Finite Group Databasebeta

← C59×#8756 #28420865

Subgroups — C59×#8756 #28420865

Order 15104.

546 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2315C211yesmaximal, characteristic
2C59×#1462C212yesmaximal
3C59×#1305C214yesmaximal, complemented
4C22×C22⋊C4×C59C411yescharacteristic
5C22×C22⋊C4×C59C411yescharacteristic
6C22×C22⋊C4×C59C2211yescharacteristic
7C59×#407C2214yes—
8C59×#385—22no—
9C59×#385—22no—
10C59×#380C412yes—
11C59×#380C2212yes—
12C59×#323—22no—
13C59×#323—22no—
14C25×C59C2×C411yescharacteristic
15C23×C4×C59—21no—
16C23×C4×C59—21no—
17C23×C4×C59C2×C411yescharacteristic
18C23×C4×C59C2311yescharacteristic
19C2×M16×C59—24no—
20C2×C4⋊C4×C59—22no—
21C2×C4⋊C4×C59—22no—
22C2×C22⋊C4×C59—24no—
23C2×C22⋊C4×C59—21no—
24C2×C22⋊C4×C59—21no—
25C2×C22⋊C4×C59—42no—
26C2×C22⋊C4×C59—42no—
27C2×C22⋊C4×C59C2×C412yes—
28C2×C22⋊C4×C59C2×C412yes—
29C2×C22⋊C4×C59D412yes—
30C2×C22⋊C4×C59D412yes—
31C22⋊C8×C59—24no—
32C22⋊C8×C59—24no—
33#95×C59—22no—
34#95×C59—22no—
35C24×C59—22no—
36C24×C59—22no—
37C24×C59—22no—
38C24×C59—81no—
39C24×C59—81no—
40C24×C59C22⋊C411yescharacteristic
41C24×C59C22⋊C411yescharacteristic
42C24×C59C22×C411yescharacteristic
43C22×C4×C59—22no—
44C22×C4×C59—22no—
45C22×C4×C59—22no—
46C22×C4×C59—42no—
47C22×C4×C59—42no—
48C22×C4×C59—81no—
49C22×C4×C59—81no—
50C22×C4×C59—81no—
51C22×C4×C59—81no—
52C22×C4×C59—81no—
53C22×C4×C59—81no—
54C22×C4×C59C22⋊C412yes—
55C22×C4×C59C2×D412yes—
56C22×C4×C59#4114yes—
57M16×C59—84no—
58C2×C8×C59—44no—
59C4⋊C4×C59—82no—
60C4⋊C4×C59—82no—
61C22⋊C4×C59—24no—
62C22⋊C4×C59—24no—
63C22⋊C4×C59—42no—
64C22⋊C4×C59—42no—
65C22⋊C4×C59—42no—
66C22⋊C4×C59—42no—
67C23×C59—28no—
68C23×C59—21no—
69C23×C59—21no—
70C23×C59—21no—
71C23×C59—21no—
72C23×C59—21no—
73C23×C59—21no—
74C23×C59—41no—
75C23×C59—41no—
76C23×C59—41no—
77C23×C59—41no—
78C23×C59—41no—
79C23×C59—41no—
80C23×C59—82no—
81C23×C59—82no—
82C23×C59—84no—
83C23×C59—84no—
84C23×C59#10012yes—
85C23×C59#10112yes—
86C23×C59C2×C22⋊C411yescharacteristic
87C23×C59#11712yes—
88C2×C4×C59—22no—
89C2×C4×C59—42no—
90C2×C4×C59—44no—
91C2×C4×C59—42no—
92C2×C4×C59—42no—
93C2×C4×C59—42no—
94C2×C4×C59—42no—
95C2×C4×C59—42no—
96C2×C4×C59—42no—
97C2×C4×C59—42no—
98C2×C4×C59—82no—
99C2×C4×C59—84no—
100C2×C4×C59—84no—
101C2×C4×C59#12314yes—
102C8×C59—84no—
103#8756C5911yesmaximal, characteristic, direct product factor, Sylow
104C22×C59—21no—
105C22×C59—21no—
106C22×C59—22no—
107C22×C59—22no—
108C22×C59—22no—
109C22×C59—22no—
110C22×C59—22no—
111C22×C59—42no—
112C22×C59—42no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59—42no—
117C22×C59—41no—
118C22×C59—41no—
119C22×C59—41no—
120C22×C59—41no—
121C22×C59—88no—
122C22×C59#38111yescharacteristic
123C22×C59C2×#10011yescharacteristic
124C22×C59C2×#10111yescharacteristic
125C4×C59—24no—
126C4×C59—42no—
127C4×C59—82no—
128C4×C59—82no—
129#2315C2×C5911yescharacteristic
130#1462C2×C5912yes—
131#1305C2×C5914yescomplemented
132C2×C59—21no—
133C2×C59—21no—
134C2×C59—42no—
135C2×C59—42no—
136C2×C59—42no—
137C2×C59#182111yescharacteristic
138C2×C59#182811yescharacteristic
139C2×C59#182911yescharacteristic
140C22×C22⋊C4C4×C5911yescharacteristic
141C22×C22⋊C4C4×C5911yescharacteristic
142C22×C22⋊C4C22×C5911yescharacteristic
143#407C22×C5914yes—
144#385—22no—
145#385—22no—
146#380C4×C5912yes—
147#380C22×C5912yes—
148#323—22no—
149#323—22no—
150C59#875611yescharacteristic, direct product factor, Sylow
151C25C2×C4×C5911yescharacteristic
152C23×C4—21no—
153C23×C4—21no—
154C23×C4C2×C4×C5911yescharacteristic
155C23×C4C23×C5911yescharacteristic
156C2×M16—24no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—42no—
163C2×C22⋊C4—42no—
164C2×C22⋊C4C2×C4×C5912yes—
165C2×C22⋊C4C2×C4×C5912yes—
166C2×C22⋊C4D4×C5912yes—
167C2×C22⋊C4D4×C5912yes—
168C22⋊C8—24no—
169C22⋊C8—24no—
170#95—22no—
171#95—22no—
172C24—22no—
173C24—22no—
174C24—22no—
175C24—81no—
176C24—81no—
177C24C22⋊C4×C5911yescharacteristic
178C24C22⋊C4×C5911yescharacteristic
179C24C22×C4×C5911yescharacteristic
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4C22⋊C4×C5912yes—
192C22×C4C2×D4×C5912yes—
193C22×C4#41×C5914yes—
194M16—84no—
195C2×C8—44no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C22⋊C4—24no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C23—28no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23#100×C5912yes—
222C23#101×C5912yes—
223C23C2×C22⋊C4×C5911yescharacteristic
224C23#117×C5912yes—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C2×C4—84no—
238C2×C4#123×C5914yes—
239C8—84no—
240C22—21no—
241C22—21no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—88no—
258C22C59×#38111yescharacteristic
259C22C2×#100×C5911yescharacteristic
260C22C2×#101×C5911yescharacteristic
261C4—24no—
262C4—42no—
263C4—82no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—42no—
269C2—42no—
270C2C59×#182111yescharacteristic
271C2C59×#182811yescharacteristic
272C2C59×#182911yescharacteristic
subgroupG/H
center, socleC22×C59#381
commutatorC24C22×C4×C59
Frattini, cosocleC23×C4C23×C59
prime radicalC25×C59C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1305C2semidirect
103. #8756C59direct (N × H)
131. #1305C2×C59semidirect
150. C59#8756direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#23152
C59×#14622
C59×#13052
#875659