Finite Group Databasebeta

← #11771237

Subgroups — #11771237

Order 1152.

390 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593812C211yesmaximal, characteristic
2#10591159C211yesmaximal, characteristic
3#10591074C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×C4⋊#157—21no—
7C2×C3×#208—21no—
8C2×#3712C412yescomplemented
9#63781—21no—
10C3×#830—21no—
11#63557—21no—
12#63557—21no—
13#63557C412yescomplemented
14#5126—61no—
15#4726—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×#157—22no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3Q811yescharacteristic
20C2×C4×C3⋊D3—42no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C22⋊#157—42no—
26C4⋊#157—42no—
27C3×#208—42no—
28C2×C3×C3⋊C8—22no—
29C2×C3×C3⋊C8—22no—
30#3712—42no—
31#1305—91nomaximal, Sylow
32C22×C4×D3—61no—
33C22×C4×D3—61no—
34C2×C3×M16—61no—
35C2×#208—21no—
36C2×ΓL(1,𝔽25)—62no—
37C3×C22⋊C8—61no—
38#830—21no—
39(C2×D3)⋊C8—62no—
40(C2×D3)⋊C8—62no—
41(C2×D3)⋊C8—62no—
42C23×C32C4⋊C411yescharacteristic
43C22×C3⋊D3—21no—
44C22×C3⋊D3—21no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3C4211yescharacteristic
48C22×C3⋊D3C22⋊C411yescharacteristic
49C2×#157—42no—
50C2×#157—42no—
51C2×#157—42no—
52C2×C32×C4—22no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C3⋊Dic3—41no—
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C4⋊C411yescharacteristic
58C4×C3⋊D3—22no—
59C4×C3⋊D3—22no—
60C4×C3⋊D3—41no—
61C4×C3⋊D3—41no—
62C3×C3⋊C8—42no—
63C3×C3⋊C8—42no—
64#407—91no—
65#407—91no—
66#380—91no—
67C23×D3—61no—
68C23×D3—61no—
69C22×C3×C4—21no—
70C22×C3×C4—21no—
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—124no—
82C2×C4×D3—122no—
83C2×C4×D3—122no—
84C3×M16—122no—
85C2×C3×C8—62no—
86C2×C3×C8—62no—
87#208—42no—
88C2×C3⋊C8—22no—
89C2×C3⋊C8—22no—
90ΓL(1,𝔽25)—124no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#9511yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—42no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3#10011yescharacteristic
103C2×C3⋊D3#10111yescharacteristic
104#157—82no—
105C32×C4—21no—
106C32×C4#9912yes—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C23×C4—91no—
110C2×M16—61no—
111C2×M16—92no—
112C2×C4⋊C4—181no—
113C2×C22⋊C4—92no—
114C22⋊C8—61no—
115C22⋊C8—92no—
116C22⋊C8—181no—
117C22⋊C8—181no—
118#95—181no—
119C23×C3—21no—
120C23×C3—21no—
121C22×D3—61no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3—61no—
125C22×D3—121no—
126C22×D3—121no—
127C22×D3—121no—
128C22×D3—121no—
129C22×D3—122no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—122no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—42no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146C4×D3—64no—
147C4×D3—122no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151C4×D3—121no—
152C4×D3—121no—
153C4×D3—121no—
154C4×D3—121no—
155C4×D3—122no—
156C3×C8—122no—
157C3×C8—122no—
158C3⋊C8—42no—
159C3⋊C8—42no—
160C2×C32—41no—
161C2×C32#34211yescharacteristic
162C2×C32#34311yescharacteristic
163C2×C32#34411yescharacteristic
164C3⋊D3—21no—
165C3⋊D3—21no—
166C3⋊D3—41no—
167C24—91no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—182no—
174C22×C4—362no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176M16—122no—
177M16—362no—
178C2×C8—62no—
179C2×C8—62no—
180C4⋊C4—362no—
181C22⋊C4—362no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—41no—
187C22×C3—41no—
188C22×C3—41no—
189C22×C3—41no—
190C2×D3—61no—
191C2×D3—61no—
192C2×D3—61no—
193C2×D3—61no—
194C2×D3—62no—
195C2×D3—62no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—121no—
199C2×D3—121no—
200C2×D3—121no—
201C2×D3—121no—
202C2×D3—121no—
203C2×D3—121no—
204C2×D3—124no—
205C2×D3—124no—
206C2×D3—124no—
207C2×D3—124no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213Dic3—62no—
214Dic3—121no—
215Dic3—121no—
216Dic3—121no—
217C32#130511yescharacteristic, complemented, Sylow
218C23—91no—
219C23—91no—
220C23—181no—
221C23—181no—
222C23—361no—
223C23—361no—
224C23#377311yescharacteristic
225C2×C4—22no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4—362no—
234C2×C4—362no—
235C2×C4—362no—
236C2×C4D32⋊C411yescharacteristic
237C2×C4D32⋊C411yescharacteristic
238C8—122no—
239C8—122no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—42no—
247C2×C3—42no—
248D3—121no—
249D3—121no—
250D3—121no—
251D3—121no—
252D3—122no—
253D3—122no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—91no—
258C22—91no—
259C22—181no—
260C22—181no—
261C22—181no—
262C22—181no—
263C22—181no—
264C22—362no—
265C22—362no—
266C22#6373711yescharacteristic
267C4—21no—
268C4—181no—
269C4—181no—
270C4—722no—
271C4#6373812yes—
272C3—21no—
273C3—21no—
274C2—41no—
275C2—181no—
276C2—181no—
277C2—361no—
278C2#1059005311yescharacteristic
279C2#1059005511yescharacteristic
280C2#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#1305
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
8. C2×#3712C4semidirect
13. #63557C4semidirect
217. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938122
#105911592
#105910742
#13059