Finite Group Databasebeta

← #11776857

Subgroups — #11776857

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×#3792C211yesmaximal, characteristic
2C2×#63572C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×#3792C411yescharacteristic
7C2×#3792C411yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3×C3⋊C8—21no—
10#63777C412yes—
11C4×#622C2212yes—
12C3×#830—21no—
13#63572—21no—
14#63572C2211yescharacteristic
15#63572C2211yescharacteristic
16#63572C2212yes—
17#63553—21no—
18C2×Dic3⋊C8—61no—
19#4718—61no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3Q811yescharacteristic
23#3792—22no—
24#3792C814yescomplemented
25C2×#622C2×C412yes—
26C2×#622C2×C412yes—
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3×C3⋊C8—22no—
32C2×C3×C3⋊C8—21no—
33C2×C3×C3⋊C8—21no—
34C2×C3×C3⋊C8—42no—
35#1565—91nomaximal, Sylow
36C22×C3×C8—61no—
37C2×C4×Dic3—61no—
38C2×C4×Dic3—61no—
39C22×C3⋊C8—21no—
40C3×C22⋊C8—61no—
41#830—21no—
42Dic3⋊C8—61no—
43Dic3⋊C8—61no—
44Dic3⋊C8—62no—
45Dic3⋊C8—62no—
46C8×Dic3—61no—
47C8×Dic3—61no—
48C23×C32C4⋊C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C32×C4C2×D411yescharacteristic
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C2×C3⋊Dic3C2×C812yes—
57C2×C3⋊Dic3M1612yes—
58C2×C3⋊Dic3C22×C411yescharacteristic
59C2×C3⋊Dic3C2×Q811yescharacteristic
60#622—22no—
61#622C2×C814yescomplemented
62C3×C3⋊C8—41no—
63C3×C3⋊C8—42no—
64C3×C3⋊C8—41no—
65#431—91no—
66C2×C4⋊C8—91no—
67C4×M16—91no—
68#335—92no—
69#334—92no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×Dic3—61no—
73C22×Dic3—61no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C2×C3×C8—61no—
77C2×C3×C8—61no—
78C2×C3×C8—62no—
79C2×C3×C8—122no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—21no—
90C2×C3⋊C8—22no—
91C2×C3⋊C8—42no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32C4⋊C812yes—
95C22×C32C2×C4⋊C411yescharacteristic
96C32×C4—21no—
97C32×C4AGL(1,ℤ/8)11yescharacteristic
98C32×C4#13711yescharacteristic
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C3⋊Dic3C4⋊C812yes—
102C3⋊Dic3C22×C811yescharacteristic
103C3⋊Dic3C2×M1611yescharacteristic
104C2×M16—91no—
105C2×M16—91no—
106C22×C8—61no—
107C2×C42—91no—
108C4⋊C8—91no—
109C4⋊C8—92no—
110C4⋊C8—91no—
111C4⋊C8—181no—
112C22⋊C8—61no—
113#97—92no—
114C4×C8—92no—
115C4×C8—181no—
116C23×C3—21no—
117C23×C3—21no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—41no—
125C2×C3×C4—41no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—122no—
139C2×Dic3—122no—
140C3×C8—121no—
141C3×C8—121no—
142C3×C8—122no—
143C3⋊C8—41no—
144C3⋊C8—41no—
145C3⋊C8—42no—
146C2×C32—22no—
147C2×C32C2×C4⋊C811yescharacteristic
148C2×C32#42811yescharacteristic
149C2×C32#43011yescharacteristic
150C22×C4—91no—
151C22×C4—91no—
152C22×C4GO+(4,𝔽2)11yescharacteristic
153M16—94no—
154M16—182no—
155C2×C8—61no—
156C2×C8—61no—
157C2×C8—62no—
158C2×C8—92no—
159C2×C8—92no—
160C2×C8—122no—
161C42—91no—
162C42—91no—
163C42—91no—
164C42—91no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3—21no—
168C22×C3—21no—
169C22×C3—22no—
170C22×C3—22no—
171C22×C3—41no—
172C22×C3—41no—
173C3×C4—22no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—41no—
179Dic3—62no—
180Dic3—62no—
181Dic3—61no—
182Dic3—61no—
183Dic3—61no—
184Dic3—61no—
185Dic3—62no—
186Dic3—121no—
187Dic3—121no—
188Dic3—121no—
189C32#156511yescharacteristic, complemented, Sylow
190C23#377311yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—92no—
196C2×C4—92no—
197C2×C4—91no—
198C2×C4—91no—
199C2×C4—361no—
200C2×C4#377311yescharacteristic
201C2×C4C2×GO+(4,𝔽2)11yescharacteristic
202C8—94no—
203C8—122no—
204C8—121no—
205C8—121no—
206C8—182no—
207C2×C3—24no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—42no—
215C22—21no—
216C22—21no—
217C22#6373212yes—
218C22C2×#377311yescharacteristic
219C4—21no—
220C4—91no—
221C4—91no—
222C4—92no—
223C4—181no—
224C4—181no—
225C4#6423611yescharacteristic
226C4#6423911yescharacteristic
227C3—21no—
228C3—21no—
229C2—22no—
230C2C2×#6373211yescharacteristic
231C2#1059333011yescharacteristic
232C2#1059350711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1565
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
24. #3792C8semidirect
61. #622C2×C8semidirect
189. C32#1565semidirect

Maximal subgroups

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

subgroupindex
C4×#37922
C2×#635722
#105910612
#105900422
#105900412
#15659