Finite Group Databasebeta

← #76667⋊C3 #11921166

Subgroups — #76667⋊C3 #11921166

Order 1152.

358 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 30 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×#392⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#399⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#376⋊C3)C211yesmaximal, characteristic, complemented
4#76667C311yesmaximal, characteristic, complemented
5#2397⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C2×D4×Dic3—31no—
9C2×#67⋊C4—31no—
10C3×#392C2×C311yescharacteristic, complemented
11#5223—31no—
12#4949—31no—
13#4677C2×C311yescharacteristic
14#4648C2×C311yescharacteristic, complemented
15#399⋊C3—31no—
16#392⋊C3—21no—
17#392⋊C3D311yescharacteristic, complemented
18#376⋊C3—31no—
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22#2397—31noSylow
23C22×C3×D4—31no—
24C22×#67—31no—
25C23×Dic3—31no—
26C22×C4×D3A411yescharacteristic
27C2×C4×A4—121no—
28C2×C3×C22⋊C4—31no—
29C2×#217—32no—
30D4×Dic3—62no—
31D4×Dic3—62no—
32C2×(C2×D3)⋊C4—31no—
33C2×C4⋊Dic3—31no—
34C2×Dic3⋊C4—31no—
35C2×C4×Dic3—31no—
36#67⋊C4—62no—
37#67⋊C4—62no—
38C3×#95C22×C311yescharacteristic
39C3⋊#95—31no—
40#95⋊C3—21no—
41#95⋊C3C2×D311yescharacteristic
42C2×C3×A4—41no—
43D3×A4—42no—
44C3×C4×D3—161no—
45C2×C4×D4—91no—
46C2×C4×D4—91no—
47#399—31no—
48#399—91no—
49#392—91no—
50#392C3×D311yescharacteristic, complemented
51#376—31no—
52C24×C3—31no—
53C23×D3C2×A411yescharacteristic
54C22×A4—121no—
55C2×C3×D4—62no—
56C2×C3×D4—64no—
57C22×C3×C4—31no—
58C22×C3×C4C2×A411yescharacteristic
59C2×#67—62no—
60C2×#67—62no—
61C2×#67—62no—
62C22×Dic3—31no—
63C22×Dic3—31no—
64C22×Dic3—61no—
65C22×Dic3—61no—
66C22×Dic3—62no—
67C22×Dic3—62no—
68C22×Dic3C2×A411yescharacteristic
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C4×A4—41no—
72C4×A4—81no—
73C4×A4—121no—
74C3×C22⋊C4—62no—
75#217—64no—
76(C2×D3)⋊C4—62no—
77C4⋊Dic3—62no—
78Dic3⋊C4—62no—
79C4×Dic3—32no—
80C4×Dic3—32no—
81C2×C3×D3—161no—
82C3×A4—41no—
83C32×C4—161no—
84C3×Dic3—161no—
85C22×D4—31no—
86C22×D4—91no—
87C23×C4—31no—
88C23×C4—91no—
89C4×D4—182no—
90C4×D4—182no—
91C4×D4—182no—
92C4×D4—182no—
93C2×C4⋊C4—91no—
94C2×C4⋊C4—91no—
95C2×C22⋊C4—31no—
96C2×C22⋊C4—91no—
97C2×C22⋊C4—92no—
98C2×C42—91no—
99#95—91no—
100#95C2×C3×D311yescharacteristic
101C23×C3—32no—
102C23×C3—62no—
103C23×C3—61no—
104C23×C3—62no—
105C23×C3—61no—
106C23×C3C22×A411yescharacteristic
107C22×D3—61no—
108C22×D3—61no—
109C22×D3#41⋊C312yes—
110C2×A4—41no—
111C2×A4—81no—
112C2×A4—122no—
113C3×D4—68no—
114C2×C3×C4—32no—
115C2×C3×C4—61no—
116C2×C3×C4—62no—
117C2×C3×C4—481no—
118#67—68no—
119C2×Dic3—31no—
120C2×Dic3—31no—
121C2×Dic3—32no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—62no—
126C2×Dic3—121no—
127C2×Dic3—122no—
128C2×Dic3—121no—
129C4×D3—41no—
130C4×D3—121no—
131C2×C32—161no—
132C3×D3—162no—
133C24—31no—
134C24—31no—
135C2×D4—62no—
136C2×D4—64no—
137C2×D4—182no—
138C2×D4—182no—
139C2×D4—182no—
140C22×C4—31no—
141C22×C4—31no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—181no—
145C22×C4—181no—
146C22×C4—181no—
147C22×C4—182no—
148C22×C4—181no—
149C22×C4—182no—
150C22×C4D3×A411yescharacteristic
151C4⋊C4—182no—
152C4⋊C4—182no—
153C22⋊C4—62no—
154C22⋊C4—182no—
155C22⋊C4—184no—
156C42—92no—
157C42—92no—
158C22×C3—31no—
159C22×C3—31no—
160C22×C3—62no—
161C22×C3—64no—
162C22×C3—122no—
163C22×C3—121no—
164C22×C3—121no—
165C22×C3—481no—
166C22×C3C2×#41⋊C311yescharacteristic
167C2×D3—41no—
168C2×D3—62no—
169C2×D3—121no—
170A4—41no—
171A4—81no—
172C3×C4—41no—
173C3×C4—62no—
174C3×C4—161no—
175C3×C4—321no—
176C3×C4—481no—
177Dic3—31no—
178Dic3—62no—
179Dic3—121no—
180Dic3#127⋊C311yescharacteristic
181C32—161noSylow
182C23—32no—
183C23—32no—
184C23—61no—
185C23—62no—
186C23—62no—
187C23—61no—
188C23—181no—
189C23—181no—
190C23C2×D3×A411yescharacteristic
191D4—68no—
192D4—188no—
193C2×C4—32no—
194C2×C4—61no—
195C2×C4—62no—
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—92no—
199C2×C4—121no—
200C2×C4—181no—
201C2×C4—181no—
202C2×C4—181no—
203C2×C4—182no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4—362no—
208C2×C3—31no—
209C2×C3—31no—
210C2×C3—122no—
211C2×C3—161no—
212C2×C3—321no—
213C2×C3—482no—
214C2×C3C2×#127⋊C311yescharacteristic
215D3—42no—
216C22—31no—
217C22—31no—
218C22—64no—
219C22—62no—
220C22—121no—
221C22—122no—
222C22—121no—
223C22—121no—
224C22—182no—
225C22—361no—
226C22D3×#41⋊C311yescharacteristic
227C4—31no—
228C4—41no—
229C4—62no—
230C4—91no—
231C4—182no—
232C4—361no—
233C3—161no—
234C3—321no—
235C3#2397⋊C311yescharacteristic, complemented
236C2—31no—
237C2—31no—
238C2—122no—
239C2—122no—
240C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#392C2×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×#392⋊C3C2semidirect
2. C3⋊(#399⋊C3)C2semidirect
3. C3⋊(#376⋊C3)C2semidirect
4. #76667C3semidirect
10. C3×#392C2×C3semidirect
14. #4648C2×C3semidirect
17. #392⋊C3D3semidirect
50. #392C3×D3semidirect
235. C3#2397⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
C3⋊(#399⋊C3)2
C3⋊(#376⋊C3)2
#766673
#2397⋊C33
C4×D3×A44