Finite Group Databasebeta

← #28487836

Subgroups — #28487836

Order 15104.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434655C211yesmaximal, characteristic
2#21425039C211yesmaximal, characteristic, complemented
3#21425014C211yesmaximal, characteristic
4#21422594C211yesmaximal, characteristic, complemented
5#21422590C211yesmaximal, characteristic
6C8×#11745664C211yesmaximal, characteristic, complemented
7C4×#106×C59C211yesmaximal, characteristic, complemented
8#16837959C2211yescharacteristic
9#16837952C2211yescharacteristic
10#16837800C411yescharacteristic, complemented
11#16837775C411yescharacteristic, complemented
12#16837753C411yescharacteristic, complemented
13#16837749C411yescharacteristic, complemented
14#16837631—21no—
15#16837631—21no—
16C4×#11745660—21no—
17C4×#11745660—21no—
18#16837455C2211yescharacteristic
19C2×#14273655—22no—
20C4×#11745664C2211yescharacteristic
21#16837162—22no—
22#16837138—22no—
23#16837135—22no—
24#16837124—21no—
25C8×C59⋊C8—21no—
26C2×#106×C59—21no—
27C2×C4×C8×C59C2211yescharacteristic
28C4×C4⋊C4×C59C2211yescharacteristic
29C4×C4⋊C4×C59C2211yescharacteristic
30C59×#340—21no—
31C2×#11745685—21no—
32C2×#11745660—21no—
33C2×#11745660—21no—
34C2×#11745664D412yes—
35#14273727C2×C411yescharacteristic
36#14273727C2×C411yescharacteristic
37#14273727C2×C411yescharacteristic
38#14273724C2×C411yescharacteristic
39#14273719—21no—
40#14273715—21no—
41#14273706—21no—
42#14273706—21no—
43#14273701—21no—
44#14273701—21no—
45C4×Dic118—21no—
46C4×Dic118—21no—
47C4×D236—21no—
48C4×D236—21no—
49#14273686—21no—
50#14273659—21no—
51#14273659—21no—
52C4⋊(C59⋊C8)—21no—
53#14273655—44no—
54#14273652—21no—
55#14273652—21no—
56#14273649—21no—
57#14273649—21no—
58C22⋊(C59⋊C8)D412yes—
59#14273638—21no—
60C4×C59⋊C8—21no—
61C4×C59⋊C8—21no—
62C22×C8×C59D411yescharacteristic
63C22×C8×C59D411yescharacteristic
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C42×C59—21no—
67C2×C42×C59—21no—
68C2×C42×C59C2311yescharacteristic
69#106×C59—24no—
70C4×C8×C59C2×C411yescharacteristic
71C4×C8×C59C2×C411yescharacteristic
72C4×C8×C59D411yescharacteristic
73C4×C8×C59D411yescharacteristic
74#95×C59—21no—
75#95×C59—21no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59C2×D411yescharacteristic
81C2×C22⋊D59—41no—
82#11745685—42no—
83#11745685—42no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236—21no—
87C2×C4×D59—41no—
88C2×Dic118—21no—
89C2×Dic118—21no—
90C2×Dic118—21no—
91C2×C8×C59—22no—
92C2×C8×C59—41no—
93C2×C8×C59C22⋊C411yescharacteristic
94C2×C8×C59C22⋊C411yescharacteristic
95C2×C8×C59C22⋊C411yescharacteristic
96C2×C8×C59C22⋊C411yescharacteristic
97C4⋊C4×C59—22no—
98C4⋊C4×C59—22no—
99C4⋊C4×C59—41no—
100C4⋊C4×C59—41no—
101C42×C59—42no—
102C42×C59—42no—
103C42×C59C22×C411yescharacteristic
104C42×C59C2×D411yescharacteristic
105C42×C59#4111yescharacteristic
106C42×C59#4111yescharacteristic
107C22⋊Dic59—41no—
108(C2×D59)⋊C4—41no—
109(C2×D59)⋊C4—41no—
110C4⋊Dic59—21no—
111C4⋊Dic59—21no—
112C4⋊Dic59—21no—
113C4⋊Dic59—21no—
114C4⋊Dic59—21no—
115C4⋊Dic59—21no—
116Dic59⋊C4—41no—
117Dic59⋊C4—41no—
118C4×Dic59—41no—
119#11745664—22no—
120#11745664SD1614yescomplemented
121C2×C59⋊C8—22no—
122C2×C59⋊C8—22no—
123#11745660—42no—
124#11745660—42no—
125C23×C59#12711yescharacteristic
126C22×D59—41no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—41no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59—81no—
133C2×C4×C59—81no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59C2×C22⋊C411yescharacteristic
137C2×C4×C59C4×D411yescharacteristic
138C2×C4×C59C4×D411yescharacteristic
139C2×C4×C59#12111yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12411yescharacteristic
142C2×C4×C59C2×SD1612yes—
143C2×C4×C59#13512yes—
144C22⋊D59—81no—
145C22⋊D59—81no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149D236—41no—
150D236—41no—
151D236—42no—
152D236—81no—
153C4×D59—82no—
154Dic118—41no—
155Dic118—41no—
156Dic118—42no—
157Dic118—81no—
158C8×C59—21no—
159C8×C59—21no—
160C8×C59—21no—
161C8×C59#10412yescomplemented
162C59⋊C8—24no—
163C59⋊C8—42no—
164#9717—591nomaximal, Sylow
165C22×C59—21no—
166C22×C59—21no—
167C22×C59#39011yescharacteristic
168C22×C59#49211yescharacteristic
169C22×C59#49511yescharacteristic
170C2×D59—81no—
171C2×D59—81no—
172C2×D59—81no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—82no—
177C4×C59—82no—
178C4×C59C2×#10411yescharacteristic
179C4×C59#42111yescharacteristic
180C4×C59C4×SD1612yes—
181C4×C59#46512yes—
182Dic59—81no—
183Dic59—81no—
184Dic59—81no—
185#3167—591no—
186#1986—591no—
187#1980—591no—
188C4×#106D5911yescharacteristic, complemented
189#1503—591no—
190#1502—591no—
191C8×M16—591no—
192C2×C59—21no—
193C2×C59—21no—
194C2×C59#196811yescharacteristic
195C2×C59#197611yescharacteristic
196C2×C59#198011yescharacteristic
197D59—161no—
198#533—591no—
199#532—591no—
200#498—591no—
201#492—591no—
202#487—591no—
203#486—591no—
204#465—1181no—
205#465—1181no—
206C4×SD16—1181no—
207C4×SD16—1181no—
208#431—591no—
209C2×#106—21no—
210C2×#104—1182no—
211C4×M16—591no—
212C2×C4×C8C2×D5911yescharacteristic
213C4×C4⋊C4C2×D5911yescharacteristic
214C4×C4⋊C4C2×D5911yescharacteristic
215#340—21no—
216#339—1182no—
217#328—1182no—
218#327—1182no—
219#322—1181no—
220C82—1181no—
221C59#971711yescharacteristic, complemented, Sylow
222C2×#41—1181no—
223C2×SD16—1181no—
224C2×SD16—1181no—
225C2×M16—592no—
226C22×C8C22⋊D5911yescharacteristic
227C22×C8C22⋊D5911yescharacteristic
228C4⋊Q8—591no—
229C4⋊Q8—591no—
230C4⋊Q8—591no—
231#127—591no—
232#125—1181no—
233#124—1181no—
234C22⋊Q8—1181no—
235C22⋊Q8—1181no—
236#121—1181no—
237#121—1181no—
238C4×Q8—1181no—
239C4×Q8—1181no—
240C4×D4—1181no—
241C4×D4—1181no—
242#117—1181no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C22×D5911yescharacteristic
248#106—24no—
249#106—1181no—
250#106—1181no—
251C4⋊C8—1181no—
252#104—2364no—
253#103—1181no—
254#103—1181no—
255#102—1181no—
256#102—1181no—
257C22⋊C8—592no—
258#97—1181no—
259C4×C8—1181no—
260C4×C8—1181no—
261C4×C8C4×D5911yescharacteristic
262C4×C8C4×D5911yescharacteristic
263C4×C8D23611yescharacteristic
264C4×C8D23611yescharacteristic
265#95—21no—
266#95—21no—
267#41—2362no—
268#41—2362no—
269C2×Q8—1181no—
270C2×Q8—1181no—
271C2×Q8—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—2361no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—2361no—
279C22×C4D4×D5911yescharacteristic
280C22×C4D4×D5911yescharacteristic
281C22×C4C2×C22⋊D5911yescharacteristic
282SD16—2362no—
283SD16—2362no—
284M16—594no—
285M16—1182no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—1182no—
289C2×C8—1182no—
290C2×C8(C2×D59)⋊C411yescharacteristic
291C2×C8(C2×D59)⋊C411yescharacteristic
292C2×C8(C2×D59)⋊C411yescharacteristic
293C2×C8(C2×D59)⋊C411yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4—1181no—
302C4⋊C4—1181no—
303C4⋊C4—1181no—
304C4⋊C4—2361no—
305C4⋊C4—2361no—
306C22⋊C4—2361no—
307C22⋊C4—2361no—
308C22⋊C4—2361no—
309C42—42no—
310C42—42no—
311C42—2361no—
312C42C2×C4×D5911yescharacteristic
313C42C2×D23611yescharacteristic
314C42#1174568911yescharacteristic
315C42#1174568911yescharacteristic
316C23—2361no—
317C23#1427372311yescharacteristic
318Q8—4721no—
319Q8—2361no—
320Q8—2361no—
321Q8—2362no—
322D4—4721no—
323D4—4721no—
324D4—4721no—
325D4—2361no—
326D4—2361no—
327D4—2362no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—4722no—
338C2×C4—2361no—
339C2×C4—2361no—
340C2×C4—2361no—
341C2×C4C2×(C2×D59)⋊C411yescharacteristic
342C2×C4#1427368911yescharacteristic
343C2×C4#1427368911yescharacteristic
344C2×C4#1427370211yescharacteristic
345C2×C4#1427370211yescharacteristic
346C2×C4#1427371611yescharacteristic
347C2×C4SD16×D5912yes—
348C2×C4#1427374812yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—1184no—
353C8—2362no—
354C8#1427365512yescomplemented
355C22—21no—
356C22—21no—
357C22—4721no—
358C22—4721no—
359C22—4721no—
360C22#1683730311yescharacteristic
361C22#1683777311yescharacteristic
362C22#1683778311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—4721no—
369C4—4721no—
370C4—4721no—
371C4C2×#1427365511yescharacteristic
372C4#1683742011yescharacteristic
373C4#1683748912yes—
374C4#1683763212yes—
375C2—21no—
376C2—21no—
377C2—9441no—
378C2#2142494811yescharacteristic
379C2#2142499211yescharacteristic
380C2#2142501411yescharacteristic
subgroupG/H
centerC2×C4#14273702
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#106×C59C2
socleC22×C59#390
prime radical#16837952C22
cosocleC2×C42×C59C23
hypercenterC4×#106D59
hypocenterC59#9717
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. #21425039C2semidirect
4. #21422594C2semidirect
6. C8×#11745664C2semidirect
7. C4×#106×C59C2semidirect
10. #16837800C4semidirect
11. #16837775C4semidirect
12. #16837753C4semidirect
13. #16837749C4semidirect
120. #11745664SD16semidirect
161. C8×C59#104semidirect
188. C4×#106D59semidirect
221. C59#9717semidirect
354. C8#14273655semidirect

Maximal subgroups

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

subgroupindex
#214346552
#214250392
#214250142
#214225942
#214225902
C8×#117456642
C4×#106×C592
#971759