Finite Group Databasebeta

← #28476271

Subgroups — #28476271

Order 15104.

214 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 39 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#21422026C211yesmaximal, characteristic
2#21422004C211yesmaximal, characteristic
3C59×#2030C211yesmaximal, characteristic
4#16837366—21no—
5#16837126—21no—
6C59×#543C411yescharacteristic
7C59×#381—21no—
8C59×#381C2211yescharacteristic
9C59×#342—21no—
10C59×#342C411yescharacteristic
11C2×#11745664—41no—
12C22⋊(C59⋊C8)—22no—
13C22⋊(C59⋊C8)—41no—
14C22⋊(C59⋊C8)—41no—
15C23×C4×C59D411yescharacteristic
16C22⋊Q8×C59—42no—
17C22⋊Q8×C59—41no—
18C2×C22⋊C4×C59—21no—
19C2×C22⋊C4×C59—21no—
20C2×C22⋊C4×C59C2×C411yescharacteristic
21C2×C22⋊C4×C59D411yescharacteristic
22#95×C59—41no—
23#95×C59—42no—
24C24×C59C22⋊C411yescharacteristic
25C2×Q8×C59—41no—
26C22×C4×C59—21no—
27C22×C4×C59—21no—
28C22×C4×C59—22no—
29C22×C4×C59—21no—
30C22×C4×C59—21no—
31C22×C4×C59—41no—
32C22×C4×C59—41no—
33C22×C4×C59—41no—
34C22×C4×C59SD1611yescharacteristic
35C22×C4×C59Q1611yescharacteristic
36C4⋊C4×C59—41no—
37C4⋊C4×C59—42no—
38C22⋊C4×C59—41no—
39C22⋊C4×C59—41no—
40C22⋊C4×C59—41no—
41C22⋊C4×C59—41no—
42C22⋊C4×C59—41no—
43C22⋊C4×C59—41no—
44#11745664—81no—
45#11745664—81no—
46C2×C59⋊C8—42no—
47C2×C59⋊C8—81no—
48C23×C59—21no—
49C23×C59—21no—
50C23×C59—81no—
51C23×C59#9911yescharacteristic
52C23×C59#10311yescharacteristic
53C23×C59#10411yescharacteristic
54Q8×C59—161no—
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—42no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—81no—
65C2×C4×C59—81no—
66C2×C4×C59—81no—
67C2×C4×C59—82no—
68C2×C4×C59—81no—
69C2×C4×C59—82no—
70C59⋊C8—82no—
71C59⋊C8—161no—
72#7427—591nomaximal, Sylow
73C22×C59—21no—
74C22×C59—21no—
75C22×C59—41no—
76C22×C59—41no—
77C22×C59—41no—
78C22×C59—42no—
79C22×C59—81no—
80C22×C59#32811yescharacteristic
81C22×C59AΣL(1,𝔽16)11yescharacteristic
82C22×C59#35411yescharacteristic
83C4×C59—41no—
84C4×C59—41no—
85C4×C59—81no—
86C4×C59—82no—
87C4×C59—81no—
88C4×C59—161no—
89#2030D5911yescharacteristic
90#1317—591no—
91#1306—591no—
92C2×C59—21no—
93C2×C59—21no—
94C2×C59—21no—
95C2×C59—41no—
96C2×C59—41no—
97C2×C59#135111yescharacteristic
98#543Dic5911yescharacteristic
99#407—1181no—
100#381—21no—
101#381C2×D5911yescharacteristic
102#342—21no—
103#342Dic5911yescharacteristic
104#323—1181no—
105C59#742711yescharacteristic, complemented, Sylow
106C23×C4C22⋊D5911yescharacteristic
107C2×M16—2361no—
108C22⋊Q8—42no—
109C22⋊Q8—41no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C22⋊C4C2×Dic5911yescharacteristic
113C2×C22⋊C4C22⋊D5911yescharacteristic
114C22⋊C8—1182no—
115C22⋊C8—2361no—
116C22⋊C8—2361no—
117#95—41no—
118#95—42no—
119C24C22⋊Dic5911yescharacteristic
120C2×Q8—41no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4#1174567111yescharacteristic
130C22×C4#1174567211yescharacteristic
131M16—4721no—
132M16—4721no—
133C2×C8—4721no—
134C2×C8—2362no—
135C4⋊C4—42no—
136C4⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C22⋊C4—41no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1427364211yescharacteristic
147C23#1427365111yescharacteristic
148C23#1427365411yescharacteristic
149Q8—161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—9441no—
166C8—4722no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1683713911yescharacteristic
175C22#1683718911yescharacteristic
176C22#1683719711yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—161no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#2142211711yescharacteristic
subgroupG/H
centerC2#21422117
commutatorC2×C22⋊C4×C59C2×C4
Frattini#381C2×D59
FittingC59×#2030C2
socleC2×C59#1351
prime radicalC24×C59C22⋊C4
cosocleC59×#381C22
hypercenter#2030D59
hypocenterC59#7427
LCSG ▷ C2×C22⋊C4×C59 ▷ C24×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2030

Complements

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

NH ≅ G/Ntype
105. C59#7427semidirect

Maximal subgroups

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

subgroupindex
#214220262
#214220042
C59×#20302
#742759