Finite Group Databasebeta

← #37525359

Subgroups — #37525359

Order 22932.

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

normal subgroups only

This group has 184 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⋊#16838464C211yesmaximal, characteristic, complemented
2C3⋊#16838463C211yesmaximal, characteristic, complemented
3C3×#16838452C211yesmaximal, characteristic, complemented
4D21⋊D91C311yesmaximal, characteristic, complemented
5#21439617—31nomaximal
6C3×C13⋊#3862C2211yescharacteristic, complemented, Hall
7C7×D273C2×C311yescharacteristic, complemented
8C7×C13×D21C2×C311yescharacteristic, complemented
9C3×C7⋊D91C2×C311yescharacteristic, complemented
10#16838464—31no—
11#16838463—31no—
12#16838452—21no—
13#16838452D311yescharacteristic, complemented
14#10587722⋊D3—71nomaximal
15D3×#10587723—71nomaximal
16D7×D91—31noHall
17C3×C72×C13C22×C311yescharacteristic, complemented
18C13⋊#3862—21no—
19C13⋊#3862C2×D311yescharacteristic, complemented
20#13183636—131nomaximal, Hall
21C3⋊#10587723—141no—
22C3⋊#10587720—141no—
23C3⋊#10587716—71no—
24D3×#63271—71no—
25C3×#10587722—71no—
26C3×#10587723—71no—
27C7⋊D91C3×D311yescharacteristic, complemented
28C7×D91—31no—
29C7×C13×D7—31no—
30D21⋊D13—71no—
31D3×D91—71no—
32C2×#10587723—211no—
33#10587716⋊C2—211no—
34C3⋊#64422—131no—
35C3⋊#64422—131no—
36C3×#64425—131no—
37C3×#63271—141no—
38C3×#63270—141no—
39C72×C13C2×C3×D311yescharacteristic, complemented, Hall
40D21⋊D7—131no—
41#64422⋊C2—391no—
42D273AGL(1,𝔽7)11yescharacteristic, complemented
43C13×D21AGL(1,𝔽7)11yescharacteristic, complemented
44C7×D39—71no—
45D3×C7×C13—71no—
46C3×D91—71no—
47C3×D91—71no—
48C3×D91—421no—
49C2×#63271—211no—
50#10587723—71no—
51#10587723—141no—
52#10587723—421no—
53#10587722—71no—
54#10587722—141no—
55#10587720—421no—
56#10587716—211no—
57D3×D13⋊C3—491noHall
58C3×#3862—131noHall
59C2×D91—211no—
60D7×D13—211no—
61C7×D21—131no—
62C7×D21D13⋊C311yescharacteristic, complemented
63C3×C7⋊D7—131no—
64#64425—131no—
65#64425—261no—
66#64422—391no—
67#64422—781no—
68C3×C7×C13—61no—
69C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
70C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
71#63271—141no—
72#63271—281no—
73#63270—141no—
74#63270—281no—
75D3×AGL(1,𝔽7)—911no—
76D3×AGL(1,𝔽7)—911no—
77C3⋊(D13⋊C3)—981no—
78D3×C13⋊C3—491no—
79C3×D13⋊C3—491no—
80D72—391noHall
81C2×C7×C13—211no—
82D91—31no—
83D91—71no—
84D91—71no—
85D91—421no—
86C7×D13—211no—
87C13×D7—31no—
88D3×D13—491no—
89C2×D13⋊C3—1471no—
90C3×C72C2×D13⋊C311yescharacteristic, complemented
91#3862—261no—
92#3862—521no—
93C3⋊AGL(1,𝔽7)—1821no—
94C3⋊AGL(1,𝔽7)—1821no—
95D3×ΓL(1,𝔽8)—911no—
96D3×ΓL(1,𝔽8)—1821no—
97C3×AGL(1,𝔽7)—911no—
98C3×AGL(1,𝔽7)—911no—
99C3×C13⋊C3—1961noHall
100C7⋊D7—131no—
101C7×D7—31no—
102C7×D7—391no—
103C7×C13—61no—
104C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
105C7×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented
106D3×D7—911no—
107D3×D7—911no—
108C2×AGL(1,𝔽7)—2731no—
109C2×AGL(1,𝔽7)—2731no—
110D39—71no—
111C3×D13—491no—
112D3×C13—71no—
113C2×C13⋊C3—2941no—
114D13⋊C3—2941no—
115D13⋊C3—491no—
116D13⋊C3—981no—
117C3×ΓL(1,𝔽8)—3641no—
118C3×ΓL(1,𝔽8)—1821no—
119C2×D13—1471noHall
120C72D3×D13⋊C311yescharacteristic, complemented, Sylow
121D21—131no—
122D21#1058772311yescharacteristic, complemented
123C3×D7—5461no—
124C3×D7—911no—
125C3×D7—911no—
126D3×C7—71no—
127D3×C7—911no—
128C2×ΓL(1,𝔽8)—2731no—
129C2×ΓL(1,𝔽8)—5461no—
130AGL(1,𝔽7)—5461no—
131AGL(1,𝔽7)—5461no—
132AGL(1,𝔽7)—911no—
133AGL(1,𝔽7)—911no—
134AGL(1,𝔽7)—1821no—
135AGL(1,𝔽7)—1821no—
136C3×C13#64422⋊C211yescharacteristic, complemented
137C13⋊C3—1961no—
138C13⋊C3—1961no—
139C2×C3×D3—6371noHall
140C2×D7—2731no—
141C2×D7—2731no—
142C2×C13—211no—
143D13—211no—
144D13—491no—
145C3×C7—61no—
146C3×C7#10587716⋊C211yescharacteristic, complemented
147C3×C7C2×#1058772311yescharacteristic, complemented
148ΓL(1,𝔽8)—3641no—
149ΓL(1,𝔽8)—3641no—
150ΓL(1,𝔽8)—1821no—
151ΓL(1,𝔽8)—1821no—
152C2×C32—6371no—
153C3×D3—12741no—
154C3×D3—12741no—
155C2×C7—2731no—
156C2×C7—211no—
157D7—31no—
158D7—5461no—
159D7—391no—
160D7—911no—
161D7—911no—
162C13#1318363611yescharacteristic, complemented, Sylow
163C22×C3—19111no—
164C2×D3—6371no—
165C32—25481noSylow
166C7—61no—
167C7D3×#1058772311yescharacteristic, complemented
168C7#10587722⋊D311yescharacteristic, complemented
169C2×C3—6371no—
170C2×C3—6371no—
171C2×C3—38221no—
172C2×C3—38221no—
173C2×C3—12741no—
174D3—71no—
175D3—911no—
176C22—19111noSylow
177C3—25481no—
178C3—25481no—
179C3#2143961711yescharacteristic, complemented
180C2—2731no—
181C2—211no—
182C2—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⋊#16838464C2semidirect
2. C3⋊#16838463C2semidirect
3. C3×#16838452C2semidirect
4. D21⋊D91C3semidirect
6. C3×C13⋊#3862C22semidirect
7. C7×D273C2×C3semidirect
8. C7×C13×D21C2×C3semidirect
9. C3×C7⋊D91C2×C3semidirect
13. #16838452D3semidirect
17. C3×C72×C13C22×C3semidirect
19. C13⋊#3862C2×D3semidirect
27. C7⋊D91C3×D3semidirect
39. C72×C13C2×C3×D3semidirect
42. D273AGL(1,𝔽7)semidirect
43. C13×D21AGL(1,𝔽7)semidirect
62. C7×D21D13⋊C3semidirect
69. C3×C7×C13C2×AGL(1,𝔽7)semidirect
70. C3×C7×C13C2×AGL(1,𝔽7)semidirect
90. C3×C72C2×D13⋊C3semidirect
104. C7×C13D3×AGL(1,𝔽7)semidirect
105. C7×C13D3×AGL(1,𝔽7)semidirect
120. C72D3×D13⋊C3semidirect
122. D21#10587723semidirect
136. C3×C13#64422⋊C2semidirect
146. C3×C7#10587716⋊C2semidirect
147. C3×C7C2×#10587723semidirect
162. C13#13183636semidirect
167. C7D3×#10587723semidirect
168. C7#10587722⋊D3semidirect
179. C3#21439617semidirect

Maximal subgroups

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

subgroupindex
C3⋊#168384642
C3⋊#168384632
C3×#168384522
D21⋊D913
#214396173
#10587722⋊D37
D3×#105877237
#1318363613