Finite Group Databasebeta

← #28493042

Subgroups — #28493042

Order 15104.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#21424564C212yesmaximal
3#21422615C212yesmaximal
4#21421973C211yesmaximal, characteristic
5C59×#1851C211yesmaximal, characteristic
6C2×#14273706C2212yes—
7#16837738—22no—
8#16837643—21no—
9#16837643—21no—
10#16837560—22no—
11C2×#14273645—22no—
12#16837366C2212yes—
13#16837170—22no—
14#16837138—22no—
15#16837138—22no—
16C22×M16×C59C2211yescharacteristic
17C2×C4⋊C8×C59—21no—
18C2×C22⋊C8×C59C2211yescharacteristic
19C4×C22⋊C4×C59C2211yescharacteristic
20C59×#336—21no—
21C22×Dic118D412yes—
22C2×Dic236—21no—
23C2×Dic236—21no—
24C2×#11745664—22no—
25#14273706—22no—
26#14273706—22no—
27#14273706—22no—
28#14273706—22no—
29C2×C4⋊Dic59D412yes—
30C2×Dic59⋊C4—22no—
31C2×C22⋊Dic59—22no—
32#14273661—21no—
33#14273661—21no—
34#14273652—22no—
35#14273652—22no—
36#14273645—44no—
37C22⋊(C59⋊C8)—22no—
38C22⋊(C59⋊C8)—22no—
39C23×C4×C59C2311yescharacteristic
40C2×M16×C59—22no—
41C2×M16×C59—42no—
42C22×C8×C59—21no—
43C22×C8×C59D411yescharacteristic
44C22×C8×C59D411yescharacteristic
45C2×C22⋊C4×C59—21no—
46C2×C42×C59—21no—
47C4⋊C8×C59—42no—
48C22⋊C8×C59—22no—
49#95×C59D411yescharacteristic
50#95×C59D411yescharacteristic
51C24×C59#4111yescharacteristic
52C22×C4×C59—21no—
53C22×C4×C59—21no—
54C22×C4×C59—41no—
55C22×C4×C59—41no—
56C22×C4×C59C2×D412yes—
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59#4112yes—
60C22×Dic59—22no—
61C22×Dic59—22no—
62C2×Dic118—22no—
63C2×Dic118—22no—
64C2×Dic118—42no—
65C2×Dic118—42no—
66M16×C59—24no—
67M16×C59—42no—
68C2×C8×C59—22no—
69C2×C8×C59—21no—
70C2×C8×C59—21no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C22⋊C4×C59—42no—
76C42×C59—41no—
77C42×C59—41no—
78C22⋊Dic59—42no—
79C22⋊Dic59—42no—
80C4⋊Dic59—22no—
81C4⋊Dic59—22no—
82Dic59⋊C4—42no—
83Dic59⋊C4—42no—
84#11745664—42no—
85#11745664—42no—
86C2×C59⋊C8—42no—
87Dic236—81no—
88Dic236—81no—
89C23×C59—21no—
90C23×C59—21no—
91C23×C59—41no—
92C23×C59—41no—
93C23×C59#12111yescharacteristic
94C23×C59#12312yes—
95C2×C4×C59—22no—
96C2×C4×C59—21no—
97C2×C4×C59—22no—
98C2×C4×C59—21no—
99C2×C4×C59—22no—
100C2×C4×C59—41no—
101C2×C4×C59—42no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59#12011yescharacteristic
108C2×C4×C59#12112yes—
109C2×C4×C59#12411yescharacteristic
110C2×Dic59—44no—
111C2×Dic59—42no—
112C2×Dic59—42no—
113C2×Dic59—82no—
114Dic118—42no—
115Dic118—42no—
116Dic118—82no—
117C8×C59—41no—
118C8×C59—42no—
119C8×C59—41no—
120C59⋊C8—82no—
121#10559—591nomaximal, Sylow
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—81no—
128C22×C59—81no—
129C22×C59#39411yescharacteristic
130C22×C59#47311yescharacteristic
131C22×C59#47311yescharacteristic
132C4×C59—22no—
133C4×C59—21no—
134C4×C59—42no—
135C4×C59—81no—
136C4×C59B(4,𝔽2)11yescharacteristic
137C4×C59#45811yescharacteristic
138Dic59—82no—
139Dic59—82no—
140#3189—591no—
141#1901—592no—
142#1851D5911yescharacteristic
143#1508—592no—
144#1293—591no—
145C2×C59—21no—
146C2×C59—21no—
147C2×C59—42no—
148C2×C59#204411yescharacteristic
149C2×C59#204711yescharacteristic
150C2×C59#205011yescharacteristic
151C22×M16C2×D5911yescharacteristic
152C2×C22⋊Q8—592no—
153#484—1182no—
154#467—1181no—
155#467—1181no—
156#451—1182no—
157C2×C4⋊C8—21no—
158C2×#101—1182no—
159#407—592no—
160C2×C22⋊C8C2×D5911yescharacteristic
161C4×C22⋊C4C2×D5911yescharacteristic
162#343—1182no—
163#336—21no—
164#328—1182no—
165#328—1182no—
166C59#1055911yescharacteristic, complemented, Sylow
167C22×Q8—592no—
168C23×C4C22×D5911yescharacteristic
169C2×Q16—1181no—
170C2×Q16—1181no—
171C2×M16—22no—
172C2×M16—42no—
173C2×M16—1182no—
174C22×C8—21no—
175C22×C8C22⋊D5911yescharacteristic
176C22×C8C22⋊D5911yescharacteristic
177C22⋊Q8—1182no—
178C22⋊Q8—1182no—
179C22⋊Q8—1182no—
180C22⋊Q8—1182no—
181C2×C4⋊C4—592no—
182C2×C4⋊C4—1182no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—1182no—
185C2×C42—21no—
186#107—1181no—
187#107—1181no—
188C4⋊C8—42no—
189#103—1182no—
190#103—1182no—
191#101—2364no—
192C22⋊C8—22no—
193C22⋊C8—1182no—
194C22⋊C8—1182no—
195#95D23611yescharacteristic
196#95D23611yescharacteristic
197C24#1174568511yescharacteristic
198C2×Q8—1182no—
199C2×Q8—1182no—
200C2×Q8—2362no—
201C2×Q8—2362no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—1182no—
207C22×C4—1182no—
208C22×C4C2×D23611yescharacteristic
209C22×C4D4×D5912yes—
210C22×C4#1174568912yes—
211C22×C4C2×C22⋊D5911yescharacteristic
212Q16—4721no—
213Q16—4721no—
214M16—24no—
215M16—42no—
216M16—2362no—
217M16—2362no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—2362no—
226C4⋊C4—1182no—
227C4⋊C4—1182no—
228C4⋊C4—2362no—
229C4⋊C4—2362no—
230C22⋊C4—42no—
231C22⋊C4—2362no—
232C22⋊C4—2362no—
233C42—41no—
234C42—41no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#1427370111yescharacteristic
240C23#1427371212yes—
241Q8—4722no—
242Q8—2362no—
243Q8—2362no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—4722no—
257C2×C4—2364no—
258C2×C4—2362no—
259C2×C4—2362no—
260C2×C4#1427369511yescharacteristic
261C2×C4#1427370212yes—
262C2×C4#1427371611yescharacteristic
263C8—42no—
264C8—41no—
265C8—41no—
266C8—4722no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1683731911yescharacteristic
275C22#1683767711yescharacteristic
276C22#1683767711yescharacteristic
277C4—22no—
278C4—21no—
279C4—42no—
280C4—81no—
281C4—4722no—
282C4—4722no—
283C4#1683758811yescharacteristic
284C4#1683759111yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#2142534711yescharacteristic
289C2#2142536411yescharacteristic
290C2#2142538311yescharacteristic
subgroupG/H
centerC22#16837319
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1851C2
socleC22×C59#394
prime radicalC24×C59#41
hypercenter#1851D59
hypocenterC59#10559
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
166. C59#10559semidirect

Maximal subgroups

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

subgroupindex
#214348712
#214245642
#214226152
#214219732
C59×#18512
#1055959