Finite Group Databasebeta

← #10594981

Subgroups — #10594981

Order 576.

550 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C2×#3752C211yesmaximal, characteristic
2C3×#924C212yesmaximal, complemented
3#63982C212yesmaximal, complemented
4#63974C212yesmaximal
5#63895C214yesmaximal, complemented
6#63888C214yesmaximal, complemented
7#5634—32nomaximal
8C23×C3⋊D3C2211yescharacteristic
9C22×C32×C4C2211yescharacteristic
10C22×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic6C2212yescomplemented
12C2×#627C2212yescomplemented
13C2×#624C2212yes—
14C2×#624C2212yes—
15#3752C2214yes—
16C3×#217C2214yes—
17C3×C4⋊Dic3C2212yescomplemented
18C3×Dic3⋊C4C2214yescomplemented
19#3724C2212yescomplemented
20Dic3⋊Dic3C2214yescomplemented
21#3722C2214yes—
22C3×C22⋊Q8—32no—
23#946—34no—
24C2×(C2×D3)⋊C4—32no—
25C2×(C2×D3)⋊C4—61no—
26#924D312yescomplemented
27#897—34no—
28#896—34no—
29#896—34no—
30D3×C22⋊C4—34no—
31#878—34no—
32C23×C32C2311yescharacteristic
33C22×C3⋊D3—41no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3Q814yescomplemented
36C22×C3⋊D3C2312yes—
37C2×C32×C4—41no—
38C2×C32×C4C2312yes—
39C2×C3⋊Dic3—41no—
40C2×C3⋊Dic3C2312yes—
41C2×C3×Dic3C2314yes—
42C2×C3×Dic3C2314yes—
43C3×Dic6—42no—
44#627—42no—
45#624—42no—
46#624—42no—
47#543—91noSylow
48C23×D3—32no—
49C23×D3—61no—
50C2×C3×Q8—32no—
51C22×C3×C4—21no—
52C22×C3×C4C2×D312yes—
53C22×Dic3—32no—
54C22×Dic3—61no—
55C2×C4×D3—34no—
56C2×C4×D3—34no—
57C2×Dic6—34no—
58C2×Dic6C2×D312yescomplemented
59C3×C4⋊C4—32no—
60C3×C4⋊C4—34no—
61C3×C22⋊C4—34no—
62#217C2×D314yes—
63(C2×D3)⋊C4—34no—
64(C2×D3)⋊C4—34no—
65(C2×D3)⋊C4—34no—
66(C2×D3)⋊C4—34no—
67(C2×D3)⋊C4—64no—
68C4⋊Dic3—34no—
69C4⋊Dic3C2×D312yescomplemented
70Dic3⋊C4—34no—
71Dic3⋊C4—34no—
72Dic3⋊C4C2×D314yescomplemented
73C22×C32—21no—
74C22×C32—21no—
75C22×C32C2×Q812yes—
76C22×C32C2411yescharacteristic
77C2×C3⋊D3—22no—
78C2×C3⋊D3—22no—
79C2×C3⋊D3—44no—
80C2×C3⋊D3C2×Q814yes—
81C32×C4—22no—
82C3⋊Dic3—22no—
83C3×Dic3—24no—
84C3×Dic3—24no—
85C22⋊Q8—32no—
86C22⋊Q8—92no—
87C22⋊Q8—94no—
88C22⋊Q8—94no—
89C2×C22⋊C4—92no—
90C2×C22⋊C4—91no—
91C23×C3—21no—
92C23×C3C22×D312yes—
93C22×D3—34no—
94C22×D3—38no—
95C22×D3—64no—
96C22×D3—62no—
97C22×D3—122no—
98C22×D3—122no—
99C22×D3—122no—
100C22×D3—122no—
101C3×Q8—122no—
102C2×C3×C4—22no—
103C2×C3×C4—34no—
104C2×C3×C4—34no—
105C2×C3×C4—42no—
106C2×C3×C4—42no—
107C2×C3×C4C22×D312yes—
108C2×C3×C4C22×D312yes—
109C2×Dic3—34no—
110C2×Dic3—62no—
111C2×Dic3—122no—
112C2×Dic3—122no—
113C2×Dic3C22×D314yes—
114C2×Dic3C22×D314yes—
115C4×D3—124no—
116C4×D3—124no—
117Dic6—42no—
118Dic6—124no—
119C2×C32—22no—
120C2×C32C22×Q811yescharacteristic
121C2×C32H(5,𝔽2)11yescharacteristic
122C2×C32H(5,𝔽2)11yescharacteristic
123C3⋊D3—24no—
124C24—91no—
125C2×Q8—32no—
126C2×Q8—92no—
127C22×C4—92no—
128C22×C4—92no—
129C22×C4—91no—
130C22×C4D3211yescharacteristic
131C4⋊C4—34no—
132C4⋊C4—32no—
133C4⋊C4—92no—
134C4⋊C4—94no—
135C22⋊C4—34no—
136C22⋊C4—94no—
137C22⋊C4—94no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—22no—
141C22×C3—22no—
142C22×C3—21no—
143C22×C3—22no—
144C22×C3D3×Q814yes—
145C22×C3C23×D312yes—
146C2×D3—38no—
147C2×D3—64no—
148C2×D3—64no—
149C2×D3—64no—
150C2×D3—122no—
151C2×D3—122no—
152C2×D3—128no—
153C2×D3—128no—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4—42no—
157C3×C4—64no—
158C3×C4—64no—
159Dic3—24no—
160Dic3—24no—
161Dic3—64no—
162Dic3—122no—
163C32#54311yescharacteristic, complemented, Sylow
164C23—92no—
165C23—94no—
166C23—361no—
167C23—361no—
168C23C2×D3211yescharacteristic
169Q8—122no—
170Q8—362no—
171C2×C4—34no—
172C2×C4—34no—
173C2×C4—41no—
174C2×C4—92no—
175C2×C4—362no—
176C2×C4—362no—
177C2×C4—361no—
178C2×C4C2×D3212yes—
179C2×C3—24no—
180C2×C3—24no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3#100412yes—
185C2×C3C2×D3×Q812yes—
186C2×C3#100912yes—
187D3—68no—
188D3—124no—
189C22—21no—
190C22—21no—
191C22—94no—
192C22—182no—
193C22—182no—
194C22—364no—
195C22#379712yes—
196C22C22×D3211yescharacteristic
197C4—22no—
198C4—64no—
199C4—64no—
200C4—182no—
201C3—21no—
202C3#563412yescomplemented
203C2—22no—
204C2—184no—
205C2C2×#379711yescharacteristic
206C2#6430811yescharacteristic
207C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
prime radicalC23×C3⋊D3C22
hypercenterC22×C4D32
hypocenterC32#543
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C3×#924C2semidirect
3. #63982C2semidirect
5. #63895C2semidirect
6. #63888C2semidirect
11. C2×C3×Dic6C22semidirect
12. C2×#627C22semidirect
17. C3×C4⋊Dic3C22semidirect
18. C3×Dic3⋊C4C22semidirect
19. #3724C22semidirect
20. Dic3⋊Dic3C22semidirect
26. #924D3semidirect
35. C22×C3⋊D3Q8semidirect
58. C2×Dic6C2×D3semidirect
69. C4⋊Dic3C2×D3semidirect
72. Dic3⋊C4C2×D3semidirect
163. C32#543semidirect
202. C3#5634semidirect

Maximal subgroups

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

subgroupindex
C2×#37522
C3×#9242
#639822
#639742
#638952
#638882
#56343