Finite Group Databasebeta

← D69⋊D105 #44394607

Subgroups — D69⋊D105 #44394607

Order 28980.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×D69C211yesmaximal, characteristic, complemented
2C3×D2415C211yesmaximal, characteristic, complemented
3C23×C3⋊D105C211yesmaximal, characteristic, complemented
4D69⋊D35—31nomaximal
5D23×D105—31nomaximal
6C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
7D69⋊D21—51nomaximal, Hall
8D2415D311yescharacteristic, complemented
9C23×D105—31no—
10C23×D105—31no—
11C23×D105—61no—
12C5×C7×D69D311yescharacteristic, complemented
13C3×D805—31no—
14C3×C5×C7×D23—31no—
15D69⋊D15—71nomaximal, Hall
16D23×D35—91noHall
17C23×C3⋊D21—51no—
18C3×D483—51no—
19C3×C7×D69D511yescharacteristic, complemented
20C3×C5×C7×C23—21no—
21C3×C5×C7×C23C2×D311yescharacteristic, complemented
22C3×C5×C7×C23C2×D311yescharacteristic, complemented
23C23×C3⋊D15—71no—
24C3×D345—71no—
25C3×C5×D69D711yescharacteristic, complemented
26D21⋊D23—151no—
27D21×D23—151no—
28D805—31no—
29C23×D35—91no—
30C5×C7×D23—31no—
31C32×C7×C23C2×D511yescharacteristic, complemented, Hall
32D15⋊D23—211no—
33D15×D23—211no—
34D3×D105—231nomaximal, Hall
35C32×C5×C23C2×D711yescharacteristic, complemented, Hall
36D483—51no—
37C23×D21—151no—
38C23×D21—151no—
39C23×D21—301no—
40C7×D69D1511yescharacteristic, complemented
41C3×D161—151no—
42C3×C7×D23—31no—
43(C3⋊D3)⋊D23—351noHall
44C5×C7×C23D3211yescharacteristic, complemented, Hall
45D345—71no—
46C23×D15—211no—
47C23×D15—211no—
48C23×D15—421no—
49C5×D69D2111yescharacteristic, complemented
50C3×D115—211no—
51C3×C5×D23—31no—
52D7×D23—451noHall
53C3⋊D105D2311yescharacteristic, complemented
54C3×D105—231no—
55C3×C5×D3×C7—231no—
56C3×C7×C23—21no—
57C3×C7×C23D3×D511yescharacteristic, complemented
58C3×C7×C23C2×D1511yescharacteristic, complemented
59D5×D23—631noHall
60C2×D105—691no—
61D3×D35—691no—
62C3⋊D3×C23—351no—
63C3×D69—351no—
64C3×D69D3511yescharacteristic, complemented
65C3×C5×C23—21no—
66C3×C5×C23D3×D711yescharacteristic, complemented
67C3×C5×C23C2×D2111yescharacteristic, complemented
68D161—151no—
69C7×D23—31no—
70D7×C23—451no—
71C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
72D3×D23—1051no—
73D3×D23—1051no—
74D3×D21—1151noHall
75D115—211no—
76C5×D23—31no—
77D5×C23—631no—
78C2×C3×C5×C7—691no—
79D105—31no—
80D105—31no—
81D105—61no—
82D105—231no—
83C5×D3×C7—231no—
84C3×D35—691no—
85C32×C23C2×D3511yescharacteristic, complemented, Hall
86D3×D15—1611noHall
87C7×C23D3×D1511yescharacteristic, complemented, Hall
88C2×D35—2071noHall
89D69—351no—
90D69D10511yescharacteristic, complemented
91C3×D23—31no—
92C3×D23—1051no—
93D3×C23—1051no—
94D3×C23—1051no—
95D3×C23—2101no—
96C3⋊D21—51no—
97C3×D21—1151no—
98C3×D3×C7—231no—
99C5×C23D3×D2111yescharacteristic, complemented, Hall
100C3×C5×C7—21no—
101C3×C5×C7D3×D2311yescharacteristic, complemented
102C3×C5×C7D3×D2311yescharacteristic, complemented
103C2×D23—3151noHall
104C3⋊D15—71no—
105C3×D15—1611no—
106C3×C5×D3—231no—
107C2×D21—3451no—
108D3×D7—3451no—
109C2×C5×C7—691no—
110D35—91no—
111D35—691no—
112C3×C23—21no—
113C3×C23D3×D3511yescharacteristic, complemented
114C3×C23C2×D10511yescharacteristic, complemented
115C32×C7D5×D2311yescharacteristic, complemented, Hall
116C2×D15—4831no—
117D3×D5—4831no—
118C2×C23—3151no—
119D23—31no—
120D23—1051no—
121C32×C5D7×D2311yescharacteristic, complemented, Hall
122C2×C3×C7—691no—
123D21—151no—
124D21—151no—
125D21—301no—
126D21—1151no—
127C3×D7—3451no—
128D3×C7—231no—
129D32—8051noHall
130C5×C7(C3⋊D3)⋊D2311yescharacteristic, complemented, Hall
131C2×C3×C5—691no—
132D15—211no—
133D15—211no—
134D15—421no—
135D15—1611no—
136C3×D5—4831no—
137C5×D3—231no—
138C2×D7—10351noHall
139C23D3×D10511yescharacteristic, complemented, Sylow
140C3×C7—21no—
141C3×C7D15×D2311yescharacteristic, complemented
142C3×C7D15⋊D2311yescharacteristic, complemented
143C2×D5—14491noHall
144C3⋊D3—351no—
145C3×D3—231no—
146C3×D3—8051no—
147C3×C5—21no—
148C3×C5D21×D2311yescharacteristic, complemented
149C3×C5D21⋊D2311yescharacteristic, complemented
150C2×C7—691no—
151D7—451no—
152D7—3451no—
153C2×D3—24151no—
154C2×D3—24151no—
155C2×C5—691no—
156D5—631no—
157D5—4831no—
158C32D23×D3511yescharacteristic, complemented, Sylow
159C7D69⋊D1511yescharacteristic, complemented, Sylow
160C2×C3—691no—
161C2×C3—24151no—
162D3—231no—
163D3—8051no—
164D3—1051no—
165D3—1051no—
166D3—2101no—
167C5D69⋊D2111yescharacteristic, complemented, Sylow
168C22—72451noSylow
169C3—21no—
170C3D23×D10511yescharacteristic, complemented
171C3D69⋊D3511yescharacteristic, complemented
172C2—3151no—
173C2—691no—
174C2—24151no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D69C2semidirect
2. C3×D2415C2semidirect
3. C23×C3⋊D105C2semidirect
6. C32×C5×C7×C23C22semidirect
8. D2415D3semidirect
12. C5×C7×D69D3semidirect
19. C3×C7×D69D5semidirect
21. C3×C5×C7×C23C2×D3semidirect
22. C3×C5×C7×C23C2×D3semidirect
25. C3×C5×D69D7semidirect
31. C32×C7×C23C2×D5semidirect
35. C32×C5×C23C2×D7semidirect
40. C7×D69D15semidirect
44. C5×C7×C23D32semidirect
49. C5×D69D21semidirect
53. C3⋊D105D23semidirect
57. C3×C7×C23D3×D5semidirect
58. C3×C7×C23C2×D15semidirect
64. C3×D69D35semidirect
66. C3×C5×C23D3×D7semidirect
67. C3×C5×C23C2×D21semidirect
71. C32×C5×C7C2×D23semidirect
85. C32×C23C2×D35semidirect
87. C7×C23D3×D15semidirect
90. D69D105semidirect
99. C5×C23D3×D21semidirect
101. C3×C5×C7D3×D23semidirect
102. C3×C5×C7D3×D23semidirect
113. C3×C23D3×D35semidirect
114. C3×C23C2×D105semidirect
115. C32×C7D5×D23semidirect
121. C32×C5D7×D23semidirect
130. C5×C7(C3⋊D3)⋊D23semidirect
139. C23D3×D105semidirect
141. C3×C7D15×D23semidirect
142. C3×C7D15⋊D23semidirect
148. C3×C5D21×D23semidirect
149. C3×C5D21⋊D23semidirect
158. C32D23×D35semidirect
159. C7D69⋊D15semidirect
167. C5D69⋊D21semidirect
170. C3D23×D105semidirect
171. C3D69⋊D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D692
C3×D24152
C23×C3⋊D1052
D69⋊D353
D23×D1053
D69⋊D215
D69⋊D157
D3×D10523