Finite Group Databasebeta

← #11802795

Subgroups — #11802795

Order 1152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C32×#381C211yesmaximal, characteristic
3#10592910C211yesmaximal, characteristic
4#10592641C212yesmaximal
5C22⋊C4×C3⋊Dic3C212yesmaximal
6#10592353C214yesmaximal, complemented
7#10592352C214yesmaximal, complemented
8#74054—34nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C2×C32×C22⋊C4C2212yes—
13C2×#3757C2212yes—
14C2×C4⋊(C3⋊Dic3)C418yescomplemented
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C2×C4⋊(C3⋊Dic3)C2212yes—
17C2×#3750C2214yes—
18C2×C4×C3⋊Dic3C2214yes—
19C32×#95C2212yes—
20C32×#95C2212yes—
21#63658C2212yes—
22#63658C2214yes—
23#63658C2214yes—
24#63658C2212yes—
25C22×C4⋊Dic3—34no—
26C3×#381D314yes—
27#5211—34no—
28#4942—38no—
29Dic3×C22⋊C4—38no—
30#4654—316no—
31#4653—316no—
32C24×C32C2311yescharacteristic
33C22×C32×C4—24no—
34C22×C32×C4C2×C414yes—
35C22×C32×C4C2314yes—
36C22×C32×C4C2311yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—42no—
39C22×C3⋊Dic3—42no—
40C22×C3⋊Dic3C2×C414yes—
41C22×C3⋊Dic3C2×C414yes—
42C22×C3⋊Dic3C2314yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2312yes—
45C32×C22⋊C4—24no—
46#3757—24no—
47C4⋊(C3⋊Dic3)C2×C418yes—
48C4⋊(C3⋊Dic3)C2×C418yes—
49#3750—44no—
50C4×C3⋊Dic3—44no—
51#2313—91noSylow
52C23×C3×C4C2×D314yes—
53C23×Dic3—34no—
54C23×Dic3—34no—
55C2×C3×C22⋊C4C2×D318yes—
56C2×#217—38no—
57C2×C4⋊Dic3—332no—
58C2×C4⋊Dic3—38no—
59C2×C4⋊Dic3—38no—
60C2×Dic3⋊C4—316no—
61C2×C4×Dic3—316no—
62C3×#95C2×D318yes—
63C3×#95C2×D318yes—
64C3⋊#95—38no—
65C3⋊#95—316no—
66C3⋊#95—316no—
67C3⋊#95—38no—
68C23×C32—22no—
69C23×C32—22no—
70C23×C32C22×C412yes—
71C23×C32#4114yes—
72C23×C32C2411yescharacteristic
73C2×C32×C4—28no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—24no—
77C2×C32×C4—24no—
78C2×C32×C4—24no—
79C2×C32×C4C22×C412yes—
80C2×C32×C4C22×C412yes—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3—24no—
84C2×C3⋊Dic3—24no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3—44no—
87C2×C3⋊Dic3—44no—
88C2×C3⋊Dic3C22×C414yes—
89C2×C3⋊Dic3C22×C414yes—
90C22×C4⋊C4—91no—
91#387—94no—
92#387—94no—
93#381—91no—
94#381C3⋊D311yescharacteristic
95#380—92no—
96C4×C22⋊C4—92no—
97C24×C3C22×D314yes—
98C22×C3×C4—216no—
99C22×C3×C4C4×D3116yes—
100C22×C3×C4C22×D3116yes—
101C22×C3×C4C22×D314yes—
102C22×C3×C4C22×D314yes—
103C22×Dic3—38no—
104C22×Dic3—38no—
105C22×Dic3—316no—
106C22×Dic3—316no—
107C22×Dic3—316no—
108C22×Dic3—128no—
109C22×Dic3—128no—
110C3×C22⋊C4—216no—
111#217—616no—
112C4⋊Dic3—332no—
113C4⋊Dic3—332no—
114Dic3⋊C4—1216no—
115C4×Dic3—1216no—
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—22no—
125C32×C4—22no—
126C32×C4—44no—
127C3⋊Dic3—24no—
128C3⋊Dic3—24no—
129C3⋊Dic3—44no—
130C23×C4—91no—
131C23×C4—91no—
132C23×C4C2×C3⋊D311yescharacteristic
133C2×C4⋊C4—98no—
134C2×C4⋊C4—92no—
135C2×C4⋊C4—92no—
136C2×C4⋊C4—94no—
137C2×C22⋊C4—92no—
138C2×C22⋊C4C2×C3⋊D312yes—
139C2×C42—94no—
140#95—94no—
141#95—94no—
142#95—92no—
143#95—92no—
144#95C2×C3⋊D312yes—
145#95C2×C3⋊D312yes—
146C23×C3—28no—
147C23×C3—28no—
148C23×C3C2×C4×D318yes—
149C23×C3#237116yes—
150C23×C3C23×D314yes—
151C2×C3×C4—232no—
152C2×C3×C4—28no—
153C2×C3×C4—28no—
154C2×C3×C4—216no—
155C2×C3×C4—216no—
156C2×C3×C4—216no—
157C2×C3×C4C2×C4×D318yes—
158C2×C3×C4C2×C4×D318yes—
159C2×Dic3—316no—
160C2×Dic3—316no—
161C2×Dic3—616no—
162C2×Dic3—616no—
163C2×Dic3—616no—
164C2×Dic3—616no—
165C2×Dic3—616no—
166C2×Dic3—1216no—
167C2×Dic3—1216no—
168C2×C32—24no—
169C2×C32C2×#11711yescharacteristic
170C2×C32#51811yescharacteristic
171C2×C32#51911yescharacteristic
172C2×C32#53914yes—
173C24C22×C3⋊D311yescharacteristic
174C22×C4—24no—
175C22×C4—92no—
176C22×C4—92no—
177C22×C4—94no—
178C22×C4—94no—
179C22×C4—94no—
180C22×C4—362no—
181C22×C4—362no—
182C22×C4C4×C3⋊D314yes—
183C22×C4C22×C3⋊D314yes—
184C22×C4C22×C3⋊D311yescharacteristic
185C22×C4C22×C3⋊D311yescharacteristic
186C4⋊C4—98no—
187C4⋊C4—98no—
188C4⋊C4—364no—
189C22⋊C4—24no—
190C22⋊C4—184no—
191C42—364no—
192C22×C3—232no—
193C22×C3—28no—
194C22×C3—28no—
195C22×C3#877116yes—
196C22×C3C22×C4×D314yes—
197C22×C3C2×#23718yes—
198C22×C3#100918yes—
199C22×C3#101018yes—
200C3×C4—28no—
201C3×C4—28no—
202C3×C4—416no—
203Dic3—616no—
204Dic3—616no—
205Dic3—1216no—
206C32#231311yescharacteristic, complemented, Sylow
207C23—22no—
208C23—22no—
209C23C2×C4×C3⋊D312yes—
210C23#383014yes—
211C23C23×C3⋊D311yescharacteristic
212C2×C4—28no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—94no—
219C2×C4—94no—
220C2×C4—184no—
221C2×C4—184no—
222C2×C4—184no—
223C2×C4—184no—
224C2×C4—184no—
225C2×C4—364no—
226C2×C4—364no—
227C2×C4C2×C4×C3⋊D312yes—
228C2×C4C2×C4×C3⋊D312yes—
229C2×C3—216no—
230C2×C3C2×#87714yes—
231C2×C3#551614yes—
232C2×C3#552114yes—
233C2×C3#5665116yes—
234C22—28no—
235C22—22no—
236C22—22no—
237C22#6408614yes—
238C22C22×C4×C3⋊D311yescharacteristic
239C22C2×#383012yes—
240C22#6436612yes—
241C22#6436712yes—
242C4—22no—
243C4—22no—
244C4—44no—
245C4—184no—
246C4—184no—
247C4—364no—
248C3#7405414yescomplemented
249C2—24no—
250C2C2×#6408611yescharacteristic
251C2#1059598711yescharacteristic
252C2#1059599211yescharacteristic
253C2#1059613614yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#381C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenter#381C3⋊D3
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #10592353C2semidirect
7. #10592352C2semidirect
14. C2×C4⋊(C3⋊Dic3)C4semidirect
206. C32#2313semidirect
248. 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
C32×#3812
#105929102
#105926412
C22⋊C4×C3⋊Dic32
#105923532
#105923522
#740543