Finite Group Databasebeta

← C59×#7486 #28419595

Subgroups — C59×#7486 #28419595

Order 15104.

286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2126C211yesmaximal, characteristic
2C59×#1884C211yesmaximal, characteristic
3C59×#1525C211yesmaximal, characteristic
4C59×#568C411yescharacteristic, complemented
5C59×#532C2211yescharacteristic
6C59×#421—21no—
7C59×#410—21no—
8C59×#410C411yescharacteristic, complemented
9C4×M16×C59—21no—
10C59×#354—21no—
11C59×#353C412yescomplemented
12C59×#339—21no—
13C59×#329—21no—
14C59×#329C412yescomplemented
15C2×#41×C59C2×C411yescharacteristic
16C2×#41×C59D411yescharacteristic
17#131×C59—42no—
18C2×M16×C59—21no—
19C2×M16×C59—41no—
20C2×M16×C59—41no—
21C4⋊Q8×C59Q811yescharacteristic
22#127×C59C2×C411yescharacteristic
23#124×C59C2×C411yescharacteristic
24#124×C59D411yescharacteristic
25#121×C59—41no—
26C4×D4×C59—41no—
27#117×C59—21no—
28#117×C59—41no—
29C2×C42×C59D411yescharacteristic
30#104×C59—42no—
31#99×C59—22no—
32#99×C59—41no—
33#99×C59—41no—
34#97×C59—22no—
35C4×C8×C59—41no—
36#41×C59—41no—
37#41×C59—41no—
38#41×C59—41no—
39#41×C59—41no—
40C2×Q8×C59C4⋊C411yescharacteristic
41C2×Q8×C59C4⋊C411yescharacteristic
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59—41no—
45C2×D4×C59C4211yescharacteristic
46C2×D4×C59C22⋊C411yescharacteristic
47C22×C4×C59—21no—
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59C22⋊C411yescharacteristic
51M16×C59—22no—
52M16×C59—44no—
53M16×C59—42no—
54M16×C59—41no—
55C2×C8×C59—42no—
56C2×C8×C59—41no—
57C2×C8×C59—42no—
58C4⋊C4×C59—41no—
59C4⋊C4×C59—41no—
60C4⋊C4×C59—81no—
61C22⋊C4×C59—41no—
62C22⋊C4×C59—41no—
63C22⋊C4×C59—42no—
64C22⋊C4×C59—41no—
65C42×C59—21no—
66C42×C59—41no—
67C42×C59—81no—
68C42×C59C22⋊C411yescharacteristic
69C42×C59C4⋊C411yescharacteristic
70C23×C59—21no—
71C23×C59—21no—
72C23×C59#9911yescharacteristic
73Q8×C59—41no—
74Q8×C59—41no—
75D4×C59—41no—
76D4×C59—41no—
77D4×C59—42no—
78D4×C59—82no—
79D4×C59—81no—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—42no—
87C2×C4×C59—41no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59—41no—
91C2×C4×C59—81no—
92C2×C4×C59—82no—
93C2×C4×C59#9511yescharacteristic
94C2×C4×C59#9911yescharacteristic
95C8×C59—44no—
96C8×C59—42no—
97#7486C5911yesmaximal, characteristic, direct product factor, Sylow
98C22×C59—21no—
99C22×C59—41no—
100C22×C59—41no—
101C22×C59—41no—
102C22×C59—81no—
103C22×C59—81no—
104C22×C59#34211yescharacteristic
105C4×C59—22no—
106C4×C59—21no—
107C4×C59—41no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59—161no—
111C4×C59—162no—
112C4×C59AΣL(1,𝔽16)11yescharacteristic
113C4×C59#35211yescharacteristic
114#2126C2×C5911yescharacteristic
115#1884C2×C5911yescharacteristic
116#1525C2×C5911yescharacteristic
117C2×C59—21no—
118C2×C59—41no—
119C2×C59—81no—
120C2×C59—81no—
121C2×C59#139011yescharacteristic
122#568C4×C5911yescharacteristic, complemented
123#532C22×C5911yescharacteristic
124#421—21no—
125#410—21no—
126#410C4×C5911yescharacteristic, complemented
127C4×M16—21no—
128#354—21no—
129#353C4×C5912yescomplemented
130#339—21no—
131#329—21no—
132#329C4×C5912yescomplemented
133C59#748611yescharacteristic, direct product factor, Sylow
134C2×#41C2×C4×C5911yescharacteristic
135C2×#41D4×C5911yescharacteristic
136#131—42no—
137C2×M16—21no—
138C2×M16—41no—
139C2×M16—41no—
140C4⋊Q8Q8×C5911yescharacteristic
141#127C2×C4×C5911yescharacteristic
142#124C2×C4×C5911yescharacteristic
143#124D4×C5911yescharacteristic
144#121—41no—
145C4×D4—41no—
146#117—21no—
147#117—41no—
148C2×C42D4×C5911yescharacteristic
149#104—42no—
150#99—22no—
151#99—41no—
152#99—41no—
153#97—22no—
154C4×C8—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159C2×Q8C4⋊C4×C5911yescharacteristic
160C2×Q8C4⋊C4×C5911yescharacteristic
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—41no—
164C2×D4C42×C5911yescharacteristic
165C2×D4C22⋊C4×C5911yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4C22⋊C4×C5911yescharacteristic
170M16—22no—
171M16—42no—
172M16—44no—
173M16—41no—
174C2×C8—42no—
175C2×C8—41no—
176C2×C8—42no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—81no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C42—21no—
185C42—41no—
186C42—81no—
187C42C22⋊C4×C5911yescharacteristic
188C42C4⋊C4×C5911yescharacteristic
189C23—21no—
190C23—21no—
191C23#99×C5911yescharacteristic
192Q8—41no—
193Q8—41no—
194D4—41no—
195D4—41no—
196D4—42no—
197D4—82no—
198D4—81no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—82no—
212C2×C4#95×C5911yescharacteristic
213C2×C4#99×C5911yescharacteristic
214C8—44no—
215C8—42no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22C59×#34211yescharacteristic
223C4—22no—
224C4—21no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—161no—
229C4—162no—
230C4C59×AΣL(1,𝔽16)11yescharacteristic
231C4C59×#35211yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—81no—
236C2C59×#139011yescharacteristic
subgroupG/H
centerC4×C59AΣL(1,𝔽16)
commutatorC2×D4C42×C59
Frattini, cosocle#532C22×C59
socleC2×C59#1390
prime radicalC59×#532C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C59×#532 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#568C4semidirect
8. C59×#410C4semidirect
11. C59×#353C4semidirect
14. C59×#329C4semidirect
97. #7486C59direct (N × H)
122. #568C4×C59semidirect
126. #410C4×C59semidirect
129. #353C4×C59semidirect
132. #329C4×C59semidirect
133. C59#7486direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#21262
C59×#18842
C59×#15252
#748659