×C32#34111yescharacteristic
105C3⋊D3—22no—
106C22×C4—91no—
107C22×C4—91no—
108C22×C4—91no—
109M16—94no—
110M16—182no—
111C2×C8—21no—
112C2×C8—182no—
113C2×C8—182no—
114C2×C8—182no—
115C2×C8—182no—
116C2×C8—181no—
117C42—91no—
118C42—91no—
119C42—91no—
120C42C2×#15711yescharacteristic
121C22×C3—22no—
122C2×D3—64no—
123C2×D3—122no—
124C2×D3—122no—
125C3×C4—22no—
126C3×C4—22no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—42no—
130Dic3—64no—
131Dic3—64no—
132Dic3—122no—
133C32#127811yescharacteristic, complemented, Sylow
134C23—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—92no—
138C2×C4—92no—
139C2×C4—91no—
140C2×C4—182no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4C4×#15711yescharacteristic
144C2×C4C4⋊#15711yescharacteristic
145C2×C4C22⋊#15711yescharacteristic
146C8—41no—
147C8—184no—
148C8—184no—
149C8—361no—
150C2×C3—22no—
151C2×C3—22no—
152C2×C3—22no—
153D3—124no—
154C22—92no—
155C22—181no—
156C22—181no—
157C22#6378111yescharacteristic
158C4—21no—
159C4—92no—
160C4—92no—
161C4—181no—
162C4C8×#15711yescharacteristic
163C4#6376711yescharacteristic
164C4#6378311yescharacteristic
165C4#6378511yescharacteristic
166C3—22no—
167C2—182no—
168C2#1059016411yescharacteristic
169C2#1059018111yescharacteristic
170C2#1059019011yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C4×C8
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1278
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
22. #3788C8semidirect
133. C32#1278semidirect

Maximal subgroups

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

subgroupindex
C4×#37882
C4×#37872
#105925322
#12789