Finite Group Databasebeta

← #28478000

Subgroups — #28478000

Order 15104.

350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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#21432081C211yesmaximal, characteristic
2#21425660C211yesmaximal, characteristic
3#21425659C211yesmaximal, characteristic
4#21425633C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273661—21no—
9C2×#14273652—21no—
10#16837344—21no—
11#16837333—21no—
12#16837332—21no—
13#16837308C2211yescharacteristic
14#16837306—21no—
15#16837300C2211yescharacteristic
16#16837288—21no—
17#16837283—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837164—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×Dic118D411yescharacteristic
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×C4×Dic59—21no—
39#14273661—42no—
40#14273652—42no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C22×C8×C59—21no—
50C22×C8×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C4⋊C4×C59D411yescharacteristic
54C2×C42×C59C2311yescharacteristic
55#95×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×Dic59—21no—
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—41no—
66C2×Dic118—21no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C2×Dic118Q1612yes—
70C2×C8×C59—22no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C42×C59—41no—
82C4⋊Dic59—21no—
83C4⋊Dic59—21no—
84C4⋊Dic59—41no—
85C4⋊Dic59—41no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59—42no—
89C4⋊Dic59—42no—
90Dic59⋊C4—41no—
91Dic59⋊C4—41no—
92Dic59⋊C4—81no—
93Dic59⋊C4—81no—
94C4×Dic59—81no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C23×C59#12011yescharacteristic
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59C2×Q1611yescharacteristic
112C2×C4×C59#13511yescharacteristic
113C2×C4×C59#13511yescharacteristic
114C2×C4×C59#13711yescharacteristic
115C2×C4×C59#13711yescharacteristic
116C2×C4×C59#13711yescharacteristic
117C2×Dic59—22no—
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—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—81no—
130C2×Dic59—81no—
131C2×Dic59—81no—
132Dic118—42no—
133Dic118—81no—
134C8×C59—42no—
135C8×C59—81no—
136C59⋊C8—81no—
137#7831—591nomaximal, Sylow
138C22×C59#45111yescharacteristic
139C22×C59#45211yescharacteristic
140C22×C59#45211yescharacteristic
141C22×C59#45311yescharacteristic
142C22×C59#45411yescharacteristic
143C22×C59#45411yescharacteristic
144C22×C59#45811yescharacteristic
145C4×C59—21no—
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—81no—
152C4×C59—81no—
153Dic59—42no—
154Dic59—81no—
155Dic59—81no—
156Dic59—81no—
157Dic59—161no—
158#2809—591no—
159#2100—591no—
160#2100—591no—
161#2095—591no—
162#1272—591no—
163#1271—591no—
164#1271D5911yescharacteristic
165C2×C59#161411yescharacteristic
166C2×C59#161511yescharacteristic
167C2×C59#161511yescharacteristic
168C2×C59#163411yescharacteristic
169C2×C59#163611yescharacteristic
170C2×C59#163611yescharacteristic
171C2×C59#165711yescharacteristic
172C2×#107—1181no—
173C2×#103—1181no—
174#400—1181no—
175#398—1181no—
176#398—1181no—
177#391—591no—
178#391—1181no—
179#389—591no—
180#389C2×D5911yescharacteristic
181#387—1181no—
182#387—1181no—
183#384—591no—
184#340—1181no—
185#340—1181no—
186#340—1181no—
187#340—1181no—
188#336—591no—
189#336C2×D5911yescharacteristic
190#336C2×D5911yescharacteristic
191C59#783111yescharacteristic, complemented, Sylow
192C22×Q8—591no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—1181no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1181no—
204C2×C4⋊C4—1181no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4D23611yescharacteristic
207C2×C4⋊C4D23611yescharacteristic
208C2×C42—1181no—
209C2×C42C22×D5911yescharacteristic
210#107—2362no—
211#103—2362no—
212#95—21no—
213#95—1181no—
214#95—1181no—
215#95—1181no—
216#95—1181no—
217#95—1181no—
218#95—1181no—
219#95—1181no—
220#95—1181no—
221C2×Q8—592no—
222C2×Q8—1181no—
223C2×Q8—2361no—
224C2×Q8—2361no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—1181no—
228C22×C4—1181no—
229C22×C4—1181no—
230C22×C4—1181no—
231C22×C4—2361no—
232C22×C4C2×D23611yescharacteristic
233C22×C4D4×D5911yescharacteristic
234C22×C4D4×D5911yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8—2361no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—1181no—
250C4⋊C4—1181no—
251C4⋊C4—4721no—
252C4⋊C4—4721no—
253C4⋊C4—2361no—
254C4⋊C4—2361no—
255C4⋊C4—2362no—
256C4⋊C4—2362no—
257C4⋊C4—2361no—
258C4⋊C4—2361no—
259C4⋊C4—2361no—
260C4⋊C4—2361no—
261C42—41no—
262C42—4721no—
263C23#1427369711yescharacteristic
264Q8—4721no—
265Q8—2362no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—1182no—
279C2×C4—4721no—
280C2×C4—4721no—
281C2×C4—4721no—
282C2×C4—2361no—
283C2×C4—2361no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2361no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4—2361no—
293C2×C4Q16×D5911yescharacteristic
294C2×C4#1427374611yescharacteristic
295C2×C4#1427374911yescharacteristic
296C2×C4#1427375611yescharacteristic
297C2×C4#1427375611yescharacteristic
298C2×C4#1427376011yescharacteristic
299C8—42no—
300C8—81no—
301C8—4721no—
302C22#1683755911yescharacteristic
303C22#1683756511yescharacteristic
304C22#1683756611yescharacteristic
305C22#1683757111yescharacteristic
306C22#1683757611yescharacteristic
307C22#1683757711yescharacteristic
308C22#1683759311yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—9441no—
318C4—4721no—
319C4—4721no—
320C4—4721no—
321C4—2362no—
322C2#2142312211yescharacteristic
323C2#2142312811yescharacteristic
324C2#2142312911yescharacteristic
325C2#2142324311yescharacteristic
326C2#2142325511yescharacteristic
327C2#2142325611yescharacteristic
328C2#2142339611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59#120
hypercenter#1271D59
hypocenterC59#7831
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
191. C59#7831semidirect

Maximal subgroups

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

subgroupindex
#214320812
#214256602
#214256592
#214256332
#214219212
#214219182
C59×#12712
#783159