Finite Group Databasebeta

← #11721185

Subgroups — #11721185

Order 864.

208 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C3×#3699C211yesmaximal, characteristic, complemented
2#88635C211yesmaximal, characteristic, complemented
3#88544C211yesmaximal, characteristic, complemented
4C9×#214C211yesmaximal, characteristic, complemented
5#88427C211yesmaximal, characteristic, complemented
6#88416C211yesmaximal, characteristic, complemented
7D9×C3⋊C8C211yesmaximal, characteristic, complemented
8#63935—31nomaximal
9#63478—31nomaximal
10C3×D4×C9C2211yescharacteristic
11C4⋊(C3⋊D9)C2211yescharacteristic
12C3×#611—21no—
13C2×C3×Dic9—21no—
14C3×C4×D9C2211yescharacteristic
15C9×Dic6C2211yescharacteristic
16C3×Dic18C2211yescharacteristic
17#6192—21no—
18(C3⋊D9)⋊C4—21no—
19C3⋊(C9⋊C8)C2211yescharacteristic
20C9×C3⋊C8C2211yescharacteristic
21C3×#237—31no—
22#3799—31no—
23#3753—31no—
24C3×#214D311yescharacteristic
25#3718—31no—
26#3717—31no—
27D3×C3⋊C8—31no—
28#3701—31no—
29#3699D311yescharacteristic, complemented
30C9×SD16—31no—
31#3674—31no—
32#3673—31no—
33#3673—61no—
34#3664—31no—
35C8×D9—31no—
36C22×C3×C9—21no—
37C2×C3⋊D9—21no—
38C2×C3×D9D411yescharacteristic
39C3×C4×C9C2311yescharacteristic
40C9×Dic3—21no—
41C3×Dic9—21no—
42C3×Dic9D411yescharacteristic
43#950—91no—
44#916—91no—
45C32×D4C2×D311yescharacteristic
46C4⋊(C3⋊D3)—31no—
47C3×#67—61no—
48C2×C3×Dic3—61no—
49C3×C4×D3—31no—
50C3×Dic6—31no—
51C3×Dic6C2×D311yescharacteristic
52#626—61no—
53#624—61no—
54C3⋊(C3⋊C8)—31no—
55C3×C3⋊C8C2×D311yescharacteristic
56Q8×C9—31no—
57D4×C9—21no—
58D4×C9C2×D311yescharacteristic
59#611—21no—
60C2×Dic9—21no—
61D36—31no—
62D36—61no—
63D36—61no—
64C4×D9—61no—
65C4×D9C2×D311yescharacteristic
66Dic18C2×D311yescharacteristic
67C8×C9—31no—
68C9⋊C8—31no—
69C9⋊C8—61no—
70C2×C3×C9—41no—
71C2×C3×C9C2×D411yescharacteristic
72C3⋊D9—41no—
73C3×D9—21no—
74C3×#41—91no—
75#239—91no—
76#237—31no—
77#235—91no—
78C3×SD16—31no—
79#216—91no—
80#216—91no—
81#215—91no—
82#214D911yescharacteristic, complemented
83#213—91no—
84#213—91no—
85#213—181no—
86C2×C3⋊C8—91no—
87#204—91no—
88D3×C8—91no—
89C22×C32—21no—
90C2×C3⋊D3—61no—
91C2×C3×D3—31no—
92C32×C4C22×D311yescharacteristic
93C3×Dic3—21no—
94C3×Dic3—31no—
95C3×Dic3—61no—
96C22×C9—21no—
97C22×C9—41no—
98C2×D9—61no—
99C2×D9—121no—
100C2×D9#6711yescharacteristic
101C4×C9—21no—
102C4×C9—61no—
103C4×C9C22×D311yescharacteristic
104Dic9—21no—
105Dic9#6711yescharacteristic
106#135—271noSylow
107C3×C9#13511yescharacteristic, complemented, Sylow
108C3×Q8—31no—
109C3×Q8—91no—
110C3×D4—21no—
111C3×D4—181no—
112C3×D4C2×D911yescharacteristic
113C3×D4D3211yescharacteristic
114C2×C3×C4—91no—
115C2×C3×C4—181no—
116#67—61no—
117#67—181no—
118C2×Dic3—61no—
119D12—91no—
120D12—91no—
121D12—181no—
122D12—181no—
123C4×D3—31no—
124C4×D3—181no—
125C4×D3—181no—
126Dic6—31no—
127Dic6C2×D911yescharacteristic
128C3×C8—31no—
129C3⋊C8—91no—
130C3⋊C8—91no—
131C3⋊C8—181no—
132C3⋊C8C2×D911yescharacteristic
133C2×C32—41no—
134C2×C32D3×D411yescharacteristic
135C3⋊D3—121no—
136C3×D3—61no—
137C2×C9—21no—
138C2×C9—41no—
139C2×C9—81no—
140C2×C9C2×#6711yescharacteristic
141D9—21no—
142D9—121no—
143D9—241no—
144#41—91no—
145#41—271no—
146Q16—271no—
147SD16—31no—
148SD16—271no—
149D8—271no—
150C2×C8—271no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—41no—
154C22×C3—91no—
155C2×D3—31no—
156C2×D3—181no—
157C2×D3—181no—
158C2×D3—361no—
159C3×C4—21no—
160C3×C4—61no—
161C3×C4—91no—
162C3×C4—181no—
163C3×C4C22×D911yescharacteristic
164C3×C4C2×D3211yescharacteristic
165Dic3—21no—
166Dic3—31no—
167Dic3—61no—
168C32#91611yescharacteristic
169C9—21no—
170C9#95011yescharacteristic, complemented
171Q8—31no—
172Q8—91no—
173D4—181no—
174D4—271no—
175D4—541no—
176D4D3×D911yescharacteristic
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—541no—
180C8—31no—
181C8—271no—
182C2×C3—21no—
183C2×C3—41no—
184C2×C3—41no—
185C2×C3—81no—
186C2×C3—181no—
187C2×C3D4×D911yescharacteristic
188C2×C3D3×#6711yescharacteristic
189D3—61no—
190D3—361no—
191D3—361no—
192D3—721no—
193C22—21no—
194C22—91no—
195C22—541no—
196C4—61no—
197C4—91no—
198C4—181no—
199C4C2×D3×D911yescharacteristic
200C3—21no—
201C3#6347811yescharacteristic, complemented
202C3#6393511yescharacteristic
203C2—41no—
204C2—181no—
205C2—1081no—
206C2D9×#6711yescharacteristic
subgroupG/H
centerC2D9×#67
commutator, cosocleC3×C4×C9C23
FrattiniC3×C4C2×D32
FittingC3×D4×C9C22
socleC2×C32D3×D4
hypercenterD4D3×D9
hypocenterC3×C9#135
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C3×#3699C2semidirect
2. #88635C2semidirect
3. #88544C2semidirect
4. C9×#214C2semidirect
5. #88427C2semidirect
6. #88416C2semidirect
7. D9×C3⋊C8C2semidirect
29. #3699D3semidirect
82. #214D9semidirect
107. C3×C9#135semidirect
170. C9#950semidirect
201. C3#63478semidirect

Maximal subgroups

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

subgroupindex
C3×#36992
#886352
#885442
C9×#2142
#884272
#884162
D9×C3⋊C82
#639353
#634783