Finite Group Databasebeta

← #28503095

Subgroups — #28503095

Order 15104.

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

normal subgroups only

This group has 196 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#21426339C211yesmaximal, characteristic, complemented
2#21426269C211yesmaximal, characteristic, complemented
3#21426173C211yesmaximal, characteristic
4#21425937C211yesmaximal, characteristic, complemented
5#21422163C211yesmaximal, characteristic, complemented
6#21422132C211yesmaximal, characteristic, complemented
7C59×#1366C211yesmaximal, characteristic, complemented
8#16837840—21no—
9#16837820—21no—
10#16837779C2211yescharacteristic
11#16837520C2211yescharacteristic
12#16837224—21no—
13#16837223C2211yescharacteristic
14#16837216—21no—
15#16837211—21no—
16#16837202—21no—
17#16837202—21no—
18#16837187—21no—
19#16837178C2211yescharacteristic
20C59×#499C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#364C2211yescharacteristic
23#14273749D411yescharacteristic
24C2×D472—21no—
25C2×D472—21no—
26#14273733—21no—
27#14273724—21no—
28#14273672—41no—
29D944—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×D236—41no—
45C2×D236—81no—
46C2×C8×C59C2×D411yescharacteristic
47C2×C8×C59C2×D411yescharacteristic
48C4⋊C4×C59—41no—
49C4⋊C4×C59—81no—
50C42×C59#4111yescharacteristic
51#11745664—21no—
52Dic236SD1611yescharacteristic
53D472—41no—
54D472—41no—
55D472—41no—
56D472—41no—
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—
66C22×D59—81no—
67C2×C4×C59—21no—
68C2×C4×C59—81no—
69C2×C4×C59#12111yescharacteristic
70C22⋊D59—41no—
71D236—21no—
72D236—81no—
73D236—81no—
74D236—162no—
75C4×D59—41no—
76Dic118—21no—
77C8×C59C2×SD1611yescharacteristic
78C8×C59#13511yescharacteristic
79C8×C59#13511yescharacteristic
80C8×C59AGL(1,ℤ/8)11yescharacteristic
81C59⋊C8—41no—
82#12465—591nomaximal, Sylow
83C22×C59#47211yescharacteristic
84C2×D59—41no—
85C2×D59—162no—
86C2×D59—161no—
87C4×C59—41no—
88C4×C59—161no—
89C4×C59#46311yescharacteristic
90C4×C59#46511yescharacteristic
91Dic59—41no—
92#2244—591no—
93#2231—591no—
94#2213—591no—
95#2171—591no—
96#1369—591no—
97#1366D5911yescharacteristic, complemented
98#1357—591no—
99C2×C59—21no—
100C2×C59#167711yescharacteristic
101D59—81no—
102D59—321no—
103#509—1181no—
104#504—1181no—
105#499C2×D5911yescharacteristic
106#493—591no—
107#443—591no—
108#365—1181no—
109#364—591no—
110#364C2×D5911yescharacteristic
111#364C2×D5911yescharacteristic
112#361—1181no—
113#360—1181no—
114#357—1181no—
115#357—1181no—
116#350—1181no—
117#346—591no—
118C59#1246511yescharacteristic, complemented, Sylow
119#135—591no—
120C2×D8—1181no—
121C2×D8—1181no—
122#131—1181no—
123#127—1181no—
124#125—21no—
125SD32—2361no—
126D16—2361no—
127M32—21no—
128M32—21no—
129M32—1181no—
130M32—2361no—
131C2×C16—591no—
132C2×C16—591no—
133C2×C16—2361no—
134#108—591no—
135#107—21no—
136#106—21no—
137#104—1181no—
138C4×C8C22×D5911yescharacteristic
139#41—1181no—
140C2×D4—4721no—
141C2×D4—2361no—
142Q16—591no—
143SD16—1181no—
144D8—591no—
145D8—2361no—
146D8—2361no—
147D8—2361no—
148D8—2361no—
149M16—1181no—
150M16—2361no—
151C2×C8—2361no—
152C2×C8D4×D5911yescharacteristic
153C2×C8D4×D5911yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1174568511yescharacteristic
157C16—41no—
158C16—41no—
159C16—1181no—
160C16—1181no—
161C16—2361no—
162C23—4721no—
163Q8—1181no—
164D4—1181no—
165D4—9442no—
166D4—4721no—
167D4—4721no—
168D4—2361no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—2361no—
172C2×C4#1427370011yescharacteristic
173C8—2361no—
174C8SD16×D5911yescharacteristic
175C8#1427375011yescharacteristic
176C8#1427375011yescharacteristic
177C8#1427375411yescharacteristic
178C22—9442no—
179C22—9441no—
180C22—2361no—
181C22#1683767111yescharacteristic
182C4—41no—
183C4—161no—
184C4—2361no—
185C4#1683762011yescharacteristic
186C4#1683763411yescharacteristic
187C2—21no—
188C2—18881no—
189C2—4721no—
190C2#2142350811yescharacteristic
subgroupG/H
centerC2#21423508
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1366C2
socleC2×C59#1677
prime radical#21426173C2
hypercenter#1366D59
hypocenterC59#12465
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. #21426339C2semidirect
2. #21426269C2semidirect
4. #21425937C2semidirect
5. #21422163C2semidirect
6. #21422132C2semidirect
7. C59×#1366C2semidirect
97. #1366D59semidirect
118. C59#12465semidirect

Maximal subgroups

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

subgroupindex
#214263392
#214262692
#214261732
#214259372
#214221632
#214221322
C59×#13662
#1246559