Finite Group Databasebeta

← #28489284

Subgroups — #28489284

Order 15104.

632 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#16837732C212yesmaximal
2#21430210C211yesmaximal, characteristic
3C2×#16837138C212yesmaximal
4#21421939C211yesmaximal, characteristic
5C59×#1445C211yesmaximal, characteristic
6C2×#14273706C2212yes—
7#16837732—24no—
8#16837732—24no—
9C2×#14273658—22no—
10C2×#14273650—22no—
11C2×C22⋊(C59⋊C8)C2212yes—
12#16837334—22no—
13#16837323—22no—
14#16837262—22no—
15#16837138—24no—
16C22×C4⋊C4×C59C2211yescharacteristic
17C2×#95×C59—22no—
18C2×#95×C59C2211yescharacteristic
19C2×#95×C59C2211yescharacteristic
20C22×Dic118D412yes—
21C22×C59⋊C8—22no—
22#14273706—22no—
23#14273706—22no—
24#14273706—22no—
25#14273706—22no—
26C2×C4⋊Dic59—22no—
27C2×C4⋊Dic59—22no—
28C2×C4⋊Dic59D412yes—
29C2×Dic59⋊C4—22no—
30C2×C22⋊Dic59—22no—
31#14273658—28no—
32#14273650—28no—
33C22⋊(C59⋊C8)—22no—
34C22⋊(C59⋊C8)D414yes—
35C59⋊#95—24no—
36C23×C4×C59—21no—
37C23×C4×C59—21no—
38C23×C4×C59D412yes—
39C23×C4×C59C2311yescharacteristic
40C2×C4⋊C4×C59—22no—
41C2×C4⋊C4×C59—22no—
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59D412yes—
44#95×C59—22no—
45#95×C59—22no—
46#95×C59—44no—
47C24×C59C2×D411yescharacteristic
48C22×C4×C59—22no—
49C22×C4×C59—22no—
50C22×C4×C59—22no—
51C22×C4×C59—22no—
52C22×C4×C59—42no—
53C22×C4×C59—42no—
54C22×C4×C59—42no—
55C22×C4×C59—41no—
56C22×C4×C59—42no—
57C22×C4×C59—41no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59—42no—
61C22×C4×C59—42no—
62C22×C4×C59—42no—
63C22×C4×C59SD1614yes—
64C22×C4×C59C2×D412yes—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D412yes—
67C22×C4×C59#4111yescharacteristic
68C22×Dic59—22no—
69C22×Dic59—22no—
70C2×Dic118—22no—
71C2×Dic118—22no—
72C2×Dic118—44no—
73C4⋊C4×C59—24no—
74C4⋊C4×C59—42no—
75C22⋊Dic59—42no—
76C22⋊Dic59—42no—
77C4⋊Dic59—22no—
78C4⋊Dic59—22no—
79C4⋊Dic59—82no—
80C4⋊Dic59—82no—
81Dic59⋊C4—42no—
82Dic59⋊C4—42no—
83C2×C59⋊C8—24no—
84C2×C59⋊C8—44no—
85C23×C59—21no—
86C23×C59—21no—
87C23×C59—22no—
88C23×C59#12011yescharacteristic
89C23×C59#12111yescharacteristic
90C23×C59#12711yescharacteristic
91C23×C59C2×SD1612yes—
92C23×C59#13712yes—
93C2×C4×C59—24no—
94C2×C4×C59—24no—
95C2×C4×C59—41no—
96C2×C4×C59—42no—
97C2×C4×C59—41no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—44no—
101C2×C4×C59—44no—
102C2×C4×C59—42no—
103C2×C4×C59—42no—
104C2×C4×C59—44no—
105C2×C4×C59—82no—
106C2×C4×C59—82no—
107C2×C4×C59—81no—
108C2×C4×C59—82no—
109C2×C4×C59—81no—
110C2×C4×C59—81no—
111C2×C4×C59—81no—
112C2×C4×C59#12012yes—
113C2×C4×C59#12112yes—
114C2×Dic59—42no—
115C2×Dic59—42no—
116C2×Dic59—42no—
117C2×Dic59—42no—
118C2×Dic59—44no—
119Dic118—44no—
120Dic118—82no—
121C59⋊C8—44no—
122#9973—591nomaximal, Sylow
123C22×C59—22no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—21no—
128C22×C59—21no—
129C22×C59—21no—
130C22×C59—21no—
131C22×C59#39211yescharacteristic
132C22×C59#44812yes—
133C22×C59#45511yescharacteristic
134C22×C59#45611yescharacteristic
135C22×C59#45812yes—
136C22×C59#46112yes—
137C22×C59#49211yescharacteristic
138C22×C59#49711yescharacteristic
139C4×C59—22no—
140C4×C59—22no—
141C4×C59—44no—
142C4×C59—82no—
143C4×C59—82no—
144Dic59—82no—
145Dic59—82no—
146C2×#483—592no—
147#2659—591no—
148C2×#328—592no—
149#1445D5911yescharacteristic
150#1280—591no—
151C2×C59—21no—
152C2×C59—22no—
153C2×C59—21no—
154C2×C59#160812yes—
155C2×C59#161112yes—
156C2×C59#200711yescharacteristic
157C2×C59#201311yescharacteristic
158C2×C59#202211yescharacteristic
159C2×C22⋊Q8—592no—
160C22×C4⋊C4C2×D5911yescharacteristic
161#483—1184no—
162#483—1184no—
163C2×#106—1182no—
164C2×#103—1182no—
165C2×C22⋊C8—592no—
166#398—1182no—
167#395—1182no—
168#380—1182no—
169C2×#95—22no—
170C2×#95C2×D5911yescharacteristic
171C2×#95C2×D5911yescharacteristic
172#328—1184no—
173C59#997311yescharacteristic, complemented, Sylow
174C22×Q8—592no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4C22⋊D5912yes—
178C23×C4C22×D5911yescharacteristic
179C22×C8—1182no—
180C22⋊Q8—1182no—
181C22⋊Q8—1182no—
182C22⋊Q8—1182no—
183C22⋊Q8—1182no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—592no—
188C2×C4⋊C4—1182no—
189C2×C4⋊C4—1182no—
190C2×C4⋊C4—1182no—
191C2×C4⋊C4D23612yes—
192C2×C22⋊C4—1182no—
193#106—1188no—
194#103—1188no—
195C22⋊C8—594no—
196C22⋊C8—1182no—
197#95—22no—
198#95—22no—
199#95—44no—
200#95—1184no—
201C24C2×C22⋊D5911yescharacteristic
202C2×Q8—1182no—
203C2×Q8—1182no—
204C2×Q8—2364no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—1182no—
221C22×C4—1182no—
222C22×C4#1174567014yes—
223C22×C4C2×D23611yescharacteristic
224C22×C4#1174568511yescharacteristic
225C22×C4D4×D5912yes—
226C22×C4D4×D5912yes—
227C2×C8—1184no—
228C2×C8—2364no—
229C4⋊C4—24no—
230C4⋊C4—42no—
231C4⋊C4—1182no—
232C4⋊C4—1182no—
233C4⋊C4—4722no—
234C4⋊C4—4722no—
235C4⋊C4—2362no—
236C4⋊C4—2362no—
237C22⋊C4—2362no—
238C22⋊C4—2362no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1427369511yescharacteristic
243C23#1427370111yescharacteristic
244C23#1427372311yescharacteristic
245C23C2×#1174567012yes—
246C23#1427375712yes—
247Q8—4722no—
248Q8—2364no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4—2362no—
269C2×C4—2362no—
270C2×C4—2362no—
271C2×C4—2362no—
272C2×C4—2364no—
273C2×C4#1427369712yes—
274C2×C4#1427370012yes—
275C8—2364no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22#1683731111yescharacteristic
285C22#1683754012yes—
286C22#1683757911yescharacteristic
287C22#1683758411yescharacteristic
288C22#1683759112yes—
289C22#1683760712yes—
290C22#1683777411yescharacteristic
291C22#1683779711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—4722no—
298C4—4722no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2#2142308612yes—
303C2#2142310312yes—
304C2#2142514211yescharacteristic
305C2#2142517811yescharacteristic
306C2#2142522711yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1445C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenter#1445D59
hypocenterC59#9973
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
173. C59#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#168377322
#214302102
C2×#168371382
#214219392
C59×#14452
#997359