Finite Group Databasebeta

← #11783419

Subgroups — #11783419

Order 1152.

718 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×#3792C212yesmaximal
2C2×#64086C211yesmaximal, characteristic
3#10590208C214yesmaximal, complemented
4C23×C3⋊Dic3C2211yescharacteristic
5C2×#3792—24no—
6C2×#3792—22no—
7C2×#3792C418yescomplemented
8C2×#3792C2214yes—
9C22×#622—22no—
10C2×C32×C22⋊C4C411yescharacteristic
11C2×#3757C411yescharacteristic
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C412yes—
14#64086—22no—
15#64086—22no—
16C2×#877—62no—
17C24×C32C2×C411yescharacteristic
18C22×C32×C4C2×C412yes—
19C22×C3⋊Dic3C2×C412yes—
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C414yes—
22C22×C3⋊Dic3D412yes—
23C22×C3⋊Dic3D412yes—
24C22×C3⋊Dic3D412yes—
25C22×C3⋊Dic3Q812yes—
26C22×C3⋊Dic3C2311yescharacteristic
27#3792—28no—
28#3792—24no—
29#3792C2×C418yes—
30C2×#622—28no—
31C2×#622—24no—
32C32×C22⋊C4—22no—
33#3757—22no—
34#3750—24no—
35C4×C3⋊Dic3—22no—
36C4×C3⋊Dic3—22no—
37#1742—91nomaximal, Sylow
38C23×Dic3—62no—
39C2×C3×C22⋊C4—22no—
40C2×#217—62no—
41C2×Dic3⋊C4—64no—
42C2×C4×Dic3—64no—
43#877—68no—
44#877—68no—
45C23×C32—42no—
46C23×C32C4212yes—
47C23×C32C22⋊C412yes—
48C23×C32C4⋊C412yes—
49C23×C32C22×C411yescharacteristic
50C2×C32×C4—22no—
51C2×C32×C4—42no—
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3—42no—
54C2×C3⋊Dic3C4212yes—
55C2×C3⋊Dic3C22⋊C411yescharacteristic
56C2×C3⋊Dic3C22⋊C411yescharacteristic
57C2×C3⋊Dic3C22⋊C414yes—
58C2×C3⋊Dic3C22⋊C414yes—
59C2×C3⋊Dic3C4⋊C412yes—
60C2×C3⋊Dic3C4⋊C414yes—
61C2×C3⋊Dic3C4⋊C414yes—
62C2×C3⋊Dic3C22×C412yes—
63C2×C3⋊Dic3C2×D411yescharacteristic
64C2×C3⋊Dic3C2×D412yes—
65C2×C3⋊Dic3C2×Q811yescharacteristic
66#622—28no—
67C22×M16—92no—
68C2×#117—91no—
69#343—94no—
70C24×C3—22no—
71C22×C3×C4—24no—
72C22×Dic3—64no—
73C22×Dic3—64no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C22×Dic3—68no—
77C22×Dic3—64no—
78C22×Dic3—64no—
79C22×Dic3—64no—
80C3×C22⋊C4—28no—
81#217—68no—
82Dic3⋊C4—616no—
83C4×Dic3—68no—
84C4×Dic3—68no—
85C22×C32—22no—
86C22×C32—24no—
87C22×C32—42no—
88C22×C32—42no—
89C22×C32#9514yes—
90C22×C32C2×C4211yescharacteristic
91C22×C32C2×C22⋊C411yescharacteristic
92C22×C32C2×C4⋊C411yescharacteristic
93C32×C4—42no—
94C3⋊Dic3—42no—
95C3⋊Dic3#9512yes—
96C3⋊Dic3#9512yes—
97C3⋊Dic3C2×C22⋊C412yes—
98C3⋊Dic3C2×C4⋊C412yes—
99C23×C4—91no—
100C2×M16—98no—
101C2×M16—94no—
102C2×M16—184no—
103C2×M16—182no—
104C22×C8—182no—
105#117—182no—
106#117—182no—
107C2×C4⋊C4—92no—
108C2×C22⋊C4—91no—
109C2×C22⋊C4#15711yescharacteristic
110C2×C42—92no—
111C23×C3—22no—
112C23×C3—24no—
113C23×C3—24no—
114C23×C3—24no—
115C23×C3—48no—
116C2×C3×C4—28no—
117C2×C3×C4—48no—
118C2×Dic3—64no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—68no—
122C2×Dic3—68no—
123C2×Dic3—64no—
124C2×Dic3—68no—
125C2×Dic3—68no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—68no—
131C2×Dic3—128no—
132C2×C32—21no—
133C2×C32—21no—
134C2×C32—24no—
135C2×C32C2×#9511yescharacteristic
136C2×C32#41312yes—
137C24C2×#15711yescharacteristic
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—94no—
141C22×C4—92no—
142C22×C4—92no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—92no—
146C22×C4C2×#15712yes—
147M16—98no—
148M16—184no—
149M16—188no—
150C2×C8—188no—
151C2×C8—184no—
152C4⋊C4—184no—
153C22⋊C4—22no—
154C22⋊C4—182no—
155C42—182no—
156C42—182no—
157C22×C3—28no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—28no—
161C22×C3—22no—
162C22×C3—48no—
163C22×C3—48no—
164C22×C3—48no—
165C3×C4—48no—
166Dic3—64no—
167Dic3—64no—
168Dic3—64no—
169Dic3—64no—
170Dic3—128no—
171C32#174211yescharacteristic, complemented, Sylow
172C23—42no—
173C23C4×#15712yes—
174C23C4⋊#15712yes—
175C23C22⋊#15712yes—
176C23C22×#15711yescharacteristic
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—92no—
180C2×C4—92no—
181C2×C4—91no—
182C2×C4—92no—
183C2×C4—91no—
184C2×C4—94no—
185C2×C4—94no—
186C2×C4—94no—
187C2×C4—94no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—92no—
191C2×C4—182no—
192C2×C4—362no—
193C8—188no—
194C2×C3—24no—
195C2×C3—24no—
196C2×C3—22no—
197C2×C3—24no—
198C2×C3—48no—
199C22—22no—
200C22—24no—
201C22—42no—
202C22—42no—
203C22#6378114yes—
204C22C2×C4×#15711yescharacteristic
205C22C2×C4⋊#15711yescharacteristic
206C22C2×C22⋊#15711yescharacteristic
207C4—42no—
208C4—92no—
209C4—92no—
210C4—92no—
211C4—92no—
212C4—362no—
213C3—22no—
214C2—21no—
215C2—21no—
216C2—24no—
217C2C2×#6378111yescharacteristic
218C2#1059382412yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1742
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
7. C2×#3792C4semidirect
171. C32#1742semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#640862
#105902082
#17429