Finite Group Databasebeta

← #28488037

Subgroups — #28488037

Order 15104.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434421C211yesmaximal, characteristic
2C4⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
3#21422842C211yesmaximal, characteristic, complemented
4#21422590C211yesmaximal, characteristic
5#21422499C211yesmaximal, characteristic, complemented
6#21422496C211yesmaximal, characteristic
7C59×#1503C211yesmaximal, characteristic, complemented
8#16837952C2211yescharacteristic
9#16837759—21no—
10#16837759—21no—
11#16837754C411yescharacteristic, complemented
12#16837754C411yescharacteristic, complemented
13#16837750C411yescharacteristic, complemented
14#16837750C411yescharacteristic, complemented
15#16837455C2211yescharacteristic
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17#16837396—21no—
18#16837396—21no—
19C2×C4×C59⋊C8—21no—
20C2×C4×C59⋊C8C2211yescharacteristic
21#16837157—21no—
22#16837154—21no—
23#16837152—21no—
24#16837135—22no—
25Q8⋊(C59⋊C8)—22no—
26#16837131—22no—
27C59×#533C2211yescharacteristic
28C59×#431C2211yescharacteristic
29C4×C4⋊C4×C59C2211yescharacteristic
30C59×#328—22no—
31C2×#11745685—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8D411yescharacteristic
34C22×C59⋊C8D411yescharacteristic
35#14273727C2×C411yescharacteristic
36#14273724C2×C411yescharacteristic
37#14273715—21no—
38#14273701—21no—
39#14273701—21no—
40C4×D236—21no—
41C4×D236—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)D412yes—
45#14273650—21no—
46#14273650—21no—
47#14273650—21no—
48#14273650—21no—
49#14273647—21no—
50#14273647—21no—
51#14273647—21no—
52#14273647—21no—
53C22⋊(C59⋊C8)—21no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8—42no—
56C4×C59⋊C8C2×C411yescharacteristic
57C4×C59⋊C8C2×C411yescharacteristic
58C4×C59⋊C8D411yescharacteristic
59C4×C59⋊C8D411yescharacteristic
60C4⋊Q8×C59C2×C411yescharacteristic
61C4⋊Q8×C59C2×C411yescharacteristic
62#125×C59—21no—
63C22⋊Q8×C59—21no—
64C22⋊Q8×C59—21no—
65C4×Q8×C59—21no—
66C4×Q8×C59—21no—
67#117×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C42×C59—21no—
70C2×C42×C59C2311yescharacteristic
71C4⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73C4×C8×C59—21no—
74#95×C59D412yes—
75C2×Q8×C59—21no—
76C2×Q8×C59—21no—
77C22×C4×C59—22no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C2×C22⋊D59—41no—
82#11745685—41no—
83#11745685—41no—
84#11745685—41no—
85#11745685—41no—
86C2×D236—21no—
87C2×D236—21no—
88C2×D236—21no—
89C2×C4×D59—41no—
90C2×Dic118—21no—
91C2×C8×C59—41no—
92C4⋊C4×C59—24no—
93C4⋊C4×C59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59—21no—
96C4⋊C4×C59—21no—
97C4⋊C4×C59—41no—
98C4⋊C4×C59—41no—
99C22⋊C4×C59—41no—
100C42×C59—41no—
101C42×C59—41no—
102C42×C59—41no—
103C42×C59C22×C411yescharacteristic
104C42×C59C2×D411yescharacteristic
105C42×C59C2×D411yescharacteristic
106C42×C59#4111yescharacteristic
107(C2×D59)⋊C4—41no—
108(C2×D59)⋊C4—41no—
109C4⋊Dic59—21no—
110C4⋊Dic59—21no—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8—21no—
115C2×C59⋊C8—22no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8C22⋊C411yescharacteristic
120C2×C59⋊C8C22⋊C411yescharacteristic
121C2×C59⋊C8C22⋊C411yescharacteristic
122C2×C59⋊C8C22⋊C411yescharacteristic
123C23×C59#12111yescharacteristic
124C22×D59—41no—
125Q8×C59—42no—
126Q8×C59—81no—
127C2×C4×C59—22no—
128C2×C4×C59—24no—
129C2×C4×C59—41no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59C2×C22⋊C411yescharacteristic
135C2×C4×C59C4×D411yescharacteristic
136C2×C4×C59C4×D411yescharacteristic
137C2×C4×C59#12111yescharacteristic
138C2×C4×C59#12411yescharacteristic
139C2×C4×C59#12711yescharacteristic
140C2×C4×C59#13511yescharacteristic
141C2×C4×C59#13511yescharacteristic
142C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C59#13711yescharacteristic
144C22⋊D59—81no—
145C22⋊D59—81no—
146C2×Dic59—41no—
147D236—41no—
148D236—41no—
149D236—42no—
150D236—81no—
151C4×D59—81no—
152C4×D59—81no—
153Dic118—41no—
154Dic118—41no—
155C8×C59—81no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C59⋊C8—42no—
161C59⋊C8—81no—
162#9751—591nomaximal, Sylow
163C22×C59—21no—
164C22×C59—21no—
165C22×C59#39011yescharacteristic
166C22×C59#46311yescharacteristic
167C22×C59#46411yescharacteristic
168C2×D59—81no—
169C2×D59—81no—
170C2×D59—81no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—44no—
175C4×C59—81no—
176C4×C59—81no—
177C4×C59#41611yescharacteristic
178C4×C59#41711yescharacteristic
179C4×C59#44312yes—
180C4×C59#46311yescharacteristic
181C4×C59#46411yescharacteristic
182Dic59—81no—
183#3131—591no—
184C8×C4⋊C4—591no—
185#1564—591no—
186#1503D5911yescharacteristic, complemented
187#1502—591no—
188#1481—591no—
189#1480—591no—
190C2×C59—21no—
191C2×C59—21no—
192C2×C59#197411yescharacteristic
193C2×C59#197611yescharacteristic
194C2×C59#198311yescharacteristic
195D59—161no—
196#533C2×D5911yescharacteristic
197#532—591no—
198#488—1181no—
199#488—1181no—
200#487—591no—
201#487—591no—
202#486—591no—
203#486—591no—
204#431—591no—
205#431C2×D5911yescharacteristic
206C2×C4⋊C8—591no—
207#416—1181no—
208#416—1181no—
209C2×C4×C8—591no—
210C2×C4×C8—1181no—
211C4×C4⋊C4C2×D5911yescharacteristic
212#336—1181no—
213#335—1181no—
214#334—1181no—
215#328—22no—
216#327—1182no—
217Q8⋊C8—1182no—
218D4⋊C8—1182no—
219C59#975111yescharacteristic, complemented, Sylow
220C2×#41—1181no—
221C22×C8—591no—
222C22×C8—591no—
223C22×C8—1181no—
224C4⋊Q8—591no—
225C4⋊Q8C4×D5911yescharacteristic
226C4⋊Q8C4×D5911yescharacteristic
227#127—591no—
228#125—21no—
229#124—1181no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—1181no—
233#121—1181no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—1181no—
237C4×D4—1181no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D5911yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—592no—
244C4⋊C8—1181no—
245C4⋊C8—1181no—
246#103—1181no—
247#103—1181no—
248#103—1181no—
249#103—1181no—
250#102—1181no—
251#102—1181no—
252#102—1181no—
253#102—1181no—
254C22⋊C8—21no—
255C22⋊C8—1181no—
256C4×C8—21no—
257C4×C8—591no—
258C4×C8—591no—
259C4×C8—591no—
260C4×C8—591no—
261C4×C8—1181no—
262C4×C8—2362no—
263#95C22⋊D5912yes—
264#41—2361no—
265#41—2361no—
266#41—2361no—
267#41—2361no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—2361no—
275C22×C4—22no—
276C22×C4—2361no—
277C22×C4D4×D5911yescharacteristic
278C22×C4#1174568711yescharacteristic
279C22×C4C2×C22⋊D5911yescharacteristic
280C2×C8—41no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8—1181no—
286C2×C8—1181no—
287C2×C8—1181no—
288C2×C8—1181no—
289C2×C8—1182no—
290C2×C8—2361no—
291C2×C8—2361no—
292C2×C8—2361no—
293C4⋊C4—24no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1181no—
301C4⋊C4—1181no—
302C22⋊C4—41no—
303C22⋊C4—2361no—
304C22⋊C4—2361no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×C4×D5911yescharacteristic
309C42#1174568511yescharacteristic
310C42D4×D5911yescharacteristic
311C42D4×D5911yescharacteristic
312C23—2361no—
313C23#1427369911yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—2361no—
317Q8—2361no—
318D4—4721no—
319D4—4721no—
320D4—4721no—
321D4—2361no—
322D4—2361no—
323D4—2362no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—4721no—
332C2×C4—4721no—
333C2×C4—2361no—
334C2×C4C22⋊C4×D5911yescharacteristic
335C2×C4(C22⋊D59)⋊C411yescharacteristic
336C2×C4C4×C22⋊D5911yescharacteristic
337C2×C4#1427370011yescharacteristic
338C2×C4#1427371311yescharacteristic
339C2×C4#1427372311yescharacteristic
340C2×C4#1427374811yescharacteristic
341C2×C4#1427375011yescharacteristic
342C2×C4#1427375411yescharacteristic
343C2×C4#1427375911yescharacteristic
344C8—81no—
345C8—1181no—
346C8—1181no—
347C8—1181no—
348C8—1181no—
349C8—4721no—
350C8—2362no—
351C22—21no—
352C22—21no—
353C22—4721no—
354C22—4721no—
355C22—4721no—
356C22#1683730211yescharacteristic
357C22#1683761911yescharacteristic
358C22#1683762611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—81no—
364C4—81no—
365C4—4721no—
366C4#1683739711yescharacteristic
367C4#1683740211yescharacteristic
368C4#1683751612yes—
369C4#1683762011yescharacteristic
370C4#1683762711yescharacteristic
371C2—21no—
372C2—21no—
373C2—9441no—
374C2#2142498111yescharacteristic
375C2#2142499111yescharacteristic
376C2#2142502511yescharacteristic
subgroupG/H
centerC2×C4#14273700
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1503C2
socleC22×C59#390
prime radical#16837952C22
cosocleC2×C42×C59C23
hypercenter#1503D59
hypocenterC59#9751
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C59⋊C8C2semidirect
3. #21422842C2semidirect
5. #21422499C2semidirect
7. C59×#1503C2semidirect
11. #16837754C4semidirect
12. #16837754C4semidirect
13. #16837750C4semidirect
14. #16837750C4semidirect
186. #1503D59semidirect
219. C59#9751semidirect

Maximal subgroups

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

subgroupindex
#214344212
C4⋊C4×C59⋊C82
#214228422
#214225902
#214224992
#214224962
C59×#15032
#975159