Finite Group Databasebeta

← D175⋊D33 #37528307

Subgroups — D175⋊D33 #37528307

Order 23100.

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 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
1C7×D825C211yesmaximal, characteristic, complemented
2C25×D231C211yesmaximal, characteristic, complemented
3C3×C11×D175C211yesmaximal, characteristic, complemented
4D77⋊D25—31nomaximal, Hall
5C3×C7×C11×C25C2211yescharacteristic, complemented, Hall
6D35⋊D33—51nomaximal
7C11×D175D311yescharacteristic, complemented
8C7×D275—31no—
9C25×D77—31no—
10D25×D33—71nomaximal, Hall
11C7×D165—51no—
12C5×D231D511yescharacteristic
13C3×C11×D35—51no—
14D21⋊D25—111nomaximal, Hall
15C7×C11×C25C2×D311yescharacteristic, complemented, Hall
16D825D711yescharacteristic, complemented
17C25×D33—71no—
18C3×C11×D25—71no—
19D35⋊D11—151no—
20C3×C5×C7×C11C2×D511yescharacteristic
21D11×D25—211noHall
22C7×D75—111no—
23C25×D21—111no—
24C3×D175D1111yescharacteristic, complemented
25D7×D33—251noHall
26C3×C11×C25C2×D711yescharacteristic, complemented, Hall
27C11×D35—51no—
28C7×D55—151no—
29C5×D77—31no—
30D7×D25—331noHall
31D5×D33—351no—
32D275—31no—
33D11×C25—211no—
34C11×D25—71no—
35C3×C7×C25C2×D1111yescharacteristic, complemented, Hall
36D231D2511yescharacteristic, complemented
37C7×D33—251no—
38C3×C11×D7—251no—
39D15⋊D7—551no—
40C5×C7×C11D3×D511yescharacteristic
41D175D3311yescharacteristic, complemented
42D7×C25—331no—
43C7×D25—331no—
44D165—51no—
45C5×D33—71no—
46C3×D5×C11—351no—
47D7×D11—751noHall
48D3×D25—771noHall
49C11×C25D3×D711yescharacteristic, complemented, Hall
50C3×C7×C11C2×D2511yescharacteristic, complemented, Hall
51D5×D11—1051no—
52C7×D15—551no—
53C5×D21—111no—
54C3×D35—51no—
55C7×C25C2×D3311yescharacteristic, complemented, Hall
56C3×C5×C11D5×D711yescharacteristic
57D77—31no—
58C7×D11—751no—
59C11×D7—251no—
60D75—111no—
61C3×D25—71no—
62D3×C25—771no—
63D5×D7—1651no—
64C2×D33—1751noHall
65D55—151no—
66C5×D11—211no—
67D5×C11—351no—
68C3×C5×C7D5×D1111yescharacteristic
69C2×D25—2311noHall
70D3×D7—2751noHall
71C7×C11D3×D2511yescharacteristic, complemented, Hall
72C3×C25D7×D1111yescharacteristic, complemented, Hall
73D35—51no—
74C5×D7—331no—
75C7×D5—1651no—
76C2×C3×C11—1751no—
77D33—71no—
78D33—251no—
79D3×D5—3851no—
80C5×C11D15⋊D711yescharacteristic
81C2×C25—2311no—
82D25—71no—
83D25—331no—
84C2×D11—5251noHall
85D21—111no—
86C3×D7—251no—
87D3×C7—2751no—
88C5×C7D5×D3311yescharacteristic
89C3×C11D7×D2511yescharacteristic, complemented, Hall
90D15—551no—
91C3×D5—351no—
92C5×D3—771no—
93C2×D7—8251noHall
94C25D7×D3311yescharacteristic, complemented, Sylow
95C2×C11—1751no—
96D11—211no—
97D11—751no—
98C3×C7D11×D2511yescharacteristic, complemented, Hall
99C2×D5—11551no—
100C3×C5D35⋊D1111yescharacteristic
101C2×C7—8251no—
102D7—251no—
103D7—331no—
104C2×D3—19251noHall
105C11D21⋊D2511yescharacteristic, complemented, Sylow
106C2×C5—2311no—
107D5—351no—
108D5—1651no—
109C7D25×D3311yescharacteristic, complemented, Sylow
110C2×C3—1751no—
111D3—2751no—
112D3—771no—
113C5D35⋊D3311yescharacteristic
114C22—57751noSylow
115C3D77⋊D2511yescharacteristic, complemented, Sylow
116C2—8251no—
117C2—1751no—
118C2—2311no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C7×C11×C25C22
FrattiniC5D35⋊D33
socleC3×C5×C7×C11C2×D5
LCSG ▷ C3×C7×C11×C25
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×D825C2semidirect
2. C25×D231C2semidirect
3. C3×C11×D175C2semidirect
5. C3×C7×C11×C25C22semidirect
7. C11×D175D3semidirect
15. C7×C11×C25C2×D3semidirect
16. D825D7semidirect
24. C3×D175D11semidirect
26. C3×C11×C25C2×D7semidirect
35. C3×C7×C25C2×D11semidirect
36. D231D25semidirect
41. D175D33semidirect
49. C11×C25D3×D7semidirect
50. C3×C7×C11C2×D25semidirect
55. C7×C25C2×D33semidirect
71. C7×C11D3×D25semidirect
72. C3×C25D7×D11semidirect
89. C3×C11D7×D25semidirect
94. C25D7×D33semidirect
98. C3×C7D11×D25semidirect
105. C11D21⋊D25semidirect
109. C7D25×D33semidirect
115. C3D77⋊D25semidirect

Maximal subgroups

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

subgroupindex
C7×D8252
C25×D2312
C3×C11×D1752
D77⋊D253
D35⋊D335
D25×D337
D21⋊D2511