Finite Group Databasebeta

← #10589661

Subgroups — #10589661

Order 576.

354 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C4×D4×C9C211yesmaximal, characteristic, complemented
2#63502C211yesmaximal, characteristic
3#63498C211yesmaximal, characteristic, complemented
4#63491C212yesmaximal, complemented
5C4×#611C212yesmaximal, complemented
6#63455C211yesmaximal, characteristic, complemented
7#63449C211yesmaximal, characteristic, complemented
8#63447C212yesmaximal, complemented
9#63445C212yesmaximal, complemented
10#63437C211yesmaximal, characteristic, complemented
11C4×Dic18C211yesmaximal, characteristic, complemented
12#5559—31nomaximal
13C2×D4×C9C2211yescharacteristic
14C22×C4×C9C2212yes—
15C2×#611C2212yes—
16C2×#611C2212yes—
17C2×D36C2211yescharacteristic
18C2×C4×D9C2212yes—
19C2×Dic18C2211yescharacteristic
20C2×Dic18C2211yescharacteristic
21C9×C4⋊C4C2211yescharacteristic
22C9×C22⋊C4C2212yes—
23C42×C9C2211yescharacteristic
24#3676C2212yes—
25#3676C2212yes—
26(C2×D9)⋊C4C2212yes—
27(C2×D9)⋊C4C2212yes—
28(C2×D9)⋊C4C2212yes—
29C4⋊Dic9C2211yescharacteristic
30Dic9⋊C4C2211yescharacteristic
31Dic9⋊C4C2211yescharacteristic
32Dic9⋊C4C2212yes—
33C4×Dic9C2212yes—
34C4×Dic9C2211yescharacteristic
35C4×Dic9C2211yescharacteristic
36C3×C4×D4D311yescharacteristic
37#940—31no—
38#936—31no—
39#929—32no—
40C4×#67—32no—
41#893—31no—
42#887—31no—
43#885—32no—
44#883—32no—
45#875—31no—
46C4×Dic6—31no—
47C23×C9C2312yes—
48C22×D9C2312yes—
49D4×C9—22no—
50C2×C4×C9—42no—
51C2×C4×C9C2312yes—
52C2×C4×C9C2311yescharacteristic
53C2×C4×C9C2311yescharacteristic
54C2×C4×C9C2311yescharacteristic
55#611—24no—
56#611—42no—
57C2×Dic9C2311yescharacteristic
58C2×Dic9C2311yescharacteristic
59C2×Dic9C2312yes—
60C2×Dic9C2311yescharacteristic
61C2×Dic9C2311yescharacteristic
62D36—22no—
63C4×D9—42no—
64Dic18—22no—
65Dic18—22no—
66#559—91noSylow
67C2×C3×D4C2×D311yescharacteristic
68C22×C3×C4C2×D312yes—
69C2×#67—32no—
70C2×#67—32no—
71C2×D12—31no—
72C2×C4×D3—32no—
73C2×Dic6—31no—
74C2×Dic6—31no—
75C3×C4⋊C4C2×D311yescharacteristic
76C3×C22⋊C4C2×D312yes—
77C3×C42C2×D311yescharacteristic
78#217—32no—
79#217—32no—
80(C2×D3)⋊C4—32no—
81(C2×D3)⋊C4—32no—
82(C2×D3)⋊C4—32no—
83C4⋊Dic3—31no—
84Dic3⋊C4—31no—
85Dic3⋊C4—31no—
86Dic3⋊C4—32no—
87C4×Dic3—31no—
88C4×Dic3—31no—
89C4×Dic3—32no—
90C22×C9—22no—
91C22×C9—22no—
92C22×C9—22no—
93C22×C9C2411yescharacteristic
94C2×D9—22no—
95C2×D9—22no—
96C2×D9—22no—
97C4×C9—21no—
98C4×C9—22no—
99C4×C9—21no—
100C4×C9#4112yes—
101Dic9—22no—
102Dic9—21no—
103Dic9—21no—
104Dic9—21no—
105Dic9#4112yes—
106#127—91no—
107#124—91no—
108#124—92no—
109#124—91no—
110#123—92no—
111#123—92no—
112C4×Q8—91no—
113C4×Q8—91no—
114C4×D4—92no—
115C4×D4—91no—
116C4×D4D911yescharacteristic, complemented
117C23×C3C22×D312yes—
118C22×D3—32no—
119C3×D4—22no—
120C2×C3×C4—42no—
121C2×C3×C4C22×D312yes—
122C2×C3×C4C22×D311yescharacteristic
123C2×C3×C4C22×D311yescharacteristic
124C2×C3×C4C22×D311yescharacteristic
125#67—64no—
126#67—122no—
127C2×Dic3—31no—
128C2×Dic3—31no—
129C2×Dic3—31no—
130C2×Dic3—32no—
131C2×Dic3—31no—
132D12—62no—
133C4×D3—122no—
134Dic6—62no—
135Dic6—62no—
136C2×C9—42no—
137C2×C9C2×#4111yescharacteristic
138C2×C9C2×#4111yescharacteristic
139C2×C9H(5,𝔽2)11yescharacteristic
140D9—42no—
141C2×Q8—91no—
142C2×Q8—91no—
143C2×D4—92no—
144C2×D4—92no—
145C2×D4—91no—
146C2×D4C2×D911yescharacteristic
147C22×C4—92no—
148C22×C4C2×D912yes—
149C4⋊C4—91no—
150C4⋊C4—92no—
151C4⋊C4—91no—
152C4⋊C4—91no—
153C4⋊C4C2×D911yescharacteristic
154C22⋊C4—92no—
155C22⋊C4—92no—
156C22⋊C4—92no—
157C22⋊C4—92no—
158C22⋊C4—92no—
159C22⋊C4C2×D912yes—
160C42—92no—
161C42—91no—
162C42—91no—
163C42C2×D911yescharacteristic
164C22×C3—22no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3C23×D311yescharacteristic
168C2×D3—62no—
169C2×D3—62no—
170C2×D3—62no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4#23512yes—
175Dic3—32no—
176Dic3—62no—
177Dic3—61no—
178Dic3—61no—
179Dic3—61no—
180C9#55911yescharacteristic, complemented, Sylow
181C23—92no—
182C23C22×D912yes—
183Q8—182no—
184Q8—182no—
185D4—22no—
186D4—184no—
187D4—182no—
188D4—362no—
189C2×C4—42no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—362no—
196C2×C4C22×D912yes—
197C2×C4C22×D911yescharacteristic
198C2×C4C22×D911yescharacteristic
199C2×C4C22×D911yescharacteristic
200C2×C3—42no—
201C2×C3C2×#23511yescharacteristic
202C2×C3#100411yescharacteristic
203C2×C3D3×#4111yescharacteristic
204D3—122no—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—182no—
209C22—182no—
210C22—182no—
211C22C23×D911yescharacteristic
212C4—21no—
213C4—22no—
214C4—21no—
215C4—92no—
216C4—182no—
217C4—181no—
218C4—181no—
219C4—181no—
220C4#369712yes—
221C3#555911yescharacteristic
222C2—42no—
223C2—362no—
224C2C2×#369711yescharacteristic
225C2#6371011yescharacteristic
226C2#41×D911yescharacteristic
subgroupG/H
centerC22C23×D9
commutator, cosocleC22×C9C24
Frattini, socleC22×C3C23×D3
FittingC4×D4×C9C2
prime radical#63502C2
hypercenterC4×D4D9
hypocenterC9#559
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×D4×C9C2semidirect
3. #63498C2semidirect
4. #63491C2semidirect
5. C4×#611C2semidirect
6. #63455C2semidirect
7. #63449C2semidirect
8. #63447C2semidirect
9. #63445C2semidirect
10. #63437C2semidirect
11. C4×Dic18C2semidirect
116. C4×D4D9semidirect
180. C9#559semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C92
#635022
#634982
#634912
C4×#6112
#634552
#634492
#634472
#634452
#634372
C4×Dic182
#55593