Finite Group Databasebeta

← #45692322

Subgroups — #45692322

Order 33516.

184 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊#19150306C211yesmaximal, characteristic, complemented
2C7×C3⋊#11716325C211yesmaximal, characteristic, complemented
3C3×#19150317C211yesmaximal, characteristic, complemented
4D21×D133C311yesmaximal, characteristic, complemented
5#11716325⋊D7—31nomaximal
6C3×C7×#87704C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8C7×C19×D21C2×C311yescharacteristic, complemented
9C3×C7×D133C2×C311yescharacteristic, complemented
10#19150317—21no—
11#19150317D311yescharacteristic, complemented
12#19150306—31no—
13C7×#11716325—31no—
14D3×(C19⋊C3)⋊D7—71nomaximal
15#11716321⋊D3—71nomaximal
16D7×D133—31noHall
17C7×#87704—21no—
18C7×#87704C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20C3⋊((C19⋊C3)⋊D7)—71no—
21C3⋊#11716325D711yescharacteristic, complemented
22C3⋊#11716327—71no—
23D3×C7×C19⋊C3—71no—
24C3×(C19⋊C3)⋊D7—71no—
25C3×#11716321—71no—
26C7⋊D133—31no—
27C7×D133C3×D311yescharacteristic, complemented
28C7×D7×C19—31no—
29D7×C3⋊AGL(1,𝔽7)—191nomaximal, Hall
30D3×D133—71no—
31D19×D21—71no—
32C2×(C19⋊C3)⋊D7—211no—
33#11716321⋊C2—211no—
34C3×#87704C2×D711yescharacteristic, complemented
35C3×C7×C19⋊C3—71no—
36C72×C19C2×C3×D311yescharacteristic, complemented, Hall
37C3⋊(ΓL(1,𝔽8)⋊D7)—191no—
38C7×C3⋊AGL(1,𝔽7)—191no—
39C3×D7×ΓL(1,𝔽8)—191no—
40D399—71no—
41D399—71no—
42D399—421no—
43C19×D21C3×D711yescharacteristic, complemented
44D3×C7×C19—71no—
45C3×D133AGL(1,𝔽7)11yescharacteristic, complemented
46C3×C7×D19—71no—
47C2×C7×C19⋊C3—211no—
48#11716327—211no—
49#11716325—31no—
50#11716321—71no—
51#11716321—141no—
52(C19⋊C3)⋊D7—71no—
53(C19⋊C3)⋊D7—141no—
54(C19⋊C3)⋊D7—211no—
55D3×D19⋊C3—491noHall
56D7×D21—191no—
57D7×AGL(1,𝔽7)—571no—
58C2×D133—211no—
59D7×D19—211no—
60C3×C7×ΓL(1,𝔽8)—191noHall
61C3×C7×C19—61no—
62C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
63C3×C7×C19C2×C3×D711yescharacteristic, complemented
64#87704—21no—
65#87704D3×D711yescharacteristic, complemented
66C7×C19⋊C3—71no—
67C7×C19⋊C3—141no—
68C3⋊(D19⋊C3)—491no—
69D3×C19⋊C3—71no—
70C3×D19⋊C3—491no—
71C3⋊(C7⋊D7)—191no—
72C7×D21D19⋊C311yescharacteristic, complemented
73C3×C7×D7—191no—
74ΓL(1,𝔽8)⋊D7—571no—
75D7×ΓL(1,𝔽8)—191no—
76D7×ΓL(1,𝔽8)—381no—
77C7×AGL(1,𝔽7)—571no—
78C2×C7×C19—211no—
79D133—211no—
80D133—211no—
81D133—1261no—
82D133C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
83C7×D19—71no—
84D7×C19—31no—
85C3×D3×D7—1331no—
86C2×C3⋊AGL(1,𝔽7)—1331no—
87D3×D19—491no—
88C2×D19⋊C3—1471no—
89D72—571noHall
90C3×C19⋊C3—71noHall
91C3×C72C2×D19⋊C311yescharacteristic, complemented
92C7×ΓL(1,𝔽8)—191no—
93C7×ΓL(1,𝔽8)—381no—
94C7×C19—61no—
95C7×C19C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
96C7×C19C3×D3×D711yescharacteristic, complemented
97C3×D21—1331no—
98C3×D3×C7—1331no—
99C32×D7—1331no—
100C2×C3×ΓL(1,𝔽8)—1331no—
101C3⋊AGL(1,𝔽7)—191no—
102C3⋊AGL(1,𝔽7)—1331no—
103D57—491no—
104C3×D19—71no—
105D3×C19—71no—
106C2×C19⋊C3—211no—
107D19⋊C3—491no—
108D19⋊C3—981no—
109D19⋊C3—1471no—
110C7⋊D7—571no—
111C7×D7—31no—
112C7×D7—191no—
113C2×D21—1331no—
114C2×C3×D7—3991no—
115D3×D7—1331no—
116C2×AGL(1,𝔽7)—3991no—
117C2×D19—1471noHall
118C32×C7—1331no—
119C3×ΓL(1,𝔽8)—191no—
120C3×C19D7×AGL(1,𝔽7)11yescharacteristic, complemented
121C19⋊C3—71no—
122C19⋊C3—141no—
123C72D3×D19⋊C311yescharacteristic, complemented, Sylow
124C2×C3×C7—1331no—
125C2×C3×C7—3991no—
126D21—7981no—
127D21—1331no—
128D21—1331no—
129D21(C19⋊C3)⋊D711yescharacteristic, complemented
130C3×D7—2661no—
131C3×D7—191no—
132C3×D7—1331no—
133C3×D7—3991no—
134D3×C7—71no—
135C2×ΓL(1,𝔽8)—2661no—
136C2×ΓL(1,𝔽8)—1331no—
137AGL(1,𝔽7)—571no—
138AGL(1,𝔽7)—3991no—
139C2×C19—211no—
140D19—71no—
141D19—1471no—
142C2×C3×D3—9311noHall
143C2×D7—3991no—
144C2×D7—3991no—
145C3×C7—61no—
146C3×C7—2661no—
147C3×C7—1331no—
148C3×C7#11716321⋊C211yescharacteristic, complemented
149C3×C7C2×(C19⋊C3)⋊D711yescharacteristic, complemented
150ΓL(1,𝔽8)—191no—
151ΓL(1,𝔽8)—381no—
152C19D7×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
153C2×C32—9311no—
154C3×D3—1331no—
155C3×D3—9311no—
156C2×C7—211no—
157C2×C7—1331no—
158D7—31no—
159D7—191no—
160D7—23941no—
161D7—3991no—
162D7—3991no—
163C22×C3—27931no—
164C2×D3—9311no—
165C32—1331noSylow
166C7—61no—
167C7#11716321⋊D311yescharacteristic, complemented
168C7D3×(C19⋊C3)⋊D711yescharacteristic, complemented
169C2×C3—18621no—
170C2×C3—1331no—
171C2×C3—3991no—
172C2×C3—9311no—
173C2×C3—27931no—
174D3—71no—
175D3—9311no—
176C22—27931noSylow
177C3—2661no—
178C3—1331no—
179C3#11716325⋊D711yescharacteristic, complemented
180C2—211no—
181C2—1331no—
182C2—27931no—
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⋊#19150306C2semidirect
2. C7×C3⋊#11716325C2semidirect
3. C3×#19150317C2semidirect
4. D21×D133C3semidirect
6. C3×C7×#87704C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. C7×C19×D21C2×C3semidirect
9. C3×C7×D133C2×C3semidirect
11. #19150317D3semidirect
18. C7×#87704C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
21. C3⋊#11716325D7semidirect
27. C7×D133C3×D3semidirect
34. C3×#87704C2×D7semidirect
36. C72×C19C2×C3×D3semidirect
43. C19×D21C3×D7semidirect
45. C3×D133AGL(1,𝔽7)semidirect
62. C3×C7×C19C2×AGL(1,𝔽7)semidirect
63. C3×C7×C19C2×C3×D7semidirect
65. #87704D3×D7semidirect
72. C7×D21D19⋊C3semidirect
82. D133C3⋊AGL(1,𝔽7)semidirect
91. C3×C72C2×D19⋊C3semidirect
95. C7×C19C2×C3⋊AGL(1,𝔽7)semidirect
96. C7×C19C3×D3×D7semidirect
120. C3×C19D7×AGL(1,𝔽7)semidirect
123. C72D3×D19⋊C3semidirect
129. D21(C19⋊C3)⋊D7semidirect
148. C3×C7#11716321⋊C2semidirect
149. C3×C7C2×(C19⋊C3)⋊D7semidirect
152. C19D7×C3⋊AGL(1,𝔽7)semidirect
167. C7#11716321⋊D3semidirect
168. C7D3×(C19⋊C3)⋊D7semidirect
179. C3#11716325⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3⋊#191503062
C7×C3⋊#117163252
C3×#191503172
D21×D1333
#11716325⋊D73
D3×(C19⋊C3)⋊D77
#11716321⋊D37
D7×C3⋊AGL(1,𝔽7)19