Finite Group Databasebeta

← #49141615

Subgroups — #49141615

Order 36540.

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

normal subgroups only

This group has 176 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×C5×D609C211yesmaximal, characteristic, complemented
2C3×C29×D105C211yesmaximal, characteristic, complemented
3C7×C3⋊D435C211yesmaximal, characteristic, complemented
4D35⋊D87—31nomaximal
5D203⋊D15—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D21⋊D87—51nomaximal, Hall
8C29×D105D311yescharacteristic, complemented
9C7×D435—31no—
10C7×D435—31no—
11C7×D435—61no—
12C5×D609D311yescharacteristic, complemented
13C3×C29×D35—31no—
14C3×C5×D203—31no—
15D15×D87—71nomaximal, Hall
16D35⋊D29—91noHall
17C7×C3⋊D87—51no—
18C3×D609D511yescharacteristic, complemented
19C3×C29×D21—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C3⋊D435D711yescharacteristic, complemented
24C3×C29×D15—71no—
25C3×C5×D87—71no—
26D21⋊D29—151no—
27D7×D87—151no—
28C29×D35—31no—
29C7×D145—91no—
30C5×D203—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D5×D87—211no—
33D15×D29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D21⋊D15—291nomaximal, Hall
36D609D1511yescharacteristic, complemented
37C29×D21—51no—
38C7×D87—151no—
39C7×D87—151no—
40C7×D87—301no—
41C3×D203—31no—
42C3×D7×C29—151no—
43D3×D87—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45D435—31no—
46D435—31no—
47D435—61no—
48C29×D15—71no—
49C5×D87—71no—
50C3×D5×C29—211no—
51C3×C5×D29—211no—
52D7×D29—451noHall
53C7×C3⋊D15—291no—
54C3×D105D2911yescharacteristic, complemented
55C3×C5×D21—291no—
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×D1511yescharacteristic, complemented
59D5×D29—631noHall
60C3⋊D87—51no—
61C3×D87—71no—
62C3×D3×C29—351no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29D3×D711yescharacteristic, complemented
66D15⋊D7—871no—
67D7×D15—871no—
68D203—31no—
69C7×D29—451no—
70D7×C29—151no—
71C2×D87—1051no—
72D3×D29—1051no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74D145—91no—
75C5×D29—211no—
76D5×C29—211no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78(C3⋊D3)⋊D7—1451noHall
79D105D8711yescharacteristic, complemented
80C7×D15—871no—
81C7×D15—871no—
82C7×D15—1741no—
83C5×D21—291no—
84C3×D35—31no—
85C3×C5×D7—871no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—2031noHall
88C2×C3×C29—1051no—
89D87—71no—
90D87—151no—
91D87—151no—
92D87—301no—
93C3×D29—211no—
94D3×C29—351no—
95C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
96D5×D7—2611noHall
97C7×C3⋊D3—1451no—
98C3×D21—51no—
99C3×D21—291no—
100C2×D29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C3⋊D15—291no—
105C3×D15—71no—
106C3×C5×D3—2031no—
107C3×C29—21no—
108C3×C29D7×D1511yescharacteristic, complemented
109C3×C29D15⋊D711yescharacteristic, complemented
110D3×D7—4351no—
111D3×D7—4351no—
112D35—31no—
113C5×D7—871no—
114C7×D5—2611no—
115C32×C7D5×D2911yescharacteristic, complemented, Hall
116C2×D15—6091no—
117D3×D5—6091no—
118C2×C29—1051no—
119D29—211no—
120D29—451no—
121C32×C5D7×D2911yescharacteristic, complemented, Hall
122D21—51no—
123D21—291no—
124C3×D7—151no—
125C3×D7—871no—
126D3×C7—8701no—
127D3×C7—4351no—
128D3×C7—4351no—
129D32—10151noHall
130C5×C7D3×D8711yescharacteristic, complemented, Hall
131C2×C3×C5—6091no—
132D15—71no—
133D15—871no—
134D15—871no—
135D15—1741no—
136C3×D5—211no—
137C5×D3—2031no—
138C29D21⋊D1511yescharacteristic, complemented, Sylow
139C2×D7—13051noHall
140C3×C7—21no—
141C3×C7D15×D2911yescharacteristic, complemented
142C3×C7D5×D8711yescharacteristic, complemented
143C2×D5—18271noHall
144C3⋊D3—1451no—
145C3×D3—351no—
146C3×D3—2031no—
147C3×C5—21no—
148C3×C5D7×D8711yescharacteristic, complemented
149C3×C5D21⋊D2911yescharacteristic, complemented
150C2×C7—13051no—
151D7—151no—
152D7—871no—
153C2×D3—30451no—
154C2×D3—30451no—
155C2×C5—6091no—
156D5—2611no—
157D5—211no—
158C32D35⋊D2911yescharacteristic, complemented, Sylow
159C7D15×D8711yescharacteristic, complemented, Sylow
160C2×C3—6091no—
161C2×C3—1051no—
162D3—351no—
163D3—8701no—
164D3—4351no—
165D3—4351no—
166D3—2031no—
167C5D21⋊D8711yescharacteristic, complemented, Sylow
168C22—91351noSylow
169C3—21no—
170C3D203⋊D1511yescharacteristic, complemented
171C3D35⋊D8711yescharacteristic, complemented
172C2—13051no—
173C2—6091no—
174C2—1051no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D609C2semidirect
2. C3×C29×D105C2semidirect
3. C7×C3⋊D435C2semidirect
6. C32×C5×C7×C29C22semidirect
8. C29×D105D3semidirect
12. C5×D609D3semidirect
18. C3×D609D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
23. C3⋊D435D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
36. D609D15semidirect
44. C5×C7×C29D32semidirect
54. C3×D105D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29D3×D7semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29D5×D7semidirect
79. D105D87semidirect
86. C7×C29D3×D15semidirect
95. C5×C29(C3⋊D3)⋊D7semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×D87semidirect
108. C3×C29D7×D15semidirect
109. C3×C29D15⋊D7semidirect
115. C32×C7D5×D29semidirect
121. C32×C5D7×D29semidirect
130. C5×C7D3×D87semidirect
138. C29D21⋊D15semidirect
141. C3×C7D15×D29semidirect
142. C3×C7D5×D87semidirect
148. C3×C5D7×D87semidirect
149. C3×C5D21⋊D29semidirect
158. C32D35⋊D29semidirect
159. C7D15×D87semidirect
167. C5D21⋊D87semidirect
170. C3D203⋊D15semidirect
171. C3D35⋊D87semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D6092
C3×C29×D1052
C7×C3⋊D4352
D35⋊D873
D203⋊D153
D21⋊D875
D15×D877
D21⋊D1529