Finite Group Databasebeta

← #28477915

Subgroups — #28477915

Order 15104.

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

normal subgroups only

This group has 362 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#21432055C211yesmaximal, characteristic
2#21425655C211yesmaximal, characteristic
3#21425506C211yesmaximal, characteristic
4#21425504C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1272C211yesmaximal, characteristic
8C2×#14273652—21no—
9C2×#14273651—21no—
10#16837336—21no—
11#16837336—21no—
12#16837321—21no—
13#16837308C2211yescharacteristic
14#16837306—21no—
15#16837300C2211yescharacteristic
16#16837297—21no—
17#16837287—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837165—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#391C2211yescharacteristic
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×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×C4×Dic59—21no—
41#14273652—42no—
42#14273651—42no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C22×Q8×C59D411yescharacteristic
50C22×C8×C59—21no—
51C22×C8×C59—21no—
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C42×C59C2311yescharacteristic
54#95×C59—21no—
55#95×C59—21no—
56C2×Q8×C59—21no—
57C2×Q8×C59—21no—
58C2×Q8×C59—41no—
59C2×Q8×C59—41no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—41no—
70C2×Dic118—21no—
71C2×Dic118—41no—
72C2×Dic118—41no—
73C2×Dic118SD1612yes—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C4⋊C4×C59—41no—
81C42×C59—41no—
82C4⋊Dic59—21no—
83C4⋊Dic59—41no—
84C4⋊Dic59—41no—
85C4⋊Dic59—42no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59Q1612yes—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93Dic59⋊C4—81no—
94Dic59⋊C4—81no—
95Dic59⋊C4—81no—
96Dic59⋊C4—81no—
97C4×Dic59—81no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C23×C59#12011yescharacteristic
102Q8×C59—42no—
103Q8×C59—81no—
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×C59C2×SD1611yescharacteristic
117C2×C4×C59C2×Q1611yescharacteristic
118C2×C4×C59#13511yescharacteristic
119C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×C4×C59#13711yescharacteristic
122C2×Dic59—22no—
123C2×Dic59—22no—
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—41no—
134C2×Dic59—81no—
135C2×Dic59—81no—
136C2×Dic59—81no—
137Dic118—42no—
138Dic118—81no—
139C8×C59—81no—
140C8×C59—81no—
141C59⋊C8—81no—
142#7816—591nomaximal, Sylow
143C22×C59#44811yescharacteristic
144C22×C59#44911yescharacteristic
145C22×C59#45111yescharacteristic
146C22×C59#45411yescharacteristic
147C22×C59#45511yescharacteristic
148C22×C59#45511yescharacteristic
149C22×C59#45811yescharacteristic
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—81no—
157C4×C59—81no—
158Dic59—42no—
159Dic59—42no—
160Dic59—81no—
161Dic59—81no—
162Dic59—161no—
163#2806—591no—
164#2099—591no—
165#2072—591no—
166#2072—591no—
167#1272—591no—
168#1272D5911yescharacteristic
169#1271—591no—
170C2×C59#160811yescharacteristic
171C2×C59#161211yescharacteristic
172C2×C59#161711yescharacteristic
173C2×C59#162611yescharacteristic
174C2×C59#164411yescharacteristic
175C2×C59#164511yescharacteristic
176C2×C59#166211yescharacteristic
177C2×#103—1181no—
178C2×#103—1181no—
179#398—1181no—
180#398—1181no—
181#395—1181no—
182#391—591no—
183#391—1181no—
184#391C2×D5911yescharacteristic
185#389—591no—
186#389—1181no—
187#387—1181no—
188#384—591no—
189#340—1181no—
190#340—1181no—
191#340—1181no—
192#340—1181no—
193#336—591no—
194#336C2×D5911yescharacteristic
195#336C2×D5911yescharacteristic
196C59#781611yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8D23611yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1181no—
202C2×C4⋊C4—591no—
203C2×C4⋊C4—591no—
204C2×C4⋊C4—591no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4—1181no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4D23611yescharacteristic
214C2×C42—1181no—
215C2×C42C22×D5911yescharacteristic
216#103—2362no—
217#103—2362no—
218#95—21no—
219#95—21no—
220#95—1181no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—592no—
231C2×Q8—1181no—
232C2×Q8—2361no—
233C2×Q8—2361no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—1181no—
237C22×C4—1181no—
238C22×C4—1181no—
239C22×C4—1181no—
240C22×C4—2361no—
241C22×C4C2×D23611yescharacteristic
242C22×C4D4×D5911yescharacteristic
243C22×C4D4×D5911yescharacteristic
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2361no—
251C2×C8—2361no—
252C2×C8—2361no—
253C4⋊C4—41no—
254C4⋊C4—592no—
255C4⋊C4—1181no—
256C4⋊C4—4721no—
257C4⋊C4—4721no—
258C4⋊C4—4721no—
259C4⋊C4—4721no—
260C4⋊C4—2362no—
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—42no—
273Q8—81no—
274Q8—4721no—
275Q8—2362no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—1182no—
289C2×C4—1182no—
290C2×C4—4721no—
291C2×C4—4721no—
292C2×C4—4721no—
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×C4—2361no—
302C2×C4—2361no—
303C2×C4SD16×D5911yescharacteristic
304C2×C4Q16×D5911yescharacteristic
305C2×C4#1427374911yescharacteristic
306C2×C4#1427375511yescharacteristic
307C2×C4#1427375611yescharacteristic
308C2×C4#1427375911yescharacteristic
309C8—81no—
310C8—81no—
311C8—4721no—
312C22#1683754211yescharacteristic
313C22#1683754911yescharacteristic
314C22#1683755911yescharacteristic
315C22#1683757611yescharacteristic
316C22#1683758111yescharacteristic
317C22#1683758211yescharacteristic
318C22#1683759311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—9441no—
328C4—4721no—
329C4—4721no—
330C4—2362no—
331C4—2362no—
332C2#2142308811yescharacteristic
333C2#2142311211yescharacteristic
334C2#2142313911yescharacteristic
335C2#2142319411yescharacteristic
336C2#2142331211yescharacteristic
337C2#2142331811yescharacteristic
338C2#2142342111yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59#120
hypercenter#1272D59
hypocenterC59#7816
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
196. C59#7816semidirect

Maximal subgroups

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

subgroupindex
#214320552
#214256552
#214255062
#214255042
#214219212
#214219182
C59×#12722
#781659