Finite Group Databasebeta

← C3×D21×D91 #37525591

Subgroups — C3×D21×D91 #37525591

Order 22932.

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

normal subgroups only

This group has 230 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
1C32×C7×D91C211yesmaximal, characteristic, complemented
2C3×C7×C13×D21C211yesmaximal, characteristic, complemented
3C3×C3⋊(C7⋊D91)C211yesmaximal, characteristic, complemented
4D21×D91C311yesmaximal, characteristic, direct product factor
5C3×D7×D91—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C7×C13×D21C2×C311yescharacteristic, complemented
9C3×C7⋊D91—31no—
10C3×C7×D91—21no—
11C3×C7×D91D311yescharacteristic, complemented
12C3×C7×D91C2×C311yescharacteristic, complemented
13C3×C7×C13×D7—31no—
14C3×D3×D91—71nomaximal
15C3×D13×D21—71nomaximal
16D7×D91—31noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C22×C311yescharacteristic, complemented
20C3×D7×D21—131nomaximal, Hall
21C3×D273—71no—
22C3×D273—71no—
23C3×D273—143no—
24C3×C13×D21D711yescharacteristic, complemented
25C3×D3×C7×C13—71no—
26C32×D91D711yescharacteristic, complemented
27C32×C7×D13—71no—
28C7⋊D91—31no—
29C7×D91C3×D311yescharacteristic, complemented
30C7×C13×D7—31no—
31C2×C3×D91—211no—
32D3×D91—71no—
33D13×D21—71no—
34C3×D7×D13—211no—
35C3×C3⋊(C7⋊D7)—131no—
36C3×C7×D21D1311yescharacteristic, complemented
37C32×C7×D7—131no—
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C2×D711yescharacteristic, complemented
41C72×C13C2×C3×D311yescharacteristic, complemented, Hall
42D7×D21—131no—
43C3×D72—391no—
44C2×C3×C7×C13—211no—
45D273—71no—
46D273—71no—
47D273—143no—
48C13×D21C3×D711yescharacteristic, complemented
49D3×C7×C13—71no—
50C3×D91—21no—
51C3×D91—211no—
52C3×D91—211no—
53C3×D91—423no—
54C3×D91C3×D711yescharacteristic, complemented
55C3×D91D2111yescharacteristic, direct product factor
56C3×C13×D7—31no—
57C3×C7×D13—71no—
58C3×C7×D13—71no—
59C3×C7×D13—141no—
60C3×D3×D13—491noHall
61C32×C72C2×D1311yescharacteristic, complemented, Hall
62C2×D91—211no—
63D7×D13—211no—
64C3⋊(C7⋊D7)—131no—
65C7×D21C3×D1311yescharacteristic, complemented
66C3×C7⋊D7—391no—
67C3×C7×D7—31no—
68C3×C7×D7—131no—
69C3×C7×D7—131no—
70C3×C7×D7—261no—
71C3×C7×C13—23no—
72C3×C7×C13—23no—
73C3×C7×C13—21no—
74C3×C7×C13—21no—
75C3×C7×C13—43no—
76C3×C7×C13D3×D711yescharacteristic, complemented
77C3×C7×C13C2×C3×D711yescharacteristic, complemented
78C3×C7×C13C2×C3×D711yescharacteristic, complemented
79C3×C7×C13C2×D2111yescharacteristic, complemented
80C2×C3×D21—911no—
81C3×D3×D7—911no—
82C3×D39—491no—
83C3×D3×C13—71no—
84C32×D13—71no—
85D72—391noHall
86C2×C7×C13—211no—
87D91—211no—
88D91—211no—
89D91—423no—
90D91C3×D2111yescharacteristic, direct product factor
91C7×D13—71no—
92C13×D7—31no—
93C2×C3×D13—1471no—
94D3×D13—491no—
95C3×C72—21no—
96C3×C72D3×D1311yescharacteristic, complemented
97C3×C72C2×C3×D1311yescharacteristic, complemented
98C2×C32×C7—911no—
99C3×D21—911no—
100C3×D21—911no—
101C3×D21—1823no—
102C3×D21D9111yescharacteristic, direct product factor
103C3×D3×C7—71no—
104C32×D7—131no—
105C32×C13D7211yescharacteristic, complemented, Hall
106C7⋊D7—391no—
107C7×D7—31no—
108C7×D7—131no—
109C7×C13—23no—
110C7×C13C3×D3×D711yescharacteristic, complemented
111C7×C13C2×C3×D2111yescharacteristic, complemented
112C2×D21—911no—
113C2×C3×D7—2731no—
114C2×C3×D7—2731no—
115D3×D7—911no—
116C2×C3×C13—211no—
117D39—491no—
118C3×D13—71no—
119C3×D13—71no—
120C3×D13—141no—
121C3×D13—1471no—
122D3×C13—71no—
123C32×C7—23no—
124C32×C7D7×D1311yescharacteristic, complemented
125C32×C7C2×D9111yescharacteristic, complemented
126C2×D13—1471noHall
127C72C3×D3×D1311yescharacteristic, complemented, Sylow
128C2×C3×C7—211no—
129C2×C3×C7—911no—
130C2×C3×C7—911no—
131C2×C3×C7—1821no—
132D21—911no—
133D21—911no—
134D21—1823no—
135D21C3×D9111yescharacteristic, direct product factor
136C3×D7—31no—
137C3×D7—131no—
138C3×D7—131no—
139C3×D7—2731no—
140C3×D7—2731no—
141C3×D7—261no—
142C3×D7—5463no—
143D3×C7—71no—
144C3×C13—21no—
145C3×C13C3×D7211yescharacteristic, complemented
146C3×C13D7×D2111yescharacteristic, complemented
147C2×C3×D3—6371noHall
148C2×D7—2731no—
149C2×D7—2731no—
150C2×C13—211no—
151D13—71no—
152D13—1471no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7C3×D7×D1311yescharacteristic, complemented
159C3×C7D13×D2111yescharacteristic, complemented
160C3×C7D3×D9111yescharacteristic, complemented
161C3×C7C2×C3×D9111yescharacteristic, complemented
162C2×C32—911no—
163C3×D3—71no—
164C3×D3—6371no—
165C2×C7—211no—
166C2×C7—911no—
167D7—31no—
168D7—131no—
169D7—2731no—
170D7—2731no—
171D7—5463no—
172C13C3×D7×D2111yescharacteristic, complemented, Sylow
173C22×C3—19111no—
174C2×D3—6371no—
175C32D7×D9111yescharacteristic, complemented, Sylow
176C7—23no—
177C7C3×D13×D2111yescharacteristic, complemented
178C7C3×D3×D9111yescharacteristic, complemented
179C2×C3—211no—
180C2×C3—911no—
181C2×C3—911no—
182C2×C3—19111no—
183C2×C3—1821no—
184D3—71no—
185D3—6371no—
186C22—19111noSylow
187C3—21no—
188C3C3×D7×D9111yescharacteristic, complemented
189C3D21×D9111yescharacteristic, direct product factor
190C2—211no—
191C2—911no—
192C2—19111no—
subgroupG/H
center, hypercenterC3D21×D91
commutator, cosocle, hypocenterC3×C72×C13C22×C3
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C3×C72×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C7×D91C2semidirect
2. C3×C7×C13×D21C2semidirect
3. C3×C3⋊(C7⋊D91)C2semidirect
4. D21×D91C3direct (N × H)
6. C32×C72×C13C22semidirect
7. C3⋊(C7⋊D91)C2×C3semidirect
8. C7×C13×D21C2×C3semidirect
11. C3×C7×D91D3semidirect
12. C3×C7×D91C2×C3semidirect
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C22×C3semidirect
24. C3×C13×D21D7semidirect
26. C32×D91D7semidirect
29. C7×D91C3×D3semidirect
36. C3×C7×D21D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C2×D7semidirect
41. C72×C13C2×C3×D3semidirect
48. C13×D21C3×D7semidirect
54. C3×D91C3×D7semidirect
55. C3×D91D21direct (N × H)
61. C32×C72C2×D13semidirect
65. C7×D21C3×D13semidirect
76. C3×C7×C13D3×D7semidirect
77. C3×C7×C13C2×C3×D7semidirect
78. C3×C7×C13C2×C3×D7semidirect
79. C3×C7×C13C2×D21semidirect
90. D91C3×D21direct (N × H)
96. C3×C72D3×D13semidirect
97. C3×C72C2×C3×D13semidirect
102. C3×D21D91direct (N × H)
105. C32×C13D72semidirect
110. C7×C13C3×D3×D7semidirect
111. C7×C13C2×C3×D21semidirect
124. C32×C7D7×D13semidirect
125. C32×C7C2×D91semidirect
127. C72C3×D3×D13semidirect
135. D21C3×D91direct (N × H)
145. C3×C13C3×D72semidirect
146. C3×C13D7×D21semidirect
158. C3×C7C3×D7×D13semidirect
159. C3×C7D13×D21semidirect
160. C3×C7D3×D91semidirect
161. C3×C7C2×C3×D91semidirect
172. C13C3×D7×D21semidirect
175. C32D7×D91semidirect
177. C7C3×D13×D21semidirect
178. C7C3×D3×D91semidirect
188. C3C3×D7×D91semidirect
189. C3D21×D91direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D912
C3×C7×C13×D212
C3×C3⋊(C7⋊D91)2
D21×D913
C3×D7×D913
C3×D3×D917
C3×D13×D217
C3×D7×D2113