Finite Group Databasebeta

← #44568908

Subgroups — #44568908

Order 32340.

208 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C3×C7×D385C211yesmaximal, characteristic, complemented
2C5×C3⋊(C7⋊D77)C211yesmaximal, characteristic, complemented
3C7×C11×D105C211yesmaximal, characteristic, complemented
4D35⋊D77—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D21×D77—51nomaximal, Hall
7C7×D385D311yescharacteristic, complemented
8C7×C11×D35—31no—
9C5×C7⋊D77—31no—
10D15⋊D77—71nomaximal
11D55⋊D21—71nomaximal
12C3⋊(C7⋊D77)D511yescharacteristic, complemented
13C7×C11×D21—51no—
14C3×C7×D77—51no—
15D35⋊D21—111nomaximal, Hall
16C5×C72×C11C2×D311yescharacteristic, complemented, Hall
17C11×D105D711yescharacteristic, complemented
18C7×C11×D15—71no—
19C5×D231—71no—
20C5×D231—71no—
21C5×D231—143no—
22C3×D385D711yescharacteristic, complemented
23C3×C7×D55—71no—
24D7×D77—151noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D35⋊D11—211no—
27D5×D77—211no—
28C7×D105D1111yescharacteristic, complemented
29C5×C3⋊(C7⋊D7)—111no—
30C3×C7×D35—111no—
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C2×D711yescharacteristic, complemented
34C7⋊D77—31no—
35C7×D77—51no—
36C7×C11×D7—151no—
37D35⋊D7—331noHall
38D3×D77—351no—
39D11×D21—351no—
40D385D2111yescharacteristic, complemented
41C11×D35—31no—
42C7×D55—71no—
43C7×D5×C11—211no—
44C5×D77—211no—
45C5×D77—211no—
46C5×D77—423no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48D15⋊D11—491noHall
49D7×D21—551noHall
50C72×C11D3×D511yescharacteristic, complemented, Hall
51C7×D35—31no—
52C7×D35—111no—
53C5×C7⋊D7—331no—
54D231—71no—
55D231—71no—
56D231—143no—
57C11×D21—51no—
58D3×C7×C11—351no—
59C3×D77—51no—
60C3×C7×D11—351no—
61D15⋊D7—771no—
62D5×D21—771no—
63C5×C7×C11—23no—
64C5×C7×C11D3×D711yescharacteristic, complemented
65C5×C7×C11C2×D2111yescharacteristic, complemented
66C11×D15—71no—
67C5×D33—491no—
68C3×D55—71no—
69C2×D77—1051no—
70D7×D11—1051no—
71C3⋊(C7⋊D7)—111no—
72C7×D21—51no—
73C3×C7×D7—551no—
74C5×C72D3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11D5×D711yescharacteristic, complemented
78D5×D11—1471noHall
79D105D7711yescharacteristic, complemented
80C7×D15—71no—
81C5×D21—771no—
82C5×D21—771no—
83C5×D21—1543no—
84C3×D35—111no—
85C3×C7×D5—771no—
86D72—1651noHall
87C3×C5×C11D7211yescharacteristic, complemented, Hall
88C2×C7×C11—1051no—
89D77—51no—
90D77—211no—
91D77—211no—
92D77—423no—
93C7×D11—351no—
94C11×D7—151no—
95C3×C72D5×D1111yescharacteristic, complemented, Hall
96D5×D7—2311no—
97D5×D7—2311no—
98D3×D11—2451noHall
99D55—71no—
100C5×D11—1471no—
101D5×C11—211no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1111yescharacteristic, complemented
104C3×C5×C7C2×D7711yescharacteristic, complemented
105C7⋊D7—331no—
106C7×D7—151no—
107C7×D7—551no—
108C2×D21—3851no—
109D3×D7—3851no—
110C7×C11—23no—
111C7×C11D5×D2111yescharacteristic, complemented
112C7×C11D15⋊D711yescharacteristic, complemented
113D35—31no—
114D35—111no—
115C5×D7—4623no—
116C5×D7—2311no—
117C5×D7—2311no—
118C7×D5—211no—
119C7×D5—771no—
120D33—491no—
121C3×D11—351no—
122D3×C11—351no—
123D3×D5—5391noHall
124C5×C11D7×D2111yescharacteristic, complemented, Hall
125C72D15⋊D1111yescharacteristic, complemented, Sylow
126C2×D11—7351noHall
127C2×C3×C7—3851no—
128D21—51no—
129D21—771no—
130D21—771no—
131D21—1543no—
132C3×D7—551no—
133D3×C7—351no—
134C5×C7—23no—
135C5×C7D11×D2111yescharacteristic, complemented
136C5×C7D3×D7711yescharacteristic, complemented
137C3×C11D35⋊D711yescharacteristic, complemented, Hall
138D15—71no—
139C3×D5—771no—
140C5×D3—5391no—
141C2×D7—11551no—
142C2×D7—11551no—
143C2×C11—1051no—
144D11—351no—
145D11—1471no—
146C3×C7—23no—
147C3×C7D5×D7711yescharacteristic, complemented
148C3×C7D35⋊D1111yescharacteristic, complemented
149C2×D5—16171noHall
150C3×C5D7×D7711yescharacteristic, complemented, Hall
151C2×C7—1051no—
152C2×C7—3851no—
153D7—151no—
154D7—551no—
155D7—4623no—
156D7—2311no—
157D7—2311no—
158C2×D3—26951noHall
159C11D35⋊D2111yescharacteristic, complemented, Sylow
160C2×C5—16171no—
161D5—211no—
162D5—771no—
163C7—23no—
164C7D55⋊D2111yescharacteristic, complemented
165C7D15⋊D7711yescharacteristic, complemented
166C2×C3—3851no—
167D3—5391no—
168D3—351no—
169C5D21×D7711yescharacteristic, complemented, Sylow
170C22—80851noSylow
171C3D35⋊D7711yescharacteristic, complemented, Sylow
172C2—16171no—
173C2—1051no—
174C2—3851no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×D385C2semidirect
2. C5×C3⋊(C7⋊D77)C2semidirect
3. C7×C11×D105C2semidirect
5. C3×C5×C72×C11C22semidirect
7. C7×D385D3semidirect
12. C3⋊(C7⋊D77)D5semidirect
16. C5×C72×C11C2×D3semidirect
17. C11×D105D7semidirect
22. C3×D385D7semidirect
25. C3×C72×C11C2×D5semidirect
28. C7×D105D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C2×D7semidirect
40. D385D21semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11D3×D5semidirect
64. C5×C7×C11D3×D7semidirect
65. C5×C7×C11C2×D21semidirect
74. C5×C72D3×D11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11D5×D7semidirect
79. D105D77semidirect
87. C3×C5×C11D72semidirect
95. C3×C72D5×D11semidirect
103. C3×C5×C7D7×D11semidirect
104. C3×C5×C7C2×D77semidirect
111. C7×C11D5×D21semidirect
112. C7×C11D15⋊D7semidirect
124. C5×C11D7×D21semidirect
125. C72D15⋊D11semidirect
135. C5×C7D11×D21semidirect
136. C5×C7D3×D77semidirect
137. C3×C11D35⋊D7semidirect
147. C3×C7D5×D77semidirect
148. C3×C7D35⋊D11semidirect
150. C3×C5D7×D77semidirect
159. C11D35⋊D21semidirect
164. C7D55⋊D21semidirect
165. C7D15⋊D77semidirect
169. C5D21×D77semidirect
171. C3D35⋊D77semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3852
C5×C3⋊(C7⋊D77)2
C7×C11×D1052
D35⋊D773
D21×D775
D15⋊D777
D55⋊D217
D35⋊D2111