Finite Group Databasebeta

← #37525375

Subgroups — #37525375

Order 22932.

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

normal subgroups only

This group has 216 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⋊(D13⋊#3862)C211yesmaximal, characteristic, complemented
2C3⋊#16838453C211yesmaximal, characteristic, complemented
3C3×#16838452C211yesmaximal, characteristic, complemented
4D39⋊(C7⋊D7)C311yesmaximal, characteristic, complemented
5D13⋊#64425—31nomaximal
6C3×C13⋊#3862C2211yescharacteristic, complemented, Hall
7C13×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D39C2×C311yescharacteristic, complemented
9C3×C7⋊D91C2×C311yescharacteristic, complemented
10D13⋊#3862—31no—
11#16838453—31no—
12#16838452—21no—
13#16838452D311yescharacteristic, complemented
14#10587723⋊D3—71nomaximal
15#10587722⋊D3—71nomaximal
16D13×C7⋊D7—31noHall
17C3×C72×C13C22×C311yescharacteristic, complemented
18C13⋊#3862—21no—
19C13⋊#3862C2×D311yescharacteristic, complemented
20D3×#64425—131nomaximal, Hall
21C3⋊#10587720—71no—
22C3⋊#10587721—71no—
23C3⋊#10587716—71no—
24C3⋊#10587717—141no—
25C3×#10587722—71no—
26C3×#10587723—71no—
27C7⋊D91C3×D311yescharacteristic, complemented
28C13×C7⋊D7—31no—
29C72×D13—31no—
30D21⋊D13—71no—
31D21⋊D13—71no—
32D21⋊D13—212no—
33#10587716⋊C2—211no—
34#10587717⋊C2—211no—
35C3⋊#64425—261no—
36D3×#3862—131no—
37C3×#64425—131no—
38C3×#63271—141no—
39C3×#63270—71no—
40C72×C13C2×C3×D311yescharacteristic, complemented, Hall
41D3×C7⋊D7—131no—
42C2×#64425—391no—
43C13×D21—71no—
44C13×D21—71no—
45C13×D21—212no—
46C7×D39—32no—
47C7×D39AGL(1,𝔽7)11yescharacteristic, complemented
48C7×D39AGL(1,𝔽7)11yescharacteristic, complemented
49C3×D91—71no—
50C3×D91—71no—
51C3×D91—212no—
52#10587723—71no—
53#10587723—141no—
54#10587722—71no—
55#10587722—141no—
56#10587721—211no—
57#10587720—211no—
58#10587717—211no—
59#10587716—421no—
60D3×D13⋊C3—491noHall
61C3×#3862—261noHall
62D7×D13—211no—
63D7×D13—211no—
64D7×D13—632no—
65C3⋊(C7⋊D7)D13⋊C311yescharacteristic, complemented
66D3×C72—131no—
67C3×C7⋊D7—131no—
68C2×#3862—391no—
69#64425—131no—
70#64425—261no—
71#64425—781no—
72C3×C7×C13—32no—
73C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
74C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
75#63271—71no—
76#63271—281no—
77#63270—141no—
78#63270—141no—
79D3×AGL(1,𝔽7)—911no—
80D3×AGL(1,𝔽7)—911no—
81C3⋊(D13⋊C3)—981no—
82D3×C13⋊C3—491no—
83C3×D13⋊C3—491no—
84C2×C7⋊D7—391noHall
85D91—71no—
86D91—71no—
87D91—212no—
88C7×D13—31no—
89C7×D13—31no—
90C7×D13—92no—
91C13×D7—211no—
92C13×D7—211no—
93C13×D7—632no—
94D3×D13—491no—
95C2×D13⋊C3—1471no—
96C3×C72C2×D13⋊C311yescharacteristic, complemented
97#3862—261no—
98#3862—521no—
99C3⋊AGL(1,𝔽7)—911no—
100C3⋊AGL(1,𝔽7)—1821no—
101D3×ΓL(1,𝔽8)—1821no—
102D3×ΓL(1,𝔽8)—1821no—
103C3×AGL(1,𝔽7)—911no—
104C3×AGL(1,𝔽7)—911no—
105C3×C13⋊C3—981noHall
106C2×C72—391no—
107C7⋊D7—31no—
108C7⋊D7—131no—
109C7×C13—32no—
110C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
111C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
112D3×D7—2732no—
113D3×D7—911no—
114D3×D7—911no—
115C2×AGL(1,𝔽7)—2731no—
116C2×AGL(1,𝔽7)—2731no—
117D39#6442511yescharacteristic, complemented
118C3×D13—491no—
119D3×C13—491no—
120C2×C13⋊C3—1471no—
121D13⋊C3—2941no—
122D13⋊C3—491no—
123D13⋊C3—981no—
124C3×ΓL(1,𝔽8)—3641no—
125C3×ΓL(1,𝔽8)—3641no—
126C2×D13—1471noHall
127C72D3×D13⋊C311yescharacteristic, complemented, Sylow
128D21—71no—
129D21—71no—
130D21—212no—
131C3×D7—2732no—
132C3×D7—911no—
133C3×D7—911no—
134D3×C7—131no—
135D3×C7—131no—
136D3×C7—392no—
137C2×ΓL(1,𝔽8)—5461no—
138C2×ΓL(1,𝔽8)—5461no—
139AGL(1,𝔽7)—5461no—
140AGL(1,𝔽7)—5461no—
141AGL(1,𝔽7)—911no—
142AGL(1,𝔽7)—911no—
143AGL(1,𝔽7)—1821no—
144AGL(1,𝔽7)—1821no—
145C3×C13C2×#6442511yescharacteristic, complemented
146C13⋊C3—981no—
147C13⋊C3—1961no—
148C2×C3×D3—6371noHall
149C2×D7—2731no—
150C2×D7—2731no—
151C2×D7—8192no—
152C2×C13—1471no—
153D13—31no—
154D13—491no—
155C3×C7—32no—
156C3×C7#10587717⋊C211yescharacteristic, complemented
157C3×C7#10587716⋊C211yescharacteristic, complemented
158ΓL(1,𝔽8)—3641no—
159ΓL(1,𝔽8)—3641no—
160ΓL(1,𝔽8)—1821no—
161ΓL(1,𝔽8)—1821no—
162C2×C32—6371no—
163C3×D3—12741no—
164C3×D3—12741no—
165C2×C7—391no—
166C2×C7—391no—
167C2×C7—1172no—
168D7—2732no—
169D7—211no—
170D7—211no—
171D7—632no—
172D7—911no—
173D7—911no—
174C13D3×#6442511yescharacteristic, complemented, Sylow
175C22×C3—19111no—
176C2×D3—6371no—
177C32—25481noSylow
178C7—32no—
179C7#10587722⋊D311yescharacteristic, complemented
180C7#10587723⋊D311yescharacteristic, complemented
181C2×C3—6371no—
182C2×C3—6371no—
183C2×C3—38221no—
184C2×C3—38221no—
185C2×C3—12741no—
186D3—131no—
187D3—491no—
188C22—19111noSylow
189C3—25481no—
190C3—25481no—
191C3D13⋊#6442511yescharacteristic, complemented
192C2—391no—
193C2—6371no—
194C2—1471no—
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⋊(D13⋊#3862)C2semidirect
2. C3⋊#16838453C2semidirect
3. C3×#16838452C2semidirect
4. D39⋊(C7⋊D7)C3semidirect
6. C3×C13⋊#3862C22semidirect
7. C13×C3⋊(C7⋊D7)C2×C3semidirect
8. C72×D39C2×C3semidirect
9. C3×C7⋊D91C2×C3semidirect
13. #16838452D3semidirect
17. C3×C72×C13C22×C3semidirect
19. C13⋊#3862C2×D3semidirect
27. C7⋊D91C3×D3semidirect
40. C72×C13C2×C3×D3semidirect
47. C7×D39AGL(1,𝔽7)semidirect
48. C7×D39AGL(1,𝔽7)semidirect
65. C3⋊(C7⋊D7)D13⋊C3semidirect
73. C3×C7×C13C2×AGL(1,𝔽7)semidirect
74. C3×C7×C13C2×AGL(1,𝔽7)semidirect
96. C3×C72C2×D13⋊C3semidirect
110. C7×C13D3×AGL(1,𝔽7)semidirect
111. C7×C13D3×AGL(1,𝔽7)semidirect
117. D39#64425semidirect
127. C72D3×D13⋊C3semidirect
145. C3×C13C2×#64425semidirect
156. C3×C7#10587717⋊C2semidirect
157. C3×C7#10587716⋊C2semidirect
174. C13D3×#64425semidirect
179. C7#10587722⋊D3semidirect
180. C7#10587723⋊D3semidirect
191. C3D13⋊#64425semidirect

Maximal subgroups

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

subgroupindex
C3⋊(D13⋊#3862)2
C3⋊#168384532
C3×#168384522
D39⋊(C7⋊D7)3
D13⋊#644253
#10587723⋊D37
#10587722⋊D37
D3×#6442513