Finite Group Databasebeta

← #28477754

Subgroups — #28477754

Order 15104.

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

normal subgroups only

This group has 374 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#21431048C211yesmaximal, characteristic
2#21425655C211yesmaximal, characteristic
3#21425569C211yesmaximal, characteristic
4#21425567C211yesmaximal, characteristic
5#21421918C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273717—21no—
9C2×#14273661—21no—
10C2×#14273660—21no—
11#16837334—21no—
12#16837332—21no—
13#16837332—21no—
14#16837301—21no—
15#16837300C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837287—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837165—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28#14273717—42no—
29#14273717—42no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×C4⋊Dic59D411yescharacteristic
39C2×Dic59⋊C4—21no—
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—21no—
42C2×Dic59⋊C4—21no—
43C2×C4×Dic59—21no—
44#14273661—42no—
45#14273660—42no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—41no—
68C2×C8×C59—22no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59D812yes—
79C42×C59—41no—
80C4⋊Dic59—21no—
81C4⋊Dic59—21no—
82C4⋊Dic59—21no—
83C4⋊Dic59—42no—
84C4⋊Dic59—41no—
85C4⋊Dic59—41no—
86C4⋊Dic59—42no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—81no—
92C4⋊Dic59Q1612yes—
93Dic59⋊C4—42no—
94Dic59⋊C4—42no—
95Dic59⋊C4—41no—
96Dic59⋊C4—41no—
97Dic59⋊C4—41no—
98Dic59⋊C4—41no—
99C4×Dic59—42no—
100C2×C59⋊C8—22no—
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—22no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59C2×D811yescharacteristic
117C2×C4×C59C2×Q1611yescharacteristic
118C2×C4×C59#13511yescharacteristic
119C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C59#13711yescharacteristic
122C2×Dic59—22no—
123C2×Dic59—41no—
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—
137C8×C59—42no—
138C8×C59—81no—
139C59⋊C8—42no—
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—42no—
155C4×C59—81no—
156Dic59—42no—
157Dic59—81no—
158Dic59—81no—
159Dic59—81no—
160Dic59—161no—
161#2726—591no—
162#2099—591no—
163#2083—591no—
164#2083—591no—
165#1271—591no—
166#1271—591no—
167#1271D5911yescharacteristic
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—1181no—
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#384—591no—
187#340—1181no—
188#340—1181no—
189#340—1181no—
190#340—1181no—
191#336—591no—
192#336C2×D5911yescharacteristic
193#336C2×D5911yescharacteristic
194C59#779211yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1181no—
198#125—2362no—
199#125—2362no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—591no—
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⋊C4—1181no—
214C2×C4⋊C4D23611yescharacteristic
215C2×C4⋊C4D23611yescharacteristic
216C2×C42—1181no—
217C2×C42C22×D5911yescharacteristic
218#107—2362no—
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—1181no—
229C22×C4—1181no—
230C22×C4—1181no—
231C22×C4—1181no—
232C22×C4—2361no—
233C22×C4C2×D23611yescharacteristic
234C22×C4D4×D5911yescharacteristic
235C22×C4D4×D5911yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—1182no—
243C2×C8—2361no—
244C2×C8—2361no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—592no—
250C4⋊C4—1181no—
251C4⋊C4—1181no—
252C4⋊C4—1181no—
253C4⋊C4—4721no—
254C4⋊C4—2362no—
255C4⋊C4—2361no—
256C4⋊C4—2361no—
257C4⋊C4—2362no—
258C4⋊C4—2362no—
259C4⋊C4—2362no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C4⋊C4—2361no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4D47212yes—
269C42—41no—
270C42—2362no—
271C23#1427369711yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—1182no—
285C2×C4—4721no—
286C2×C4—4721no—
287C2×C4—4721no—
288C2×C4—2361no—
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×C4C2×D47211yescharacteristic
300C2×C4Q16×D5911yescharacteristic
301C2×C4#1427374811yescharacteristic
302C2×C4#1427375111yescharacteristic
303C2×C4#1427375511yescharacteristic
304C2×C4#1427375611yescharacteristic
305C8—42no—
306C8—81no—
307C8—2362no—
308C22#1683753811yescharacteristic
309C22#1683754811yescharacteristic
310C22#1683755911yescharacteristic
311C22#1683757611yescharacteristic
312C22#1683758611yescharacteristic
313C22#1683758711yescharacteristic
314C22#1683759311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—9441no—
324C4—4721no—
325C4—4721no—
326C4—4721no—
327C4—2362no—
328C2#2142309411yescharacteristic
329C2#2142310111yescharacteristic
330C2#2142313911yescharacteristic
331C2#2142318711yescharacteristic
332C2#2142333911yescharacteristic
333C2#2142334711yescharacteristic
334C2#2142342611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59#120
hypercenter#1271D59
hypocenterC59#7792
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

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
#214310482
#214256552
#214255692
#214255672
#214219182
C59×#12712
#779259