Finite Group Databasebeta

← C59×#7812 #28419921

Subgroups — C59×#7812 #28419921

Order 15104.

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

normal subgroups only

This group has 398 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×#2811C211yesmaximal, characteristic
2C59×#2096C211yesmaximal, characteristic
3C59×#2072C212yesmaximal
4C59×#1272C211yesmaximal, characteristic
5C59×#1272C212yesmaximal
6C2×#106×C59—21no—
7C2×#103×C59—22no—
8C2×#103×C59—21no—
9C59×#395—22no—
10C59×#395—21no—
11C59×#391—22no—
12C59×#391—21no—
13C59×#391C2212yes—
14C59×#391C2211yescharacteristic
15C59×#384C2211yescharacteristic
16C59×#340—22no—
17C59×#336C2212yes—
18C59×#336C2211yescharacteristic
19C22×Q8×C59—21no—
20C22×Q8×C59D412yes—
21C22×Q8×C59D411yescharacteristic
22C22×C8×C59—21no—
23C22×C8×C59—22no—
24C2×C4⋊C4×C59—22no—
25C2×C4⋊C4×C59—21no—
26C2×C4⋊C4×C59—21no—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59D412yes—
29C2×C4⋊C4×C59D411yescharacteristic
30C2×C42×C59—21no—
31C2×C42×C59C2311yescharacteristic
32#106×C59—42no—
33#103×C59—42no—
34#103×C59—44no—
35#95×C59—21no—
36#95×C59—22no—
37#95×C59—22no—
38#95×C59—22no—
39#95×C59—22no—
40C2×Q8×C59—22no—
41C2×Q8×C59—21no—
42C2×Q8×C59—41no—
43C2×Q8×C59—42no—
44C2×Q8×C59—42no—
45C2×Q8×C59—41no—
46C2×Q8×C59—81no—
47C2×Q8×C59—82no—
48C2×Q8×C59SD1614yes—
49C2×Q8×C59Q1612yes—
50C22×C4×C59—22no—
51C22×C4×C59—21no—
52C22×C4×C59—21no—
53C22×C4×C59—22no—
54C22×C4×C59—41no—
55C22×C4×C59C2×D412yes—
56C22×C4×C59C2×D411yescharacteristic
57C2×C8×C59—22no—
58C2×C8×C59—41no—
59C2×C8×C59—41no—
60C2×C8×C59—42no—
61C2×C8×C59—42no—
62C2×C8×C59—42no—
63C4⋊C4×C59—41no—
64C4⋊C4×C59—42no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—42no—
68C4⋊C4×C59—42no—
69C4⋊C4×C59—81no—
70C4⋊C4×C59—82no—
71C42×C59—41no—
72C42×C59—81no—
73C23×C59#12011yescharacteristic
74Q8×C59—44no—
75Q8×C59—42no—
76Q8×C59—82no—
77Q8×C59—81no—
78Q8×C59—84no—
79C2×C4×C59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—24no—
84C2×C4×C59—22no—
85C2×C4×C59—41no—
86C2×C4×C59—42no—
87C2×C4×C59—42no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59—42no—
91C2×C4×C59—42no—
92C2×C4×C59—42no—
93C2×C4×C59—42no—
94C2×C4×C59—82no—
95C2×C4×C59—81no—
96C2×C4×C59C2×SD1612yes—
97C2×C4×C59C2×Q1611yescharacteristic
98C2×C4×C59#13712yes—
99C2×C4×C59#13711yescharacteristic
100C8×C59—42no—
101C8×C59—82no—
102#7812C5911yesmaximal, characteristic, direct product factor, Sylow
103C22×C59#44812yes—
104C22×C59#45111yescharacteristic
105C22×C59#45311yescharacteristic
106C22×C59#45512yes—
107C22×C59#45811yescharacteristic
108C4×C59—22no—
109C4×C59—22no—
110C4×C59—21no—
111C4×C59—21no—
112C4×C59—44no—
113C4×C59—42no—
114C4×C59—81no—
115C4×C59—82no—
116C4×C59—161no—
117#2811C2×C5911yescharacteristic
118#2096C2×C5911yescharacteristic
119#2072C2×C5912yes—
120#1272C2×C5911yescharacteristic
121#1272C2×C5912yes—
122C2×C59#160812yes—
123C2×C59#161411yescharacteristic
124C2×C59#162311yescharacteristic
125C2×C59#164512yes—
126C2×C59#165911yescharacteristic
127C2×#106—21no—
128C2×#103—22no—
129C2×#103—21no—
130#395—22no—
131#395—21no—
132#391—22no—
133#391—21no—
134#391C22×C5912yes—
135#391C22×C5911yescharacteristic
136#384C22×C5911yescharacteristic
137#340—22no—
138#336C22×C5912yes—
139#336C22×C5911yescharacteristic
140C59#781211yescharacteristic, direct product factor, Sylow
141C22×Q8—21no—
142C22×Q8D4×C5912yes—
143C22×Q8D4×C5911yescharacteristic
144C22×C8—21no—
145C22×C8—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C5912yes—
151C2×C4⋊C4D4×C5911yescharacteristic
152C2×C42—21no—
153C2×C42C23×C5911yescharacteristic
154#106—42no—
155#103—42no—
156#103—44no—
157#95—21no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—82no—
170C2×Q8SD16×C5914yes—
171C2×Q8Q16×C5912yes—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4C2×D4×C5912yes—
178C22×C4C2×D4×C5911yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—82no—
193C42—41no—
194C42—81no—
195C23#120×C5911yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—81no—
218C2×C4C2×SD16×C5912yes—
219C2×C4C2×Q16×C5911yescharacteristic
220C2×C4#137×C5912yes—
221C2×C4#137×C5911yescharacteristic
222C8—42no—
223C8—82no—
224C22C59×#44812yes—
225C22C59×#45111yescharacteristic
226C22C59×#45311yescharacteristic
227C22C59×#45512yes—
228C22C59×#45811yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—161no—
238C2C59×#160812yes—
239C2C59×#161411yescharacteristic
240C2C59×#162311yescharacteristic
241C2C59×#164512yes—
242C2C59×#165911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
102. #7812C59direct (N × H)
140. C59#7812direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#28112
C59×#20962
C59×#20722
C59×#12722
#781259