Finite Group Databasebeta

← #78128⋊C3 #11921195

Subgroups — #78128⋊C3 #11921195

Order 1152.

318 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 39 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×#399⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#396⋊C3)C212yesmaximal, complemented
3#78128C311yesmaximal, characteristic, complemented
4#2842⋊C3—31nomaximal
5C22×D3×A4—41nomaximal
6C3×#95⋊C3C2211yescharacteristic, complemented
7C3×#399C2×C311yescharacteristic, complemented
8#4994—32no—
9#4955—31no—
10#4949—31no—
11#4676C2×C312yescomplemented
12#399⋊C3—21no—
13#399⋊C3D311yescharacteristic, complemented
14#396⋊C3—32no—
15C22×C3×A4—41no—
16C2×D3×A4—44no—
17C2×D3×A4—42no—
18#2842—31noSylow
19C24×D3A411yescharacteristic
20C23×A4—121no—
21C2×C3×C4⋊C4—31no—
22C2×C3×C22⋊C4—31no—
23C2×#217—31no—
24C2×(C2×D3)⋊C4—32no—
25C2×(C2×D3)⋊C4—32no—
26C2×C4⋊Dic3—31no—
27C2×Dic3⋊C4—32no—
28C3×#95C22×C311yescharacteristic, complemented
29C3⋊#95—31no—
30#95⋊C3—21no—
31#95⋊C3C2×D311yescharacteristic, complemented
32C22×C3×D3—161no—
33C2×C3×A4—42no—
34C2×C3×A4—41no—
35D3×A4—44no—
36#399—91no—
37#399C3×D311yescharacteristic, complemented
38#396—32no—
39#396—92no—
40#379—91no—
41C24×C3C2×A411yescharacteristic
42C23×D3—121no—
43C23×D3—121no—
44C23×D3SL(2,𝔽3)14yes—
45C23×D3C2×A412yes—
46C22×A4—41no—
47C22×A4—81no—
48C22×A4—122no—
49C22×A4—124no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×Dic3—32no—
53C3×C4⋊C4—121no—
54C3×C22⋊C4—121no—
55#217—121no—
56(C2×D3)⋊C4—122no—
57(C2×D3)⋊C4—122no—
58C4⋊Dic3—121no—
59Dic3⋊C4—122no—
60C22×C32—161no—
61C2×C3×D3—164no—
62C2×C3×D3—162no—
63C3×A4—41no—
64C25—31no—
65C2×C4⋊C4—31no—
66C2×C4⋊C4—92no—
67C2×C4⋊C4—91no—
68C2×C22⋊C4—31no—
69C2×C22⋊C4—92no—
70C2×C22⋊C4—92no—
71C2×C22⋊C4—91no—
72#95—91no—
73#95C2×C3×D311yescharacteristic, complemented
74C23×C3—61no—
75C23×C3—61no—
76C23×C3—481no—
77C23×C3C2×SL(2,𝔽3)12yes—
78C23×C3C22×A411yescharacteristic
79C22×D3—41no—
80C22×D3—62no—
81C22×D3—62no—
82C22×D3—121no—
83C22×D3—124no—
84C22×D3—124no—
85C22×D3C2×SL(2,𝔽3)14yes—
86C2×A4—41no—
87C2×A4—42no—
88C2×A4—81no—
89C2×A4—82no—
90C2×A4—124no—
91C2×C3×C4—62no—
92C2×C3×C4—61no—
93C2×C3×C4—62no—
94C2×C3×C4—61no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×C32—162no—
99C2×C32—161no—
100C3×D3—164no—
101C24—32no—
102C24—34no—
103C24—361no—
104C24—361no—
105C24D3×A411yescharacteristic
106C22×C4—31no—
107C22×C4—31no—
108C22×C4—92no—
109C4⋊C4—121no—
110C4⋊C4—362no—
111C4⋊C4—361no—
112C22⋊C4—121no—
113C22⋊C4—362no—
114C22⋊C4—362no—
115C22⋊C4—361no—
116C22×C3—31no—
117C22×C3—31no—
118C22×C3—41no—
119C22×C3—62no—
120C22×C3—121no—
121C22×C3—161no—
122C22×C3—321no—
123C22×C3—484no—
124C22×C3—482no—
125C22×C3C22×SL(2,𝔽3)11yescharacteristic
126C2×D3—44no—
127C2×D3—42no—
128C2×D3—64no—
129C2×D3—122no—
130C2×D3—124no—
131A4—41no—
132A4—81no—
133C3×C4—121no—
134C3×C4—121no—
135Dic3—122no—
136C32—161noSylow
137C23—34no—
138C23—61no—
139C23—61no—
140C23—121no—
141C23—182no—
142C23—182no—
143C23—361no—
144C23—364no—
145C23—364no—
146C23D3×SL(2,𝔽3)12yes—
147C23C2×D3×A411yescharacteristic
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—62no—
151C2×C4—62no—
152C2×C4—182no—
153C2×C4—182no—
154C2×C4—182no—
155C2×C3—31no—
156C2×C3—31no—
157C2×C3—42no—
158C2×C3—162no—
159C2×C3—161no—
160C2×C3—322no—
161C2×C3—321no—
162C2×C3—484no—
163C2×C3#560⋊C311yescharacteristic
164D3—44no—
165C22—31no—
166C22—31no—
167C22—41no—
168C22—62no—
169C22—121no—
170C22—124no—
171C22—122no—
172C22—184no—
173C22—362no—
174C22—364no—
175C22C2×D3×SL(2,𝔽3)11yescharacteristic
176C4—121no—
177C4—121no—
178C4—362no—
179C3—161no—
180C3—321no—
181C3#2842⋊C311yescharacteristic, complemented
182C2—31no—
183C2—31no—
184C2—42no—
185C2—124no—
186C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#399C2×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×#399⋊C3C2semidirect
2. C3⋊(#396⋊C3)C2semidirect
3. #78128C3semidirect
6. C3×#95⋊C3C22semidirect
7. C3×#399C2×C3semidirect
11. #4676C2×C3semidirect
13. #399⋊C3D3semidirect
28. C3×#95C22×C3semidirect
31. #95⋊C3C2×D3semidirect
37. #399C3×D3semidirect
73. #95C2×C3×D3semidirect
181. C3#2842⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
C3⋊(#396⋊C3)2
#781283
#2842⋊C33
C22×D3×A44