Finite Group Databasebeta

← #28477999

Subgroups — #28477999

Order 15104.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#21425659C212yesmaximal
2#21425634C211yesmaximal, characteristic
3#21421922C211yesmaximal, characteristic
4#21421919C212yesmaximal
5C59×#2809C211yesmaximal, characteristic
6C2×#14273660—21no—
7C2×#14273651—21no—
8#16837272C2211yescharacteristic
9#16837164—22no—
10#16837164—22no—
11#16837157C2211yescharacteristic
12#16837157C2212yes—
13C59×#400—21no—
14C59×#398—22no—
15C59×#391—21no—
16C59×#391C2211yescharacteristic
17C59×#389C2212yes—
18C59×#387—22no—
19C22×C59⋊C8—21no—
20C22×C59⋊C8—22no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59—22no—
23#14273660—42no—
24#14273651—42no—
25C22×Q8×C59D411yescharacteristic
26C2×C4⋊C4×C59—22no—
27C2×C4⋊C4×C59—21no—
28C2×C4⋊C4×C59—21no—
29C2×C4⋊C4×C59D412yes—
30C2×C4⋊C4×C59D412yes—
31C2×C4⋊C4×C59D411yescharacteristic
32C2×C42×C59—21no—
33C2×C42×C59C2311yescharacteristic
34#95×C59—21no—
35#95×C59—22no—
36#95×C59—22no—
37#95×C59—22no—
38#95×C59—22no—
39C2×Q8×C59—21no—
40C2×Q8×C59—41no—
41C2×Q8×C59—41no—
42C2×Q8×C59Q1612yes—
43C22×C4×C59—21no—
44C22×C4×C59—21no—
45C22×C4×C59—22no—
46C22×C4×C59—22no—
47C22×C4×C59C2×D411yescharacteristic
48C22×C4×C59C2×D412yes—
49C22×Dic59—41no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—42no—
53C4⋊C4×C59—41no—
54C4⋊C4×C59—42no—
55C4⋊C4×C59—42no—
56C4⋊C4×C59—81no—
57C4⋊C4×C59—81no—
58C42×C59—41no—
59C42×C59—81no—
60C4⋊Dic59—41no—
61C4⋊Dic59—41no—
62C4⋊Dic59—44no—
63C2×C59⋊C8—22no—
64C2×C59⋊C8—41no—
65C2×C59⋊C8—41no—
66C2×C59⋊C8—42no—
67C2×C59⋊C8—42no—
68C2×C59⋊C8—42no—
69C23×C59#12011yescharacteristic
70Q8×C59—42no—
71Q8×C59—81no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—41no—
78C2×C4×C59—41no—
79C2×C4×C59—42no—
80C2×C4×C59—42no—
81C2×C4×C59—42no—
82C2×C4×C59—41no—
83C2×C4×C59—42no—
84C2×C4×C59—42no—
85C2×C4×C59—42no—
86C2×C4×C59—42no—
87C2×C4×C59C2×Q1611yescharacteristic
88C2×C4×C59#13512yes—
89C2×C4×C59#13712yes—
90C2×C4×C59#13711yescharacteristic
91C2×Dic59—81no—
92C2×Dic59—82no—
93C59⋊C8—42no—
94C59⋊C8—82no—
95#7831—591nomaximal, Sylow
96C22×C59#45111yescharacteristic
97C22×C59#45212yes—
98C22×C59#45311yescharacteristic
99C22×C59#45412yes—
100C22×C59#45811yescharacteristic
101C4×C59—21no—
102C4×C59—21no—
103C4×C59—22no—
104C4×C59—22no—
105C4×C59—42no—
106C4×C59—82no—
107C4×C59—82no—
108C4×C59—81no—
109Dic59—161no—
110#2809D5911yescharacteristic
111#2100—592no—
112#2095—591no—
113#1272—591no—
114#1271—592no—
115C2×C59#161411yescharacteristic
116C2×C59#161512yes—
117C2×C59#163411yescharacteristic
118C2×C59#163612yes—
119C2×C59#165711yescharacteristic
120C2×#107—1181no—
121C2×#103—1181no—
122#400—21no—
123#398—22no—
124#391—21no—
125#391C2×D5911yescharacteristic
126#389C2×D5912yes—
127#387—22no—
128#384—591no—
129#340—1182no—
130#340—1182no—
131#336—591no—
132#336—592no—
133C59#783111yescharacteristic, complemented, Sylow
134C22×Q8C22⋊D5911yescharacteristic
135C22×C8—1181no—
136C22×C8—1182no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—1182no—
141C2×C4⋊C4—1181no—
142C2×C4⋊C4C22⋊D5912yes—
143C2×C4⋊C4C22⋊D5912yes—
144C2×C4⋊C4C22⋊D5911yescharacteristic
145C2×C42—21no—
146C2×C42C22×D5911yescharacteristic
147#107—2362no—
148#103—2362no—
149#95—21no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8#1174567212yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—2361no—
163C22×C4C2×C22⋊D5911yescharacteristic
164C22×C4C2×C22⋊D5912yes—
165C2×C8—1182no—
166C2×C8—2362no—
167C2×C8—2362no—
168C2×C8—2362no—
169C2×C8—2361no—
170C2×C8—2361no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C4⋊C4—2361no—
180C4⋊C4—2361no—
181C4⋊C4—2364no—
182C42—41no—
183C42—81no—
184C23#1427369611yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—4721no—
203C2×C4—4722no—
204C2×C4C2×#1174567211yescharacteristic
205C2×C4#1427374712yes—
206C2×C4#1427375712yes—
207C2×C4#1427375811yescharacteristic
208C8—4722no—
209C8—2362no—
210C22#1683755811yescharacteristic
211C22#1683756412yes—
212C22#1683757011yescharacteristic
213C22#1683757512yes—
214C22#1683759211yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—81no—
222C4—82no—
223C4—9441no—
224C2#2142312111yescharacteristic
225C2#2142312712yes—
226C2#2142324111yescharacteristic
227C2#2142325412yes—
228C2#2142339411yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2809C2
socle, prime radicalC23×C59#120
hypercenter#2809D59
hypocenterC59#7831
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
133. C59#7831semidirect

Maximal subgroups

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

subgroupindex
#214256592
#214256342
#214219222
#214219192
C59×#28092
#783159