Finite Group Databasebeta

← #28491937

Subgroups — #28491937

Order 15104.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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#21429766C211yesmaximal, characteristic
2#21424193C212yesmaximal
3#21424171C211yesmaximal, characteristic
4#21421950C212yesmaximal
5C59×#1306C211yesmaximal, characteristic
6C2×#14273686C2211yescharacteristic
7#16837325—22no—
8#16837299—22no—
9#16837285—22no—
10#16837265C2211yescharacteristic
11C4×C22⋊Dic59C2212yes—
12#16837168—22no—
13#16837163—22no—
14#16837163—22no—
15C59×#407C2212yes—
16C59×#381C2211yescharacteristic
17#14273686—22no—
18#14273686—22no—
19C2×C4⋊Dic59—22no—
20C2×C4⋊Dic59Q812yes—
21C2×Dic59⋊C4—22no—
22C2×Dic59⋊C4—22no—
23C2×C22⋊Dic59—21no—
24C2×C22⋊Dic59—22no—
25C2×C22⋊Dic59—21no—
26C2×C4×Dic59—21no—
27C2×C4×Dic59D412yes—
28C2×C4×Dic59D412yes—
29C59⋊#95—22no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C23×C4×C59C2311yescharacteristic
33C2×M16×C59—22no—
34C2×C22⋊C4×C59D412yes—
35C22⋊C8×C59—22no—
36C22⋊C8×C59—22no—
37#95×C59—22no—
38C24×C59C2×D411yescharacteristic
39C22×C4×C59—22no—
40C22×C4×C59—42no—
41C22×C4×C59C2×D412yes—
42C22×C4×C59C2×Q811yescharacteristic
43C22×C4×C59#4112yes—
44C22×C4×C59#4111yescharacteristic
45C22×Dic59—22no—
46C22×Dic59—22no—
47C22×Dic59—22no—
48C22×Dic59—41no—
49M16×C59—42no—
50M16×C59—42no—
51C2×C8×C59—42no—
52C22⋊C4×C59—42no—
53C22⋊Dic59—44no—
54C22⋊Dic59—41no—
55C22⋊Dic59—41no—
56C22⋊Dic59—42no—
57C4⋊Dic59—24no—
58C4⋊Dic59—44no—
59Dic59⋊C4—44no—
60Dic59⋊C4—82no—
61C4×Dic59—42no—
62C4×Dic59—42no—
63C4×Dic59—42no—
64C23×C59—22no—
65C23×C59—42no—
66C23×C59#12011yescharacteristic
67C23×C59C22⋊Q811yescharacteristic
68C23×C59#12411yescharacteristic
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—41no—
72C2×C4×C59—42no—
73C2×C4×C59—41no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59—42no—
77C2×C4×C59C22⋊Q812yes—
78C2×C4×C59#12412yes—
79C2×Dic59—24no—
80C2×Dic59—42no—
81C2×Dic59—42no—
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—82no—
87C2×Dic59—81no—
88C2×Dic59—82no—
89C8×C59—82no—
90#10389—591nomaximal, Sylow
91C22×C59—22no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59—22no—
95C22×C59—22no—
96C22×C59—82no—
97C22×C59#39311yescharacteristic
98C22×C59#45812yes—
99C4×C59—22no—
100C4×C59—22no—
101C4×C59—82no—
102Dic59—44no—
103Dic59—82no—
104Dic59—82no—
105Dic59—161no—
106#2608—591no—
107#1826—592no—
108#1820—591no—
109#1306D5911yescharacteristic
110#1284—592no—
111C2×C59—22no—
112C2×C59—41no—
113C2×C59—41no—
114C2×C59#203011yescharacteristic
115C2×C59#203112yes—
116C2×#117—591no—
117#407C2×D5912yes—
118#396—1182no—
119#389—1182no—
120#387—1182no—
121#381—591no—
122#381C2×D5911yescharacteristic
123C4×C22⋊C4—592no—
124#342—1182no—
125#339—1182no—
126#339—1182no—
127C59#1038911yescharacteristic, complemented, Sylow
128C23×C4C22×D5911yescharacteristic
129C2×M16—22no—
130#117—1182no—
131#117—1182no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—1182no—
134C2×C4⋊C4—1182no—
135C2×C4⋊C4—1182no—
136C2×C22⋊C4—1181no—
137C2×C22⋊C4—1182no—
138C2×C22⋊C4—1181no—
139C2×C22⋊C4D23612yes—
140C2×C42—592no—
141C2×C42—592no—
142C2×C42—1181no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145#95—22no—
146#95—1182no—
147#95—1182no—
148#95—1182no—
149C24C2×D23611yescharacteristic
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—1182no—
153C22×C4—1182no—
154C22×C4—1182no—
155C22×C4—2361no—
156C22×C4#1174568512yes—
157C22×C4D4×D5912yes—
158C22×C4#1174568711yescharacteristic
159C22×C4Q8×D5911yescharacteristic
160M16—42no—
161M16—42no—
162C2×C8—42no—
163C4⋊C4—1184no—
164C4⋊C4—4722no—
165C4⋊C4—2364no—
166C4⋊C4—2364no—
167C22⋊C4—42no—
168C22⋊C4—2364no—
169C22⋊C4—2362no—
170C22⋊C4—2361no—
171C22⋊C4—2361no—
172C42—2362no—
173C42—2362no—
174C42—2362no—
175C23—22no—
176C23—42no—
177C23#1427369711yescharacteristic
178C23#1427370711yescharacteristic
179C23#1427371511yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—1184no—
189C2×C4—4721no—
190C2×C4—4722no—
191C2×C4—4722no—
192C2×C4—2362no—
193C2×C4—2362no—
194C2×C4—2362no—
195C2×C4—2362no—
196C2×C4—2362no—
197C2×C4—2362no—
198C2×C4#1427370512yes—
199C2×C4#1427371312yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1683731511yescharacteristic
208C22#1683759312yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—9441no—
213C4—4722no—
214C4—4722no—
215C4—2364no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2142526411yescharacteristic
220C2#2142527112yes—
subgroupG/H
centerC22#16837315
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1306C2
socleC22×C59#393
prime radicalC24×C59C2×D4
hypercenter#1306D59
hypocenterC59#10389
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
127. C59#10389semidirect

Maximal subgroups

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

subgroupindex
#214297662
#214241932
#214241712
#214219502
C59×#13062
#1038959