Finite Group Databasebeta

← #28498583

Subgroups — #28498583

Order 15104.

328 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 93 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#21433059C211yesmaximal, characteristic
2#21425897C211yesmaximal, characteristic, complemented
3C4⋊C16×D59C211yesmaximal, characteristic, complemented
4#21422079C211yesmaximal, characteristic, complemented
5#21422077C211yesmaximal, characteristic, complemented
6#21422054C211yesmaximal, characteristic, complemented
7C59×#1330C211yesmaximal, characteristic, complemented
8C4×#11745687C411yescharacteristic
9C2×C16×D59—21no—
10#16837532C2211yescharacteristic
11#16837529C411yescharacteristic
12#16837480C411yescharacteristic
13#16837476—21no—
14#16837471—21no—
15#16837454C411yescharacteristic
16#16837452—21no—
17M16×Dic59—21no—
18C4×C8×D59C2211yescharacteristic
19C4⋊(C59⋊C16)C2211yescharacteristic
20Dic59⋊C16—21no—
21Dic59⋊C16—21no—
22(C2×D59)⋊C16—21no—
23#16837178C2211yescharacteristic
24C59×#436C2211yescharacteristic
25C59×C4⋊C16C2211yescharacteristic
26C59×#346C2211yescharacteristic
27C2×#11745687C811yescharacteristic
28C2×#11745664—21no—
29C2×C8×D59D411yescharacteristic
30C2×C8×D59D411yescharacteristic
31C4×Dic118C2×C411yescharacteristic
32#14273692C811yescharacteristic
33D4×Dic59C811yescharacteristic
34C4×C22⋊D59—21no—
35(C22⋊D59)⋊C4—21no—
36#14273685C811yescharacteristic
37#14273683—21no—
38C2×C4×Dic59—21no—
39C42×D59C2×C411yescharacteristic
40C2×C59⋊C16—21no—
41C2×C59⋊C16—21no—
42C16×D59—42no—
43C4⋊(C59⋊C8)C2×C411yescharacteristic
44Dic59⋊C8—21no—
45Dic59⋊C8—21no—
46C22⋊(C59⋊C8)—21no—
47(C2×D59)⋊C8—21no—
48#14273637—21no—
49#14273637—21no—
50C4×C59⋊C8C2×C411yescharacteristic
51C8×Dic59—21no—
52C8×Dic59D411yescharacteristic
53C8×Dic59D411yescharacteristic
54C2×M16×C59—21no—
55C4×D4×C59C2×C411yescharacteristic
56C2×C16×C59—21no—
57C2×C16×C59—21no—
58C4⋊C8×C59C2×C411yescharacteristic
59C22⋊C8×C59—21no—
60C4×C8×C59C2311yescharacteristic
61C2×D4×C59C2×C811yescharacteristic
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66#11745687—42no—
67C2×C4×D59C22⋊C411yescharacteristic
68C2×C4×D59C2×C811yescharacteristic
69C2×C4×D59M1611yescharacteristic
70C2×Dic118C2×C811yescharacteristic
71M16×C59—41no—
72M16×C59—41no—
73C2×C8×C59—21no—
74C2×C8×C59C2×D411yescharacteristic
75C2×C8×C59C2×D411yescharacteristic
76C4⋊C4×C59C2×C811yescharacteristic
77C22⋊C4×C59—21no—
78C42×C59C22×C411yescharacteristic
79C22⋊Dic59—21no—
80(C2×D59)⋊C4—21no—
81C4⋊Dic59C2×C811yescharacteristic
82Dic59⋊C4—21no—
83Dic59⋊C4—21no—
84C4×Dic59—21no—
85C4×Dic59—21no—
86C4×Dic59—21no—
87C4×Dic59C22⋊C411yescharacteristic
88C4×Dic59C2×C811yescharacteristic
89C4×Dic59M1611yescharacteristic
90#11745664—42no—
91C2×C59⋊C8—21no—
92C2×C59⋊C8C22⋊C411yescharacteristic
93C2×C59⋊C8C22⋊C411yescharacteristic
94C8×D59—21no—
95C8×D59—21no—
96C8×D59—41no—
97C16×C59—41no—
98C16×C59—41no—
99C59⋊C16—41no—
100C59⋊C16—41no—
101C23×C59—21no—
102C22×D59C22⋊C811yescharacteristic
103D4×C59—41no—
104C2×C4×C59—21no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59C2×C22⋊C411yescharacteristic
108C2×C4×C59C22×C811yescharacteristic
109C2×C4×C59C2×M1611yescharacteristic
110C22⋊D59—42no—
111C2×Dic59—21no—
112C2×Dic59—21no—
113C2×Dic59—42no—
114C2×Dic59—42no—
115C2×Dic59C22⋊C811yescharacteristic
116C2×Dic59C22⋊C811yescharacteristic
117C2×Dic59C22⋊C811yescharacteristic
118C4×D59—22no—
119C4×D59—21no—
120C4×D59—21no—
121C4×D59—22no—
122Dic118—41no—
123C8×C59—21no—
124C8×C59—41no—
125C8×C59AGL(1,ℤ/8)11yescharacteristic
126C8×C59#13711yescharacteristic
127C59⋊C8—21no—
128C59⋊C8—21no—
129C59⋊C8—41no—
130#11626—591nomaximal, Sylow
131C22×C59—41no—
132C22×C59—41no—
133C22×C59—41no—
134C22×C59C2×C22⋊C811yescharacteristic
135C2×D59—21no—
136C2×D59—21no—
137C2×D59#34912yes—
138C4×C59—21no—
139C4×C59—21no—
140C4×C59—41no—
141C4×C59#41711yescharacteristic
142C4×C59#42111yescharacteristic
143Dic59—21no—
144Dic59—21no—
145Dic59—41no—
146Dic59—41no—
147Dic59#35012yes—
148#2965—591no—
149#2163—591no—
150C2×C4⋊C16—591no—
151#1338—591no—
152#1338—591no—
153#1330—591no—
154#1330D5911yescharacteristic, complemented
155C2×C59—81no—
156C2×C59#147711yescharacteristic
157C2×C59C2×#34911yescharacteristic
158C2×C59C2×#35011yescharacteristic
159D59—22no—
160C4×#41—591no—
161C22×C16—1181no—
162#446—591no—
163#446—591no—
164#436—591no—
165#436C2×D5911yescharacteristic
166#435—1181no—
167#435—1181no—
168#431—591no—
169#431—1181no—
170C4×M16—1181no—
171C2×C4×C8—591no—
172C4⋊C16—591no—
173C4⋊C16—1181no—
174C4⋊C16—1181no—
175C4⋊C16C2×D5911yescharacteristic
176C22⋊C16—1181no—
177#346—591no—
178#346C2×D5911yescharacteristic
179C59#1162611yescharacteristic, complemented, Sylow
180C2×#41—591no—
181C2×M16—21no—
182C2×M16—1181no—
183C22×C8—591no—
184C22×C8—591no—
185C4×Q8—591no—
186C4×Q8—591no—
187C4×D4—591no—
188C4×D4—1181no—
189C4×D4—1181no—
190C4×D4C4×D5911yescharacteristic
191#117—591no—
192#117—1181no—
193C2×C42—591no—
194C2×C42—1181no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—1181no—
198C2×C16—1181no—
199C2×C16—2362no—
200C4⋊C8—591no—
201C4⋊C8—1181no—
202C4⋊C8—1181no—
203C4⋊C8C4×D5911yescharacteristic
204C22⋊C8—21no—
205C22⋊C8—1181no—
206C22⋊C8—1181no—
207#97—1181no—
208#97—1181no—
209C4×C8—591no—
210C4×C8—591no—
211C4×C8—591no—
212C4×C8—1181no—
213C4×C8C22×D5911yescharacteristic
214#41—2362no—
215C2×Q8—591no—
216C2×D4—1181no—
217C2×D4C8×D5911yescharacteristic
218C22×C4—21no—
219C22×C4—591no—
220C22×C4—591no—
221C22×C4—591no—
222C22×C4—1181no—
223C22×C4—1181no—
224M16—41no—
225M16—41no—
226M16—2362no—
227C2×C8—21no—
228C2×C8—591no—
229C2×C8—591no—
230C2×C8—1181no—
231C2×C8—1181no—
232C2×C8—1181no—
233C2×C8—2361no—
234C2×C8D4×D5911yescharacteristic
235C2×C8D4×D5911yescharacteristic
236C4⋊C4—591no—
237C4⋊C4—1181no—
238C4⋊C4—1181no—
239C4⋊C4C8×D5911yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—1181no—
242C22⋊C4—1181no—
243C42—591no—
244C42—591no—
245C42—591no—
246C42—1181no—
247C42—1181no—
248C42—1181no—
249C42C2×C4×D5911yescharacteristic
250C16—41no—
251C16—41no—
252C16—2361no—
253C16—2361no—
254C23—21no—
255C23—591no—
256Q8—2361no—
257D4—41no—
258D4—2362no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—591no—
263C2×C4—591no—
264C2×C4—591no—
265C2×C4—1182no—
266C2×C4—1182no—
267C2×C4—1181no—
268C2×C4—1181no—
269C2×C4—1181no—
270C2×C4—1181no—
271C2×C4—2362no—
272C2×C4—2362no—
273C2×C4C22⋊C4×D5911yescharacteristic
274C2×C4C2×C8×D5911yescharacteristic
275C2×C4M16×D5911yescharacteristic
276C8—21no—
277C8—41no—
278C8—1181no—
279C8—1181no—
280C8—2361no—
281C8#1427375111yescharacteristic
282C8#1427375611yescharacteristic
283C22—41no—
284C22—41no—
285C22—41no—
286C22—592no—
287C22—1181no—
288C22—1181no—
289C22C22⋊C8×D5911yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—592no—
294C4—1181no—
295C4—1181no—
296C4—2361no—
297C4—2361no—
298C4#1683740011yescharacteristic
299C4#1683741711yescharacteristic
300C2—81no—
301C2—1182no—
302C2#2142248011yescharacteristic
303C2#349×D5911yescharacteristic
304C2#350×D5911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC2×C4×C59C22×C8
FrattiniC4×C8C22×D59
FittingC59×#1330C2
socleC22×C59C2×C22⋊C8
prime radicalC2×#11745687C8
cosocleC4×C8×C59C23
hypercenter#1330D59
hypocenterC59#11626
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21425897C2semidirect
3. C4⋊C16×D59C2semidirect
4. #21422079C2semidirect
5. #21422077C2semidirect
6. #21422054C2semidirect
7. C59×#1330C2semidirect
154. #1330D59semidirect
179. C59#11626semidirect

Maximal subgroups

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

subgroupindex
#214330592
#214258972
C4⋊C16×D592
#214220792
#214220772
#214220542
C59×#13302
#1162659