Finite Group Databasebeta

← #37525617

Subgroups — #37525617

Order 22932.

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

normal subgroups only

This group has 230 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×C7×D273C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D91)C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4D21⋊D91—31nomaximal
5D21×D91—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D91)D311yescharacteristic, complemented
8C7×D273D311yescharacteristic, complemented
9C7×C13×D21—31no—
10C7×C13×D21—31no—
11C7×C13×D21—61no—
12C3×C7⋊D91—31no—
13C3×C7×D91—31no—
14(C3⋊D3)⋊D91—71nomaximal
15D39⋊D21—71nomaximal
16D7×D91—91noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C2×D311yescharacteristic, complemented
20D21⋊D21—131nomaximal, Hall
21C13×C3⋊D21D711yescharacteristic, complemented
22C7×C13×C3⋊D3—71no—
23C3×D273—71no—
24C3×D273—71no—
25C3×D273—143no—
26C3×D273D711yescharacteristic, complemented
27C3×C7×D39—71no—
28C7⋊D91—31no—
29C7×D91—31no—
30C7×C13×D7—91no—
31D21⋊D13—211no—
32D3×D91—211no—
33D3×D91—211no—
34D13×D21—211no—
35C7×C3⋊D21D1311yescharacteristic, complemented
36C3×C3⋊(C7⋊D7)—131no—
37C3×C7×D21—131no—
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C2×D711yescharacteristic, complemented
41C72×C13D3211yescharacteristic, complemented, Hall
42D21⋊D7—391no—
43D7×D21—391no—
44D273—71no—
45D273—71no—
46D273—143no—
47D273D2111yescharacteristic, complemented
48C13×D21—31no—
49C13×D21—31no—
50C13×D21—61no—
51C7×D39—71no—
52D3×C7×C13—211no—
53D3×C7×C13—211no—
54D3×C7×C13—421no—
55C3×D91—31no—
56C3×D91—211no—
57C3×D91—211no—
58C3×D91—423no—
59C3×C7×D13—211no—
60(C3⋊D3)⋊D13—491noHall
61C32×C72C2×D1311yescharacteristic, complemented, Hall
62C2×D91—631no—
63D7×D13—631no—
64C3⋊(C7⋊D7)—131no—
65C7×D21—31no—
66C7×D21—31no—
67C7×D21—61no—
68C7×D21—131no—
69C3×C7⋊D7—391no—
70C3×C7×D7—391no—
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×C13D3×D711yescharacteristic, complemented
78C3×C7×C13D3×D711yescharacteristic, complemented
79C3×C7×C13C2×D2111yescharacteristic, complemented
80(C3⋊D3)⋊D7—911no—
81D3×D21—911no—
82C13×C3⋊D3—71no—
83C3×D39—71no—
84C3×D39—491no—
85D72—1171noHall
86C2×C7×C13—631no—
87D91—31no—
88D91—211no—
89D91—211no—
90D91—423no—
91C7×D13—211no—
92C13×D7—91no—
93D3×D13—1471no—
94D3×D13—1471no—
95C3×C72—21no—
96C3×C72D3×D1311yescharacteristic, complemented
97C3×C72D3×D1311yescharacteristic, complemented
98C3⋊D21D9111yescharacteristic, complemented
99C7×C3⋊D3—71no—
100C3×D21—131no—
101C3×D21—911no—
102C3×D21—911no—
103C3×D21—1823no—
104C3×D3×C7—911no—
105C32×C13D7211yescharacteristic, complemented, Hall
106C7⋊D7—391no—
107C7×D7—91no—
108C7×D7—391no—
109C7×C13—23no—
110C7×C13D3×D2111yescharacteristic, complemented
111C7×C13(C3⋊D3)⋊D711yescharacteristic, complemented
112C2×D21—2731no—
113D3×D7—2731no—
114D3×D7—2731no—
115D3×D7—2731no—
116D39—71no—
117D39—491no—
118C3×D13—211no—
119C3×D13—1471no—
120D3×C13—211no—
121D3×C13—211no—
122D3×C13—421no—
123C32×C7—23no—
124C32×C7D7×D1311yescharacteristic, complemented
125C32×C7C2×D9111yescharacteristic, complemented
126C2×D13—4411noHall
127C72(C3⋊D3)⋊D1311yescharacteristic, complemented, Sylow
128C2×C3×C7—2731no—
129D21—31no—
130D21—31no—
131D21—61no—
132D21—131no—
133D21—911no—
134D21—911no—
135D21—1823no—
136C3×D7—2731no—
137C3×D7—2731no—
138C3×D7—5463no—
139C3×D7—391no—
140D3×C7—211no—
141D3×C7—211no—
142D3×C7—421no—
143D3×C7—911no—
144C3×C13—21no—
145C3×C13D7×D2111yescharacteristic, complemented
146C3×C13D21⋊D711yescharacteristic, complemented
147D32—6371noHall
148C2×D7—8191no—
149C2×D7—8191no—
150C2×C13—631no—
151D13—211no—
152D13—1471no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D13×D2111yescharacteristic, complemented
159C3×C7D3×D9111yescharacteristic, complemented
160C3×C7D3×D9111yescharacteristic, complemented
161C3×C7D21⋊D1311yescharacteristic, complemented
162C3⋊D3—71no—
163C3×D3—911no—
164C3×D3—6371no—
165C2×C7—2731no—
166C2×C7—631no—
167D7—91no—
168D7—2731no—
169D7—2731no—
170D7—5463no—
171D7—391no—
172C13D21⋊D2111yescharacteristic, complemented, Sylow
173C2×D3—19111no—
174C2×D3—19111no—
175C32D7×D9111yescharacteristic, complemented, Sylow
176C7—23no—
177C7D39⋊D2111yescharacteristic, complemented
178C7(C3⋊D3)⋊D9111yescharacteristic, complemented
179C2×C3—2731no—
180C2×C3—19111no—
181D3—211no—
182D3—211no—
183D3—421no—
184D3—911no—
185D3—6371no—
186C22—57331noSylow
187C3—21no—
188C3D21×D9111yescharacteristic, complemented
189C3D21⋊D9111yescharacteristic, complemented
190C2—2731no—
191C2—631no—
192C2—19111no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C13C22
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×D273C2semidirect
2. C3×C3⋊(C7⋊D91)C2semidirect
3. C7×C13×C3⋊D21C2semidirect
6. C32×C72×C13C22semidirect
7. C3⋊(C7⋊D91)D3semidirect
8. C7×D273D3semidirect
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C2×D3semidirect
21. C13×C3⋊D21D7semidirect
26. C3×D273D7semidirect
35. C7×C3⋊D21D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C2×D7semidirect
41. C72×C13D32semidirect
47. D273D21semidirect
61. C32×C72C2×D13semidirect
76. C3×C7×C13D3×D7semidirect
77. C3×C7×C13D3×D7semidirect
78. C3×C7×C13D3×D7semidirect
79. C3×C7×C13C2×D21semidirect
96. C3×C72D3×D13semidirect
97. C3×C72D3×D13semidirect
98. C3⋊D21D91semidirect
105. C32×C13D72semidirect
110. C7×C13D3×D21semidirect
111. C7×C13(C3⋊D3)⋊D7semidirect
124. C32×C7D7×D13semidirect
125. C32×C7C2×D91semidirect
127. C72(C3⋊D3)⋊D13semidirect
145. C3×C13D7×D21semidirect
146. C3×C13D21⋊D7semidirect
158. C3×C7D13×D21semidirect
159. C3×C7D3×D91semidirect
160. C3×C7D3×D91semidirect
161. C3×C7D21⋊D13semidirect
172. C13D21⋊D21semidirect
175. C32D7×D91semidirect
177. C7D39⋊D21semidirect
178. C7(C3⋊D3)⋊D91semidirect
188. C3D21×D91semidirect
189. C3D21⋊D91semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D2732
C3×C3⋊(C7⋊D91)2
C7×C13×C3⋊D212
D21⋊D913
D21×D913
(C3⋊D3)⋊D917
D39⋊D217
D21⋊D2113