Finite Group Databasebeta

← #28493173

Subgroups — #28493173

Order 15104.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429132C211yesmaximal, characteristic
2#21424855C211yesmaximal, characteristic
3#21424855C211yesmaximal, characteristic
4#21424223C211yesmaximal, characteristic
5#21421935C211yesmaximal, characteristic
6#21421935C211yesmaximal, characteristic
7C59×#1296C211yesmaximal, characteristic
8C2×#14273718—21no—
9C2×#14273661—21no—
10C2×#14273661—21no—
11C2×C4×C59⋊C8C2211yescharacteristic
12#16837335—22no—
13#16837301—21no—
14#16837298—21no—
15#16837272C2211yescharacteristic
16#16837271—21no—
17C4×C4⋊Dic59C2211yescharacteristic
18C4×C4⋊Dic59C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837164—22no—
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C22×C59⋊C8—21no—
26#14273718—42no—
27#14273718—42no—
28C2×C4⋊Dic59—22no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×Dic59⋊C4—22no—
37C2×Dic59⋊C4—22no—
38C2×C4×Dic59—21no—
39C2×C4×Dic59—21no—
40#14273661—42no—
41#14273661—42no—
42C4×C59⋊C8—21no—
43C4×C59⋊C8Q812yes—
44C59⋊#95—22no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C22×C8×C59—21no—
48C22×C8×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59D412yes—
52C2×C42×C59C2311yescharacteristic
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59Q812yes—
56C4⋊C8×C59Q812yes—
57C22×C4×C59—22no—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×Dic59—21no—
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—41no—
66C2×C8×C59—22no—
67C2×C8×C59—22no—
68C2×C8×C59—41no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C4⋊C4×C59—42no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C42×C59C2×Q811yescharacteristic
78C42×C59C2×Q811yescharacteristic
79C42×C59C2×Q811yescharacteristic
80C42×C59#4111yescharacteristic
81C4⋊Dic59—21no—
82C4⋊Dic59—21no—
83C4⋊Dic59—21no—
84C4⋊Dic59—21no—
85C4⋊Dic59—21no—
86C4⋊Dic59—21no—
87C4⋊Dic59—44no—
88C4⋊Dic59—42no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59D812yes—
94C4⋊Dic59Q1612yes—
95Dic59⋊C4—44no—
96Dic59⋊C4—82no—
97C4×Dic59—41no—
98C4×Dic59—41no—
99C4×Dic59—41no—
100C4×Dic59—41no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C23×C59#12011yescharacteristic
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—42no—
108C2×C4×C59—42no—
109C2×C4×C59—42no—
110C2×C4×C59C22⋊Q811yescharacteristic
111C2×C4×C59C22⋊Q811yescharacteristic
112C2×C4×C59C22⋊Q811yescharacteristic
113C2×C4×C59C4⋊Q811yescharacteristic
114C2×C4×C59C4⋊Q811yescharacteristic
115C2×C4×C59C4⋊Q811yescharacteristic
116C2×C4×C59C2×D811yescharacteristic
117C2×C4×C59C2×Q1611yescharacteristic
118C2×C4×C59#13511yescharacteristic
119C2×C4×C59#13511yescharacteristic
120C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C59#13711yescharacteristic
123C2×C4×C59#13711yescharacteristic
124C2×Dic59—22no—
125C2×Dic59—22no—
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—41no—
135C2×Dic59—41no—
136C2×Dic59—81no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C8×C59—42no—
140C8×C59—42no—
141C59⋊C8—42no—
142#10581—591nomaximal, Sylow
143C22×C59#39511yescharacteristic
144C22×C59#44711yescharacteristic
145C22×C59#44911yescharacteristic
146C22×C59#45111yescharacteristic
147C22×C59#45211yescharacteristic
148C22×C59#45411yescharacteristic
149C22×C59#45511yescharacteristic
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—82no—
153C4×C59#47411yescharacteristic
154C4×C59#47711yescharacteristic
155C4×C59#47811yescharacteristic
156C4×C59#47911yescharacteristic
157C4×C59#49911yescharacteristic
158C4×C59#50011yescharacteristic
159C4×C59#50111yescharacteristic
160C4×C59#50111yescharacteristic
161Dic59—42no—
162Dic59—42no—
163Dic59—81no—
164Dic59—81no—
165Dic59—161no—
166#2552—591no—
167#1947—591no—
168#1947—591no—
169#1834—591no—
170#1296D5911yescharacteristic
171#1279—591no—
172#1279—591no—
173C2×C59#162511yescharacteristic
174C2×C59#163611yescharacteristic
175C2×C59#164111yescharacteristic
176C2×C59#164411yescharacteristic
177C2×C59#205711yescharacteristic
178C2×C59#205911yescharacteristic
179C2×C59#206111yescharacteristic
180C2×#125—1181no—
181C2×#107—1181no—
182C2×#107—1181no—
183C2×C4⋊C8C2×D5911yescharacteristic
184C2×C4⋊C8C2×D5911yescharacteristic
185C2×C4×C8—591no—
186#398—1182no—
187#389—1181no—
188#389—1181no—
189#384—591no—
190#384—1181no—
191#384C2×D5911yescharacteristic
192C4×C4⋊C4—591no—
193C4×C4⋊C4—591no—
194#340—1181no—
195#340—1181no—
196#340—1182no—
197C59#1058111yescharacteristic, complemented, Sylow
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—1181no—
201#125—2362no—
202#125—2362no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—591no—
206C2×C4⋊C4—591no—
207C2×C4⋊C4—591no—
208C2×C4⋊C4—591no—
209C2×C4⋊C4—1182no—
210C2×C4⋊C4—1182no—
211C2×C4⋊C4—1182no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4D23612yes—
216C2×C42—1181no—
217C2×C42—1181no—
218C2×C42C22×D5911yescharacteristic
219#107—2362no—
220#107—2362no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8Dic11812yes—
224C4⋊C8Dic11812yes—
225C4×C8—592no—
226C4×C8—1181no—
227#95—1182no—
228#95—1181no—
229#95—1181no—
230C22×C4—22no—
231C22×C4—1181no—
232C22×C4—1181no—
233C22×C4—1181no—
234C22×C4—1181no—
235C22×C4—2361no—
236C22×C4C2×D23611yescharacteristic
237C22×C4D4×D5911yescharacteristic
238C22×C4D4×D5911yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—1182no—
246C2×C8—2361no—
247C2×C8—2361no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—592no—
254C4⋊C4—592no—
255C4⋊C4—1181no—
256C4⋊C4—1181no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—4722no—
262C4⋊C4—2362no—
263C4⋊C4—2364no—
264C4⋊C4—2364no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C42—2361no—
270C42—2361no—
271C42—2361no—
272C42—2361no—
273C42C2×Dic11811yescharacteristic
274C42C2×Dic11811yescharacteristic
275C42#1174568711yescharacteristic
276C42Q8×D5911yescharacteristic
277C23#1427369711yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—1182no—
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#1427370411yescharacteristic
299C2×C4#1427370411yescharacteristic
300C2×C4#1427370711yescharacteristic
301C2×C4#1427372611yescharacteristic
302C2×C4#1427372611yescharacteristic
303C2×C4#1427372711yescharacteristic
304C2×C4D8×D5911yescharacteristic
305C2×C4Q16×D5911yescharacteristic
306C2×C4#1427374611yescharacteristic
307C2×C4#1427375011yescharacteristic
308C2×C4#1427375411yescharacteristic
309C2×C4#1427375411yescharacteristic
310C2×C4#1427375611yescharacteristic
311C2×C4#1427375611yescharacteristic
312C8—42no—
313C8—42no—
314C8—2362no—
315C22#1683732311yescharacteristic
316C22#1683753711yescharacteristic
317C22#1683755011yescharacteristic
318C22#1683755911yescharacteristic
319C22#1683756511yescharacteristic
320C22#1683757711yescharacteristic
321C22#1683758211yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—9441no—
326C4—4721no—
327C4—4721no—
328C4—2362no—
329C4—2362no—
330C4#1683768011yescharacteristic
331C4#1683769511yescharacteristic
332C4#1683770011yescharacteristic
333C4#1683771111yescharacteristic
334C4#1683780311yescharacteristic
335C4#1683780611yescharacteristic
336C4#1683780911yescharacteristic
337C4#1683780911yescharacteristic
338C2#2142318611yescharacteristic
339C2#2142325511yescharacteristic
340C2#2142329011yescharacteristic
341C2#2142331111yescharacteristic
342C2#2142542311yescharacteristic
343C2#2142543711yescharacteristic
344C2#2142544711yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socle, prime radicalC23×C59#120
hypercenter#1296D59
hypocenterC59#10581
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
197. C59#10581semidirect

Maximal subgroups

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

subgroupindex
#214291322
#214248552
#214242232
#214219352
C59×#12962
#1058159