Finite Group Databasebeta

← #45692461

Subgroups — #45692461

Order 33516.

184 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊#19150304C211yesmaximal, characteristic, complemented
2C19×C3⋊#64425C211yesmaximal, characteristic, complemented
3C3×#19150304C211yesmaximal, characteristic, complemented
4D133⋊D21C311yesmaximal, characteristic, complemented
5#26013904—31nomaximal
6C3×C19×#3862C2211yescharacteristic, complemented, Hall
7C19×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C7×D399C2×C311yescharacteristic, complemented
9C3×C7×D133C2×C311yescharacteristic, complemented
10#19150304—21no—
11#19150304—31no—
12#19150304D311yescharacteristic, complemented
13C19×#64425—31no—
14(C3⋊AGL(1,𝔽7))⋊D19—71nomaximal
15D19×C3⋊AGL(1,𝔽7)—71nomaximal
16(C7⋊D7)⋊D19—31noHall
17C19×#3862—21no—
18C19×#3862C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20ΓL(1,𝔽8)×D57—71no—
21C3⋊(ΓL(1,𝔽8)⋊D19)—71no—
22C19×C3⋊AGL(1,𝔽7)—71no—
23C19×C3⋊AGL(1,𝔽7)—71no—
24C3×ΓL(1,𝔽8)×D19—71no—
25C3×ΓL(1,𝔽8)⋊D19—71no—
26C19×C7⋊D7—31no—
27C7×D133—31no—
28C7×D133C3×D311yescharacteristic, complemented
29#64422⋊D3—191nomaximal, Hall
30D21⋊D19—71no—
31D19×D21—71no—
32D19×AGL(1,𝔽7)—211no—
33D19×AGL(1,𝔽7)—211no—
34C3×C19×ΓL(1,𝔽8)—71no—
35C3×C19×ΓL(1,𝔽8)—71no—
36C72×C19C2×C3×D311yescharacteristic, complemented, Hall
37C3⋊#64425D1911yescharacteristic, complemented
38C3⋊#64422—191no—
39C3×#64422—191no—
40D399AGL(1,𝔽7)11yescharacteristic, complemented
41C19×D21—71no—
42C19×D21—71no—
43C19×D21—421no—
44C7×D57—71no—
45C3×D133AGL(1,𝔽7)11yescharacteristic, complemented
46C3×C7×D19—71no—
47ΓL(1,𝔽8)⋊D19—71no—
48ΓL(1,𝔽8)⋊D19—141no—
49ΓL(1,𝔽8)⋊D19—211no—
50C19×AGL(1,𝔽7)—211no—
51C19×AGL(1,𝔽7)—211no—
52ΓL(1,𝔽8)×D19—71no—
53ΓL(1,𝔽8)×D19—141no—
54ΓL(1,𝔽8)×D19—211no—
55C3×D3×D19—491noHall
56D7×D21—191no—
57#64422⋊C2—571no—
58D7×D19—211no—
59D7×D19—211no—
60C3×#3862C2×D1911yescharacteristic, complemented, Hall
61C3×C7×C19—61no—
62C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
63C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
64C19×ΓL(1,𝔽8)—71no—
65C19×ΓL(1,𝔽8)—71no—
66C19×ΓL(1,𝔽8)—141no—
67C19×ΓL(1,𝔽8)—141no—
68C3×D57—491no—
69C3×D3×C19—491no—
70C32×D19—491no—
71C3⋊(C7⋊D7)C3×D1911yescharacteristic, complemented
72C7×D21—191no—
73C3×C7×D7—191no—
74#64425—31no—
75#64422—191no—
76#64422—381no—
77#64422—571no—
78D133—31no—
79D133C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
80C7×D19—71no—
81C7×D19—211no—
82D7×C19—211no—
83D7×C19—211no—
84D7×C19—1261no—
85C2×C3⋊AGL(1,𝔽7)—1331no—
86D3×AGL(1,𝔽7)—1331no—
87C2×C3×D19—1471no—
88D3×D19—491no—
89D72—571noHall
90C32×C19—491noHall
91C3×C72C2×C3×D1911yescharacteristic, complemented
92#3862—21no—
93#3862D3×D1911yescharacteristic, complemented
94C7×C19—61no—
95C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
96C7×C19C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
97C2×C3×ΓL(1,𝔽8)—1331no—
98C3⋊AGL(1,𝔽7)—71no—
99C3⋊AGL(1,𝔽7)—71no—
100C3⋊AGL(1,𝔽7)—1331no—
101D3×ΓL(1,𝔽8)—1331no—
102C3×AGL(1,𝔽7)—1331no—
103C2×C3×C19—1471no—
104D57—71no—
105C3×D19—71no—
106C3×D19—491no—
107C3×D19—981no—
108C3×D19—1471no—
109D3×C19—491no—
110C7⋊D7—31no—
111C7×D7—191no—
112C7×D7—571no—
113C2×D21—1331no—
114D3×D7—1331no—
115C2×AGL(1,𝔽7)—3991no—
116C2×AGL(1,𝔽7)—3991no—
117C2×D19—1471noHall
118C3×ΓL(1,𝔽8)—71no—
119C3×ΓL(1,𝔽8)—71no—
120C3×C19—491no—
121C3×C19—981no—
122C3×C19#64422⋊C211yescharacteristic, complemented
123C72C3×D3×D1911yescharacteristic, complemented, Sylow
124C2×C3×C7—1331no—
125D21—71no—
126D21—71no—
127D21—191no—
128D21—421no—
129C3×D7—191no—
130D3×C7—1331no—
131C2×ΓL(1,𝔽8)—2661no—
132C2×ΓL(1,𝔽8)—1331no—
133C2×ΓL(1,𝔽8)—3991no—
134AGL(1,𝔽7)—2661no—
135AGL(1,𝔽7)—211no—
136AGL(1,𝔽7)—211no—
137AGL(1,𝔽7)—1331no—
138AGL(1,𝔽7)—3991no—
139C2×C19—1471no—
140D19—71no—
141D19—211no—
142C2×C3×D3—9311noHall
143C2×D7—3991no—
144C2×D7—3991no—
145C3×C7—61no—
146C3×C7D19×AGL(1,𝔽7)11yescharacteristic, complemented
147C3×C7D19×AGL(1,𝔽7)11yescharacteristic, complemented
148ΓL(1,𝔽8)—71no—
149ΓL(1,𝔽8)—71no—
150ΓL(1,𝔽8)—141no—
151ΓL(1,𝔽8)—141no—
152C19#64422⋊D311yescharacteristic, complemented, Sylow
153C2×C32—9311no—
154C3×D3—491no—
155C3×D3—9311no—
156C2×C7—1331no—
157C2×C7—3991no—
158D7—191no—
159D7—211no—
160D7—211no—
161D7—571no—
162D7—1261no—
163C22×C3—27931no—
164C2×D3—9311no—
165C32—491noSylow
166C7—61no—
167C7D19×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
168C7(C3⋊AGL(1,𝔽7))⋊D1911yescharacteristic, complemented
169C2×C3—18621no—
170C2×C3—1331no—
171C2×C3—1471no—
172C2×C3—9311no—
173C2×C3—27931no—
174D3—491no—
175D3—1331no—
176C22—27931noSylow
177C3—491no—
178C3—981no—
179C3#2601390411yescharacteristic, complemented
180C2—1331no—
181C2—3991no—
182C2—1471no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C19C22×C3
LCSG ▷ C3×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#19150304C2semidirect
2. C19×C3⋊#64425C2semidirect
3. C3×#19150304C2semidirect
4. D133⋊D21C3semidirect
6. C3×C19×#3862C22semidirect
7. C19×C3⋊(C7⋊D7)C2×C3semidirect
8. C7×D399C2×C3semidirect
9. C3×C7×D133C2×C3semidirect
12. #19150304D3semidirect
18. C19×#3862C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
28. C7×D133C3×D3semidirect
36. C72×C19C2×C3×D3semidirect
37. C3⋊#64425D19semidirect
40. D399AGL(1,𝔽7)semidirect
45. C3×D133AGL(1,𝔽7)semidirect
60. C3×#3862C2×D19semidirect
62. C3×C7×C19C2×AGL(1,𝔽7)semidirect
63. C3×C7×C19C2×AGL(1,𝔽7)semidirect
71. C3⋊(C7⋊D7)C3×D19semidirect
79. D133C3⋊AGL(1,𝔽7)semidirect
91. C3×C72C2×C3×D19semidirect
93. #3862D3×D19semidirect
95. C7×C19D3×AGL(1,𝔽7)semidirect
96. C7×C19C2×C3⋊AGL(1,𝔽7)semidirect
122. C3×C19#64422⋊C2semidirect
123. C72C3×D3×D19semidirect
146. C3×C7D19×AGL(1,𝔽7)semidirect
147. C3×C7D19×AGL(1,𝔽7)semidirect
152. C19#64422⋊D3semidirect
167. C7D19×C3⋊AGL(1,𝔽7)semidirect
168. C7(C3⋊AGL(1,𝔽7))⋊D19semidirect
179. C3#26013904semidirect

Maximal subgroups

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

subgroupindex
C3⋊#191503042
C19×C3⋊#644252
C3×#191503042
D133⋊D213
#260139043
(C3⋊AGL(1,𝔽7))⋊D197
D19×C3⋊AGL(1,𝔽7)7
#64422⋊D319