Finite Group Databasebeta

← #11771251

Subgroups — #11771251

Order 1152.

396 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593802C211yesmaximal, characteristic
2#10591219C211yesmaximal, characteristic
3#10591074C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3792—21no—
6C2×C3×#208—21no—
7C2×#3722C412yes—
8#63778—21no—
9#63778C412yescomplemented
10C3×C3⋊#95—21no—
11#63579—21no—
12#63557—21no—
13#63557C412yescomplemented
14#5126—61no—
15#4664—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C22×C3×Dic3—22no—
25#3792—42no—
26C2×#622—22no—
27C3×#208—42no—
28C2×C3×C3⋊C8—22no—
29#3722—42no—
30#1306—91nomaximal, Sylow
31C22×C4×D3—61no—
32C22×C4×D3—61no—
33C2×C3×M16—61no—
34C2×(C2×D3)⋊C4—62no—
35C2×#208—21no—
36C3×#95—61no—
37C3⋊#95—21no—
38C3⋊#95—62no—
39(C2×D3)⋊C8—62no—
40(C2×D3)⋊C8—62no—
41C23×C32C22⋊C411yescharacteristic
42C22×C3⋊D3—22no—
43C22×C3⋊D3—41no—
44C22×C3⋊D3—41no—
45C22×C3⋊D3C4211yescharacteristic
46C22×C3⋊D3C4⋊C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C4⋊C411yescharacteristic
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3C22⋊C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C4×C3⋊D3—41no—
54C4×C3⋊D3—41no—
55C4×C3⋊D3—41no—
56C4×C3⋊D3—41no—
57C2×C3×Dic3—42no—
58C2×C3×Dic3—42no—
59C2×C3×Dic3—42no—
60#622—42no—
61C3×C3⋊C8—42no—
62#407—91no—
63#407—91no—
64#381—91no—
65C23×D3—61no—
66C23×D3—61no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—62no—
70C22×Dic3—22no—
71C22×Dic3—61no—
72C22×Dic3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—122no—
82C2×C4×D3—122no—
83C2×C4×D3—124no—
84C3×M16—122no—
85C2×C3×C8—62no—
86(C2×D3)⋊C4—124no—
87#208—42no—
88C2×C3⋊C8—22no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32#9511yescharacteristic
92C22×C32#9912yes—
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—44no—
100C32×C4—21no—
101C32×C4—21no—
102C3⋊Dic3—21no—
103C3⋊Dic3—21no—
104C3×Dic3—82no—
105C23×C4—91no—
106C2×M16—61no—
107C2×M16—181no—
108C2×C22⋊C4—92no—
109C22⋊C8—92no—
110C22⋊C8—92no—
111C22⋊C8—181no—
112C22⋊C8—181no—
113#95—61no—
114#95—181no—
115C23×C3—21no—
116C23×C3—21no—
117C22×D3—61no—
118C22×D3—61no—
119C22×D3—61no—
120C22×D3—61no—
121C22×D3—64no—
122C22×D3—122no—
123C22×D3—122no—
124C22×D3—122no—
125C22×D3—121no—
126C22×D3—122no—
127C22×D3—121no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—42no—
135C2×C3×C4—122no—
136C2×C3×C4—122no—
137C2×C3×C4—122no—
138C2×Dic3—42no—
139C2×Dic3—42no—
140C2×Dic3—42no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—122no—
146C2×Dic3—122no—
147C4×D3—121no—
148C4×D3—121no—
149C4×D3—121no—
150C4×D3—121no—
151C4×D3—122no—
152C4×D3—122no—
153C4×D3—122no—
154C4×D3—122no—
155C4×D3—122no—
156C4×D3—122no—
157C3×C8—122no—
158C3⋊C8—42no—
159C2×C32—22no—
160C2×C32#34211yescharacteristic
161C2×C32#34411yescharacteristic
162C2×C32#34411yescharacteristic
163C3⋊D3—41no—
164C3⋊D3—41no—
165C24—91no—
166C22×C4—62no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—362no—
173C22×C4GO+(4,𝔽2)11yescharacteristic
174M16—122no—
175M16—362no—
176C2×C8—62no—
177C2×C8—182no—
178C22⋊C4—362no—
179C22×C3—21no—
180C22×C3—22no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—41no—
187C22×C3—41no—
188C2×D3—62no—
189C2×D3—62no—
190C2×D3—62no—
191C2×D3—62no—
192C2×D3—121no—
193C2×D3—121no—
194C2×D3—121no—
195C2×D3—121no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—121no—
199C2×D3—121no—
200C2×D3—124no—
201C2×D3—124no—
202C2×D3—128no—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—22no—
206C3×C4—41no—
207C3×C4—41no—
208C3×C4—242no—
209Dic3—82no—
210Dic3—121no—
211Dic3—121no—
212Dic3—121no—
213Dic3—121no—
214C32#130611yescharacteristic, complemented, Sylow
215C23—91no—
216C23—91no—
217C23—182no—
218C23—361no—
219C23—361no—
220C23D32⋊C411yescharacteristic
221C2×C4—22no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—122no—
225C2×C4—122no—
226C2×C4—122no—
227C2×C4—182no—
228C2×C4—361no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4D32⋊C411yescharacteristic
233C2×C4#377311yescharacteristic
234C8—122no—
235C8—362no—
236C2×C3—22no—
237C2×C3—22no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—42no—
245D3—122no—
246D3—122no—
247D3—122no—
248D3—122no—
249C22—21no—
250C22—21no—
251C22—181no—
252C22—181no—
253C22—181no—
254C22—181no—
255C22—181no—
256C22—181no—
257C22—364no—
258C22#6373711yescharacteristic
259C22#6373812yes—
260C4—21no—
261C4—21no—
262C4—181no—
263C4—181no—
264C4—242no—
265C3—21no—
266C3—21no—
267C2—22no—
268C2—361no—
269C2—361no—
270C2#1059005411yescharacteristic
271C2#1059005611yescharacteristic
272C2#1059007611yescharacteristic
subgroupG/H
centerC22#63737
commutatorC22×C3⋊D3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1306
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
9. #63778C4semidirect
13. #63557C4semidirect
214. C32#1306semidirect

Maximal subgroups

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

subgroupindex
#105938022
#105912192
#105910742
#13069