Finite Group Databasebeta

← #28479682

Subgroups — #28479682

Order 15104.

510 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432790C211yesmaximal, characteristic
2#21423872C211yesmaximal, characteristic, complemented
3#21422588C211yesmaximal, characteristic
4#21422585C211yesmaximal, characteristic
5#21421984C211yesmaximal, characteristic, complemented
6#21421982C211yesmaximal, characteristic, complemented
7C59×#1752C211yesmaximal, characteristic, complemented
8C2×#14273733C411yescharacteristic, complemented
9#16837913C2211yescharacteristic
10#16837473—21no—
11#16837473—21no—
12C8×C22⋊D59—21no—
13C8×C22⋊D59—21no—
14#16837428C411yescharacteristic, complemented
15#16837368C411yescharacteristic, complemented
16#16837366C2211yescharacteristic
17C2×C22⋊(C59⋊C8)C2211yescharacteristic
18#16837357C411yescharacteristic, complemented
19C2×#14273637—21no—
20C4×C22⋊Dic59C2211yescharacteristic
21#16837156—21no—
22#16837140C412yescomplemented
23#16837138C412yescomplemented
24#16837137C412yescomplemented
25#16837135C412yescomplemented
26C23×C8×C59C2211yescharacteristic
27C2×C22⋊C8×C59C2211yescharacteristic
28C2×#97×C59—21no—
29C4×C22⋊C4×C59C2211yescharacteristic
30C59×#336—21no—
31C2×#11745685C2×C411yescharacteristic
32#14273733—42no—
33C2×#11745664C2×C411yescharacteristic
34C2×#11745664C2×C411yescharacteristic
35C2×#11745659—21no—
36C22×C59⋊C8—21no—
37C2×C8×D59—21no—
38#14273710—21no—
39#14273706C2×C411yescharacteristic
40#14273706C2×C411yescharacteristic
41#14273701C2×C411yescharacteristic
42#14273701C2×C411yescharacteristic
43#14273696—21no—
44C4×C22⋊D59—21no—
45C4×C22⋊D59—21no—
46#14273686C2×C411yescharacteristic
47C2×C22⋊Dic59—21no—
48C2×C4×Dic59—21no—
49Dic59⋊C8—21no—
50Dic59⋊C8—21no—
51C22⋊(C59⋊C8)—21no—
52C22⋊(C59⋊C8)—21no—
53C22⋊(C59⋊C8)—21no—
54C22⋊(C59⋊C8)C2×C412yes—
55(C2×D59)⋊C8—21no—
56(C2×D59)⋊C8—21no—
57#14273637—21no—
58#14273637—42no—
59C8×Dic59—21no—
60C59⋊#95C2×C412yes—
61C23×C4×C59C2311yescharacteristic
62C22×C8×C59—21no—
63C22×C8×C59—42no—
64C22×C8×C59C2×C411yescharacteristic
65C22×C8×C59C2×C411yescharacteristic
66C22×C8×C59D411yescharacteristic
67C22×C8×C59D411yescharacteristic
68C22×C8×C59D411yescharacteristic
69C22×C8×C59D411yescharacteristic
70C2×C22⋊C4×C59—21no—
71C2×C42×C59—21no—
72C22⋊C8×C59—21no—
73C22⋊C8×C59C2×C412yes—
74#97×C59—42no—
75#95×C59C2×C412yes—
76C24×C59#4111yescharacteristic
77C22×C4×C59—22no—
78C22×C4×C59—41no—
79C22×C4×C59—41no—
80C22×C4×C59C22×C411yescharacteristic
81C22×C4×C59C22×C411yescharacteristic
82C22×C4×C59C22×C411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59#4111yescharacteristic
86C2×C22⋊D59—21no—
87C2×C22⋊D59—21no—
88C2×C22⋊D59—21no—
89C22×Dic59—22no—
90#11745685—41no—
91#11745685—41no—
92C2×D236C4211yescharacteristic
93C2×C4×D59—21no—
94C2×Dic118C4211yescharacteristic
95C2×C8×C59—22no—
96C2×C8×C59—22no—
97C2×C8×C59—22no—
98C2×C8×C59—22no—
99C2×C8×C59—41no—
100C2×C8×C59—41no—
101C2×C8×C59—41no—
102C2×C8×C59—41no—
103C2×C8×C59—41no—
104C2×C8×C59C22⋊C411yescharacteristic
105C2×C8×C59C22⋊C411yescharacteristic
106C2×C8×C59C22⋊C411yescharacteristic
107C2×C8×C59C22⋊C411yescharacteristic
108C22⋊C4×C59—42no—
109C42×C59—41no—
110C42×C59—41no—
111C22⋊Dic59—21no—
112C22⋊Dic59—21no—
113C22⋊Dic59—21no—
114C22⋊Dic59—42no—
115(C2×D59)⋊C4—21no—
116(C2×D59)⋊C4—21no—
117C4⋊Dic59C4211yescharacteristic
118C4⋊Dic59C4211yescharacteristic
119Dic59⋊C4—21no—
120Dic59⋊C4—21no—
121C4×Dic59—21no—
122C4×Dic59—41no—
123C4×Dic59—41no—
124#11745664—41no—
125#11745664—41no—
126C2×C59⋊C8—21no—
127C2×C59⋊C8—21no—
128C2×C59⋊C8—22no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131#11745659—42no—
132C8×D59—42no—
133C23×C59—22no—
134C23×C59—22no—
135C23×C59—41no—
136C23×C59#11711yescharacteristic
137C23×C59C4×D411yescharacteristic
138C23×C59C4×D411yescharacteristic
139C22×D59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—42no—
152C2×C4×C59C2×C4211yescharacteristic
153C2×C4×C59C2×C22⋊C411yescharacteristic
154C2×C4×C59C4×D411yescharacteristic
155C2×C4×C59C4×D411yescharacteristic
156C22⋊D59—42no—
157C22⋊D59—42no—
158C22⋊D59—42no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—42no—
163C2×Dic59—42no—
164C2×Dic59—42no—
165D236—41no—
166C4×D59—41no—
167C4×D59—41no—
168Dic118—41no—
169C8×C59—21no—
170C8×C59—21no—
171C8×C59—21no—
172C8×C59—42no—
173C8×C59#9912yes—
174C59⋊C8—42no—
175C59⋊C8—41no—
176C59⋊C8—41no—
177#8239—591nomaximal, Sylow
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—44no—
186C22×C59C4×C22⋊C411yescharacteristic
187C22×C59#44412yes—
188C22×C59#44412yes—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—82no—
196C4×C59C2×#9911yescharacteristic
197C4×C59#41011yescharacteristic
198Dic59—41no—
199Dic59—41no—
200Dic59—41no—
201Dic59—82no—
202#2929—591no—
203#1752—591no—
204#1752D5911yescharacteristic, complemented
205#1501—591no—
206#1501—591no—
207#1298—591no—
208#1297—591no—
209C2×C59—22no—
210C2×C59—22no—
211C2×C59—41no—
212C2×C59C4×#9911yescharacteristic
213C2×C59#176511yescharacteristic
214C2×C59#176511yescharacteristic
215D59—81no—
216C2×#131—591no—
217C23×C8C2×D5911yescharacteristic
218#525—591no—
219#435—1181no—
220#435—1181no—
221C8×D4—1181no—
222C8×D4—1181no—
223#424—591no—
224#408—591no—
225#407—591no—
226C2×C22⋊C8—591no—
227C2×C22⋊C8C2×D5911yescharacteristic
228#405—591no—
229C2×#97—21no—
230C2×#97—1181no—
231C4×C22⋊C4—591no—
232C4×C22⋊C4C2×D5911yescharacteristic
233#336—21no—
234#336—1181no—
235#328—592no—
236#328—592no—
237#327—592no—
238#327—592no—
239C59#823911yescharacteristic, complemented, Sylow
240C2×#41—591no—
241C23×C4C22×D5911yescharacteristic
242#131—2362no—
243C2×M16—591no—
244C2×M16—591no—
245C2×M16—1181no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—1181no—
249C22×C8—1181no—
250C22×C8C4×D5911yescharacteristic
251C22×C8C4×D5911yescharacteristic
252C22×C8D23611yescharacteristic
253C22×C8D23611yescharacteristic
254C22×C8C22⋊D5911yescharacteristic
255C22×C8C22⋊D5911yescharacteristic
256#123—1181no—
257C22⋊Q8—591no—
258C22⋊Q8—591no—
259#121—591no—
260#121—591no—
261#120—1181no—
262C4×D4—1181no—
263C4×D4—1181no—
264#117—591no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—1181no—
267C2×C42—21no—
268C2×C42—1181no—
269C4⋊C8—1181no—
270C4⋊C8—1181no—
271C22⋊C8—21no—
272C22⋊C8—592no—
273C22⋊C8—1181no—
274C22⋊C8—1181no—
275C22⋊C8—1181no—
276C22⋊C8—1181no—
277C22⋊C8—1181no—
278C22⋊C8C4×D5912yes—
279#97—42no—
280#97—1181no—
281#97—2362no—
282C4×C8—1181no—
283#95—592no—
284#95C4×D5912yes—
285C24#1174568511yescharacteristic
286#41—2361no—
287#41—2361no—
288C2×Q8—591no—
289C2×D4—591no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1181no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—1181no—
297C22×C4—1182no—
298C22×C4C2×C4×D5911yescharacteristic
299C22×C4C2×C4×D5911yescharacteristic
300C22×C4C2×C4×D5911yescharacteristic
301C22×C4C2×D23611yescharacteristic
302C22×C4#1174568511yescharacteristic
303C22×C4C2×C22⋊D5911yescharacteristic
304M16—2362no—
305M16—2361no—
306M16—2361no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—1181no—
317C2×C8—1181no—
318C2×C8—1182no—
319C2×C8—2361no—
320C2×C8—2361no—
321C2×C8—2362no—
322C2×C8(C2×D59)⋊C411yescharacteristic
323C2×C8(C2×D59)⋊C411yescharacteristic
324C2×C8(C2×D59)⋊C411yescharacteristic
325C2×C8(C2×D59)⋊C411yescharacteristic
326C4⋊C4—591no—
327C4⋊C4—591no—
328C4⋊C4—1181no—
329C4⋊C4—1181no—
330C22⋊C4—42no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C22⋊C4—2362no—
337C42—41no—
338C42—41no—
339C42—1181no—
340C42—2361no—
341C42—2361no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—1181no—
346C23#1427368411yescharacteristic
347C23C4×C22⋊D5911yescharacteristic
348C23C4×D23611yescharacteristic
349Q8—2361no—
350D4—2361no—
351D4—2362no—
352D4—2362no—
353D4—2362no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4—2362no—
372C2×C4—2361no—
373C2×C4—2361no—
374C2×C4C42×D5911yescharacteristic
375C2×C4C2×(C2×D59)⋊C411yescharacteristic
376C2×C4C4×C22⋊D5911yescharacteristic
377C2×C4C4×D23611yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—2362no—
383C8—2361no—
384C8—2361no—
385C8#1427364112yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C4×(C2×D59)⋊C411yescharacteristic
398C22#1683752212yes—
399C22#1683752512yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—82no—
404C4—4722no—
405C4—2361no—
406C4—2361no—
407C4—2361no—
408C4C2×#1427364111yescharacteristic
409C4#1683737511yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—4721no—
414C2C4×#1427364111yescharacteristic
415C2#2142394011yescharacteristic
416C2#2142394211yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC59×#1752C2
socleC22×C59C4×C22⋊C4
prime radical#16837913C22
cosocleC23×C4×C59C23
hypercenter#1752D59
hypocenterC59#8239
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. #21423872C2semidirect
5. #21421984C2semidirect
6. #21421982C2semidirect
7. C59×#1752C2semidirect
8. C2×#14273733C4semidirect
14. #16837428C4semidirect
15. #16837368C4semidirect
18. #16837357C4semidirect
22. #16837140C4semidirect
23. #16837138C4semidirect
24. #16837137C4semidirect
25. #16837135C4semidirect
204. #1752D59semidirect
239. C59#8239semidirect

Maximal subgroups

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

subgroupindex
#214327902
#214238722
#214225882
#214225852
#214219842
#214219822
C59×#17522
#823959