Finite Group Databasebeta

← #28477974

Subgroups — #28477974

Order 15104.

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

normal subgroups only

This group has 358 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#21431046C211yesmaximal, characteristic
2#21425658C211yesmaximal, characteristic
3#21425658C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2100C211yesmaximal, characteristic
8C2×#14273717—21no—
9#16837336—21no—
10#16837335—21no—
11#16837333—21no—
12#16837300C2211yescharacteristic
13#16837300C2211yescharacteristic
14#16837297—21no—
15#16837285—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—
29#14273717—42no—
30#14273717—42no—
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×Dic59⋊C4—21no—
40C2×Dic59⋊C4—21no—
41C2×C4×Dic59—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C22×C8×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×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×C59—41no—
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C2×C8×C59—41no—
67C2×C8×C59—41no—
68C2×C8×C59—41no—
69C4⋊C4×C59—21no—
70C4⋊C4×C59—21no—
71C4⋊C4×C59—41no—
72C4⋊C4×C59—42no—
73C4⋊C4×C59—42no—
74C4⋊C4×C59—42no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C42×C59—41no—
78C4⋊Dic59—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59—41no—
81C4⋊Dic59—41no—
82C4⋊Dic59SD1612yes—
83C4⋊Dic59Q1612yes—
84Dic59⋊C4—42no—
85Dic59⋊C4—42no—
86Dic59⋊C4—42no—
87Dic59⋊C4—41no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90Dic59⋊C4—41no—
91Dic59⋊C4—81no—
92C4×Dic59—42no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59#12011yescharacteristic
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—81no—
113C2×C4×C59—81no—
114C2×C4×C59—81no—
115C2×C4×C59C2×SD1611yescharacteristic
116C2×C4×C59C2×Q1611yescharacteristic
117C2×C4×C59#13511yescharacteristic
118C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C59#13711yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×Dic59—22no—
122C2×Dic59—22no—
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—41no—
133C8×C59—81no—
134C59⋊C8—81no—
135C59⋊C8—81no—
136#7827—591nomaximal, Sylow
137C22×C59#45011yescharacteristic
138C22×C59#45111yescharacteristic
139C22×C59#45211yescharacteristic
140C22×C59#45411yescharacteristic
141C22×C59#45411yescharacteristic
142C22×C59#45411yescharacteristic
143C22×C59#45811yescharacteristic
144C4×C59—21no—
145C4×C59—21no—
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—81no—
151C4×C59—81no—
152C4×C59—161no—
153Dic59—42no—
154Dic59—42no—
155Dic59—81no—
156Dic59—81no—
157#2726—591no—
158#2100—591no—
159#2100—591no—
160#2100D5911yescharacteristic
161#1271—591no—
162#1271—591no—
163#1271—591no—
164C2×C59#161511yescharacteristic
165C2×C59#161611yescharacteristic
166C2×C59#161711yescharacteristic
167C2×C59#163511yescharacteristic
168C2×C59#163611yescharacteristic
169C2×C59#163711yescharacteristic
170C2×C59#165811yescharacteristic
171C2×#125—1181no—
172#398—1181no—
173#398—1181no—
174#398—1181no—
175#389—591no—
176#389—591no—
177#389—1181no—
178#389C2×D5911yescharacteristic
179#387—1181no—
180#384C2×D5911yescharacteristic
181#340—21no—
182#340—21no—
183#340—1181no—
184#340—1181no—
185#340—1181no—
186#340—1181no—
187#336—591no—
188#336—591no—
189#336C2×D5911yescharacteristic
190C59#782711yescharacteristic, complemented, Sylow
191C22×C8—21no—
192C22×C8—1181no—
193C22×C8—1181no—
194#125—2362no—
195#125—2362no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—591no—
201C2×C4⋊C4—591no—
202C2×C4⋊C4—591no—
203C2×C4⋊C4—591no—
204C2×C4⋊C4—1181no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4C22⋊D5911yescharacteristic
211C2×C4⋊C4C22⋊D5911yescharacteristic
212C2×C42—1181no—
213C2×C42C22×D5911yescharacteristic
214#95—21no—
215#95—1181no—
216#95—1181no—
217#95—1181no—
218#95—1181no—
219#95—1181no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—1181no—
224C22×C4—1181no—
225C22×C4—1181no—
226C22×C4—1181no—
227C22×C4D4×D5911yescharacteristic
228C22×C4D4×D5911yescharacteristic
229C22×C4C2×C22⋊D5911yescharacteristic
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—2361no—
234C2×C8—2361no—
235C2×C8—2361no—
236C2×C8—2361no—
237C2×C8—2361no—
238C2×C8—2361no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—592no—
248C4⋊C4—592no—
249C4⋊C4—1181no—
250C4⋊C4—1181no—
251C4⋊C4—4721no—
252C4⋊C4—2361no—
253C4⋊C4—2361no—
254C4⋊C4—2362no—
255C4⋊C4—2362no—
256C4⋊C4—2362no—
257C4⋊C4—2361no—
258C4⋊C4—2361no—
259C4⋊C4—2361no—
260C4⋊C4—2361no—
261C42—41no—
262C42—2362no—
263C23#1427369511yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—1182no—
280C2×C4—1182no—
281C2×C4—2361no—
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×C4SD16×D5911yescharacteristic
292C2×C4Q16×D5911yescharacteristic
293C2×C4#1427374711yescharacteristic
294C2×C4#1427375411yescharacteristic
295C2×C4#1427375811yescharacteristic
296C2×C4#1427375911yescharacteristic
297C8—81no—
298C8—4721no—
299C8—4721no—
300C22#1683755111yescharacteristic
301C22#1683755611yescharacteristic
302C22#1683756211yescharacteristic
303C22#1683757311yescharacteristic
304C22#1683757311yescharacteristic
305C22#1683757411yescharacteristic
306C22#1683759111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—81no—
315C4—161no—
316C4—4721no—
317C4—4721no—
318C4—2362no—
319C4—2362no—
320C2#2142312511yescharacteristic
321C2#2142313111yescharacteristic
322C2#2142313611yescharacteristic
323C2#2142324611yescharacteristic
324C2#2142325211yescharacteristic
325C2#2142325811yescharacteristic
326C2#2142339711yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2100C2
socle, prime radicalC23×C59#120
hypercenter#2100D59
hypocenterC59#7827
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
190. C59#7827semidirect

Maximal subgroups

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

subgroupindex
#214310462
#214256582
#214219202
#214219192
#214219182
C59×#21002
#782759