Finite Group Databasebeta

← #44568907

Subgroups — #44568907

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×C11×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C7×D1155C211yesmaximal, characteristic, complemented
4(C7⋊D7)⋊D55—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D77⋊D21—51nomaximal, Hall
7C7×D385—31no—
8C7×D385D311yescharacteristic, complemented
9C5×C11×C7⋊D7—31no—
10D21⋊D55—71nomaximal
11D21×D55—71nomaximal
12C11×C3⋊(C7⋊D7)D511yescharacteristic, complemented
13C7×D231—51no—
14C3×C7×D77—51no—
15D35⋊D21—111nomaximal, Hall
16C5×C72×C11C2×D311yescharacteristic, complemented, Hall
17D1155D711yescharacteristic, complemented
18C7×D165—71no—
19C5×C11×D21—71no—
20C5×C11×D21—71no—
21C5×C11×D21—143no—
22C3×D385D711yescharacteristic, complemented
23C3×C7×D55—71no—
24(C7⋊D7)⋊D11—151noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D7×D55—211no—
27D7×D55—211no—
28C7×D105—111no—
29C5×C3⋊(C7⋊D7)D1111yescharacteristic, complemented
30C3×C7×D35—111no—
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C2×D711yescharacteristic, complemented
34C11×C7⋊D7—31no—
35C7×D77—51no—
36C7×D77—151no—
37D35⋊D7—331noHall
38D21⋊D11—351no—
39D11×D21—351no—
40D385—31no—
41D385D2111yescharacteristic, complemented
42C7×D55—71no—
43C7×D55—211no—
44C5×C11×D7—211no—
45C5×C11×D7—211no—
46C5×C11×D7—423no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48D3×D55—491noHall
49D7×D21—551noHall
50C72×C11D3×D511yescharacteristic, complemented, Hall
51C7×D35—111no—
52C7×D35—331no—
53C5×C7⋊D7—31no—
54D231—51no—
55C11×D21—71no—
56C11×D21—71no—
57C11×D21—143no—
58C7×D33—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
66D165—71no—
67C5×D3×C11—491no—
68C3×D55—71no—
69D7×D11—1051no—
70D7×D11—1051no—
71C3⋊(C7⋊D7)D5511yescharacteristic, complemented
72C7×D21—551no—
73C3×C7×D7—551no—
74C5×C72D3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11D5×D711yescharacteristic, complemented
78C2×D55—1471noHall
79D105—111no—
80C7×D15—771no—
81C5×D21—71no—
82C5×D21—71no—
83C5×D21—143no—
84C3×D35—111no—
85C3×C7×D5—771no—
86D72—1651noHall
87C3×C5×C11D7211yescharacteristic, complemented, Hall
88D77—51no—
89D77—151no—
90C7×D11—351no—
91C7×D11—1051no—
92C11×D7—211no—
93C11×D7—211no—
94C11×D7—423no—
95C3×C72C2×D5511yescharacteristic, complemented, Hall
96D5×D7—2311no—
97D5×D7—2311no—
98D3×D11—2451noHall
99C2×C5×C11—1471no—
100D55—71no—
101D55—211no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1111yescharacteristic, complemented
104C3×C5×C7D7×D1111yescharacteristic, complemented
105C7⋊D7—31no—
106C7×D7—551no—
107C7×D7—1651no—
108C2×D21—3851no—
109D3×D7—3851no—
110C7×C11—23no—
111C7×C11D5×D2111yescharacteristic, complemented
112C7×C11D15⋊D711yescharacteristic, complemented
113D35—111no—
114D35—331no—
115C5×D7—211no—
116C5×D7—211no—
117C5×D7—423no—
118C7×D5—771no—
119C7×D5—2311no—
120D33—351no—
121C3×D11—351no—
122D3×C11—491no—
123D3×D5—5391noHall
124C5×C11D7×D2111yescharacteristic, complemented, Hall
125C72D3×D5511yescharacteristic, complemented, Sylow
126C2×D11—7351noHall
127C2×C3×C7—3851no—
128D21—71no—
129D21—71no—
130D21—143no—
131D21—551no—
132C3×D7—551no—
133D3×C7—3851no—
134C5×C7—23no—
135C5×C7D11×D2111yescharacteristic, complemented
136C5×C7D21⋊D1111yescharacteristic, complemented
137C3×C11D35⋊D711yescharacteristic, complemented, Hall
138D15—771no—
139C3×D5—771no—
140C5×D3—491no—
141C2×D7—11551no—
142C2×D7—11551no—
143C2×C11—1471no—
144D11—351no—
145D11—1051no—
146C3×C7—23no—
147C3×C7D7×D5511yescharacteristic, complemented
148C3×C7D7×D5511yescharacteristic, complemented
149C2×D5—16171noHall
150C3×C5(C7⋊D7)⋊D1111yescharacteristic, complemented, Hall
151C2×C7—3851no—
152C2×C7—11551no—
153D7—211no—
154D7—211no—
155D7—423no—
156D7—551no—
157D7—1651no—
158C2×D3—26951noHall
159C11D35⋊D2111yescharacteristic, complemented, Sylow
160C2×C5—1471no—
161D5—771no—
162D5—2311no—
163C7—23no—
164C7D21×D5511yescharacteristic, complemented
165C7D21⋊D5511yescharacteristic, complemented
166C2×C3—3851no—
167D3—491no—
168D3—3851no—
169C5D77⋊D2111yescharacteristic, complemented, Sylow
170C22—80851noSylow
171C3(C7⋊D7)⋊D5511yescharacteristic, complemented, Sylow
172C2—3851no—
173C2—11551no—
174C2—1471no—
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×C11×C3⋊(C7⋊D7)C2semidirect
3. C7×D1155C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C7×D385D3semidirect
12. C11×C3⋊(C7⋊D7)D5semidirect
16. C5×C72×C11C2×D3semidirect
17. D1155D7semidirect
22. C3×D385D7semidirect
25. C3×C72×C11C2×D5semidirect
29. C5×C3⋊(C7⋊D7)D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C2×D7semidirect
41. D385D21semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11D3×D5semidirect
64. C5×C7×C11D3×D7semidirect
65. C5×C7×C11C2×D21semidirect
71. C3⋊(C7⋊D7)D55semidirect
74. C5×C72D3×D11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11D5×D7semidirect
87. C3×C5×C11D72semidirect
95. C3×C72C2×D55semidirect
103. C3×C5×C7D7×D11semidirect
104. C3×C5×C7D7×D11semidirect
111. C7×C11D5×D21semidirect
112. C7×C11D15⋊D7semidirect
124. C5×C11D7×D21semidirect
125. C72D3×D55semidirect
135. C5×C7D11×D21semidirect
136. C5×C7D21⋊D11semidirect
137. C3×C11D35⋊D7semidirect
147. C3×C7D7×D55semidirect
148. C3×C7D7×D55semidirect
150. C3×C5(C7⋊D7)⋊D11semidirect
159. C11D35⋊D21semidirect
164. C7D21×D55semidirect
165. C7D21⋊D55semidirect
169. C5D77⋊D21semidirect
171. C3(C7⋊D7)⋊D55semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3852
C5×C11×C3⋊(C7⋊D7)2
C7×D11552
(C7⋊D7)⋊D553
D77⋊D215
D21⋊D557
D21×D557
D35⋊D2111