Finite Group Databasebeta

← #28477927

Subgroups — #28477927

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#21432051C211yesmaximal, characteristic
2#21425655C211yesmaximal, characteristic
3#21425574C211yesmaximal, characteristic
4#21425504C211yesmaximal, characteristic
5#21421920C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1272C211yesmaximal, characteristic
8C2×#14273659—21no—
9C2×#14273651—21no—
10#16837344—21no—
11#16837342—21no—
12#16837321—21no—
13#16837300C2211yescharacteristic
14#16837300C2211yescharacteristic
15#16837299—21no—
16#16837285—21no—
17#16837283—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837165—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#391C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×C4×Dic59—21no—
40#14273659—42no—
41#14273651—42no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C22×Q8×C59D411yescharacteristic
50C22×C8×C59—21no—
51C22×C8×C59—21no—
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C42×C59C2311yescharacteristic
54#95×C59—21no—
55#95×C59—21no—
56C2×Q8×C59—21no—
57C2×Q8×C59—21no—
58C2×Q8×C59—41no—
59C2×Q8×C59—41no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—41no—
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—41no—
77C42×C59—41no—
78C4⋊Dic59—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59—21no—
81C4⋊Dic59—41no—
82C4⋊Dic59—41no—
83C4⋊Dic59—42no—
84C4⋊Dic59—41no—
85C4⋊Dic59—41no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59SD1612yes—
89Dic59⋊C4—41no—
90Dic59⋊C4—41no—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93Dic59⋊C4—81no—
94Dic59⋊C4—81no—
95C4×Dic59—81no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59#12011yescharacteristic
100Q8×C59—42no—
101Q8×C59—81no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59C2×SD1611yescharacteristic
115C2×C4×C59#13511yescharacteristic
116C2×C4×C59#13511yescharacteristic
117C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C59#13711yescharacteristic
119C2×C4×C59#13711yescharacteristic
120C2×Dic59—22no—
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—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—81no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C8×C59—42no—
136C8×C59—81no—
137C59⋊C8—81no—
138#7818—591nomaximal, Sylow
139C22×C59#44811yescharacteristic
140C22×C59#44911yescharacteristic
141C22×C59#45211yescharacteristic
142C22×C59#45411yescharacteristic
143C22×C59#45511yescharacteristic
144C22×C59#45611yescharacteristic
145C22×C59#45811yescharacteristic
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—81no—
153C4×C59—81no—
154Dic59—42no—
155Dic59—81no—
156Dic59—81no—
157Dic59—81no—
158Dic59—161no—
159#2805—591no—
160#2099—591no—
161#2084—591no—
162#2072—591no—
163#1272D5911yescharacteristic
164#1271—591no—
165#1271—591no—
166C2×C59#161111yescharacteristic
167C2×C59#161211yescharacteristic
168C2×C59#161511yescharacteristic
169C2×C59#162611yescharacteristic
170C2×C59#164311yescharacteristic
171C2×C59#165211yescharacteristic
172C2×C59#166411yescharacteristic
173C2×#106—1181no—
174C2×#103—1181no—
175#400—1181no—
176#400—1181no—
177#395—1181no—
178#391C2×D5911yescharacteristic
179#389—591no—
180#389—591no—
181#389—1181no—
182#387—1181no—
183#387—1181no—
184#384—591no—
185#340—1181no—
186#340—1181no—
187#340—1181no—
188#340—1181no—
189#336—591no—
190#336C2×D5911yescharacteristic
191#336C2×D5911yescharacteristic
192C59#781811yescharacteristic, complemented, Sylow
193C22×Q8D23611yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—1181no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—591no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1181no—
204C2×C4⋊C4—1181no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4D23611yescharacteristic
209C2×C42—1181no—
210C2×C42C22×D5911yescharacteristic
211#106—2362no—
212#103—2362no—
213#95—21no—
214#95—21no—
215#95—1181no—
216#95—1181no—
217#95—1181no—
218#95—1181no—
219#95—1181no—
220#95—1181no—
221#95—1181no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—1181no—
229C22×C4—1181no—
230C22×C4—1181no—
231C22×C4—1181no—
232C22×C4—2361no—
233C22×C4C2×D23611yescharacteristic
234C22×C4D4×D5911yescharacteristic
235C22×C4D4×D5911yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2361no—
243C2×C8—2361no—
244C2×C8—2361no—
245C4⋊C4—41no—
246C4⋊C4—592no—
247C4⋊C4—1181no—
248C4⋊C4—1181no—
249C4⋊C4—1181no—
250C4⋊C4—4721no—
251C4⋊C4—4721no—
252C4⋊C4—2362no—
253C4⋊C4—2361no—
254C4⋊C4—2361no—
255C4⋊C4—2361no—
256C4⋊C4—2361no—
257C4⋊C4—2361no—
258C4⋊C4—2361no—
259C4⋊C4—2361no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C42—41no—
264C42—4721no—
265C23#1427369711yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—1182no—
281C2×C4—4721no—
282C2×C4—4721no—
283C2×C4—4721no—
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×C4—2361no—
294C2×C4—2361no—
295C2×C4SD16×D5911yescharacteristic
296C2×C4#1427374811yescharacteristic
297C2×C4#1427374911yescharacteristic
298C2×C4#1427375511yescharacteristic
299C2×C4#1427375911yescharacteristic
300C2×C4#1427375911yescharacteristic
301C8—42no—
302C8—81no—
303C8—4721no—
304C22#1683754211yescharacteristic
305C22#1683754911yescharacteristic
306C22#1683756711yescharacteristic
307C22#1683757611yescharacteristic
308C22#1683758211yescharacteristic
309C22#1683758611yescharacteristic
310C22#1683759311yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—9441no—
320C4—4721no—
321C4—4721no—
322C4—4721no—
323C4—2362no—
324C2#2142310511yescharacteristic
325C2#2142311211yescharacteristic
326C2#2142313011yescharacteristic
327C2#2142319411yescharacteristic
328C2#2142330411yescharacteristic
329C2#2142336811yescharacteristic
330C2#2142343311yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59#120
hypercenter#1272D59
hypocenterC59#7818
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
192. C59#7818semidirect

Maximal subgroups

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

subgroupindex
#214320512
#214256552
#214255742
#214255042
#214219202
#214219182
C59×#12722
#781859