Finite Group Databasebeta

← C59×#11564 #28423673

Subgroups — C59×#11564 #28423673

Order 15104.

444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2547C211yesmaximal, characteristic
2C59×#1465C211yesmaximal, characteristic
3C59×#1459C211yesmaximal, characteristic
4C59×#1319C214yesmaximal, complemented
5C2×C4⋊Q8×C59C411yescharacteristic
6C2×#124×C59C412yes—
7C2×C4×D4×C59C2211yescharacteristic
8C59×#407—21no—
9C2×C22⋊C8×C59—21no—
10C59×#397—21no—
11C59×#397—21no—
12C59×#391C2212yes—
13C59×#380—21no—
14C59×#380—21no—
15C4×C4⋊C4×C59C411yescharacteristic
16C59×#324C2212yes—
17C59×#324C2212yes—
18C59×#323—21no—
19C59×#323—21no—
20C22×Q8×C59C2×C412yes—
21C22×D4×C59C2×C411yescharacteristic
22C23×C4×C59D411yescharacteristic
23C23×C4×C59D411yescharacteristic
24C2×M16×C59—41no—
25C22×C8×C59—41no—
26C4⋊Q8×C59—41no—
27C4⋊Q8×C59—41no—
28#124×C59—44no—
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×C59C2311yescharacteristic
35C2×C22⋊C4×C59—22no—
36C2×C22⋊C4×C59—22no—
37C2×C22⋊C4×C59D411yescharacteristic
38C2×C22⋊C4×C59D411yescharacteristic
39C2×C42×C59C2×C411yescharacteristic
40C2×C42×C59C2×C412yes—
41C22⋊C8×C59—22no—
42C22⋊C8×C59—22no—
43C22⋊C8×C59—41no—
44C22⋊C8×C59—41no—
45#95×C59—21no—
46#95×C59—22no—
47#95×C59—22no—
48C24×C59C22⋊C411yescharacteristic
49C24×C59C22⋊C411yescharacteristic
50C2×Q8×C59—24no—
51C2×Q8×C59—42no—
52C2×Q8×C59—42no—
53C2×D4×C59—22no—
54C2×D4×C59—22no—
55C2×D4×C59—41no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—22no—
61C22×C4×C59—22no—
62C22×C4×C59—42no—
63C22×C4×C59—42no—
64C22×C4×C59C22⋊C411yescharacteristic
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22×C411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69M16×C59—82no—
70C2×C8×C59—42no—
71C2×C8×C59—42no—
72C2×C8×C59—82no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—42no—
75C4⋊C4×C59—42no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C22⋊C4×C59—41no—
79C22⋊C4×C59—41no—
80C22⋊C4×C59—44no—
81C22⋊C4×C59—44no—
82C42×C59—21no—
83C42×C59—21no—
84C42×C59—42no—
85C23×C59—21no—
86C23×C59—21no—
87C23×C59—21no—
88C23×C59—21no—
89C23×C59—21no—
90C23×C59—41no—
91C23×C59—41no—
92C23×C59—41no—
93C23×C59—41no—
94C23×C59#10012yes—
95C23×C59C2×C22⋊C411yescharacteristic
96Q8×C59—84no—
97D4×C59—44no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—22no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—42no—
105C2×C4×C59—42no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—42no—
110C2×C4×C59—42no—
111C2×C4×C59—42no—
112C2×C4×C59—42no—
113C2×C4×C59—42no—
114C2×C4×C59—42no—
115C2×C4×C59—81no—
116C2×C4×C59—81no—
117C2×C4×C59#9911yescharacteristic
118C2×C4×C59#9911yescharacteristic
119C2×C4×C59#13112yes—
120C8×C59—82no—
121C8×C59—82no—
122#11564C5911yesmaximal, characteristic, direct product factor, Sylow
123C22×C59—21no—
124C22×C59—21no—
125C22×C59—22no—
126C22×C59—42no—
127C22×C59—42no—
128C22×C59—41no—
129C22×C59—41no—
130C22×C59—41no—
131C22×C59—41no—
132C22×C59—41no—
133C22×C59—81no—
134C22×C59—81no—
135C22×C59#40811yescharacteristic
136C22×C59C2×#9911yescharacteristic
137C22×C59C2×#10011yescharacteristic
138C4×C59—21no—
139C4×C59—22no—
140C4×C59—41no—
141C4×C59—41no—
142C4×C59—41no—
143C4×C59—82no—
144C4×C59—82no—
145C4×C59#35412yes—
146#2547C2×C5911yescharacteristic
147#1465C2×C5911yescharacteristic
148#1459C2×C5911yescharacteristic
149#1319C2×C5914yescomplemented
150C2×C59—21no—
151C2×C59—21no—
152C2×C59—42no—
153C2×C59—81no—
154C2×C59#147111yescharacteristic
155C2×C59C2×#35411yescharacteristic
156C2×C59#213511yescharacteristic
157C2×C4⋊Q8C4×C5911yescharacteristic
158C2×#124C4×C5912yes—
159C2×C4×D4C22×C5911yescharacteristic
160#407—21no—
161C2×C22⋊C8—21no—
162#397—21no—
163#397—21no—
164#391C22×C5912yes—
165#380—21no—
166#380—21no—
167C4×C4⋊C4C4×C5911yescharacteristic
168#324C22×C5912yes—
169#324C22×C5912yes—
170#323—21no—
171#323—21no—
172C59#1156411yescharacteristic, direct product factor, Sylow
173C22×Q8C2×C4×C5912yes—
174C22×D4C2×C4×C5911yescharacteristic
175C23×C4D4×C5911yescharacteristic
176C23×C4D4×C5911yescharacteristic
177C2×M16—41no—
178C22×C8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181#124—44no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C23×C5911yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4D4×C5911yescharacteristic
191C2×C22⋊C4D4×C5911yescharacteristic
192C2×C42C2×C4×C5911yescharacteristic
193C2×C42C2×C4×C5912yes—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#95—21no—
199#95—22no—
200#95—22no—
201C24C22⋊C4×C5911yescharacteristic
202C24C22⋊C4×C5911yescharacteristic
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4C22⋊C4×C5911yescharacteristic
218C22×C4C22⋊C4×C5911yescharacteristic
219C22×C4C22×C4×C5911yescharacteristic
220C22×C4C2×D4×C5911yescharacteristic
221C22×C4C2×D4×C5911yescharacteristic
222M16—82no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—82no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—44no—
234C22⋊C4—44no—
235C42—21no—
236C42—21no—
237C42—42no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23#100×C5912yes—
248C23C2×C22⋊C4×C5911yescharacteristic
249Q8—84no—
250D4—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4#99×C5911yescharacteristic
271C2×C4#99×C5911yescharacteristic
272C2×C4#131×C5912yes—
273C8—82no—
274C8—82no—
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22C59×#40811yescharacteristic
288C22C2×#99×C5911yescharacteristic
289C22C2×#100×C5911yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4C59×#35412yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2C59×#147111yescharacteristic
303C2C2×C59×#35411yescharacteristic
304C2C59×#213511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C4⋊C4C23×C59
prime radicalC22×D4×C59C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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×#1319C2semidirect
122. #11564C59direct (N × H)
149. #1319C2×C59semidirect
172. C59#11564direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#25472
C59×#14652
C59×#14592
C59×#13192
#1156459