Finite Group Databasebeta

← #11771145

Subgroups — #11771145

Order 1152.

350 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593806C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10592347C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4×C3⋊Dic3—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C22⋊#622—21no—
8#63777—21no—
9#63777C412yescomplemented
10C4⋊#622C412yescomplemented
11C4×#622—21no—
12C32×#95C411yescharacteristic
13#63658—21no—
14#63658C411yescharacteristic
15#4648—62no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21#3792—22no—
22#3792—22no—
23C2×#622—22no—
24C2×#622—22no—
25C4×C3⋊Dic3—24no—
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30#1300—91nomaximal, Sylow
31C2×C4×Dic3—62no—
32C2×C4×Dic3—64no—
33C3×#95—22no—
34C3⋊#95—62no—
35C3⋊#95—64no—
36C23×C32C22⋊C411yescharacteristic
37C2×C32×C4—22no—
38C2×C32×C4—41no—
39C2×C32×C4—41no—
40C2×C32×C4—41no—
41C2×C32×C4C4211yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—21no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C22⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53#622—24no—
54#622—42no—
55#432—91no—
56C4×M16—91no—
57#376—91no—
58C22×C3×C4—24no—
59C22×C3×C4—22no—
60C22×Dic3—62no—
61C22×Dic3—62no—
62C22×Dic3—64no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—616no—
68C22×C32—21no—
69C22×C32—21no—
70C22×C32#9511yescharacteristic
71C22×C32#10411yescharacteristic
72C22×C32#10411yescharacteristic
73C32×C4—21no—
74C32×C4—21no—
75C32×C4—42no—
76C3⋊Dic3—21no—
77C3⋊Dic3—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3—42no—
80C3⋊Dic3#10412yes—
81C2×M16—181no—
82C2×C42—91no—
83C2×C42—181no—
84C4⋊C8—92no—
85C22⋊C8—181no—
86#97—92no—
87#97—181no—
88C4×C8—181no—
89#95—91no—
90#95—181no—
91#95#15711yescharacteristic
92C23×C3—22no—
93C2×C3×C4—28no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—44no—
97C2×C3×C4—44no—
98C2×C3×C4—44no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—62no—
103C2×Dic3—68no—
104C2×Dic3—68no—
105C2×Dic3—122no—
106C2×Dic3—122no—
107C2×Dic3—124no—
108C2×Dic3—124no—
109C2×C32—21no—
110C2×C32—21no—
111C2×C32#33911yescharacteristic
112C2×C32#33911yescharacteristic
113C2×C32#34411yescharacteristic
114C22×C4—21no—
115C22×C4—91no—
116C22×C4—91no—
117C22×C4—181no—
118C22×C4C2×#15711yescharacteristic
119M16—182no—
120M16—182no—
121C2×C8—182no—
122C2×C8—182no—
123C42—91no—
124C42—91no—
125C42—91no—
126C42—91no—
127C42—184no—
128C22×C3—24no—
129C22×C3—24no—
130C22×C3—22no—
131C22×C3—22no—
132C22×C3—22no—
133C3×C4—42no—
134C3×C4—42no—
135C3×C4—48no—
136Dic3—64no—
137Dic3—64no—
138Dic3—122no—
139Dic3—122no—
140Dic3—128no—
141C32#130011yescharacteristic, complemented, Sylow
142C23C22⋊#15711yescharacteristic
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—182no—
152C2×C4—181no—
153C2×C4—181no—
154C2×C4—182no—
155C2×C4—361no—
156C2×C4—361no—
157C2×C4C4×#15711yescharacteristic
158C2×C4C4⋊#15711yescharacteristic
159C8—184no—
160C8—362no—
161C2×C3—24no—
162C2×C3—24no—
163C2×C3—22no—
164C2×C3—22no—
165C2×C3—22no—
166C22—21no—
167C22—21no—
168C22#6378111yescharacteristic
169C22#6378311yescharacteristic
170C22#6378511yescharacteristic
171C4—21no—
172C4—21no—
173C4—42no—
174C4—92no—
175C4—181no—
176C4—181no—
177C4—181no—
178C4—362no—
179C3—22no—
180C2—21no—
181C2—21no—
182C2#1059015111yescharacteristic
183C2#1059015611yescharacteristic
184C2#1059016411yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenter#95#157
hypocenterC32#1300
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
9. #63777C4semidirect
10. C4⋊#622C4semidirect
141. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105938062
C4×#37922
#105923472
#13009