Finite Group Databasebeta

← #82580⋊C3 #11921284

Subgroups — #82580⋊C3 #11921284

Order 1152.

335 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 335 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×C3×#120⋊C3C211yesmaximal, characteristic
2C3⋊(#379⋊C3)C212yesmaximal, complemented
3#82580C311yesmaximal, characteristic, complemented
4#2375⋊C3—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6C2×Dic3×A4—41nomaximal
7C3×#120⋊C3C412yescomplemented
8C2×C3×#120C2×C311yescharacteristic
9C2×#120⋊C3—21no—
10C2×#120⋊C3D311yescharacteristic
11#5247C2×C312yescomplemented
12#5221—31no—
13#5220—31no—
14#4951—32no—
15#379⋊C3—32no—
16C3×C22⋊A4C2×C411yescharacteristic, complemented
17C22×C3×A4—41no—
18Dic3×A4—42no—
19#2375—31noSylow
20C25×C3C22×C311yescharacteristic
21C2×C22⋊A4—21no—
22C2×C22⋊A4C2×D311yescharacteristic
23C22×C3×D4—31no—
24C23×Dic3A411yescharacteristic, complemented
25C2×C4×A4—121no—
26C3×#120—32no—
27C3×#120C3×C412yescomplemented
28C2×C3×C22⋊C4—31no—
29C2×#217—31no—
30C2×#217—32no—
31C2×#217—32no—
32C2×C4⋊Dic3—31no—
33C2×C4×Dic3—31no—
34#120⋊C3—22no—
35#120⋊C3Dic312yescomplemented
36C3⋊#95—32no—
37C2×C3×A4—42no—
38C2×C3×A4—41no—
39C2×C3×A4—161no—
40C2×C3×Dic3—161no—
41C2×#120C3×D311yescharacteristic
42#390—91no—
43#388—92no—
44#386—91no—
45#379—32no—
46C24×C3—31no—
47C24×C3—31no—
48C24×C3—121no—
49C24×C3—121no—
50C24×C3C2×C3×C411yescharacteristic, complemented
51C24×C3C2×A411yescharacteristic
52C22⋊A4—21no—
53C22⋊A4C2×Dic311yescharacteristic, complemented
54C22×A4—41no—
55C22×A4—81no—
56C2×C3×D4—32no—
57C2×C3×D4—32no—
58C2×C3×D4—121no—
59C2×C3×D4—121no—
60C22×C3×C4—31no—
61C22×Dic3—32no—
62C22×Dic3—121no—
63C22×Dic3C2×A412yes—
64C4×A4—122no—
65C3×C22⋊C4—32no—
66C3×C22⋊C4—32no—
67#217—122no—
68#217—122no—
69#217—121no—
70C4⋊Dic3—121no—
71C4×Dic3—121no—
72C22×C32—161no—
73C3×A4—41no—
74C3×A4—161no—
75C3×Dic3—162no—
76C25C2×C3×D311yescharacteristic
77C22×D4—31no—
78C23×C4—31no—
79#120—32no—
80#120C3×Dic312yescomplemented
81C2×C4⋊C4—91no—
82C2×C22⋊C4—31no—
83C2×C22⋊C4—92no—
84C2×C22⋊C4—91no—
85C2×C22⋊C4—92no—
86C2×C42—91no—
87#95—92no—
88C23×C3—31no—
89C23×C3—31no—
90C23×C3—41no—
91C23×C3—61no—
92C23×C3—61no—
93C23×C3—62no—
94C23×C3—62no—
95C23×C3—61no—
96C23×C3—61no—
97C23×C3—121no—
98C23×C3—121no—
99C23×C3—121no—
100C23×C3—122no—
101C23×C3—121no—
102C23×C3—123no—
103C23×C3C4×A412yes—
104C23×C3C22×A411yescharacteristic
105C2×A4—41no—
106C2×A4—42no—
107C2×A4—81no—
108C2×A4—82no—
109C2×A4—161no—
110C2×A4—162no—
111C3×D4—122no—
112C3×D4—122no—
113C2×C3×C4—32no—
114C2×C3×C4—61no—
115C2×C3×C4—61no—
116C2×C3×C4—481no—
117C2×Dic3—41no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—62no—
122C2×Dic3—121no—
123C2×C32—162no—
124C2×C32—161no—
125C24—31no—
126C24—31no—
127C24—121no—
128C24—121no—
129C24C2×C3×Dic311yescharacteristic, complemented
130C24D3×A411yescharacteristic
131C2×D4—32no—
132C2×D4—32no—
133C2×D4—121no—
134C2×D4—121no—
135C22×C4—31no—
136C22×C4—32no—
137C22×C4—92no—
138C22×C4—361no—
139C4⋊C4—361no—
140C22⋊C4—32no—
141C22⋊C4—32no—
142C22⋊C4—362no—
143C22⋊C4—362no—
144C22⋊C4—361no—
145C42—361no—
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—41no—
149C22×C3—41no—
150C22×C3—62no—
151C22×C3—61no—
152C22×C3—61no—
153C22×C3—62no—
154C22×C3—62no—
155C22×C3—121no—
156C22×C3—121no—
157C22×C3—122no—
158C22×C3—121no—
159C22×C3—121no—
160C22×C3—123no—
161C22×C3—121no—
162C22×C3—161no—
163C22×C3—321no—
164C22×C3C2×C4×A411yescharacteristic
165A4—41no—
166A4—81no—
167A4—161no—
168A4—162no—
169C3×C4—62no—
170C3×C4—482no—
171Dic3—42no—
172Dic3—122no—
173C32—161noSylow
174C23—31no—
175C23—31no—
176C23—41no—
177C23—61no—
178C23—61no—
179C23—62no—
180C23—62no—
181C23—61no—
182C23—61no—
183C23—121no—
184C23—121no—
185C23—121no—
186C23—122no—
187C23—121no—
188C23—123no—
189C23Dic3×A412yes—
190C23C2×D3×A411yescharacteristic
191D4—122no—
192D4—122no—
193C2×C4—32no—
194C2×C4—61no—
195C2×C4—61no—
196C2×C4—121no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—182no—
200C2×C4—182no—
201C2×C4—361no—
202C2×C3—31no—
203C2×C3—31no—
204C2×C3—42no—
205C2×C3—121no—
206C2×C3—121no—
207C2×C3—162no—
208C2×C3—161no—
209C2×C3—322no—
210C2×C3—321no—
211C2×C3#545011yescharacteristic
212C22—31no—
213C22—31no—
214C22—41no—
215C22—41no—
216C22—62no—
217C22—61no—
218C22—61no—
219C22—62no—
220C22—62no—
221C22—121no—
222C22—121no—
223C22—122no—
224C22—121no—
225C22—121no—
226C22—123no—
227C22—121no—
228C22C2×Dic3×A411yescharacteristic
229C4—62no—
230C4—122no—
231C4—362no—
232C3—161no—
233C3—321no—
234C3#2375⋊C311yescharacteristic, complemented
235C2—31no—
236C2—31no—
237C2—42no—
238C2—121no—
239C2—121no—
240C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, hypocenterC24×C3C2×C3×C4
FrattiniC23C2×D3×A4
FittingC2×C3×#120C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×#120⋊C3C2
cosocleC25×C3C22×C3
LCSG ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(#379⋊C3)C2semidirect
3. #82580C3semidirect
7. C3×#120⋊C3C4semidirect
11. #5247C2×C3semidirect
16. C3×C22⋊A4C2×C4semidirect
24. C23×Dic3A4semidirect
27. C3×#120C3×C4semidirect
35. #120⋊C3Dic3semidirect
50. C24×C3C2×C3×C4semidirect
53. C22⋊A4C2×Dic3semidirect
80. #120C3×Dic3semidirect
129. C24C2×C3×Dic3semidirect
234. C3#2375⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#120⋊C32
C3⋊(#379⋊C3)2
#825803
#2375⋊C33
C2×Dic3×A44