Finite Group Databasebeta

← #28476315

Subgroups — #28476315

Order 15104.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#21425446C211yesmaximal, characteristic
2#21422040C211yesmaximal, characteristic
3C59×#1295C211yesmaximal, characteristic
4#16838033C411yescharacteristic
5#16837442—21no—
6#16837171C411yescharacteristic
7#16837162—21no—
8#16837128—21no—
9C2×#97×C59—21no—
10C59×#382C2211yescharacteristic
11C2×#11745664—21no—
12#14273726—41no—
13#14273718—41no—
14#14273706—41no—
15#14273686—21no—
16#14273660—41no—
17#14273658—41no—
18C22⋊(C59⋊C8)—41no—
19C22×C8×C59—41no—
20C2×C4⋊C4×C59C2×C411yescharacteristic
21C2×C4⋊C4×C59D411yescharacteristic
22C2×C42×C59D411yescharacteristic
23#97×C59—22no—
24#97×C59—41no—
25#95×C59—41no—
26C22×C4×C59—21no—
27C22×C4×C59—21no—
28C22×C4×C59—21no—
29C22×C4×C59C22⋊C411yescharacteristic
30C2×Dic118—41no—
31C2×C8×C59—42no—
32C2×C8×C59—42no—
33C2×C8×C59—42no—
34C4⋊C4×C59—41no—
35C4⋊C4×C59—41no—
36C42×C59—21no—
37C42×C59SD1611yescharacteristic
38C42×C59Q1611yescharacteristic
39C22⋊Dic59—41no—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—41no—
43Dic59⋊C4—42no—
44C4×Dic59—41no—
45#11745664—22no—
46#11745664—41no—
47C2×C59⋊C8—41no—
48C2×C59⋊C8—81no—
49C23×C59#9911yescharacteristic
50C2×C4×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59—81no—
59C2×C4×C59—81no—
60C2×C4×C59#10311yescharacteristic
61C2×C4×C59#10411yescharacteristic
62C2×Dic59—41no—
63C2×Dic59—41no—
64Dic118—161no—
65C8×C59—44no—
66C59⋊C8—42no—
67C59⋊C8—161no—
68#7442—591nomaximal, Sylow
69C22×C59—21no—
70C22×C59—21no—
71C22×C59#32811yescharacteristic
72C22×C59AΣL(1,𝔽16)11yescharacteristic
73C22×C59#35611yescharacteristic
74C4×C59—21no—
75C4×C59—21no—
76C4×C59—41no—
77C4×C59—41no—
78C4×C59—81no—
79C4×C59—81no—
80Dic59—81no—
81Dic59—81no—
82#2061—591no—
83#1324—591no—
84#1295D5911yescharacteristic
85C2×C59—21no—
86C2×C59—21no—
87C2×C59#135411yescharacteristic
88C2×C59#140311yescharacteristic
89C2×C59#140411yescharacteristic
90#544—591no—
91#428—1181no—
92C2×#97—21no—
93#382C2×D5911yescharacteristic
94#343—591no—
95#339—1181no—
96#324—1181no—
97C59#744211yescharacteristic, complemented, Sylow
98C2×M16—1181no—
99C22×C8—41no—
100C4⋊Q8—2361no—
101#125—2361no—
102C22⋊Q8—2361no—
103#117—1181no—
104C2×C4⋊C4C4×D5911yescharacteristic
105C2×C4⋊C4D23611yescharacteristic
106C2×C42C22⋊D5911yescharacteristic
107#107—2361no—
108#106—2361no—
109C22⋊C8—2361no—
110#97—22no—
111#97—41no—
112#95—41no—
113C2×Q8—2361no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4(C2×D59)⋊C411yescharacteristic
118M16—1182no—
119M16—2361no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—4721no—
124C2×C8—2361no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4—2361no—
130C4⋊C4—2362no—
131C22⋊C4—2361no—
132C42—21no—
133C42—2361no—
134C42#1174567011yescharacteristic
135C42#1174567211yescharacteristic
136C23#1427364111yescharacteristic
137Q8—9441no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—2361no—
149C2×C4—2361no—
150C2×C4#1427365011yescharacteristic
151C2×C4#1427365511yescharacteristic
152C8—44no—
153C8—9441no—
154C8—2362no—
155C22—21no—
156C22—21no—
157C22#1683713811yescharacteristic
158C22#1683719011yescharacteristic
159C22#1683720011yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—4721no—
167C4—4721no—
168C2—21no—
169C2—21no—
170C2#2142212511yescharacteristic
171C2#2142224511yescharacteristic
172C2#2142224811yescharacteristic
subgroupG/H
centerC22#16837190
commutatorC2×C4⋊C4×C59C2×C4
Frattini#382C2×D59
FittingC59×#1295C2
socleC22×C59AΣL(1,𝔽16)
prime radicalC23×C59#99
cosocleC59×#382C22
hypercenter#1295D59
hypocenterC59#7442
LCSG ▷ C2×C4⋊C4×C59 ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1295

Complements

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

NH ≅ G/Ntype
97. C59#7442semidirect

Maximal subgroups

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

subgroupindex
#214254462
#214220402
C59×#12952
#744259