Finite Group Databasebeta

← #11759607

Subgroups — #11759607

Order 1008.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C4×C3⋊D21C211yesmaximal, characteristic, complemented
2C3×C4×D21C211yesmaximal, characteristic, complemented
3C3×C4×D3×C7C211yesmaximal, characteristic, complemented
4#92691C211yesmaximal, characteristic, complemented
5#92690C211yesmaximal, characteristic, complemented
6#92689C211yesmaximal, characteristic, complemented
7#92688C211yesmaximal, characteristic, complemented
8#66728—31nomaximal
9#66675—31nomaximal
10C2×C3⋊D21C2211yescharacteristic
11C2×C3×D21C2211yescharacteristic
12C2×C3×D3×C7C2211yescharacteristic
13C32×C4×C7C2211yescharacteristic
14C3⋊Dic21C2211yescharacteristic
15C3×Dic21C2211yescharacteristic
16C3×C7×Dic3C2211yescharacteristic
17C2×C3×C4×C7—31no—
18#4268—31no—
19#4268—31no—
20D84—31no—
21C4×D21—31no—
22C4×D21—31no—
23C4×D21—61no—
24C4×D21D311yescharacteristic, complemented
25Dic42—31no—
26C4×D3×C7D311yescharacteristic, complemented
27C3×C4×D7—31no—
28#4248—31no—
29#4247—31no—
30#4246—31no—
31#4245—31no—
32#3798—71nomaximal, Hall
33C2×C32×C7C2311yescharacteristic
34C3⋊D21—21no—
35C3×D21—21no—
36C3×D3×C7—21no—
37#1157—91noHall
38C22×C3×C7—31no—
39C2×D21—31no—
40C2×D21—31no—
41C2×D21—61no—
42C2×D21C2×D311yescharacteristic
43C2×D3×C7C2×D311yescharacteristic
44C2×C3×D7—31no—
45C3×C4×C7—21no—
46C3×C4×C7—31no—
47C3×C4×C7C2×D311yescharacteristic
48C3×C4×C7C2×D311yescharacteristic
49Dic21—31no—
50Dic21—31no—
51Dic21—61no—
52Dic21C2×D311yescharacteristic
53C3×Dic7—31no—
54C7×Dic3C2×D311yescharacteristic
55C4×C3⋊D3—71no—
56C3×C4×D3—71no—
57C3×C4×D3D711yescharacteristic, complemented
58#627—71no—
59#626—71no—
60#626—71no—
61#625—71no—
62C32×C7#4111yescharacteristic, complemented, Hall
63C2×C4×C7—31no—
64C22⋊D7—91no—
65C22⋊D7—91no—
66D28—91no—
67C4×D7—31no—
68C4×D7—91no—
69Dic14—91no—
70#235—211no—
71#235—211no—
72C2×C3×C7—21no—
73C2×C3×C7—61no—
74C2×C3×C7C22×D311yescharacteristic
75C2×C3×C7C22×D311yescharacteristic
76D21—21no—
77D21—62no—
78D21—61no—
79D21—61no—
80C3×D7—61no—
81D3×C7—21no—
82C2×C3⋊D3—71no—
83C2×C3×D3—71no—
84C2×C3×D3C2×D711yescharacteristic
85C32×C4C2×D711yescharacteristic
86C3⋊Dic3—71no—
87C3×Dic3—71no—
88C3×Dic3C2×D711yescharacteristic
89C22×C7—31no—
90C2×D7—31no—
91C2×D7—91no—
92C4×C7—31no—
93C4×C7D3211yescharacteristic
94Dic7—31no—
95Dic7—91no—
96C2×C3×C4—31no—
97C2×C3×C4—211no—
98#67—211no—
99#67—211no—
100#67—211no—
101#67—211no—
102D12—211no—
103D12—211no—
104C4×D3—71no—
105C4×D3—211no—
106C4×D3—211no—
107C4×D3—421no—
108C4×D3D2111yescharacteristic, complemented
109Dic6—211no—
110Dic6—211no—
111C3×C7—21no—
112C3×C7#23511yescharacteristic, complemented
113C3×C7#23511yescharacteristic, complemented
114C2×C32C22×D711yescharacteristic
115C3⋊D3—141no—
116C3×D3—21no—
117C3×D3—141no—
118#41—631noSylow
119C2×C7—61no—
120C2×C7C2×D3211yescharacteristic
121D7—61no—
122D7—181no—
123C22×C3—31no—
124C22×C3—211no—
125C2×D3—71no—
126C2×D3—211no—
127C2×D3—211no—
128C2×D3—421no—
129C2×D3C2×D2111yescharacteristic
130C3×C4—21no—
131C3×C4—31no—
132C3×C4—211no—
133C3×C4D3×D711yescharacteristic
134C3×C4C2×D2111yescharacteristic
135Dic3—71no—
136Dic3—211no—
137Dic3—211no—
138Dic3—421no—
139Dic3C2×D2111yescharacteristic
140C32#115711yescharacteristic, complemented, Sylow
141Q8—631no—
142D4—631no—
143D4—631no—
144D4—631no—
145C2×C4—31no—
146C2×C4—211no—
147C2×C4—631no—
148C7#379811yescharacteristic, complemented, Sylow
149C2×C3—21no—
150C2×C3—61no—
151C2×C3—421no—
152C2×C3C2×D3×D711yescharacteristic
153C2×C3C22×D2111yescharacteristic
154D3—21no—
155D3—141no—
156D3—422no—
157D3—421no—
158D3—421no—
159C22—31no—
160C22—211no—
161C22—631no—
162C4—31no—
163C4—211no—
164C4—631no—
165C4D3×D2111yescharacteristic
166C3—21no—
167C3#6667511yescharacteristic, complemented
168C3#6672811yescharacteristic, complemented
169C2—61no—
170C2—421no—
171C2—1261no—
172C2C2×D3×D2111yescharacteristic
subgroupG/H
center, hypercenterC4D3×D21
commutator, socle, cosocleC2×C32×C7C23
FrattiniC2C2×D3×D21
FittingC32×C4×C7C22
hypocenterC32×C7#41
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4×C3⋊D21C2semidirect
2. C3×C4×D21C2semidirect
3. C3×C4×D3×C7C2semidirect
4. #92691C2semidirect
5. #92690C2semidirect
6. #92689C2semidirect
7. #92688C2semidirect
24. C4×D21D3semidirect
26. C4×D3×C7D3semidirect
57. C3×C4×D3D7semidirect
62. C32×C7#41semidirect
108. C4×D3D21semidirect
112. C3×C7#235semidirect
113. C3×C7#235semidirect
140. C32#1157semidirect
148. C7#3798semidirect
167. C3#66675semidirect
168. C3#66728semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊D212
C3×C4×D212
C3×C4×D3×C72
#926912
#926902
#926892
#926882
#667283
#666753
#37987