Finite Group Databasebeta

← #11770861

Subgroups — #11770861

Order 1152.

298 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 60 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#10593801C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3C2×#63641C211yesmaximal, characteristic
4C2×#3792C412yes—
5C22×C32×C8C411yescharacteristic
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C22×C3⋊(C3⋊C8)C411yescharacteristic
8C22⋊#622C412yes—
9#63779—21no—
10#63777—21no—
11C4×#622—21no—
12C4×#622—21no—
13#63641—21no—
14#63641—21no—
15C2×Dic3⋊C8—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×C32×C8—21no—
24C2×C32×C8—41no—
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30C2×C3⋊(C3⋊C8)—41no—
31#1283—91nomaximal, Sylow
32C22×C3×C8—22no—
33C2×C4×Dic3—62no—
34C22×C3⋊C8—62no—
35Dic3⋊C8—64no—
36Dic3⋊C8—64no—
37C23×C32C4211yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3C22⋊C411yescharacteristic
44C2×C3⋊Dic3C22⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47C2×C3⋊Dic3C2×C812yes—
48C2×C3⋊Dic3M1612yes—
49#622—24no—
50#622—42no—
51C32×C8—41no—
52C3⋊(C3⋊C8)—41no—
53#431—91no—
54C2×C4⋊C8—91no—
55C4×M16—91no—
56C22×C3×C4—22no—
57C22×Dic3—62no—
58C22×Dic3—62no—
59C2×C3×C8—24no—
60C2×C3×C8—44no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C2×C3⋊C8—64no—
66C2×C3⋊C8—124no—
67C22×C32—21no—
68C22×C32—21no—
69C22×C32#9511yescharacteristic
70C22×C32C4×C811yescharacteristic
71C22×C32#9711yescharacteristic
72C32×C4—21no—
73C32×C4#10011yescharacteristic
74C32×C4#10111yescharacteristic
75C3⋊Dic3—21no—
76C3⋊Dic3—21no—
77C3⋊Dic3C22⋊C812yes—
78C3⋊Dic3C4⋊C812yes—
79C2×M16—92no—
80C22×C8—91no—
81C22×C8#15711yescharacteristic
82C2×C42—91no—
83C4⋊C8—181no—
84C4⋊C8—181no—
85C4⋊C8—181no—
86C22⋊C8—92no—
87#97—181no—
88C4×C8—181no—
89C4×C8—181no—
90C23×C3—22no—
91C2×C3×C4—24no—
92C2×C3×C4—24no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—64no—
98C2×Dic3—64no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—124no—
102C3×C8—44no—
103C3⋊C8—124no—
104C2×C32—21no—
105C2×C32—21no—
106C2×C32#33611yescharacteristic
107C2×C32#34311yescharacteristic
108C2×C32#34411yescharacteristic
109C22×C4—91no—
110C22×C4—91no—
111C22×C4C2×#15711yescharacteristic
112M16—94no—
113M16—182no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—182no—
117C2×C8—182no—
118C2×C8—181no—
119C2×C8—361no—
120C42—91no—
121C42—91no—
122C42—91no—
123C42—91no—
124C22×C3—24no—
125C22×C3—24no—
126C22×C3—22no—
127C22×C3—22no—
128C22×C3—22no—
129C3×C4—24no—
130C3×C4—22no—
131C3×C4—22no—
132Dic3—64no—
133Dic3—64no—
134Dic3—122no—
135Dic3—122no—
136C32#128311yescharacteristic, complemented, Sylow
137C23C4×#15711yescharacteristic
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—92no—
141C2×C4—92no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—361no—
147C2×C4C4⋊#15711yescharacteristic
148C2×C4C22⋊#15711yescharacteristic
149C8—41no—
150C8—184no—
151C8—362no—
152C8—361no—
153C2×C3—24no—
154C2×C3—24no—
155C2×C3—22no—
156C2×C3—22no—
157C2×C3—22no—
158C22—21no—
159C22—21no—
160C22C8×#15711yescharacteristic
161C22#6376711yescharacteristic
162C22#6378111yescharacteristic
163C4—21no—
164C4—92no—
165C4—92no—
166C4—181no—
167C4—181no—
168C4#6378011yescharacteristic
169C4#6378811yescharacteristic
170C3—22no—
171C2—21no—
172C2—21no—
173C2#1059018111yescharacteristic
174C2#1059018311yescharacteristic
175C2#1059020811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C4×C8
FrattiniC22×C4C2×#157
FittingC22×C32×C8C4
socleC22×C32#95
prime radicalC23×C32C42
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22×C8#157
hypocenterC32#1283
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

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

Maximal subgroups

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

subgroupindex
#105938012
C4×#37922
C2×#636412
#12839