Finite Group Databasebeta

← #11759618

Subgroups — #11759618

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
1#92726C211yesmaximal, characteristic, complemented
2C2×C3×Dic21C211yesmaximal, characteristic, complemented
3C3×C7×#67C211yesmaximal, characteristic, complemented
4#92691C211yesmaximal, characteristic, complemented
5#92690C211yesmaximal, characteristic, complemented
6#92687C211yesmaximal, characteristic, complemented
7D3×Dic21C211yesmaximal, characteristic, complemented
8#66730—31nomaximal
9#66686—31nomaximal
10C22×C32×C7C2211yescharacteristic
11C2×C3⋊D21C2211yescharacteristic
12C2×C3×D3×C7C2211yescharacteristic
13C3⋊Dic21C2211yescharacteristic
14C3×Dic21C2211yescharacteristic
15C3×Dic21C2211yescharacteristic
16C3×C7×Dic3C2211yescharacteristic
17C3×C7×D4—31no—
18#4268—31no—
19#4268—31no—
20#4268—31no—
21#4268—61no—
22C2×Dic21—31no—
23C2×Dic21D311yescharacteristic, complemented
24C4×D21—31no—
25Dic42—31no—
26C7×#67D311yescharacteristic, complemented
27C2×C3×Dic7—31no—
28#4248—31no—
29#4247—31no—
30D21⋊C4—31no—
31D3×Dic7—31no—
32#3804—71nomaximal, Hall
33C2×C32×C7—21no—
34C2×C32×C7C2311yescharacteristic
35C3⋊D21—21no—
36C3×D3×C7—21no—
37#1159—91noHall
38C22×C3×C7—21no—
39C22×C3×C7—31no—
40C22×C3×C7C2×D311yescharacteristic
41C22×C3×C7C2×D311yescharacteristic
42C2×D21—31no—
43C2×D21—31no—
44C2×D21—61no—
45C2×D3×C7C2×D311yescharacteristic
46C3×C4×C7—31no—
47Dic21—31no—
48Dic21—31no—
49Dic21—61no—
50Dic21C2×D311yescharacteristic
51Dic21C2×D311yescharacteristic
52C3×Dic7—31no—
53C3×Dic7—31no—
54C7×Dic3C2×D311yescharacteristic
55#638—71no—
56C3×#67D711yescharacteristic, complemented
57C2×C3×Dic3—71no—
58#627—71no—
59#626—71no—
60#624—71no—
61D3×Dic3—71no—
62C32×C7#4111yescharacteristic, complemented, Hall
63C7×D4—31no—
64C22⋊D7—91no—
65C22⋊D7—91no—
66C2×Dic7—31no—
67C2×Dic7—91no—
68C4×D7—91no—
69Dic14—91no—
70#237—211no—
71#235—211no—
72C2×C3×C7—21no—
73C2×C3×C7—21no—
74C2×C3×C7—21no—
75C2×C3×C7—41no—
76C2×C3×C7—61no—
77C2×C3×C7C22×D311yescharacteristic
78C2×C3×C7C22×D311yescharacteristic
79D21—61no—
80D21—61no—
81D21—121no—
82D3×C7—21no—
83C22×C32C2×D711yescharacteristic
84C2×C3⋊D3—71no—
85C2×C3×D3C2×D711yescharacteristic
86C3⋊Dic3—71no—
87C3×Dic3—71no—
88C3×Dic3—71no—
89C3×Dic3C2×D711yescharacteristic
90C22×C7—31no—
91C22×C7D3211yescharacteristic
92C2×D7—91no—
93C4×C7—31no—
94Dic7—31no—
95Dic7—31no—
96Dic7—91no—
97C3×D4—31no—
98C2×C3×C4—211no—
99#67—211no—
100#67—211no—
101#67—211no—
102#67—421no—
103#67D2111yescharacteristic, complemented
104C2×Dic3—71no—
105C2×Dic3—211no—
106D12—211no—
107C4×D3—211no—
108C4×D3—211no—
109C4×D3—211no—
110Dic6—211no—
111Dic6—211no—
112C3×C7—21no—
113C3×C7#23511yescharacteristic, complemented
114C3×C7#23711yescharacteristic, complemented
115C2×C32—21no—
116C2×C32C22×D711yescharacteristic
117C3⋊D3—141no—
118C3×D3—21no—
119#41—631noSylow
120C2×C7—21no—
121C2×C7—61no—
122C2×C7C2×D3211yescharacteristic
123D7—181no—
124C22×C3—21no—
125C22×C3—31no—
126C22×C3D3×D711yescharacteristic
127C22×C3C2×D2111yescharacteristic
128C2×D3—211no—
129C2×D3—211no—
130C2×D3—421no—
131C2×D3C2×D2111yescharacteristic
132C3×C4—31no—
133C3×C4—211no—
134C3×C4—211no—
135Dic3—71no—
136Dic3—71no—
137Dic3—211no—
138Dic3—211no—
139Dic3—421no—
140Dic3C2×D2111yescharacteristic
141C32#115911yescharacteristic, complemented, Sylow
142Q8—631no—
143D4—31no—
144D4—631no—
145D4—631no—
146C2×C4—211no—
147C2×C4—631no—
148C2×C4—631no—
149C7#380411yescharacteristic, complemented, Sylow
150C2×C3—21no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—41no—
154C2×C3—61no—
155C2×C3C2×D3×D711yescharacteristic
156C2×C3C22×D2111yescharacteristic
157D3—21no—
158D3—421no—
159D3—421no—
160D3—841no—
161C22—31no—
162C22—631no—
163C22D3×D2111yescharacteristic
164C4—31no—
165C4—211no—
166C4—211no—
167C4—631no—
168C3—21no—
169C3#6668611yescharacteristic, complemented
170C3#6673011yescharacteristic, complemented
171C2—21no—
172C2—61no—
173C2—1261no—
174C2C2×D3×D2111yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×D21
commutator, socle, cosocleC2×C32×C7C23
FittingC22×C32×C7C22
hypercenterC22D3×D21
hypocenterC32×C7#41
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #92726C2semidirect
2. C2×C3×Dic21C2semidirect
3. C3×C7×#67C2semidirect
4. #92691C2semidirect
5. #92690C2semidirect
6. #92687C2semidirect
7. D3×Dic21C2semidirect
23. C2×Dic21D3semidirect
26. C7×#67D3semidirect
56. C3×#67D7semidirect
62. C32×C7#41semidirect
103. #67D21semidirect
113. C3×C7#235semidirect
114. C3×C7#237semidirect
141. C32#1159semidirect
149. C7#3804semidirect
169. C3#66686semidirect
170. C3#66730semidirect

Maximal subgroups

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

subgroupindex
#927262
C2×C3×Dic212
C3×C7×#672
#926912
#926902
#926872
D3×Dic212
#667303
#666863
#38047