Finite Group Databasebeta

← #28477607

Subgroups — #28477607

Order 15104.

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

normal subgroups only

This group has 392 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#21432084C211yesmaximal, characteristic
2#21425421C211yesmaximal, characteristic
3#21425339C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421918C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2024C211yesmaximal, characteristic
8C2×#14273660—21no—
9C2×#14273651—21no—
10C2×#14273651—21no—
11#16837341—21no—
12#16837334—21no—
13#16837334—21no—
14#16837309—21no—
15#16837300C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837289—21no—
18#16837289—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×#103×C59—21no—
24C59×#391C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×C4×Dic59—21no—
38#14273660—42no—
39#14273651—42no—
40#14273651—42no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C22×Q8×C59—21no—
49C22×Q8×C59D411yescharacteristic
50C22×C8×C59—21no—
51C4⋊Q8×C59—42no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#103×C59—42no—
57#95×C59—21no—
58#95×C59—21no—
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59—41no—
68C2×Q8×C59Q1612yes—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—41no—
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×Dic59—21no—
76C22×Dic59—21no—
77C22×Dic59—21no—
78C22×Dic59—21no—
79C2×C8×C59—41no—
80C2×C8×C59—41no—
81C2×C8×C59—41no—
82C4⋊C4×C59—22no—
83C4⋊C4×C59—22no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C42×C59—41no—
88C4⋊Dic59—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94C4⋊Dic59—81no—
95C4⋊Dic59—81no—
96Dic59⋊C4—41no—
97Dic59⋊C4—41no—
98Dic59⋊C4—41no—
99Dic59⋊C4—41no—
100C4×Dic59—81no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C23×C59#12011yescharacteristic
108Q8×C59—42no—
109Q8×C59—42no—
110Q8×C59—42no—
111Q8×C59—81no—
112Q8×C59—81no—
113Q8×C59—81no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—22no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—42no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59C2×Q1611yescharacteristic
130C2×C4×C59#13511yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C59#13711yescharacteristic
134C2×C4×C59#13711yescharacteristic
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C8×C59—81no—
148C59⋊C8—42no—
149C59⋊C8—81no—
150#7771—591nomaximal, Sylow
151C22×C59#44911yescharacteristic
152C22×C59#45111yescharacteristic
153C22×C59#45211yescharacteristic
154C22×C59#45411yescharacteristic
155C22×C59#45511yescharacteristic
156C22×C59#45611yescharacteristic
157C22×C59B(4,𝔽2)11yescharacteristic
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—42no—
165C4×C59—82no—
166C4×C59—81no—
167Dic59—81no—
168Dic59—81no—
169Dic59—81no—
170Dic59—81no—
171#2809—591no—
172#2057—591no—
173#2043—591no—
174#2024D5911yescharacteristic
175#1272—591no—
176#1271—591no—
177#1271—591no—
178C2×C59#159711yescharacteristic
179C2×C59#160211yescharacteristic
180C2×C59#160311yescharacteristic
181C2×C59#163611yescharacteristic
182C2×C59#164611yescharacteristic
183C2×C59#164811yescharacteristic
184C2×C59#166411yescharacteristic
185C2×C4⋊Q8C2×D5911yescharacteristic
186C2×#107—1181no—
187C2×#103—21no—
188C2×#103—1181no—
189C2×#103—1181no—
190#400—1181no—
191#398—1181no—
192#398—1181no—
193#391—1181no—
194#391C2×D5911yescharacteristic
195#389—591no—
196#389—591no—
197#387—1181no—
198#387—1181no—
199#340—21no—
200#340—1181no—
201#336—591no—
202#336—591no—
203#336C2×D5911yescharacteristic
204C59#777111yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×Q8C22⋊D5911yescharacteristic
207C22×C8—21no—
208C22×C8—1181no—
209C22×C8—1181no—
210C4⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—591no—
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×C42—1181no—
223C2×C42C22×D5911yescharacteristic
224#107—2362no—
225#103—42no—
226#103—2362no—
227#103—2362no—
228#95—21no—
229#95—21no—
230#95—1181no—
231#95—1181no—
232#95—1181no—
233#95—1181no—
234#95—1181no—
235#95—1181no—
236#95—1181no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8#1174567212yes—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4D4×D5911yescharacteristic
255C22×C4D4×D5911yescharacteristic
256C22×C4C2×C22⋊D5911yescharacteristic
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1182no—
261C2×C8—2361no—
262C2×C8—2361no—
263C2×C8—2361no—
264C2×C8—2361no—
265C2×C8—2361no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—4721no—
276C4⋊C4—4721no—
277C4⋊C4—2361no—
278C4⋊C4—2361no—
279C4⋊C4—2361no—
280C4⋊C4—2361no—
281C4⋊C4—2361no—
282C4⋊C4—2361no—
283C42—41no—
284C42—4721no—
285C23#1427369511yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—81no—
306C2×C4—81no—
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×C4—2361no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4C2×#1174567211yescharacteristic
320C2×C4#1427374811yescharacteristic
321C2×C4#1427375011yescharacteristic
322C2×C4#1427375411yescharacteristic
323C2×C4#1427375711yescharacteristic
324C2×C4#1427375911yescharacteristic
325C8—81no—
326C8—4721no—
327C8—2362no—
328C22#1683754611yescharacteristic
329C22#1683755711yescharacteristic
330C22#1683756311yescharacteristic
331C22#1683757311yescharacteristic
332C22#1683757911yescharacteristic
333C22#1683758311yescharacteristic
334C22#1683758811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—82no—
344C4—4721no—
345C4—4721no—
346C4—4721no—
347C4—4721no—
348C2#2142302411yescharacteristic
349C2#2142305211yescharacteristic
350C2#2142305811yescharacteristic
351C2#2142325311yescharacteristic
352C2#2142332111yescharacteristic
353C2#2142333711yescharacteristic
354C2#2142342911yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2024C2
socle, prime radicalC23×C59#120
hypercenter#2024D59
hypocenterC59#7771
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
204. C59#7771semidirect

Maximal subgroups

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

subgroupindex
#214320842
#214254212
#214253392
#214219222
#214219182
C59×#20242
#777159