Finite Group Databasebeta

← #28509650

Subgroups — #28509650

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#21426200C211yesmaximal, characteristic
2#21425889C211yesmaximal, characteristic, complemented
3#21422301C211yesmaximal, characteristic, complemented
4#21422287C211yesmaximal, characteristic, complemented
5#21422285C211yesmaximal, characteristic, complemented
6#21422235C211yesmaximal, characteristic, complemented
7C59×#1426C211yesmaximal, characteristic, complemented
8C2×D944C2211yescharacteristic
9C2×#14273666C2211yescharacteristic
10#16837639—21no—
11#108×D59—21no—
12#16837236C2211yescharacteristic
13#16837232C2211yescharacteristic
14#16837231—21no—
15#16837202—21no—
16C59×M64C2211yescharacteristic
17C59×#368C2211yescharacteristic
18C59×#367C2211yescharacteristic
19C2×D472—21no—
20M16×D59—41no—
21C2×C8×D59D411yescharacteristic
22#14273702—41no—
23D944—21no—
24D944—21no—
25#14273666—21no—
26#14273666—21no—
27C2×C59⋊C16D411yescharacteristic
28#14273663—21no—
29#14273662—41no—
30#14273647—41no—
31C59⋊C32—21no—
32C2×C16×C59C2311yescharacteristic
33#108×C59—21no—
34#107×C59—21no—
35C32×C59—21no—
36C2×D236—41no—
37C2×D236—81no—
38C2×C4×D59D811yescharacteristic
39M16×C59—41no—
40C2×C8×C59C2×D411yescharacteristic
41C4⋊C4×C59—41no—
42(C2×D59)⋊C4—81no—
43#11745664—41no—
44C2×C59⋊C8D811yescharacteristic
45D472—41no—
46D472—41no—
47#11745659—81no—
48C8×D59—21no—
49C8×D59—21no—
50C8×D59—81no—
51C16×C59#4111yescharacteristic
52C16×C59#4111yescharacteristic
53C59⋊C16—21no—
54C22×D59—81no—
55C22×D59SD3211yescharacteristic
56C2×C4×C59—81no—
57C2×C4×C59C2×D811yescharacteristic
58C2×Dic59SD3211yescharacteristic
59D236—81no—
60D236—81no—
61D236—162no—
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×C59C2×SD3211yescharacteristic
71C2×D59—21no—
72C2×D59—41no—
73C2×D59—161no—
74C2×D59—161no—
75C2×D59—161no—
76C4×C59—161no—
77C4×C59#48011yescharacteristic
78C4×C59#50911yescharacteristic
79Dic59—21no—
80#2218—591no—
81#2161—591no—
82#1426—591no—
83#1426D5911yescharacteristic, complemented
84#1419—591no—
85#1419—591no—
86#1400—591no—
87C2×C59—21no—
88C2×C59#223311yescharacteristic
89D59—41no—
90D59—321no—
91C2×D16—591no—
92C2×M32—591no—
93#466—1181no—
94C2×#108—1181no—
95M64—591no—
96M64C2×D5911yescharacteristic
97#368—591no—
98#368—1181no—
99#368C2×D5911yescharacteristic
100#367C2×D5911yescharacteristic
101#357—1181no—
102C59#1371711yescharacteristic, complemented, Sylow
103C2×D8—1181no—
104C2×M16—2361no—
105C22×C8—591no—
106#121—2361no—
107D16—1181no—
108D16—1181no—
109M32—1181no—
110M32—1181no—
111C2×C16—591no—
112C2×C16C22×D5911yescharacteristic
113#108—21no—
114#108—1181no—
115#108—2361no—
116#107—21no—
117#102—2361no—
118C32—21no—
119C32—1181no—
120C2×D4—4721no—
121C2×D4—2361no—
122C22×C4—591no—
123D8—2361no—
124D8—2361no—
125M16—41no—
126M16—4721no—
127M16—2361no—
128C2×C8—591no—
129C2×C8—1181no—
130C2×C8—1181no—
131C2×C8—4721no—
132C2×C8D4×D5911yescharacteristic
133C4⋊C4—41no—
134C22⋊C4—4721no—
135C16—1181no—
136C16#1174568511yescharacteristic
137C16#1174568911yescharacteristic
138C23—591no—
139C23—4721no—
140D4—9442no—
141D4—4721no—
142D4—4721no—
143C2×C4—81no—
144C2×C4—591no—
145C2×C4—1181no—
146C2×C4—1181no—
147C2×C4D8×D5911yescharacteristic
148C8—81no—
149C8—1181no—
150C8—4721no—
151C8#1427371211yescharacteristic
152C8#1427375911yescharacteristic
153C22—1181no—
154C22—9441no—
155C22—9441no—
156C22—9441no—
157C22—2361no—
158C22SD32×D5911yescharacteristic
159C4—161no—
160C4—1181no—
161C4#1683771711yescharacteristic
162C4#1683783911yescharacteristic
163C2—21no—
164C2—18881no—
165C2—2361no—
166C2#2142628311yescharacteristic
subgroupG/H
centerC2#21426283
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1426C2
socleC2×C59#2233
prime radical#21426200C2
hypercenter#1426D59
hypocenterC59#13717
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
2. #21425889C2semidirect
3. #21422301C2semidirect
4. #21422287C2semidirect
5. #21422285C2semidirect
6. #21422235C2semidirect
7. C59×#1426C2semidirect
83. #1426D59semidirect
102. C59#13717semidirect

Maximal subgroups

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

subgroupindex
#214262002
#214258892
#214223012
#214222872
#214222852
#214222352
C59×#14262
#1371759