Finite Group Databasebeta

← #28492183

Subgroups — #28492183

Order 15104.

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

normal subgroups only

This group has 386 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#21432164C211yesmaximal, characteristic
2#21425064C212yesmaximal
3C2×#16837143C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#1836C211yesmaximal, characteristic
6C2×#14273719C2212yes—
7C2×#14273638C2212yes—
8#16837342—22no—
9#16837334—22no—
10#16837332—22no—
11#16837164—22no—
12#16837164—22no—
13#16837143—24no—
14C2×#97×C59C2211yescharacteristic
15C59×#384C2211yescharacteristic
16C59×#382C2211yescharacteristic
17C59×#340—22no—
18C22×C59⋊C8—22no—
19#14273719—22no—
20#14273719—22no—
21#14273719—22no—
22#14273719—22no—
23C2×C4⋊Dic59—22no—
24C2×C4⋊Dic59D412yes—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27C2×Dic59⋊C4—22no—
28#14273638—22no—
29#14273638—22no—
30C59⋊#95—24no—
31C59⋊#95—22no—
32C22×C8×C59—21no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59D412yes—
36C2×C42×C59C2311yescharacteristic
37#97×C59—21no—
38#97×C59D412yes—
39#95×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59—41no—
42C22×C4×C59C2×D412yes—
43C22×C4×C59C2×D411yescharacteristic
44C22×Dic59—22no—
45C22×Dic59—22no—
46C2×C8×C59—22no—
47C2×C8×C59—41no—
48C2×C8×C59—41no—
49C4⋊C4×C59—42no—
50C4⋊C4×C59—44no—
51C4⋊C4×C59—42no—
52C42×C59C2×D411yescharacteristic
53C42×C59#4111yescharacteristic
54C42×C59#4112yes—
55C4⋊Dic59—22no—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—82no—
60Dic59⋊C4—42no—
61Dic59⋊C4—42no—
62Dic59⋊C4—42no—
63Dic59⋊C4—42no—
64C2×C59⋊C8—24no—
65C2×C59⋊C8—42no—
66C2×C59⋊C8—42no—
67C23×C59#12011yescharacteristic
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—82no—
76C2×C4×C59—81no—
77C2×C4×C59#12111yescharacteristic
78C2×C4×C59#12112yes—
79C2×C4×C59#12312yes—
80C2×C4×C59#12411yescharacteristic
81C2×Dic59—42no—
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—42no—
87C8×C59—42no—
88C59⋊C8—44no—
89#10428—591nomaximal, Sylow
90C22×C59#39411yescharacteristic
91C22×C59#45412yes—
92C22×C59#45411yescharacteristic
93C22×C59#45511yescharacteristic
94C22×C59#45612yes—
95C4×C59—22no—
96C4×C59—22no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—82no—
100C4×C59—161no—
101Dic59—82no—
102Dic59—82no—
103#2822—591no—
104#1992—592no—
105#1836D5911yescharacteristic
106C2×#330—592no—
107#1295—591no—
108C2×C59#165811yescharacteristic
109C2×C59#166311yescharacteristic
110C2×C59#166412yes—
111C2×C59#203812yes—
112C2×C59#204011yescharacteristic
113C2×#125—592no—
114C2×#97—592no—
115C2×#97C2×D5911yescharacteristic
116#400—1182no—
117#398—1182no—
118#398—1182no—
119#384C2×D5911yescharacteristic
120#382C2×D5911yescharacteristic
121#340—22no—
122#340—1182no—
123#340—1182no—
124#330—1184no—
125C59#1042811yescharacteristic, complemented, Sylow
126C22×C8—21no—
127C22×C8—1182no—
128#125—1182no—
129#125—1182no—
130#125—1182no—
131#125—1182no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4—1182no—
138C2×C4⋊C4—1182no—
139C2×C4⋊C4C22⋊D5912yes—
140C2×C42C22×D5911yescharacteristic
141#97—21no—
142#97—1182no—
143#97—1182no—
144#97D23612yes—
145#95—22no—
146#95—1184no—
147#95—1182no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—1182no—
151C22×C4—1182no—
152C22×C4D4×D5912yes—
153C22×C4C2×C22⋊D5911yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—1184no—
158C2×C8—2362no—
159C2×C8—2362no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4—4722no—
168C4⋊C4—2362no—
169C4⋊C4—2362no—
170C4⋊C4—2362no—
171C4⋊C4—2362no—
172C42C2×D23611yescharacteristic
173C42#1174568511yescharacteristic
174C42#1174568912yes—
175C23#1427369511yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—2362no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4—2362no—
189C2×C4—2362no—
190C2×C4—2362no—
191C2×C4#1427370111yescharacteristic
192C2×C4#1427370212yes—
193C2×C4#1427371212yes—
194C2×C4#1427371611yescharacteristic
195C8—42no—
196C8—2364no—
197C22#1683731911yescharacteristic
198C22#1683757312yes—
199C22#1683757411yescharacteristic
200C22#1683757911yescharacteristic
201C22#1683758312yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—4722no—
209C4—4722no—
210C2#2142339711yescharacteristic
211C2#2142342211yescharacteristic
212C2#2142342912yes—
213C2#2142531512yes—
214C2#2142532511yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1836C2
socle, prime radicalC23×C59#120
hypercenter#1836D59
hypocenterC59#10428
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
125. C59#10428semidirect

Maximal subgroups

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

subgroupindex
#214321642
#214250642
C2×#168371432
#214219772
C59×#18362
#1042859