Finite Group Databasebeta

← #11802820

Subgroups — #11802820

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×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C3×#5211C212yesmaximal
3#10591720C212yesmaximal
4#10591705C212yesmaximal
5#10591271C218yesmaximal, complemented
6#74054—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C418yescomplemented
11C2×C4⋊(C3⋊Dic3)C2214yes—
12C2×C3×#217C2214yes—
13C2×#3724C2214yes—
14C2×Dic32C2214yes—
15C3×C3⋊#95C2214yes—
16C3×C3⋊#95C2214yes—
17#63579C2214yes—
18#63579C2214yes—
19C22×C4⋊Dic3—32no—
20C22×C4⋊Dic3—61no—
21C3×#381—32no—
22#5211D312yes—
23#4942—34no—
24Dic3×C22⋊C4—34no—
25#4654—38no—
26#4653—38no—
27C24×C32C2311yescharacteristic
28C22×C32×C4—24no—
29C22×C32×C4C2×C414yes—
30C22×C32×C4C2312yes—
31C22×C3⋊Dic3—42no—
32C22×C3⋊Dic3—42no—
33C22×C3⋊Dic3C2×C414yes—
34C22×C3⋊Dic3C2×C414yes—
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2312yes—
37C22×C3×Dic3C2318yes—
38C4⋊(C3⋊Dic3)C2×C4116yes—
39C3×#217—28no—
40#3724—44no—
41Dic32—44no—
42#2313—91noSylow
43C23×C3×C4—21no—
44C23×C3×C4C2×D312yes—
45C23×Dic3—32no—
46C23×Dic3—32no—
47C23×Dic3—61no—
48C23×Dic3—61no—
49C2×C3×C22⋊C4—34no—
50C2×#217C2×D314yes—
51C2×C4⋊Dic3—316no—
52C2×C4⋊Dic3—34no—
53C2×C4⋊Dic3—34no—
54C2×C4⋊Dic3—68no—
55C2×C4⋊Dic3—64no—
56C2×Dic3⋊C4—38no—
57C2×C4×Dic3—38no—
58C3×#95—34no—
59C3×#95—34no—
60C3⋊#95—38no—
61C3⋊#95—38no—
62C3⋊#95C2×D314yes—
63C3⋊#95C2×D314yes—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32C22×C412yes—
67C23×C32#4114yes—
68C23×C32C2411yescharacteristic
69C2×C32×C4—28no—
70C2×C32×C4—24no—
71C2×C32×C4C22×C414yes—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3—44no—
75C2×C3⋊Dic3—44no—
76C2×C3⋊Dic3C22×C414yes—
77C2×C3⋊Dic3C22×C414yes—
78C2×C3×Dic3—28no—
79C2×C3×Dic3—28no—
80C2×C3×Dic3—28no—
81C22×C4⋊C4—91no—
82#387—98no—
83#381—32no—
84#380—92no—
85C4×C22⋊C4—92no—
86C24×C3—21no—
87C24×C3C22×D312yes—
88C22×C3×C4—28no—
89C22×C3×C4—28no—
90C22×C3×C4—24no—
91C22×C3×C4—22no—
92C22×C3×C4—38no—
93C22×C3×C4C4×D318yes—
94C22×C3×C4C22×D312yes—
95C22×C3×C4C22×D312yes—
96C22×Dic3—34no—
97C22×Dic3—34no—
98C22×Dic3—38no—
99C22×Dic3—38no—
100C22×Dic3—64no—
101C22×Dic3—64no—
102C22×Dic3—62no—
103C22×Dic3—62no—
104C22×Dic3—124no—
105C22×Dic3—124no—
106C22×Dic3—124no—
107C22×Dic3—124no—
108C22×Dic3C22×D318yes—
109C3×C22⋊C4—68no—
110#217—28no—
111C4⋊Dic3—316no—
112C4⋊Dic3—316no—
113C4⋊Dic3—616no—
114Dic3⋊C4—128no—
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—98no—
132C2×C4⋊C4—94no—
133C2×C4⋊C4—94no—
134C2×C22⋊C4—34no—
135C2×C42—94no—
136#95—34no—
137#95—34no—
138#95—94no—
139#95—94no—
140C23×C3—24no—
141C23×C3—24no—
142C23×C3—24no—
143C23×C3—24no—
144C23×C3—21no—
145C23×C3—24no—
146C23×C3—22no—
147C23×C3C2×C4×D314yes—
148C23×C3#23718yes—
149C23×C3C23×D312yes—
150C2×C3×C4—28no—
151C2×C3×C4—216no—
152C2×C3×C4—216no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
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—68no—
170C2×Dic3—124no—
171C2×Dic3—124no—
172C2×Dic3—128no—
173C2×Dic3—128no—
174C2×Dic3—128no—
175C2×Dic3—128no—
176C2×C32—24no—
177C2×C32C2×#11711yescharacteristic
178C2×C32#51811yescharacteristic
179C2×C32#51911yescharacteristic
180C2×C32#53914yes—
181C24C2×D3211yescharacteristic
182C22×C4—24no—
183C22×C4—38no—
184C22×C4—92no—
185C22×C4—92no—
186C22×C4—94no—
187C22×C4—94no—
188C22×C4—362no—
189C22×C4—362no—
190C22×C4#62414yes—
191C22×C4C2×D3212yes—
192C4⋊C4—916no—
193C4⋊C4—364no—
194C22⋊C4—68no—
195C42—364no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3—216no—
199C22×C3—216no—
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—21no—
206C22×C3—24no—
207C22×C3#87718yes—
208C22×C3C22×C4×D312yes—
209C22×C3C2×#23714yes—
210C22×C3#100914yes—
211C22×C3#101014yes—
212C3×C4—28no—
213C3×C4—24no—
214C3×C4—24no—
215C3×C4—128no—
216Dic3—48no—
217Dic3—68no—
218Dic3—68no—
219Dic3—124no—
220Dic3—124no—
221C32#231311yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23#380514yes—
225C23C2×#62412yes—
226C23C22×D3211yescharacteristic
227C2×C4—24no—
228C2×C4—28no—
229C2×C4—68no—
230C2×C4—68no—
231C2×C4—68no—
232C2×C4—94no—
233C2×C4—94no—
234C2×C4—184no—
235C2×C4—184no—
236C2×C4—364no—
237C2×C4—364no—
238C2×C4C2×#62414yes—
239C2×C3—28no—
240C2×C3—28no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—24no—
244C2×C3—21no—
245C2×C3C2×#87712yes—
246C2×C3#551612yes—
247C2×C3#552112yes—
248C2×C3#566518yes—
249C22—22no—
250C22—28no—
251C22—22no—
252C22#6395714yes—
253C22#6429812yes—
254C22#6430812yes—
255C22C2×#380512yes—
256C22C22×#62411yescharacteristic
257C4—24no—
258C4—128no—
259C4—184no—
260C4—184no—
261C3—21no—
262C3#7405412yescomplemented
263C2—24no—
264C2#1059482811yescharacteristic
265C2#1059499414yes—
266C2#1059499611yescharacteristic
267C2C2×#6395711yescharacteristic
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. #10591271C2semidirect
10. C2×C4⋊(C3⋊Dic3)C4semidirect
221. C32#2313semidirect
262. C3#74054semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C3×#52112
#105917202
#105917052
#105912712
#740543