Finite Group Databasebeta

← #11807136

Subgroups — #11807136

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C212yesmaximal
3#10591273C214yesmaximal
4Dic3×C4⋊Dic3C214yesmaximal
5#10591212C214yesmaximal
6#73656—32nomaximal
7C22×#634C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2214yes—
10#64078C418yescomplemented
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×C4×Dic3C2214yes—
14C2×#3724C2214yes—
15C2×Dic32C2214yes—
16C3×C3⋊#95C2214yes—
17#63579C2218yes—
18C2×#869—32no—
19C2×#869—61no—
20C3×C4×C4⋊C4—32no—
21Dic3×C4⋊C4—34no—
22#4972—34no—
23C4×C4⋊Dic3—34no—
24C4×C4⋊Dic3D312yes—
25#4928—34no—
26#4646—38no—
27C22×C32×C4C2311yescharacteristic
28C22×C32×C4C2312yes—
29C22×C3⋊Dic3C2314yes—
30C2×#634—42no—
31C2×#634—42no—
32C2×#634C2×C418yes—
33C22×C3×Dic3C2314yes—
34C22×C3×Dic3C2314yes—
35C32×C42C2×C414yes—
36C4⋊(C3⋊Dic3)C2×C4116yes—
37C3×C4⋊Dic3—24no—
38C3×C4⋊Dic3Q818yescomplemented
39C3×C4×Dic3—28no—
40#3724—44no—
41Dic32—44no—
42#2369—91noSylow
43C22×Dic6—34no—
44C22×Dic6—62no—
45C2×C3×C4⋊C4—32no—
46C2×C3×C4⋊C4—32no—
47C2×C3×C42—21no—
48C2×C3×C42—34no—
49C2×C3×C42C2×D312yes—
50C2×C4⋊Dic3—34no—
51C2×C4⋊Dic3—34no—
52C2×C4⋊Dic3—64no—
53C2×C4⋊Dic3C2×D312yes—
54C2×C4⋊Dic3C2×D312yes—
55C2×Dic3⋊C4—38no—
56C2×C4×Dic3—38no—
57C2×C4×Dic3C2×D314yes—
58#869—316no—
59#869—68no—
60C3×#95—34no—
61C3⋊#95—38no—
62C3⋊#95—38no—
63C3⋊#95C2×D314yes—
64C23×C32C2411yescharacteristic
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4C22×C412yes—
68C2×C32×C4C22×C414yes—
69C2×C32×C4C2×Q814yes—
70C2×C32×C4#4114yes—
71C2×C3⋊Dic3—24no—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3C22×C418yes—
74#634—48no—
75C2×C3×Dic3—24no—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—24no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3C2×Q818yes—
81C2×C4⋊Q8—91no—
82#391—94no—
83#389—94no—
84C4×C4⋊C4—32no—
85C4×C4⋊C4—94no—
86C22×C3×C4—22no—
87C22×C3×C4—21no—
88C22×C3×C4—34no—
89C22×C3×C4—34no—
90C22×C3×C4C22×D312yes—
91C22×C3×C4C22×D312yes—
92C22×C3×C4C22×D312yes—
93C22×Dic3—38no—
94C22×Dic3—64no—
95C22×Dic3C22×D314yes—
96C22×Dic3C22×D314yes—
97C2×Dic6—316no—
98C2×Dic6—68no—
99C2×Dic6—124no—
100C2×Dic6—124no—
101C2×Dic6—124no—
102C2×Dic6—124no—
103C3×C4⋊C4—38no—
104C3×C4⋊C4—64no—
105C3×C42—24no—
106C3×C42—68no—
107C3×C42C4×D318yes—
108C4⋊Dic3—24no—
109C4⋊Dic3—316no—
110C4⋊Dic3—316no—
111C4⋊Dic3—616no—
112C4⋊Dic3Dic618yescomplemented
113Dic3⋊C4—128no—
114C4×Dic3—28no—
115C4×Dic3—128no—
116C22×C32C23×C411yescharacteristic
117C22×C32C22×Q812yes—
118C22×C32C2×#4112yes—
119C22×C32H(5,𝔽2)11yescharacteristic
120C22×C32H(5,𝔽2)11yescharacteristic
121C32×C4—22no—
122C32×C4C4×Q818yes—
123C3⋊Dic3—28no—
124C3×Dic3—28no—
125C3×Dic3—44no—
126C22×Q8—92no—
127C4⋊Q8—98no—
128C2×C4⋊C4—32no—
129C2×C4⋊C4—32no—
130C2×C4⋊C4—94no—
131C2×C4⋊C4—94no—
132C2×C42—34no—
133C2×C42—94no—
134C2×C42D3211yescharacteristic
135#95—34no—
136#95—98no—
137C23×C3—21no—
138C23×C3C23×D312yes—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—22no—
147C2×C3×C4—38no—
148C2×C3×C4—64no—
149C2×C3×C4—64no—
150C2×C3×C4—64no—
151C2×C3×C4—64no—
152C2×C3×C4—64no—
153C2×C3×C4C2×Dic614yes—
154C2×C3×C4C2×C4×D314yes—
155C2×C3×C4C2×C4×D314yes—
156C2×C3×C4C2×C4×D314yes—
157C2×C3×C4#23514yes—
158C2×C3×C4#23714yes—
159C2×C3×C4D3×Q814yes—
160C2×Dic3—24no—
161C2×Dic3—24no—
162C2×Dic3—24no—
163C2×Dic3—24no—
164C2×Dic3—24no—
165C2×Dic3—316no—
166C2×Dic3—68no—
167C2×Dic3—68no—
168C2×Dic3—68no—
169C2×Dic3—124no—
170C2×Dic3—124no—
171C2×Dic3C2×Dic618yes—
172Dic6—1216no—
173Dic6—1216no—
174C2×C32C2×C4×Q812yes—
175C2×C32#51811yescharacteristic
176C2×C32#55412yes—
177C2×C32#55511yescharacteristic
178C2×C32Q8211yescharacteristic
179C2×Q8—98no—
180C2×Q8—362no—
181C2×Q8—362no—
182C22×C4—34no—
183C22×C4—34no—
184C22×C4—94no—
185C22×C4C2×D3211yescharacteristic
186C22×C4C2×D3212yes—
187C4⋊C4—38no—
188C4⋊C4—64no—
189C4⋊C4—916no—
190C4⋊C4—364no—
191C42—68no—
192C42—364no—
193C42#62414yes—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3C22×Dic612yes—
200C22×C3C22×C4×D312yes—
201C22×C3C2×#23512yes—
202C22×C3C2×#23712yes—
203C22×C3C2×D3×Q812yes—
204C22×C3#100912yes—
205C22×C3#100912yes—
206C3×C4—24no—
207C3×C4—24no—
208C3×C4—28no—
209C3×C4—68no—
210C3×C4—124no—
211C3×C4C4×Dic618yes—
212C3×C4#88718yes—
213Dic3—28no—
214Dic3—44no—
215Dic3—616no—
216Dic3—128no—
217C32#236911yescharacteristic, complemented, Sylow
218C23C22×D3211yescharacteristic
219Q8—368no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—38no—
223C2×C4—64no—
224C2×C4—64no—
225C2×C4—64no—
226C2×C4—64no—
227C2×C4—64no—
228C2×C4—98no—
229C2×C4—184no—
230C2×C4—184no—
231C2×C4D3×Dic614yes—
232C2×C4#379514yes—
233C2×C4C2×#62412yes—
234C2×C4C2×#62414yes—
235C2×C3—22no—
236C2×C3—21no—
237C2×C3—22no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3C2×C4×Dic612yes—
241C2×C3C2×#88712yes—
242C2×C3#552112yes—
243C2×C3#554312yes—
244C2×C3#556312yes—
245C2×C3Q8×Dic612yes—
246C2×C3#557912yes—
247C22C2×D3×Dic612yes—
248C22C2×#379512yes—
249C22#6430811yescharacteristic
250C22#6430811yescharacteristic
251C22C22×#62411yescharacteristic
252C4—22no—
253C4—68no—
254C4—124no—
255C4—188no—
256C4#6384418yes—
257C3—21no—
258C3#7365612yescomplemented
259C2Dic6211yescharacteristic
260C2#1059396012yes—
261C2#1059398811yescharacteristic
262C2C2×#6384412yes—
263C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
10. #64078C4semidirect
38. C3×C4⋊Dic3Q8semidirect
112. C4⋊Dic3Dic6semidirect
217. C32#2369semidirect
258. C3#73656semidirect

Maximal subgroups

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

subgroupindex
C2×#640782
C3×C4×C4⋊Dic32
#105912732
Dic3×C4⋊Dic32
#105912122
#736563