Finite Group Databasebeta

← #11802822

Subgroups — #11802822

Order 1152.

1233 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1233 conjugacy classes of subgroups — too many to draw. Only its 276 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
1C22×#3750C211yesmaximal, characteristic
2C3×#5212C212yesmaximal
3#10591705C212yesmaximal
4#10591697C212yesmaximal
5#10591263C218yesmaximal, complemented
6#73867—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3750C418yescomplemented
11C2×#3750C2214yes—
12C2×C3×#217C2214yes—
13C2×C3×C4⋊Dic3C2214yes—
14C2×Dic32C2214yes—
15C3×C3⋊#95C2214yes—
16#63579C2218yes—
17#63579C2214yes—
18C22×Dic3⋊C4—32no—
19C22×Dic3⋊C4—61no—
20C3×#380—32no—
21#5212D312yes—
22#4978—38no—
23#4943—34no—
24Dic3×C22⋊C4—34no—
25#4655—38no—
26C24×C32C2311yescharacteristic
27C22×C32×C4—42no—
28C22×C32×C4C2×C414yes—
29C22×C32×C4C2312yes—
30C22×C3⋊Dic3—24no—
31C22×C3⋊Dic3—42no—
32C22×C3⋊Dic3C2×C414yes—
33C22×C3⋊Dic3C2×C414yes—
34C22×C3⋊Dic3C2312yes—
35C22×C3⋊Dic3C2312yes—
36C22×C3×Dic3C2318yes—
37#3750C2×C4116yes—
38C3×#217—28no—
39C3×C4⋊Dic3—44no—
40Dic32—44no—
41#2313—91noSylow
42C23×C3×C4—21no—
43C23×C3×C4C2×D312yes—
44C23×Dic3—32no—
45C23×Dic3—32no—
46C23×Dic3—61no—
47C23×Dic3—61no—
48C2×C3×C4⋊C4—34no—
49C2×C3×C22⋊C4—34no—
50C2×#217C2×D314yes—
51C2×C4⋊Dic3C2×D314yes—
52C2×Dic3⋊C4—316no—
53C2×Dic3⋊C4—34no—
54C2×Dic3⋊C4—34no—
55C2×Dic3⋊C4—68no—
56C2×Dic3⋊C4—64no—
57C2×C4×Dic3—38no—
58C3×#95—34no—
59C3⋊#95—38no—
60C3⋊#95—316no—
61C3⋊#95C2×D314yes—
62C23×C32—22no—
63C23×C32—22no—
64C23×C32C22×C412yes—
65C23×C32#4114yes—
66C23×C32C2411yescharacteristic
67C2×C32×C4—24no—
68C2×C32×C4—44no—
69C2×C32×C4C22×C414yes—
70C2×C3⋊Dic3—28no—
71C2×C3⋊Dic3—24no—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3—44no—
74C2×C3⋊Dic3C22×C414yes—
75C2×C3⋊Dic3C22×C414yes—
76C2×C3×Dic3—28no—
77C2×C3×Dic3—28no—
78C2×C3×Dic3—28no—
79C22×C4⋊C4—91no—
80#387—98no—
81#381—92no—
82#380—32no—
83C4×C22⋊C4—92no—
84C24×C3—21no—
85C24×C3C22×D312yes—
86C22×C3×C4—24no—
87C22×C3×C4—22no—
88C22×C3×C4—38no—
89C22×C3×C4—44no—
90C22×C3×C4—44no—
91C22×C3×C4C4×D318yes—
92C22×C3×C4C22×D312yes—
93C22×C3×C4C22×D312yes—
94C22×Dic3—38no—
95C22×Dic3—34no—
96C22×Dic3—34no—
97C22×Dic3—38no—
98C22×Dic3—64no—
99C22×Dic3—62no—
100C22×Dic3—64no—
101C22×Dic3—62no—
102C22×Dic3—68no—
103C22×Dic3—64no—
104C22×Dic3—64no—
105C22×Dic3—124no—
106C22×Dic3—124no—
107C22×Dic3C22×D318yes—
108C3×C4⋊C4—124no—
109C3×C22⋊C4—68no—
110#217—28no—
111C4⋊Dic3—44no—
112Dic3⋊C4—316no—
113Dic3⋊C4—316no—
114Dic3⋊C4—616no—
115C4×Dic3—128no—
116C22×C32—22no—
117C22×C32—22no—
118C22×C32—28no—
119C22×C32#11714yes—
120C22×C32C23×C411yescharacteristic
121C22×C32C2×#4112yes—
122C22×C32H(5,𝔽2)12yes—
123C22×C322−1+412yes—
124C32×C4—24no—
125C3⋊Dic3—24no—
126C3⋊Dic3—24no—
127C3×Dic3—48no—
128C23×C4—91no—
129C23×C4—91no—
130C23×C4D3211yescharacteristic
131C2×C4⋊C4—34no—
132C2×C4⋊C4—98no—
133C2×C4⋊C4—94no—
134C2×C22⋊C4—34no—
135C2×C42—94no—
136#95—34no—
137#95—94no—
138#95—98no—
139C23×C3—24no—
140C23×C3—24no—
141C23×C3—24no—
142C23×C3—24no—
143C23×C3—21no—
144C23×C3—24no—
145C23×C3—22no—
146C23×C3C2×C4×D314yes—
147C23×C3#23714yes—
148C23×C3#23914yes—
149C23×C3C23×D312yes—
150C2×C3×C4—24no—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4—44no—
154C2×C3×C4—48no—
155C2×C3×C4—48no—
156C2×C3×C4—68no—
157C2×C3×C4—68no—
158C2×C3×C4—68no—
159C2×C3×C4C2×C4×D314yes—
160C2×C3×C4C2×C4×D314yes—
161C2×Dic3—28no—
162C2×Dic3—28no—
163C2×Dic3—28no—
164C2×Dic3—38no—
165C2×Dic3—38no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—68no—
169C2×Dic3—616no—
170C2×Dic3—616no—
171C2×Dic3—64no—
172C2×Dic3—68no—
173C2×Dic3—64no—
174C2×Dic3—124no—
175C2×Dic3—128no—
176C2×Dic3—128no—
177C2×C32—24no—
178C2×C32C2×#11711yescharacteristic
179C2×C32#51811yescharacteristic
180C2×C32#51911yescharacteristic
181C2×C32#53914yes—
182C24C2×D3211yescharacteristic
183C22×C4—38no—
184C22×C4—42no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—94no—
188C22×C4—94no—
189C22×C4—184no—
190C22×C4—362no—
191C22×C4#62414yes—
192C22×C4C2×D3212yes—
193C4⋊C4—916no—
194C4⋊C4—124no—
195C22⋊C4—68no—
196C42—364no—
197C22×C3—24no—
198C22×C3—24no—
199C22×C3—216no—
200C22×C3—28no—
201C22×C3—24no—
202C22×C3—24no—
203C22×C3—28no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—22no—
208C22×C3—24no—
209C22×C3#89218yes—
210C22×C3C22×C4×D312yes—
211C22×C3C2×#23712yes—
212C22×C3#100414yes—
213C22×C3C2×#23912yes—
214C22×C3#101014yes—
215C3×C4—24no—
216C3×C4—24no—
217C3×C4—44no—
218C3×C4—128no—
219Dic3—48no—
220Dic3—68no—
221Dic3—68no—
222Dic3—68no—
223Dic3—124no—
224C32#231311yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23#379614yes—
228C23C2×#62412yes—
229C23C22×D3211yescharacteristic
230C2×C4—24no—
231C2×C4—44no—
232C2×C4—68no—
233C2×C4—68no—
234C2×C4—68no—
235C2×C4—94no—
236C2×C4—94no—
237C2×C4—184no—
238C2×C4—184no—
239C2×C4—188no—
240C2×C4—364no—
241C2×C4C2×#62414yes—
242C2×C3—28no—
243C2×C3—28no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—24no—
247C2×C3—21no—
248C2×C3#548612yes—
249C2×C3C2×#89212yes—
250C2×C3#551612yes—
251C2×C3#560214yes—
252C2×C3#564514yes—
253C22—22no—
254C22—28no—
255C22—22no—
256C22#6384914yes—
257C22C2×#379612yes—
258C22#6429812yes—
259C22C22×#62411yescharacteristic
260C22#6433012yes—
261C4—24no—
262C4—128no—
263C4—184no—
264C4—184no—
265C3—21no—
266C3#7386712yescomplemented
267C2—24no—
268C2C2×#6384911yescharacteristic
269C2#1059482811yescharacteristic
270C2#1059497414yes—
271C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. #10591263C2semidirect
10. C2×#3750C4semidirect
224. C32#2313semidirect
266. C3#73867semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C3×#52122
#105917052
#105916972
#105912632
#738673