Finite Group Databasebeta

← C7×D15×D77 #44568871

Subgroups — C7×D15×D77 #44568871

Order 32340.

208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 52 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×C5×C7×D77C211yesmaximal, characteristic, complemented
2C72×C11×D15C211yesmaximal, characteristic, complemented
3C7×D1155C211yesmaximal, characteristic, complemented
4C7×D5×D77—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D3×C7×D77—51nomaximal, Hall
7C7×D385—31no—
8C72×D5×C11—31no—
9C5×C7×D77D311yescharacteristic, complemented
10D15×D77C711yesmaximal, characteristic, direct product factor
11C7×D11×D15—71nomaximal
12C7×D231—51no—
13D3×C72×C11—51no—
14C3×C7×D77D511yescharacteristic, complemented
15C7×D7×D15—111nomaximal, Hall
16C5×C72×C11C2×D311yescharacteristic, complemented, Hall
17D1155C2×C711yescharacteristic, complemented
18C7×D165—71no—
19C7×C11×D15—23no—
20C7×C11×D15D711yescharacteristic, complemented
21C7×C11×D15C2×C711yescharacteristic, complemented
22C3×C5×D77C2×C711yescharacteristic, complemented
23C3×C5×C7×D11—71no—
24C2×C7×D77—151noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D5×D77—31no—
27C7×D5×D11—211no—
28C7×D105—111no—
29C72×D15D1111yescharacteristic, complemented
30C3×C5×C7×D7—111no—
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C22×C711yescharacteristic, complemented
34C2×C72×C11—151no—
35C7×D77—151no—
36C7×D77D1511yescharacteristic, direct product factor
37C7×D5×D7—331noHall
38D3×D77—51no—
39D3×C7×D11—351no—
40D385—31no—
41C7×D55—211no—
42C7×D5×C11—31no—
43C7×D5×C11—31no—
44C7×D5×C11—63no—
45C5×D77D3×C711yescharacteristic, complemented
46C5×C7×D11—71no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48D11×D15—71noHall
49D3×C7×D7—551noHall
50C72×C11C2×D1511yescharacteristic, complemented, Hall
51C7×D35—331no—
52C72×D5—31no—
53C5×C7×D7—111no—
54D231—51no—
55C7×D33—351no—
56D3×C7×C11—51no—
57D3×C7×C11—51no—
58D3×C7×C11—103no—
59C3×D77C7×D511yescharacteristic, complemented
60C3×C7×D11—71no—
61C2×C7×D15—771no—
62D7×D15—111no—
63C5×C7×C11—23no—
64C5×C7×C11D3×D711yescharacteristic, complemented
65C5×C7×C11C2×D3×C711yescharacteristic, complemented
66D165—71no—
67C11×D15C7×D711yescharacteristic, complemented
68C3×C5×D11—71no—
69C2×D77—151no—
70C2×C7×D11—1051no—
71C7×D21—551no—
72D3×C72—51no—
73C3×C7×D7—111no—
74C5×C72D3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11C2×C7×D511yescharacteristic, complemented
78D5×D11—211noHall
79C2×C3×C5×C7—771no—
80D105—111no—
81C7×D15—23no—
82C7×D15—771no—
83C7×D15C7×D1111yescharacteristic, complemented
84C7×D15D7711yescharacteristic, direct product factor
85C3×C5×D7—111no—
86C2×C7×D7—1651noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—151no—
89C2×C7×C11—151no—
90C2×C7×C11—303no—
91D77—151no—
92D77C7×D1511yescharacteristic, direct product factor
93C7×D11—71no—
94C7×D11—1051no—
95C3×C72D5×D1111yescharacteristic, complemented, Hall
96C2×C7×D5—2311no—
97D5×D7—331no—
98D3×D11—351noHall
99D55—211no—
100C5×D11—71no—
101D5×C11—31no—
102C3×C5×C7—23no—
103C3×C5×C7C2×C7×D1111yescharacteristic, complemented
104C3×C5×C7C2×D7711yescharacteristic, complemented
105C2×C72—151no—
106C7×D7—111no—
107C7×D7—1651no—
108C2×D3×C7—3851no—
109D3×D7—551no—
110C7×C11—23no—
111C7×C11D7×D1511yescharacteristic, complemented
112C7×C11C2×C7×D1511yescharacteristic, complemented
113C2×C5×C7—771no—
114D35—331no—
115C5×D7—111no—
116C7×D5—31no—
117C7×D5—31no—
118C7×D5—63no—
119C7×D5—2311no—
120D33—351no—
121C3×D11—71no—
122D3×C11—51no—
123C2×D15—771noHall
124C5×C11D3×C7×D711yescharacteristic, complemented, Hall
125C72D11×D1511yescharacteristic, complemented, Sylow
126C2×D11—1051noHall
127C2×C3×C7—771no—
128D21—551no—
129C3×D7—111no—
130D3×C7—51no—
131D3×C7—51no—
132D3×C7—103no—
133D3×C7—3851no—
134C5×C7—23no—
135C5×C7D3×C7×D1111yescharacteristic, complemented
136C5×C7D3×D7711yescharacteristic, complemented
137C3×C11C7×D5×D711yescharacteristic, complemented, Hall
138C2×C3×C5—771no—
139D15—771no—
140D15C7×D7711yescharacteristic, direct product factor
141C22×C7—11551no—
142C2×D7—1651no—
143C2×C11—151no—
144D11—71no—
145D11—1051no—
146C3×C7—23no—
147C3×C7C7×D5×D1111yescharacteristic, complemented
148C3×C7D5×D7711yescharacteristic, complemented
149C2×D5—2311noHall
150C3×C5C2×C7×D7711yescharacteristic, complemented, Hall
151C2×C7—151no—
152C2×C7—151no—
153C2×C7—303no—
154C2×C7—771no—
155C2×C7—11551no—
156D7—111no—
157D7—1651no—
158C2×D3—3851noHall
159C11C7×D7×D1511yescharacteristic, complemented, Sylow
160C2×C5—771no—
161D5—31no—
162D5—2311no—
163C7—23no—
164C7C7×D11×D1511yescharacteristic, complemented
165C7D15×D7711yescharacteristic, direct product factor
166C2×C3—771no—
167D3—51no—
168D3—3851no—
169C5D3×C7×D7711yescharacteristic, complemented, Sylow
170C22—11551noSylow
171C3C7×D5×D7711yescharacteristic, complemented, Sylow
172C2—151no—
173C2—771no—
174C2—11551no—
subgroupG/H
center, hypercenterC7D15×D77
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D77C2semidirect
2. C72×C11×D15C2semidirect
3. C7×D1155C2semidirect
5. C3×C5×C72×C11C22semidirect
9. C5×C7×D77D3semidirect
10. D15×D77C7direct (N × H)
14. C3×C7×D77D5semidirect
16. C5×C72×C11C2×D3semidirect
17. D1155C2×C7semidirect
20. C7×C11×D15D7semidirect
21. C7×C11×D15C2×C7semidirect
22. C3×C5×D77C2×C7semidirect
25. C3×C72×C11C2×D5semidirect
29. C72×D15D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
36. C7×D77D15direct (N × H)
45. C5×D77D3×C7semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11C2×D15semidirect
59. C3×D77C7×D5semidirect
64. C5×C7×C11D3×D7semidirect
65. C5×C7×C11C2×D3×C7semidirect
67. C11×D15C7×D7semidirect
74. C5×C72D3×D11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11C2×C7×D5semidirect
83. C7×D15C7×D11semidirect
84. C7×D15D77direct (N × H)
87. C3×C5×C11C2×C7×D7semidirect
92. D77C7×D15direct (N × H)
95. C3×C72D5×D11semidirect
103. C3×C5×C7C2×C7×D11semidirect
104. C3×C5×C7C2×D77semidirect
111. C7×C11D7×D15semidirect
112. C7×C11C2×C7×D15semidirect
124. C5×C11D3×C7×D7semidirect
125. C72D11×D15semidirect
135. C5×C7D3×C7×D11semidirect
136. C5×C7D3×D77semidirect
137. C3×C11C7×D5×D7semidirect
140. D15C7×D77direct (N × H)
147. C3×C7C7×D5×D11semidirect
148. C3×C7D5×D77semidirect
150. C3×C5C2×C7×D77semidirect
159. C11C7×D7×D15semidirect
164. C7C7×D11×D15semidirect
165. C7D15×D77direct (N × H)
169. C5D3×C7×D77semidirect
171. C3C7×D5×D77semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D772
C72×C11×D152
C7×D11552
C7×D5×D773
D3×C7×D775
D15×D777
C7×D11×D157
C7×D7×D1511