Finite Group Databasebeta

← #11722508

Subgroups — #11722508

Order 864.

476 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 131 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
1Q8×C3⋊D9C211yesmaximal, characteristic, complemented
2C9×#239C211yesmaximal, characteristic, complemented
3C3×Q8×D9C211yesmaximal, characteristic, complemented
4#88640C213yesmaximal, complemented
5#88639C213yesmaximal, complemented
6#88638C213yesmaximal, complemented
7D3×Dic18C213yesmaximal, complemented
8#64315—31nomaximal
9#63716—31nomaximal
10C3×Q8×C9C2211yescharacteristic
11C4×C3⋊D9C2213yes—
12#6226C2213yes—
13C9×D12C2213yes—
14C4×D3×C9C2213yes—
15C3×C4×D9C2213yes—
16C3×Dic18C2213yes—
17#6195C2213yes—
18#6194C2213yes—
19D3×Dic9C2216yes—
20#6192C2211yescharacteristic
21#6189C2213yes—
22Q8×C3⋊D3—31no—
23C3×#239D311yescharacteristic
24C3×D3×Q8—31no—
25#3798—33no—
26#3796—33no—
27#3795—33no—
28D3×Dic6—33no—
29C9×#41—31no—
30Q8×D9—31no—
31Q8×D9—61no—
32Q8×D9D311yescharacteristic, complemented
33#3699—33no—
34#3699—33no—
35#3697—33no—
36C2×Dic18—33no—
37C2×C3⋊D9C2311yescharacteristic
38C2×D3×C9C2313yes—
39C2×C3×D9C2311yescharacteristic
40C3×C4×C9C2313yes—
41C3⋊Dic9C2313yes—
42C9×Dic3C2311yescharacteristic
43C3×Dic9C2313yes—
44#1010—91no—
45#1007—91no—
46C32×Q8C2×D311yescharacteristic
47C4×C3⋊D3—33no—
48#634—33no—
49C3×D12C2×D313yes—
50C3×C4×D3—33no—
51C3×C4×D3C2×D313yes—
52C3×Dic6—33no—
53#627—33no—
54#626—33no—
55#626—31no—
56#625—33no—
57D3×Dic3—36no—
58Q8×C9—21no—
59Q8×C9C2×D311yescharacteristic
60D4×C9—33no—
61C2×C4×C9—33no—
62#611—33no—
63#611—33no—
64C2×Dic9—36no—
65D36—31no—
66C4×D9—33no—
67C4×D9—63no—
68C4×D9C2×D313yes—
69Dic18—33no—
70Dic18—33no—
71Dic18—63no—
72Dic18C2×D313yes—
73C2×C3×C9C2411yescharacteristic
74C3⋊D9—21no—
75D3×C9—23no—
76C3×D9—21no—
77C3×#41—31no—
78C2×C3×Q8—91no—
79#239—93no—
80#239D911yescharacteristic, complemented
81D3×Q8—31no—
82D3×Q8—91no—
83D3×Q8—91no—
84D3×Q8—93no—
85D3×Q8—181no—
86#237—93no—
87#237—93no—
88#235—93no—
89#235—93no—
90#235—93no—
91C2×Dic6—93no—
92C2×C3⋊D3—31no—
93C2×C3×D3—31no—
94C2×C3×D3C22×D313yes—
95C32×C4C22×D313yes—
96C3⋊Dic3—33no—
97C3×Dic3—33no—
98C3×Dic3C22×D311yescharacteristic
99C22×C9—33no—
100C2×D9—31no—
101C2×D9—61no—
102C2×D9C22×D311yescharacteristic
103C4×C9—23no—
104C4×C9—31no—
105C4×C9C22×D313yes—
106Dic9—33no—
107Dic9—63no—
108Dic9C22×D313yes—
1092−1+4—271noSylow
110C3×C92−1+411yescharacteristic, complemented, Sylow
111C3×Q8—21no—
112C3×Q8—93no—
113C3×Q8C2×D911yescharacteristic
114C3×Q8D3211yescharacteristic
115C3×D4—33no—
116C2×C3×C4—33no—
117C2×C3×C4—93no—
118#67—93no—
119#67—93no—
120#67—93no—
121#67—91no—
122C2×Dic3—96no—
123D12—91no—
124D12—93no—
125D12C2×D913yes—
126C4×D3—33no—
127C4×D3—96no—
128C4×D3—93no—
129C4×D3—93no—
130C4×D3—183no—
131C4×D3C2×D913yes—
132Dic6—33no—
133Dic6—93no—
134Dic6—93no—
135Dic6—93no—
136Dic6—93no—
137Dic6—183no—
138C2×C32C23×D311yescharacteristic
139C3⋊D3—61no—
140C3×D3—23no—
141C3×D3—61no—
142C2×C9—21no—
143C2×C9—63no—
144C2×C9C23×D311yescharacteristic
145D9—21no—
146D9—62no—
147D9—61no—
148#41—31no—
149#41—273no—
150#41—273no—
151#41—273no—
152C2×Q8—91no—
153C2×Q8—273no—
154C2×Q8—271no—
155C22×C3—33no—
156C22×C3—91no—
157C2×D3—31no—
158C2×D3—91no—
159C2×D3—91no—
160C2×D3—181no—
161C2×D3C22×D913yes—
162C3×C4—23no—
163C3×C4—31no—
164C3×C4—93no—
165C3×C4C22×D913yes—
166C3×C4C2×D3213yes—
167Dic3—33no—
168Dic3—93no—
169Dic3—93no—
170Dic3—183no—
171Dic3C22×D911yescharacteristic
172C32#101011yescharacteristic
173C9—21no—
174C9#100711yescharacteristic, complemented
175Q8—93no—
176Q8—273no—
177Q8—273no—
178Q8D3×D911yescharacteristic
179D4—33no—
180D4—271no—
181D4—273no—
182D4—273no—
183C2×C4—33no—
184C2×C4—93no—
185C2×C4—276no—
186C2×C4—273no—
187C2×C3—21no—
188C2×C3—63no—
189C2×C3—181no—
190C2×C3C23×D911yescharacteristic
191C2×C3C22×D3211yescharacteristic
192D3—23no—
193D3—61no—
194D3—182no—
195D3—181no—
196D3—181no—
197C22—33no—
198C22—91no—
199C22—271no—
200C4—31no—
201C4—93no—
202C4—273no—
203C4C2×D3×D913yes—
204C3—21no—
205C3#6371611yescharacteristic, complemented
206C3#6431511yescharacteristic
207C2—63no—
208C2—181no—
209C2—541no—
210C2C22×D3×D911yescharacteristic
subgroupG/H
centerC2C22×D3×D9
commutator, cosocleC2×C3×C9C24
FrattiniC2×C3C22×D32
FittingC3×Q8×C9C22
socleC2×C32C23×D3
hypercenterQ8D3×D9
hypocenterC3×C92−1+4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. Q8×C3⋊D9C2semidirect
2. C9×#239C2semidirect
3. C3×Q8×D9C2semidirect
4. #88640C2semidirect
5. #88639C2semidirect
6. #88638C2semidirect
7. D3×Dic18C2semidirect
32. Q8×D9D3semidirect
80. #239D9semidirect
110. C3×C92−1+4semidirect
174. C9#1007semidirect
205. C3#63716semidirect

Maximal subgroups

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

subgroupindex
Q8×C3⋊D92
C9×#2392
C3×Q8×D92
#886402
#886392
#886382
D3×Dic182
#643153
#637163