Finite Group Databasebeta

← #78057⋊C3 #11921197

Subgroups — #78057⋊C3 #11921197

Order 1152.

286 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 28 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⋊(#399⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#376⋊C3)C211yesmaximal, characteristic, complemented
4#78057C311yesmaximal, characteristic, complemented
5#2658⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C2×#888—31no—
9C2×#885—31no—
10C3×#399C2×C311yescharacteristic, complemented
11#4993—31no—
12#4949—31no—
13#4677C2×C311yescharacteristic, complemented
14#4648C2×C311yescharacteristic, complemented
15#399⋊C3—21no—
16#399⋊C3—31no—
17#399⋊C3D311yescharacteristic, complemented
18#376⋊C3—31no—
19C22×C3×A4—41no—
20C2×D3×A4—41no—
21Dic3×A4—41no—
22#2658—31noSylow
23C22×#67A411yescharacteristic
24C22×Dic6—31no—
25D4×A4—121no—
26C2×C3×C4⋊C4—31no—
27C2×C3×C22⋊C4—31no—
28C2×#217—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×(C2×D3)⋊C4—31no—
31C2×C4⋊Dic3—31no—
32C2×Dic3⋊C4—32no—
33C2×C4×Dic3—31no—
34#888—62no—
35#888—62no—
36#885—62no—
37#885—62no—
38C3×#95C22×C311yescharacteristic
39C3⋊#95—31no—
40#95⋊C3—21no—
41#95⋊C3C2×D311yescharacteristic
42C2×C3×A4—41no—
43C2×C3×A4—81no—
44D3×A4—81no—
45C3×#67—161no—
46C2×C4⋊Q8—91no—
47C2×#124—91no—
48#399—31no—
49#399—91no—
50#399—91no—
51#399C3×D311yescharacteristic, complemented
52#376—31no—
53C24×C3C2×A411yescharacteristic
54C23×D3C2×A411yescharacteristic
55C22×A4—41no—
56C22×A4—81no—
57C22×A4—121no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C2×#67—61no—
61C2×#67—61no—
62C22×Dic3—31no—
63C22×Dic3—31no—
64C22×Dic3C2×A411yescharacteristic
65C2×Dic6—61no—
66C2×Dic6—61no—
67C2×Dic6—62no—
68C2×Dic6—62no—
69C4×A4—121no—
70C3×C4⋊C4—62no—
71C3×C22⋊C4—62no—
72#217—62no—
73(C2×D3)⋊C4—62no—
74(C2×D3)⋊C4—62no—
75C4⋊Dic3—62no—
76Dic3⋊C4—64no—
77C4×Dic3—32no—
78C4×Dic3—32no—
79C22×C32—161no—
80C2×C3×D3—161no—
81C3×A4—41no—
82C3×Dic3—161no—
83C22×Q8—91no—
84C22×D4—31no—
85C4⋊Q8—182no—
86C4⋊Q8—182no—
87#124—182no—
88#124—182no—
89C2×C4⋊C4—31no—
90C2×C4⋊C4—91no—
91C2×C4⋊C4—92no—
92C2×C22⋊C4—31no—
93C2×C22⋊C4—91no—
94C2×C22⋊C4—91no—
95C2×C22⋊C4—91no—
96C2×C42—91no—
97#95—91no—
98#95C2×C3×D311yescharacteristic
99C23×C3—21no—
100C23×C3—61no—
101C23×C3—61no—
102C23×C3C22×A411yescharacteristic
103C22×D3—21no—
104C22×D3—61no—
105C22×D3—61no—
106C2×A4—41no—
107C2×A4—81no—
108C2×A4—82no—
109C2×A4—81no—
110C2×A4—241no—
111C3×D4—481no—
112C2×C3×C4—32no—
113C2×C3×C4—62no—
114C2×C3×C4—62no—
115C2×C3×C4—61no—
116#67—41no—
117#67—121no—
118C2×Dic3—31no—
119C2×Dic3—31no—
120C2×Dic3—32no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3—62no—
124C2×Dic3—61no—
125Dic6—122no—
126Dic6—121no—
127Dic6—121no—
128C2×C32—161no—
129C2×C32—321no—
130C3×D3—321no—
131C24—31no—
132C24D3×A411yescharacteristic
133C2×Q8—181no—
134C2×Q8—181no—
135C2×Q8—182no—
136C2×Q8—182no—
137C2×D4—181no—
138C2×D4—181no—
139C22×C4—31no—
140C22×C4—31no—
141C22×C4—31no—
142C22×C4—91no—
143C22×C4—91no—
144C4⋊C4—62no—
145C4⋊C4—182no—
146C4⋊C4—184no—
147C22⋊C4—62no—
148C22⋊C4—182no—
149C22⋊C4—182no—
150C22⋊C4—182no—
151C42—92no—
152C42—92no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—41no—
156C22×C3—121no—
157C22×C3—121no—
158C22×C3—161no—
159C22×C3—321no—
160C22×C3—481no—
161C22×C32−1+4⋊C311yescharacteristic
162C2×D3—41no—
163C2×D3—121no—
164C2×D3—121no—
165A4—41no—
166A4—81no—
167C3×C4—62no—
168C3×C4—121no—
169C3×C4—481no—
170Dic3—31no—
171Dic3—62no—
172Dic3—121no—
173Dic3#127⋊C311yescharacteristic
174C32—161noSylow
175C23—21no—
176C23—61no—
177C23—61no—
178C23—61no—
179C23—181no—
180C23—181no—
181C23C2×D3×A411yescharacteristic
182Q8—361no—
183Q8—361no—
184Q8—362no—
185D4—121no—
186D4—361no—
187C2×C4—32no—
188C2×C4—62no—
189C2×C4—61no—
190C2×C4—62no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—92no—
194C2×C4—181no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—182no—
198C2×C3—31no—
199C2×C3—31no—
200C2×C3—81no—
201C2×C3—161no—
202C2×C3—321no—
203C2×C3—322no—
204C2×C3—321no—
205C2×C3—961no—
206C2×C3C2×#127⋊C311yescharacteristic
207D3—81no—
208C22—31no—
209C22—31no—
210C22—41no—
211C22—121no—
212C22—121no—
213C22—121no—
214C22—361no—
215C22—361no—
216C22#1007⋊C311yescharacteristic
217C4—31no—
218C4—62no—
219C4—91no—
220C4—121no—
221C4—182no—
222C4—361no—
223C3—161no—
224C3—321no—
225C3#2658⋊C311yescharacteristic, complemented
226C2—31no—
227C2—31no—
228C2—81no—
229C2—241no—
230C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊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⋊(#399⋊C3)C2semidirect
3. C3⋊(#376⋊C3)C2semidirect
4. #78057C3semidirect
10. C3×#399C2×C3semidirect
13. #4677C2×C3semidirect
14. #4648C2×C3semidirect
17. #399⋊C3D3semidirect
51. #399C3×D3semidirect
225. C3#2658⋊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⋊(#399⋊C3)2
C3⋊(#376⋊C3)2
#780573
#2658⋊C33
A4×#674