Finite Group Databasebeta

← #28477897

Subgroups — #28477897

Order 15104.

378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 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#21432060C211yesmaximal, characteristic
2#21425640C211yesmaximal, characteristic
3#21425573C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2072C211yesmaximal, characteristic
8C2×#14273658—21no—
9C2×#14273658—21no—
10C2×#14273650—21no—
11#16837335—21no—
12#16837334—21no—
13#16837323—21no—
14#16837309—21no—
15#16837308C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837299—21no—
18#16837285—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#103×C59—21no—
23C59×#391C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×Dic118D411yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—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#14273658—42no—
40#14273658—42no—
41#14273650—42no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C22×Q8×C59D411yescharacteristic
49C22×C8×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59D411yescharacteristic
54C2×C42×C59C2311yescharacteristic
55#103×C59—42no—
56#95×C59—21no—
57#95×C59—21no—
58C2×Q8×C59—21no—
59C2×Q8×C59—41no—
60C2×Q8×C59—41no—
61C2×Q8×C59SD1612yes—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59—41no—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72C2×Dic118—21no—
73C2×Dic118—21no—
74C2×Dic118—41no—
75C2×Dic118—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C42×C59—41no—
87C4⋊Dic59—21no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—81no—
91C4⋊Dic59—81no—
92C4⋊Dic59SD1612yes—
93Dic59⋊C4—41no—
94Dic59⋊C4—41no—
95Dic59⋊C4—81no—
96Dic59⋊C4—81no—
97C4×Dic59—81no—
98C2×C59⋊C8—22no—
99C2×C59⋊C8—22no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C23×C59#12011yescharacteristic
105Q8×C59—42no—
106Q8×C59—81no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—22no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—81no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59C2×SD1611yescharacteristic
123C2×C4×C59C2×SD1611yescharacteristic
124C2×C4×C59#13511yescharacteristic
125C2×C4×C59#13711yescharacteristic
126C2×C4×C59#13711yescharacteristic
127C2×C4×C59#13711yescharacteristic
128C2×Dic59—22no—
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—
138C2×Dic59—41no—
139C2×Dic59—41no—
140Dic118—42no—
141Dic118—81no—
142C8×C59—81no—
143C59⋊C8—42no—
144C59⋊C8—42no—
145#7814—591nomaximal, Sylow
146C22×C59#44811yescharacteristic
147C22×C59#44811yescharacteristic
148C22×C59#45211yescharacteristic
149C22×C59#45311yescharacteristic
150C22×C59#45511yescharacteristic
151C22×C59#45611yescharacteristic
152C22×C59#45811yescharacteristic
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—42no—
160C4×C59—81no—
161C4×C59—161no—
162Dic59—42no—
163Dic59—81no—
164Dic59—81no—
165Dic59—81no—
166#2806—591no—
167#2096—591no—
168#2084—591no—
169#2072D5911yescharacteristic
170#1272—591no—
171#1272—591no—
172#1271—591no—
173C2×C59#160811yescharacteristic
174C2×C59#161111yescharacteristic
175C2×C59#161811yescharacteristic
176C2×C59#162311yescharacteristic
177C2×C59#164311yescharacteristic
178C2×C59#165311yescharacteristic
179C2×C59#166111yescharacteristic
180C2×#106—1181no—
181C2×#106—1181no—
182C2×#103—21no—
183C2×#103—1181no—
184#398—1181no—
185#398—1181no—
186#395—1181no—
187#391—591no—
188#391—1181no—
189#391C2×D5911yescharacteristic
190#389—591no—
191#389—1181no—
192#387—1181no—
193#384C2×D5911yescharacteristic
194#340—21no—
195#340—1181no—
196#336—591no—
197#336—591no—
198#336C2×D5911yescharacteristic
199C59#781411yescharacteristic, complemented, Sylow
200C22×Q8—591no—
201C22×Q8C22⋊D5911yescharacteristic
202C22×C8—21no—
203C22×C8—1181no—
204C22×C8—1181no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—591no—
209C2×C4⋊C4—591no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4C22⋊D5911yescharacteristic
217C2×C42—1181no—
218C2×C42C22×D5911yescharacteristic
219#106—2362no—
220#106—2362no—
221#103—42no—
222#103—2362no—
223#95—21no—
224#95—21no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230#95—1181no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—1181no—
235C2×Q8—1181no—
236C2×Q8—2361no—
237C2×Q8—2361no—
238C2×Q8#1174567012yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4D4×D5911yescharacteristic
247C22×C4D4×D5911yescharacteristic
248C22×C4C2×C22⋊D5911yescharacteristic
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—1182no—
253C2×C8—1182no—
254C2×C8—2361no—
255C2×C8—2361no—
256C2×C8—2361no—
257C2×C8—2361no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—592no—
266C4⋊C4—1181no—
267C4⋊C4—4721no—
268C4⋊C4—4721no—
269C4⋊C4—4721no—
270C4⋊C4—4721no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2361no—
274C4⋊C4—2361no—
275C42—41no—
276C42—4721no—
277C23#1427369511yescharacteristic
278Q8—42no—
279Q8—81no—
280Q8—4721no—
281Q8—2362no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—1182no—
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×C4—2361no—
308C2×C4—2361no—
309C2×C4SD16×D5911yescharacteristic
310C2×C4C2×#1174567011yescharacteristic
311C2×C4#1427375011yescharacteristic
312C2×C4#1427375611yescharacteristic
313C2×C4#1427375711yescharacteristic
314C2×C4#1427375911yescharacteristic
315C8—81no—
316C8—2362no—
317C8—2362no—
318C22#1683753911yescharacteristic
319C22#1683754011yescharacteristic
320C22#1683756311yescharacteristic
321C22#1683756811yescharacteristic
322C22#1683757911yescharacteristic
323C22#1683758311yescharacteristic
324C22#1683759111yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—161no—
334C4—4721no—
335C4—4721no—
336C4—4721no—
337C4—2362no—
338C2#2142308611yescharacteristic
339C2#2142310211yescharacteristic
340C2#2142314311yescharacteristic
341C2#2142317311yescharacteristic
342C2#2142330011yescharacteristic
343C2#2142337111yescharacteristic
344C2#2142341211yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2072C2
socle, prime radicalC23×C59#120
hypercenter#2072D59
hypocenterC59#7814
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
199. C59#7814semidirect

Maximal subgroups

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

subgroupindex
#214320602
#214256402
#214255732
#214219222
#214219212
#214219182
C59×#20722
#781459