Finite Group Databasebeta

← #28491833

Subgroups — #28491833

Order 15104.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#21427401C211yesmaximal, characteristic
2#21425077C211yesmaximal, characteristic
3#21422596C212yesmaximal
4#21421998C212yesmaximal
5C59×#1274C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837426C2211yescharacteristic
8#16837344—22no—
9#16837336—22no—
10C4×Dic59⋊C4—22no—
11C4×C4⋊Dic59C2212yes—
12#16837162—22no—
13#16837140—22no—
14#16837140—22no—
15C59×#431C2212yes—
16C59×#376C2211yescharacteristic
17C2×#11745664—21no—
18#14273727Q812yes—
19#14273719—21no—
20#14273706—22no—
21C4×Dic118—22no—
22#14273686—21no—
23C2×C4⋊Dic59—22no—
24C2×Dic59⋊C4—22no—
25C2×Dic59⋊C4—22no—
26C2×C4×Dic59—22no—
27C4⋊(C59⋊C8)—22no—
28C59⋊#95—22no—
29C59⋊#95—22no—
30C59⋊#95D412yes—
31C59⋊#95D412yes—
32C2×C42×C59D412yes—
33C2×C42×C59C2311yescharacteristic
34C4⋊C8×C59—22no—
35C22⋊C8×C59—22no—
36C4×C8×C59—22no—
37#95×C59—22no—
38C22×C4×C59—22no—
39C22×C4×C59C2×D412yes—
40C22×C4×C59C2×D411yescharacteristic
41C22×Dic59—22no—
42C22×Dic59—22no—
43C2×Dic118—22no—
44C2×C8×C59—42no—
45C42×C59—22no—
46C42×C59—22no—
47C42×C59C2×Q811yescharacteristic
48C42×C59#4112yes—
49C42×C59#4111yescharacteristic
50C22⋊Dic59—41no—
51C4⋊Dic59—22no—
52C4⋊Dic59—22no—
53C4⋊Dic59—44no—
54Dic59⋊C4—44no—
55Dic59⋊C4—44no—
56Dic59⋊C4—42no—
57C4×Dic59—41no—
58C4×Dic59—42no—
59C4×Dic59—42no—
60#11745664—42no—
61C2×C59⋊C8—41no—
62C23×C59#12011yescharacteristic
63C2×C4×C59—42no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59C22⋊Q812yes—
68C2×C4×C59C22⋊Q811yescharacteristic
69C2×C4×C59#12412yes—
70C2×C4×C59#12411yescharacteristic
71C2×C4×C59#13512yes—
72C2×C4×C59#13712yes—
73C2×Dic59—24no—
74C2×Dic59—42no—
75C2×Dic59—42no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78C2×Dic59—42no—
79C2×Dic59—42no—
80Dic118—82no—
81C8×C59—82no—
82C59⋊C8—81no—
83#10373—591nomaximal, Sylow
84C22×C59—22no—
85C22×C59#39311yescharacteristic
86C22×C59#45212yes—
87C4×C59—22no—
88C4×C59—22no—
89C4×C59—82no—
90C4×C59#47912yes—
91C4×C59#48811yescharacteristic
92C4×C59#49111yescharacteristic
93Dic59—44no—
94Dic59—82no—
95Dic59—82no—
96#2402—591no—
97#1995—591no—
98#1503—592no—
99#1303—592no—
100#1274D5911yescharacteristic
101C2×C59—22no—
102C2×C59#202611yescharacteristic
103C2×C59#203112yes—
104#533—591no—
105#431C2×D5912yes—
106#423—591no—
107#400—1182no—
108#398—1182no—
109C4×C4⋊C4—592no—
110C4×C4⋊C4—1182no—
111#376C2×D5911yescharacteristic
112#339—1182no—
113#328—1182no—
114#328—1182no—
115C59#1037311yescharacteristic, complemented, Sylow
116C2×M16—1181no—
117C4⋊Q8—592no—
118#125—1181no—
119C22⋊Q8—1182no—
120C4×Q8—1182no—
121#117—1181no—
122C2×C4⋊C4—1182no—
123C2×C4⋊C4—1182no—
124C2×C4⋊C4—1182no—
125C2×C42—1182no—
126C2×C42D23612yes—
127C2×C42C22×D5911yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1182no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—592no—
134#95—592no—
135#95—1182no—
136#95—1182no—
137C2×Q8—1182no—
138C22×C4—22no—
139C22×C4—1182no—
140C22×C4—1182no—
141C22×C4C2×D23611yescharacteristic
142C22×C4D4×D5912yes—
143M16—2362no—
144C2×C8—42no—
145C2×C8—2361no—
146C4⋊C4—1182no—
147C4⋊C4—1182no—
148C4⋊C4—2364no—
149C4⋊C4—2364no—
150C4⋊C4—2364no—
151C4⋊C4—2362no—
152C22⋊C4—2361no—
153C42—22no—
154C42—22no—
155C42—2361no—
156C42—2362no—
157C42—2362no—
158C42#1174568512yes—
159C42#1174568711yescharacteristic
160C42Q8×D5911yescharacteristic
161C23#1427369711yescharacteristic
162Q8—4722no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—1184no—
168C2×C4—2362no—
169C2×C4—2362no—
170C2×C4—2362no—
171C2×C4—2362no—
172C2×C4—2362no—
173C2×C4—2362no—
174C2×C4#1427370512yes—
175C2×C4#1427370711yescharacteristic
176C2×C4#1427371312yes—
177C2×C4#1427371511yescharacteristic
178C2×C4#1427374912yes—
179C2×C4#1427376012yes—
180C8—82no—
181C8—4721no—
182C22—22no—
183C22#1683731511yescharacteristic
184C22#1683756612yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—4722no—
189C4—4722no—
190C4—2364no—
191C4#1683771012yes—
192C4#1683775711yescharacteristic
193C4#1683777111yescharacteristic
194C2—22no—
195C2#2142524811yescharacteristic
196C2#2142526712yes—
subgroupG/H
centerC2×C4#14273715
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1274C2
socleC22×C59#393
prime radicalC23×C59#120
hypercenter#1274D59
hypocenterC59#10373
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
115. C59#10373semidirect

Maximal subgroups

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

subgroupindex
#214274012
#214250772
#214225962
#214219982
C59×#12742
#1037359