Finite Group Databasebeta

← #28485123

Subgroups — #28485123

Order 15104.

524 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837738C211yesmaximal, characteristic
2#21426975C211yesmaximal, characteristic
3#21425080C211yesmaximal, characteristic
4#21424184C211yesmaximal, characteristic
5#21422667C211yesmaximal, characteristic
6#21421943C211yesmaximal, characteristic
7C59×#1289C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9C22×C4⋊Dic59C2211yescharacteristic
10#16837738—22no—
11#16837738—21no—
12#16837738—21no—
13C2×#14273661C412yescomplemented
14C2×#14273652C412yescomplemented
15C2×C22⋊(C59⋊C8)C2211yescharacteristic
16#16837298—21no—
17#16837287—22no—
18#16837260—21no—
19C4⋊C4×Dic59—21no—
20C22⋊C4×Dic59—21no—
21C4×C22⋊Dic59C2211yescharacteristic
22#16837168—21no—
23#16837168—21no—
24#16837164—22no—
25#16837138—22no—
26C2×C22⋊C8×C59C2211yescharacteristic
27C59×#380C2211yescharacteristic
28C59×#380C2211yescharacteristic
29C22×Dic118C2×C411yescharacteristic
30C23×Dic59—21no—
31C22×C59⋊C8—21no—
32#14273706—21no—
33#14273706—21no—
34#14273706—21no—
35#14273706—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—21no—
38C2×C4⋊Dic59—21no—
39C2×C4⋊Dic59C2×C411yescharacteristic
40C2×C4⋊Dic59C2×C412yes—
41C2×C4⋊Dic59D412yes—
42C2×C4⋊Dic59D411yescharacteristic
43C2×C4⋊Dic59D411yescharacteristic
44C2×Dic59⋊C4—21no—
45C2×Dic59⋊C4—22no—
46C2×C22⋊Dic59—21no—
47C2×C22⋊Dic59D411yescharacteristic
48C2×C22⋊Dic59D411yescharacteristic
49C2×C4×Dic59—21no—
50C2×C4×Dic59—22no—
51#14273661—22no—
52#14273661—22no—
53#14273652—22no—
54#14273652—22no—
55C22⋊(C59⋊C8)—21no—
56C22⋊(C59⋊C8)—21no—
57C59⋊#95—22no—
58C59⋊#95—22no—
59C59⋊#95—21no—
60C23×C4×C59C2311yescharacteristic
61C22×C8×C59C2×C412yes—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C22⋊C4×C59—21no—
65C2×C22⋊C4×C59—21no—
66C22⋊C8×C59—21no—
67C22⋊C8×C59—21no—
68#95×C59—21no—
69#95×C59D412yes—
70C24×C59C2×D411yescharacteristic
71C22×C4×C59—22no—
72C22×C4×C59—42no—
73C22×C4×C59—41no—
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59#4111yescharacteristic
79C22×C4×C59#4111yescharacteristic
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C22×Dic59—22no—
84C22×Dic59—22no—
85C22×Dic59—21no—
86C22×Dic59—21no—
87C22×Dic59—21no—
88C22×Dic59—82no—
89C2×Dic118—21no—
90C2×Dic118—21no—
91C2×Dic118—42no—
92C2×C8×C59—22no—
93C2×C8×C59—42no—
94C4⋊C4×C59—42no—
95C4⋊C4×C59—42no—
96C22⋊C4×C59—41no—
97C22⋊C4×C59—41no—
98C22⋊C4×C59—41no—
99C22⋊C4×C59—41no—
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102C22⋊Dic59—21no—
103C22⋊Dic59—41no—
104C22⋊Dic59—41no—
105C22⋊Dic59Q1612yes—
106C4⋊Dic59—22no—
107C4⋊Dic59—22no—
108C4⋊Dic59—21no—
109C4⋊Dic59—21no—
110C4⋊Dic59—21no—
111C4⋊Dic59—21no—
112C4⋊Dic59C22⋊C412yes—
113C4⋊Dic59C22⋊C412yes—
114Dic59⋊C4—41no—
115Dic59⋊C4—41no—
116Dic59⋊C4—82no—
117C4×Dic59—42no—
118C4×Dic59—82no—
119C2×C59⋊C8—42no—
120C2×C59⋊C8—41no—
121C23×C59—41no—
122C23×C59—41no—
123C23×C59C4×D411yescharacteristic
124C23×C59#12011yescharacteristic
125C23×C59#12111yescharacteristic
126C23×C59C2×Q1611yescharacteristic
127C23×C59#13511yescharacteristic
128C23×C59#13711yescharacteristic
129C23×C59#13711yescharacteristic
130C2×C4×C59—22no—
131C2×C4×C59—22no—
132C2×C4×C59—22no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—42no—
137C2×C4×C59—42no—
138C2×C4×C59—42no—
139C2×C4×C59—81no—
140C2×C4×C59—81no—
141C2×C4×C59—81no—
142C2×C4×C59C2×C22⋊C411yescharacteristic
143C2×C4×C59C4×D411yescharacteristic
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12311yescharacteristic
146C2×Dic59—22no—
147C2×Dic59—22no—
148C2×Dic59—22no—
149C2×Dic59—41no—
150C2×Dic59—41no—
151C2×Dic59—42no—
152C2×Dic59—42no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158C2×Dic59—82no—
159C2×Dic59—82no—
160C2×Dic59—81no—
161C2×Dic59—81no—
162Dic118—42no—
163Dic118—81no—
164C8×C59—42no—
165C59⋊C8—81no—
166#9257—591nomaximal, Sylow
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59#38611yescharacteristic
178C22×C59C4×Q1611yescharacteristic
179C22×C59#44111yescharacteristic
180C22×C59#45111yescharacteristic
181C22×C59#45211yescharacteristic
182C22×C59#46211yescharacteristic
183C22×C59#46411yescharacteristic
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—82no—
188C4×C59—161no—
189C4×C59#41012yes—
190Dic59—42no—
191Dic59—42no—
192Dic59—42no—
193Dic59—81no—
194Dic59—81no—
195Dic59—81no—
196C2×#484—591no—
197#2345—591no—
198#1996—591no—
199#1824—591no—
200#1520—591no—
201#1289D5911yescharacteristic
202#1282—591no—
203C2×C59—21no—
204C2×C59—21no—
205C2×C59—21no—
206C2×C59—21no—
207C2×C59—21no—
208C2×C59—21no—
209C2×C59#187811yescharacteristic
210C2×C59#189911yescharacteristic
211C2×C59#190411yescharacteristic
212C2×C22⋊Q8—591no—
213C22×C4⋊C4—591no—
214#484—1182no—
215#484—1181no—
216#484—1181no—
217C2×#107—592no—
218C2×#103—592no—
219C2×C22⋊C8—591no—
220C2×C22⋊C8C2×D5911yescharacteristic
221#389—1181no—
222#387—1182no—
223#380—1181no—
224#380C2×D5911yescharacteristic
225#380C2×D5911yescharacteristic
226C4×C4⋊C4—1181no—
227C4×C22⋊C4—591no—
228C4×C22⋊C4—1181no—
229#342—1181no—
230#342—1181no—
231#340—1182no—
232#328—1182no—
233C59#925711yescharacteristic, complemented, Sylow
234C22×Q8—591no—
235C23×C4—1181no—
236C23×C4C22×D5911yescharacteristic
237C22×C8—1181no—
238C22×C8C4×D5912yes—
239C22⋊Q8—1181no—
240C22⋊Q8—1181no—
241C22⋊Q8—1181no—
242C22⋊Q8—1181no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—592no—
246C2×C4⋊C4—592no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4—591no—
249C2×C4⋊C4—591no—
250C2×C4⋊C4—1181no—
251C2×C4⋊C4—1181no—
252C2×C4⋊C4—1181no—
253C2×C4⋊C4—1182no—
254C2×C4⋊C4—1181no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—591no—
258C2×C22⋊C4—591no—
259C2×C22⋊C4—1181no—
260C2×C42—1182no—
261C2×C42—1181no—
262#107—1182no—
263#107—1182no—
264#103—1182no—
265#103—1182no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—1181no—
269C22⋊C8—1181no—
270#95—21no—
271#95—1182no—
272#95—1182no—
273#95—1181no—
274#95D23612yes—
275C24D4×D5911yescharacteristic
276C2×Q8—1181no—
277C2×Q8—1181no—
278C2×Q8—2362no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—1182no—
283C22×C4—1182no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—4722no—
291C22×C4C2×C4×D5911yescharacteristic
292C22×C4C2×D23611yescharacteristic
293C22×C4#1174568511yescharacteristic
294C22×C4D4×D5911yescharacteristic
295C22×C4D4×D5911yescharacteristic
296C22×C4#1174568911yescharacteristic
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—2362no—
300C2×C8—2361no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—592no—
304C4⋊C4—592no—
305C4⋊C4—1182no—
306C4⋊C4—1182no—
307C4⋊C4—1181no—
308C4⋊C4—1181no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4—4722no—
312C4⋊C4—2361no—
313C4⋊C4—2361no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—592no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—2361no—
323C22⋊C4—2361no—
324C42—4722no—
325C42—2362no—
326C23—41no—
327C23—41no—
328C23#1427368911yescharacteristic
329C23#1427369711yescharacteristic
330C23#1427370011yescharacteristic
331C23Q16×D5911yescharacteristic
332C23#1427374611yescharacteristic
333C23#1427375611yescharacteristic
334C23#1427375611yescharacteristic
335Q8—4721no—
336Q8—2362no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—1182no—
350C2×C4—1182no—
351C2×C4—1182no—
352C2×C4—4721no—
353C2×C4—4721no—
354C2×C4—4722no—
355C2×C4—4722no—
356C2×C4—2361no—
357C2×C4—2361no—
358C2×C4—2361no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4—2362no—
363C2×C4—2361no—
364C2×C4—2362no—
365C2×C4C22⋊C4×D5911yescharacteristic
366C2×C4C4×D23611yescharacteristic
367C2×C4#1427370211yescharacteristic
368C2×C4#1427371211yescharacteristic
369C8—42no—
370C8—4721no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22#1683728011yescharacteristic
382C22#1683749611yescharacteristic
383C22#1683750811yescharacteristic
384C22#1683755911yescharacteristic
385C22#1683756511yescharacteristic
386C22#1683761111yescharacteristic
387C22#1683762311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—161no—
393C4—4721no—
394C4—4721no—
395C4—4721no—
396C4—2362no—
397C4—2362no—
398C4—2362no—
399C4#1683737412yes—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#2142443811yescharacteristic
407C2#2142455311yescharacteristic
408C2#2142458411yescharacteristic
subgroupG/H
centerC22#16837280
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1289C2
socleC22×C59#386
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenter#1289D59
hypocenterC59#9257
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
13. C2×#14273661C4semidirect
14. C2×#14273652C4semidirect
233. C59#9257semidirect

Maximal subgroups

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

subgroupindex
C2×#168377382
#214269752
#214250802
#214241842
#214226672
#214219432
C59×#12892
#925759