Finite Group Databasebeta

← #11771034

Subgroups — #11771034

Order 1152.

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

normal subgroups only

This group has 374 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#10593802C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3#10592425C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3792—21no—
6C2×#3787C412yes—
7C2×#3743—21no—
8C22⋊#622—21no—
9#63778—21no—
10#63778—21no—
11#63778C412yes—
12C32×C22⋊C8C411yescharacteristic
13#63657C411yescharacteristic
14#63647—21no—
15#4726—62no—
16C23×C3⋊D3Q811yescharacteristic
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24#3792—42no—
25C2×#622—22no—
26C2×#622—22no—
27#3787—42no—
28C2×C32×C8—21no—
29C2×C3⋊(C3⋊C8)—21no—
30#3743—42no—
31#1293—91nomaximal, Sylow
32C22×C4×D3—62no—
33C2×ΓL(1,𝔽25)—64no—
34C3×C22⋊C8—22no—
35#830—62no—
36(C2×D3)⋊C8—64no—
37C23×C32C4⋊C411yescharacteristic
38C22×C3⋊D3—22no—
39C22×C3⋊D3—41no—
40C22×C3⋊D3—41no—
41C22×C3⋊D3C4⋊C411yescharacteristic
42C22×C3⋊D3C4⋊C411yescharacteristic
43C2×C32×C4—41no—
44C2×C32×C4C4211yescharacteristic
45C2×C32×C4C22⋊C411yescharacteristic
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3C22⋊C411yescharacteristic
48C2×C3⋊Dic3C22⋊C411yescharacteristic
49C4×C3⋊D3—22no—
50C4×C3⋊D3—22no—
51C4×C3⋊D3—41no—
52C4×C3⋊D3—41no—
53#622—42no—
54#622—42no—
55C32×C8—41no—
56C3⋊(C3⋊C8)—41no—
57#407—91no—
58#407—91no—
59C2×C22⋊C8—91no—
60C23×D3—62no—
61C22×C3×C4—22no—
62C22×Dic3—62no—
63C2×C4×D3—62no—
64C2×C4×D3—62no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×C4×D3—128no—
68C2×C3×C8—24no—
69C2×C3⋊C8—64no—
70ΓL(1,𝔽25)—128no—
71C22×C32—21no—
72C22×C32—21no—
73C22×C32—21no—
74C22×C32#9511yescharacteristic
75C2×C3⋊D3—21no—
76C2×C3⋊D3—21no—
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C2×C3⋊D3—44no—
81C2×C3⋊D3#10812yes—
82C32×C4—21no—
83C32×C4—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3#9912yes—
86C23×C4—91no—
87C2×M16—181no—
88C2×M16—181no—
89C22×C8—92no—
90C22⋊C8—92no—
91C22⋊C8—91no—
92C22⋊C8—181no—
93C22⋊C8—181no—
94C22⋊C8—181no—
95C22⋊C8—181no—
96C22⋊C8#15711yescharacteristic
97C23×C3—22no—
98C22×D3—62no—
99C22×D3—62no—
100C22×D3—124no—
101C22×D3—124no—
102C22×D3—124no—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—44no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—124no—
109C4×D3—68no—
110C4×D3—124no—
111C4×D3—124no—
112C4×D3—124no—
113C3×C8—44no—
114C3⋊C8—124no—
115C2×C32—41no—
116C2×C32#33811yescharacteristic
117C2×C32#34111yescharacteristic
118C2×C32#34211yescharacteristic
119C3⋊D3—22no—
120C3⋊D3—41no—
121C24—91no—
122C22×C4—91no—
123C22×C4—91no—
124C22×C4—91no—
125C22×C4—91no—
126C22×C4—91no—
127C22×C4—362no—
128C22×C4C2×#15711yescharacteristic
129M16—362no—
130M16—362no—
131C2×C8—21no—
132C2×C8—182no—
133C2×C8—182no—
134C2×C8—181no—
135C2×C8—362no—
136C22×C3—24no—
137C22×C3—22no—
138C22×C3—42no—
139C22×C3—42no—
140C2×D3—64no—
141C2×D3—64no—
142C2×D3—122no—
143C2×D3—122no—
144C2×D3—122no—
145C2×D3—122no—
146C2×D3—1216no—
147C3×C4—24no—
148C3×C4—42no—
149Dic3—64no—
150Dic3—122no—
151C32#129311yescharacteristic, complemented, Sylow
152C23—91no—
153C23—91no—
154C23—182no—
155C23—361no—
156C23—361no—
157C23C4⋊#15711yescharacteristic
158C2×C4—41no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—182no—
162C2×C4—182no—
163C2×C4—182no—
164C2×C4—361no—
165C2×C4—361no—
166C2×C4C4×#15711yescharacteristic
167C2×C4C22⋊#15711yescharacteristic
168C8—41no—
169C8—361no—
170C8—362no—
171C8—362no—
172C2×C3—22no—
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—44no—
176D3—124no—
177D3—124no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—92no—
182C22—181no—
183C22—181no—
184C22—181no—
185C22—181no—
186C22—181no—
187C22—364no—
188C22#6378111yescharacteristic
189C4—21no—
190C4—21no—
191C4—92no—
192C4—181no—
193C3—22no—
194C2—41no—
195C2—182no—
196C2—361no—
197C2#1059015511yescharacteristic
198C2#1059018611yescharacteristic
199C2#1059019011yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C3⋊D3Q8
cosocleC22×C4×C3⋊D3C22
hypercenterC22⋊C8#157
hypocenterC32#1293
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
151. C32#1293semidirect

Maximal subgroups

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

subgroupindex
#105938022
#105938002
#105924252
#12939