Finite Group Databasebeta

← #10591692

Subgroups — #10591692

Order 576.

470 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 106 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×#627C211yesmaximal, characteristic, complemented
2C2×#3757C211yesmaximal, characteristic
3C2×C3×#217C212yesmaximal
4#63579C211yesmaximal, characteristic, complemented
5#63579C212yesmaximal, complemented
6#4947—32nomaximal
7C24×C32C2211yescharacteristic
8C22×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12C2×#627—22no—
13C2×#627—24no—
14#3757—22no—
15C3×#217—24no—
16C22×Dic6—32no—
17C2×C3×C22⋊C4—32no—
18C2×#217—32no—
19C2×#217—61no—
20C2×#217D312yes—
21C3⋊#95—32no—
22C3⋊#95—32no—
23C3⋊#95—32no—
24C23×C32—21no—
25C23×C32—21no—
26C23×C32—22no—
27C23×C32—22no—
28C23×C32Q812yescomplemented
29C23×C32C2311yescharacteristic
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—22no—
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3D412yes—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—22no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3D414yes—
40#627—28no—
41#393—91noSylow
42C24×C3—21no—
43C24×C3C2×D312yes—
44C22×C3×C4—32no—
45C22×C3×C4—32no—
46C22×Dic3—32no—
47C22×Dic3—32no—
48C22×Dic3—61no—
49C22×Dic3—61no—
50C22×Dic3C2×D312yes—
51C22×Dic3C2×D312yes—
52C2×Dic6—64no—
53C2×Dic6—64no—
54C2×Dic6—64no—
55C3×C22⋊C4—64no—
56#217—24no—
57#217—64no—
58#217—64no—
59C22×C32—22no—
60C22×C32—24no—
61C22×C32—41no—
62C22×C32—41no—
63C22×C32—42no—
64C22×C32C2×D411yescharacteristic
65C22×C32C2×D412yes—
66C22×C32C2×Q811yescharacteristic
67C22×C32#4112yes—
68C22×C32#4111yescharacteristic
69C3⋊Dic3—22no—
70C3⋊Dic3—41no—
71C3×Dic3—24no—
72C3×Dic3—42no—
73C22×Q8—91no—
74C2×C22⋊C4—32no—
75C2×C22⋊C4—91no—
76#95—92no—
77#95—91no—
78C23×C3—22no—
79C23×C3—22no—
80C23×C3—22no—
81C23×C3—22no—
82C23×C3—22no—
83C23×C3—22no—
84C23×C3—22no—
85C23×C3—22no—
86C23×C3—22no—
87C23×C3—21no—
88C23×C3—42no—
89C23×C3—42no—
90C23×C3Dic614yescomplemented
91C23×C3C22×D312yes—
92C2×C3×C4—34no—
93C2×C3×C4—62no—
94C2×C3×C4—62no—
95C2×C3×C4—62no—
96C2×C3×C4—62no—
97C2×C3×C4—62no—
98C2×Dic3—22no—
99C2×Dic3—22no—
100C2×Dic3—22no—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—34no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—122no—
112C2×Dic3—122no—
113C2×Dic3#6714yes—
114Dic6—616no—
115C2×C32—42no—
116C2×C32#12011yescharacteristic
117C2×C32C22⋊Q811yescharacteristic
118C2×C32C22⋊Q812yes—
119C2×C32#12411yescharacteristic
120C2×C32#12412yes—
121C24D3211yescharacteristic
122C2×Q8—184no—
123C2×Q8—182no—
124C22×C4—32no—
125C22×C4—32no—
126C22×C4—91no—
127C22×C4—91no—
128C22⋊C4—64no—
129C22⋊C4—182no—
130C22×C3—24no—
131C22×C3—24no—
132C22×C3—24no—
133C22×C3—24no—
134C22×C3—22no—
135C22×C3—21no—
136C22×C3—21no—
137C22×C3—22no—
138C22×C3—21no—
139C22×C3—44no—
140C22×C3—42no—
141C22×C3—44no—
142C22×C3—42no—
143C22×C3—42no—
144C22×C3—42no—
145C22×C3—42no—
146C22×C3—42no—
147C22×C3C2×Dic612yes—
148C22×C3#23512yes—
149C22×C3D3×D412yes—
150C22×C3D3×D412yes—
151C22×C3#23712yes—
152C22×C3#23712yes—
153C22×C3C2×#6712yes—
154C3×C4—64no—
155C3×C4—122no—
156Dic3—24no—
157Dic3—42no—
158Dic3—64no—
159Dic3—122no—
160Dic3—122no—
161Dic3—122no—
162C32#39311yescharacteristic, complemented, Sylow
163C23—22no—
164C23—21no—
165C23—22no—
166C23—21no—
167C23#62712yescomplemented
168C23C2×D3211yescharacteristic
169Q8—188no—
170C2×C4—34no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4—92no—
177C2×C4—182no—
178C2×C4—182no—
179C2×C4—181no—
180C2×C3—21no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—44no—
186C2×C3—44no—
187C2×C3#87812yes—
188C2×C3#87812yes—
189C2×C3#88512yes—
190C2×C3#88512yes—
191C2×C3#92412yes—
192C2×C3#93612yes—
193C2×C3#93712yes—
194C22—24no—
195C22—22no—
196C22—41no—
197C22—42no—
198C22—41no—
199C22#380412yes—
200C22#380511yescharacteristic
201C22C2×#62711yescharacteristic
202C22D3×#6712yes—
203C22#381111yescharacteristic
204C4—64no—
205C4—122no—
206C4—182no—
207C4—361no—
208C3—21no—
209C3#494712yescomplemented
210C2—42no—
211C2#6395311yescharacteristic
212C2#6395912yes—
213C2#6396412yes—
214C2#6398211yescharacteristic
215C2#6398311yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, cosocleC23×C32C23
Fitting, prime radicalC24×C32C22
hypercenterC24D32
hypocenterC32#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#627C2semidirect
4. #63579C2semidirect
5. #63579C2semidirect
28. C23×C32Q8semidirect
90. C23×C3Dic6semidirect
162. C32#393semidirect
167. C23#627semidirect
209. C3#4947semidirect

Maximal subgroups

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

subgroupindex
C22×#6272
C2×#37572
C2×C3×#2172
#635792
#49473