Finite Group Databasebeta

← #45692312

Subgroups — #45692312

Order 33516.

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

normal subgroups only

This group has 216 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⋊#19150309C211yesmaximal, characteristic, complemented
2C7×C3⋊#11716322C211yesmaximal, characteristic, complemented
3C3×#19150307C211yesmaximal, characteristic, complemented
4D57⋊(C7⋊D7)C311yesmaximal, characteristic, complemented
5#11716322⋊D7—31nomaximal
6C3×C7×#87705C2211yescharacteristic, complemented, Hall
7C19×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D57C2×C311yescharacteristic, complemented
9C3×C7⋊D133C2×C311yescharacteristic, complemented
10#19150309—31no—
11#19150307—21no—
12#19150307D311yescharacteristic, complemented
13C7×#11716322—31no—
14(C3⋊(D19⋊C3))⋊D7—71nomaximal
15#11716328⋊D3—71nomaximal
16D19×C7⋊D7—31noHall
17C7×#87705—21no—
18C7×#87705C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20D21×C19⋊C3—71no—
21C3⋊#11716322D711yescharacteristic, complemented
22C3⋊#11716326—71no—
23C7×C3⋊(D19⋊C3)—71no—
24C3×(C19⋊C3)⋊D7—71no—
25C3×#11716328—71no—
26C7⋊D133C3×D311yescharacteristic, complemented
27C19×C7⋊D7—31no—
28C72×D19—31no—
29D3×ΓL(1,𝔽8)⋊D7—191nomaximal, Hall
30D21⋊D19—71no—
31D21⋊D19—71no—
32D21⋊D19—212no—
33#11716322⋊C2—211no—
34D7×D19⋊C3—211no—
35C3×#87705C2×D711yescharacteristic, complemented
36C3×C7×C19⋊C3—71no—
37C72×C19C2×C3×D311yescharacteristic, complemented, Hall
38C3⋊(ΓL(1,𝔽8)⋊D7)—191no—
39D3×C7×ΓL(1,𝔽8)—191no—
40C3×ΓL(1,𝔽8)⋊D7—191no—
41C19×D21—71no—
42C19×D21—71no—
43C19×D21—212no—
44C7×D57—32no—
45C7×D57AGL(1,𝔽7)11yescharacteristic, complemented
46C7×D57C3×D711yescharacteristic, complemented
47C3×D133—71no—
48C3×D133—71no—
49C3×D133—212no—
50#11716328—71no—
51#11716328—141no—
52#11716326—211no—
53#11716322—31no—
54(C19⋊C3)⋊D7—71no—
55(C19⋊C3)⋊D7—141no—
56D7×C19⋊C3—211no—
57C7×D19⋊C3—211no—
58D3×D19⋊C3—491noHall
59D3×C7⋊D7—191no—
60C2×ΓL(1,𝔽8)⋊D7—571no—
61D7×D19—211no—
62D7×D19—211no—
63D7×D19—632no—
64C3×C7×ΓL(1,𝔽8)—191noHall
65C3×C7×C19—32no—
66C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C3×C7×C19C2×C3×D711yescharacteristic, complemented
68#87705—21no—
69#87705D3×D711yescharacteristic, complemented
70C7×C19⋊C3—71no—
71C7×C19⋊C3—141no—
72C3⋊(D19⋊C3)—71no—
73D3×C19⋊C3—491no—
74C3×D19⋊C3—491no—
75C3⋊(C7⋊D7)D19⋊C311yescharacteristic, complemented
76D3×C72—191no—
77C3×C7⋊D7—191no—
78C2×C7×ΓL(1,𝔽8)—571no—
79ΓL(1,𝔽8)⋊D7—191no—
80ΓL(1,𝔽8)⋊D7—381no—
81ΓL(1,𝔽8)⋊D7—571no—
82D133—71no—
83D133—71no—
84D133—212no—
85C7×D19—31no—
86C7×D19—31no—
87C7×D19—92no—
88D7×C19—211no—
89D7×C19—211no—
90D7×C19—632no—
91C3×D3×D7—1331no—
92D3×AGL(1,𝔽7)—1331no—
93D3×D19—491no—
94C2×D19⋊C3—1471no—
95C2×C7⋊D7—571noHall
96C3×C19⋊C3—71noHall
97C3×C72C2×D19⋊C311yescharacteristic, complemented
98C7×ΓL(1,𝔽8)—191no—
99C7×ΓL(1,𝔽8)—381no—
100C7×C19—32no—
101C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
102C7×C19C3×D3×D711yescharacteristic, complemented
103C3×D21—1331no—
104C3×D3×C7—1331no—
105C32×D7—1331no—
106C3⋊AGL(1,𝔽7)—1331no—
107D3×ΓL(1,𝔽8)—191no—
108C3×AGL(1,𝔽7)—1331no—
109D57ΓL(1,𝔽8)⋊D711yescharacteristic, complemented
110C3×D19—491no—
111D3×C19—491no—
112C2×C19⋊C3—1471no—
113D19⋊C3—211no—
114D19⋊C3—491no—
115D19⋊C3—981no—
116C2×C72—571no—
117C7⋊D7—31no—
118C7⋊D7—191no—
119C2×C3×D7—3991no—
120D3×D7—1331no—
121D3×D7—1331no—
122D3×D7—3992no—
123C2×AGL(1,𝔽7)—3991no—
124C2×D19—1471noHall
125C32×C7—1331no—
126C3×ΓL(1,𝔽8)—191no—
127C3×C19C2×ΓL(1,𝔽8)⋊D711yescharacteristic, complemented
128C19⋊C3—71no—
129C19⋊C3—141no—
130C72D3×D19⋊C311yescharacteristic, complemented, Sylow
131C2×C3×C7—3991no—
132D21—71no—
133D21—71no—
134D21—212no—
135C3×D7—2661no—
136C3×D7—1331no—
137C3×D7—1331no—
138C3×D7—1331no—
139C3×D7—3992no—
140C3×D7—3991no—
141D3×C7—191no—
142D3×C7—191no—
143D3×C7—572no—
144C2×ΓL(1,𝔽8)—571no—
145AGL(1,𝔽7)—2661no—
146AGL(1,𝔽7)—1331no—
147AGL(1,𝔽7)—3991no—
148C2×C19—1471no—
149D19—31no—
150D19—491no—
151C2×C3×D3—9311noHall
152C2×D7—3991no—
153C2×D7—3991no—
154C2×D7—11972no—
155C3×C7—32no—
156C3×C7—2661no—
157C3×C7—1331no—
158C3×C7D7×D19⋊C311yescharacteristic, complemented
159C3×C7#11716322⋊C211yescharacteristic, complemented
160ΓL(1,𝔽8)—191no—
161ΓL(1,𝔽8)—381no—
162C19D3×ΓL(1,𝔽8)⋊D711yescharacteristic, complemented, Sylow
163C2×C32—9311no—
164C3×D3—1331no—
165C3×D3—9311no—
166C2×C7—571no—
167C2×C7—571no—
168C2×C7—1712no—
169D7—211no—
170D7—211no—
171D7—632no—
172D7—1331no—
173D7—1331no—
174D7—3992no—
175C22×C3—27931no—
176C2×D3—9311no—
177C32—1331noSylow
178C7—32no—
179C7#11716328⋊D311yescharacteristic, complemented
180C7(C3⋊(D19⋊C3))⋊D711yescharacteristic, complemented
181C2×C3—18621no—
182C2×C3—3991no—
183C2×C3—9311no—
184C2×C3—9311no—
185C2×C3—27931no—
186D3—191no—
187D3—491no—
188C22—27931noSylow
189C3—2661no—
190C3—1331no—
191C3#11716322⋊D711yescharacteristic, complemented
192C2—571no—
193C2—1471no—
194C2—9311no—
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⋊#19150309C2semidirect
2. C7×C3⋊#11716322C2semidirect
3. C3×#19150307C2semidirect
4. D57⋊(C7⋊D7)C3semidirect
6. C3×C7×#87705C22semidirect
7. C19×C3⋊(C7⋊D7)C2×C3semidirect
8. C72×D57C2×C3semidirect
9. C3×C7⋊D133C2×C3semidirect
12. #19150307D3semidirect
18. C7×#87705C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
21. C3⋊#11716322D7semidirect
26. C7⋊D133C3×D3semidirect
35. C3×#87705C2×D7semidirect
37. C72×C19C2×C3×D3semidirect
45. C7×D57AGL(1,𝔽7)semidirect
46. C7×D57C3×D7semidirect
66. C3×C7×C19C2×AGL(1,𝔽7)semidirect
67. C3×C7×C19C2×C3×D7semidirect
69. #87705D3×D7semidirect
75. C3⋊(C7⋊D7)D19⋊C3semidirect
97. C3×C72C2×D19⋊C3semidirect
101. C7×C19D3×AGL(1,𝔽7)semidirect
102. C7×C19C3×D3×D7semidirect
109. D57ΓL(1,𝔽8)⋊D7semidirect
127. C3×C19C2×ΓL(1,𝔽8)⋊D7semidirect
130. C72D3×D19⋊C3semidirect
158. C3×C7D7×D19⋊C3semidirect
159. C3×C7#11716322⋊C2semidirect
162. C19D3×ΓL(1,𝔽8)⋊D7semidirect
179. C7#11716328⋊D3semidirect
180. C7(C3⋊(D19⋊C3))⋊D7semidirect
191. C3#11716322⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3⋊#191503092
C7×C3⋊#117163222
C3×#191503072
D57⋊(C7⋊D7)3
#11716322⋊D73
(C3⋊(D19⋊C3))⋊D77
#11716328⋊D37
D3×ΓL(1,𝔽8)⋊D719