Finite Group Databasebeta

← #37525618

Subgroups — #37525618

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×C13×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C7×C3⋊D273C211yesmaximal, characteristic, complemented
4#21439774—31nomaximal
5D91⋊D21—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C13×C3⋊(C7⋊D7)D311yescharacteristic, complemented
8C7×D273—31no—
9C7×D273—31no—
10C7×D273—61no—
11C7×D273D311yescharacteristic, complemented
12C3×C13×C7⋊D7—31no—
13C3×C7×D91—31no—
14D21⋊D39—71nomaximal
15D21×D39—71nomaximal
16(C7⋊D7)⋊D13—91noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C2×D311yescharacteristic, complemented
20D21⋊D21—131nomaximal, Hall
21C3⋊D273D711yescharacteristic, complemented
22C7×C3⋊D39—71no—
23C3×D273D711yescharacteristic, complemented
24C3×C13×D21—71no—
25C3×C13×D21—71no—
26C3×C13×D21—143no—
27C3×C7×D39—71no—
28C13×C7⋊D7—31no—
29C7×D91—31no—
30C7×D91—91no—
31D21⋊D13—211no—
32D7×D39—211no—
33D7×D39—211no—
34D13×D21—211no—
35C7×C3⋊D21—131no—
36C3×C3⋊(C7⋊D7)D1311yescharacteristic, complemented
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—31no—
45D273—31no—
46D273—61no—
47D273D2111yescharacteristic, complemented
48C13×D21—71no—
49C13×D21—71no—
50C13×D21—143no—
51C7×D39—71no—
52C7×D39—211no—
53C7×D39—211no—
54C7×D39—421no—
55C3×D91—31no—
56C3×C13×D7—211no—
57C3×C13×D7—211no—
58C3×C13×D7—423no—
59C3×C7×D13—211no—
60D3×D39—491noHall
61C32×C72C2×D1311yescharacteristic, complemented, Hall
62D7×D13—631no—
63D7×D13—631no—
64C3⋊(C7⋊D7)D3911yescharacteristic, complemented
65C7×D21—131no—
66C7×D21—391no—
67C7×D21—391no—
68C7×D21—781no—
69C3×C7⋊D7—31no—
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—
82C3⋊D39—71no—
83C3×D39—71no—
84C3×D3×C13—491no—
85D72—1171noHall
86D91—31no—
87D91—91no—
88C7×D13—211no—
89C7×D13—631no—
90C13×D7—211no—
91C13×D7—211no—
92C13×D7—423no—
93C2×D39—1471no—
94D3×D13—1471no—
95C3×C72—21no—
96C3×C72D3×D1311yescharacteristic, complemented
97C3×C72C2×D3911yescharacteristic, complemented
98C3⋊D21—131no—
99C7×C3⋊D3—911no—
100C3×D21—71no—
101C3×D21—71no—
102C3×D21—131no—
103C3×D21—143no—
104C3×D3×C7—911no—
105C32×C13D7211yescharacteristic, complemented, Hall
106C7⋊D7—31no—
107C7×D7—391no—
108C7×D7—1171no—
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—
116C2×C3×C13—1471no—
117D39—71no—
118D39—211no—
119D39—211no—
120D39—421no—
121C3×D13—211no—
122D3×C13—491no—
123C32×C7—23no—
124C32×C7D7×D1311yescharacteristic, complemented
125C32×C7D7×D1311yescharacteristic, complemented
126C2×D13—4411noHall
127C72D3×D3911yescharacteristic, complemented, Sylow
128C2×C3×C7—2731no—
129D21—71no—
130D21—71no—
131D21—131no—
132D21—143no—
133D21—391no—
134D21—391no—
135D21—781no—
136C3×D7—211no—
137C3×D7—211no—
138C3×D7—391no—
139C3×D7—423no—
140D3×C7—2731no—
141D3×C7—2731no—
142D3×C7—5461no—
143D3×C7—911no—
144C3×C13—21no—
145C3×C13D7×D2111yescharacteristic, complemented
146C3×C13D21⋊D711yescharacteristic, complemented
147D32—6371noHall
148C2×D7—8191no—
149C2×D7—8191no—
150C2×C13—1471no—
151D13—211no—
152D13—631no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D13×D2111yescharacteristic, complemented
159C3×C7D7×D3911yescharacteristic, complemented
160C3×C7D7×D3911yescharacteristic, complemented
161C3×C7D21⋊D1311yescharacteristic, complemented
162C3⋊D3—911no—
163C3×D3—491no—
164C3×D3—911no—
165C2×C7—2731no—
166C2×C7—8191no—
167D7—211no—
168D7—211no—
169D7—391no—
170D7—423no—
171D7—1171no—
172C13D21⋊D2111yescharacteristic, complemented, Sylow
173C2×D3—19111no—
174C2×D3—19111no—
175C32(C7⋊D7)⋊D1311yescharacteristic, complemented, Sylow
176C7—23no—
177C7D21×D3911yescharacteristic, complemented
178C7D21⋊D3911yescharacteristic, complemented
179C2×C3—2731no—
180C2×C3—1471no—
181D3—2731no—
182D3—2731no—
183D3—5461no—
184D3—491no—
185D3—911no—
186C22—57331noSylow
187C3—21no—
188C3D91⋊D2111yescharacteristic, complemented
189C3#2143977411yescharacteristic, complemented
190C2—2731no—
191C2—8191no—
192C2—1471no—
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×C13×C3⋊(C7⋊D7)C2semidirect
3. C7×C3⋊D273C2semidirect
6. C32×C72×C13C22semidirect
7. C13×C3⋊(C7⋊D7)D3semidirect
11. C7×D273D3semidirect
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C2×D3semidirect
21. C3⋊D273D7semidirect
23. C3×D273D7semidirect
36. C3×C3⋊(C7⋊D7)D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C2×D7semidirect
41. C72×C13D32semidirect
47. D273D21semidirect
61. C32×C72C2×D13semidirect
64. C3⋊(C7⋊D7)D39semidirect
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×C72C2×D39semidirect
105. C32×C13D72semidirect
110. C7×C13D3×D21semidirect
111. C7×C13(C3⋊D3)⋊D7semidirect
124. C32×C7D7×D13semidirect
125. C32×C7D7×D13semidirect
127. C72D3×D39semidirect
145. C3×C13D7×D21semidirect
146. C3×C13D21⋊D7semidirect
158. C3×C7D13×D21semidirect
159. C3×C7D7×D39semidirect
160. C3×C7D7×D39semidirect
161. C3×C7D21⋊D13semidirect
172. C13D21⋊D21semidirect
175. C32(C7⋊D7)⋊D13semidirect
177. C7D21×D39semidirect
178. C7D21⋊D39semidirect
188. C3D91⋊D21semidirect
189. C3#21439774semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D2732
C3×C13×C3⋊(C7⋊D7)2
C7×C3⋊D2732
#214397743
D91⋊D213
D21⋊D397
D21×D397
D21⋊D2113