Finite Group Databasebeta

← C3⋊#73211 #11921142

Subgroups — C3⋊#73211 #11921142

Order 1152.

273 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 31 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×#379⋊C3C211yesmaximal, characteristic
2C3⋊(#379⋊C3)C212yesmaximal
3#73844C311yesmaximal, characteristic, complemented
4#73211—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6A4×Dic6—41nomaximal
7C3×#379C2×C311yescharacteristic
8#5247C2×C312yes—
9#4947—31no—
10#4947—31no—
11#4947—32no—
12#379⋊C3—21no—
13#379⋊C3—32no—
14#379⋊C3D311yescharacteristic
15C3×C22⋊A4Q811yescharacteristic, complemented
16C3×C4×A4—41no—
17Dic3×A4—42no—
18#2840—31noSylow
19C25×C3C22×C311yescharacteristic
20C2×C22⋊A4—21no—
21C2×C22⋊A4C2×D311yescharacteristic
22C22×Dic6—31no—
23C22×Dic6A411yescharacteristic, complemented
24Q8×A4—121no—
25C2×C3×C22⋊C4—31no—
26C2×C3×C22⋊C4—31no—
27C2×#217—32no—
28C2×#217—32no—
29C3⋊#95—31no—
30C3⋊#95—31no—
31C3⋊#95—32no—
32C2×C3×A4—41no—
33C2×C3×A4—161no—
34C3×Dic6—161no—
35#393—91no—
36#393—92no—
37#393—91no—
38#379—32no—
39#379C3×D311yescharacteristic
40C24×C3—31no—
41C24×C3—31no—
42C24×C3—121no—
43C24×C3—121no—
44C24×C3C3×Q811yescharacteristic, complemented
45C22⋊A4—21no—
46C22⋊A4Dic611yescharacteristic, complemented
47C22×C3×C4—31no—
48C22×C3×C4C2×A411yescharacteristic
49C22×Dic3—32no—
50C22×Dic3C2×A412yes—
51C2×Dic6—121no—
52C2×Dic6—122no—
53C2×Dic6—121no—
54C4×A4—41no—
55C4×A4—81no—
56C4×A4—122no—
57C3×C22⋊C4—121no—
58C3×C22⋊C4—121no—
59#217—122no—
60#217—122no—
61C3×A4—41no—
62C3×A4—161no—
63C32×C4—161no—
64C3×Dic3—162no—
65C25C2×C3×D311yescharacteristic
66C22×Q8—31no—
67C22×Q8—91no—
68C2×C22⋊C4—31no—
69C2×C22⋊C4—31no—
70C2×C22⋊C4—92no—
71C2×C22⋊C4—92no—
72#95—92no—
73#95—91no—
74#95—91no—
75C23×C3—31no—
76C23×C3—31no—
77C23×C3—41no—
78C23×C3—62no—
79C23×C3—62no—
80C23×C3—61no—
81C23×C3—61no—
82C23×C3—121no—
83C23×C3—121no—
84C23×C3—122no—
85C23×C3—121no—
86C23×C3—121no—
87C23×C3—123no—
88C23×C3C22×A411yescharacteristic
89C2×A4—41no—
90C2×A4—81no—
91C2×A4—161no—
92C2×A4—162no—
93C3×Q8—481no—
94C2×C3×C4—61no—
95C2×C3×C4—62no—
96C2×C3×C4—61no—
97C2×Dic3—62no—
98C2×Dic3—64no—
99C2×Dic3—62no—
100Dic6—41no—
101Dic6—121no—
102Dic6—124no—
103C2×C32—161no—
104C24—31no—
105C24—31no—
106C24—121no—
107C24—121no—
108C24C3×Dic611yescharacteristic, complemented
109C2×Q8—361no—
110C2×Q8—362no—
111C2×Q8—361no—
112C22×C4—31no—
113C22×C4—32no—
114C22×C4—92no—
115C22×C4D3×A411yescharacteristic
116C22⋊C4—121no—
117C22⋊C4—121no—
118C22⋊C4—362no—
119C22⋊C4—362no—
120C22×C3—31no—
121C22×C3—31no—
122C22×C3—41no—
123C22×C3—62no—
124C22×C3—61no—
125C22×C3—62no—
126C22×C3—61no—
127C22×C3—121no—
128C22×C3—122no—
129C22×C3—121no—
130C22×C3—121no—
131C22×C3—123no—
132C22×C3—121no—
133C22×C3Q8×A411yescharacteristic
134A4—41no—
135A4—81no—
136A4—161no—
137A4—162no—
138C3×C4—41no—
139C3×C4—121no—
140C3×C4—161no—
141C3×C4—321no—
142C3×C4—482no—
143Dic3—42no—
144Dic3—122no—
145C32—161noSylow
146C23—31no—
147C23—31no—
148C23—41no—
149C23—61no—
150C23—61no—
151C23—62no—
152C23—62no—
153C23—121no—
154C23—121no—
155C23—121no—
156C23—122no—
157C23—121no—
158C23—123no—
159C23C2×D3×A411yescharacteristic
160Q8—121no—
161Q8—361no—
162Q8—364no—
163C2×C4—61no—
164C2×C4—62no—
165C2×C4—61no—
166C2×C4—182no—
167C2×C4—184no—
168C2×C4—182no—
169C2×C3—31no—
170C2×C3—31no—
171C2×C3—121no—
172C2×C3—121no—
173C2×C3—161no—
174C2×C3—321no—
175C2×C3#545011yescharacteristic
176C22—31no—
177C22—31no—
178C22—41no—
179C22—61no—
180C22—62no—
181C22—61no—
182C22—62no—
183C22—122no—
184C22—121no—
185C22—121no—
186C22—121no—
187C22—123no—
188C22—121no—
189C22A4×Dic611yescharacteristic
190C4—41no—
191C4—121no—
192C4—122no—
193C4—362no—
194C3—161no—
195C3—321no—
196C3#7321111yescharacteristic, complemented
197C2—31no—
198C2—31no—
199C2—121no—
200C2—121no—
201C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocleC25×C3C22×C3
FrattiniC23C2×D3×A4
FittingC3×#379C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C22⋊A4C22
hypocenterC24×C3C3×Q8
LCSG ▷ C25×C3 ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. #73844C3semidirect
15. C3×C22⋊A4Q8semidirect
23. C22×Dic6A4semidirect
44. C24×C3C3×Q8semidirect
46. C22⋊A4Dic6semidirect
108. C24C3×Dic6semidirect
196. C3#73211semidirect

Maximal subgroups

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

subgroupindex
C3×#379⋊C32
C3⋊(#379⋊C3)2
#738443
#732113
A4×Dic64