Finite Group Databasebeta

← D21×#10624391 #44479119

Subgroups — D21×#10624391 #44479119

Order 30492.

136 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 21 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
2C3⋊(C7⋊#10624391)C211yesmaximal, characteristic, complemented
3C3×C7×#10624391C211yesmaximal, characteristic, complemented
4C11×D11×D21—31nomaximal
5D7×#10624391—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C11×D231—31no—
8C112×D21D311yescharacteristic, complemented
9C3×C7×C11×D11—31no—
10D7×C112⋊C3—31no—
11C7⋊#10624391—31no—
12C7⋊#10624391—61no—
13C7×#10624391D311yescharacteristic, complemented
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⋊#10624391—71no—
21C3×#10624391D711yescharacteristic, complemented
22C11×D77—91no—
23C112×D7—31no—
24C7×C11×D11—31no—
25D3×C11×D11—211no—
26C2×#10624391—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28C2×C11×D21—331no—
29D11×D21—31no—
30C7×C112D3211yescharacteristic, complemented, Hall
31C11×D33—211no—
32D3×C112—71no—
33C3×C11×D11—31no—
34C2×C112⋊C3—211no—
35#10624391—211no—
36#10624391—421no—
37#10624391D2111yescharacteristic, direct product factor
38C2×C11×D11—631noHall
39C2×C3×C7×C11—331no—
40D231—31no—
41C11×D21—61no—
42C11×D21—61no—
43C11×D21—61no—
44C11×D21—331no—
45C3×C7×D11—31no—
46C3×C112D3×D711yescharacteristic, complemented
47C112⋊C3—21no—
48C112⋊C3C2×D2111yescharacteristic, complemented
49C2×C11×D7—991no—
50D7×D11—91no—
51D3×D21—1211nomaximal, Hall
52C2×C112—211no—
53C11×D11—31no—
54C11×D11—631no—
55C3×C7×C11—61no—
56C3×C7×C11—61no—
57C3×C7×C11—61no—
58C2×C7×C11—331no—
59D77—91no—
60C7×D11—31no—
61C11×D7—181no—
62C11×D7—181no—
63C11×D7—181no—
64C11×D7—991no—
65C2×D3×C11—2311no—
66D3×D11—211no—
67C3⋊D21—1211no—
68C3×D21—1211no—
69C3×D3×C7—1211no—
70C112D3×D2111yescharacteristic, complemented, Sylow
71C2×D21—331no—
72D3×D7—3631no—
73C7×C11—61no—
74C7×C11—61no—
75C7×C11—61no—
76C2×C3×C11—331no—
77D33—211no—
78C3×D11—31no—
79D3×C11—421no—
80D3×C11—421no—
81D3×C11—421no—
82D3×C11—2311no—
83C32×C7—1211noHall
84C22×C11—6931no—
85C2×D11—631no—
86C2×C3×C7—331no—
87D21—331no—
88D21—3631no—
89D21—7261no—
90D21#1062439111yescharacteristic, direct product factor
91C3×D7—7261no—
92D3×C7—1211no—
93D32—8471noHall
94C3×C11—61no—
95C3×C11—61no—
96C3×C11—61no—
97C2×D7—991noHall
98C2×C11—331no—
99C2×C11—631no—
100C2×C11—631no—
101C2×C11—1261no—
102C2×C11—6931no—
103D11—31no—
104D11—631no—
105C3×C7—2421no—
106C3×C7—2421no—
107C3×C7C2×#1062439111yescharacteristic, complemented
108C3⋊D3—8471no—
109C3×D3—1211no—
110C3×D3—16941no—
111C2×C7—331no—
112D7—31no—
113D7—991no—
114C2×D3—2311no—
115C2×D3—25411no—
116C11—31no—
117C11—31no—
118C11—61no—
119C32—2421noSylow
120C7D3×#1062439111yescharacteristic, complemented, Sylow
121C2×C3—331no—
122C2×C3—50821no—
123D3—71no—
124D3—1211no—
125D3—50821no—
126D3—2311no—
127D3—25411no—
128C22—6931noSylow
129C3—4841no—
130C3—2421no—
131C3D7×#1062439111yescharacteristic, complemented
132C2—211no—
133C2—331no—
134C2—6931no—
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. C3⋊(C7⋊#10624391)C2semidirect
3. C3×C7×#10624391C2semidirect
6. C3×C7×C112⋊C3C22semidirect
8. C112×D21D3semidirect
13. C7×#10624391D3semidirect
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C2×D3semidirect
21. C3×#10624391D7semidirect
27. C3×C112⋊C3C2×D7semidirect
30. C7×C112D32semidirect
37. #10624391D21direct (N × H)
46. C3×C112D3×D7semidirect
48. C112⋊C3C2×D21semidirect
70. C112D3×D21semidirect
90. D21#10624391direct (N × H)
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
C3⋊(C7⋊#10624391)2
C3×C7×#106243912
C11×D11×D213
D7×#106243913
D3×#106243917
D3×D21121