Finite Group Databasebeta

← #28486809

Subgroups — #28486809

Order 15104.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424815C211yesmaximal, characteristic
2C4×#14273660C211yesmaximal, characteristic
3#21423961C211yesmaximal, characteristic
4#21421936C211yesmaximal, characteristic
5#21421930C211yesmaximal, characteristic
6C59⋊#1273C211yesmaximal, characteristic
7C59×#1279C211yesmaximal, characteristic
8C2×#14273660C411yescharacteristic
9C2×#14273660C411yescharacteristic
10C2×C4⋊(C59⋊C8)—21no—
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×C4×C59⋊C8C2211yescharacteristic
13C2×C4×C59⋊C8C2211yescharacteristic
14C2×C8×Dic59—21no—
15C4×C4⋊Dic59C2211yescharacteristic
16#16837164C411yescharacteristic
17#16837164C411yescharacteristic
18#16837157—21no—
19#16837156—21no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4×C8×C59C2211yescharacteristic
22C4×C4⋊C4×C59C2211yescharacteristic
23C22×C59⋊C8—21no—
24C22×C59⋊C8C2×C411yescharacteristic
25C22×C59⋊C8C2×C411yescharacteristic
26C22×C59⋊C8D411yescharacteristic
27C22×C59⋊C8D411yescharacteristic
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4×Dic59—21no—
31#14273660—22no—
32#14273660C814yescomplemented
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)—42no—
36C4×C59⋊C8—21no—
37C4×C59⋊C8—21no—
38C4×C59⋊C8—21no—
39C4×C59⋊C8—21no—
40C8×Dic59—42no—
41C59⋊#95—21no—
42C22×C8×C59—21no—
43C22×C8×C59—21no—
44C2×C4⋊C4×C59C2×C411yescharacteristic
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C42×C59—21no—
47C2×C42×C59C2311yescharacteristic
48C4⋊C8×C59—21no—
49C4⋊C8×C59Q812yes—
50C4×C8×C59—21no—
51C4×C8×C59—21no—
52#95×C59—21no—
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59#4111yescharacteristic
58C22×Dic59—21no—
59C22×Dic59—21no—
60C2×C8×C59—22no—
61C2×C8×C59—22no—
62C2×C8×C59—41no—
63C2×C8×C59—41no—
64C2×C8×C59—41no—
65C2×C8×C59—41no—
66C4⋊C4×C59—21no—
67C4⋊C4×C59—21no—
68C4⋊C4×C59—21no—
69C4⋊C4×C59C2×C812yes—
70C42×C59—41no—
71C42×C59—41no—
72C42×C59C2×Q811yescharacteristic
73C42×C59#4111yescharacteristic
74C42×C59#4111yescharacteristic
75C42×C59#4111yescharacteristic
76C4⋊Dic59—21no—
77C4⋊Dic59—21no—
78C4⋊Dic59C2×C812yes—
79C4⋊Dic59M1612yes—
80C4×Dic59—41no—
81C4×Dic59—41no—
82C2×C59⋊C8—21no—
83C2×C59⋊C8—21no—
84C2×C59⋊C8—21no—
85C2×C59⋊C8—21no—
86C2×C59⋊C8—21no—
87C2×C59⋊C8—21no—
88C2×C59⋊C8—21no—
89C2×C59⋊C8—21no—
90C2×C59⋊C8—21no—
91C2×C59⋊C8—21no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8C2×C812yes—
96C2×C59⋊C8D812yes—
97C23×C59C4×D411yescharacteristic
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—22no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59#11711yescharacteristic
107C2×C4×C59C4×Q811yescharacteristic
108C2×C4×C59C22⋊Q811yescharacteristic
109C2×C4×C59#12311yescharacteristic
110C2×C4×C59#12511yescharacteristic
111C2×C4×C59#12611yescharacteristic
112C2×C4×C59C22×C811yescharacteristic
113C2×C4×C59C2×M1611yescharacteristic
114C2×C4×C59#13111yescharacteristic
115C2×C4×C59#13111yescharacteristic
116C2×C4×C59C2×D811yescharacteristic
117C2×C4×C59#13511yescharacteristic
118C2×C4×C59#13711yescharacteristic
119C2×C4×C59#13711yescharacteristic
120C2×Dic59—22no—
121C2×Dic59—22no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C8×C59—42no—
127C8×C59—42no—
128C59⋊C8—22no—
129C59⋊C8—22no—
130C59⋊C8—41no—
131C59⋊C8—41no—
132C59⋊C8—81no—
133#9533—591nomaximal, Sylow
134C22×C59#38711yescharacteristic
135C22×C59C8×D411yescharacteristic
136C22×C59#43511yescharacteristic
137C22×C59C4×D811yescharacteristic
138C22×C59#44111yescharacteristic
139C22×C59#44311yescharacteristic
140C22×C59#44411yescharacteristic
141C4×C59—21no—
142C4×C59—21no—
143C4×C59—42no—
144C4×C59—81no—
145C4×C59#43111yescharacteristic
146C4×C59#43311yescharacteristic
147C4×C59C8×Q811yescharacteristic
148C4×C59#44611yescharacteristic
149C4×C59#47411yescharacteristic
150C4×C59#47911yescharacteristic
151C4×C59#48011yescharacteristic
152C4×C59#48511yescharacteristic
153Dic59—42no—
154Dic59—42no—
155#1939—591no—
156C4×#107—591no—
157C8×C4⋊C4—591no—
158#1279—591no—
159#1279D5911yescharacteristic
160#1277—591no—
161#1273—591no—
162C2×C59C8×D811yescharacteristic
163C2×C59#157911yescharacteristic
164C2×C59#158111yescharacteristic
165C2×C59#158711yescharacteristic
166C2×C59#191611yescharacteristic
167C2×C59#191811yescharacteristic
168C2×C59#192211yescharacteristic
169C2×#107—591no—
170C2×#107—591no—
171C2×C4⋊C8—591no—
172C2×C4⋊C8—1181no—
173C2×C4⋊C8C2×D5911yescharacteristic
174C2×C4×C8—591no—
175C2×C4×C8—591no—
176C2×C4×C8—1181no—
177C2×C4×C8C2×D5911yescharacteristic
178C4×C4⋊C4—591no—
179C4×C4⋊C4C2×D5911yescharacteristic
180#340—591no—
181#340—591no—
182#336—1181no—
183#336—1181no—
184C59#953311yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—591no—
188C22×C8—591no—
189C22×C8—591no—
190C22×C8—591no—
191C22×C8—1181no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—591no—
194C2×C4⋊C4C4×D5911yescharacteristic
195C2×C4⋊C4C4×D5911yescharacteristic
196C2×C42—21no—
197C2×C42—1181no—
198C2×C42C22×D5911yescharacteristic
199#107—594no—
200#107—1182no—
201C4⋊C8—21no—
202C4⋊C8—1181no—
203C4⋊C8—1181no—
204C4⋊C8—2362no—
205C4⋊C8Dic11812yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—1181no—
209C4×C8—1181no—
210C4×C8—1181no—
211C4×C8—1181no—
212C4×C8—2362no—
213#95—21no—
214#95—1181no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—1181no—
218C22×C4—1181no—
219C22×C4C2×C4×D5911yescharacteristic
220C22×C4D4×D5911yescharacteristic
221C22×C4#1174568711yescharacteristic
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—592no—
229C2×C8—592no—
230C2×C8—1181no—
231C2×C8—1181no—
232C2×C8—1181no—
233C2×C8—1181no—
234C2×C8—1181no—
235C2×C8—1181no—
236C2×C8—1181no—
237C2×C8—1181no—
238C2×C8—1181no—
239C2×C8—1181no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8—2361no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—592no—
247C4⋊C4—592no—
248C4⋊C4—1181no—
249C4⋊C4—1181no—
250C4⋊C4C8×D5912yes—
251C42—41no—
252C42—41no—
253C42—2361no—
254C42—2361no—
255C42C2×Dic11811yescharacteristic
256C42#1174568511yescharacteristic
257C42#1174568711yescharacteristic
258C42#1174568911yescharacteristic
259C23(C22⋊D59)⋊C411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—1182no—
269C2×C4—1182no—
270C2×C4—2361no—
271C2×C4—2361no—
272C2×C4—2361no—
273C2×C4—2361no—
274C2×C4#1427368511yescharacteristic
275C2×C4C4×Dic11811yescharacteristic
276C2×C4#1427370411yescharacteristic
277C2×C4#1427371211yescharacteristic
278C2×C4#1427371811yescharacteristic
279C2×C4#1427372011yescharacteristic
280C2×C4C2×C8×D5911yescharacteristic
281C2×C4M16×D5911yescharacteristic
282C2×C4#1427373311yescharacteristic
283C2×C4#1427373511yescharacteristic
284C2×C4D8×D5911yescharacteristic
285C2×C4#1427374811yescharacteristic
286C2×C4#1427375611yescharacteristic
287C2×C4#1427375911yescharacteristic
288C8—42no—
289C8—42no—
290C8—1182no—
291C8—1182no—
292C8—4721no—
293C8—2361no—
294C8—2361no—
295C22#1683728911yescharacteristic
296C22(C22⋊D59)⋊C811yescharacteristic
297C22#1683747611yescharacteristic
298C22#1683748211yescharacteristic
299C22#1683750611yescharacteristic
300C22#1683751611yescharacteristic
301C22#1683752111yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—2362no—
307C4—2362no—
308C4#1683745411yescharacteristic
309C4#1683746211yescharacteristic
310C4C8×Dic11811yescharacteristic
311C4#1683753011yescharacteristic
312C4#1683768011yescharacteristic
313C4#1683770711yescharacteristic
314C4#1683771711yescharacteristic
315C4#1683774611yescharacteristic
316C2#2142288811yescharacteristic
317C2#2142291211yescharacteristic
318C2#2142292811yescharacteristic
319C2#2142297011yescharacteristic
320C2#2142465611yescharacteristic
321C2#2142467011yescharacteristic
322C2#2142469811yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC59×#1279C2
socle, prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenter#1279D59
hypocenterC59#9533
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
32. #14273660C8semidirect
184. C59#9533semidirect

Maximal subgroups

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

subgroupindex
#214248152
C4×#142736602
#214239612
#214219362
#214219302
C59⋊#12732
C59×#12792
#953359