Finite Group Databasebeta

← #11771211

Subgroups — #11771211

Order 1152.

332 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#10593805C211yesmaximal, characteristic
2#10591274C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×C4⋊Dic3—21no—
7C2×Dic32—21no—
8#63779C412yescomplemented
9C4⋊#622—21no—
10C3×#830—21no—
11#63579C412yes—
12#63572C412yescomplemented
13#63553—21no—
14Dic3×C4⋊C4—61no—
15#4718—61no—
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3×Dic3—22no—
20#3792—41no—
21#3792—41no—
22C2×#622—22no—
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C3×C4⋊Dic3—24no—
28C2×C3×C3⋊C8—22no—
29Dic32—41no—
30Dic32—41no—
31#1303—91nomaximal, Sylow
32C2×C3×C4⋊C4—61no—
33C2×C4⋊Dic3—21no—
34C2×C4×Dic3—61no—
35C2×C4×Dic3—61no—
36C2×C4×Dic3—62no—
37C3×C22⋊C8—61no—
38C3⋊#95—62no—
39#830—21no—
40Dic3⋊C8—62no—
41C8×Dic3—62no—
42C23×C32C22⋊C411yescharacteristic
43C2×C32×C4—22no—
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3C4211yescharacteristic
48C2×C3⋊Dic3C22⋊C411yescharacteristic
49C2×C3⋊Dic3C4⋊C411yescharacteristic
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3D811yescharacteristic
52C2×C3⋊Dic3SD1611yescharacteristic
53C2×C3⋊Dic3SD1611yescharacteristic
54C2×C3⋊Dic3Q1611yescharacteristic
55C2×C3×Dic3—24no—
56C2×C3×Dic3—42no—
57C2×C3×Dic3—42no—
58#622—42no—
59C3×C3⋊C8—42no—
60#431—91no—
61#423—91no—
62C4×C4⋊C4—91no—
63C22×C3×C4—21no—
64C22×C3×C4—21no—
65C22×C3×C4—62no—
66C22×Dic3—22no—
67C22×Dic3—61no—
68C22×Dic3—61no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71C2×C3×C8—62no—
72C3×C4⋊C4—64no—
73C4⋊Dic3—24no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C4×Dic3—122no—
83C4×Dic3—122no—
84C2×C3⋊C8—22no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32#9511yescharacteristic
88C22×C32#10211yescharacteristic
89C22×C32#10311yescharacteristic
90C32×C4—21no—
91C32×C4#10412yes—
92C3⋊Dic3—21no—
93C3⋊Dic3—21no—
94C3⋊Dic3#10211yescharacteristic
95C3⋊Dic3#10311yescharacteristic
96C3⋊Dic3#10611yescharacteristic
97C3⋊Dic3#10711yescharacteristic
98C3×Dic3—44no—
99C2×M16—181no—
100C2×C4⋊C4—61no—
101C2×C42—91no—
102C2×C42—181no—
103C4⋊C8—92no—
104C4⋊C8—92no—
105C4⋊C8—181no—
106C22⋊C8—61no—
107C4×C8—181no—
108#95—92no—
109C23×C3—21no—
110C23×C3—21no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—42no—
118C2×C3×C4—64no—
119C2×C3×C4—122no—
120C2×C3×C4—122no—
121C2×Dic3—24no—
122C2×Dic3—42no—
123C2×Dic3—42no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—61no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—122no—
141C2×Dic3—121no—
142C2×Dic3—121no—
143C3×C8—122no—
144C3⋊C8—42no—
145C2×C32—21no—
146C2×C32—21no—
147C2×C32#33911yescharacteristic
148C2×C32#34011yescharacteristic
149C2×C32#34411yescharacteristic
150C22×C4—62no—
151C22×C4—91no—
152C22×C4—91no—
153C22×C4GO+(4,𝔽2)11yescharacteristic
154M16—361no—
155M16—361no—
156C2×C8—62no—
157C2×C8—182no—
158C4⋊C4—64no—
159C42—91no—
160C42—91no—
161C42—91no—
162C42—91no—
163C42—361no—
164C42—361no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—41no—
176C22×C3—41no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—22no—
180C3×C4—41no—
181C3×C4—124no—
182Dic3—44no—
183Dic3—61no—
184Dic3—61no—
185Dic3—61no—
186Dic3—61no—
187Dic3—61no—
188Dic3—61no—
189Dic3—61no—
190Dic3—61no—
191Dic3—62no—
192Dic3—121no—
193Dic3—121no—
194Dic3—121no—
195C32#130311yescharacteristic, complemented, Sylow
196C23D32⋊C411yescharacteristic
197C2×C4—22no—
198C2×C4—64no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—91no—
207C2×C4—122no—
208C2×C4—122no—
209C2×C4—361no—
210C2×C4D32⋊C411yescharacteristic
211C2×C4#377311yescharacteristic
212C8—122no—
213C8—362no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—41no—
225C2×C3—41no—
226C22—21no—
227C22—21no—
228C22#6372911yescharacteristic
229C22#6373011yescharacteristic
230C22#6373711yescharacteristic
231C4—21no—
232C4—91no—
233C4—91no—
234C4—91no—
235C4—91no—
236C4—124no—
237C4—181no—
238C4—181no—
239C4#6374112yes—
240C3—21no—
241C3—21no—
242C2—21no—
243C2—21no—
244C2#1059004911yescharacteristic
245C2#1059005611yescharacteristic
246C2#1059007411yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1303
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #63779C4semidirect
12. #63572C4semidirect
195. C32#1303semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105912742
#105910612
#13039