Finite Group Databasebeta

← #11721186

Subgroups — #11721186

Order 864.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#88742C211yesmaximal, characteristic, complemented
2#88634C211yesmaximal, characteristic, complemented
3C9×#214C211yesmaximal, characteristic, complemented
4C3×#3673C211yesmaximal, characteristic, complemented
5#88428C211yesmaximal, characteristic, complemented
6#88415C211yesmaximal, characteristic, complemented
7(C3⋊D9)⋊C8C211yesmaximal, characteristic, complemented
8#63936—31nomaximal
9#63478—31nomaximal
10C3×D4×C9C2211yescharacteristic
11#6233—21no—
12C2×C3⋊Dic9—21no—
13C4×C3⋊D9C2211yescharacteristic
14#6226C2211yescharacteristic
15C3×D36C2211yescharacteristic
16C9×Dic6C2211yescharacteristic
17#6192—21no—
18Dic3×D9—21no—
19C9×C3⋊C8C2211yescharacteristic
20C3×C9⋊C8C2211yescharacteristic
21#3830—31no—
22#3796—31no—
23C3×#214D311yescharacteristic
24C3×#213—31no—
25#3719—31no—
26#3716—31no—
27#3710—31no—
28#3701—31no—
29#3699—31no—
30#3699—61no—
31C9×SD16—31no—
32#3674—31no—
33#3673D311yescharacteristic, complemented
34#3664—31no—
35C8×D9—31no—
36C22×C3×C9—21no—
37C2×C3⋊D9D411yescharacteristic
38C2×C3×D9—21no—
39C3×C4×C9C2311yescharacteristic
40C3⋊Dic9—21no—
41C3⋊Dic9D411yescharacteristic
42C9×Dic3—21no—
43#916—91no—
44#912—91no—
45C32×D4C2×D311yescharacteristic
46#638—61no—
47C2×C3⋊Dic3—61no—
48C4×C3⋊D3—31no—
49#634—31no—
50C3×D12—31no—
51C3×Dic6C2×D311yescharacteristic
52#626—61no—
53D3×Dic3—61no—
54C3×C3⋊C8—31no—
55C3×C3⋊C8C2×D311yescharacteristic
56Q8×C9—31no—
57D4×C9—21no—
58D4×C9C2×D311yescharacteristic
59#611—61no—
60#611—62no—
61C2×Dic9—61no—
62C2×Dic9—62no—
63D36—61no—
64D36C2×D311yescharacteristic
65C4×D9—31no—
66C4×D9—61no—
67C4×D9—61no—
68Dic18—31no—
69Dic18—61no—
70C8×C9—31no—
71C9⋊C8C2×D311yescharacteristic
72C2×C3×C9—41no—
73C2×C3×C9C2×D411yescharacteristic
74C3⋊D9—21no—
75C3×D9—41no—
76#239—91no—
77#237—91no—
78#237—91no—
79#237—91no—
80#237—181no—
81C3×SD16—31no—
82C3×D8—91no—
83#216—91no—
84#214—91no—
85#214D911yescharacteristic, complemented
86#213—31no—
87Dic12—91no—
88#204—91no—
89D3×C8—91no—
90D3×C8—91no—
91C22×C32—21no—
92C2×C3⋊D3—31no—
93C2×C3×D3—61no—
94C32×C4C22×D311yescharacteristic
95C3⋊Dic3—31no—
96C3⋊Dic3—61no—
97C3×Dic3—21no—
98C22×C9—22no—
99C22×C9—21no—
100C2×D9—21no—
101C2×D9—31no—
102C2×D9—61no—
103C4×C9—21no—
104C4×C9—61no—
105C4×C9C22×D311yescharacteristic
106Dic9—31no—
107Dic9—61no—
108Dic9—62no—
109Dic9—61no—
110#135—271noSylow
111C3×C9#13511yescharacteristic, complemented, Sylow
112C3×Q8—31no—
113C3×D4—21no—
114C3×D4—91no—
115C3×D4C2×D911yescharacteristic
116C3×D4D3211yescharacteristic
117#67—181no—
118#67—181no—
119#67—181no—
120#67—182no—
121C2×Dic3—181no—
122C2×Dic3—181no—
123C2×Dic3—181no—
124C2×Dic3—182no—
125D12—31no—
126D12—181no—
127C4×D3—91no—
128C4×D3—91no—
129C4×D3—181no—
130C4×D3—181no—
131Dic6—91no—
132Dic6—91no—
133Dic6—181no—
134Dic6C2×D911yescharacteristic
135C3×C8—31no—
136C3×C8—91no—
137C3⋊C8—31no—
138C3⋊C8C2×D911yescharacteristic
139C2×C32—41no—
140C2×C32D3×D411yescharacteristic
141C3⋊D3—61no—
142C3×D3—121no—
143C2×C9—21no—
144C2×C9—42no—
145C2×C9—41no—
146C2×C9D3×D411yescharacteristic
147D9—41no—
148D9—61no—
149D9—121no—
150#41—271no—
151#41—271no—
152Q16—271no—
153SD16—31no—
154SD16—271no—
155D8—91no—
156C2×C8—271no—
157C22×C3—22no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—181no—
161C2×D3—61no—
162C2×D3—91no—
163C2×D3—91no—
164C2×D3—181no—
165C3×C4—21no—
166C3×C4—61no—
167C3×C4C22×D911yescharacteristic
168C3×C4C2×D3211yescharacteristic
169Dic3—21no—
170Dic3—91no—
171Dic3—91no—
172Dic3—181no—
173Dic3—182no—
174Dic3—181no—
175Dic3—181no—
176C32#91611yescharacteristic
177C9—21no—
178C9#91211yescharacteristic, complemented
179Q8—31no—
180Q8—271no—
181D4—91no—
182D4—541no—
183D4—541no—
184D4D3×D911yescharacteristic
185C2×C4—271no—
186C2×C4—541no—
187C2×C4—541no—
188C8—31no—
189C8—91no—
190C2×C3—21no—
191C2×C3—42no—
192C2×C3—41no—
193C2×C3—41no—
194C2×C3—361no—
195C2×C3D4×D911yescharacteristic
196C2×C3#381111yescharacteristic
197D3—121no—
198D3—181no—
199D3—181no—
200D3—361no—
201C22—21no—
202C22—181no—
203C22—271no—
204C4—61no—
205C4—271no—
206C4—541no—
207C4C2×D3×D911yescharacteristic
208C3—21no—
209C3#6347811yescharacteristic, complemented
210C3#6393611yescharacteristic
211C2—41no—
212C2—361no—
213C2—541no—
214C2#8866811yescharacteristic
subgroupG/H
centerC2#88668
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. #88742C2semidirect
2. #88634C2semidirect
3. C9×#214C2semidirect
4. C3×#3673C2semidirect
5. #88428C2semidirect
6. #88415C2semidirect
7. (C3⋊D9)⋊C8C2semidirect
33. #3673D3semidirect
85. #214D9semidirect
111. C3×C9#135semidirect
178. C9#912semidirect
209. C3#63478semidirect

Maximal subgroups

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

subgroupindex
#887422
#886342
C9×#2142
C3×#36732
#884282
#884152
(C3⋊D9)⋊C82
#639363
#634783