Finite Group Databasebeta

← D21⋊#10624391 #44479128

Subgroups — D21⋊#10624391 #44479128

Order 30492.

136 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 20 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
1D21×C112⋊C3C211yesmaximal, characteristic, complemented
2C7×C3⋊#10624391C211yesmaximal, characteristic, complemented
3C3×C7⋊#10624391C211yesmaximal, characteristic, complemented
4C11×D21⋊D11—31nomaximal
5D7×#10624391—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C112×D21D311yescharacteristic, complemented
8C7×C11×D33—31no—
9C3×C11×D77—31no—
10D7×C112⋊C3—31no—
11C7⋊#10624391D311yescharacteristic, complemented
12C7×#10624391—31no—
13C7×#10624391—61no—
14D3×#10624391—71nomaximal, Hall
15C11×D7×D11—91noHall
16C7×C112⋊C3—21no—
17C7×C112⋊C3C2×D311yescharacteristic, complemented
18C3×C7×C112C2×D311yescharacteristic, complemented
19D3×C112⋊C3—71no—
20C3⋊#10624391D711yescharacteristic, complemented
21C3×#10624391—71no—
22C11×D77—31no—
23C112×D7—31no—
24C7×C11×D11—91no—
25D3×C11×D11—211no—
26C2×#10624391—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28D21⋊D11—31no—
29D3×C11×D7—331no—
30C7×C112D3211yescharacteristic, complemented, Hall
31C11×D33—31no—
32D3×C112—71no—
33C3×C11×D11—211no—
34C2×C112⋊C3—211no—
35#10624391—31no—
36#10624391—61no—
37#10624391—71no—
38C2×C11×D11—631noHall
39C11×D21—61no—
40C11×D21—61no—
41C11×D21—61no—
42C7×D33—31no—
43D3×C7×C11—331no—
44C3×D77—31no—
45C3×C11×D7—331no—
46C3×C112D3×D711yescharacteristic, complemented
47C112⋊C3—21no—
48C112⋊C3D3×D711yescharacteristic, complemented
49C2×C11×D7—991no—
50D7×D11—91no—
51(C3⋊D3)⋊D7—1211nomaximal, Hall
52C2×C112—211no—
53C11×D11—91no—
54C11×D11—211no—
55C3×C7×C11—61no—
56C3×C7×C11—61no—
57C3×C7×C11—61no—
58C2×C7×C11—991no—
59D77—31no—
60C7×D11—91no—
61C11×D7—91no—
62C11×D7—181no—
63C11×D7—181no—
64C11×D7—331no—
65C2×D3×C11—2311no—
66D3×D11—211no—
67C7×C3⋊D3—1211no—
68C3×D21—1211no—
69C3×D21—2421no—
70C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
71D3×D7—331no—
72D3×D7—3631no—
73C7×C11—31no—
74C7×C11—61no—
75C7×C11—61no—
76C2×C3×C11—2311no—
77D33—31no—
78C3×D11—211no—
79D3×C11—331no—
80D3×C11—421no—
81D3×C11—421no—
82D3×C11—421no—
83C32×C7—2421noHall
84C22×C11—6931no—
85C2×D11—631no—
86D21—1211no—
87D21#1062439111yescharacteristic, complemented
88C3×D7—331no—
89C3×D7—7261no—
90D3×C7—331no—
91D3×C7—3631no—
92D3×C7—7261no—
93D32—8471noHall
94C3×C11—61no—
95C3×C11—61no—
96C3×C11—61no—
97C2×D7—991noHall
98C2×C11—991no—
99C2×C11—1261no—
100C2×C11—1261no—
101C2×C11—1261no—
102C2×C11—2311no—
103D11—91no—
104D11—211no—
105C3×C7—4841no—
106C3×C7—2421no—
107C3×C7C2×#1062439111yescharacteristic, complemented
108C3⋊D3—1211no—
109C3×D3—8471no—
110C3×D3—16941no—
111C2×C7—991no—
112D7—31no—
113D7—331no—
114C2×D3—2311no—
115C2×D3—25411no—
116C11—61no—
117C11—61no—
118C11—61no—
119C32—2421noSylow
120C7D3×#1062439111yescharacteristic, complemented, Sylow
121C2×C3—50821no—
122C2×C3—2311no—
123D3—71no—
124D3—331no—
125D3—8471no—
126D3—3631no—
127D3—7261no—
128C22—6931noSylow
129C3—4841no—
130C3—2421no—
131C3D7×#1062439111yescharacteristic, complemented
132C2—211no—
133C2—991no—
134C2—2311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C7×C112⋊C3C22
Fitting, socleC3×C7×C112C2×D3
LCSG ▷ C3×C7×C112⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. D21×C112⋊C3C2semidirect
2. C7×C3⋊#10624391C2semidirect
3. C3×C7⋊#10624391C2semidirect
6. C3×C7×C112⋊C3C22semidirect
7. C112×D21D3semidirect
11. C7⋊#10624391D3semidirect
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C2×D3semidirect
20. C3⋊#10624391D7semidirect
27. C3×C112⋊C3C2×D7semidirect
30. C7×C112D32semidirect
46. C3×C112D3×D7semidirect
48. C112⋊C3D3×D7semidirect
70. C112(C3⋊D3)⋊D7semidirect
87. D21#10624391semidirect
107. C3×C7C2×#10624391semidirect
120. C7D3×#10624391semidirect
131. C3D7×#10624391semidirect

Maximal subgroups

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

subgroupindex
D21×C112⋊C32
C7×C3⋊#106243912
C3×C7⋊#106243912
C11×D21⋊D113
D7×#106243913
D3×#106243917
(C3⋊D3)⋊D7121