Finite Group Databasebeta

← C3×C7×D5×D77 #44568823

Subgroups — C3×C7×D5×D77 #44568823

Order 32340.

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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
2C3×C72×D5×C11C211yesmaximal, characteristic, complemented
3C3×C7×D385C211yesmaximal, characteristic, complemented
4C7×D5×D77C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×C3×C7×D77—51nomaximal, Hall
7C7×D385C2×C311yescharacteristic, complemented
8C72×D5×C11C2×C311yescharacteristic, complemented
9C5×C7×D77C2×C311yescharacteristic, complemented
10C3×D5×D77C711yesmaximal, characteristic, direct product factor
11C3×C7×D5×D11—71nomaximal
12C3×C7×D77—51no—
13C3×C7×D77D511yescharacteristic, direct product factor
14C2×C3×C72×C11—51no—
15C3×C7×D5×D7—111nomaximal, Hall
16C5×C72×C11C22×C311yescharacteristic, complemented, Hall
17C3×D385C2×C711yescharacteristic, complemented
18C3×C7×D55—71no—
19C3×C7×D5×C11—23no—
20C3×C7×D5×C11D711yescharacteristic, complemented
21C3×C7×D5×C11C2×C711yescharacteristic, complemented
22C3×C5×D77C2×C711yescharacteristic, complemented
23C3×C5×C7×D11—71no—
24C2×C7×D77—51noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D5×D77C3×C711yescharacteristic, direct product factor
27C7×D5×D11—71no—
28C3×C7×D35—111no—
29C3×C72×D5D1111yescharacteristic, 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—51no—
35C7×D77—51no—
36C7×D77C3×D511yescharacteristic, direct product factor
37C7×D5×D7—111noHall
38C2×C3×D77—51no—
39C2×C3×C7×D11—351no—
40D385C2×C3×C711yescharacteristic, complemented
41C7×D55—71no—
42C7×D5×C11—23no—
43C7×D5×C11C3×D711yescharacteristic, complemented
44C7×D5×C11C2×C3×C711yescharacteristic, complemented
45C5×D77C2×C3×C711yescharacteristic, complemented
46C5×C7×D11—71no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48C3×D5×D11—71noHall
49C2×C3×C7×D7—551noHall
50C72×C11C2×C3×D511yescharacteristic, complemented, Hall
51C7×D35—111no—
52C72×D5C3×D1111yescharacteristic, complemented
53C5×C7×D7—111no—
54C2×C3×C7×C11—51no—
55C2×C3×C7×C11—51no—
56C2×C3×C7×C11—103no—
57C3×D77—51no—
58C3×D77C7×D511yescharacteristic, direct product factor
59C3×C7×D11—71no—
60C3×C7×D11—351no—
61C2×C3×C7×D5—771no—
62C3×D5×D7—111no—
63C5×C7×C11—23no—
64C5×C7×C11C2×C3×D711yescharacteristic, complemented
65C5×C7×C11C22×C3×C711yescharacteristic, complemented
66C3×D55—71no—
67C3×D5×C11C7×D711yescharacteristic, complemented
68C3×C5×D11—71no—
69C2×D77—51no—
70C2×C7×D11—351no—
71C2×C3×C72—51no—
72C3×C7×D7—111no—
73C3×C7×D7—551no—
74C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11C2×C7×D511yescharacteristic, complemented
78D5×D11—71noHall
79C2×C3×C5×C7—771no—
80C3×D35—111no—
81C3×C7×D5—23no—
82C3×C7×D5—771no—
83C3×C7×D5C7×D1111yescharacteristic, complemented
84C3×C7×D5D7711yescharacteristic, direct product factor
85C3×C5×D7—111no—
86C2×C7×D7—551noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—51no—
89C2×C7×C11—51no—
90C2×C7×C11—103no—
91D77—51no—
92D77C3×C7×D511yescharacteristic, direct product factor
93C7×D11—71no—
94C7×D11—351no—
95C3×C72D5×D1111yescharacteristic, complemented, Hall
96C2×C7×D5—771no—
97D5×D7—111no—
98C2×C3×D11—351noHall
99D55—71no—
100C5×D11—71no—
101D5×C11C3×C7×D711yescharacteristic, complemented
102C3×C5×C7—23no—
103C3×C5×C7C2×C7×D1111yescharacteristic, complemented
104C3×C5×C7C2×D7711yescharacteristic, complemented
105C2×C72—51no—
106C7×D7—111no—
107C7×D7—551no—
108C22×C3×C7—3851no—
109C2×C3×D7—551no—
110C7×C11—23no—
111C7×C11C3×D5×D711yescharacteristic, complemented
112C7×C11C2×C3×C7×D511yescharacteristic, complemented
113C2×C5×C7—771no—
114D35—111no—
115C5×D7—111no—
116C7×D5—23no—
117C7×D5—771no—
118C7×D5C3×C7×D1111yescharacteristic, complemented
119C7×D5C3×D7711yescharacteristic, direct product factor
120C2×C3×C11—51no—
121C3×D11—71no—
122C3×D11—351no—
123C2×C3×D5—771noHall
124C5×C11C2×C3×C7×D711yescharacteristic, complemented, Hall
125C72C3×D5×D1111yescharacteristic, complemented, Sylow
126C2×D11—351noHall
127C2×C3×C7—51no—
128C2×C3×C7—51no—
129C2×C3×C7—103no—
130C2×C3×C7—771no—
131C2×C3×C7—3851no—
132C3×D7—111no—
133C3×D7—551no—
134C5×C7—23no—
135C5×C7C2×C3×C7×D1111yescharacteristic, complemented
136C5×C7C2×C3×D7711yescharacteristic, complemented
137C3×C11C7×D5×D711yescharacteristic, complemented, Hall
138C2×C3×C5—771no—
139C3×D5—771no—
140C3×D5C7×D7711yescharacteristic, direct product factor
141C22×C7—3851no—
142C2×D7—551no—
143C2×C11—51no—
144D11—71no—
145D11—351no—
146C3×C7—23no—
147C3×C7C7×D5×D1111yescharacteristic, complemented
148C3×C7D5×D7711yescharacteristic, direct product factor
149C2×D5—771noHall
150C3×C5C2×C7×D7711yescharacteristic, complemented, Hall
151C2×C7—51no—
152C2×C7—51no—
153C2×C7—103no—
154C2×C7—771no—
155C2×C7—3851no—
156D7—111no—
157D7—551no—
158C22×C3—3851noHall
159C11C3×C7×D5×D711yescharacteristic, complemented, Sylow
160C2×C5—771no—
161D5—771no—
162D5C3×C7×D7711yescharacteristic, direct product factor
163C7—23no—
164C7C3×C7×D5×D1111yescharacteristic, complemented
165C7C3×D5×D7711yescharacteristic, direct product factor
166C2×C3—51no—
167C2×C3—771no—
168C2×C3—3851no—
169C5C2×C3×C7×D7711yescharacteristic, complemented, Sylow
170C22—3851noSylow
171C3C7×D5×D7711yescharacteristic, direct product factor, Sylow
172C2—51no—
173C2—771no—
174C2—3851no—
subgroupG/H
center, hypercenterC3×C7D5×D77
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D77C2semidirect
2. C3×C72×D5×C11C2semidirect
3. C3×C7×D385C2semidirect
4. C7×D5×D77C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
7. C7×D385C2×C3semidirect
8. C72×D5×C11C2×C3semidirect
9. C5×C7×D77C2×C3semidirect
10. C3×D5×D77C7direct (N × H)
13. C3×C7×D77D5direct (N × H)
16. C5×C72×C11C22×C3semidirect
17. C3×D385C2×C7semidirect
20. C3×C7×D5×C11D7semidirect
21. C3×C7×D5×C11C2×C7semidirect
22. C3×C5×D77C2×C7semidirect
25. C3×C72×C11C2×D5semidirect
26. D5×D77C3×C7direct (N × H)
29. C3×C72×D5D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
36. C7×D77C3×D5direct (N × H)
40. D385C2×C3×C7semidirect
43. C7×D5×C11C3×D7semidirect
44. C7×D5×C11C2×C3×C7semidirect
45. C5×D77C2×C3×C7semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11C2×C3×D5semidirect
52. C72×D5C3×D11semidirect
58. C3×D77C7×D5direct (N × H)
64. C5×C7×C11C2×C3×D7semidirect
65. C5×C7×C11C22×C3×C7semidirect
67. C3×D5×C11C7×D7semidirect
74. C5×C72C2×C3×D11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11C2×C7×D5semidirect
83. C3×C7×D5C7×D11semidirect
84. C3×C7×D5D77direct (N × H)
87. C3×C5×C11C2×C7×D7semidirect
92. D77C3×C7×D5direct (N × H)
95. C3×C72D5×D11semidirect
101. D5×C11C3×C7×D7semidirect
103. C3×C5×C7C2×C7×D11semidirect
104. C3×C5×C7C2×D77semidirect
111. C7×C11C3×D5×D7semidirect
112. C7×C11C2×C3×C7×D5semidirect
118. C7×D5C3×C7×D11semidirect
119. C7×D5C3×D77direct (N × H)
124. C5×C11C2×C3×C7×D7semidirect
125. C72C3×D5×D11semidirect
135. C5×C7C2×C3×C7×D11semidirect
136. C5×C7C2×C3×D77semidirect
137. C3×C11C7×D5×D7semidirect
140. C3×D5C7×D77direct (N × H)
147. C3×C7C7×D5×D11semidirect
148. C3×C7D5×D77direct (N × H)
150. C3×C5C2×C7×D77semidirect
159. C11C3×C7×D5×D7semidirect
162. D5C3×C7×D77direct (N × H)
164. C7C3×C7×D5×D11semidirect
165. C7C3×D5×D77direct (N × H)
169. C5C2×C3×C7×D77semidirect
171. C3C7×D5×D77direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D772
C3×C72×D5×C112
C3×C7×D3852
C7×D5×D773
C2×C3×C7×D775
C3×D5×D777
C3×C7×D5×D117
C3×C7×D5×D711