Finite Group Databasebeta

← #28482185

Subgroups — #28482185

Order 15104.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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#21422430C212yesmaximal
2#21421952C214yesmaximal, complemented
3C59×#2298C211yesmaximal, characteristic
4#16837459C2214yes—
5#16837128—22no—
6#16837126—22no—
7C2×#117×C59C2211yescharacteristic
8C59×#388—22no—
9C59×#387—22no—
10C4×C4⋊C4×C59C2212yes—
11C4×C22⋊C4×C59C412yes—
12C59×#376C411yescharacteristic
13C43×C59C411yescharacteristic
14C4⋊(C59⋊C8)—24no—
15C22⋊(C59⋊C8)—24no—
16#14273638—24no—
17C23×C4×C59C2×C411yescharacteristic
18#117×C59—24no—
19C2×C4⋊C4×C59—22no—
20C2×C4⋊C4×C59D412yes—
21C2×C22⋊C4×C59—22no—
22C2×C22⋊C4×C59D412yes—
23C2×C42×C59—22no—
24C2×C42×C59C2×C411yescharacteristic
25C2×C42×C59C2×C412yes—
26C2×C42×C59C2×C412yes—
27C2×C42×C59C2311yescharacteristic
28#95×C59—22no—
29#95×C59—22no—
30#95×C59—22no—
31C24×C59C22⋊C411yescharacteristic
32C22×C4×C59—22no—
33C22×C4×C59—22no—
34C22×C4×C59—22no—
35C22×C4×C59—42no—
36C22×C4×C59C22⋊C411yescharacteristic
37C22×C4×C59C22⋊C412yes—
38C22×C4×C59C22×C411yescharacteristic
39C22×C4×C59C2×D412yes—
40C4⋊C4×C59—24no—
41C4⋊C4×C59—44no—
42C22⋊C4×C59—24no—
43C22⋊C4×C59—44no—
44C42×C59—22no—
45C42×C59—44no—
46C42×C59—42no—
47C42×C59—42no—
48C42×C59#4114yes—
49C2×C59⋊C8—44no—
50C23×C59—21no—
51C23×C59—22no—
52C23×C59—42no—
53C23×C59C2×C22⋊C411yescharacteristic
54C2×C4×C59—22no—
55C2×C4×C59—24no—
56C2×C4×C59—22no—
57C2×C4×C59—21no—
58C2×C4×C59—22no—
59C2×C4×C59—42no—
60C2×C4×C59—44no—
61C2×C4×C59—42no—
62C2×C4×C59—42no—
63C2×C4×C59—42no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59#11712yes—
68C2×C4×C59#12314yes—
69C59⋊C8—84no—
70#8745—591nomaximal, Sylow
71C22×C59—22no—
72C22×C59—41no—
73C22×C59—42no—
74C22×C59—82no—
75C22×C59#38111yescharacteristic
76C22×C59#41312yes—
77C4×C59—22no—
78C4×C59—24no—
79C4×C59—44no—
80C4×C59—41no—
81C4×C59—42no—
82C4×C59—82no—
83#2298D5911yescharacteristic
84#1464—592no—
85#1285—594no—
86C2×C59—22no—
87C2×C59—81no—
88C2×C59#182211yescharacteristic
89C2×C59#182712yes—
90C2×#117C2×D5911yescharacteristic
91#432—594no—
92#388—22no—
93#387—22no—
94C4×C4⋊C4C2×D5912yes—
95C4×C22⋊C4Dic5912yes—
96#376Dic5911yescharacteristic
97C43Dic5911yescharacteristic
98#324—1182no—
99#323—1182no—
100C59#874511yescharacteristic, complemented, Sylow
101C23×C4C2×Dic5911yescharacteristic
102#117—24no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4C22⋊D5912yes—
105C2×C22⋊C4—22no—
106C2×C22⋊C4C22⋊D5912yes—
107C2×C42—22no—
108C2×C42C2×Dic5911yescharacteristic
109C2×C42C2×Dic5912yes—
110C2×C42C2×Dic5912yes—
111C2×C42C22×D5911yescharacteristic
112C4⋊C8—1184no—
113C22⋊C8—1184no—
114#97—1184no—
115#95—22no—
116#95—22no—
117#95—22no—
118C24C22⋊Dic5911yescharacteristic
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—42no—
123C22×C4C22⋊Dic5911yescharacteristic
124C22×C4C22⋊Dic5912yes—
125C22×C4C22×Dic5911yescharacteristic
126C22×C4C2×C22⋊D5912yes—
127C2×C8—2364no—
128C4⋊C4—24no—
129C4⋊C4—44no—
130C22⋊C4—24no—
131C22⋊C4—44no—
132C42—22no—
133C42—42no—
134C42—42no—
135C42—44no—
136C42#1174568514yes—
137C23—21no—
138C23—22no—
139C23—42no—
140C23C2×C22⋊Dic5911yescharacteristic
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4#1427368612yes—
155C2×C4#1427371014yes—
156C8—4724no—
157C22—22no—
158C22—41no—
159C22—42no—
160C22—82no—
161C22#1683726511yescharacteristic
162C22#1683738612yes—
163C4—22no—
164C4—24no—
165C4—44no—
166C4—41no—
167C4—42no—
168C4—82no—
169C2—22no—
170C2—81no—
171C2#2142417911yescharacteristic
172C2#2142420012yes—
subgroupG/H
centerC22#16837265
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2298C2
socleC22×C59#381
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2298D59
hypocenterC59#8745
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #21421952C2semidirect
100. C59#8745semidirect

Maximal subgroups

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

subgroupindex
#214224302
#214219522
C59×#22982
#874559