Finite Group Databasebeta

← D3×#3701 #11722512

Subgroups — D3×#3701 #11722512

Order 864.

532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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#88746C211yesmaximal, characteristic, complemented
2D3×Q8×C9C211yesmaximal, characteristic, complemented
3C3×#3701C211yesmaximal, characteristic, complemented
4D3×D36C213yesmaximal, complemented
5C4×D3×D9C213yesmaximal, complemented
6#88635C213yesmaximal, complemented
7#88634C213yesmaximal, complemented
8D3×#239—31nomaximal
9C2×#3701—31nomaximal
10C2×D3×D9C2213yes—
11C3×Q8×C9C2211yescharacteristic, complemented
12C4⋊(C3⋊D9)C2213yescomplemented
13C4×C3⋊D9C2213yescomplemented
14C4×D3×C9C2213yes—
15C3×D36C2213yescomplemented
16C3×C4×D9C2213yescomplemented
17C9×Dic6C2213yescomplemented
18D3×Dic9C2211yescharacteristic
19#6192C2216yescomplemented
20(C3⋊D9)⋊C4C2213yescomplemented
21Dic3×D9C2213yescomplemented
22#3832—31no—
23C3×#239—31no—
24C3×D3×Q8D311yescharacteristic
25D3×D12—33no—
26C4×D32—33no—
27#3799—33no—
28#3796—33no—
29C2×Q8×C9—31no—
30#3701—31no—
31#3701—33no—
32#3701—33no—
33#3701—61no—
34#3701D311yescharacteristic, direct product factor
35C2×D36—33no—
36C2×C4×D9—33no—
37C2×C3⋊D9C2313yes—
38C2×D3×C9C2311yescharacteristic
39C2×C3×D9C2313yes—
40D3×D9—26no—
41C3×C4×C9C2313yes—
42C3⋊Dic9C2311yescharacteristic
43C9×Dic3C2313yes—
44C3×Dic9C2311yescharacteristic
45D3×#41—91no—
46C2×#239—91no—
47C2×D32—33no—
48C32×Q8C2×D311yescharacteristic
49C4⋊(C3⋊D3)—33no—
50C4×C3⋊D3—33no—
51C3×D12—33no—
52C3×C4×D3—33no—
53C3×C4×D3C2×D313yes—
54C3×Dic6C2×D313yes—
55#626—36no—
56#624—33no—
57D3×Dic3—31no—
58D3×Dic3—33no—
59C22×D9—33no—
60Q8×C9—21no—
61Q8×C9—33no—
62Q8×C9C2×D311yescharacteristic, complemented
63C2×C4×C9—33no—
64C2×Dic9—31no—
65D36—36no—
66D36—33no—
67D36—63no—
68D36C2×D313yescomplemented
69C4×D9—33no—
70C4×D9—33no—
71C4×D9—33no—
72C4×D9—63no—
73C4×D9C2×D313yescomplemented
74C2×C3×C9C2411yescharacteristic
75C3⋊D9—23no—
76D3×C9#4112yescomplemented
77C3×D9—23no—
78C3×#41—91no—
79C2×C3×Q8—31no—
80#239—31no—
81#239—93no—
82#239—93no—
83#239—91no—
84#239—91no—
85#239—181no—
86D3×Q8D911yescharacteristic, complemented
87#237—93no—
88D3×D4—93no—
89#235—93no—
90C2×D12—93no—
91C2×C4×D3—93no—
92C2×C4×D3—93no—
93C2×C3⋊D3—33no—
94C2×C3×D3—33no—
95C2×C3×D3C22×D311yescharacteristic
96D32—66no—
97C32×C4C22×D313yes—
98C3⋊Dic3—31no—
99C3×Dic3—31no—
100C3×Dic3C22×D313yes—
101C22×C9—31no—
102C2×D9—33no—
103C2×D9—63no—
104C2×D9—66no—
105C2×D9C22×D313yes—
106C4×C9—23no—
107C4×C9—33no—
108C4×C9C22×D313yes—
109Dic9—31no—
110Dic9—61no—
111Dic9C22×D311yescharacteristic
112C2×#41—271noSylow
113C3×C9C2×#4111yescharacteristic, complemented, Sylow
114C22×D3—93no—
115C22×D3—93no—
116C3×Q8—21no—
117C3×Q8—33no—
118C3×Q8C2×D911yescharacteristic, complemented
119C3×Q8D3211yescharacteristic
120C3×D4—93no—
121C2×C3×C4—33no—
122C2×C3×C4—93no—
123#67—96no—
124C2×Dic3—91no—
125C2×Dic3—93no—
126D12—33no—
127D12—96no—
128D12—93no—
129D12—93no—
130D12—183no—
131C4×D3—33no—
132C4×D3—93no—
133C4×D3—93no—
134C4×D3—91no—
135C4×D3—93no—
136C4×D3—93no—
137C4×D3—93no—
138C4×D3—183no—
139C4×D3C2×D913yes—
140Dic6C2×D913yescomplemented
141C2×C32C23×D311yescharacteristic
142C3⋊D3—63no—
143C3×D3—63no—
144C3×D3#23912yes—
145C2×C9—21no—
146C2×C9—32no—
147C2×C9C23×D311yescharacteristic
148D9—23no—
149D9—63no—
150D9—123no—
151#41—91no—
152#41—273no—
153#41—273no—
154#41—271no—
155C2×Q8—31no—
156C2×D4—273no—
157C22×C4—273no—
158C22×C3—31no—
159C22×C3—93no—
160C2×D3—33no—
161C2×D3—93no—
162C2×D3—93no—
163C2×D3—183no—
164C2×D3—186no—
165C2×D3—186no—
166C2×D3C22×D911yescharacteristic
167C3×C4—23no—
168C3×C4—33no—
169C3×C4—91no—
170C3×C4C22×D913yes—
171C3×C4C2×D3213yes—
172Dic3—31no—
173Dic3—91no—
174Dic3—91no—
175Dic3—181no—
176Dic3C22×D913yes—
177C32C2×#23911yescharacteristic
178C9—21no—
179C9D3×#4111yescharacteristic, complemented
180C23—273no—
181Q8—33no—
182Q8D3×D911yescharacteristic, complemented
183D4—93no—
184D4—276no—
185D4—273no—
186C2×C4—33no—
187C2×C4—93no—
188C2×C4—273no—
189C2×C4—273no—
190C2×C4—271no—
191C2×C4—273no—
192C2×C3—21no—
193C2×C3—32no—
194C2×C3—183no—
195C2×C3C23×D911yescharacteristic
196C2×C3C22×D3211yescharacteristic
197D3—63no—
198D3—183no—
199D3—183no—
200D3—363no—
201D3#370112yesdirect product factor
202C22—31no—
203C22—93no—
204C22—273no—
205C22—546no—
206C4—33no—
207C4—91no—
208C4—271no—
209C4C2×D3×D913yes—
210C3—21no—
211C3C2×#370111yescharacteristic, complemented
212C3D3×#23911yescharacteristic
213C2—32no—
214C2—183no—
215C2—543no—
216C2C22×D3×D911yescharacteristic
subgroupG/H
centerC2C22×D3×D9
commutator, cosocleC2×C3×C9C24
FrattiniC2×C3C22×D32
FittingC3×Q8×C9C22
socleC2×C32C23×D3
hypercenterQ8D3×D9
hypocenterC3×C9C2×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. #88746C2semidirect
2. D3×Q8×C9C2semidirect
3. C3×#3701C2semidirect
4. D3×D36C2semidirect
5. C4×D3×D9C2semidirect
6. #88635C2semidirect
7. #88634C2semidirect
11. C3×Q8×C9C22semidirect
12. C4⋊(C3⋊D9)C22semidirect
13. C4×C3⋊D9C22semidirect
15. C3×D36C22semidirect
16. C3×C4×D9C22semidirect
17. C9×Dic6C22semidirect
19. #6192C22semidirect
20. (C3⋊D9)⋊C4C22semidirect
21. Dic3×D9C22semidirect
34. #3701D3direct (N × H)
62. Q8×C9C2×D3semidirect
68. D36C2×D3semidirect
73. C4×D9C2×D3semidirect
76. D3×C9#41semidirect
86. D3×Q8D9semidirect
113. C3×C9C2×#41semidirect
118. C3×Q8C2×D9semidirect
140. Dic6C2×D9semidirect
179. C9D3×#41semidirect
182. Q8D3×D9semidirect
201. D3#3701direct (N × H)
211. C3C2×#3701semidirect

Maximal subgroups

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

subgroupindex
#887462
D3×Q8×C92
C3×#37012
D3×D362
C4×D3×D92
#886352
#886342
D3×#2393
C2×#37013