Finite Group Databasebeta

← #28491861

Subgroups — #28491861

Order 15104.

422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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#21429320C211yesmaximal, characteristic
2#21425080C211yesmaximal, characteristic
3#21422669C211yesmaximal, characteristic
4C2×#16837138C211yesmaximal, characteristic
5#21421963C211yesmaximal, characteristic
6#21421943C211yesmaximal, characteristic
7C59×#1294C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9C2×C22⋊(C59⋊C8)C2211yescharacteristic
10#16837344—21no—
11#16837334—21no—
12#16837289—21no—
13#16837285—21no—
14#16837275—21no—
15#16837262—21no—
16#16837262C2211yescharacteristic
17C4×C22⋊Dic59C2211yescharacteristic
18#16837168—21no—
19#16837168—21no—
20#16837140—21no—
21#16837140—21no—
22#16837138—21no—
23#16837138—21no—
24C2×C22⋊C8×C59C2211yescharacteristic
25C59×#380C2211yescharacteristic
26C2×#95×C59C2211yescharacteristic
27C22×Dic118Q811yescharacteristic
28C22×C59⋊C8—21no—
29#14273706—21no—
30#14273706—21no—
31#14273706—21no—
32#14273706—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59Q811yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×C22⋊Dic59—21no—
41C2×C22⋊Dic59—21no—
42C2×C22⋊Dic59D411yescharacteristic
43C2×C22⋊Dic59D411yescharacteristic
44C2×C4×Dic59—21no—
45C22⋊(C59⋊C8)—21no—
46C22⋊(C59⋊C8)—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C59⋊#95—21no—
52C59⋊#95D411yescharacteristic
53C59⋊#95D411yescharacteristic
54C23×C4×C59—21no—
55C23×C4×C59C2311yescharacteristic
56C22×C8×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C22⋊C8×C59—21no—
60C22⋊C8×C59—21no—
61#95×C59—21no—
62#95×C59—21no—
63#95×C59D411yescharacteristic
64#95×C59D411yescharacteristic
65C24×C59C2×D411yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—42no—
69C22×C4×C59—41no—
70C22×C4×C59—41no—
71C22×C4×C59—41no—
72C22×C4×C59—81no—
73C22×C4×C59—81no—
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×Q811yescharacteristic
77C22×C4×C59#4111yescharacteristic
78C22×C4×C59#4111yescharacteristic
79C22×C4×C59#4111yescharacteristic
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C22×Dic59—21no—
84C22×Dic59—21no—
85C22×Dic59—21no—
86C2×Dic118—21no—
87C2×Dic118—21no—
88C2×Dic118—81no—
89C2×C8×C59—41no—
90C2×C8×C59—81no—
91C4⋊C4×C59—81no—
92C22⋊C4×C59—41no—
93C22⋊C4×C59—41no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—41no—
99C22⋊Dic59—41no—
100C22⋊Dic59—41no—
101C22⋊Dic59—41no—
102C4⋊Dic59—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59—42no—
105C4⋊Dic59—81no—
106C4⋊Dic59—81no—
107Dic59⋊C4—42no—
108Dic59⋊C4—41no—
109Dic59⋊C4—41no—
110Dic59⋊C4—81no—
111C4×Dic59—81no—
112C2×C59⋊C8—41no—
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—82no—
136C2×C4×C59—82no—
137C2×C4×C59—81no—
138C2×C4×C59—81no—
139C2×C4×C59—81no—
140C2×C4×C59C22⋊Q811yescharacteristic
141C2×C4×C59C22⋊Q811yescharacteristic
142C2×C4×C59#12411yescharacteristic
143C2×C4×C59#12411yescharacteristic
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59—41no—
150C2×Dic59—41no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158C2×Dic59—81no—
159C2×Dic59—81no—
160Dic118—81no—
161Dic118—81no—
162C8×C59—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—161no—
189Dic59—81no—
190Dic59—81no—
191Dic59—81no—
192Dic59—81no—
193Dic59—81no—
194Dic59—81no—
195#2569—591no—
196#1996—591no—
197#1520—591no—
198C2×#328—591no—
199#1294D5911yescharacteristic
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⋊C8C2×D5911yescharacteristic
214#400—1181no—
215#398—1181no—
216#387—1181no—
217#387—1181no—
218#385—1181no—
219#380—591no—
220#380—1181no—
221#380C2×D5911yescharacteristic
222C4×C22⋊C4—591no—
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—21no—
235C22×C8—1181no—
236C22⋊Q8—1181no—
237C22⋊Q8—1181no—
238C22⋊Q8—1181no—
239C22⋊Q8—1181no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—591no—
242C2×C4⋊C4—1181no—
243C2×C4⋊C4—1181no—
244C2×C4⋊C4—1181no—
245C2×C4⋊C4—1181no—
246C2×C4⋊C4—1181no—
247C2×C4⋊C4—1181no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—591no—
250C2×C22⋊C4—591no—
251C2×C22⋊C4—1181no—
252C2×C22⋊C4—1181no—
253C2×C42—1181no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—1181no—
257C22⋊C8—1181no—
258#95—21no—
259#95—21no—
260#95—591no—
261#95—591no—
262#95—1181no—
263#95—1181no—
264#95—1181no—
265#95—1181no—
266#95—1181no—
267#95D23611yescharacteristic
268#95D23611yescharacteristic
269C24D4×D5911yescharacteristic
270C2×Q8—1181no—
271C2×Q8—1181no—
272C2×Q8—4721no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—1181no—
282C22×C4—1181no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—1181no—
287C22×C4C2×D23611yescharacteristic
288C22×C4#1174568511yescharacteristic
289C22×C4#1174568511yescharacteristic
290C22×C4D4×D5911yescharacteristic
291C22×C4#1174568711yescharacteristic
292C22×C4Q8×D5911yescharacteristic
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—4721no—
296C2×C8—2361no—
297C4⋊C4—81no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4—4721no—
301C4⋊C4—4721no—
302C4⋊C4—4721no—
303C4⋊C4—2362no—
304C4⋊C4—2362no—
305C4⋊C4—2361no—
306C4⋊C4—2361no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—2361no—
314C22⋊C4—2361no—
315C22⋊C4—2361no—
316C22⋊C4—2361no—
317C42—4721no—
318C23—41no—
319C23—41no—
320C23#1427369711yescharacteristic
321C23#1427370511yescharacteristic
322C23#1427371311yescharacteristic
323C23#1427374611yescharacteristic
324C23#1427374811yescharacteristic
325C23#1427375611yescharacteristic
326C23#1427375911yescharacteristic
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—82no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—4721no—
347C2×C4—4721no—
348C2×C4—2361no—
349C2×C4—2361no—
350C2×C4—2361no—
351C2×C4—2361no—
352C2×C4—2361no—
353C2×C4—2361no—
354C2×C4—2361no—
355C2×C4—2361no—
356C2×C4—2361no—
357C2×C4—2361no—
358C2×C4—2361no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4#1427370511yescharacteristic
363C2×C4#1427370711yescharacteristic
364C2×C4#1427371311yescharacteristic
365C2×C4#1427371511yescharacteristic
366C8—81no—
367C8—4721no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1683731511yescharacteristic
379C22#1683756511yescharacteristic
380C22#1683756711yescharacteristic
381C22#1683770811yescharacteristic
382C22#1683771211yescharacteristic
383C22#1683775511yescharacteristic
384C22#1683776911yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—161no—
392C4—4721no—
393C4—4721no—
394C4—4721no—
395C4—4721no—
396C4—4721no—
397C4—4721no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2142524611yescharacteristic
405C2#2142526911yescharacteristic
406C2#2142527411yescharacteristic
subgroupG/H
centerC22#16837315
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1294C2
socleC22×C59#393
prime radicalC24×C59C2×D4
hypercenter#1294D59
hypocenterC59#10377
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

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
#214293202
#214250802
#214226692
C2×#168371382
#214219632
#214219432
C59×#12942
#1037759