Finite Group Databasebeta

← #45692002

Subgroups — #45692002

Order 33516.

152 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 19 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#30660727C211yesmaximal, characteristic, complemented
2#30660725C211yesmaximal, characteristic, complemented
3#30660661C211yesmaximal, characteristic, complemented
4#64418⋊D19C311yesmaximal, characteristic, complemented
5#26013891—31nomaximal
6#22552727C2211yescharacteristic, complemented, Hall
7C19⋊#64418C2×C311yescharacteristic, complemented
8C19×#64418C2×C311yescharacteristic, complemented
9#19150306—21no—
10#19150297—31no—
11#19150295—31no—
12#19150292C2×C311yescharacteristic, complemented
13#19150285D311yescharacteristic, complemented
14D7×D133—31noHall
15C19×#3862C22×C311yescharacteristic, complemented
16#14584116C2×D311yescharacteristic, complemented
17C7×#87704—21no—
18ΓL(1,𝔽8)⋊(D19⋊C3)—141no—
19C7⋊D133C3×D311yescharacteristic, complemented
20C7×D133—31no—
21C7×D7×C19—31no—
22(#64418⋊C2)⋊C3—191nomaximal, Hall
23C2×#11716328—211no—
24#11716322⋊C2—211no—
25ΓL(1,𝔽8)×C19⋊C3—141no—
26C72×C19C2×C3×D311yescharacteristic, complemented, Hall
27ΓL(1,𝔽8)⋊AGL(1,𝔽7)—191no—
28#64418⋊C3—191no—
29#64418⋊C3—191no—
30C2×#87705—211no—
31#11716328—141no—
32#11716328—211no—
33#11716328—211no—
34#11716328—211no—
35#11716327—141no—
36#11716326—211no—
37ΓL(1,𝔽8)⋊D19—141no—
38#11716322—211no—
39(C19⋊C3)⋊D7—141no—
40D3×D19⋊C3—491nomaximal, Hall
41#64423⋊C2—571no—
42#64418⋊C2—191no—
43C2×D133—211no—
44D7×D19—211no—
45ΓL(1,𝔽8)2—191noHall
46#87705—141no—
47#87705—211no—
48#87705—211no—
49#87704—21no—
50C7×C19⋊C3—141no—
51C19×ΓL(1,𝔽8)—141no—
52C3⋊(D19⋊C3)—491no—
53D3×C19⋊C3—491no—
54C3×D19⋊C3—491no—
55#64425—191no—
56#64424—191no—
57#64423—571no—
58#64423—571no—
59ΓL(1,𝔽8)⋊D7—381no—
60#64418—191no—
61#64418D19⋊C311yescharacteristic, complemented
62C2×C7×C19—211no—
63D133—31no—
64D133—141no—
65D133—211no—
66D133—211no—
67C7×D19—211no—
68D7×C19—31no—
69D3×D19—491no—
70C2×D19⋊C3—1471no—
71D72—571noHall
72C3×C19⋊C3—491noHall
73#3862C2×D19⋊C311yescharacteristic, complemented
74#3861—191no—
75C7×ΓL(1,𝔽8)—381no—
76C7×C19—21no—
77C7×C19—31no—
78C7×C19—31no—
79C3×AGL(1,𝔽7)—2661no—
80D57—491no—
81C3×D19—491no—
82D3×C19—491no—
83C2×C19⋊C3—1471no—
84D19⋊C3—491no—
85D19⋊C3—981no—
86D19⋊C3—1471no—
87C7⋊D7—191no—
88C7×D7—31no—
89C7×D7—571no—
90C2×AGL(1,𝔽7)—3991no—
91C2×AGL(1,𝔽7)—3991no—
92C2×D19—1471noHall
93C3×ΓL(1,𝔽8)—2661no—
94C3×C19—491no—
95C19⋊C3—141no—
96C19⋊C3—491no—
97C72D3×D19⋊C311yescharacteristic, complemented, Sylow
98C3×D7—2661no—
99C2×ΓL(1,𝔽8)—3991no—
100C2×ΓL(1,𝔽8)—3991no—
101AGL(1,𝔽7)—2661no—
102AGL(1,𝔽7)—2661no—
103AGL(1,𝔽7)—2661no—
104AGL(1,𝔽7)—3991no—
105AGL(1,𝔽7)—3991no—
106AGL(1,𝔽7)—3991no—
107AGL(1,𝔽7)—3991no—
108C2×C19—211no—
109D19—211no—
110D19—491no—
111C2×C3×D3—9311noHall
112C2×D7—3991no—
113C2×D7—3991no—
114C3×C7—2661no—
115ΓL(1,𝔽8)—2661no—
116ΓL(1,𝔽8)—141no—
117ΓL(1,𝔽8)—381no—
118ΓL(1,𝔽8)—3991no—
119ΓL(1,𝔽8)—3991no—
120C19(#64418⋊C2)⋊C311yescharacteristic, complemented, Sylow
121C2×C32—9311no—
122C3×D3—9311no—
123C3×D3—9311no—
124C2×C7—211no—
125C2×C7—3991no—
126D7—31no—
127D7—2661no—
128D7—571no—
129D7—3991no—
130D7—3991no—
131C22×C3—27931no—
132C2×D3—9311no—
133C32—9311noSylow
134C7—21no—
135C7—31no—
136C7—31no—
137C2×C3—18621no—
138C2×C3—9311no—
139C2×C3—9311no—
140C2×C3—27931no—
141C2×C3—27931no—
142D3—491no—
143D3—9311no—
144C22—27931noSylow
145C3—2661no—
146C3—491no—
147C3—9311no—
148C2—211no—
149C2—3991no—
150C2—9311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC19×#3862C22×C3
Fitting, socleC72×C19C2×C3×D3
LCSG ▷ C19×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
1. #30660727C2semidirect
2. #30660725C2semidirect
3. #30660661C2semidirect
4. #64418⋊D19C3semidirect
6. #22552727C22semidirect
7. C19⋊#64418C2×C3semidirect
8. C19×#64418C2×C3semidirect
12. #19150292C2×C3semidirect
13. #19150285D3semidirect
15. C19×#3862C22×C3semidirect
16. #14584116C2×D3semidirect
19. C7⋊D133C3×D3semidirect
26. C72×C19C2×C3×D3semidirect
61. #64418D19⋊C3semidirect
73. #3862C2×D19⋊C3semidirect
97. C72D3×D19⋊C3semidirect
120. C19(#64418⋊C2)⋊C3semidirect

Maximal subgroups

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

subgroupindex
#306607272
#306607252
#306606612
#64418⋊D193
#260138913
(#64418⋊C2)⋊C319
D3×D19⋊C349