Finite Group Databasebeta

← #11783514

Subgroups — #11783514

Order 1152.

418 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 98 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×#63777C211yesmaximal, characteristic
2C2×C4×#622C211yesmaximal, characteristic
3#10592347C211yesmaximal, characteristic
4#10590207C214yesmaximal
5C22×#622C2212yes—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#63777C414yescomplemented
10C4×#622C414yescomplemented
11C32×#95C411yescharacteristic
12#63658C411yescharacteristic
13#63658C412yes—
14#4648—62no—
15C22×C32×C4C2×C412yes—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C412yes—
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20C2×#622—24no—
21C2×#622—24no—
22C2×#622C2×C414yes—
23C2×#622C2×C414yes—
24C4×C3⋊Dic3—24no—
25C4×C3⋊Dic3C2×C412yes—
26C4×C3⋊Dic3C2×C412yes—
27#1746—91nomaximal, Sylow
28C2×C4×Dic3—62no—
29C2×C4×Dic3—64no—
30C3×#95—22no—
31C3⋊#95—64no—
32C3⋊#95—62no—
33C23×C32C22×C411yescharacteristic
34C2×C32×C4—22no—
35C2×C32×C4—22no—
36C2×C32×C4—22no—
37C2×C32×C4—22no—
38C2×C32×C4C4212yes—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—22no—
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3C4212yes—
45C2×C3⋊Dic3C22×C411yescharacteristic
46C2×C3⋊Dic3C22×C411yescharacteristic
47C2×C3⋊Dic3#4114yes—
48#622—24no—
49#622—24no—
50C2×#97—91no—
51C2×C4×C8—91no—
52#376—91no—
53#336—94no—
54C22×C3×C4—24no—
55C22×C3×C4—22no—
56C22×Dic3—62no—
57C22×Dic3—62no—
58C22×Dic3—64no—
59C4×Dic3—64no—
60C4×Dic3—64no—
61C4×Dic3—616no—
62C22×C32C2×C4211yescharacteristic
63C22×C32#11712yes—
64C22×C32#13111yescharacteristic
65C22×C32#13111yescharacteristic
66C22×C32#13112yes—
67C32×C4—22no—
68C32×C4—42no—
69C3⋊Dic3—22no—
70C3⋊Dic3—42no—
71C3⋊Dic3#11712yes—
72C3⋊Dic3#11712yes—
73C22×C8—92no—
74C22×C8—92no—
75C2×C42—91no—
76C2×C42—92no—
77#97—94no—
78C4×C8—94no—
79#95—92no—
80#95—91no—
81#95#15711yescharacteristic
82C23×C3—22no—
83C2×C3×C4—28no—
84C2×C3×C4—24no—
85C2×C3×C4—44no—
86C2×C3×C4—44no—
87C2×C3×C4—44no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—68no—
91C2×Dic3—64no—
92C2×Dic3—68no—
93C2×Dic3—122no—
94C2×Dic3—122no—
95C2×Dic3—124no—
96C2×Dic3—124no—
97C2×C32#37611yescharacteristic
98C2×C32#40511yescharacteristic
99C2×C32#40511yescharacteristic
100C2×C32#43312yes—
101C2×C32#43312yes—
102C22×C4—91no—
103C22×C4—91no—
104C22×C4—92no—
105C22×C4C2×#15712yes—
106C22×C4C2×#15711yescharacteristic
107C2×C8—94no—
108C2×C8—94no—
109C2×C8—184no—
110C2×C8—184no—
111C42—92no—
112C42—92no—
113C42—184no—
114C22×C3—22no—
115C22×C3—24no—
116C22×C3—24no—
117C22×C3—22no—
118C22×C3—22no—
119C3×C4—44no—
120C3×C4—48no—
121Dic3—64no—
122Dic3—64no—
123Dic3—124no—
124Dic3—128no—
125C32#174611yescharacteristic, complemented, Sylow
126C23C22×#15711yescharacteristic
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—94no—
134C2×C4—92no—
135C2×C4—181no—
136C2×C4—181no—
137C2×C4—182no—
138C2×C4—182no—
139C2×C4—182no—
140C2×C4C4×#15712yes—
141C8—184no—
142C8—184no—
143C2×C3—22no—
144C2×C3—22no—
145C2×C3—24no—
146C2×C3—22no—
147C2×C3—24no—
148C22C2×C4×#15711yescharacteristic
149C22#6428612yes—
150C22#6428712yes—
151C22#6428711yescharacteristic
152C22#6428911yescharacteristic
153C4—22no—
154C4—42no—
155C4—92no—
156C4—92no—
157C4—182no—
158C4—362no—
159C3—22no—
160C2#1059373311yescharacteristic
161C2#1059373811yescharacteristic
162C2#1059374412yes—
163C2#1059374811yescharacteristic
164C2#1059375312yes—
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC32×#95C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1746
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
9. #63777C4semidirect
10. C4×#622C4semidirect
125. C32#1746semidirect

Maximal subgroups

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

subgroupindex
C2×#637772
C2×C4×#6222
#105923472
#105902072
#17469