Finite Group Databasebeta

← #73860⋊C3 #11921147

Subgroups — #73860⋊C3 #11921147

Order 1152.

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

normal subgroups only

This group has 337 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
1C2×C3⋊(#120⋊C3)C212yesmaximal, complemented
2C3×#379⋊C3C211yesmaximal, characteristic, complemented
3#73860C311yesmaximal, characteristic, complemented
4#2812⋊C3—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6A4×D12—41nomaximal
7C3⋊(#120⋊C3)—22no—
8C2×#953C2×C312yescomplemented
9C2×#120⋊C3—32no—
10C3×#379C2×C311yescharacteristic, complemented
11#4961—32no—
12#4960—31no—
13#4953—31no—
14#379⋊C3—21no—
15#379⋊C3D311yescharacteristic, complemented
16C3×C22⋊A4D411yescharacteristic, complemented
17C2×D3×A4—42no—
18C3×C4×A4—41no—
19#2812—31noSylow
20C25×C3C22×C311yescharacteristic
21C2×C22⋊A4—21no—
22C2×C22⋊A4C2×D311yescharacteristic
23C22×#67—32no—
24C22×D12A411yescharacteristic, complemented
25D4×A4—121no—
26C2×C3×C22⋊C4—31no—
27C2×C3×C22⋊C4—31no—
28#953—22no—
29#953—62no—
30C2×#217—32no—
31C2×(C2×D3)⋊C4—32no—
32C2×C4⋊Dic3—31no—
33#120⋊C3—62no—
34C3⋊#95—31no—
35C3⋊#95—31no—
36C2×C3×A4—41no—
37C2×C3×A4—161no—
38D3×A4—82no—
39C3×D12—161no—
40C2×#120—32no—
41#397—91no—
42#394—92no—
43#392—91no—
44#379C3×D311yescharacteristic, complemented
45C24×C3—31no—
46C24×C3—31no—
47C24×C3—121no—
48C24×C3—121no—
49C24×C3C3×D411yescharacteristic, complemented
50C23×D3C2×A412yes—
51C22⋊A4—21no—
52C22⋊A4D1211yescharacteristic, complemented
53C22×A4—122no—
54C22×C3×C4—31no—
55C22×C3×C4C2×A411yescharacteristic
56C2×#67—62no—
57C2×#67—62no—
58C2×#67—122no—
59C2×#67—122no—
60C22×Dic3—32no—
61C2×D12—121no—
62C4×A4—41no—
63C4×A4—81no—
64C3×C22⋊C4—121no—
65C3×C22⋊C4—121no—
66#217—62no—
67#217—62no—
68(C2×D3)⋊C4—122no—
69C4⋊Dic3—121no—
70C2×C3×D3—162no—
71C3×A4—41no—
72C3×A4—161no—
73C32×C4—161no—
74C25C2×C3×D311yescharacteristic
75C22×D4—31no—
76C22×D4—92no—
77#120—62no—
78#120—182no—
79C2×C4⋊C4—91no—
80C2×C22⋊C4—31no—
81C2×C22⋊C4—31no—
82C2×C22⋊C4—92no—
83C2×C22⋊C4—92no—
84#95—91no—
85#95—91no—
86C23×C3—31no—
87C23×C3—31no—
88C23×C3—41no—
89C23×C3—61no—
90C23×C3—61no—
91C23×C3—62no—
92C23×C3—62no—
93C23×C3—121no—
94C23×C3—121no—
95C23×C3—122no—
96C23×C3—121no—
97C23×C3—121no—
98C23×C3—123no—
99C23×C3C22×A411yescharacteristic
100C22×D3—22no—
101C22×D3—62no—
102C22×D3—62no—
103C2×A4—41no—
104C2×A4—81no—
105C2×A4—161no—
106C2×A4—162no—
107C2×A4—242no—
108C3×D4—481no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—62no—
112#67—124no—
113#67—124no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117D12—41no—
118D12—121no—
119C2×C32—161no—
120C3×D3—322no—
121C24—31no—
122C24—31no—
123C24—32no—
124C24—121no—
125C24—121no—
126C24C3×D1211yescharacteristic, complemented
127C2×D4—182no—
128C2×D4—182no—
129C2×D4—361no—
130C2×D4—362no—
131C2×D4—362no—
132C22×C4—31no—
133C22×C4—92no—
134C22×C4D3×A411yescharacteristic
135C4⋊C4—361no—
136C22⋊C4—121no—
137C22⋊C4—121no—
138C22⋊C4—182no—
139C22⋊C4—182no—
140C22⋊C4—362no—
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—41no—
144C22×C3—62no—
145C22×C3—62no—
146C22×C3—61no—
147C22×C3—61no—
148C22×C3—122no—
149C22×C3—121no—
150C22×C3—121no—
151C22×C3—121no—
152C22×C3—123no—
153C22×C3—121no—
154C22×C3—482no—
155C22×C3D4×A411yescharacteristic
156C2×D3—42no—
157C2×D3—122no—
158C2×D3—122no—
159A4—41no—
160A4—81no—
161A4—161no—
162A4—162no—
163C3×C4—41no—
164C3×C4—121no—
165C3×C4—161no—
166C3×C4—321no—
167Dic3—122no—
168C32—161noSylow
169C23—31no—
170C23—31no—
171C23—41no—
172C23—61no—
173C23—61no—
174C23—62no—
175C23—62no—
176C23—62no—
177C23—121no—
178C23—121no—
179C23—122no—
180C23—121no—
181C23—121no—
182C23—123no—
183C23—182no—
184C23—182no—
185C23C2×D3×A411yescharacteristic
186D4—121no—
187D4—361no—
188D4—364no—
189D4—364no—
190C2×C4—61no—
191C2×C4—62no—
192C2×C4—61no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—182no—
196C2×C3—31no—
197C2×C3—31no—
198C2×C3—121no—
199C2×C3—121no—
200C2×C3—161no—
201C2×C3—321no—
202C2×C3—962no—
203C2×C3#545011yescharacteristic
204D3—82no—
205C22—31no—
206C22—31no—
207C22—41no—
208C22—62no—
209C22—62no—
210C22—61no—
211C22—61no—
212C22—122no—
213C22—121no—
214C22—121no—
215C22—121no—
216C22—123no—
217C22—121no—
218C22—122no—
219C22—362no—
220C22—362no—
221C22A4×D1211yescharacteristic
222C4—41no—
223C4—121no—
224C4—362no—
225C3—161no—
226C3—321no—
227C3#2812⋊C311yescharacteristic, complemented
228C2—31no—
229C2—31no—
230C2—121no—
231C2—121no—
232C2—242no—
233C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocleC25×C3C22×C3
FrattiniC23C2×D3×A4
FittingC3×#379C2×C3
socleC23×C3C22×A4
hypocenterC24×C3C3×D4
LCSG ▷ C25×C3 ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(#120⋊C3)C2semidirect
2. C3×#379⋊C3C2semidirect
3. #73860C3semidirect
8. C2×#953C2×C3semidirect
10. C3×#379C2×C3semidirect
15. #379⋊C3D3semidirect
16. C3×C22⋊A4D4semidirect
24. C22×D12A4semidirect
44. #379C3×D3semidirect
49. C24×C3C3×D4semidirect
52. C22⋊A4D12semidirect
126. C24C3×D12semidirect
227. C3#2812⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#120⋊C3)2
C3×#379⋊C32
#738603
#2812⋊C33
A4×D124