Finite Group Databasebeta

← #28599629

Subgroups — #28599629

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426574C211yesmaximal, characteristic
2#21425037C211yesmaximal, characteristic
3#21424819C211yesmaximal, characteristic
4#21424817C211yesmaximal, characteristic
5#21424661C212yesmaximal
6#21424659C212yesmaximal
7#21424240C212yesmaximal
8#21424214C212yesmaximal
9#21423951C211yesmaximal, characteristic
10#21423844C211yesmaximal, characteristic
11C59×#1985C211yesmaximal, characteristic
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×Dic59⋊C8C2212yes—
14C2×Dic59⋊C8C2212yes—
15C2×#14273638C2211yescharacteristic
16C2×#14273637C2212yes—
17#16837309C412yes—
18#16837301C412yes—
19#16837288C414yes—
20C4×C4⋊Dic59C2212yes—
21C4×C4⋊Dic59C2211yescharacteristic
22#16837248C2212yes—
23C42×Dic59C2211yescharacteristic
24#16837157C2212yes—
25#16837157C2212yes—
26#16837156C2211yescharacteristic
27#16837156C2212yes—
28#16837156C2211yescharacteristic
29#16837156C2212yes—
30#16837156C2212yes—
31#16837156C2211yescharacteristic
32#16837156C2211yescharacteristic
33C2×C4×Q8×C59C2211yescharacteristic
34C2×C4⋊C8×C59C2211yescharacteristic
35C2×#97×C59C2211yescharacteristic
36C59×#336C2212yes—
37C59×#336C2212yes—
38C22×C59⋊C8C2311yescharacteristic
39C22×C59⋊C8C2311yescharacteristic
40C22×C59⋊C8C2312yes—
41C2×C4⋊Dic59C2×C414yes—
42C2×C4⋊Dic59C2×C412yes—
43C2×C4×Dic59C2×C412yes—
44C2×C4×Dic59C2×C412yes—
45C2×C4×Dic59C2311yescharacteristic
46C2×C4×Dic59C2312yes—
47C2×C4×Dic59C2311yescharacteristic
48C4⋊(C59⋊C8)—22no—
49Dic59⋊C8—42no—
50Dic59⋊C8—42no—
51#14273638—22no—
52#14273637—42no—
53C59⋊#95C2×C414yes—
54C59⋊#95C2×C414yes—
55C59⋊#95C2×C412yes—
56C59⋊#95C2×C414yes—
57C22×Q8×C59C2×C411yescharacteristic
58C22×C8×C59C2311yescharacteristic
59C22×C8×C59C2311yescharacteristic
60C22×C8×C59C2312yes—
61C4×Q8×C59—22no—
62C4×Q8×C59—22no—
63C2×C4⋊C4×C59C2×C412yes—
64C2×C4⋊C4×C59C2×C411yescharacteristic
65C2×C42×C59C2312yes—
66C2×C42×C59C2311yescharacteristic
67C4⋊C8×C59—22no—
68#97×C59—22no—
69C2×Q8×C59—22no—
70C2×Q8×C59—42no—
71C22×C4×C59C22×C412yes—
72C22×C4×C59C22×C412yes—
73C22×C4×C59C22×C411yescharacteristic
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2411yescharacteristic
76C22×Dic59C22×C412yes—
77C22×Dic59C22×C414yes—
78C22×Dic59C22×C412yes—
79C2×C8×C59—21no—
80C2×C8×C59—21no—
81C2×C8×C59—22no—
82C2×C8×C59—22no—
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—21no—
86C2×C8×C59—22no—
87C2×C8×C59—21no—
88C4⋊C4×C59—22no—
89C4⋊C4×C59—24no—
90C42×C59—22no—
91C42×C59—22no—
92C42×C59#4112yes—
93C42×C59#4112yes—
94C4⋊Dic59—44no—
95C4⋊Dic59—42no—
96C4×Dic59—21no—
97C4×Dic59—22no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100C4×Dic59—22no—
101C4×Dic59—21no—
102C4×Dic59—42no—
103C4×Dic59—42no—
104C2×C59⋊C8—21no—
105C2×C59⋊C8—21no—
106C2×C59⋊C8—22no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—21no—
109C2×C59⋊C8—21no—
110C2×C59⋊C8—21no—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—22no—
113C23×C59C23×C411yescharacteristic
114Q8×C59—44no—
115C2×C4×C59—22no—
116C2×C4×C59—22no—
117C2×C4×C59—22no—
118C2×C4×C59—22no—
119C2×C4×C59—24no—
120C2×C4×C59—24no—
121C2×C4×C59#11712yes—
122C2×C4×C59#11712yes—
123C2×C4×C59C2×#4111yescharacteristic
124C2×C4×C59C2×#4111yescharacteristic
125C2×C4×C59H(5,𝔽2)11yescharacteristic
126C2×C4×C592−1+411yescharacteristic
127C2×C4×C592−1+411yescharacteristic
128C2×C4×C592−1+411yescharacteristic
129C2×Dic59—22no—
130C2×Dic59—22no—
131C2×Dic59—24no—
132C2×Dic59—22no—
133C2×Dic59—22no—
134C2×Dic59—22no—
135C2×Dic59—22no—
136C2×Dic59—24no—
137C2×Dic59—24no—
138C8×C59—41no—
139C8×C59—42no—
140C8×C59—41no—
141C59⋊C8—41no—
142C59⋊C8—41no—
143C59⋊C8—42no—
144#22025—591nomaximal, Sylow
145C22×C59C2×#11711yescharacteristic
146C22×C59#51911yescharacteristic
147C22×C59#52011yescharacteristic
148C22×C59#56812yes—
149C22×C59#56812yes—
150C4×C59—22no—
151C4×C59—22no—
152C4×C59—42no—
153C4×C59—42no—
154C4×C59#54111yescharacteristic
155C4×C59#54111yescharacteristic
156C4×C59#54211yescharacteristic
157C4×C59#54211yescharacteristic
158Dic59—42no—
159Dic59—42no—
160Dic59—44no—
161#2295—591no—
162#1985—591no—
163#1985D5911yescharacteristic
164#1940—591no—
165#1940—591no—
166#1917—592no—
167#1917—592no—
168#1840—592no—
169#1832—592no—
170#1767—591no—
171#1745—591no—
172C2×C59#232011yescharacteristic
173C2×C59#292111yescharacteristic
174C2×C59#292311yescharacteristic
175C2×C59#298712yes—
176C2×C59#299512yes—
177C2×C4×Q8C2×D5911yescharacteristic
178C2×C4⋊C8—591no—
179C2×C4⋊C8—592no—
180C2×C4⋊C8—592no—
181C2×C4⋊C8C2×D5911yescharacteristic
182C2×#97—591no—
183C2×#97—592no—
184C2×#97C2×D5911yescharacteristic
185#391—592no—
186#389—592no—
187#387—594no—
188C4×C4⋊C4—592no—
189C4×C4⋊C4—591no—
190#376—592no—
191C43—591no—
192#336—591no—
193#336—592no—
194#336—591no—
195#336—592no—
196#336—592no—
197#336—591no—
198#336—591no—
199#336—592no—
200#336—592no—
201#336C2×D5912yes—
202#336C2×D5912yes—
203C59#2202511yescharacteristic, complemented, Sylow
204C22×Q8C4×D5911yescharacteristic
205C22×C8—591no—
206C22×C8—591no—
207C22×C8—592no—
208C22×C8C22×D5911yescharacteristic
209C22×C8C22×D5912yes—
210C22×C8C22×D5911yescharacteristic
211C4×Q8—22no—
212C4×Q8—22no—
213C2×C4⋊C4—594no—
214C2×C4⋊C4—592no—
215C2×C4⋊C4C4×D5912yes—
216C2×C4⋊C4C4×D5911yescharacteristic
217C2×C42—591no—
218C2×C42—591no—
219C2×C42—592no—
220C2×C42—592no—
221C2×C42—592no—
222C2×C42C22×D5912yes—
223C2×C42C22×D5911yescharacteristic
224C4⋊C8—22no—
225C4⋊C8—1182no—
226C4⋊C8—2362no—
227C4⋊C8—2362no—
228#97—22no—
229#97—1182no—
230#97—2362no—
231#95—594no—
232#95—594no—
233#95—592no—
234#95—594no—
235C2×Q8—22no—
236C2×Q8—42no—
237C22×C4—592no—
238C22×C4—594no—
239C22×C4—592no—
240C22×C4C2×C4×D5912yes—
241C22×C4C2×C4×D5912yes—
242C22×C4C2×C4×D5911yescharacteristic
243C22×C4C2×C4×D5911yescharacteristic
244C22×C4C23×D5911yescharacteristic
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—1181no—
255C2×C8—1181no—
256C2×C8—1182no—
257C2×C8—1182no—
258C2×C8—1181no—
259C2×C8—1181no—
260C2×C8—1181no—
261C2×C8—1181no—
262C2×C8—1182no—
263C4⋊C4—22no—
264C4⋊C4—24no—
265C4⋊C4—2362no—
266C4⋊C4—2364no—
267C42—22no—
268C42—22no—
269C42—1181no—
270C42—1182no—
271C42—1181no—
272C42—1181no—
273C42—1181no—
274C42—1182no—
275C42—2362no—
276C42—2362no—
277C42#1174568712yes—
278C42#1174568712yes—
279C23C22×C4×D5911yescharacteristic
280Q8—44no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—1182no—
288C2×C4—1182no—
289C2×C4—1184no—
290C2×C4—1182no—
291C2×C4—1182no—
292C2×C4—1184no—
293C2×C4—1182no—
294C2×C4—1182no—
295C2×C4—1184no—
296C2×C4#1427368312yes—
297C2×C4#1427368312yes—
298C2×C4C2×#1174568711yescharacteristic
299C2×C4C2×#1174568711yescharacteristic
300C2×C4#1427377311yescharacteristic
301C2×C4#1427377411yescharacteristic
302C2×C4#1427377511yescharacteristic
303C2×C4#1427377511yescharacteristic
304C8—41no—
305C8—42no—
306C8—41no—
307C8—2361no—
308C8—2361no—
309C8—2362no—
310C22C2×#1427368311yescharacteristic
311C22#1683787811yescharacteristic
312C22#1683788411yescharacteristic
313C22#1683816712yes—
314C22#1683816812yes—
315C4—22no—
316C4—22no—
317C4—42no—
318C4—42no—
319C4—2362no—
320C4—2362no—
321C4—2364no—
322C4#1683801211yescharacteristic
323C4#1683801311yescharacteristic
324C4#1683802111yescharacteristic
325C4#1683802511yescharacteristic
326C2#2142674111yescharacteristic
327C2#2143273111yescharacteristic
328C2#2143274311yescharacteristic
329C2#2143319912yes—
330C2#2143326512yes—
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socle, prime radicalC23×C59C23×C4
FittingC59×#1985C2
cosocleC22×C4×C59C24
hypercenter#1985D59
hypocenterC59#22025
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
203. C59#22025semidirect

Maximal subgroups

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

subgroupindex
#214265742
#214250372
#214248192
#214248172
#214246612
#214246592
#214242402
#214242142
#214239512
#214238442
C59×#19852
#2202559