Finite Group Databasebeta

← #28477917

Subgroups — #28477917

Order 15104.

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

normal subgroups only

This group has 410 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#21425640C211yesmaximal, characteristic
3#21425573C211yesmaximal, characteristic
4#21421921C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2084C211yesmaximal, characteristic
8C2×#14273726—21no—
9C2×#14273658—21no—
10C2×#14273658—21no—
11C2×#14273650—21no—
12#16837335—21no—
13#16837323—21no—
14#16837322—21no—
15#16837308C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837288—21no—
18#16837285—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#106×C59—21no—
23C59×#389C2211yescharacteristic
24C59×#384C2211yescharacteristic
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#14273658—42no—
42#14273658—42no—
43#14273650—42no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C22×C8×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C42×C59C2311yescharacteristic
58#106×C59—42no—
59#95×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—41no—
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C2×Dic118—21no—
71C2×Dic118—41no—
72C2×Dic118—41no—
73C2×Dic118—42no—
74C2×Dic118—81no—
75C2×Dic118—81no—
76C2×Dic118SD1612yes—
77C2×C8×C59—22no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59SD1612yes—
91C42×C59—41no—
92C4⋊Dic59—21no—
93C4⋊Dic59—42no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96C4⋊Dic59SD1612yes—
97Dic59⋊C4—42no—
98Dic59⋊C4—41no—
99Dic59⋊C4—41no—
100Dic59⋊C4—81no—
101C4×Dic59—42no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—22no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C23×C59#12011yescharacteristic
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—22no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—81no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59C2×SD1611yescharacteristic
125C2×C4×C59C2×SD1611yescharacteristic
126C2×C4×C59C2×SD1611yescharacteristic
127C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C59#13711yescharacteristic
129C2×C4×C59#13711yescharacteristic
130C2×Dic59—22no—
131C2×Dic59—22no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142Dic118—42no—
143Dic118—81no—
144Dic118—84no—
145C8×C59—42no—
146C59⋊C8—42no—
147C59⋊C8—42no—
148#7817—591nomaximal, Sylow
149C22×C59#44811yescharacteristic
150C22×C59#44811yescharacteristic
151C22×C59#45011yescharacteristic
152C22×C59#45311yescharacteristic
153C22×C59#45611yescharacteristic
154C22×C59#45611yescharacteristic
155C22×C59#45811yescharacteristic
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—42no—
163C4×C59—81no—
164C4×C59—161no—
165Dic59—42no—
166Dic59—42no—
167Dic59—81no—
168Dic59—81no—
169#2734—591no—
170#2096—591no—
171#2084—591no—
172#2084D5911yescharacteristic
173#1272—591no—
174#1271—591no—
175#1271—591no—
176C2×C59#161111yescharacteristic
177C2×C59#161111yescharacteristic
178C2×C59#161311yescharacteristic
179C2×C59#162311yescharacteristic
180C2×C59#165111yescharacteristic
181C2×C59#165111yescharacteristic
182C2×C59#166011yescharacteristic
183C2×C4⋊Q8—1181no—
184C2×#106—21no—
185C2×#106—1181no—
186C2×#106—1181no—
187C2×#103—1181no—
188#398—1181no—
189#395—1181no—
190#395—1181no—
191#391—591no—
192#389—591no—
193#389C2×D5911yescharacteristic
194#387—1181no—
195#387—1181no—
196#384C2×D5911yescharacteristic
197#340—21no—
198#340—1181no—
199#336—591no—
200#336—591no—
201#336C2×D5911yescharacteristic
202C59#781711yescharacteristic, complemented, Sylow
203C22×Q8—591no—
204C22×Q8—1181no—
205C22×C8—21no—
206C22×C8—1181no—
207C22×C8—1181no—
208C4⋊Q8—2362no—
209C4⋊Q8—2362no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—591no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4—591no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C4⋊C4—1181no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4C22⋊D5911yescharacteristic
222C2×C4⋊C4C22⋊D5911yescharacteristic
223C2×C42—1181no—
224C2×C42C22×D5911yescharacteristic
225#106—42no—
226#106—2362no—
227#106—2362no—
228#103—2362no—
229#95—21no—
230#95—1181no—
231#95—1181no—
232#95—1181no—
233#95—1181no—
234#95—1181no—
235#95—1181no—
236C2×Q8—592no—
237C2×Q8—1181no—
238C2×Q8—4721no—
239C2×Q8—4721no—
240C2×Q8—2361no—
241C2×Q8—2361no—
242C2×Q8—2362no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4D4×D5911yescharacteristic
251C22×C4D4×D5911yescharacteristic
252C22×C4C2×C22⋊D5911yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—1182no—
257C2×C8—1182no—
258C2×C8—2361no—
259C2×C8—2361no—
260C2×C8—2361no—
261C2×C8—2361no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—592no—
273C4⋊C4—1181no—
274C4⋊C4—4721no—
275C4⋊C4—2361no—
276C4⋊C4—2361no—
277C4⋊C4—2362no—
278C4⋊C4—2362no—
279C4⋊C4—2361no—
280C4⋊C4—2361no—
281C4⋊C4#1174567012yes—
282C42—41no—
283C42—2362no—
284C23#1427369511yescharacteristic
285Q8—4721no—
286Q8—4724no—
287Q8—2362no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—1182no—
304C2×C4—1182no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4SD16×D5911yescharacteristic
316C2×C4SD16×D5911yescharacteristic
317C2×C4C2×#1174567011yescharacteristic
318C2×C4#1427375411yescharacteristic
319C2×C4#1427375611yescharacteristic
320C2×C4#1427375711yescharacteristic
321C8—42no—
322C8—2362no—
323C8—2362no—
324C22#1683753911yescharacteristic
325C22#1683754011yescharacteristic
326C22#1683755111yescharacteristic
327C22#1683756811yescharacteristic
328C22#1683758311yescharacteristic
329C22#1683758411yescharacteristic
330C22#1683759111yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—161no—
340C4—4721no—
341C4—4721no—
342C4—2362no—
343C4—2362no—
344C2#2142310211yescharacteristic
345C2#2142310311yescharacteristic
346C2#2142311411yescharacteristic
347C2#2142317311yescharacteristic
348C2#2142335611yescharacteristic
349C2#2142335711yescharacteristic
350C2#2142340611yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2084C2
socle, prime radicalC23×C59#120
hypercenter#2084D59
hypocenterC59#7817
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
202. C59#7817semidirect

Maximal subgroups

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

subgroupindex
#214311272
#214256402
#214255732
#214219212
#214219192
#214219182
C59×#20842
#781759