Finite Group Databasebeta

← #11783519

Subgroups — #11783519

Order 1152.

569 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 569 conjugacy classes of subgroups — too many to draw. Only its 180 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
1#10592631C211yesmaximal, characteristic
2C2×#63555C211yesmaximal, characteristic
3C2×#63553C211yesmaximal, characteristic
4C3×#4524C212yesmaximal
5#10589156C212yesmaximal
6#68598—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3×C3⋊C8C2212yes—
11C22×C3×C3⋊C8C2212yes—
12#63658C414yes—
13#63555C414yescomplemented
14#63553C414yescomplemented
15C2×#815—32no—
16C2×C8×Dic3—32no—
17#4932—32no—
18#4932—61no—
19C3×#336—32no—
20#4550—32no—
21#4550—32no—
22#4524D312yes—
23C22×C32×C4C2×C412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C32×C42—22no—
28C4×C3⋊Dic3—22no—
29C4×C3⋊Dic3C2×C412yes—
30C4×C3⋊Dic3C2×C412yes—
31C2×C3×C3⋊C8—22no—
32C2×C3×C3⋊C8—22no—
33C2×C3×C3⋊C8—22no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8C2×C414yes—
36C2×C3×C3⋊C8C2×C414yes—
37#1746—91noSylow
38C22×C3×C8—32no—
39C22×C3×C8—32no—
40C2×C3×C42—21no—
41C2×C3×C42C2×D312yes—
42C2×C4×Dic3—32no—
43C2×C4×Dic3—32no—
44C2×C4×Dic3—61no—
45C2×C4×Dic3—61no—
46C22×C3⋊C8C2×D312yes—
47C22×C3⋊C8C2×D312yes—
48C3⋊#95—34no—
49C3⋊#95—34no—
50C3⋊#95—64no—
51#815—38no—
52C8×Dic3—38no—
53C23×C32C22×C411yescharacteristic
54C2×C32×C4—22no—
55C2×C32×C4—24no—
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4#4112yes—
59C2×C32×C4#4112yes—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—24no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3C4214yes—
64C3×C3⋊C8—24no—
65C3×C3⋊C8—24no—
66C2×#97—91no—
67C2×C4×C8—91no—
68#376—91no—
69#336—32no—
70#336—92no—
71C22×C3×C4—22no—
72C22×C3×C4—21no—
73C22×C3×C4C4×D314yes—
74C22×C3×C4C22×D312yes—
75C22×Dic3—32no—
76C22×Dic3—32no—
77C22×Dic3—34no—
78C22×Dic3—62no—
79C22×Dic3—62no—
80C2×C3×C8—34no—
81C2×C3×C8—34no—
82C2×C3×C8—62no—
83C2×C3×C8—62no—
84C2×C3×C8—62no—
85C2×C3×C8—62no—
86C3×C42—24no—
87C3×C42—22no—
88C3×C42—22no—
89C4×Dic3—34no—
90C4×Dic3—34no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—64no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C2×C3⋊C8—22no—
97C2×C3⋊C8—22no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8C4×D314yes—
101C2×C3⋊C8C4×D314yes—
102C22×C32C2×C4211yescharacteristic
103C22×C32#11711yescharacteristic
104C22×C32#11711yescharacteristic
105C22×C32#13114yes—
106C32×C4—42no—
107C32×C4#11712yes—
108C32×C4#11712yes—
109C3⋊Dic3—24no—
110C3⋊Dic3—42no—
111C22×C8—32no—
112C22×C8—32no—
113C2×C42—91no—
114C2×C42—91no—
115C2×C42D3211yescharacteristic
116#97—94no—
117C4×C8—94no—
118#95—94no—
119C23×C3—21no—
120C23×C3C2×C4×D312yes—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—24no—
124C2×C3×C4—24no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—22no—
129C2×C3×C4—44no—
130C2×C3×C4C2×C4×D312yes—
131C2×C3×C4C2×C4×D312yes—
132C2×C3×C4#23712yes—
133C2×C3×C4#23712yes—
134C2×C3×C4#23712yes—
135C2×C3×C4#23912yes—
136C2×Dic3—34no—
137C2×Dic3—34no—
138C2×Dic3—64no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144C2×Dic3—64no—
145C2×Dic3—124no—
146C2×Dic3—124no—
147C3×C8—64no—
148C3×C8—64no—
149C3⋊C8—24no—
150C3⋊C8—24no—
151C2×C32#37611yescharacteristic
152C2×C32#40512yes—
153C2×C32#43312yes—
154C2×C32#43312yes—
155C22×C4—92no—
156C22×C4—92no—
157C22×C4#62412yes—
158C22×C4C2×D3211yescharacteristic
159C2×C8—34no—
160C2×C8—34no—
161C2×C8—62no—
162C2×C8—62no—
163C2×C8—62no—
164C2×C8—62no—
165C42—22no—
166C42—92no—
167C42—92no—
168C42—182no—
169C22×C3—24no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3C42×D312yes—
174C22×C3#87712yes—
175C22×C3#89212yes—
176C22×C3#90114yes—
177C22×C3#90714yes—
178C3×C4—22no—
179C3×C4—22no—
180C3×C4—44no—
181C3×C4—44no—
182C3×C4#87712yes—
183C3×C4#87712yes—
184C3×C4#89212yes—
185C3×C4#89212yes—
186Dic3—64no—
187Dic3—64no—
188Dic3—124no—
189Dic3—124no—
190Dic3—124no—
191C32#174611yescharacteristic, complemented, Sylow
192C23C2×#62411yescharacteristic
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—94no—
196C2×C4—184no—
197C2×C4—184no—
198C2×C4—182no—
199C2×C4#379612yes—
200C2×C4C4×D3211yescharacteristic
201C2×C4C4×D3211yescharacteristic
202C2×C4#380512yes—
203C8—64no—
204C8—64no—
205C2×C3—21no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3#464812yes—
210C2×C3#468912yes—
211C2×C3#470812yes—
212C2×C3#472014yes—
213C2×C3#484014yes—
214C22#6381714yes—
215C22#6384911yescharacteristic
216C22C4×#62411yescharacteristic
217C22#6395711yescharacteristic
218C4—42no—
219C4—184no—
220C4—362no—
221C4#6387812yes—
222C4#6387812yes—
223C3—21no—
224C3#6859812yescomplemented
225C2#1059025712yes—
226C2#1059032112yes—
227C2#1059106212yes—
228C2#1059125211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC2×C32×C42C22
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1746
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
13. #63555C4semidirect
14. #63553C4semidirect
191. C32#1746semidirect
224. C3#68598semidirect

Maximal subgroups

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

subgroupindex
#105926312
C2×#635552
C2×#635532
C3×#45242
#105891562
#685983