Finite Group Databasebeta

← #28489318

Subgroups — #28489318

Order 15104.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#21434871C211yesmaximal, characteristic
2#21434044C212yesmaximal
3#21422459C212yesmaximal
4#21421973C211yesmaximal, characteristic
5C59×#1818C211yesmaximal, characteristic
6C2×#14273706C2212yes—
7#16837743—24no—
8#16837738—22no—
9#16837737—22no—
10#16837732—22no—
11#16837643—22no—
12#16837560—22no—
13#16837445—22no—
14#16837410—22no—
15#16837366C2212yes—
16#16837127—24no—
17C2×#117×C59C2211yescharacteristic
18C2×C22⋊C8×C59C2211yescharacteristic
19C2×C22⋊C8×C59C2211yescharacteristic
20C59×#336—22no—
21C22×Dic118D412yes—
22C2×Dic236—22no—
23C2×#11745664—22no—
24#14273706—22no—
25#14273706—22no—
26#14273706—22no—
27#14273706—22no—
28C2×C4⋊Dic59D412yes—
29C2×Dic59⋊C4—22no—
30C2×C22⋊Dic59—22no—
31#14273661—22no—
32#14273660—24no—
33#14273658—24no—
34#14273652—24no—
35#14273650—24no—
36#14273650—24no—
37C22⋊(C59⋊C8)—22no—
38C22⋊(C59⋊C8)D414yes—
39C23×C4×C59C2311yescharacteristic
40C22×C8×C59—21no—
41C22×C8×C59D412yes—
42#117×C59—22no—
43#117×C59—22no—
44C2×C4⋊C4×C59D411yescharacteristic
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C22⋊C4×C59—21no—
47C2×C42×C59—21no—
48C22⋊C8×C59—22no—
49C22⋊C8×C59—22no—
50C24×C59#4111yescharacteristic
51C22×C4×C59—21no—
52C22×C4×C59—21no—
53C22×C4×C59—42no—
54C22×C4×C59C2×D412yes—
55C22×C4×C59C2×D411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59C2×D412yes—
58C22×Dic59—22no—
59C22×Dic59—22no—
60C2×Dic118—22no—
61C2×Dic118—22no—
62C2×Dic118—44no—
63C2×C8×C59—22no—
64C2×C8×C59—42no—
65C2×C8×C59—42no—
66C2×C8×C59—41no—
67C4⋊C4×C59—22no—
68C4⋊C4×C59—22no—
69C22⋊C4×C59—42no—
70C42×C59—41no—
71C42×C59—41no—
72C22⋊Dic59—42no—
73C22⋊Dic59—42no—
74C4⋊Dic59—22no—
75C4⋊Dic59—22no—
76Dic59⋊C4—42no—
77Dic59⋊C4—42no—
78#11745664—44no—
79C2×C59⋊C8—24no—
80Dic236—82no—
81C23×C59—22no—
82C23×C59—41no—
83C23×C59—41no—
84C23×C59#12112yes—
85C23×C59#12111yescharacteristic
86C2×C4×C59—24no—
87C2×C4×C59—22no—
88C2×C4×C59—41no—
89C2×C4×C59—42no—
90C2×C4×C59—42no—
91C2×C4×C59—41no—
92C2×C4×C59—41no—
93C2×C4×C59—42no—
94C2×C4×C59#12011yescharacteristic
95C2×C4×C59#12012yes—
96C2×C4×C59#12711yescharacteristic
97C2×Dic59—44no—
98C2×Dic59—42no—
99C2×Dic59—42no—
100C2×Dic59—82no—
101Dic118—44no—
102Dic118—44no—
103C8×C59—42no—
104C8×C59—81no—
105C59⋊C8—44no—
106#9979—591nomaximal, Sylow
107C22×C59—21no—
108C22×C59—21no—
109C22×C59—22no—
110C22×C59—22no—
111C22×C59—22no—
112C22×C59—82no—
113C22×C59#39211yescharacteristic
114C22×C59#47312yes—
115C4×C59—22no—
116C4×C59—21no—
117C4×C59—81no—
118C4×C59—81no—
119C4×C59#45812yes—
120Dic59—82no—
121Dic59—82no—
122#3189—591no—
123#3095—592no—
124#1818D5911yescharacteristic
125#1472—592no—
126#1293—591no—
127C2×C59—22no—
128C2×C59—42no—
129C2×C59#201711yescharacteristic
130C2×C59#202011yescharacteristic
131C2×C59#202211yescharacteristic
132C2×C22⋊Q8—592no—
133C2×#117C2×D5911yescharacteristic
134#485—1184no—
135#484—1182no—
136#484—1182no—
137#483—1182no—
138#467—1182no—
139#451—1182no—
140#428—1182no—
141#419—1182no—
142#407—592no—
143C2×C22⋊C8C2×D5911yescharacteristic
144C2×C22⋊C8C2×D5911yescharacteristic
145#336—22no—
146#324—1184no—
147C59#997911yescharacteristic, complemented, Sylow
148C22×Q8—592no—
149C23×C4C22×D5911yescharacteristic
150C2×Q16—1182no—
151C2×M16—1182no—
152C22×C8—21no—
153C22×C8C22⋊D5912yes—
154C22⋊Q8—1182no—
155C22⋊Q8—1182no—
156C22⋊Q8—1182no—
157C22⋊Q8—1182no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—592no—
161C2×C4⋊C4—1182no—
162C2×C4⋊C4D23611yescharacteristic
163C2×C4⋊C4D23611yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—1182no—
166C2×C42—21no—
167#107—1184no—
168#107—1182no—
169#106—1184no—
170#103—1184no—
171#103—1184no—
172#103—1184no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—594no—
176C22⋊C8—1182no—
177C24#1174568511yescharacteristic
178C2×Q8—1182no—
179C2×Q8—1182no—
180C2×Q8—2364no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—42no—
184C22×C4—1182no—
185C22×C4—1182no—
186C22×C4C2×D23611yescharacteristic
187C22×C4D4×D5912yes—
188C22×C4D4×D5912yes—
189C22×C4C2×C22⋊D5911yescharacteristic
190Q16—4722no—
191M16—2364no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—1184no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—1182no—
200C4⋊C4—1182no—
201C4⋊C4—2362no—
202C4⋊C4—2362no—
203C22⋊C4—42no—
204C22⋊C4—2362no—
205C22⋊C4—2362no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#1427370012yes—
212C23#1427370111yescharacteristic
213Q8—2364no—
214Q8—2364no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—4722no—
224C2×C4—2364no—
225C2×C4—2362no—
226C2×C4—2362no—
227C2×C4#1427369511yescharacteristic
228C2×C4#1427369712yes—
229C2×C4#1427372311yescharacteristic
230C8—42no—
231C8—81no—
232C8—2364no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1683731111yescharacteristic
240C22#1683767712yes—
241C4—21no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—4722no—
246C4—4722no—
247C4#1683759112yes—
248C2—22no—
249C2—42no—
250C2#2142520011yescharacteristic
251C2#2142521711yescharacteristic
252C2#2142522711yescharacteristic
subgroupG/H
centerC22#16837311
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1818C2
socleC22×C59#392
prime radicalC24×C59#41
hypercenter#1818D59
hypocenterC59#9979
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
147. C59#9979semidirect

Maximal subgroups

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

subgroupindex
#214348712
#214340442
#214224592
#214219732
C59×#18182
#997959