Finite Group Databasebeta

← #28503102

Subgroups — #28503102

Order 15104.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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#21426343C211yesmaximal, characteristic, complemented
2#21426269C211yesmaximal, characteristic
3#21426178C211yesmaximal, characteristic
4#21425937C211yesmaximal, characteristic
5#21422163C211yesmaximal, characteristic, complemented
6#21422134C211yesmaximal, characteristic, complemented
7C59×#1366C211yesmaximal, characteristic, complemented
8#16837845—21no—
9#16837820—21no—
10#16837782C2211yescharacteristic
11#16837520C2211yescharacteristic
12#16837224—21no—
13#16837223C2211yescharacteristic
14#16837219—21no—
15#16837211—21no—
16#16837205—21no—
17#16837205—21no—
18#16837187—21no—
19#16837178C2211yescharacteristic
20C59×#499C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#364C2211yescharacteristic
23#14273749D411yescharacteristic
24C2×Dic236—21no—
25C2×Dic236—21no—
26#14273733—21no—
27#14273727—21no—
28Dic472—41no—
29#14273672—41no—
30#14273667—21no—
31#14273666—41no—
32C2×C59⋊C16D411yescharacteristic
33C2×C59⋊C16D411yescharacteristic
34C16×D59—41no—
35#14273663D411yescharacteristic
36#14273655—21no—
37#125×C59—21no—
38M32×C59—21no—
39M32×C59—21no—
40#107×C59—21no—
41#106×C59—21no—
42C4×C8×C59C2311yescharacteristic
43#11745685—21no—
44C2×Dic118—41no—
45C2×C8×C59C2×D411yescharacteristic
46C2×C8×C59C2×D411yescharacteristic
47C4⋊C4×C59—41no—
48C4⋊C4×C59—81no—
49C42×C59#4111yescharacteristic
50C4⋊Dic59—81no—
51#11745664—21no—
52Dic236—41no—
53Dic236—41no—
54Dic236—41no—
55Dic236—41no—
56Dic236SD1611yescharacteristic
57D472SD1611yescharacteristic
58#11745660—21no—
59#11745659—41no—
60C8×D59—41no—
61C16×C59—41no—
62C16×C59—41no—
63C59⋊C16—21no—
64C59⋊C16—21no—
65C59⋊C16—41no—
66C2×C4×C59—21no—
67C2×C4×C59—81no—
68C2×C4×C59#12111yescharacteristic
69C22⋊D59—41no—
70C2×Dic59—81no—
71D236—21no—
72C4×D59—41no—
73Dic118—21no—
74Dic118—81no—
75Dic118—81no—
76C8×C59C2×SD1611yescharacteristic
77C8×C59#13511yescharacteristic
78C8×C59#13511yescharacteristic
79C8×C59AGL(1,ℤ/8)11yescharacteristic
80C59⋊C8—41no—
81#12466—591nomaximal, Sylow
82C22×C59#47211yescharacteristic
83C2×D59—41no—
84C4×C59—41no—
85C4×C59—161no—
86C4×C59#46311yescharacteristic
87C4×C59#46511yescharacteristic
88Dic59—41no—
89Dic59—161no—
90#2245—591no—
91#2231—591no—
92#2214—591no—
93#2171—591no—
94#1369—591no—
95#1366D5911yescharacteristic, complemented
96#1358—591no—
97C2×C59—21no—
98C2×C59#167711yescharacteristic
99D59—81no—
100#510—1181no—
101#504—1181no—
102#499C2×D5911yescharacteristic
103#494—591no—
104#443—591no—
105#365—1181no—
106#364—591no—
107#364C2×D5911yescharacteristic
108#364C2×D5911yescharacteristic
109#362—1181no—
110#360—1181no—
111#358—1181no—
112#358—1181no—
113#350—1181no—
114#346—591no—
115C59#1246611yescharacteristic, complemented, Sylow
116#135—591no—
117C2×Q16—1181no—
118C2×Q16—1181no—
119#131—1181no—
120C4⋊Q8—1181no—
121#125—21no—
122Q32—2361no—
123SD32—2361no—
124M32—21no—
125M32—21no—
126M32—1181no—
127M32—2361no—
128C2×C16—591no—
129C2×C16—591no—
130C2×C16—2361no—
131#108—591no—
132#107—21no—
133#106—21no—
134#104—1181no—
135C4×C8C22×D5911yescharacteristic
136#41—1181no—
137C2×Q8—2361no—
138Q16—591no—
139Q16—2361no—
140Q16—2361no—
141Q16—2361no—
142Q16—2361no—
143SD16—1181no—
144D8—591no—
145M16—1181no—
146M16—2361no—
147C2×C8—2361no—
148C2×C8D4×D5911yescharacteristic
149C2×C8D4×D5911yescharacteristic
150C4⋊C4—41no—
151C4⋊C4—81no—
152C4⋊C4—4721no—
153C42#1174568511yescharacteristic
154C16—41no—
155C16—41no—
156C16—1181no—
157C16—1181no—
158C16—2361no—
159Q8—1181no—
160Q8—4721no—
161Q8—4721no—
162D4—1181no—
163D4—2361no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—4721no—
167C2×C4—2361no—
168C2×C4#1427370011yescharacteristic
169C8—2361no—
170C8SD16×D5911yescharacteristic
171C8#1427375011yescharacteristic
172C8#1427375011yescharacteristic
173C8#1427375411yescharacteristic
174C22—2361no—
175C22#1683767111yescharacteristic
176C4—41no—
177C4—161no—
178C4—9441no—
179C4—2361no—
180C4#1683762011yescharacteristic
181C4#1683763411yescharacteristic
182C2—21no—
183C2—4721no—
184C2#2142350811yescharacteristic
subgroupG/H
centerC2#21423508
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1366C2
socleC2×C59#1677
prime radical#14273749D4
hypercenter#1366D59
hypocenterC59#12466
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #21426343C2semidirect
5. #21422163C2semidirect
6. #21422134C2semidirect
7. C59×#1366C2semidirect
95. #1366D59semidirect
115. C59#12466semidirect

Maximal subgroups

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

subgroupindex
#214263432
#214262692
#214261782
#214259372
#214221632
#214221342
C59×#13662
#1246659