Finite Group Databasebeta

← #10595306

Subgroups — #10595306

Order 576.

742 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 144 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×#3830C211yesmaximal, characteristic, complemented
2C2×C4×D32C211yesmaximal, characteristic, complemented
3C3×#938C212yesmaximal, complemented
4#63983C212yesmaximal, complemented
5#63975C212yesmaximal, complemented
6#67⋊Dic3C214yesmaximal, complemented
7#63857C212yesmaximal, complemented
8#63849C211yesmaximal, characteristic, complemented
9#5606—32nomaximal
10C22×D32C2211yescharacteristic
11C2×C32×D4C2211yescharacteristic, complemented
12C2×#638C2212yes—
13C22×C3⋊Dic3C2212yescomplemented
14#3830—24no—
15C2×C4×C3⋊D3C2211yescharacteristic
16C2×#634C2211yescharacteristic, complemented
17C2×C3×#67C2214yes—
18C2×C3×C4×D3C2212yes—
19C2×#624C2211yescharacteristic
20C2×D3×Dic3C2212yes—
21C4×D32—24no—
22C3×#217C2214yescomplemented
23C3×C4⋊Dic3C2212yescomplemented
24Dic3⋊Dic3C2214yescomplemented
25#3722C2212yes—
26(C2×D3)⋊Dic3C2214yes—
27Dic32C2212yescomplemented
28C2×#237—32no—
29C2×#237—61no—
30C22×C4×D3—32no—
31C3×#121—32no—
32#938D312yescomplemented
33#937—34no—
34D4×Dic3—34no—
35#924—32no—
36#897—32no—
37#892—32no—
38#883—34no—
39#67⋊C4—34no—
40C23×C32C2312yes—
41C22×C3⋊D3C2311yescharacteristic
42C22×C3×D3C2312yes—
43C2×D32—22no—
44C2×D32—24no—
45C32×D4—22no—
46C2×C32×C4C2311yescharacteristic
47#638—24no—
48C2×C3⋊Dic3—24no—
49C2×C3⋊Dic3C2312yes—
50C2×C3⋊Dic3C2311yescharacteristic
51C4×C3⋊D3D414yescomplemented
52#634—22no—
53C3×#67—28no—
54C2×C3×Dic3C2314yes—
55C2×C3×Dic3C2312yes—
56C3×C4×D3—24no—
57#624—22no—
58D3×Dic3—24no—
59#525—91noSylow
60C23×D3—32no—
61C2×C3×D4—21no—
62C2×C3×D4—34no—
63C2×C3×D4C2×D312yescomplemented
64C22×C3×C4—32no—
65C2×#67—34no—
66C2×#67—62no—
67C2×#67C2×D314yes—
68C22×Dic3—34no—
69C22×Dic3—32no—
70C22×Dic3—62no—
71#237—68no—
72#237—68no—
73C2×C4×D3—32no—
74C2×C4×D3—32no—
75C2×C4×D3—32no—
76C2×C4×D3—61no—
77C2×C4×D3—68no—
78C2×C4×D3C2×D312yes—
79C2×Dic6—32no—
80C2×Dic6—61no—
81C3×C4⋊C4—32no—
82C3×C22⋊C4—34no—
83#217—34no—
84#217C2×D314yescomplemented
85(C2×D3)⋊C4—34no—
86(C2×D3)⋊C4—34no—
87C4⋊Dic3—34no—
88C4⋊Dic3C2×D312yescomplemented
89Dic3⋊C4—34no—
90C4×Dic3—34no—
91C22×C32—22no—
92C22×C32—24no—
93C22×C32C2411yescharacteristic
94C2×C3⋊D3—22no—
95C2×C3⋊D3C2×D412yes—
96C2×C3×D3—22no—
97C2×C3×D3—22no—
98C2×C3×D3#4114yescomplemented
99D32—28no—
100C32×C4C2×D412yes—
101C3⋊Dic3—22no—
102C3⋊Dic3C2×D412yes—
103C3×Dic3—22no—
104C3×Dic3—24no—
105C2×#41—91no—
106C23×C4—91no—
107#123—92no—
108C22⋊Q8—92no—
109#121—32no—
110#120—92no—
111C4×D4—94no—
112#117—91no—
113C23×C3—22no—
114C23×C3—32no—
115C23×C3C22×D314yes—
116C22×D3—32no—
117C22×D3—61no—
118C22×D3—64no—
119C22×D3—64no—
120C22×D3—64no—
121C22×D3C22×D312yes—
122C3×D4—24no—
123C3×D4—24no—
124C3×D4—68no—
125C2×C3×C4—21no—
126C2×C3×C4—34no—
127C2×C3×C4—32no—
128C2×C3×C4—64no—
129C2×C3×C4C22×D312yes—
130#67—28no—
131#67—68no—
132#67—68no—
133C2×Dic3—32no—
134C2×Dic3—34no—
135C2×Dic3—62no—
136C2×Dic3—61no—
137C2×Dic3—64no—
138C2×Dic3—68no—
139C2×Dic3—68no—
140C2×Dic3C22×D314yes—
141C2×Dic3C22×D312yes—
142C4×D3—24no—
143C4×D3—38no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—64no—
147Dic6—64no—
148Dic6—64no—
149C2×C32—42no—
150C2×C32C22×D411yescharacteristic
151C2×C32C2×#4112yes—
152C3⋊D3—22no—
153C3×D3—24no—
154C24—91no—
155#41—184no—
156C2×Q8—91no—
157C2×D4—34no—
158C2×D4—92no—
159C2×D4D3211yescharacteristic, complemented
160C22×C4—32no—
161C22×C4—91no—
162C22×C4—92no—
163C22×C4—91no—
164C22×C4—92no—
165C22×C4—184no—
166C4⋊C4—32no—
167C4⋊C4—94no—
168C22⋊C4—34no—
169C22⋊C4—92no—
170C22⋊C4—94no—
171C42—92no—
172C22×C3—24no—
173C22×C3—24no—
174C22×C3—24no—
175C22×C3—24no—
176C22×C3—21no—
177C22×C3—34no—
178C22×C3—44no—
179C22×C3—62no—
180C22×C3—62no—
181C22×C3C23×D312yes—
182C2×D3—22no—
183C2×D3—22no—
184C2×D3—34no—
185C2×D3—62no—
186C2×D3—616no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—122no—
190C2×D3#23714yescomplemented
191C3×C4—22no—
192C3×C4—62no—
193C3×C4—64no—
194C3×C4D3×D414yes—
195Dic3—22no—
196Dic3—24no—
197Dic3—34no—
198Dic3—62no—
199Dic3—64no—
200Dic3—64no—
201C32#52511yescharacteristic, complemented, Sylow
202C23—32no—
203C23—91no—
204C23—184no—
205C23—182no—
206C23C2×D3212yes—
207Q8—182no—
208D4—22no—
209D4—68no—
210D4—184no—
211C2×C4—34no—
212C2×C4—32no—
213C2×C4—64no—
214C2×C4—91no—
215C2×C4—94no—
216C2×C4—92no—
217C2×C4—182no—
218C2×C4—184no—
219C2×C4—184no—
220C2×C4C2×D3211yescharacteristic
221C2×C3—22no—
222C2×C3—21no—
223C2×C3—44no—
224C2×C3—44no—
225C2×C3—64no—
226C2×C3C2×D3×D412yes—
227C2×C3C2×#23712yes—
228C2×C3D3×#4112yes—
229D3—24no—
230D3—64no—
231D3—122no—
232C22—24no—
233C22—22no—
234C22—34no—
235C22—62no—
236C22—62no—
237C22—92no—
238C22—188no—
239C22—182no—
240C22C22×D3211yescharacteristic
241C4—64no—
242C4—62no—
243C4—92no—
244C4—182no—
245C4#381112yes—
246C3—21no—
247C3#560612yescomplemented
248C2—42no—
249C2—64no—
250C2—182no—
251C2D3×#23712yes—
252C2C2×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#3830C2semidirect
2. C2×C4×D32C2semidirect
3. C3×#938C2semidirect
4. #63983C2semidirect
5. #63975C2semidirect
6. #67⋊Dic3C2semidirect
7. #63857C2semidirect
8. #63849C2semidirect
11. C2×C32×D4C22semidirect
13. C22×C3⋊Dic3C22semidirect
16. C2×#634C22semidirect
22. C3×#217C22semidirect
23. C3×C4⋊Dic3C22semidirect
24. Dic3⋊Dic3C22semidirect
27. Dic32C22semidirect
32. #938D3semidirect
51. C4×C3⋊D3D4semidirect
63. C2×C3×D4C2×D3semidirect
84. #217C2×D3semidirect
88. C4⋊Dic3C2×D3semidirect
98. C2×C3×D3#41semidirect
159. C2×D4D32semidirect
190. C2×D3#237semidirect
201. C32#525semidirect
247. C3#5606semidirect

Maximal subgroups

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

subgroupindex
C2×#38302
C2×C4×D322
C3×#9382
#639832
#639752
#67⋊Dic32
#638572
#638492
#56063