Finite Group Databasebeta

← #28477988

Subgroups — #28477988

Order 15104.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#21431127C211yesmaximal, characteristic
2#21425658C211yesmaximal, characteristic
3#21425635C211yesmaximal, characteristic
4#21421921C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2100C211yesmaximal, characteristic
8C2×#14273726—21no—
9C2×#14273660—21no—
10C2×#14273650—21no—
11#16837335—21no—
12#16837323—21no—
13#16837322—21no—
14#16837308C2211yescharacteristic
15#16837300C2211yescharacteristic
16#16837288—21no—
17#16837285—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C59×#389C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C59×#340—21no—
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×Dic118—21no—
28C22×Dic118D411yescharacteristic
29C22×C59⋊C8—21no—
30C22×C59⋊C8—21no—
31#14273726—42no—
32#14273726—42no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×C4×Dic59—21no—
41#14273660—42no—
42#14273650—42no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C22×C8×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—41no—
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C2×Dic118—21no—
69C2×Dic118—41no—
70C2×Dic118—41no—
71C2×Dic118—42no—
72C2×Dic118—81no—
73C2×Dic118—81no—
74C2×Dic118SD1612yes—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—42no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59Q1612yes—
87C42×C59—41no—
88C4⋊Dic59—21no—
89C4⋊Dic59—42no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59Q1612yes—
93Dic59⋊C4—42no—
94Dic59⋊C4—41no—
95Dic59⋊C4—41no—
96Dic59⋊C4—81no—
97C4×Dic59—42no—
98C2×C59⋊C8—22no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C23×C59#12011yescharacteristic
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—22no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—81no—
118C2×C4×C59—81no—
119C2×C4×C59—81no—
120C2×C4×C59C2×SD1611yescharacteristic
121C2×C4×C59C2×Q1611yescharacteristic
122C2×C4×C59C2×Q1611yescharacteristic
123C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×C4×C59#13711yescharacteristic
126C2×Dic59—22no—
127C2×Dic59—22no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138Dic118—42no—
139Dic118—81no—
140Dic118—84no—
141C8×C59—81no—
142C59⋊C8—42no—
143C59⋊C8—81no—
144#7829—591nomaximal, Sylow
145C22×C59#45011yescharacteristic
146C22×C59#45111yescharacteristic
147C22×C59#45111yescharacteristic
148C22×C59#45311yescharacteristic
149C22×C59#45411yescharacteristic
150C22×C59#45411yescharacteristic
151C22×C59#45811yescharacteristic
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—42no—
159C4×C59—81no—
160C4×C59—161no—
161Dic59—42no—
162Dic59—42no—
163Dic59—81no—
164Dic59—81no—
165#2734—591no—
166#2100—591no—
167#2100D5911yescharacteristic
168#2095—591no—
169#1272—591no—
170#1271—591no—
171#1271—591no—
172C2×C59#161311yescharacteristic
173C2×C59#161711yescharacteristic
174C2×C59#161711yescharacteristic
175C2×C59#163311yescharacteristic
176C2×C59#163711yescharacteristic
177C2×C59#163711yescharacteristic
178C2×C59#165711yescharacteristic
179C2×C4⋊Q8—1181no—
180C2×#107—1181no—
181C2×#103—1181no—
182#398—1181no—
183#395—1181no—
184#395—1181no—
185#391—591no—
186#389—591no—
187#389C2×D5911yescharacteristic
188#387—1181no—
189#387—1181no—
190#384C2×D5911yescharacteristic
191#340—21no—
192#340—21no—
193#340—1181no—
194#340—1181no—
195#336—591no—
196#336—591no—
197#336C2×D5911yescharacteristic
198C59#782911yescharacteristic, complemented, Sylow
199C22×Q8—591no—
200C22×Q8—1181no—
201C22×C8—21no—
202C22×C8—1181no—
203C22×C8—1181no—
204C4⋊Q8—2362no—
205C4⋊Q8—2362no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4—1181no—
217C2×C4⋊C4C22⋊D5911yescharacteristic
218C2×C4⋊C4C22⋊D5911yescharacteristic
219C2×C42—1181no—
220C2×C42C22×D5911yescharacteristic
221#107—2362no—
222#103—2362no—
223#95—21no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230C2×Q8—592no—
231C2×Q8—1181no—
232C2×Q8—4721no—
233C2×Q8—4721no—
234C2×Q8—2361no—
235C2×Q8—2361no—
236C2×Q8—2362no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—1181no—
241C22×C4—1181no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4D4×D5911yescharacteristic
245C22×C4D4×D5911yescharacteristic
246C22×C4C2×C22⋊D5911yescharacteristic
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—1182no—
251C2×C8—2361no—
252C2×C8—2361no—
253C2×C8—2361no—
254C2×C8—2361no—
255C2×C8—2361no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—592no—
265C4⋊C4—1181no—
266C4⋊C4—4721no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C4⋊C4—2362no—
270C4⋊C4—2362no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4#1174567212yes—
274C42—41no—
275C42—2362no—
276C23#1427369511yescharacteristic
277Q8—4721no—
278Q8—4724no—
279Q8—2362no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—1182no—
296C2×C4—1182no—
297C2×C4—2361no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4SD16×D5911yescharacteristic
308C2×C4Q16×D5911yescharacteristic
309C2×C4C2×#1174567211yescharacteristic
310C2×C4#1427375411yescharacteristic
311C2×C4#1427375711yescharacteristic
312C2×C4#1427375911yescharacteristic
313C8—81no—
314C8—4721no—
315C8—2362no—
316C22#1683755111yescharacteristic
317C22#1683755611yescharacteristic
318C22#1683755711yescharacteristic
319C22#1683756811yescharacteristic
320C22#1683757311yescharacteristic
321C22#1683757411yescharacteristic
322C22#1683759111yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—161no—
332C4—4721no—
333C4—4721no—
334C4—2362no—
335C4—2362no—
336C2#2142311411yescharacteristic
337C2#2142313611yescharacteristic
338C2#2142313711yescharacteristic
339C2#2142323511yescharacteristic
340C2#2142325811yescharacteristic
341C2#2142326011yescharacteristic
342C2#2142339311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2100C2
socle, prime radicalC23×C59#120
hypercenter#2100D59
hypocenterC59#7829
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
198. C59#7829semidirect

Maximal subgroups

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

subgroupindex
#214311272
#214256582
#214256352
#214219212
#214219192
#214219182
C59×#21002
#782959