Finite Group Databasebeta

← #76737⋊C3 #11921164

Subgroups — #76737⋊C3 #11921164

Order 1152.

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

normal subgroups only

This group has 238 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
2C3⋊(#401⋊C3)C212yesmaximal, complemented
3#76737C311yesmaximal, characteristic, complemented
4#2760⋊C3—31nomaximal
5A4×Dic6—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C3×#392C2×C311yescharacteristic
8#5220—32no—
9#4947—31no—
10#4943—31no—
11C3⋊#401C2×C312yes—
12#401⋊C3—32no—
13#392⋊C3—21no—
14#392⋊C3D311yescharacteristic
15C3×C4×A4—41no—
16Dic3×A4—42no—
17#2760—31noSylow
18C22×C3×D4—31no—
19C23×Dic3—31no—
20C22×Dic6A411yescharacteristic
21Q8×A4—121no—
22C2×C3×C22⋊C4—31no—
23C2×#217—31no—
24C2×#217—32no—
25C3×#95C22×C311yescharacteristic
26C3⋊#95—31no—
27C3⋊#95—32no—
28C3⋊#95—32no—
29#95⋊C3—21no—
30#95⋊C3C2×D311yescharacteristic
31C2×C3×A4—41no—
32C3×Dic6—161no—
33#401—32no—
34#393—91no—
35#392C3×D311yescharacteristic
36#386—92no—
37#381—91no—
38C24×C3—31no—
39C2×C3×D4—64no—
40C2×C3×D4—121no—
41C22×C3×C4—31no—
42C22×C3×C4C2×A411yescharacteristic
43C22×Dic3—32no—
44C22×Dic3—62no—
45C22×Dic3—121no—
46C22×Dic3—121no—
47C22×Dic3C2×A412yes—
48C2×Dic6—121no—
49C4×A4—41no—
50C4×A4—81no—
51C4×A4—122no—
52C3×C22⋊C4—121no—
53#217—122no—
54#217—121no—
55C3×A4—41no—
56C32×C4—161no—
57C3×Dic3—162no—
58C22×Q8—31no—
59C22×D4—31no—
60C23×C4—91no—
61C2×C22⋊C4—31no—
62C2×C22⋊C4—92no—
63C2×C22⋊C4—91no—
64#95—92no—
65#95—92no—
66#95—91no—
67#95C2×C3×D311yescharacteristic
68C23×C3—32no—
69C23×C3—62no—
70C23×C3—61no—
71C23×C3—62no—
72C23×C3—61no—
73C23×C3C22×A411yescharacteristic
74C2×A4—41no—
75C2×A4—81no—
76C3×Q8—481no—
77C3×D4—124no—
78C2×C3×C4—61no—
79C2×C3×C4—61no—
80C2×C3×C4—62no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—124no—
86Dic6—41no—
87Dic6—121no—
88C2×C32—161no—
89C24—31no—
90C2×Q8—361no—
91C2×D4—64no—
92C2×D4—121no—
93C22×C4—31no—
94C22×C4—32no—
95C22×C4—92no—
96C22×C4—182no—
97C22×C4—361no—
98C22×C4—361no—
99C22×C4D3×A411yescharacteristic
100C22⋊C4—121no—
101C22⋊C4—362no—
102C22⋊C4—361no—
103C22×C3—31no—
104C22×C3—31no—
105C22×C3—62no—
106C22×C3—64no—
107C22×C3—122no—
108C22×C3—121no—
109C22×C3—121no—
110C22×C3#99411yescharacteristic
111A4—41no—
112A4—81no—
113C3×C4—41no—
114C3×C4—121no—
115C3×C4—161no—
116C3×C4—321no—
117C3×C4—482no—
118Dic3—42no—
119Dic3—122no—
120C32—161noSylow
121C23—32no—
122C23—61no—
123C23—62no—
124C23—62no—
125C23—61no—
126C23C2×D3×A411yescharacteristic
127Q8—121no—
128Q8—361no—
129D4—124no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—62no—
133C2×C4—182no—
134C2×C4—182no—
135C2×C4—182no—
136C2×C4—182no—
137C2×C4—364no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—122no—
141C2×C3—161no—
142C2×C3—321no—
143C2×C3#560⋊C311yescharacteristic
144C22—31no—
145C22—31no—
146C22—62no—
147C22—64no—
148C22—121no—
149C22—122no—
150C22—121no—
151C22C3⋊#99411yescharacteristic
152C4—41no—
153C4—121no—
154C4—122no—
155C4—362no—
156C3—161no—
157C3—321no—
158C3#2760⋊C311yescharacteristic, complemented
159C2—31no—
160C2—31no—
161C2—122no—
162C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#392C2×C3
socleC23×C3C22×A4
prime radicalC3×#392⋊C3C2
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(#401⋊C3)C2semidirect
3. #76737C3semidirect
158. C3#2760⋊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⋊(#401⋊C3)2
#767373
#2760⋊C33
A4×Dic64