Finite Group Databasebeta

← #28477751

Subgroups — #28477751

Order 15104.

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

normal subgroups only

This group has 374 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#21425653C211yesmaximal, characteristic
3#21425568C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2083C211yesmaximal, characteristic
8C2×#14273717—21no—
9C2×#14273660—21no—
10#16837336—21no—
11#16837335—21no—
12#16837333—21no—
13#16837300C2211yescharacteristic
14#16837300C2211yescharacteristic
15#16837297—21no—
16#16837285—21no—
17#16837164—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#107×C59—21no—
23C59×#389C2211yescharacteristic
24C59×#384C2211yescharacteristic
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—
42#14273660—42no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C22×C8×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59D411yescharacteristic
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#107×C59—42no—
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×C8×C59—22no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C4⋊C4×C59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—42no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
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⋊Dic59D812yes—
87C4⋊Dic59Q1612yes—
88Dic59⋊C4—42no—
89Dic59⋊C4—42no—
90Dic59⋊C4—42no—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93Dic59⋊C4—41no—
94Dic59⋊C4—41no—
95Dic59⋊C4—81no—
96C4×Dic59—42no—
97C2×C59⋊C8—22no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C23×C59#12011yescharacteristic
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—81no—
117C2×C4×C59—81no—
118C2×C4×C59—81no—
119C2×C4×C59C2×D811yescharacteristic
120C2×C4×C59C2×Q1611yescharacteristic
121C2×C4×C59#13511yescharacteristic
122C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×Dic59—22no—
126C2×Dic59—22no—
127C2×Dic59—41no—
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—
137C8×C59—42no—
138C59⋊C8—42no—
139C59⋊C8—81no—
140#7792—591nomaximal, Sylow
141C22×C59#44711yescharacteristic
142C22×C59#44911yescharacteristic
143C22×C59#45111yescharacteristic
144C22×C59#45411yescharacteristic
145C22×C59#45611yescharacteristic
146C22×C59#45611yescharacteristic
147C22×C59#45811yescharacteristic
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—81no—
155C4×C59—81no—
156C4×C59—161no—
157Dic59—42no—
158Dic59—42no—
159Dic59—81no—
160Dic59—81no—
161#2726—591no—
162#2099—591no—
163#2083—591no—
164#2083D5911yescharacteristic
165#1271—591no—
166#1271—591no—
167#1271—591no—
168C2×C59#160911yescharacteristic
169C2×C59#161011yescharacteristic
170C2×C59#161711yescharacteristic
171C2×C59#162511yescharacteristic
172C2×C59#164811yescharacteristic
173C2×C59#164911yescharacteristic
174C2×C59#166311yescharacteristic
175C2×#125—1181no—
176C2×#107—21no—
177C2×#107—1181no—
178#398—1181no—
179#398—1181no—
180#398—1181no—
181#389—591no—
182#389—591no—
183#389—1181no—
184#389C2×D5911yescharacteristic
185#387—1181no—
186#384C2×D5911yescharacteristic
187#340—21no—
188#340—1181no—
189#340—1181no—
190#340—1181no—
191#336—591no—
192#336—591no—
193#336C2×D5911yescharacteristic
194C59#779211yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—1181no—
197C22×C8—1181no—
198#125—2362no—
199#125—2362no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—591no—
205C2×C4⋊C4—591no—
206C2×C4⋊C4—591no—
207C2×C4⋊C4—591no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4—1181no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4C22⋊D5911yescharacteristic
215C2×C4⋊C4C22⋊D5911yescharacteristic
216C2×C42—1181no—
217C2×C42C22×D5911yescharacteristic
218#107—42no—
219#107—2362no—
220#95—21no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—1181no—
230C22×C4—1181no—
231C22×C4—1181no—
232C22×C4—1181no—
233C22×C4D4×D5911yescharacteristic
234C22×C4D4×D5911yescharacteristic
235C22×C4C2×C22⋊D5911yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—1182no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8—2361no—
244C2×C8—2361no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—592no—
256C4⋊C4—592no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C4⋊C4—4721no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2362no—
263C4⋊C4—2362no—
264C4⋊C4—2362no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C42—41no—
270C42—2362no—
271C23#1427369511yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—1182no—
288C2×C4—1182no—
289C2×C4—2361no—
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×C4D8×D5911yescharacteristic
300C2×C4Q16×D5911yescharacteristic
301C2×C4#1427374711yescharacteristic
302C2×C4#1427375111yescharacteristic
303C2×C4#1427375311yescharacteristic
304C2×C4#1427375911yescharacteristic
305C8—42no—
306C8—4721no—
307C8—2362no—
308C22#1683753411yescharacteristic
309C22#1683754511yescharacteristic
310C22#1683755611yescharacteristic
311C22#1683757311yescharacteristic
312C22#1683758311yescharacteristic
313C22#1683758411yescharacteristic
314C22#1683759111yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—81no—
322C4—81no—
323C4—161no—
324C4—4721no—
325C4—4721no—
326C4—2362no—
327C4—2362no—
328C2#2142309111yescharacteristic
329C2#2142309711yescharacteristic
330C2#2142313611yescharacteristic
331C2#2142318411yescharacteristic
332C2#2142333611yescharacteristic
333C2#2142334211yescharacteristic
334C2#2142342311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2083C2
socle, prime radicalC23×C59#120
hypercenter#2083D59
hypocenterC59#7792
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
194. C59#7792semidirect

Maximal subgroups

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

subgroupindex
#214310462
#214256532
#214255682
#214219202
#214219192
#214219182
C59×#20832
#779259