Finite Group Databasebeta

← D91⋊D105 #50304441

Subgroups — D91⋊D105 #50304441

Order 38220.

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

normal subgroups only

This group has 208 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×D91C211yesmaximal, characteristic, complemented
2C7×D1365C211yesmaximal, characteristic, complemented
3C13×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D91⋊D35—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D91⋊D21—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)—31no—
8C7×D455—31no—
9C5×C7×D91D311yescharacteristic, complemented
10D91⋊D15—71nomaximal
11D13×D105—71nomaximal
12C13×C3⋊(C7⋊D7)—51no—
13C7×D273—51no—
14C3×C7×D91D511yescharacteristic, complemented
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D7×D105—131nomaximal, Hall
17D1365D711yescharacteristic, complemented
18C13×D105—71no—
19C13×D105—71no—
20C13×D105—143no—
21C7×D195—71no—
22C3×C5×D91D711yescharacteristic, complemented
23C3×C5×C7×D13—71no—
24(C7⋊D7)⋊D13—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26D35⋊D13—211no—
27D13×D35—211no—
28C3⋊(C5⋊(C7⋊D7))D1311yescharacteristic, complemented
29C7×D105—131no—
30C3×C5×C7×D7—131no—
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C2×D711yescharacteristic, complemented
34C13×C7⋊D7—151no—
35C7×D91—151no—
36C7×D91D1511yescharacteristic, complemented
37D21⋊D13—351no—
38D13×D21—351no—
39D7×D35—391noHall
40D455—31no—
41C13×D35—211no—
42C13×D35—211no—
43C13×D35—423no—
44C7×D65—211no—
45C5×D91D2111yescharacteristic, complemented
46C5×C7×D13—71no—
47D13×D15—491noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13C2×D1511yescharacteristic, complemented, Hall
50D7×D21—651noHall
51D273—51no—
52C13×D21—351no—
53C13×D21—351no—
54C13×D21—703no—
55C7×D39—351no—
56C3×D91D3511yescharacteristic, complemented
57C3×C7×D13—71no—
58C5⋊(C7⋊D7)—31no—
59C7×D35—391no—
60C5×C7×D7—131no—
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64C2×D105—911no—
65D7×D15—911no—
66D195—71no—
67C13×D15—491no—
68C3×C5×D13—71no—
69D7×D13—1051no—
70D7×D13—1051no—
71C3⋊(C7⋊D7)—51no—
72C7×D21—651no—
73C3×C7×D7—131no—
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77D5×D13—1471noHall
78C5×C72D3×D1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—911no—
80D105—71no—
81D105—71no—
82D105—131no—
83D105—143no—
84C7×D15—911no—
85C3×C5×D7—131no—
86D72—1951noHall
87C3×C5×C13D7211yescharacteristic, complemented, Hall
88D91—151no—
89D91D10511yescharacteristic, complemented
90C7×D13—71no—
91C7×D13—1051no—
92C13×D7—1051no—
93C13×D7—1051no—
94C13×D7—2103no—
95D3×D13—2451noHall
96C3×C72D5×D1311yescharacteristic, complemented, Hall
97C2×D35—2731no—
98D5×D7—2731no—
99D65—211no—
100C5×D13—71no—
101D5×C13—1471no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7D7×D1311yescharacteristic, complemented
105C7⋊D7—151no—
106C7×D7—131no—
107C7×D7—1951no—
108C7×C13—23no—
109C7×C13D7×D1511yescharacteristic, complemented
110C7×C13C2×D10511yescharacteristic, complemented
111C2×D21—4551no—
112D3×D7—4551no—
113D39—351no—
114C3×D13—71no—
115D3×C13—2451no—
116C2×C5×C7—911no—
117D35—211no—
118D35—211no—
119D35—391no—
120D35—423no—
121C5×D7—131no—
122C7×D5—2731no—
123C5×C13D7×D2111yescharacteristic, complemented, Hall
124C2×D15—6371noHall
125C2×D13—7351noHall
126C72D13×D1511yescharacteristic, complemented, Sylow
127C2×C3×C7—911no—
128D21—351no—
129D21—351no—
130D21—651no—
131D21—703no—
132C3×D7—131no—
133D3×C7—4551no—
134C3×C13D7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D13×D2111yescharacteristic, complemented
137C5×C7D21⋊D1311yescharacteristic, complemented
138C2×C3×C5—911no—
139D15—491no—
140D15—911no—
141C2×D7—13651no—
142C2×D7—13651no—
143C2×C13—7351no—
144D13—71no—
145D13—1051no—
146C3×C7—23no—
147C3×C7D13×D3511yescharacteristic, complemented
148C3×C7D35⋊D1311yescharacteristic, complemented
149C2×D5—19111noHall
150C3×C5(C7⋊D7)⋊D1311yescharacteristic, complemented, Hall
151C2×C7—13651no—
152C2×C7—911no—
153D7—131no—
154D7—1051no—
155D7—1051no—
156D7—1951no—
157D7—2103no—
158C13D7×D10511yescharacteristic, complemented, Sylow
159C2×D3—31851noHall
160C2×C5—911no—
161D5—2731no—
162D5—1471no—
163C7—23no—
164C7D13×D10511yescharacteristic, complemented
165C7D91⋊D1511yescharacteristic, complemented
166C2×C3—911no—
167D3—4551no—
168D3—2451no—
169C5D91⋊D2111yescharacteristic, complemented, Sylow
170C22—95551noSylow
171C3D91⋊D3511yescharacteristic, complemented, Sylow
172C2—13651no—
173C2—911no—
174C2—7351no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D91C2semidirect
2. C7×D1365C2semidirect
3. C13×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C7×D91D3semidirect
14. C3×C7×D91D5semidirect
15. C5×C72×C13C2×D3semidirect
17. D1365D7semidirect
22. C3×C5×D91D7semidirect
25. C3×C72×C13C2×D5semidirect
28. C3⋊(C5⋊(C7⋊D7))D13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C2×D7semidirect
36. C7×D91D15semidirect
45. C5×D91D21semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13C2×D15semidirect
56. C3×D91D35semidirect
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D21semidirect
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72D3×D13semidirect
87. C3×C5×C13D72semidirect
89. D91D105semidirect
96. C3×C72D5×D13semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7D7×D13semidirect
109. C7×C13D7×D15semidirect
110. C7×C13C2×D105semidirect
123. C5×C13D7×D21semidirect
126. C72D13×D15semidirect
134. C3×C13D7×D35semidirect
136. C5×C7D13×D21semidirect
137. C5×C7D21⋊D13semidirect
147. C3×C7D13×D35semidirect
148. C3×C7D35⋊D13semidirect
150. C3×C5(C7⋊D7)⋊D13semidirect
158. C13D7×D105semidirect
164. C7D13×D105semidirect
165. C7D91⋊D15semidirect
169. C5D91⋊D21semidirect
171. C3D91⋊D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D912
C7×D13652
C13×C3⋊(C5⋊(C7⋊D7))2
D91⋊D353
D91⋊D215
D91⋊D157
D13×D1057
D7×D10513