Finite Group Databasebeta

← #11770860

Subgroups — #11770860

Order 1152.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#63779C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4C2×#3792C412yes—
5C22×#622C412yes—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7#63779—21no—
8#63779—21no—
9#63777—21no—
10C4×#622—21no—
11C32×C22⋊C8C411yescharacteristic
12#63657C411yescharacteristic
13#63641—21no—
14C8×C3⋊Dic3—21no—
15#4718—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19#3792—22no—
20#3792C814yescomplemented
21C2×#622—22no—
22C2×#622—22no—
23C2×#622—42no—
24C2×C32×C8—21no—
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30#1283—91nomaximal, Sylow
31C2×C4×Dic3—62no—
32C3×C22⋊C8—22no—
33#830—62no—
34Dic3⋊C8—64no—
35C8×Dic3—64no—
36C23×C32C4211yescharacteristic
37C2×C32×C4—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C32×C4C4⋊C411yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C22⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C2×C812yes—
47C2×C3⋊Dic3M1612yes—
48#622—24no—
49#622—42no—
50C32×C8—41no—
51C3⋊(C3⋊C8)—41no—
52#431—91no—
53C2×C4⋊C8—91no—
54C4×M16—91no—
55C22×C3×C4—22no—
56C22×Dic3—62no—
57C22×Dic3—62no—
58C2×C3×C8—24no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C2×C3⋊C8—64no—
64C22×C32—21no—
65C22×C32—21no—
66C22×C32#9511yescharacteristic
67C22×C32C4×C811yescharacteristic
68C22×C32#9711yescharacteristic
69C32×C4—21no—
70C32×C4—21no—
71C3⋊Dic3—21no—
72C3⋊Dic3C22⋊C812yes—
73C3⋊Dic3#10011yescharacteristic
74C3⋊Dic3#10111yescharacteristic
75C3⋊Dic3C4⋊C812yes—
76C2×M16—92no—
77C22×C8—92no—
78C2×C42—91no—
79C4⋊C8—181no—
80C4⋊C8—181no—
81C4⋊C8—181no—
82C22⋊C8—91no—
83C22⋊C8#15711yescharacteristic
84#97—181no—
85C4×C8—181no—
86C4×C8—181no—
87C23×C3—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—44no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—64no—
95C2×Dic3—64no—
96C2×Dic3—62no—
97C2×Dic3—122no—
98C2×Dic3—122no—
99C3×C8—44no—
100C3⋊C8—124no—
101C2×C32—21no—
102C2×C32—21no—
103C2×C32#33611yescharacteristic
104C2×C32#34311yescharacteristic
105C2×C32#34411yescharacteristic
106C22×C4—91no—
107C22×C4—91no—
108C22×C4C2×#15711yescharacteristic
109M16—94no—
110M16—182no—
111C2×C8—21no—
112C2×C8—182no—
113C2×C8—182no—
114C2×C8—181no—
115C2×C8—362no—
116C42—91no—
117C42—91no—
118C42—91no—
119C42—91no—
120C22×C3—22no—
121C22×C3—22no—
122C22×C3—22no—
123C22×C3—42no—
124C22×C3—42no—
125C3×C4—24no—
126C3×C4—42no—
127Dic3—64no—
128Dic3—64no—
129Dic3—62no—
130Dic3—62no—
131Dic3—122no—
132C32#128311yescharacteristic, complemented, Sylow
133C23C4×#15711yescharacteristic
134C2×C4—41no—
135C2×C4—92no—
136C2×C4—92no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—91no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4C4⋊#15711yescharacteristic
144C2×C4C22⋊#15711yescharacteristic
145C8—41no—
146C8—184no—
147C8—361no—
148C8—362no—
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—22no—
152C2×C3—42no—
153C2×C3—42no—
154C22—21no—
155C22—21no—
156C22C8×#15711yescharacteristic
157C22#6376711yescharacteristic
158C22#6378111yescharacteristic
159C4—21no—
160C4—21no—
161C4—92no—
162C4—92no—
163C4—91no—
164C4—91no—
165C4—181no—
166C3—22no—
167C2—21no—
168C2—21no—
169C2#1059015611yescharacteristic
170C2#1059018111yescharacteristic
171C2#1059018811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC22×C32C4×C8
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C32C42
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22⋊C8#157
hypocenterC32#1283
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
20. #3792C8semidirect
132. C32#1283semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C4×#37922
#105924172
#12839