Finite Group Databasebeta

← #76713⋊C3 #11921169

Subgroups — #76713⋊C3 #11921169

Order 1152.

346 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 27 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
1C3×#392⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#396⋊C3)C212yesmaximal, complemented
3#76713C311yesmaximal, characteristic, complemented
4#2675⋊C3—31nomaximal
5A4×D12—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C2×#939—32no—
8C3×#392C2×C311yescharacteristic, complemented
9#4960—31no—
10#4946—31no—
11#4676C2×C312yescomplemented
12#396⋊C3—32no—
13#392⋊C3—21no—
14#392⋊C3D311yescharacteristic, complemented
15C2×D3×A4—42no—
16C3×C4×A4—41no—
17#2675—31noSylow
18C22×C3×D4—31no—
19C22×#67—32no—
20C23×Dic3—31no—
21C22×D12A411yescharacteristic
22D4×A4—121no—
23C2×C3×C22⋊C4—31no—
24C2×#217—31no—
25#939—68no—
26C2×(C2×D3)⋊C4—32no—
27C2×Dic3⋊C4—32no—
28C3×#95C22×C311yescharacteristic
29C3⋊#95—31no—
30#95⋊C3—21no—
31#95⋊C3C2×D311yescharacteristic
32C2×C3×A4—41no—
33D3×A4—82no—
34C3×D12—161no—
35C2×#121—92no—
36#396—32no—
37#392—91no—
38#392C3×D311yescharacteristic, complemented
39#385—91no—
40C24×C3—31no—
41C23×D3C2×A412yes—
42C22×A4—122no—
43C2×C3×D4—64no—
44C2×C3×D4—121no—
45C22×C3×C4—31no—
46C22×C3×C4C2×A411yescharacteristic
47C2×#67—64no—
48C2×#67—64no—
49C2×#67—122no—
50C22×Dic3—32no—
51C22×Dic3—64no—
52C22×Dic3—121no—
53C2×D12—121no—
54C4×A4—41no—
55C4×A4—81no—
56C3×C22⋊C4—121no—
57#217—34no—
58(C2×D3)⋊C4—64no—
59Dic3⋊C4—64no—
60C2×C3×D3—162no—
61C3×A4—41no—
62C32×C4—161no—
63C22×D4—31no—
64C22×D4—31no—
65C22×D4—92no—
66C23×C4—91no—
67#121—188no—
68C2×C4⋊C4—92no—
69C2×C22⋊C4—31no—
70C2×C22⋊C4—91no—
71C2×C22⋊C4—92no—
72#95—91no—
73#95C2×C3×D311yescharacteristic
74C23×C3—32no—
75C23×C3—61no—
76C23×C3—62no—
77C23×C3—62no—
78C23×C3—61no—
79C23×C3C22×A411yescharacteristic
80C22×D3—22no—
81C22×D3—62no—
82C22×D3—62no—
83C2×A4—41no—
84C2×A4—81no—
85C2×A4—242no—
86C3×D4—124no—
87C3×D4—481no—
88C2×C3×C4—61no—
89C2×C3×C4—62no—
90C2×C3×C4—61no—
91#67—128no—
92C2×Dic3—34no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—124no—
96D12—41no—
97D12—121no—
98C2×C32—161no—
99C3×D3—322no—
100C24—31no—
101C24—32no—
102C2×D4—64no—
103C2×D4—121no—
104C2×D4—184no—
105C2×D4—184no—
106C2×D4—361no—
107C2×D4—362no—
108C22×C4—31no—
109C22×C4—92no—
110C22×C4—184no—
111C22×C4—361no—
112C22×C4D3×A411yescharacteristic
113C4⋊C4—184no—
114C22⋊C4—94no—
115C22⋊C4—121no—
116C22⋊C4—184no—
117C22×C3—31no—
118C22×C3—31no—
119C22×C3—64no—
120C22×C3—62no—
121C22×C3—121no—
122C22×C3—122no—
123C22×C3—121no—
124C22×C3—482no—
125C22×C32−1+4⋊C311yescharacteristic
126C2×D3—42no—
127C2×D3—122no—
128C2×D3—122no—
129A4—41no—
130A4—81no—
131C3×C4—41no—
132C3×C4—121no—
133C3×C4—161no—
134C3×C4—321no—
135Dic3—64no—
136C32—161noSylow
137C23—32no—
138C23—61no—
139C23—62no—
140C23—62no—
141C23—61no—
142C23—62no—
143C23—182no—
144C23—182no—
145C23C2×D3×A411yescharacteristic
146D4—121no—
147D4—124no—
148D4—361no—
149D4—368no—
150C2×C4—61no—
151C2×C4—61no—
152C2×C4—62no—
153C2×C4—94no—
154C2×C4—182no—
155C2×C4—182no—
156C2×C4—364no—
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—122no—
160C2×C3—161no—
161C2×C3—321no—
162C2×C3—962no—
163C2×C3#560⋊C311yescharacteristic
164D3—82no—
165C22—31no—
166C22—31no—
167C22—64no—
168C22—62no—
169C22—121no—
170C22—122no—
171C22—121no—
172C22—122no—
173C22—362no—
174C22—362no—
175C22#1010⋊C311yescharacteristic
176C4—41no—
177C4—121no—
178C4—184no—
179C3—161no—
180C3—321no—
181C3#2675⋊C311yescharacteristic, complemented
182C2—31no—
183C2—31no—
184C2—122no—
185C2—242no—
186C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#392C2×C3
socleC23×C3C22×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#392⋊C3C2semidirect
2. C3⋊(#396⋊C3)C2semidirect
3. #76713C3semidirect
8. C3×#392C2×C3semidirect
11. #4676C2×C3semidirect
14. #392⋊C3D3semidirect
38. #392C3×D3semidirect
181. C3#2675⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
C3⋊(#396⋊C3)2
#767133
#2675⋊C33
A4×D124