Finite Group Databasebeta

← D3×#4268 #11759625

Subgroups — D3×#4268 #11759625

Order 1008.

232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C22×C3×D3×C7C211yesmaximal, characteristic, complemented
2C2×D3×D21C211yesmaximal, characteristic, complemented
3#92726C211yesmaximal, characteristic, complemented
4C3×#4268C211yesmaximal, characteristic, complemented
5#92690C211yesmaximal, characteristic, complemented
6#92688C211yesmaximal, characteristic, complemented
7D3×Dic21C211yesmaximal, characteristic, complemented
8C2×#4268—31nomaximal
9D3×C22⋊D7—31nomaximal
10C22×C32×C7C2211yescharacteristic, complemented
11C2×C3⋊D21C2211yescharacteristic, complemented
12C2×C3×D21C2211yescharacteristic, complemented
13C2×C3×D3×C7—22no—
14C2×C3×D3×C7C2211yescharacteristic
15C2×C3×D3×C7C2211yescharacteristic, complemented
16D3×D21—22no—
17C3⋊Dic21C2211yescharacteristic, complemented
18C3×Dic21C2211yescharacteristic, complemented
19C23×C3×C7—31no—
20C22×D21—31no—
21C22×D3×C7D311yescharacteristic, complemented
22C2×D3×D7—31no—
23#4268—31no—
24#4268—31no—
25#4268—31no—
26#4268—31no—
27#4268—61no—
28#4268D311yescharacteristic, direct product factor
29C2×Dic21—31no—
30C3×C22⋊D7—31no—
31#4247—31no—
32#4245—31no—
33D3×Dic7—31no—
34D3×#67—71nomaximal, Hall
35C2×C32×C7—21no—
36C2×C32×C7C2311yescharacteristic
37C3⋊D21—21no—
38C3×D21—21no—
39C3×D3×C7—21no—
40C3×D3×C7D412yescomplemented
41C2×C22⋊D7—91noHall
42C22×C3×C7—21no—
43C22×C3×C7—31no—
44C22×C3×C7—31no—
45C22×C3×C7—62no—
46C22×C3×C7C2×D311yescharacteristic, complemented
47C22×C3×C7C2×D311yescharacteristic, complemented
48C2×D21—31no—
49C2×D21—31no—
50C2×D21—61no—
51C2×D21—62no—
52C2×D21C2×D311yescharacteristic, complemented
53C2×D3×C7—22no—
54C2×D3×C7C2×D311yescharacteristic
55C2×D3×C7C2×D311yescharacteristic, complemented
56C2×C3×D7—31no—
57D3×D7—62no—
58Dic21—31no—
59Dic21—31no—
60Dic21—61no—
61Dic21C2×D311yescharacteristic, complemented
62C3×Dic7—31no—
63C22×C3×D3D711yescharacteristic, complemented
64C2×D32—71no—
65#638—71no—
66C3×#67—71no—
67#626—71no—
68#625—71no—
69D3×Dic3—71no—
70C32×C7C2×D411yescharacteristic, complemented, Hall
71C23×C7—31no—
72C22×D7—91no—
73C22⋊D7—31no—
74C22⋊D7—91no—
75C22⋊D7—91no—
76C22⋊D7—91no—
77C2×Dic7—91no—
78C2×#67—211no—
79D3×D4—211no—
80C2×C3×C7—21no—
81C2×C3×C7—21no—
82C2×C3×C7—21no—
83C2×C3×C7—32no—
84C2×C3×C7—41no—
85C2×C3×C7—61no—
86C2×C3×C7C22×D311yescharacteristic
87C2×C3×C7C22×D311yescharacteristic
88D21—21no—
89D21—61no—
90D21—61no—
91D21—121no—
92C3×D7—61no—
93D3×C7—21no—
94D3×C7#6712yescomplemented
95C22×C32C2×D711yescharacteristic, complemented
96C2×C3⋊D3—71no—
97C2×C3×D3—22no—
98C2×C3×D3—71no—
99C2×C3×D3C2×D711yescharacteristic
100C2×C3×D3C2×D711yescharacteristic, complemented
101D32—142no—
102C3⋊Dic3—71no—
103C3×Dic3—71no—
104C22×C7—31no—
105C22×C7—31no—
106C22×C7—62no—
107C22×C7D3211yescharacteristic, complemented
108C2×D7—31no—
109C2×D7—91no—
110C2×D7—182no—
111Dic7—31no—
112Dic7—91no—
113C23×C3—31no—
114C22×D3—211no—
115C22×D3—211no—
116C22×D3D2111yescharacteristic, complemented
117C3×D4—211no—
118#67—71no—
119#67—211no—
120#67—211no—
121#67—211no—
122#67—211no—
123#67—211no—
124#67—421no—
125C2×Dic3—211no—
126D12—211no—
127C4×D3—211no—
128C3×C7—21no—
129C3×C7D3×D411yescharacteristic, complemented
130C3×C7C2×#6711yescharacteristic, complemented
131C2×C32—21no—
132C2×C32C22×D711yescharacteristic
133C3⋊D3—141no—
134C3×D3—21no—
135C3×D3—141no—
136C3×D3C22⋊D712yescomplemented
137C2×D4—631noSylow
138C2×C7—21no—
139C2×C7—32no—
140C2×C7—61no—
141C2×C7C2×D3211yescharacteristic
142D7—61no—
143D7—181no—
144C22×C3—21no—
145C22×C3—31no—
146C22×C3—31no—
147C22×C3—62no—
148C22×C3—211no—
149C22×C3D3×D711yescharacteristic, complemented
150C22×C3C2×D2111yescharacteristic, complemented
151C2×D3—22no—
152C2×D3—71no—
153C2×D3—211no—
154C2×D3—211no—
155C2×D3—421no—
156C2×D3—422no—
157C2×D3—422no—
158C2×D3C2×D2111yescharacteristic
159C2×D3C2×D2111yescharacteristic, complemented
160C3×C4—211no—
161Dic3—71no—
162Dic3—211no—
163Dic3—211no—
164Dic3—421no—
165C32C2×C22⋊D711yescharacteristic, complemented, Sylow
166C23—31no—
167C23—631no—
168D4—211no—
169D4—631no—
170D4—631no—
171D4—631no—
172C2×C4—631no—
173C7D3×#6711yescharacteristic, complemented, Sylow
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—32no—
178C2×C3—41no—
179C2×C3—61no—
180C2×C3—421no—
181C2×C3C2×D3×D711yescharacteristic
182C2×C3C22×D2111yescharacteristic
183D3—21no—
184D3—141no—
185D3—421no—
186D3—421no—
187D3—841no—
188D3#426812yesdirect product factor
189C22—31no—
190C22—31no—
191C22—62no—
192C22—211no—
193C22—631no—
194C22—1262no—
195C22D3×D2111yescharacteristic, complemented
196C4—211no—
197C4—631no—
198C3—21no—
199C3D3×C22⋊D711yescharacteristic, complemented
200C3C2×#426811yescharacteristic, complemented
201C2—21no—
202C2—32no—
203C2—61no—
204C2—421no—
205C2—1261no—
206C2C2×D3×D2111yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×D21
commutator, socle, cosocleC2×C32×C7C23
FittingC22×C32×C7C22
hypercenterC22D3×D21
hypocenterC32×C7C2×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C7C2semidirect
2. C2×D3×D21C2semidirect
3. #92726C2semidirect
4. C3×#4268C2semidirect
5. #92690C2semidirect
6. #92688C2semidirect
7. D3×Dic21C2semidirect
10. C22×C32×C7C22semidirect
11. C2×C3⋊D21C22semidirect
12. C2×C3×D21C22semidirect
15. C2×C3×D3×C7C22semidirect
17. C3⋊Dic21C22semidirect
18. C3×Dic21C22semidirect
21. C22×D3×C7D3semidirect
28. #4268D3direct (N × H)
40. C3×D3×C7D4semidirect
46. C22×C3×C7C2×D3semidirect
47. C22×C3×C7C2×D3semidirect
52. C2×D21C2×D3semidirect
55. C2×D3×C7C2×D3semidirect
61. Dic21C2×D3semidirect
63. C22×C3×D3D7semidirect
70. C32×C7C2×D4semidirect
94. D3×C7#67semidirect
95. C22×C32C2×D7semidirect
100. C2×C3×D3C2×D7semidirect
107. C22×C7D32semidirect
116. C22×D3D21semidirect
129. C3×C7D3×D4semidirect
130. C3×C7C2×#67semidirect
136. C3×D3C22⋊D7semidirect
149. C22×C3D3×D7semidirect
150. C22×C3C2×D21semidirect
159. C2×D3C2×D21semidirect
165. C32C2×C22⋊D7semidirect
173. C7D3×#67semidirect
188. D3#4268direct (N × H)
195. C22D3×D21semidirect
199. C3D3×C22⋊D7semidirect
200. C3C2×#4268semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C72
C2×D3×D212
#927262
C3×#42682
#926902
#926882
D3×Dic212
C2×#42683
D3×C22⋊D73
D3×#677