Finite Group Databasebeta

← #28509647

Subgroups — #28509647

Order 15104.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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#21426196C211yesmaximal, characteristic
2#21425889C211yesmaximal, characteristic, complemented
3#21422303C211yesmaximal, characteristic, complemented
4#21422302C211yesmaximal, characteristic, complemented
5#21422286C211yesmaximal, characteristic, complemented
6#21422235C211yesmaximal, characteristic, complemented
7C59×#1419C211yesmaximal, characteristic, complemented
8C2×#14273666C2211yescharacteristic
9#16837635—21no—
10#108×D59—21no—
11#16837236C2211yescharacteristic
12#16837232C2211yescharacteristic
13#16837231—21no—
14#16837230C2211yescharacteristic
15#16837203—21no—
16C2×D16×C59C2211yescharacteristic
17C59×M64C2211yescharacteristic
18C59×#368C2211yescharacteristic
19M16×D59—41no—
20C2×C8×D59D411yescharacteristic
21#14273698—41no—
22#14273666—21no—
23#14273666—21no—
24C2×C59⋊C16D411yescharacteristic
25#14273663—21no—
26#14273662—41no—
27#14273661—21no—
28#14273648—41no—
29C59⋊C32—21no—
30C2×D8×C59—21no—
31D16×C59—21no—
32D16×C59—21no—
33C2×C16×C59C2311yescharacteristic
34#108×C59—21no—
35C32×C59—21no—
36C2×D4×C59—41no—
37C2×C22⋊D59—81no—
38C2×C4×D59D811yescharacteristic
39D8×C59—41no—
40D8×C59—41no—
41M16×C59—41no—
42C2×C8×C59C2×D411yescharacteristic
43C22⋊Dic59—81no—
44C4⋊Dic59—41no—
45#11745664—41no—
46C2×C59⋊C8D811yescharacteristic
47#11745659—81no—
48C8×D59—21no—
49C8×D59—21no—
50C8×D59—81no—
51C16×C59#4111yescharacteristic
52C16×C59#4111yescharacteristic
53C59⋊C16—21no—
54C23×C59—81no—
55C22×D59SD3211yescharacteristic
56D4×C59—81no—
57D4×C59—81no—
58C2×C4×C59C2×D811yescharacteristic
59C22⋊D59—162no—
60C2×Dic59—81no—
61C2×Dic59SD3211yescharacteristic
62C4×D59—21no—
63C4×D59—21no—
64C8×C59—81no—
65C8×C59#12311yescharacteristic
66C8×C59#13711yescharacteristic
67C59⋊C8—21no—
68C59⋊C8—81no—
69#13717—591nomaximal, Sylow
70C22×C59—161no—
71C22×C59—161no—
72C22×C59—161no—
73C22×C59C2×SD3211yescharacteristic
74C2×D59—21no—
75C2×D59—41no—
76C4×C59#48011yescharacteristic
77C4×C59#50911yescharacteristic
78Dic59—21no—
79Dic59—161no—
80#2218—591no—
81#2161—591no—
82#1426—591no—
83#1426—591no—
84#1419—591no—
85#1419D5911yescharacteristic, complemented
86#1400—591no—
87C2×C59—21no—
88C2×C59—321no—
89C2×C59#223311yescharacteristic
90D59—41no—
91C2×D16C2×D5911yescharacteristic
92C2×M32—591no—
93#466—1181no—
94C2×#108—1181no—
95M64—591no—
96M64C2×D5911yescharacteristic
97#368—591no—
98#368—1181no—
99#368C2×D5911yescharacteristic
100#367—591no—
101#357—1181no—
102C59#1371711yescharacteristic, complemented, Sylow
103C2×D8—21no—
104C2×M16—2361no—
105C22×C8—591no—
106#121—2361no—
107D16—21no—
108D16—21no—
109M32—1181no—
110M32—1181no—
111C2×C16—591no—
112C2×C16C22×D5911yescharacteristic
113#108—21no—
114#108—1181no—
115#108—2361no—
116#107—1181no—
117#102—2361no—
118C32—21no—
119C32—1181no—
120C2×D4—41no—
121C2×D4—4721no—
122C22×C4—591no—
123D8—41no—
124D8—41no—
125M16—41no—
126M16—4721no—
127M16—2361no—
128C2×C8—591no—
129C2×C8—1181no—
130C2×C8—1181no—
131C2×C8—4721no—
132C2×C8D4×D5911yescharacteristic
133C4⋊C4—2361no—
134C22⋊C4—4721no—
135C16—1181no—
136C16#1174568511yescharacteristic
137C16#1174568711yescharacteristic
138C23—81no—
139C23—591no—
140D4—81no—
141D4—81no—
142D4—9442no—
143C2×C4—591no—
144C2×C4—1181no—
145C2×C4—1181no—
146C2×C4—4721no—
147C2×C4D8×D5911yescharacteristic
148C8—81no—
149C8—1181no—
150C8—4721no—
151C8#1427370911yescharacteristic
152C8#1427375611yescharacteristic
153C22—161no—
154C22—161no—
155C22—161no—
156C22—1181no—
157C22—2361no—
158C22SD32×D5911yescharacteristic
159C4—1181no—
160C4—9441no—
161C4#1683771411yescharacteristic
162C4#1683783611yescharacteristic
163C2—21no—
164C2—321no—
165C2—2361no—
166C2#2142628011yescharacteristic
subgroupG/H
centerC2#21426280
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1419C2
socleC2×C59#2233
prime radical#21426196C2
hypercenter#1419D59
hypocenterC59#13717
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
2. #21425889C2semidirect
3. #21422303C2semidirect
4. #21422302C2semidirect
5. #21422286C2semidirect
6. #21422235C2semidirect
7. C59×#1419C2semidirect
85. #1419D59semidirect
102. C59#13717semidirect

Maximal subgroups

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

subgroupindex
#214261962
#214258892
#214223032
#214223022
#214222862
#214222352
C59×#14192
#1371759