Finite Group Databasebeta

← C2×#63912 #10595014

Subgroups — C2×#63912 #10595014

Order 576.

970 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 970 conjugacy classes of subgroups — too many to draw. Only its 176 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×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#626C212yesmaximal, complemented
3C22×#625C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×#3724C211yesmaximal, characteristic, complemented
6#63912C218yesmaximal, direct product factor
7C2×#884—32nomaximal
8C23×C3⋊D3C2211yescharacteristic
9C23×C3×D3C2212yes—
10C22×C32×C4C2211yescharacteristic
11C22×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊D3—24no—
13C2×C4×C3⋊D3C2214yescomplemented
14C22×C3×Dic3C2212yes—
15C2×#626—28no—
16C2×#626C2218yescomplemented
17C2×#625—24no—
18C2×#625C2214yescomplemented
19C3×(C2×D3)⋊C4C2218yescomplemented
20#3724C2214yescomplemented
21C22×#67—32no—
22C22×#67—32no—
23C22×D12—32no—
24C22×C4×D3—32no—
25C22×C4×D3—61no—
26C2×C3×C22⋊C4—32no—
27C2×(C2×D3)⋊C4D312yescomplemented
28C2×Dic3⋊C4—32no—
29#884—316no—
30C23×C32C2311yescharacteristic
31C22×C3⋊D3—22no—
32C22×C3⋊D3—22no—
33C22×C3⋊D3D414yescomplemented
34C22×C3⋊D3C2312yes—
35C22×C3×D3—24no—
36C22×C3×D3—24no—
37C22×C3×D3—24no—
38C22×C3×D3C2314yes—
39C2×C32×C4—22no—
40C2×C32×C4C2312yes—
41C2×C3⋊Dic3D414yescomplemented
42C2×C3⋊Dic3C2312yes—
43C4×C3⋊D3—28no—
44C2×C3×Dic3—24no—
45C2×C3×Dic3C2314yes—
46#626—216no—
47#625—28no—
48C2×#121—91noSylow
49C24×C3—32no—
50C23×D3—32no—
51C23×D3—61no—
52C23×D3C2×D312yes—
53C22×C3×C4—21no—
54C22×C3×C4—32no—
55C22×C3×C4C2×D312yes—
56C2×#67—38no—
57C2×#67—38no—
58C2×#67—68no—
59C2×#67—68no—
60C22×Dic3—32no—
61C22×Dic3—61no—
62C22×Dic3C2×D312yes—
63C2×D12—38no—
64C2×D12—68no—
65C2×C4×D3—38no—
66C2×C4×D3—64no—
67C2×C4×D3—68no—
68C2×C4×D3—68no—
69C3×C22⋊C4—38no—
70(C2×D3)⋊C4C2×D318yescomplemented
71Dic3⋊C4—38no—
72C22×C32C2×D412yes—
73C22×C32C2×D412yes—
74C22×C32#4112yes—
75C22×C32C2411yescharacteristic
76C2×C3⋊D3—28no—
77C2×C3⋊D3—22no—
78C2×C3⋊D3—22no—
79C2×C3⋊D3C2×D414yescomplemented
80C2×C3×D3—24no—
81C2×C3×D3—24no—
82C2×C3×D3—24no—
83C2×C3×D3—48no—
84C32×C4—22no—
85C3⋊Dic3C2×D414yescomplemented
86C3×Dic3—24no—
87C22×D4—92no—
88C22×D4—91no—
89C23×C4—91no—
90#121—98no—
91C2×C4⋊C4—91no—
92C2×C22⋊C4—32no—
93C23×C3—21no—
94C23×C3—34no—
95C23×C3—64no—
96C23×C3—64no—
97C23×C3—64no—
98C23×C3C22×D312yes—
99C22×D3—24no—
100C22×D3—24no—
101C22×D3—24no—
102C22×D3—38no—
103C22×D3—34no—
104C22×D3—64no—
105C22×D3—62no—
106C22×D3—64no—
107C22×D3—64no—
108C22×D3—64no—
109C22×D3—64no—
110C22×D3C22×D314yes—
111C2×C3×C4—24no—
112C2×C3×C4—24no—
113C2×C3×C4—22no—
114C2×C3×C4—34no—
115C2×C3×C4—64no—
116C2×C3×C4C22×D314yes—
117#67—616no—
118#67—616no—
119C2×Dic3—24no—
120C2×Dic3—38no—
121C2×Dic3—34no—
122C2×Dic3—64no—
123C2×Dic3—62no—
124C2×Dic3C22×D314yes—
125D12—616no—
126C4×D3—616no—
127C4×D3—616no—
128C2×C32#12114yescomplemented
129C2×C32C22×D411yescharacteristic
130C2×C32C22×D411yescharacteristic
131C2×C32C2×#4111yescharacteristic
132C3⋊D3—24no—
133C3×D3—44no—
134C24—32no—
135C24—91no—
136C2×D4—98no—
137C2×D4—94no—
138C2×D4—188no—
139C2×D4—184no—
140C22×C4—32no—
141C22×C4—91no—
142C22×C4—94no—
143C22×C4—184no—
144C22×C4D3211yescharacteristic
145C4⋊C4—94no—
146C22⋊C4—38no—
147C22×C3—21no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—64no—
152C22×C3—64no—
153C22×C3—64no—
154C22×C3—128no—
155C22×C3#23514yes—
156C22×C3D3×D414yes—
157C22×C3D3×D414yes—
158C22×C3C23×D312yes—
159C2×D3—24no—
160C2×D3—24no—
161C2×D3—24no—
162C2×D3—38no—
163C2×D3—48no—
164C2×D3—64no—
165C2×D3—64no—
166C2×D3—64no—
167C2×D3—616no—
168C2×D3—616no—
169C2×D3—64no—
170C2×D3—64no—
171C3×C4—24no—
172C3×C4—24no—
173C3×C4—64no—
174Dic3—24no—
175Dic3—38no—
176Dic3—64no—
177C32C2×#12111yescharacteristic, complemented, Sylow
178C23—34no—
179C23—64no—
180C23—64no—
181C23—64no—
182C23—92no—
183C23—94no—
184C23—182no—
185C23—182no—
186C23C2×D3211yescharacteristic
187D4—1816no—
188D4—188no—
189C2×C4—22no—
190C2×C4—34no—
191C2×C4—64no—
192C2×C4—92no—
193C2×C4—94no—
194C2×C4—188no—
195C2×C4C2×D3212yes—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—24no—
200C2×C3—124no—
201C2×C3#88418yescomplemented
202C2×C3C2×#23512yes—
203C2×C3C2×D3×D412yes—
204C2×C3C2×D3×D412yes—
205D3—44no—
206D3—68no—
207D3—68no—
208C22—64no—
209C22—64no—
210C22—64no—
211C22—94no—
212C22—128no—
213C22—182no—
214C22—182no—
215C22—188no—
216C22#379812yes—
217C22#380212yes—
218C22#381112yes—
219C22C22×D3211yescharacteristic
220C4—22no—
221C4—64no—
222C4—94no—
223C3—21no—
224C3C2×#88412yescomplemented
225C2—124no—
226C2—184no—
227C2#6391214yesdirect product factor
228C2C2×#379811yescharacteristic
229C2C2×#380211yescharacteristic
230C2C2×#381111yescharacteristic
subgroupG/H
centerC23C2×D32
commutator, cosocleC22×C32C24
FrattiniC22C22×D32
FittingC22×C32×C4C22
socleC23×C32C23
hypercenterC22×C4D32
hypocenterC32C2×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊D3C2semidirect
2. C22×#626C2semidirect
3. C22×#625C2semidirect
4. C2×C3×(C2×D3)⋊C4C2semidirect
5. C2×#3724C2semidirect
6. #63912C2direct (N × H)
13. C2×C4×C3⋊D3C22semidirect
16. C2×#626C22semidirect
18. C2×#625C22semidirect
19. C3×(C2×D3)⋊C4C22semidirect
20. #3724C22semidirect
27. C2×(C2×D3)⋊C4D3semidirect
33. C22×C3⋊D3D4semidirect
41. C2×C3⋊Dic3D4semidirect
70. (C2×D3)⋊C4C2×D3semidirect
79. C2×C3⋊D3C2×D4semidirect
85. C3⋊Dic3C2×D4semidirect
128. C2×C32#121semidirect
177. C32C2×#121semidirect
201. C2×C3#884semidirect
224. C3C2×#884semidirect
227. C2#63912direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D32
C22×#6262
C22×#6252
C2×C3×(C2×D3)⋊C42
C2×#37242
#639122
C2×#8843