Finite Group Databasebeta

← #28504993

Subgroups — #28504993

Order 15104.

420 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D59C211yesmaximal, characteristic
2#21425706C211yesmaximal, characteristic
3#21424118C211yesmaximal, characteristic
4#21422203C211yesmaximal, characteristic, complemented
5#21422202C211yesmaximal, characteristic, complemented
6#21422201C211yesmaximal, characteristic, complemented
7C59×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D59C2211yescharacteristic
9#117×D59—21no—
10C2×#14273667C2211yescharacteristic
11#16837440C2211yescharacteristic
12#16837439C411yescharacteristic, complemented
13#16837439C411yescharacteristic, complemented
14#16837438—21no—
15#16837437—21no—
16#107×D59C411yescharacteristic, complemented
17#107×D59C411yescharacteristic, complemented
18C2×#14273659C2211yescharacteristic
19#106×D59—21no—
20#16837259—21no—
21(C2×D59)⋊C16—21no—
22(C2×D59)⋊C16—21no—
23#16837164—21no—
24C2×M32×C59C2211yescharacteristic
25C59×#427C2211yescharacteristic
26C2×#106×C59C2211yescharacteristic
27C22×C4×D59D411yescharacteristic
28C22×C59⋊C8D411yescharacteristic
29C2×C8×D59—21no—
30C2×C8×D59—21no—
31C2×C8×D59—21no—
32C2×C8×D59—21no—
33C2×C8×D59C2×C411yescharacteristic
34C2×C8×D59C2×C411yescharacteristic
35C2×C8×D59D411yescharacteristic
36C2×C8×D59D411yescharacteristic
37#14273686—21no—
38#14273685—21no—
39#14273685—21no—
40#14273684—41no—
41#14273683—41no—
42C2×C4⋊Dic59—21no—
43C4⋊C4×D59—21no—
44C4⋊C4×D59—21no—
45C2×(C2×D59)⋊C4—41no—
46C22⋊C4×D59—41no—
47C42×D59—41no—
48#14273667—21no—
49#14273667—21no—
50C2×C59⋊C16—21no—
51#14273661C2×C411yescharacteristic
52#14273661C2×C411yescharacteristic
53#14273660—21no—
54#14273660—21no—
55#14273659—21no—
56#14273659—21no—
57#14273659—21no—
58#14273658—21no—
59#14273658—21no—
60C59⋊#95—41no—
61C22×C8×C59C2311yescharacteristic
62#117×C59—21no—
63C2×C4⋊C4×C59—21no—
64M32×C59—21no—
65M32×C59—21no—
66C2×C16×C59—21no—
67#107×C59C2×C411yescharacteristic
68#107×C59C2×C411yescharacteristic
69#106×C59—21no—
70#106×C59—21no—
71#106×C59—21no—
72C23×D59D811yescharacteristic
73C22×C4×C59—41no—
74C22×C4×C59C2×D411yescharacteristic
75C22×Dic59—41no—
76C22×Dic59D811yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×C4×D59C22⋊C411yescharacteristic
84C2×C4×D59C22⋊C411yescharacteristic
85C2×C4×D59SD1611yescharacteristic
86C2×C4×D59SD1611yescharacteristic
87C2×C8×C59C22×C411yescharacteristic
88C2×C8×C59C2×D411yescharacteristic
89C2×C8×C59#4111yescharacteristic
90C2×C8×C59#4111yescharacteristic
91C2×C8×C59#4111yescharacteristic
92C2×C8×C59#4111yescharacteristic
93C4⋊C4×C59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59—41no—
96C4⋊C4×C59—41no—
97C22⋊C4×C59—41no—
98C42×C59—41no—
99C22⋊Dic59—41no—
100(C2×D59)⋊C4—41no—
101(C2×D59)⋊C4—41no—
102(C2×D59)⋊C4—82no—
103C4⋊Dic59—21no—
104C4⋊Dic59—21no—
105C4⋊Dic59—41no—
106C4⋊Dic59—41no—
107Dic59⋊C4—41no—
108Dic59⋊C4—41no—
109C4×Dic59—41no—
110C4×Dic59—41no—
111C4×Dic59—41no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8C22⋊C411yescharacteristic
115C2×C59⋊C8C22⋊C411yescharacteristic
116C8×D59—21no—
117C8×D59—21no—
118C8×D59—21no—
119C8×D59—21no—
120C8×D59—21no—
121C8×D59—21no—
122C8×D59—21no—
123C8×D59—21no—
124C16×C59—41no—
125C59⋊C16—41no—
126C23×C59C2×D811yescharacteristic
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—22no—
130C22×D59—41no—
131C22×D59#10211yescharacteristic
132C22×D59#10211yescharacteristic
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—81no—
136C2×C4×C59—81no—
137C2×C4×C59—81no—
138C2×C4×C59C2×C22⋊C411yescharacteristic
139C2×C4×C59#12311yescharacteristic
140C2×C4×C59#12311yescharacteristic
141C2×C4×C59C2×SD1611yescharacteristic
142C2×C4×C59#13711yescharacteristic
143C2×C4×C59#13711yescharacteristic
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—81no—
149C2×Dic59—81no—
150C2×Dic59—81no—
151C2×Dic59#10211yescharacteristic
152C2×Dic59#10211yescharacteristic
153C4×D59—21no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—21no—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—82no—
162C4×D59—82no—
163C8×C59#11711yescharacteristic
164C8×C59#11711yescharacteristic
165C8×C59#12311yescharacteristic
166C8×C59#12311yescharacteristic
167C59⋊C8—21no—
168C59⋊C8—21no—
169#12870—591nomaximal, Sylow
170C22×C59—21no—
171C22×C59—21no—
172C22×C59C2×#10211yescharacteristic
173C22×C59#48011yescharacteristic
174C22×C59#48011yescharacteristic
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—42no—
181C2×D59—42no—
182C2×D59#36012yes—
183C4×C59—81no—
184C4×C59—81no—
185C4×C59—161no—
186C4×C59#38111yescharacteristic
187C4×C59#41911yescharacteristic
188C4×C59#48311yescharacteristic
189C4×C59#48311yescharacteristic
190Dic59—21no—
191Dic59—21no—
192Dic59—81no—
193Dic59—81no—
194Dic59—161no—
195C2×#427—591no—
196#2112—591no—
197#1807—591no—
198#1386—591no—
199#1386—591no—
200#1386—591no—
201#1386D5911yescharacteristic, complemented
202C2×C59—21no—
203C2×C59—21no—
204C2×C59#182311yescharacteristic
205C2×C59C2×#36011yescharacteristic
206C2×C59#214511yescharacteristic
207D59—22no—
208D59—41no—
209C23×C8—591no—
210C2×#117—1181no—
211C2×M32—591no—
212C2×M32C2×D5911yescharacteristic
213#427—591no—
214#427—591no—
215#427—591no—
216#427—1181no—
217#427—1181no—
218#427C2×D5911yescharacteristic
219C2×#107—591no—
220C2×#107—591no—
221C2×#106—591no—
222C2×#106—1181no—
223C2×#106C2×D5911yescharacteristic
224#380—1181no—
225C22⋊C16—1181no—
226C22⋊C16—1181no—
227#340—1181no—
228C59#1287011yescharacteristic, complemented, Sylow
229C23×C4—591no—
230C22×C8—591no—
231C22×C8—591no—
232C22×C8—591no—
233C22×C8—591no—
234C22×C8—591no—
235C22×C8—1181no—
236C22×C8—1181no—
237C22×C8—1181no—
238C22×C8—1181no—
239C22×C8C22×D5911yescharacteristic
240#117—21no—
241#117—1181no—
242#117—1181no—
243#117—1181no—
244#117—2361no—
245#117—2361no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1181no—
248C2×C4⋊C4—1181no—
249C2×C4⋊C4—1181no—
250C2×C22⋊C4—2361no—
251C2×C22⋊C4—2361no—
252C2×C42—2361no—
253M32—21no—
254M32—21no—
255M32—1181no—
256M32—1181no—
257C2×C16—21no—
258C2×C16—1181no—
259#107—591no—
260#107—591no—
261#107—1181no—
262#107—1181no—
263#107C4×D5911yescharacteristic
264#107C4×D5911yescharacteristic
265#106—21no—
266#106—21no—
267#106—21no—
268#106—1181no—
269#106—1181no—
270#106—1181no—
271#106—1181no—
272#106—1181no—
273#95—2361no—
274C24—591no—
275C22×C4—41no—
276C22×C4—591no—
277C22×C4—591no—
278C22×C4—591no—
279C22×C4—591no—
280C22×C4—591no—
281C22×C4—1181no—
282C22×C4—1181no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—2361no—
286C22×C4—2361no—
287C22×C4—2361no—
288C22×C4D4×D5911yescharacteristic
289C2×C8—591no—
290C2×C8—591no—
291C2×C8—1181no—
292C2×C8—1181no—
293C2×C8—1181no—
294C2×C8—1181no—
295C2×C8—1181no—
296C2×C8—1181no—
297C2×C8—1181no—
298C2×C8—1181no—
299C2×C8—1181no—
300C2×C8—1181no—
301C2×C8C2×C4×D5911yescharacteristic
302C2×C8#1174568511yescharacteristic
303C2×C8#1174568511yescharacteristic
304C2×C8D4×D5911yescharacteristic
305C2×C8#1174568711yescharacteristic
306C2×C8#1174568911yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—2361no—
314C4⋊C4—2361no—
315C4⋊C4—2361no—
316C4⋊C4—2361no—
317C22⋊C4—41no—
318C22⋊C4—4722no—
319C22⋊C4—2361no—
320C22⋊C4—2361no—
321C22⋊C4—2361no—
322C42—41no—
323C42—2361no—
324C42—2361no—
325C42—2361no—
326C16—41no—
327C16—2361no—
328C23—591no—
329C23—591no—
330C23—1182no—
331C23—1181no—
332C23—1181no—
333C23—2361no—
334C23D8×D5911yescharacteristic
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—4722no—
353C2×C4—4722no—
354C2×C4—4721no—
355C2×C4—4721no—
356C2×C4—4721no—
357C2×C4—2361no—
358C2×C4—2361no—
359C2×C4C22⋊C4×D5911yescharacteristic
360C2×C4#1427370911yescharacteristic
361C2×C4#1427371211yescharacteristic
362C2×C4SD16×D5911yescharacteristic
363C2×C4#1427375611yescharacteristic
364C2×C4#1427375911yescharacteristic
365C8—1181no—
366C8—1181no—
367C8#1427368411yescharacteristic
368C8#1427368511yescharacteristic
369C8#1427370911yescharacteristic
370C8#1427371211yescharacteristic
371C22—21no—
372C22—21no—
373C22—592no—
374C22—1181no—
375C22—1181no—
376C22—1181no—
377C22—1181no—
378C22—1181no—
379C22—2362no—
380C22—2362no—
381C22#102×D5911yescharacteristic
382C22#1683771411yescharacteristic
383C22#1683771711yescharacteristic
384C4—81no—
385C4—81no—
386C4—161no—
387C4—1181no—
388C4—1181no—
389C4—9441no—
390C4—4721no—
391C4—4721no—
392C4#1683726411yescharacteristic
393C4#1683740911yescharacteristic
394C4#1683773111yescharacteristic
395C4#1683773411yescharacteristic
396C2—21no—
397C2—21no—
398C2—1182no—
399C2—2361no—
400C2#2142418111yescharacteristic
401C2#360×D5911yescharacteristic
402C2#2142583011yescharacteristic
subgroupG/H
centerC22#102×D59
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC59×#1386C2
socleC22×C59C2×#102
prime radicalC23×D59D8
cosocleC22×C8×C59C23
hypercenter#1386D59
hypocenterC59#12870
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #21422203C2semidirect
5. #21422202C2semidirect
6. #21422201C2semidirect
7. C59×#1386C2semidirect
12. #16837439C4semidirect
13. #16837439C4semidirect
16. #107×D59C4semidirect
17. #107×D59C4semidirect
201. #1386D59semidirect
228. C59#12870semidirect

Maximal subgroups

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

subgroupindex
#427×D592
#214257062
#214241182
#214222032
#214222022
#214222012
C59×#13862
#1287059