Finite Group Databasebeta

← #28477822

Subgroups — #28477822

Order 15104.

366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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#21432084C211yesmaximal, characteristic
2#21425639C211yesmaximal, characteristic
3#21425569C212yesmaximal
4#21421920C212yesmaximal
5C59×#1272C211yesmaximal, characteristic
6C2×#14273661—22no—
7C2×#14273658—21no—
8C2×#14273651—21no—
9#16837341—21no—
10#16837334—22no—
11#16837309—21no—
12#16837300C2212yes—
13#16837289—22no—
14#16837272C2211yescharacteristic
15#16837165—22no—
16#16837157C2211yescharacteristic
17C59×#391C2211yescharacteristic
18C59×#336C2212yes—
19C22×C59⋊C8—21no—
20C2×C4⋊Dic59—21no—
21C2×C4⋊Dic59—22no—
22C2×C4⋊Dic59—21no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59D412yes—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27C2×C4×Dic59—21no—
28#14273661—44no—
29#14273658—42no—
30#14273651—42no—
31C59⋊#95—21no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C59⋊#95—22no—
35C22×Q8×C59D411yescharacteristic
36C22×C8×C59—22no—
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C42×C59C2311yescharacteristic
39#95×C59—22no—
40C2×Q8×C59—21no—
41C2×Q8×C59—41no—
42C2×Q8×C59—41no—
43C2×Q8×C59Q1612yes—
44C22×C4×C59—21no—
45C22×C4×C59—21no—
46C22×C4×C59C2×D411yescharacteristic
47C22×C4×C59C2×D412yes—
48C22×Dic59—22no—
49C22×Dic59—22no—
50C22×Dic59—41no—
51C2×C8×C59—24no—
52C2×C8×C59—42no—
53C2×C8×C59—42no—
54C4⋊C4×C59—41no—
55C42×C59—41no—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59—42no—
59C4⋊Dic59—41no—
60C4⋊Dic59—41no—
61C4⋊Dic59—42no—
62C4⋊Dic59—42no—
63C4⋊Dic59—81no—
64C4⋊Dic59—81no—
65Dic59⋊C4—42no—
66Dic59⋊C4—42no—
67C4×Dic59—81no—
68C2×C59⋊C8—22no—
69C2×C59⋊C8—41no—
70C2×C59⋊C8—41no—
71C23×C59#12011yescharacteristic
72Q8×C59—42no—
73Q8×C59—81no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—41no—
80C2×C4×C59—41no—
81C2×C4×C59—41no—
82C2×C4×C59—42no—
83C2×C4×C59C2×Q1611yescharacteristic
84C2×C4×C59#13512yes—
85C2×C4×C59AGL(1,ℤ/8)12yes—
86C2×C4×C59#13711yescharacteristic
87C2×Dic59—42no—
88C2×Dic59—42no—
89C2×Dic59—42no—
90C2×Dic59—42no—
91C2×Dic59—42no—
92C2×Dic59—42no—
93C2×Dic59—82no—
94C2×Dic59—81no—
95C8×C59—44no—
96C59⋊C8—42no—
97#7802—591nomaximal, Sylow
98C22×C59#44912yes—
99C22×C59#45111yescharacteristic
100C22×C59#45311yescharacteristic
101C22×C59#45612yes—
102C22×C59#45811yescharacteristic
103C4×C59—22no—
104C4×C59—22no—
105C4×C59—21no—
106C4×C59—21no—
107C4×C59—42no—
108C4×C59—81no—
109Dic59—82no—
110Dic59—82no—
111Dic59—161no—
112#2809—591no—
113#2096—591no—
114#2083—592no—
115#1272D5911yescharacteristic
116#1271—592no—
117C2×C59#160912yes—
118C2×C59#161411yescharacteristic
119C2×C59#162411yescharacteristic
120C2×C59#164812yes—
121C2×C59#166011yescharacteristic
122C2×#107—1182no—
123C2×#106—1181no—
124C2×#103—1181no—
125#400—1181no—
126#398—1182no—
127#391—1181no—
128#391C2×D5911yescharacteristic
129#389—592no—
130#387—1182no—
131#384—591no—
132#340—1182no—
133#336—591no—
134#336C2×D5912yes—
135C59#780211yescharacteristic, complemented, Sylow
136C22×Q8D23611yescharacteristic
137C22×C8—22no—
138C22×C8—1181no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—1181no—
142C2×C4⋊C4—1181no—
143C2×C4⋊C4—1182no—
144C2×C4⋊C4—1181no—
145C2×C4⋊C4—1182no—
146C2×C4⋊C4D23611yescharacteristic
147C2×C42—1181no—
148C2×C42C22×D5911yescharacteristic
149#107—2364no—
150#106—2362no—
151#103—2362no—
152#95—22no—
153#95—1181no—
154#95—1182no—
155#95—1182no—
156#95—1182no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8Dic23612yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—1182no—
164C22×C4—1182no—
165C22×C4—2361no—
166C22×C4C2×D23611yescharacteristic
167C22×C4D4×D5912yes—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—1182no—
172C2×C8—2361no—
173C2×C8—2361no—
174C4⋊C4—41no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—4721no—
178C4⋊C4—4721no—
179C4⋊C4—2361no—
180C4⋊C4—2361no—
181C4⋊C4—2362no—
182C4⋊C4—2362no—
183C4⋊C4—2362no—
184C4⋊C4—2362no—
185C4⋊C4—2362no—
186C42—41no—
187C42—4721no—
188C23#1427369711yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—4722no—
201C2×C4—4721no—
202C2×C4—2362no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4—2362no—
207C2×C4—2362no—
208C2×C4C2×Dic23611yescharacteristic
209C2×C4#1427375012yes—
210C2×C4#1427375412yes—
211C2×C4#1427376011yescharacteristic
212C8—44no—
213C8—2362no—
214C22#1683755012yes—
215C22#1683756011yescharacteristic
216C22#1683757211yescharacteristic
217C22#1683758612yes—
218C22#1683759311yescharacteristic
219C4—21no—
220C4—21no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—81no—
225C4—9441no—
226C4—4722no—
227C4—4722no—
228C2#2142309612yes—
229C2#2142312311yescharacteristic
230C2#2142318011yescharacteristic
231C2#2142334112yes—
232C2#2142340811yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59#120
hypercenter#1272D59
hypocenterC59#7802
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
135. C59#7802semidirect

Maximal subgroups

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

subgroupindex
#214320842
#214256392
#214255692
#214219202
C59×#12722
#780259