Finite Group Databasebeta

← #76706⋊C3 #11921163

Subgroups — #76706⋊C3 #11921163

Order 1152.

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

normal subgroups only

This group has 346 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×#392⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#376⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#392⋊C3)C211yesmaximal, characteristic, complemented
4#76706C311yesmaximal, characteristic, complemented
5#2657⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C2×#940—31no—
9C2×#885—31no—
10C3×#392C2×C311yescharacteristic
11#5223—31no—
12#4960—31no—
13#4671C2×C311yescharacteristic
14#4648C2×C311yescharacteristic
15#392⋊C3—21no—
16#392⋊C3—31no—
17#392⋊C3D311yescharacteristic, complemented
18#376⋊C3—31no—
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22#2657—31noSylow
23C22×C3×D4—31no—
24C22×#67—32no—
25C22×#67—31no—
26C22×D12—31no—
27C22×Dic6A411yescharacteristic
28Q8×A4—121no—
29C2×C3×C22⋊C4—31no—
30C2×#217—31no—
31#940—62no—
32#940—62no—
33C2×(C2×D3)⋊C4—31no—
34C2×(C2×D3)⋊C4—31no—
35C2×C4×Dic3—31no—
36#885—62no—
37#885—62no—
38C3×#95C22×C311yescharacteristic
39C3⋊#95—31no—
40#95⋊C3—21no—
41#95⋊C3C2×D311yescharacteristic
42C2×C3×A4—41no—
43C3×Dic6—161no—
44C2×#127—91no—
45C2×#124—91no—
46#392—31no—
47#392—91no—
48#392—91no—
49#392C3×D311yescharacteristic
50#376—31no—
51C24×C3—31no—
52C23×D3—31no—
53C2×C3×D4—62no—
54C2×C3×D4—122no—
55C22×C3×C4—31no—
56C22×C3×C4C2×A411yescharacteristic
57C2×#67—61no—
58C2×#67—61no—
59C2×#67—62no—
60C2×#67—62no—
61C2×#67—64no—
62C2×#67—122no—
63C2×#67—122no—
64C22×Dic3—31no—
65C22×Dic3C2×A411yescharacteristic
66C22×Dic3C2×A411yescharacteristic
67C2×D12—62no—
68C2×D12—122no—
69C2×Dic6—61no—
70C2×Dic6—61no—
71C4×A4—41no—
72C4×A4—81no—
73C4×A4—121no—
74C4×A4—121no—
75C3×C22⋊C4—62no—
76#217—62no—
77(C2×D3)⋊C4—62no—
78(C2×D3)⋊C4—62no—
79C4×Dic3—32no—
80C4×Dic3—32no—
81C3×A4—41no—
82C32×C4—161no—
83C3×Dic3—161no—
84C3×Dic3—161no—
85C22×Q8—31no—
86C22×D4—31no—
87C22×D4—91no—
88C22×D4—91no—
89C22×D4—92no—
90#127—182no—
91#127—182no—
92#124—182no—
93#124—182no—
94C2×C22⋊C4—31no—
95C2×C22⋊C4—91no—
96C2×C22⋊C4—91no—
97C2×C22⋊C4—91no—
98C2×C42—91no—
99#95—91no—
100#95C2×C3×D311yescharacteristic
101C23×C3—61no—
102C23×C3—62no—
103C23×C3—62no—
104C23×C3—61no—
105C23×C3—61no—
106C23×C3C22×A411yescharacteristic
107C22×D3—61no—
108C22×D3—62no—
109C22×D3—61no—
110C22×D3—62no—
111C22×D3—61no—
112C2×A4—41no—
113C2×A4—81no—
114C3×Q8—481no—
115C3×D4—124no—
116C2×C3×C4—32no—
117C2×C3×C4—61no—
118C2×C3×C4—62no—
119#67—121no—
120#67—122no—
121#67—128no—
122#67—121no—
123C2×Dic3—31no—
124C2×Dic3—31no—
125C2×Dic3—32no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129D12—124no—
130Dic6—41no—
131Dic6—121no—
132C2×C32—161no—
133C24—31no—
134C24—91no—
135C2×Q8—181no—
136C2×Q8—181no—
137C2×D4—62no—
138C2×D4—122no—
139C2×D4—182no—
140C2×D4—181no—
141C2×D4—181no—
142C2×D4—182no—
143C2×D4—182no—
144C2×D4—184no—
145C2×D4—362no—
146C2×D4—362no—
147C2×D4—362no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—91no—
152C22×C4D3×A411yescharacteristic
153C22⋊C4—62no—
154C22⋊C4—182no—
155C22⋊C4—182no—
156C22⋊C4—182no—
157C42—92no—
158C42—92no—
159C22×C3—31no—
160C22×C3—31no—
161C22×C3—122no—
162C22×C3—122no—
163C22×C3—121no—
164C22×C3—121no—
165C22×C3—121no—
166C22×C3#99411yescharacteristic
167C2×D3—122no—
168C2×D3—122no—
169C2×D3—121no—
170C2×D3—121no—
171C2×D3—121no—
172A4—41no—
173A4—81no—
174C3×C4—41no—
175C3×C4—62no—
176C3×C4—161no—
177C3×C4—321no—
178C3×C4—481no—
179C3×C4—481no—
180Dic3—31no—
181Dic3—41no—
182Dic3—62no—
183Dic3#127⋊C311yescharacteristic
184C32—161noSylow
185C23—61no—
186C23—62no—
187C23—61no—
188C23—62no—
189C23—61no—
190C23—181no—
191C23—182no—
192C23—181no—
193C23—182no—
194C23—181no—
195C23C2×D3×A411yescharacteristic
196Q8—121no—
197Q8—361no—
198D4—124no—
199D4—361no—
200D4—364no—
201D4—361no—
202D4—362no—
203D4—368no—
204C2×C4—32no—
205C2×C4—61no—
206C2×C4—62no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—92no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C3—31no—
214C2×C3—31no—
215C2×C3—161no—
216C2×C3—241no—
217C2×C3—321no—
218C2×C3C2×#127⋊C311yescharacteristic
219D3—241no—
220C22—31no—
221C22—31no—
222C22—122no—
223C22—122no—
224C22—121no—
225C22—121no—
226C22—121no—
227C22—362no—
228C22—362no—
229C22—361no—
230C22—361no—
231C22—361no—
232C22C3⋊#99411yescharacteristic
233C4—31no—
234C4—41no—
235C4—62no—
236C4—91no—
237C4—121no—
238C4—182no—
239C3—161no—
240C3—321no—
241C3#2657⋊C311yescharacteristic, complemented
242C2—31no—
243C2—31no—
244C2—241no—
245C2—721no—
246C2D3×#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⋊(#376⋊C3)C2semidirect
3. C3⋊(#392⋊C3)C2semidirect
4. #76706C3semidirect
17. #392⋊C3D3semidirect
241. C3#2657⋊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⋊(#376⋊C3)2
C3⋊(#392⋊C3)2
#767063
#2657⋊C33
A4×Dic64