Finite Group Databasebeta

← C59×#11827 #28423936

Subgroups — C59×#11827 #28423936

Order 15104.

418 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C59×#2633C211yesmaximal, characteristic
2C59×#1799C211yesmaximal, characteristic
3C59×#1465C211yesmaximal, characteristic
4C59×#1352C212yesmaximal, complemented
5C59×#1344C212yesmaximal, complemented
6C2×#125×C59C411yescharacteristic, complemented
7C2×C4×D4×C59C2211yescharacteristic
8C2×#99×C59—21no—
9C59×#407—21no—
10C59×#399C411yescharacteristic, complemented
11C59×#399C2211yescharacteristic
12C59×#398—21no—
13C59×#397C411yescharacteristic, complemented
14C59×#397C2211yescharacteristic
15C59×#394—21no—
16C59×#385—21no—
17C59×#385—21no—
18C59×#383C411yescharacteristic, complemented
19C59×#380—21no—
20C59×#342C2212yes—
21C59×#324—21no—
22C59×#323C2212yes—
23C22×D4×C59D411yescharacteristic
24C23×C4×C59D411yescharacteristic
25C23×C4×C59D411yescharacteristic
26C2×M16×C59—41no—
27#125×C59—41no—
28#125×C59—41no—
29C4×D4×C59—41no—
30C4×D4×C59—41no—
31C2×C4⋊C4×C59—21no—
32C2×C4⋊C4×C59—21no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—41no—
36C2×C4⋊C4×C59C2×C411yescharacteristic
37C2×C4⋊C4×C59C2×C411yescharacteristic
38C2×C4⋊C4×C59D411yescharacteristic
39C2×C22⋊C4×C59—21no—
40C2×C22⋊C4×C59—21no—
41C2×C22⋊C4×C59—22no—
42C2×C22⋊C4×C59—21no—
43C2×C22⋊C4×C59—21no—
44C2×C22⋊C4×C59C2×C411yescharacteristic
45C2×C22⋊C4×C59C2311yescharacteristic
46C2×C42×C59C2×C411yescharacteristic
47#99×C59—42no—
48C22⋊C8×C59—22no—
49C22⋊C8×C59—41no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—41no—
55#95×C59C2×C411yescharacteristic
56#95×C59C2×C411yescharacteristic
57C24×C59C22⋊C411yescharacteristic
58C24×C59C2×D411yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—41no—
62C2×D4×C59—41no—
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—42no—
72C22×C4×C59—81no—
73C22×C4×C59—81no—
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22×C411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79M16×C59—82no—
80C2×C8×C59—42no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—42no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—81no—
88C4⋊C4×C59—81no—
89C4⋊C4×C59—82no—
90C22⋊C4×C59—41no—
91C22⋊C4×C59—41no—
92C22⋊C4×C59—42no—
93C22⋊C4×C59—41no—
94C22⋊C4×C59—41no—
95C22⋊C4×C59—42no—
96C22⋊C4×C59—42no—
97C22⋊C4×C59—81no—
98C22⋊C4×C59—81no—
99C42×C59—21no—
100C42×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—41no—
107C23×C59—41no—
108C23×C59—41no—
109C23×C59—41no—
110C23×C59C2×C22⋊C411yescharacteristic
111C23×C59AGL(1,ℤ/8)11yescharacteristic
112C23×C59#13711yescharacteristic
113D4×C59—42no—
114D4×C59—42no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59—42no—
123C2×C4×C59—42no—
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—81no—
140C2×C4×C59—81no—
141C2×C4×C59—82no—
142C2×C4×C59—82no—
143C2×C4×C59—82no—
144C2×C4×C59#9911yescharacteristic
145C2×C4×C59#9911yescharacteristic
146C8×C59—82no—
147#11827C5911yesmaximal, characteristic, direct product factor, Sylow
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—42no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—81no—
161C22×C59—81no—
162C22×C59C2×#9911yescharacteristic
163C22×C59#41711yescharacteristic
164C22×C59#42111yescharacteristic
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—81no—
172C4×C59—81no—
173C4×C59—81no—
174C4×C59—81no—
175C4×C59—162no—
176#2633C2×C5911yescharacteristic
177#1799C2×C5911yescharacteristic
178#1465C2×C5911yescharacteristic
179#1352C2×C5912yescomplemented
180#1344C2×C5912yescomplemented
181C2×C59—21no—
182C2×C59—21no—
183C2×C59—41no—
184C2×C59—41no—
185C2×C59—81no—
186C2×C59#151311yescharacteristic
187C2×C59#212311yescharacteristic
188C2×C59#212711yescharacteristic
189C2×#125C4×C5911yescharacteristic, complemented
190C2×C4×D4C22×C5911yescharacteristic
191C2×#99—21no—
192#407—21no—
193#399C4×C5911yescharacteristic, complemented
194#399C22×C5911yescharacteristic
195#398—21no—
196#397C4×C5911yescharacteristic, complemented
197#397C22×C5911yescharacteristic
198#394—21no—
199#385—21no—
200#385—21no—
201#383C4×C5911yescharacteristic, complemented
202#380—21no—
203#342C22×C5912yes—
204#324—21no—
205#323C22×C5912yes—
206C59#1182711yescharacteristic, direct product factor, Sylow
207C22×D4D4×C5911yescharacteristic
208C23×C4D4×C5911yescharacteristic
209C23×C4D4×C5911yescharacteristic
210C2×M16—41no—
211#125—41no—
212#125—41no—
213C4×D4—41no—
214C4×D4—41no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C2×C4×C5911yescharacteristic
221C2×C4⋊C4C2×C4×C5911yescharacteristic
222C2×C4⋊C4D4×C5911yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C2×C4×C5911yescharacteristic
229C2×C22⋊C4C23×C5911yescharacteristic
230C2×C42C2×C4×C5911yescharacteristic
231#99—42no—
232C22⋊C8—22no—
233C22⋊C8—41no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—41no—
239#95C2×C4×C5911yescharacteristic
240#95C2×C4×C5911yescharacteristic
241C24C22⋊C4×C5911yescharacteristic
242C24C2×D4×C5911yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—41no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4C22⋊C4×C5911yescharacteristic
259C22×C4C22⋊C4×C5911yescharacteristic
260C22×C4C22⋊C4×C5911yescharacteristic
261C22×C4C22×C4×C5911yescharacteristic
262C22×C4C2×D4×C5911yescharacteristic
263M16—82no—
264C2×C8—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—82no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C42—21no—
284C42—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C2×C22⋊C4×C5911yescharacteristic
295C23AGL(1,ℤ/8)×C5911yescharacteristic
296C23#137×C5911yescharacteristic
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#99×C5911yescharacteristic
329C2×C4#99×C5911yescharacteristic
330C8—82no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22C2×#99×C5911yescharacteristic
346C22C59×#41711yescharacteristic
347C22C59×#42111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—162no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2C59×#151311yescharacteristic
365C2C59×#212311yescharacteristic
366C2C59×#212711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C22⋊C4C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#1352C2semidirect
5. C59×#1344C2semidirect
6. C2×#125×C59C4semidirect
10. C59×#399C4semidirect
13. C59×#397C4semidirect
18. C59×#383C4semidirect
147. #11827C59direct (N × H)
179. #1352C2×C59semidirect
180. #1344C2×C59semidirect
189. C2×#125C4×C59semidirect
193. #399C4×C59semidirect
196. #397C4×C59semidirect
201. #383C4×C59semidirect
206. C59#11827direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#26332
C59×#17992
C59×#14652
C59×#13522
C59×#13442
#1182759