Finite Group Databasebeta

← #11776858

Subgroups — #11776858

Order 1152.

308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#3788C211yesmaximal, characteristic
2#10590331C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×#3788C411yescharacteristic
7C2×#3788C411yescharacteristic
8C42×C3⋊D3C2211yescharacteristic
9C2×#3710—21no—
10#63777C412yes—
11C4×#622C2212yes—
12C3×C4⋊(C3⋊C8)—21no—
13C3×C4×C3⋊C8—21no—
14#63572C2211yescharacteristic
15#63572C2212yes—
16#63572C2211yescharacteristic
17#63557—21no—
18D3×C4⋊C8—61no—
19#4685—61no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3Q811yescharacteristic
23C2×#622C2×C412yes—
24C2×#622C2×C412yes—
25#3788—22no—
26#3788C814yescomplemented
27C32×C42D411yescharacteristic
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3×C3⋊C8—21no—
32C2×C3×C3⋊C8—21no—
33C2×C3×C3⋊C8—22no—
34#3710—42no—
35#1565—91nomaximal, Sylow
36C2×D3×C8—62no—
37C42×D3—61no—
38C42×D3—61no—
39C3×C4⋊C8—61no—
40C3×C4×C8—61no—
41(C2×D3)⋊C8—61no—
42(C2×D3)⋊C8—61no—
43Dic3⋊C8—61no—
44Dic3⋊C8—61no—
45Dic3⋊C8—62no—
46C4⋊(C3⋊C8)—21no—
47C4×C3⋊C8—21no—
48C22×C3⋊D3C4⋊C411yescharacteristic
49C2×C32×C4C4⋊C411yescharacteristic
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C2×C3⋊Dic3C22×C411yescharacteristic
54C2×C3⋊Dic3C2×Q811yescharacteristic
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3—41no—
58C4×C3⋊D3C2×C812yes—
59C4×C3⋊D3M1612yes—
60#622—22no—
61#622C2×C814yescomplemented
62C3×C3⋊C8—42no—
63C3×C3⋊C8—41no—
64C3×C3⋊C8—41no—
65#431—91no—
66C2×C4⋊C8—91no—
67C4×M16—91no—
68#335—92no—
69#334—92no—
70C2×C4×D3—61no—
71C2×C4×D3—61no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C3×C8—61no—
77C2×C3×C8—61no—
78C2×C3×C8—62no—
79C3×C42—21no—
80C3×C42—21no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87C2×C3⋊C8—21no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—22no—
90D3×C8—124no—
91C22×C32C2×C4⋊C411yescharacteristic
92C2×C3⋊D3—21no—
93C2×C3⋊D3—21no—
94C2×C3⋊D3C4⋊C812yes—
95C32×C4—21no—
96C32×C4C4⋊C812yes—
97C32×C4AGL(1,ℤ/8)11yescharacteristic
98C32×C4#13711yescharacteristic
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C3⋊Dic3C22×C811yescharacteristic
102C3⋊Dic3C2×M1611yescharacteristic
103C2×M16—91no—
104C2×M16—91no—
105C22×C8—181no—
106C2×C42—91no—
107C4⋊C8—61no—
108C4⋊C8—91no—
109C4⋊C8—92no—
110C4⋊C8—91no—
111C22⋊C8—181no—
112#97—92no—
113C4×C8—61no—
114C4×C8—92no—
115C22×D3—61no—
116C22×D3—61no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—62no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—121no—
136C4×D3—121no—
137C4×D3—122no—
138C4×D3—122no—
139C3×C8—122no—
140C3×C8—121no—
141C3×C8—121no—
142C3⋊C8—42no—
143C3⋊C8—41no—
144C3⋊C8—41no—
145C2×C32C2×C4⋊C811yescharacteristic
146C2×C32#42811yescharacteristic
147C2×C32#43011yescharacteristic
148C3⋊D3—22no—
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—91no—
152M16—94no—
153M16—182no—
154C2×C8—61no—
155C2×C8—61no—
156C2×C8—62no—
157C2×C8—92no—
158C2×C8—92no—
159C2×C8—362no—
160C42—91no—
161C42—91no—
162C42—91no—
163C42GO+(4,𝔽2)11yescharacteristic
164C22×C3—21no—
165C22×C3—21no—
166C2×D3—62no—
167C2×D3—62no—
168C2×D3—62no—
169C2×D3—62no—
170C2×D3—121no—
171C2×D3—121no—
172C3×C4—22no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—41no—
180Dic3—61no—
181Dic3—61no—
182Dic3—61no—
183Dic3—61no—
184Dic3—62no—
185Dic3—121no—
186Dic3—121no—
187Dic3—121no—
188C32#156511yescharacteristic, complemented, Sylow
189C23—91no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—361no—
198C2×C4#377311yescharacteristic
199C2×C4#377311yescharacteristic
200C2×C4C2×GO+(4,𝔽2)11yescharacteristic
201C8—94no—
202C8—122no—
203C8—121no—
204C8—121no—
205C8—182no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212D3—64no—
213D3—122no—
214C22—92no—
215C22—181no—
216C22—181no—
217C22C2×#377311yescharacteristic
218C4—21no—
219C4—91no—
220C4—91no—
221C4—181no—
222C4—181no—
223C4#6373212yes—
224C4#6422411yescharacteristic
225C4#6422611yescharacteristic
226C3—21no—
227C3—21no—
228C2—182no—
229C2C2×#6373211yescharacteristic
230C2#1059333011yescharacteristic
231C2#1059339411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1565
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
26. #3788C8semidirect
61. #622C2×C8semidirect
188. C32#1565semidirect

Maximal subgroups

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

subgroupindex
C4×#37882
#105903312
#105902972
#105900422
#105900412
#15659