Finite Group Databasebeta

← #37525321

Subgroups — #37525321

Order 22932.

248 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 32 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⋊#16838458C211yesmaximal, characteristic, complemented
2C3⋊#16838456C211yesmaximal, characteristic, complemented
3C3×#16838446C211yesmaximal, characteristic, complemented
4D21⋊D91C311yesmaximal, characteristic, complemented
5#21439608—31nomaximal
6C3×#14274263C2211yescharacteristic, complemented, Hall
7C7×D273C2×C311yescharacteristic, complemented
8C7×C13×D21C2×C311yescharacteristic, complemented
9C3×C7⋊D91C2×C311yescharacteristic, complemented
10#16838458—31no—
11#16838456—31no—
12#16838446—21no—
13#16838446D311yescharacteristic, complemented
14#10587722⋊D3—71nomaximal
15D3×#10587722—71nomaximal
16D7×D91—31noHall
17C3×C72×C13C22×C311yescharacteristic, complemented
18#14274263—21no—
19#14274263C2×D311yescharacteristic, complemented
20#13183634—131nomaximal, Hall
21C3⋊#10587722—71no—
22C3⋊#10587720—71no—
23C3⋊#10587716—71no—
24D3×#63270—71no—
25C3×#10587722—71no—
26C3×#10587722—71no—
27C3×#10587722—143no—
28C7⋊D91C3×D311yescharacteristic, complemented
29C7×D91—31no—
30C7×C13×D7—31no—
31D21⋊D13—71no—
32D3×D91—71no—
33C2×#10587722—211no—
34#10587716⋊C2—211no—
35C3⋊#64423—131no—
36C3⋊#64423—131no—
37C3×#64424—131no—
38C3×#63270—71no—
39C3×#63270—71no—
40C3×#63270—143no—
41C72×C13C2×C3×D311yescharacteristic, complemented, Hall
42D21⋊D7—131no—
43#64423⋊C2—391no—
44D273AGL(1,𝔽7)11yescharacteristic, complemented
45C13×D21AGL(1,𝔽7)11yescharacteristic, complemented
46C7×D39—71no—
47D3×C7×C13—71no—
48C3×D91—71no—
49C3×D91—71no—
50C3×D91—143no—
51C2×#63270—211no—
52#10587722—71no—
53#10587722—71no—
54#10587722—141no—
55#10587722—141no—
56#10587722—143no—
57#10587722—146no—
58#10587722—211no—
59#10587720—211no—
60#10587716—211no—
61D3×D13⋊C3—491noHall
62C3×#3861—131noHall
63C2×D91—211no—
64D7×D13—211no—
65C7×D21—131no—
66C7×D21D13⋊C311yescharacteristic, complemented
67C3×C7⋊D7—131no—
68#64424—131no—
69#64424—261no—
70#64423—391no—
71#64423—391no—
72C3×C7×C13—23no—
73C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
74C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
75#63270—71no—
76#63270—71no—
77#63270—143no—
78#63270—146no—
79#63270—141no—
80#63270—141no—
81D3×AGL(1,𝔽7)—911no—
82D3×AGL(1,𝔽7)—911no—
83C3⋊(D13⋊C3)—491no—
84D3×C13⋊C3—491no—
85C3×D13⋊C3—491no—
86D72—391noHall
87C2×C7×C13—211no—
88D91—31no—
89D91—71no—
90D91—71no—
91D91—143no—
92C7×D13—211no—
93C13×D7—31no—
94D3×D13—491no—
95C2×D13⋊C3—1471no—
96C3×C72C2×D13⋊C311yescharacteristic, complemented
97#3861—131no—
98#3861—261no—
99C3⋊AGL(1,𝔽7)—911no—
100C3⋊AGL(1,𝔽7)—911no—
101D3×ΓL(1,𝔽8)—911no—
102D3×ΓL(1,𝔽8)—911no—
103C3×AGL(1,𝔽7)—911no—
104C3×AGL(1,𝔽7)—911no—
105C3×AGL(1,𝔽7)—1823no—
106C3×C13⋊C3—491noHall
107C7⋊D7—131no—
108C7×D7—31no—
109C7×D7—391no—
110C7×C13—23no—
111C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
112C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
113D3×D7—911no—
114D3×D7—911no—
115C2×AGL(1,𝔽7)—2731no—
116C2×AGL(1,𝔽7)—2731no—
117D39—71no—
118C3×D13—491no—
119D3×C13—71no—
120C2×C13⋊C3—1471no—
121D13⋊C3—491no—
122D13⋊C3—981no—
123D13⋊C3—1471no—
124C3×ΓL(1,𝔽8)—911no—
125C3×ΓL(1,𝔽8)—911no—
126C3×ΓL(1,𝔽8)—1823no—
127C2×D13—1471noHall
128C72D3×D13⋊C311yescharacteristic, complemented, Sylow
129D21—131no—
130D21#1058772211yescharacteristic, complemented
131C3×D7—911no—
132C3×D7—911no—
133C3×D7—1823no—
134D3×C7—71no—
135D3×C7—911no—
136C2×ΓL(1,𝔽8)—2731no—
137C2×ΓL(1,𝔽8)—2731no—
138AGL(1,𝔽7)—2731no—
139AGL(1,𝔽7)—2731no—
140AGL(1,𝔽7)—911no—
141AGL(1,𝔽7)—911no—
142AGL(1,𝔽7)—1823no—
143AGL(1,𝔽7)—1821no—
144AGL(1,𝔽7)—1821no—
145AGL(1,𝔽7)—1826no—
146C3×C13#64423⋊C211yescharacteristic, complemented
147C13⋊C3—491no—
148C13⋊C3—981no—
149C2×C3×D3—6371noHall
150C2×D7—2731no—
151C2×D7—2731no—
152C2×C13—211no—
153D13—211no—
154D13—491no—
155C3×C7—23no—
156C3×C7#10587716⋊C211yescharacteristic, complemented
157C3×C7C2×#1058772211yescharacteristic, complemented
158ΓL(1,𝔽8)—911no—
159ΓL(1,𝔽8)—911no—
160ΓL(1,𝔽8)—1823no—
161ΓL(1,𝔽8)—1826no—
162ΓL(1,𝔽8)—1821no—
163ΓL(1,𝔽8)—1821no—
164C2×C32—6371no—
165C3×D3—6371no—
166C3×D3—6371no—
167C2×C7—2731no—
168C2×C7—211no—
169D7—31no—
170D7—391no—
171D7—911no—
172D7—911no—
173D7—1823no—
174C13#1318363411yescharacteristic, complemented, Sylow
175C22×C3—19111no—
176C2×D3—6371no—
177C32—6371noSylow
178C7—23no—
179C7D3×#1058772211yescharacteristic, complemented
180C7#10587722⋊D311yescharacteristic, complemented
181C2×C3—19111no—
182C2×C3—19111no—
183C2×C3—6371no—
184C2×C3—6371no—
185C2×C3—12741no—
186D3—71no—
187D3—911no—
188C22—19111noSylow
189C3—6371no—
190C3—12741no—
191C3#2143960811yescharacteristic, complemented
192C2—2731no—
193C2—211no—
194C2—6371no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C13C22×C3
LCSG ▷ C3×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#16838458C2semidirect
2. C3⋊#16838456C2semidirect
3. C3×#16838446C2semidirect
4. D21⋊D91C3semidirect
6. C3×#14274263C22semidirect
7. C7×D273C2×C3semidirect
8. C7×C13×D21C2×C3semidirect
9. C3×C7⋊D91C2×C3semidirect
13. #16838446D3semidirect
17. C3×C72×C13C22×C3semidirect
19. #14274263C2×D3semidirect
28. C7⋊D91C3×D3semidirect
41. C72×C13C2×C3×D3semidirect
44. D273AGL(1,𝔽7)semidirect
45. C13×D21AGL(1,𝔽7)semidirect
66. C7×D21D13⋊C3semidirect
73. C3×C7×C13C2×AGL(1,𝔽7)semidirect
74. C3×C7×C13C2×AGL(1,𝔽7)semidirect
96. C3×C72C2×D13⋊C3semidirect
111. C7×C13D3×AGL(1,𝔽7)semidirect
112. C7×C13D3×AGL(1,𝔽7)semidirect
128. C72D3×D13⋊C3semidirect
130. D21#10587722semidirect
146. C3×C13#64423⋊C2semidirect
156. C3×C7#10587716⋊C2semidirect
157. C3×C7C2×#10587722semidirect
174. C13#13183634semidirect
179. C7D3×#10587722semidirect
180. C7#10587722⋊D3semidirect
191. C3#21439608semidirect

Maximal subgroups

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

subgroupindex
C3⋊#168384582
C3⋊#168384562
C3×#168384462
D21⋊D913
#214396083
#10587722⋊D37
D3×#105877227
#1318363413