Finite Group Databasebeta

← #28491832

Subgroups — #28491832

Order 15104.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#21422595C212yesmaximal
3#21421997C212yesmaximal
4#21421925C211yesmaximal, characteristic
5C59×#1995C211yesmaximal, characteristic
6#16837455C2212yes—
7#16837344—22no—
8#16837336—22no—
9C4×Dic59⋊C4—22no—
10C4×C4⋊Dic59C2212yes—
11#16837139—22no—
12#16837139—22no—
13C59×#533C2211yescharacteristic
14C59×#423C2211yescharacteristic
15C59×#376C2211yescharacteristic
16C59×#339—22no—
17C2×C4⋊Dic59—22no—
18C2×Dic59⋊C4—22no—
19C2×Dic59⋊C4—22no—
20C2×C4×Dic59—22no—
21C4⋊(C59⋊C8)—22no—
22C22⋊(C59⋊C8)—22no—
23C4×C59⋊C8—22no—
24C59⋊#95—22no—
25C59⋊#95—22no—
26C59⋊#95D412yes—
27C59⋊#95D412yes—
28C2×M16×C59—21no—
29C4⋊Q8×C59Q812yes—
30#125×C59—21no—
31C22⋊Q8×C59—22no—
32C4×Q8×C59—22no—
33#117×C59—21no—
34C2×C42×C59D412yes—
35C2×C42×C59C2311yescharacteristic
36C4⋊C8×C59—22no—
37#95×C59—22no—
38C2×Q8×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59C2×D412yes—
41C22×C4×C59C2×D411yescharacteristic
42C22×Dic59—22no—
43C22×Dic59—22no—
44M16×C59—42no—
45C2×C8×C59—41no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—22no—
48C4⋊C4×C59—42no—
49C22⋊C4×C59—41no—
50C42×C59—22no—
51C42×C59—22no—
52C42×C59—41no—
53C42×C59C2×Q811yescharacteristic
54C42×C59#4111yescharacteristic
55C42×C59#4112yes—
56C4⋊Dic59—44no—
57Dic59⋊C4—44no—
58Dic59⋊C4—44no—
59C4×Dic59—42no—
60C4×Dic59—42no—
61C2×C59⋊C8—42no—
62C23×C59#12011yescharacteristic
63Q8×C59—82no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59—42no—
68C2×C4×C59—42no—
69C2×C4×C59C22⋊Q812yes—
70C2×C4×C59C22⋊Q811yescharacteristic
71C2×C4×C59#12412yes—
72C2×C4×C59#12411yescharacteristic
73C2×C4×C59#13512yes—
74C2×C4×C59#13712yes—
75C2×Dic59—24no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78C2×Dic59—42no—
79C2×Dic59—42no—
80C2×Dic59—42no—
81C8×C59—81no—
82C59⋊C8—82no—
83#10373—591nomaximal, Sylow
84C22×C59—22no—
85C22×C59#39311yescharacteristic
86C22×C59#45212yes—
87C4×C59—22no—
88C4×C59—22no—
89C4×C59—82no—
90C4×C59—82no—
91C4×C59#47912yes—
92C4×C59#48811yescharacteristic
93C4×C59#49111yescharacteristic
94Dic59—44no—
95Dic59—82no—
96#2402—591no—
97#1995D5911yescharacteristic
98#1503—592no—
99#1303—592no—
100#1274—591no—
101C2×C59—22no—
102C2×C59#202611yescharacteristic
103C2×C59#203112yes—
104#533C2×D5911yescharacteristic
105#431—592no—
106#423C2×D5911yescharacteristic
107#400—1182no—
108#398—1182no—
109C4×C4⋊C4—592no—
110C4×C4⋊C4—1182no—
111#376C2×D5911yescharacteristic
112#339—22no—
113#328—1182no—
114#328—1182no—
115C59#1037311yescharacteristic, complemented, Sylow
116C2×M16—21no—
117C4⋊Q8Dic11812yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—1182no—
123C2×C4⋊C4—1182no—
124C2×C4⋊C4—1182no—
125C2×C42—1182no—
126C2×C42C22⋊D5912yes—
127C2×C42C22×D5911yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1182no—
130C22⋊C8—1182no—
131C4×C8—1182no—
132#95—22no—
133#95—592no—
134#95—592no—
135#95—1182no—
136#95—1182no—
137C2×Q8—22no—
138C22×C4—22no—
139C22×C4—1182no—
140C22×C4—1182no—
141C22×C4D4×D5912yes—
142C22×C4C2×C22⋊D5911yescharacteristic
143M16—42no—
144C2×C8—41no—
145C2×C8—2362no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—42no—
149C4⋊C4—2364no—
150C4⋊C4—2364no—
151C4⋊C4—2364no—
152C22⋊C4—41no—
153C42—22no—
154C42—22no—
155C42—41no—
156C42—2362no—
157C42—2362no—
158C42C2×Dic11811yescharacteristic
159C42#1174568511yescharacteristic
160C42#1174568712yes—
161C23#1427369511yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—1184no—
169C2×C4—2362no—
170C2×C4—2362no—
171C2×C4—2362no—
172C2×C4—2362no—
173C2×C4—2362no—
174C2×C4#1427370412yes—
175C2×C4#1427370611yescharacteristic
176C2×C4#1427371312yes—
177C2×C4#1427371411yescharacteristic
178C2×C4#1427374712yes—
179C2×C4#1427375812yes—
180C8—81no—
181C8—4722no—
182C22—22no—
183C22#1683731411yescharacteristic
184C22#1683756212yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—4722no—
190C4—2364no—
191C4#1683770912yes—
192C4#1683775611yescharacteristic
193C4#1683777011yescharacteristic
194C2—22no—
195C2#2142524711yescharacteristic
196C2#2142526612yes—
subgroupG/H
centerC2×C4#14273714
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1995C2
socleC22×C59#393
prime radicalC23×C59#120
hypercenter#1995D59
hypocenterC59#10373
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

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
#214225952
#214219972
#214219252
C59×#19952
#1037359