Finite Group Databasebeta

← #37524428

Subgroups — #37524428

Order 22932.

156 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#26039457C211yesmaximal, characteristic, complemented
2#26039457C211yesmaximal, characteristic, complemented
3#26039447C211yesmaximal, characteristic, complemented
4C3×C13×D72C311yesmaximal, characteristic
5#19153199C2211yescharacteristic, complemented, Hall
6C3×C13×C7⋊D7C2×C311yescharacteristic
7C3×C7×C13×D7C2×C311yescharacteristic
8C3×C7×C13×D7C2×C311yescharacteristic
9C2×#13109901—71nomaximal
10C2×#13109901—71nomaximal
11C13×D72C911yescharacteristic, complemented, Hall
12C3×C72×C13C22×C311yescharacteristic
13#11725076⋊C2—131nomaximal, Hall
14C2×#11717942—71no—
15C2×#11717942—71no—
16#13109901—71no—
17#13109901—71no—
18#13109901—71no—
19#13109901—71no—
20#13109901—141no—
21#13109901—141no—
22#13109901—141no—
23C13×C7⋊D7C2×C911yescharacteristic, complemented
24C7×C13×D7C2×C911yescharacteristic, complemented
25C7×C13×D7C2×C911yescharacteristic, complemented
26C2×C3×C13×D7—211no—
27C2×C3×C13×D7—211no—
28#11725077—131no—
29#11725076—131no—
30#11725076—131no—
31#11717942—71no—
32#11717942—71no—
33#11717942—141no—
34#11717942—141no—
35#11717942—141no—
36C72×C13C22×C911yescharacteristic, complemented, Hall
37C3×D72C13⋊C311yescharacteristic
38C2×C3×C7×C13—71no—
39C2×C3×C7×C13—211no—
40C3×C13×D7—141no—
41C3×C13×D7—141no—
42C3×C13×D7—211no—
43C3×C13×D7—211no—
44C3×C13×D7—421no—
45C3×C13×D7AGL(1,𝔽7)11yescharacteristic
46C3×C13×D7AGL(1,𝔽7)11yescharacteristic
47C22×C13⋊C9—491noHall
48#89204—131noHall
49C2×C13×D7—211no—
50C2×C13×D7—211no—
51C3×C7⋊D7C2×C13⋊C311yescharacteristic
52C3×C7×D7C2×C13⋊C311yescharacteristic
53C3×C7×D7C2×C13⋊C311yescharacteristic
54C3×C7×C13—21no—
55C3×C7×C13—21no—
56C3×C7×C13—21no—
57C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
58C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
59C2×D7⋊C9—911no—
60C2×D7⋊C9—911no—
61C2×C13⋊C9—491no—
62C2×C13⋊C9—491no—
63C2×C13⋊C9—491no—
64D72C13⋊C911yescharacteristic, complemented, Hall
65C2×C7×C13—71no—
66C2×C7×C13—211no—
67C13×D7—141no—
68C13×D7—141no—
69C13×D7—211no—
70C13×D7—211no—
71C13×D7—421no—
72C13×D7D7⋊C911yescharacteristic, complemented
73C13×D7D7⋊C911yescharacteristic, complemented
74C22×C3×C13—1471no—
75C3×C72C22×C13⋊C311yescharacteristic
76C2×C7⋊C9—911no—
77C2×C7⋊C9—911no—
78D7⋊C9—911no—
79D7⋊C9—911no—
80D7⋊C9—911no—
81D7⋊C9—911no—
82D7⋊C9—1821no—
83D7⋊C9—1821no—
84D7⋊C9—1821no—
85C13⋊C9—491noHall
86C7⋊D7C2×C13⋊C911yescharacteristic, complemented
87C7×D7C2×C13⋊C911yescharacteristic, complemented
88C7×D7C2×C13⋊C911yescharacteristic, complemented
89C7×C13—21no—
90C7×C13—21no—
91C7×C13—21no—
92C7×C13C2×D7⋊C911yescharacteristic, complemented
93C7×C13C2×D7⋊C911yescharacteristic, complemented
94C2×C3×D7—211no—
95C2×C3×D7—211no—
96C2×C3×C13—211no—
97C2×C3×C13—211no—
98C2×C3×C13—1471no—
99C7⋊C9—911no—
100C7⋊C9—911no—
101C7⋊C9—1821no—
102C7⋊C9—1821no—
103C7⋊C9—1821no—
104C22×C13—1471noHall
105C72C22×C13⋊C911yescharacteristic, complemented, Sylow
106C2×C3×C7—71no—
107C2×C3×C7—211no—
108C3×D7—141no—
109C3×D7—141no—
110C3×D7—211no—
111C3×D7—211no—
112C3×D7—421no—
113C3×D7#1058772111yescharacteristic
114C3×D7#1058772111yescharacteristic
115C3×C13#64423⋊C211yescharacteristic
116C22×C9—6371noHall
117C2×D7—211no—
118C2×D7—211no—
119C2×C13—211no—
120C2×C13—211no—
121C2×C13—1471no—
122C3×C7—21no—
123C3×C7—21no—
124C3×C7—21no—
125C3×C7C2×#1058772111yescharacteristic
126C3×C7C2×#1058772111yescharacteristic
127C2×C9—6371no—
128C2×C9—6371no—
129C2×C9—6371no—
130C2×C7—71no—
131C2×C7—211no—
132D7—141no—
133D7—141no—
134D7—211no—
135D7—211no—
136D7—421no—
137D7#1310990111yescharacteristic, complemented
138D7#1310990111yescharacteristic, complemented
139C13#11725076⋊C211yescharacteristic, complemented, Sylow
140C22×C3—1471no—
141C9—6371noSylow
142C7—21no—
143C7—21no—
144C7—21no—
145C7C2×#1310990111yescharacteristic, complemented
146C7C2×#1310990111yescharacteristic, complemented
147C2×C3—211no—
148C2×C3—211no—
149C2×C3—1471no—
150C22—1471noSylow
151C3#2143961311yescharacteristic
152C2—211no—
153C2—211no—
154C2—1471no—
subgroupG/H
center, Frattini, hypercenterC3#21439613
commutator, hypocenterC72×C13C22×C9
Fitting, socle, cosocleC3×C72×C13C22×C3
prime radicalC3×C13×D72C3
LCSG ▷ C72×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #26039457C2semidirect
2. #26039457C2semidirect
3. #26039447C2semidirect
5. #19153199C22semidirect
11. C13×D72C9semidirect
23. C13×C7⋊D7C2×C9semidirect
24. C7×C13×D7C2×C9semidirect
25. C7×C13×D7C2×C9semidirect
36. C72×C13C22×C9semidirect
64. D72C13⋊C9semidirect
72. C13×D7D7⋊C9semidirect
73. C13×D7D7⋊C9semidirect
86. C7⋊D7C2×C13⋊C9semidirect
87. C7×D7C2×C13⋊C9semidirect
88. C7×D7C2×C13⋊C9semidirect
92. C7×C13C2×D7⋊C9semidirect
93. C7×C13C2×D7⋊C9semidirect
105. C72C22×C13⋊C9semidirect
137. D7#13109901semidirect
138. D7#13109901semidirect
139. C13#11725076⋊C2semidirect
145. C7C2×#13109901semidirect
146. C7C2×#13109901semidirect

Maximal subgroups

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

subgroupindex
#260394572
#260394472
C3×C13×D723
C2×#131099017
#11725076⋊C213