Finite Group Databasebeta

← #28477396

Subgroups — #28477396

Order 15104.

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

normal subgroups only

This group has 560 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#21431026C211yesmaximal, characteristic, complemented
2#21425327C212yesmaximal, complemented
3#21421920C212yesmaximal, complemented
4#21421917C211yesmaximal, characteristic, complemented
5C59×#2011C211yesmaximal, characteristic
6C2×#14273708—21no—
7C2×#14273648—22no—
8C2×#14273648—22no—
9#16837332—21no—
10#16837327—22no—
11#16837300C2212yes—
12#16837277—22no—
13#16837157C2212yes—
14C22×D8×C59—21no—
15C2×#127×C59C2211yescharacteristic
16C2×#102×C59—21no—
17C59×#390C2211yescharacteristic
18C59×#336C2211yescharacteristic
19C23×Dic59—21no—
20C22×C59⋊C8—22no—
21#14273708—42no—
22#14273708—42no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59D412yes—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27C2×C22⋊Dic59—22no—
28C2×C22⋊Dic59—21no—
29#14273648—44no—
30#14273648—44no—
31C59⋊#95—22no—
32C59⋊#95—21no—
33C59⋊#95—22no—
34C22×D4×C59—22no—
35C22×D4×C59—21no—
36C22×D4×C59D411yescharacteristic
37C2×D8×C59—42no—
38C2×D8×C59—42no—
39C2×D8×C59—42no—
40C22×C8×C59—21no—
41#127×C59—42no—
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C22⋊C4×C59—22no—
44C2×C42×C59C2311yescharacteristic
45#102×C59—42no—
46C24×C59—21no—
47C24×C59—41no—
48C2×D4×C59—22no—
49C2×D4×C59—24no—
50C2×D4×C59—21no—
51C2×D4×C59—41no—
52C2×D4×C59—41no—
53C2×D4×C59—41no—
54C2×D4×C59—41no—
55C2×D4×C59—42no—
56C2×D4×C59—42no—
57C2×D4×C59—42no—
58C2×D4×C59—41no—
59C2×D4×C59—41no—
60C2×D4×C59—42no—
61C2×D4×C59—41no—
62C2×D4×C59—42no—
63C2×D4×C59D812yes—
64C22×C4×C59—21no—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D412yes—
67C22×Dic59—22no—
68C22×Dic59—22no—
69C22×Dic59—42no—
70C22×Dic59—81no—
71C22×Dic59—81no—
72D8×C59—48no—
73C2×C8×C59—22no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C4⋊C4×C59—41no—
77C22⋊C4×C59—42no—
78C22⋊C4×C59—42no—
79C42×C59—41no—
80C22⋊Dic59—42no—
81C22⋊Dic59—44no—
82C4⋊Dic59—22no—
83C4⋊Dic59—22no—
84C4⋊Dic59—42no—
85C4⋊Dic59—81no—
86Dic59⋊C4—42no—
87Dic59⋊C4—42no—
88C2×C59⋊C8—42no—
89C2×C59⋊C8—42no—
90C2×C59⋊C8—42no—
91C23×C59—22no—
92C23×C59—42no—
93C23×C59—41no—
94C23×C59—42no—
95C23×C59—41no—
96C23×C59—42no—
97C23×C59—81no—
98C23×C59—82no—
99C23×C59—81no—
100C23×C59—82no—
101C23×C59#12011yescharacteristic
102D4×C59—42no—
103D4×C59—42no—
104D4×C59—42no—
105D4×C59—44no—
106D4×C59—44no—
107D4×C59—81no—
108D4×C59—81no—
109D4×C59—81no—
110D4×C59—82no—
111D4×C59—82no—
112C2×C4×C59—21no—
113C2×C4×C59—22no—
114C2×C4×C59—22no—
115C2×C4×C59—21no—
116C2×C4×C59—42no—
117C2×C4×C59—41no—
118C2×C4×C59C2×D811yescharacteristic
119C2×C4×C59#13512yes—
120C2×C4×C59AGL(1,ℤ/8)12yes—
121C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
122C2×Dic59—42no—
123C2×Dic59—42no—
124C2×Dic59—42no—
125C2×Dic59—42no—
126C2×Dic59—42no—
127C2×Dic59—42no—
128C2×Dic59—84no—
129C8×C59—42no—
130C59⋊C8—82no—
131#7736—591nomaximal, Sylow
132C22×C59—42no—
133C22×C59—44no—
134C22×C59—82no—
135C22×C59—81no—
136C22×C59—81no—
137C22×C59—82no—
138C22×C59—84no—
139C22×C59—161no—
140C22×C59—162no—
141C22×C59—161no—
142C22×C59#44711yescharacteristic
143C22×C59#44912yes—
144C22×C59#45311yescharacteristic
145C22×C59#45412yes—
146C22×C59B(4,𝔽2)11yescharacteristic
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—22no—
150C4×C59—22no—
151C4×C59—81no—
152Dic59—82no—
153Dic59—82no—
154#2724—591no—
155#2041—592no—
156#2011D5911yescharacteristic
157#1271—592no—
158#1270—591no—
159C2×C59—82no—
160C2×C59—162no—
161C2×C59#159511yescharacteristic
162C2×C59#159712yes—
163C2×C59#162011yescharacteristic
164C2×C59#162512yes—
165C2×C59#165711yescharacteristic
166C22×D8—21no—
167C2×#127C2×D5911yescharacteristic
168C2×#123—1181no—
169C2×#102—21no—
170C2×#102—1182no—
171C2×#102—1182no—
172#398—1181no—
173#397—1182no—
174#390C2×D5911yescharacteristic
175#389—592no—
176#385—1182no—
177#336—592no—
178#336C2×D5911yescharacteristic
179C59#773611yescharacteristic, complemented, Sylow
180C22×D4—22no—
181C22×D4—21no—
182C22×D4C22⋊D5911yescharacteristic
183C23×C4—1181no—
184C2×D8—42no—
185C2×D8—42no—
186C2×D8—42no—
187C22×C8—21no—
188C22×C8—1182no—
189#127—42no—
190#123—2362no—
191#123—2362no—
192C2×C4⋊C4—592no—
193C2×C4⋊C4—592no—
194C2×C4⋊C4—1181no—
195C2×C4⋊C4—1182no—
196C2×C4⋊C4C22⋊D5911yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—1182no—
199C2×C22⋊C4—1181no—
200C2×C42C22×D5911yescharacteristic
201#102—42no—
202#102—2364no—
203#102—2364no—
204#95—1182no—
205#95—1181no—
206#95—1182no—
207C24—21no—
208C24—41no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—42no—
223C2×D4—41no—
224C2×D4#1174566912yes—
225C22×C4—21no—
226C22×C4—1182no—
227C22×C4—1182no—
228C22×C4—4721no—
229C22×C4—4721no—
230C22×C4—2362no—
231C22×C4D4×D5912yes—
232C22×C4C2×C22⋊D5911yescharacteristic
233D8—48no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—2362no—
238C2×C8—2362no—
239C2×C8—2362no—
240C4⋊C4—41no—
241C4⋊C4—1182no—
242C4⋊C4—1182no—
243C4⋊C4—4721no—
244C4⋊C4—2362no—
245C4⋊C4—2362no—
246C4⋊C4—2362no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—2362no—
250C22⋊C4—2364no—
251C42—41no—
252C23—22no—
253C23—42no—
254C23—41no—
255C23—42no—
256C23—41no—
257C23—42no—
258C23—81no—
259C23—82no—
260C23—81no—
261C23—82no—
262C23#1427369511yescharacteristic
263D4—42no—
264D4—42no—
265D4—42no—
266D4—44no—
267D4—44no—
268D4—81no—
269D4—81no—
270D4—81no—
271D4—82no—
272D4—82no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—4724no—
280C2×C4—2362no—
281C2×C4—2362no—
282C2×C4—2362no—
283C2×C4—2362no—
284C2×C4—2362no—
285C2×C4—2362no—
286C2×C4C2×#1174566911yescharacteristic
287C2×C4#1427374612yes—
288C2×C4#1427375112yes—
289C2×C4#1427375211yescharacteristic
290C8—42no—
291C8—4722no—
292C22—44no—
293C22—42no—
294C22—81no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—84no—
299C22—161no—
300C22—161no—
301C22—162no—
302C22#1683753511yescharacteristic
303C22#1683754412yes—
304C22#1683756911yescharacteristic
305C22#1683757312yes—
306C22#1683758811yescharacteristic
307C4—21no—
308C4—21no—
309C4—22no—
310C4—22no—
311C4—81no—
312C4—4722no—
313C4—4722no—
314C2—82no—
315C2—162no—
316C2#2142301311yescharacteristic
317C2#2142302212yes—
318C2#2142315311yescharacteristic
319C2#2142318312yes—
320C2#2142339211yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
Fitting, prime radicalC59×#2011C2
socleC23×C59#120
hypercenter#2011D59
hypocenterC59#7736
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

Complements

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

NH ≅ G/Ntype
1. #21431026C2semidirect
2. #21425327C2semidirect
3. #21421920C2semidirect
4. #21421917C2semidirect
179. C59#7736semidirect

Maximal subgroups

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

subgroupindex
#214310262
#214253272
#214219202
#214219172
C59×#20112
#773659