Finite Group Databasebeta

← #77425⋊C3 #11921187

Subgroups — #77425⋊C3 #11921187

Order 1152.

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

normal subgroups only

This group has 236 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×#396⋊C3C211yesmaximal, characteristic, complemented
2D3×#95⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4#77425C311yesmaximal, characteristic, complemented
5#2643⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#396C2×C311yescharacteristic, complemented
9#4989—31no—
10#4985—31no—
11#4956—31no—
12#4952—31no—
13D3×#95C2×C311yescharacteristic, complemented
14C3⋊#401C2×C311yescharacteristic, complemented
15#401⋊C3—31no—
16#396⋊C3—21no—
17#396⋊C3D311yescharacteristic, complemented
18C2×#95⋊C3—31no—
19C22×C3×A4—41no—
20C2×D3×A4—41no—
21Dic3×A4—41no—
22#2643—31noSylow
23C22×#67A411yescharacteristic
24C22×C4×D3—31no—
25D4×A4—121no—
26C2×C3×C4⋊C4—31no—
27C2×C3×C22⋊C4—31no—
28C2×#217—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×Dic3⋊C4—31no—
31C3×#95C22×C311yescharacteristic
32C3⋊#95—31no—
33C3⋊#95—31no—
34C3⋊#95—31no—
35C3⋊#95—31no—
36C3⋊#95—31no—
37#95⋊C3—21no—
38#95⋊C3C2×D311yescharacteristic
39C2×C3×A4—41no—
40C2×C3×A4—81no—
41D3×A4—81no—
42C3×#67—161no—
43#401—31no—
44#400—91no—
45#397—91no—
46#396C3×D311yescharacteristic, complemented
47#386—91no—
48#385—91no—
49C2×#95—31no—
50C24×C3C2×A411yescharacteristic
51C23×D3C2×A411yescharacteristic
52C22×A4—41no—
53C22×A4—81no—
54C22×A4—121no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C2×#67—61no—
58C2×#67—61no—
59C22×Dic3—31no—
60C22×Dic3—31no—
61C22×Dic3C2×A411yescharacteristic
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C4×D3—121no—
65C2×C4×D3—121no—
66C4×A4—121no—
67C3×C4⋊C4—121no—
68C3×C22⋊C4—121no—
69#217—121no—
70(C2×D3)⋊C4—61no—
71(C2×D3)⋊C4—61no—
72Dic3⋊C4—121no—
73C22×C32—161no—
74C2×C3×D3—161no—
75C3×A4—41no—
76C3×Dic3—161no—
77C22×D4—31no—
78C23×C4—91no—
79C2×C4⋊C4—31no—
80C2×C4⋊C4—91no—
81C2×C22⋊C4—31no—
82C2×C22⋊C4—91no—
83C2×C22⋊C4—91no—
84#95—91no—
85#95—91no—
86#95—91no—
87#95—91no—
88#95—91no—
89#95C2×C3×D311yescharacteristic
90C23×C3—21no—
91C23×C3—61no—
92C23×C3—61no—
93C23×C3C22×A411yescharacteristic
94C22×D3—21no—
95C22×D3—31no—
96C22×D3—31no—
97C22×D3—61no—
98C2×A4—41no—
99C2×A4—81no—
100C2×A4—82no—
101C2×A4—81no—
102C2×A4—241no—
103C3×D4—481no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110#67—41no—
111#67—121no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C4×D3—122no—
120C4×D3—122no—
121C2×C32—161no—
122C2×C32—321no—
123C3×D3—321no—
124C24—31no—
125C24D3×A411yescharacteristic
126C2×D4—181no—
127C2×D4—181no—
128C22×C4—31no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—181no—
134C22×C4—181no—
135C22×C4—361no—
136C22×C4—361no—
137C4⋊C4—121no—
138C4⋊C4—361no—
139C22⋊C4—121no—
140C22⋊C4—181no—
141C22⋊C4—181no—
142C22⋊C4—361no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—41no—
146C22×C3—121no—
147C22×C3—121no—
148C22×C3—161no—
149C22×C3—321no—
150C22×C3—481no—
151C22×C32−1+4⋊C311yescharacteristic
152C2×D3—31no—
153C2×D3—61no—
154C2×D3—61no—
155C2×D3—61no—
156C2×D3—61no—
157C2×D3#126⋊C311yescharacteristic
158A4—41no—
159A4—81no—
160C3×C4—121no—
161C3×C4—121no—
162C3×C4—481no—
163Dic3—41no—
164Dic3—121no—
165Dic3—121no—
166C32—161noSylow
167C23—21no—
168C23—61no—
169C23—61no—
170C23—61no—
171C23—91no—
172C23—91no—
173C23—181no—
174C23C2×D3×A411yescharacteristic
175D4—121no—
176D4—361no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—61no—
180C2×C4—61no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—181no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—362no—
191C2×C4—362no—
192C2×C3—31no—
193C2×C3—31no—
194C2×C3—81no—
195C2×C3—161no—
196C2×C3—321no—
197C2×C3—322no—
198C2×C3—321no—
199C2×C3—961no—
200C2×C3C2×#126⋊C311yescharacteristic
201D3—21no—
202D3—61no—
203C22—31no—
204C22—31no—
205C22—31no—
206C22—41no—
207C22—91no—
208C22—121no—
209C22—121no—
210C22—181no—
211C22—181no—
212C22—181no—
213C22—181no—
214C22#1007⋊C311yescharacteristic
215C4—121no—
216C4—121no—
217C4—121no—
218C4—361no—
219C4—361no—
220C3—161no—
221C3—321no—
222C3#2643⋊C311yescharacteristic, complemented
223C2—31no—
224C2—31no—
225C2—61no—
226C2—81no—
227C2—181no—
228C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#396C2×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×#396⋊C3C2semidirect
2. D3×#95⋊C3C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. #77425C3semidirect
8. C3×#396C2×C3semidirect
13. D3×#95C2×C3semidirect
14. C3⋊#401C2×C3semidirect
17. #396⋊C3D3semidirect
46. #396C3×D3semidirect
222. C3#2643⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#396⋊C32
D3×#95⋊C32
C3⋊(#401⋊C3)2
#774253
#2643⋊C33
A4×#674