Finite Group Databasebeta

← #28477888

Subgroups — #28477888

Order 15104.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#21432089C211yesmaximal, characteristic
2#21425639C211yesmaximal, characteristic
3#21425506C212yesmaximal
4#21421921C212yesmaximal
5C59×#1272C211yesmaximal, characteristic
6C2×#14273658—21no—
7C2×#14273652—22no—
8C2×#14273651—21no—
9#16837323—22no—
10#16837322—21no—
11#16837309—21no—
12#16837308C2212yes—
13#16837306—22no—
14#16837272C2211yescharacteristic
15#16837165—22no—
16#16837157C2211yescharacteristic
17C59×#391C2211yescharacteristic
18C59×#336C2212yes—
19C22×Dic118—21no—
20C22×Dic118D412yes—
21C22×C59⋊C8—21no—
22C2×C4⋊Dic59—21no—
23C2×C4⋊Dic59—22no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27C2×C4×Dic59—21no—
28#14273658—42no—
29#14273652—44no—
30#14273651—42no—
31C59⋊#95—21no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C59⋊#95—22no—
35C22×Q8×C59D411yescharacteristic
36C22×C8×C59—22no—
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C42×C59C2311yescharacteristic
39#95×C59—22no—
40C2×Q8×C59—21no—
41C2×Q8×C59—41no—
42C2×Q8×C59—41no—
43C2×Q8×C59Q1612yes—
44C22×C4×C59—21no—
45C22×C4×C59—21no—
46C22×C4×C59C2×D412yes—
47C22×C4×C59C2×D411yescharacteristic
48C22×Dic59—22no—
49C22×Dic59—22no—
50C22×Dic59—41no—
51C2×Dic118—22no—
52C2×Dic118—42no—
53C2×Dic118—42no—
54C2×Dic118—81no—
55C2×Dic118—82no—
56C2×Dic118SD1614yes—
57C2×C8×C59—42no—
58C2×C8×C59—42no—
59C2×C8×C59—42no—
60C4⋊C4×C59—41no—
61C42×C59—41no—
62C4⋊Dic59—42no—
63C4⋊Dic59—41no—
64C4⋊Dic59—41no—
65C4⋊Dic59—42no—
66C4⋊Dic59—42no—
67C4⋊Dic59—81no—
68Dic59⋊C4—82no—
69C4×Dic59—81no—
70C2×C59⋊C8—22no—
71C2×C59⋊C8—41no—
72C2×C59⋊C8—41no—
73C23×C59#12011yescharacteristic
74Q8×C59—42no—
75Q8×C59—81no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—41no—
82C2×C4×C59—41no—
83C2×C4×C59—41no—
84C2×C4×C59—42no—
85C2×C4×C59C2×SD1612yes—
86C2×C4×C59C2×Q1611yescharacteristic
87C2×C4×C59#13712yes—
88C2×C4×C59#13711yescharacteristic
89C2×Dic59—24no—
90C2×Dic59—42no—
91C2×Dic59—42no—
92C2×Dic59—42no—
93C2×Dic59—42no—
94C2×Dic59—42no—
95C2×Dic59—82no—
96C2×Dic59—81no—
97Dic118—44no—
98Dic118—82no—
99Dic118—84no—
100C8×C59—82no—
101C59⋊C8—42no—
102#7812—591nomaximal, Sylow
103C22×C59#44812yes—
104C22×C59#45111yescharacteristic
105C22×C59#45311yescharacteristic
106C22×C59#45512yes—
107C22×C59#45811yescharacteristic
108C4×C59—22no—
109C4×C59—22no—
110C4×C59—21no—
111C4×C59—21no—
112C4×C59—42no—
113C4×C59—81no—
114Dic59—44no—
115Dic59—82no—
116Dic59—161no—
117#2811—591no—
118#2096—591no—
119#2072—592no—
120#1272—592no—
121#1272D5911yescharacteristic
122C2×C59#160812yes—
123C2×C59#161411yescharacteristic
124C2×C59#162311yescharacteristic
125C2×C59#164512yes—
126C2×C59#165911yescharacteristic
127C2×#106—1181no—
128C2×#103—1182no—
129C2×#103—1181no—
130#395—1182no—
131#395—1181no—
132#391—592no—
133#391—1182no—
134#391—1181no—
135#391C2×D5911yescharacteristic
136#384—591no—
137#340—1182no—
138#336—591no—
139#336C2×D5912yes—
140C59#781211yescharacteristic, complemented, Sylow
141C22×Q8—592no—
142C22×Q8—1181no—
143C22×Q8D23611yescharacteristic
144C22×C8—22no—
145C22×C8—1181no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4—1182no—
148C2×C4⋊C4—1181no—
149C2×C4⋊C4—1181no—
150C2×C4⋊C4—1182no—
151C2×C4⋊C4D23611yescharacteristic
152C2×C42—1181no—
153C2×C42C22×D5911yescharacteristic
154#106—2362no—
155#103—2364no—
156#103—2362no—
157#95—22no—
158#95—1182no—
159#95—1181no—
160#95—1182no—
161#95—1182no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—594no—
166C2×Q8—1182no—
167C2×Q8—4721no—
168C2×Q8—4722no—
169C2×Q8—2362no—
170C2×Q8—2362no—
171C2×Q8Dic23612yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—1182no—
175C22×C4—1182no—
176C22×C4—2361no—
177C22×C4C2×D23611yescharacteristic
178C22×C4D4×D5912yes—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—1182no—
183C2×C8—2361no—
184C2×C8—2361no—
185C4⋊C4—41no—
186C4⋊C4—4722no—
187C4⋊C4—4721no—
188C4⋊C4—2361no—
189C4⋊C4—2361no—
190C4⋊C4—2362no—
191C4⋊C4—2362no—
192C4⋊C4—2362no—
193C42—41no—
194C42—4721no—
195C23#1427369711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—4722no—
199Q8—4724no—
200Q8—2364no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—1184no—
211C2×C4—4722no—
212C2×C4—4721no—
213C2×C4—2362no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4—2362no—
217C2×C4—2362no—
218C2×C4SD16×D5912yes—
219C2×C4C2×Dic23611yescharacteristic
220C2×C4#1427375912yes—
221C2×C4#1427376011yescharacteristic
222C8—82no—
223C8—2362no—
224C22#1683754212yes—
225C22#1683756011yescharacteristic
226C22#1683757211yescharacteristic
227C22#1683758112yes—
228C22#1683759311yescharacteristic
229C4—21no—
230C4—21no—
231C4—22no—
232C4—22no—
233C4—42no—
234C4—81no—
235C4—9441no—
236C4—4722no—
237C4—2364no—
238C2#2142308812yes—
239C2#2142312311yescharacteristic
240C2#2142317511yescharacteristic
241C2#2142332012yes—
242C2#2142340311yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59#120
hypercenter#1272D59
hypocenterC59#7812
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
140. C59#7812semidirect

Maximal subgroups

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

subgroupindex
#214320892
#214256392
#214255062
#214219212
C59×#12722
#781259