Finite Group Databasebeta

← #11770958

Subgroups — #11770958

Order 1152.

290 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 44 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#10592350C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C22⋊#622—21no—
7#63777—21no—
8#63777C412yescomplemented
9C4⋊#622—21no—
10C4×#622C412yescomplemented
11C32×#95C411yescharacteristic
12#63658—21no—
13#63658—21no—
14#63658C411yescharacteristic
15#4651—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⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29#1288—91nomaximal, Sylow
30C2×C4×Dic3—62no—
31C3×#95—22no—
32C3⋊#95—62no—
33C3⋊#95—64no—
34C3⋊#95—64no—
35C23×C32C22⋊C411yescharacteristic
36C2×C32×C4—41no—
37C2×C32×C4—41no—
38C2×C32×C4—41no—
39C2×C32×C4—41no—
40C2×C32×C4C4211yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3C22⋊C411yescharacteristic
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52#622—24no—
53#622—42no—
54#432—91no—
55C4×M16—91no—
56#383—91no—
57C22×C3×C4—24no—
58C22×C3×C4—22no—
59C22×Dic3—62no—
60C22×Dic3—62no—
61C22×Dic3—64no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C22×C32—21no—
67C22×C32—21no—
68C22×C32#9511yescharacteristic
69C22×C32#10411yescharacteristic
70C22×C32#10411yescharacteristic
71C32×C4—21no—
72C32×C4—21no—
73C32×C4—81no—
74C3⋊Dic3—21no—
75C3⋊Dic3—21no—
76C3⋊Dic3—21no—
77C3⋊Dic3—21no—
78C3⋊Dic3—81no—
79C2×M16—181no—
80C2×C42—91no—
81C4⋊C8—181no—
82C22⋊C8—181no—
83#97—92no—
84#97—181no—
85C4×C8—92no—
86#95—91no—
87#95—181no—
88#95—181no—
89#95#15711yescharacteristic
90C23×C3—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—44no—
94C2×C3×C4—44no—
95C2×C3×C4—44no—
96C2×C3×C4—44no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—122no—
102C2×Dic3—122no—
103C2×Dic3—124no—
104C2×Dic3—124no—
105C2×Dic3—124no—
106C2×Dic3—124no—
107C2×C32—21no—
108C2×C32—21no—
109C2×C32H(3,ℤ/4)11yescharacteristic
110C2×C32#33911yescharacteristic
111C2×C32#34411yescharacteristic
112C22×C4—21no—
113C22×C4—91no—
114C22×C4—91no—
115C22×C4—181no—
116C22×C4C2×#15711yescharacteristic
117M16—182no—
118M16—182no—
119C2×C8—182no—
120C2×C8—182no—
121C42—91no—
122C42—91no—
123C42—91no—
124C42—91no—
125C22×C3—24no—
126C22×C3—24no—
127C22×C3—22no—
128C22×C3—22no—
129C22×C3—22no—
130C3×C4—42no—
131C3×C4—42no—
132C3×C4—84no—
133Dic3—122no—
134Dic3—122no—
135Dic3—122no—
136Dic3—122no—
137Dic3—244no—
138C32#128811yescharacteristic, complemented, Sylow
139C23C22⋊#15711yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—181no—
149C2×C4—181no—
150C2×C4—361no—
151C2×C4—361no—
152C2×C4—361no—
153C2×C4—361no—
154C2×C4C4×#15711yescharacteristic
155C2×C4C4⋊#15711yescharacteristic
156C8—184no—
157C8—362no—
158C2×C3—24no—
159C2×C3—24no—
160C2×C3—22no—
161C2×C3—22no—
162C2×C3—22no—
163C22—21no—
164C22—21no—
165C22#6378111yescharacteristic
166C22#6378311yescharacteristic
167C22#6378511yescharacteristic
168C4—21no—
169C4—21no—
170C4—81no—
171C4—181no—
172C4—181no—
173C4—181no—
174C4—181no—
175C4—721no—
176C3—22no—
177C2—21no—
178C2—21no—
179C2#1059015211yescharacteristic
180C2#1059015611yescharacteristic
181C2#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#1288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
8. #63777C4semidirect
10. C4×#622C4semidirect
138. C32#1288semidirect

Maximal subgroups

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

subgroupindex
#105938062
C4×#37922
#105923502
#12889