Finite Group Databasebeta

← #28478002

Subgroups — #28478002

Order 15104.

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

normal subgroups only

This group has 322 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#21432087C211yesmaximal, characteristic
2#21425658C211yesmaximal, characteristic
3#21425658C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2100C211yesmaximal, characteristic
8#16837342—21no—
9#16837341—21no—
10#16837340—21no—
11#16837300C2211yescharacteristic
12#16837300C2211yescharacteristic
13#16837289—21no—
14#16837288—21no—
15#16837283—21no—
16#16837164—21no—
17#16837164—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C59×#389C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C59×#340—21no—
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59D411yescharacteristic
30C2×C4⋊Dic59D411yescharacteristic
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C4×Dic59—21no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C22×C8×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59D411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C42×C59C2311yescharacteristic
53#95×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—41no—
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×Dic59—21no—
61C22×Dic59—21no—
62C22×Dic59—21no—
63C22×Dic59—21no—
64C2×C8×C59—41no—
65C2×C8×C59—41no—
66C2×C8×C59—41no—
67C4⋊C4×C59—21no—
68C4⋊C4×C59—21no—
69C4⋊C4×C59—41no—
70C4⋊C4×C59—42no—
71C4⋊C4×C59—42no—
72C4⋊C4×C59—42no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C42×C59—41no—
76C4⋊Dic59—21no—
77C4⋊Dic59—21no—
78C4⋊Dic59—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59—41no—
81C4⋊Dic59—41no—
82Dic59⋊C4—41no—
83Dic59⋊C4—41no—
84Dic59⋊C4—41no—
85Dic59⋊C4—41no—
86C4×Dic59—81no—
87C2×C59⋊C8—41no—
88C2×C59⋊C8—41no—
89C2×C59⋊C8—41no—
90C2×C59⋊C8—41no—
91C2×C59⋊C8—41no—
92C2×C59⋊C8—41no—
93C23×C59#12011yescharacteristic
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—41no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—81no—
107C2×C4×C59—81no—
108C2×C4×C59—81no—
109C2×C4×C59#13511yescharacteristic
110C2×C4×C59#13511yescharacteristic
111C2×C4×C59#13511yescharacteristic
112C2×C4×C59#13711yescharacteristic
113C2×C4×C59#13711yescharacteristic
114C2×C4×C59#13711yescharacteristic
115C2×Dic59—41no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C8×C59—81no—
128C59⋊C8—81no—
129C59⋊C8—81no—
130#7832—591nomaximal, Sylow
131C22×C59#45211yescharacteristic
132C22×C59#45211yescharacteristic
133C22×C59#45211yescharacteristic
134C22×C59#45411yescharacteristic
135C22×C59#45411yescharacteristic
136C22×C59#45411yescharacteristic
137C22×C59#45811yescharacteristic
138C4×C59—21no—
139C4×C59—21no—
140C4×C59—21no—
141C4×C59—21no—
142C4×C59—21no—
143C4×C59—21no—
144C4×C59—81no—
145C4×C59—81no—
146C4×C59—161no—
147Dic59—81no—
148Dic59—81no—
149Dic59—81no—
150Dic59—81no—
151#2810—591no—
152#2100—591no—
153#2100—591no—
154#2100D5911yescharacteristic
155#1271—591no—
156#1271—591no—
157#1271—591no—
158C2×C59#161511yescharacteristic
159C2×C59#161511yescharacteristic
160C2×C59#161511yescharacteristic
161C2×C59#163811yescharacteristic
162C2×C59#163811yescharacteristic
163C2×C59#163811yescharacteristic
164C2×C59#165811yescharacteristic
165#400—1181no—
166#400—1181no—
167#400—1181no—
168#389—591no—
169#389—591no—
170#389C2×D5911yescharacteristic
171#387—1181no—
172#387—1181no—
173#387—1181no—
174#384C2×D5911yescharacteristic
175#340—21no—
176#340—21no—
177#340—1181no—
178#340—1181no—
179#340—1181no—
180#340—1181no—
181#336—591no—
182#336—591no—
183#336C2×D5911yescharacteristic
184C59#783211yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—1181no—
187C22×C8—1181no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—591no—
194C2×C4⋊C4—591no—
195C2×C4⋊C4—591no—
196C2×C4⋊C4—1181no—
197C2×C4⋊C4—1181no—
198C2×C4⋊C4C22⋊D5911yescharacteristic
199C2×C4⋊C4C22⋊D5911yescharacteristic
200C2×C42—1181no—
201C2×C42C22×D5911yescharacteristic
202#95—21no—
203#95—1181no—
204#95—1181no—
205#95—1181no—
206#95—1181no—
207#95—1181no—
208#95—1181no—
209#95—1181no—
210#95—1181no—
211#95—1181no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—1181no—
216C22×C4—1181no—
217C22×C4—1181no—
218C22×C4—1181no—
219C22×C4D4×D5911yescharacteristic
220C22×C4D4×D5911yescharacteristic
221C22×C4C2×C22⋊D5911yescharacteristic
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—2361no—
226C2×C8—2361no—
227C2×C8—2361no—
228C2×C8—2361no—
229C2×C8—2361no—
230C2×C8—2361no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—1181no—
240C4⋊C4—1181no—
241C4⋊C4—1181no—
242C4⋊C4—1181no—
243C4⋊C4—2361no—
244C4⋊C4—2361no—
245C4⋊C4—2361no—
246C4⋊C4—2361no—
247C4⋊C4—2361no—
248C4⋊C4—2361no—
249C42—41no—
250C42—4721no—
251C23#1427369511yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—2361no—
268C2×C4—2361no—
269C2×C4—2361no—
270C2×C4—2361no—
271C2×C4—2361no—
272C2×C4—2361no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4—2361no—
277C2×C4—2361no—
278C2×C4—2361no—
279C2×C4#1427374711yescharacteristic
280C2×C4#1427374811yescharacteristic
281C2×C4#1427375011yescharacteristic
282C2×C4#1427375611yescharacteristic
283C2×C4#1427375811yescharacteristic
284C2×C4#1427375911yescharacteristic
285C8—81no—
286C8—4721no—
287C8—4721no—
288C22#1683756111yescharacteristic
289C22#1683756211yescharacteristic
290C22#1683756311yescharacteristic
291C22#1683757311yescharacteristic
292C22#1683757311yescharacteristic
293C22#1683757411yescharacteristic
294C22#1683759111yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4—4721no—
305C4—4721no—
306C4—4721no—
307C4—4721no—
308C2#2142312411yescharacteristic
309C2#2142312511yescharacteristic
310C2#2142312611yescharacteristic
311C2#2142326511yescharacteristic
312C2#2142326611yescharacteristic
313C2#2142326711yescharacteristic
314C2#2142339711yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2100C2
socle, prime radicalC23×C59#120
hypercenter#2100D59
hypocenterC59#7832
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
184. C59#7832semidirect

Maximal subgroups

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

subgroupindex
#214320872
#214256582
#214219202
#214219192
#214219182
C59×#21002
#783259