Finite Group Databasebeta

← #28491855

Subgroups — #28491855

Order 15104.

422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#21425081C211yesmaximal, characteristic
2#21422667C211yesmaximal, characteristic
3C2×#16837138C211yesmaximal, characteristic
4#21421975C211yesmaximal, characteristic
5#21421963C211yesmaximal, characteristic
6#21421944C211yesmaximal, characteristic
7C59×#2569C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9C2×C22⋊(C59⋊C8)C2211yescharacteristic
10C2×C22⋊(C59⋊C8)C2211yescharacteristic
11#16837262C2211yescharacteristic
12#16837168—21no—
13#16837168—21no—
14#16837138—21no—
15#16837138—21no—
16#16837138—21no—
17#16837138—21no—
18C59×#400—21no—
19C59×#398—21no—
20C59×#387—21no—
21C59×#387—21no—
22C59×#385—21no—
23C59×#380—21no—
24C59×#380C2211yescharacteristic
25C4×C22⋊C4×C59C2211yescharacteristic
26C2×#95×C59C2211yescharacteristic
27C22×Dic118Q811yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30#14273706—21no—
31#14273706—21no—
32#14273706—21no—
33#14273706—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59Q811yescharacteristic
36C2×Dic59⋊C4—21no—
37C2×C22⋊Dic59—21no—
38C2×C22⋊Dic59—21no—
39C22⋊(C59⋊C8)—21no—
40C22⋊(C59⋊C8)—21no—
41C22⋊(C59⋊C8)—21no—
42C22⋊(C59⋊C8)—21no—
43C59⋊#95—21no—
44C23×C4×C59—21no—
45C23×C4×C59C2311yescharacteristic
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C22⋊C4×C59D411yescharacteristic
53C2×C22⋊C4×C59D411yescharacteristic
54C2×C42×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61#95×C59D411yescharacteristic
62#95×C59D411yescharacteristic
63#95×C59D411yescharacteristic
64#95×C59D411yescharacteristic
65C24×C59C2×D411yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—42no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—81no—
76C22×C4×C59—81no—
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×Q811yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C22×C4×C59#4111yescharacteristic
82C22×C4×C59#4111yescharacteristic
83C22×Dic59—21no—
84C22×Dic59—21no—
85C22×Dic59—41no—
86C2×Dic118—21no—
87C2×Dic118—21no—
88C2×Dic118—81no—
89C4⋊C4×C59—42no—
90C4⋊C4×C59—42no—
91C4⋊C4×C59—81no—
92C4⋊C4×C59—81no—
93C4⋊C4×C59—81no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59—41no—
99C22⋊C4×C59—41no—
100C42×C59—81no—
101C22⋊Dic59—41no—
102C22⋊Dic59—41no—
103C22⋊Dic59—41no—
104C22⋊Dic59—41no—
105C4⋊Dic59—21no—
106C4⋊Dic59—21no—
107C4⋊Dic59—81no—
108Dic59⋊C4—41no—
109Dic59⋊C4—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8—41no—
112C2×C59⋊C8—81no—
113C2×C59⋊C8—81no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59#12011yescharacteristic
117C23×C59C22⋊Q811yescharacteristic
118C23×C59#12411yescharacteristic
119C23×C59#13511yescharacteristic
120C23×C59#13511yescharacteristic
121C23×C59#13711yescharacteristic
122C23×C59#13711yescharacteristic
123C2×C4×C59—22no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—82no—
148C2×C4×C59—82no—
149C2×C4×C59C22⋊Q811yescharacteristic
150C2×C4×C59C22⋊Q811yescharacteristic
151C2×C4×C59#12411yescharacteristic
152C2×C4×C59#12411yescharacteristic
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—81no—
156C2×Dic59—81no—
157C2×Dic59—81no—
158C2×Dic59—81no—
159C2×Dic59—81no—
160Dic118—81no—
161Dic118—81no—
162C59⋊C8—81no—
163C59⋊C8—81no—
164#10377—591nomaximal, Sylow
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59#39311yescharacteristic
176C22×C59#45211yescharacteristic
177C22×C59#45211yescharacteristic
178C22×C59#47911yescharacteristic
179C22×C59#47911yescharacteristic
180C22×C59#48811yescharacteristic
181C22×C59#49111yescharacteristic
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—42no—
187C4×C59—81no—
188C4×C59—81no—
189C4×C59—81no—
190C4×C59—81no—
191C4×C59—81no—
192Dic59—81no—
193Dic59—81no—
194Dic59—161no—
195#2569D5911yescharacteristic
196#1996—591no—
197#1520—591no—
198C2×#328—591no—
199#1294—591no—
200#1289—591no—
201#1282—591no—
202C2×C59—21no—
203C2×C59—21no—
204C2×C59—21no—
205C2×C59—21no—
206C2×C59—21no—
207C2×C59—21no—
208C2×C59#202611yescharacteristic
209C2×C59#203111yescharacteristic
210C2×C59#203211yescharacteristic
211C2×C22⋊Q8—591no—
212C2×C22⋊C8—591no—
213C2×C22⋊C8—591no—
214#400—21no—
215#398—21no—
216#387—21no—
217#387—21no—
218#385—21no—
219#380—21no—
220#380—591no—
221#380C2×D5911yescharacteristic
222C4×C22⋊C4C2×D5911yescharacteristic
223C2×#95C2×D5911yescharacteristic
224#342—1181no—
225#342—1181no—
226#328—1181no—
227#328—1181no—
228#328—1181no—
229#328—1181no—
230C59#1037711yescharacteristic, complemented, Sylow
231C22×Q8—591no—
232C23×C4—21no—
233C23×C4C22×D5911yescharacteristic
234C22×C8—1181no—
235C22×C8—1181no—
236C22⋊Q8—1181no—
237C22⋊Q8—1181no—
238C22⋊Q8—1181no—
239C22⋊Q8—1181no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—1181no—
247C2×C4⋊C4—1181no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—1181no—
250C2×C22⋊C4—1181no—
251C2×C22⋊C4C22⋊D5911yescharacteristic
252C2×C22⋊C4C22⋊D5911yescharacteristic
253C2×C42—21no—
254C22⋊C8—1181no—
255C22⋊C8—1181no—
256C22⋊C8—1181no—
257C22⋊C8—1181no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—1181no—
265#95C22⋊D5911yescharacteristic
266#95C22⋊D5911yescharacteristic
267#95C22⋊D5911yescharacteristic
268#95C22⋊D5911yescharacteristic
269C24C2×C22⋊D5911yescharacteristic
270C2×Q8—1181no—
271C2×Q8—1181no—
272C2×Q8—4721no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—2361no—
287C22×C4Q8×D5911yescharacteristic
288C22×C4#1174568911yescharacteristic
289C22×C4#1174568911yescharacteristic
290C22×C4#1174568911yescharacteristic
291C22×C4C2×C22⋊D5911yescharacteristic
292C22×C4C2×C22⋊D5911yescharacteristic
293C2×C8—4721no—
294C2×C8—4721no—
295C2×C8—2361no—
296C2×C8—2361no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—1181no—
303C4⋊C4—1181no—
304C4⋊C4—4721no—
305C4⋊C4—2361no—
306C4⋊C4—2361no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—2361no—
314C22⋊C4—2361no—
315C22⋊C4—2361no—
316C22⋊C4—2361no—
317C42—81no—
318C23—41no—
319C23—41no—
320C23#1427369611yescharacteristic
321C23#1427370311yescharacteristic
322C23#1427371611yescharacteristic
323C23#1427374711yescharacteristic
324C23#1427374711yescharacteristic
325C23#1427375711yescharacteristic
326C23#1427375711yescharacteristic
327Q8—4721no—
328Q8—4721no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—4721no—
356C2×C4—4721no—
357C2×C4—4721no—
358C2×C4—4721no—
359C2×C4—4721no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4#1427370311yescharacteristic
363C2×C4#1427370311yescharacteristic
364C2×C4#1427371611yescharacteristic
365C2×C4#1427371611yescharacteristic
366C8—4721no—
367C8—4721no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1683731311yescharacteristic
379C22#1683756411yescharacteristic
380C22#1683756411yescharacteristic
381C22#1683770611yescharacteristic
382C22#1683770611yescharacteristic
383C22#1683775911yescharacteristic
384C22#1683777211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—9441no—
396C4—4721no—
397C4—4721no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2142524411yescharacteristic
405C2#2142526511yescharacteristic
406C2#2142527211yescharacteristic
subgroupG/H
centerC22#16837313
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#2569C2
socleC22×C59#393
prime radicalC24×C59C2×D4
hypercenter#2569D59
hypocenterC59#10377
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2569

Complements

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

NH ≅ G/Ntype
230. C59#10377semidirect

Maximal subgroups

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

subgroupindex
#214250812
#214226672
C2×#168371382
#214219752
#214219632
#214219442
C59×#25692
#1037759