Finite Group Databasebeta

← #11770900

Subgroups — #11770900

Order 1152.

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

normal subgroups only

This group has 358 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#10593804C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3C4×#3750C211yesmaximal, characteristic
4C2×C32×C42C411yescharacteristic
5C2×#3750—21no—
6C2×C4×C3⋊Dic3C411yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22⋊#622—21no—
9C22⋊#622—21no—
10#63779—21no—
11#63779C412yescomplemented
12#63777—21no—
13#63777C412yescomplemented
14#63658—21no—
15C4×Dic3⋊C4—62no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C2×#622—22no—
22C2×#622—22no—
23C32×C42—41no—
24#3750—24no—
25C4×C3⋊Dic3—41no—
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30#1285—91nomaximal, Sylow
31C2×C3×C42—22no—
32C2×Dic3⋊C4—64no—
33C2×C4×Dic3—62no—
34C2×C4×Dic3—62no—
35C3⋊#95—64no—
36C23×C32C22⋊C411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—22no—
40C2×C32×C4—41no—
41C2×C32×C4—41no—
42C2×C32×C4C4211yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—41no—
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—42no—
54#622—42no—
55#432—91no—
56#432—91no—
57C4×C4⋊C4—91no—
58C22×C3×C4—24no—
59C22×C3×C4—22no—
60C22×Dic3—62no—
61C22×Dic3—62no—
62C22×Dic3—64no—
63C3×C42—44no—
64Dic3⋊C4—616no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C4×Dic3—62no—
69C4×Dic3—124no—
70C22×C32—21no—
71C22×C32—21no—
72C22×C32#9511yescharacteristic
73C22×C32#10011yescharacteristic
74C22×C32#10111yescharacteristic
75C32×C4—21no—
76C32×C4—21no—
77C32×C4—42no—
78C3⋊Dic3—21no—
79C3⋊Dic3—21no—
80C3⋊Dic3—21no—
81C3⋊Dic3—42no—
82C3⋊Dic3#10412yes—
83C2×C4⋊C4—181no—
84C2×C42—91no—
85C2×C42—91no—
86C2×C42#15711yescharacteristic
87C4⋊C8—92no—
88C4⋊C8—181no—
89C22⋊C8—181no—
90C22⋊C8—181no—
91#97—92no—
92#97—181no—
93#95—181no—
94C23×C3—22no—
95C2×C3×C4—24no—
96C2×C3×C4—24no—
97C2×C3×C4—28no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—44no—
101C2×C3×C4—44no—
102C2×Dic3—62no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—68no—
107C2×Dic3—68no—
108C2×Dic3—124no—
109C2×Dic3—124no—
110C2×Dic3—124no—
111C2×C32—21no—
112C2×C32—21no—
113C2×C32H(3,ℤ/4)11yescharacteristic
114C2×C32#33911yescharacteristic
115C2×C32#34311yescharacteristic
116C22×C4—21no—
117C22×C4—91no—
118C22×C4—91no—
119C22×C4—181no—
120C22×C4C2×#15711yescharacteristic
121C2×C8—182no—
122C2×C8—182no—
123C4⋊C4—184no—
124C42—41no—
125C42—91no—
126C42—91no—
127C42—91no—
128C42—91no—
129C42—361no—
130C22×C3—24no—
131C22×C3—24no—
132C22×C3—22no—
133C22×C3—22no—
134C22×C3—22no—
135C3×C4—24no—
136C3×C4—24no—
137C3×C4—48no—
138Dic3—64no—
139Dic3—64no—
140Dic3—122no—
141Dic3—122no—
142Dic3—128no—
143C32#128511yescharacteristic, complemented, Sylow
144C23C22⋊#15711yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—182no—
155C2×C4—182no—
156C2×C4—361no—
157C2×C4—361no—
158C2×C4—361no—
159C2×C4C4×#15711yescharacteristic
160C2×C4C4⋊#15711yescharacteristic
161C8—362no—
162C8—362no—
163C2×C3—24no—
164C2×C3—24no—
165C2×C3—22no—
166C2×C3—22no—
167C2×C3—22no—
168C22—21no—
169C22—21no—
170C22#6378011yescharacteristic
171C22#6378111yescharacteristic
172C22#6378811yescharacteristic
173C4—21no—
174C4—21no—
175C4—42no—
176C4—92no—
177C4—181no—
178C4—181no—
179C4—181no—
180C4—362no—
181C3—22no—
182C2—21no—
183C2—21no—
184C2#1059015111yescharacteristic
185C2#1059015211yescharacteristic
186C2#1059020811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenterC2×C42#157
hypocenterC32#1285
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
11. #63779C4semidirect
13. #63777C4semidirect
143. C32#1285semidirect

Maximal subgroups

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

subgroupindex
#105938042
C4×#37502
#12859