Finite Group Databasebeta

← #11802818

Subgroups — #11802818

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×C4×#217C212yesmaximal
3#10591720C212yesmaximal
4#10591697C212yesmaximal
5#10591197C218yesmaximal, complemented
6#73445—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3750C418yescomplemented
11C2×#3750C2214yes—
12C2×C3×#217C2214yes—
13C2×C3×C4×Dic3C2214yes—
14C2×#3724C2214yes—
15C3×C3⋊#95C2214yes—
16#63579C2218yes—
17#63579C2214yes—
18C22×Dic3⋊C4—32no—
19C22×Dic3⋊C4—61no—
20C3×C4×C22⋊C4—32no—
21C4×#217D312yes—
22#4943—34no—
23#4942—34no—
24#4933—38no—
25#4652—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—
40#3724—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×C22⋊C4—34no—
49C2×C3×C42—34no—
50C2×#217C2×D314yes—
51C2×Dic3⋊C4—316no—
52C2×Dic3⋊C4—34no—
53C2×Dic3⋊C4—34no—
54C2×Dic3⋊C4—38no—
55C2×Dic3⋊C4—68no—
56C2×Dic3⋊C4—64no—
57C2×C4×Dic3C2×D314yes—
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—92no—
83C4×C22⋊C4—32no—
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—68no—
104C22×Dic3—124no—
105C22×Dic3—124no—
106C22×Dic3C22×D318yes—
107C3×C22⋊C4—68no—
108C3×C42—124no—
109#217—28no—
110Dic3⋊C4—316no—
111Dic3⋊C4—316no—
112Dic3⋊C4—616no—
113Dic3⋊C4—128no—
114C4×Dic3—44no—
115C22×C32—22no—
116C22×C32—22no—
117C22×C32—28no—
118C22×C32#11714yes—
119C22×C32C23×C411yescharacteristic
120C22×C32C2×#4112yes—
121C22×C32H(5,𝔽2)12yes—
122C22×C322−1+412yes—
123C32×C4—24no—
124C3⋊Dic3—24no—
125C3⋊Dic3—24no—
126C3×Dic3—48no—
127C23×C4—91no—
128C23×C4—91no—
129C23×C4D3211yescharacteristic
130C2×C4⋊C4—98no—
131C2×C4⋊C4—94no—
132C2×C4⋊C4—94no—
133C2×C22⋊C4—34no—
134C2×C42—34no—
135#95—34no—
136#95—94no—
137#95—98no—
138C23×C3—24no—
139C23×C3—24no—
140C23×C3—24no—
141C23×C3—24no—
142C23×C3—21no—
143C23×C3—24no—
144C23×C3—22no—
145C23×C3C2×C4×D314yes—
146C23×C3#23518yes—
147C23×C3C23×D312yes—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—24no—
151C2×C3×C4—44no—
152C2×C3×C4—48no—
153C2×C3×C4—48no—
154C2×C3×C4—68no—
155C2×C3×C4—68no—
156C2×C3×C4—68no—
157C2×C3×C4C2×C4×D314yes—
158C2×C3×C4C2×C4×D314yes—
159C2×Dic3—28no—
160C2×Dic3—28no—
161C2×Dic3—28no—
162C2×Dic3—38no—
163C2×Dic3—38no—
164C2×Dic3—64no—
165C2×Dic3—64no—
166C2×Dic3—68no—
167C2×Dic3—616no—
168C2×Dic3—616no—
169C2×Dic3—68no—
170C2×Dic3—68no—
171C2×Dic3—124no—
172C2×Dic3—128no—
173C2×Dic3—128no—
174C2×C32—24no—
175C2×C32C2×#11711yescharacteristic
176C2×C32#51811yescharacteristic
177C2×C32#51911yescharacteristic
178C2×C32#53914yes—
179C24C2×D3211yescharacteristic
180C22×C4—38no—
181C22×C4—42no—
182C22×C4—92no—
183C22×C4—92no—
184C22×C4—94no—
185C22×C4—94no—
186C22×C4—184no—
187C22×C4—362no—
188C22×C4#62414yes—
189C22×C4C2×D3212yes—
190C4⋊C4—916no—
191C4⋊C4—364no—
192C22⋊C4—68no—
193C42—124no—
194C22×C3—24no—
195C22×C3—24no—
196C22×C3—216no—
197C22×C3—24no—
198C22×C3—24no—
199C22×C3—216no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—22no—
204C22×C3—24no—
205C22×C3#87218yes—
206C22×C3C22×C4×D312yes—
207C22×C3C2×#23514yes—
208C22×C3#100414yes—
209C22×C3#101014yes—
210C3×C4—24no—
211C3×C4—24no—
212C3×C4—44no—
213C3×C4—128no—
214Dic3—48no—
215Dic3—68no—
216Dic3—68no—
217Dic3—68no—
218Dic3—124no—
219C32#231311yescharacteristic, complemented, Sylow
220C23—22no—
221C23—22no—
222C23#379814yes—
223C23C2×#62412yes—
224C23C22×D3211yescharacteristic
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—68no—
228C2×C4—68no—
229C2×C4—68no—
230C2×C4—94no—
231C2×C4—94no—
232C2×C4—184no—
233C2×C4—184no—
234C2×C4—188no—
235C2×C4—364no—
236C2×C4C2×#62414yes—
237C2×C3—28no—
238C2×C3—28no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—24no—
243C2×C3C2×#87212yes—
244C2×C3#548612yes—
245C2×C3#551612yes—
246C2×C3#556418yes—
247C22—22no—
248C22—22no—
249C22—28no—
250C22#6387414yes—
251C22#6429812yes—
252C22C2×#379812yes—
253C22C22×#62411yescharacteristic
254C22#6433012yes—
255C4—24no—
256C4—128no—
257C4—184no—
258C4—184no—
259C3—21no—
260C3#7344512yescomplemented
261C2—24no—
262C2#1059482811yescharacteristic
263C2C2×#6387411yescharacteristic
264C2#1059503714yes—
265C2#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. #10591197C2semidirect
10. C2×#3750C4semidirect
219. C32#2313semidirect
260. C3#73445semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C3×C4×#2172
#105917202
#105916972
#105911972
#734453