Finite Group Databasebeta

← #28477821

Subgroups — #28477821

Order 15104.

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

normal subgroups only

This group has 366 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#21425638C211yesmaximal, characteristic
3#21425569C211yesmaximal, characteristic
4#21425567C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273661—21no—
9C2×#14273660—21no—
10C2×#14273659—21no—
11C2×#14273652—21no—
12#16837344—21no—
13#16837333—21no—
14#16837332—21no—
15#16837308C2211yescharacteristic
16#16837306—21no—
17#16837300C2211yescharacteristic
18#16837288—21no—
19#16837283—21no—
20#16837272C2211yescharacteristic
21#16837165—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#14273660—42no—
41#14273659—42no—
42#14273652—42no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×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×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—41no—
68C2×Dic118—21no—
69C2×Dic118—41no—
70C2×Dic118—41no—
71C2×Dic118Q1612yes—
72C2×C8×C59—22no—
73C2×C8×C59—22no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C42×C59—41no—
84C4⋊Dic59—21no—
85C4⋊Dic59—21no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94Dic59⋊C4—41no—
95Dic59⋊C4—41no—
96Dic59⋊C4—81no—
97Dic59⋊C4—81no—
98C4×Dic59—81no—
99C2×C59⋊C8—22no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C23×C59#12011yescharacteristic
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59C2×Q1611yescharacteristic
116C2×C4×C59#13511yescharacteristic
117C2×C4×C59#13511yescharacteristic
118C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×Dic59—22no—
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—41no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C2×Dic59—81no—
136Dic118—42no—
137Dic118—81no—
138C8×C59—42no—
139C8×C59—42no—
140C59⋊C8—42no—
141#7802—591nomaximal, Sylow
142C22×C59#44911yescharacteristic
143C22×C59#44911yescharacteristic
144C22×C59#45111yescharacteristic
145C22×C59#45311yescharacteristic
146C22×C59#45611yescharacteristic
147C22×C59#45611yescharacteristic
148C22×C59#45811yescharacteristic
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—81no—
156C4×C59—81no—
157Dic59—42no—
158Dic59—81no—
159Dic59—81no—
160Dic59—81no—
161Dic59—161no—
162#2809—591no—
163#2096—591no—
164#2083—591no—
165#2083—591no—
166#1272—591no—
167#1271—591no—
168#1271D5911yescharacteristic
169C2×C59#160911yescharacteristic
170C2×C59#160911yescharacteristic
171C2×C59#161411yescharacteristic
172C2×C59#162411yescharacteristic
173C2×C59#164811yescharacteristic
174C2×C59#164811yescharacteristic
175C2×C59#166011yescharacteristic
176C2×#107—1181no—
177C2×#107—1181no—
178C2×#106—1181no—
179C2×#103—1181no—
180#400—1181no—
181#398—1181no—
182#398—1181no—
183#391—591no—
184#391—1181no—
185#389—591no—
186#389C2×D5911yescharacteristic
187#387—1181no—
188#387—1181no—
189#384—591no—
190#340—1181no—
191#340—1181no—
192#336—591no—
193#336C2×D5911yescharacteristic
194#336C2×D5911yescharacteristic
195C59#780211yescharacteristic, complemented, Sylow
196C22×Q8—591no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—1181no—
200C2×C4⋊C4—21no—
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⋊C4D23611yescharacteristic
211C2×C4⋊C4D23611yescharacteristic
212C2×C42—1181no—
213C2×C42C22×D5911yescharacteristic
214#107—2362no—
215#107—2362no—
216#106—2362no—
217#103—2362no—
218#95—21no—
219#95—1181no—
220#95—1181no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227C2×Q8—592no—
228C2×Q8—1181no—
229C2×Q8—2361no—
230C2×Q8—2361no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—1181no—
234C22×C4—1181no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4—2361no—
238C22×C4C2×D23611yescharacteristic
239C22×C4D4×D5911yescharacteristic
240C22×C4D4×D5911yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—1182no—
248C2×C8—2361no—
249C2×C8—2361no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—1181no—
256C4⋊C4—1181no—
257C4⋊C4—4721no—
258C4⋊C4—4721no—
259C4⋊C4—2361no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C4⋊C4—2361no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C42—41no—
270C42—4721no—
271C23#1427369711yescharacteristic
272Q8—4721no—
273Q8—2362no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—1182no—
287C2×C4—4721no—
288C2×C4—4721no—
289C2×C4—4721no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4—2361no—
293C2×C4—2361no—
294C2×C4—2361no—
295C2×C4—2361no—
296C2×C4—2361no—
297C2×C4—2361no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4Q16×D5911yescharacteristic
302C2×C4#1427374811yescharacteristic
303C2×C4#1427374911yescharacteristic
304C2×C4#1427375111yescharacteristic
305C2×C4#1427375511yescharacteristic
306C2×C4#1427375611yescharacteristic
307C8—42no—
308C8—42no—
309C8—2362no—
310C22#1683754811yescharacteristic
311C22#1683754911yescharacteristic
312C22#1683755911yescharacteristic
313C22#1683757111yescharacteristic
314C22#1683758611yescharacteristic
315C22#1683758711yescharacteristic
316C22#1683759311yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—9441no—
326C4—4721no—
327C4—4721no—
328C4—4721no—
329C4—2362no—
330C2#2142309411yescharacteristic
331C2#2142309511yescharacteristic
332C2#2142312211yescharacteristic
333C2#2142318111yescharacteristic
334C2#2142333911yescharacteristic
335C2#2142334011yescharacteristic
336C2#2142340911yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59#120
hypercenter#1271D59
hypocenterC59#7802
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
195. C59#7802semidirect

Maximal subgroups

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

subgroupindex
#214320812
#214256382
#214255692
#214255672
#214219212
#214219182
C59×#12712
#780259