Finite Group Databasebeta

← #11721011

Subgroups — #11721011

Order 864.

258 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 75 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×D3×Dic9C211yesmaximal, characteristic
2C4×C3⋊Dic9C211yesmaximal, characteristic, complemented
3C9×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic9C211yesmaximal, characteristic
6Dic9⋊Dic3C211yesmaximal, characteristic, complemented
7Dic3×Dic9C211yesmaximal, characteristic, complemented
8#63878—31nomaximal
9#63439—31nomaximal
10C22×D3×C9C2211yescharacteristic
11C2×C3×C4×C9C2211yescharacteristic
12C2×C3⋊Dic9C2211yescharacteristic
13C2×C3⋊Dic9C2211yescharacteristic
14C2×C9×Dic3C2211yescharacteristic
15C2×C3×Dic9C2211yescharacteristic
16C2×C3×Dic9C2211yescharacteristic
17D3×Dic9C414yescomplemented
18C2×D3×Dic3—31no—
19C4×C3⋊Dic3—31no—
20C3×(C2×D3)⋊C4D311yescharacteristic
21C3×Dic3⋊C4—31no—
22Dic3⋊Dic3—31no—
23(C2×D3)⋊Dic3—31no—
24Dic32—31no—
25C22×Dic9—31no—
26C9×C22⋊C4—31no—
27#3676—31no—
28Dic9⋊C4—31no—
29Dic9⋊C4D311yescharacteristic, complemented
30C4×Dic9—31no—
31C4×Dic9—31no—
32C4×Dic9—61no—
33C22×C3×C9C2311yescharacteristic
34C2×D3×C9—21no—
35C2×D3×C9—21no—
36C2×D3×C9C2×C412yes—
37C3×C4×C9—21no—
38C3⋊Dic9—21no—
39C3⋊Dic9C2×C412yes—
40C9×Dic3—21no—
41C3×Dic9—21no—
42C3×Dic9C2×C412yes—
43#892—91no—
44#877—91no—
45C22×C3×D3C2×D311yescharacteristic
46C2×C32×C4C2×D311yescharacteristic
47C2×C3⋊Dic3—31no—
48C2×C3⋊Dic3—31no—
49C2×C3×Dic3—31no—
50C2×C3×Dic3—31no—
51C2×C3×Dic3C2×D311yescharacteristic
52D3×Dic3—34no—
53C23×C9—31no—
54C2×C4×C9—21no—
55C2×C4×C9—31no—
56C2×C4×C9C2×D311yescharacteristic
57C2×Dic9—31no—
58C2×Dic9—34no—
59C2×Dic9—31no—
60C2×Dic9—61no—
61C2×Dic9—61no—
62C2×Dic9C2×D311yescharacteristic
63C2×Dic9C2×D311yescharacteristic
64C2×C3×C9C22×C411yescharacteristic
65C2×C3×C9#4111yescharacteristic
66C2×C3×C9#4111yescharacteristic
67D3×C9—22no—
68C22×Dic3—91no—
69C2×C4×D3—91no—
70C3×C4⋊C4—91no—
71C3×C22⋊C4—31no—
72#217—91no—
73(C2×D3)⋊C4—91no—
74(C2×D3)⋊C4D911yescharacteristic
75C4⋊Dic3—91no—
76Dic3⋊C4—31no—
77Dic3⋊C4—91no—
78C4×Dic3—91no—
79C4×Dic3—91no—
80C4×Dic3—91no—
81C4×Dic3—91no—
82C4×Dic3—181no—
83C22×C32C22×D311yescharacteristic
84C2×C3×D3—21no—
85C2×C3×D3—21no—
86C2×C3×D3C4×D312yes—
87C32×C4—21no—
88C3⋊Dic3—32no—
89C3⋊Dic3—61no—
90C3×Dic3—21no—
91C3×Dic3—32no—
92C3×Dic3—61no—
93C22×C9—21no—
94C22×C9—32no—
95C22×C9—61no—
96C22×C9—61no—
97C22×C9C22×D311yescharacteristic
98C4×C9—22no—
99C4×C9—21no—
100C4×C9—61no—
101Dic9—21no—
102Dic9—32no—
103Dic9—62no—
104Dic9—62no—
105Dic9—61no—
106Dic9C4×D312yes—
107#117—271noSylow
108C3×C9#11711yescharacteristic, complemented, Sylow
109C23×C3—31no—
110C22×D3C2×D911yescharacteristic
111C2×C3×C4—21no—
112C2×C3×C4—31no—
113C2×C3×C4—91no—
114C2×C3×C4—91no—
115C2×C3×C4C2×D911yescharacteristic
116C2×C3×C4D3211yescharacteristic
117C2×Dic3—31no—
118C2×Dic3—31no—
119C2×Dic3—94no—
120C2×Dic3—91no—
121C2×Dic3—91no—
122C2×Dic3—91no—
123C2×Dic3—91no—
124C2×Dic3—181no—
125C2×Dic3—181no—
126C2×Dic3C2×D911yescharacteristic
127C4×D3—94no—
128C2×C32C2×C4×D311yescharacteristic
129C2×C32#23711yescharacteristic
130C2×C32#23711yescharacteristic
131C3×D3—22no—
132C2×C9—21no—
133C2×C9—21no—
134C2×C9—21no—
135C2×C9—62no—
136C2×C9C2×C4×D311yescharacteristic
137C2×C9#23711yescharacteristic
138C2×C9#23911yescharacteristic
139C22×C4—271no—
140C4⋊C4—91no—
141C4⋊C4—271no—
142C22⋊C4—31no—
143C22⋊C4—271no—
144C42—271no—
145C42—271no—
146C22×C3—21no—
147C22×C3—32no—
148C22×C3—61no—
149C22×C3—61no—
150C22×C3C22×D911yescharacteristic
151C22×C3C2×D3211yescharacteristic
152C2×D3—21no—
153C2×D3—21no—
154C2×D3C4×D912yes—
155C3×C4—22no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—61no—
159C3×C4—92no—
160C3×C4—181no—
161Dic3—21no—
162Dic3—32no—
163Dic3—61no—
164Dic3—92no—
165Dic3—92no—
166Dic3—182no—
167Dic3—182no—
168Dic3—181no—
169Dic3—181no—
170C32#87711yescharacteristic
171C9—21no—
172C9#89211yescharacteristic, complemented
173C23—31no—
174C2×C4—31no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—274no—
178C2×C4—271no—
179C2×C4—271no—
180C2×C4D3×D911yescharacteristic
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—62no—
185C2×C3C2×C4×D911yescharacteristic
186C2×C3#369911yescharacteristic
187C2×C3#369911yescharacteristic
188C2×C3#379611yescharacteristic
189C2×C3C4×D3211yescharacteristic
190C2×C3#380511yescharacteristic
191D3—22no—
192C22—32no—
193C22—61no—
194C22—61no—
195C22C2×D3×D911yescharacteristic
196C4—21no—
197C4—61no—
198C4—92no—
199C4—181no—
200C4—272no—
201C4—541no—
202C3—21no—
203C3#6343911yescharacteristic, complemented
204C3#6387811yescharacteristic
205C2—62no—
206C2#8863911yescharacteristic
207C2C4×D3×D911yescharacteristic
208C2#8866311yescharacteristic
subgroupG/H
centerC22C2×D3×D9
commutatorC2×C3×C9C22×C4
FrattiniC22×C3C2×D32
FittingC2×C3×C4×C9C22
socleC22×C32C22×D3
prime radicalC22×C3×D3C2×D3
cosocleC22×C3×C9C23
hypercenterC2×C4D3×D9
hypocenterC3×C9#117
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊Dic9C2semidirect
4. C3×Dic9⋊C4C2semidirect
6. Dic9⋊Dic3C2semidirect
7. Dic3×Dic9C2semidirect
17. D3×Dic9C4semidirect
29. Dic9⋊C4D3semidirect
108. C3×C9#117semidirect
172. C9#892semidirect
203. C3#63439semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic92
C4×C3⋊Dic92
C9×(C2×D3)⋊C42
C3×Dic9⋊C42
(C2×D3)⋊Dic92
Dic9⋊Dic32
Dic3×Dic92
#638783
#634393