Finite Group Databasebeta

← #28491718

Subgroups — #28491718

Order 15104.

416 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 125 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#21425044C212yesmaximal
2#21424897C211yesmaximal, characteristic
3#21421979C211yesmaximal, characteristic
4#21421937C212yesmaximal
5C59×#2571C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7C2×C4⋊(C59⋊C8)C2212yes—
8C2×#14273650—22no—
9C2×C4×C59⋊C8C2211yescharacteristic
10#16837164—22no—
11#16837164—22no—
12C59×#400—22no—
13C59×#389—22no—
14C59×#384C2211yescharacteristic
15C59×#382—22no—
16C4×C4⋊C4×C59C2212yes—
17C22×Dic118—21no—
18C22×C59⋊C8—21no—
19C22×C59⋊C8—22no—
20#14273727—22no—
21#14273727—21no—
22#14273727Q812yes—
23C2×C4⋊Dic59—22no—
24C4⋊(C59⋊C8)—22no—
25C4⋊(C59⋊C8)—22no—
26#14273650—44no—
27C4×C59⋊C8—22no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—22no—
30C2×C4⋊C4×C59D412yes—
31C2×C4⋊C4×C59D412yes—
32C2×C4⋊C4×C59D412yes—
33C2×C42×C59—22no—
34C2×C42×C59C2311yescharacteristic
35#95×C59—22no—
36#95×C59—24no—
37#95×C59—22no—
38C22×C4×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2×D411yescharacteristic
42C22×C4×C59C2×D412yes—
43C22×Dic59—41no—
44C2×Dic118—22no—
45C2×Dic118—42no—
46C2×Dic118—42no—
47C2×Dic118—41no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59—22no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—42no—
53C4⋊C4×C59—42no—
54C4⋊C4×C59—42no—
55C4⋊C4×C59—82no—
56C42×C59—42no—
57C42×C59—42no—
58C42×C59C2×Q811yescharacteristic
59C42×C59#4112yes—
60C42×C59#4111yescharacteristic
61C4⋊Dic59—24no—
62C4⋊Dic59—42no—
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
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59—44no—
77C2×C4×C59—42no—
78C2×C4×C59—42no—
79C2×C4×C59—42no—
80C2×C4×C59C22⋊Q811yescharacteristic
81C2×C4×C59C22⋊Q812yes—
82C2×C4×C59#12411yescharacteristic
83C2×C4×C59#12412yes—
84C2×C4×C59#13512yes—
85C2×C4×C59#13512yes—
86C2×C4×C59#13712yes—
87C2×C4×C59#13712yes—
88C2×Dic59—42no—
89C2×Dic59—81no—
90C2×Dic59—81no—
91Dic118—44no—
92Dic118—82no—
93C59⋊C8—42no—
94C59⋊C8—82no—
95#10352—591nomaximal, Sylow
96C22×C59#39311yescharacteristic
97C22×C59#45212yes—
98C22×C59#45212yes—
99C22×C59#45311yescharacteristic
100C22×C59#45411yescharacteristic
101C4×C59—21no—
102C4×C59—21no—
103C4×C59—82no—
104C4×C59—82no—
105C4×C59—82no—
106C4×C59#47912yes—
107C4×C59#47912yes—
108C4×C59#48812yes—
109C4×C59#49112yes—
110Dic59—82no—
111#2571D5911yescharacteristic
112#1987—592no—
113#1956—591no—
114#1296—591no—
115#1279—592no—
116C2×C59#163011yescharacteristic
117C2×C59#163411yescharacteristic
118C2×C59#163812yes—
119C2×C59#202612yes—
120C2×C59#202711yescharacteristic
121C2×C4⋊Q8—591no—
122C2×C4⋊C8—592no—
123C2×#103—1182no—
124C2×C4×C8—591no—
125#400—22no—
126#389—22no—
127#384C2×D5911yescharacteristic
128#382—22no—
129C4×C4⋊C4C2×D5912yes—
130#340—1182no—
131#340—1182no—
132C59#1035211yescharacteristic, complemented, Sylow
133C22×Q8—1181no—
134C22×C8—1181no—
135C22×C8—1182no—
136C4⋊Q8—592no—
137C4⋊Q8—1182no—
138C4⋊Q8—1181no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—1182no—
142C2×C4⋊C4C22⋊D5912yes—
143C2×C4⋊C4C22⋊D5912yes—
144C2×C4⋊C4C22⋊D5912yes—
145C2×C42—22no—
146C2×C42C22×D5911yescharacteristic
147C4⋊C8—1182no—
148C4⋊C8—1182no—
149#103—2364no—
150C4×C8—1182no—
151#95—22no—
152#95—24no—
153#95—22no—
154C2×Q8—1182no—
155C2×Q8—2362no—
156C2×Q8—2362no—
157C2×Q8—2361no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—2361no—
162C22×C4C2×C22⋊D5911yescharacteristic
163C22×C4C2×C22⋊D5912yes—
164C2×C8—1182no—
165C2×C8—2362no—
166C2×C8—2362no—
167C2×C8—2362no—
168C2×C8—2361no—
169C2×C8—2361no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—82no—
178C4⋊C4—1184no—
179C4⋊C4—2362no—
180C42—42no—
181C42—42no—
182C42Q8×D5911yescharacteristic
183C42#1174568912yes—
184C42#1174568911yescharacteristic
185C23#1427369611yescharacteristic
186Q8—4722no—
187Q8—2364no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—4721no—
199C2×C4—4721no—
200C2×C4—2362no—
201C2×C4#1427370311yescharacteristic
202C2×C4#1427370312yes—
203C2×C4#1427371611yescharacteristic
204C2×C4#1427371612yes—
205C2×C4#1427374712yes—
206C2×C4#1427374712yes—
207C2×C4#1427375712yes—
208C2×C4#1427375712yes—
209C8—4722no—
210C8—2362no—
211C22#1683731311yescharacteristic
212C22#1683756412yes—
213C22#1683756412yes—
214C22#1683757011yescharacteristic
215C22#1683757511yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—4722no—
222C4#1683770612yes—
223C4#1683770612yes—
224C4#1683775912yes—
225C4#1683777212yes—
226C2#2142321711yescharacteristic
227C2#2142324111yescharacteristic
228C2#2142326812yes—
229C2#2142524412yes—
230C2#2142524911yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2571C2
socle, prime radicalC23×C59#120
hypercenter#2571D59
hypocenterC59#10352
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
132. C59#10352semidirect

Maximal subgroups

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

subgroupindex
#214250442
#214248972
#214219792
#214219372
C59×#25712
#1035259