Finite Group Databasebeta

← #28502399

Subgroups — #28502399

Order 15104.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#21436985C211yesmaximal, characteristic
2#21426323C211yesmaximal, characteristic
3#21423463C211yesmaximal, characteristic
4#21422150C211yesmaximal, characteristic
5#21422074C211yesmaximal, characteristic
6#21422060C211yesmaximal, characteristic
7C59×#2209C211yesmaximal, characteristic
8#16838131—21no—
9#16837807C2211yescharacteristic
10#16837803—21no—
11#16837711—22no—
12#16837687—21no—
13#16837684—21no—
14C8×Dic118C2211yescharacteristic
15Q16×Dic59—21no—
16#16837206—22no—
17C4×C59⋊C16C2211yescharacteristic
18#16837155C2211yescharacteristic
19#16837148—21no—
20C2×Q32×C59—21no—
21C59×#494C2211yescharacteristic
22C4×Q16×C59C2211yescharacteristic
23C59×C4⋊C16C2211yescharacteristic
24C59×#358—21no—
25#14273727—21no—
26#14273727—41no—
27#14273718—22no—
28#14273718—42no—
29Q8×Dic59—22no—
30C4×Dic118—41no—
31C4×Dic118D411yescharacteristic
32C2×C59⋊C16—21no—
33#14273661—21no—
34#14273661D412yes—
35#14273658—22no—
36#14273658—41no—
37C4⋊(C59⋊C8)—21no—
38C4⋊(C59⋊C8)D411yescharacteristic
39Dic59⋊C8—21no—
40#14273651—22no—
41#14273650—41no—
42C8×Dic59—21no—
43C2×Q16×C59—21no—
44C2×Q16×C59—21no—
45C2×Q16×C59D411yescharacteristic
46C4⋊Q8×C59—21no—
47C4×Q8×C59—21no—
48Q32×C59—42no—
49C2×C16×C59—21no—
50#107×C59D411yescharacteristic
51#103×C59—21no—
52C4×C8×C59C2311yescharacteristic
53C2×Q8×C59—21no—
54C2×Q8×C59—41no—
55C2×Dic118—41no—
56C2×Dic118D811yescharacteristic
57Q16×C59—21no—
58Q16×C59—42no—
59Q16×C59—41no—
60Q16×C59—41no—
61Q16×C59SD1612yes—
62C2×C8×C59C2×D411yescharacteristic
63C2×C8×C59C2×D411yescharacteristic
64C4⋊C4×C59—21no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—41no—
68C42×C59—41no—
69C42×C59C2×D411yescharacteristic
70C4⋊Dic59—22no—
71C4⋊Dic59—42no—
72C4⋊Dic59—42no—
73C4⋊Dic59—41no—
74C4⋊Dic59D811yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—42no—
77C4×Dic59—21no—
78C4×Dic59—42no—
79C2×C59⋊C8—21no—
80C2×C59⋊C8—41no—
81C16×C59—41no—
82C59⋊C16—41no—
83Q8×C59—22no—
84Q8×C59—41no—
85Q8×C59—81no—
86Q8×C59—81no—
87C2×C4×C59—41no—
88C2×C4×C59—41no—
89C2×C4×C59—81no—
90C2×C4×C59#12011yescharacteristic
91C2×C4×C59C2×D811yescharacteristic
92C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
93C2×Dic59—21no—
94C2×Dic59—21no—
95C2×Dic59—42no—
96Dic118—21no—
97Dic118—21no—
98Dic118—81no—
99Dic118—81no—
100C8×C59—21no—
101C8×C59C2×SD1611yescharacteristic
102C8×C59#13711yescharacteristic
103C59⋊C8—41no—
104C59⋊C8—81no—
105#12357—591nomaximal, Sylow
106C22×C59#44711yescharacteristic
107C4×C59—21no—
108C4×C59—42no—
109C4×C59—81no—
110C4×C59—161no—
111C4×C59#44811yescharacteristic
112C4×C59#45411yescharacteristic
113C4×C59#50811yescharacteristic
114C4×C59#51011yescharacteristic
115Dic59—41no—
116Dic59—41no—
117Dic59—82no—
118#3383—591no—
119#2241—591no—
120#2209D5911yescharacteristic
121#1670—591no—
122#1364—591no—
123Q8⋊C16—591no—
124#1332—591no—
125C2×C59#162711yescharacteristic
126C2×C59#218911yescharacteristic
127C2×C59#219511yescharacteristic
128#557—1181no—
129C2×Q32—21no—
130#500—591no—
131#499—1181no—
132#494C2×D5911yescharacteristic
133#479—1182no—
134#475—1181no—
135#475—1181no—
136C8×Q8—591no—
137C4×Q16—1181no—
138C4×Q16C2×D5911yescharacteristic
139C4⋊C16C2×D5911yescharacteristic
140#358—21no—
141#358—1182no—
142C4×C16—591no—
143#335—591no—
144#332—1181no—
145C59#1235711yescharacteristic, complemented, Sylow
146C2×Q16—21no—
147C2×Q16—21no—
148C2×Q16C22⋊D5911yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—1181no—
151C4⋊Q8—2361no—
152#125—1182no—
153#125—2362no—
154C4×Q8—21no—
155C4×Q8—591no—
156C4×Q8—1182no—
157C4×Q8—2361no—
158Q32—42no—
159C2×C16—21no—
160C2×C16—1181no—
161#107—592no—
162#107—1181no—
163#107C22⋊D5911yescharacteristic
164#106—1182no—
165#106—2361no—
166C4⋊C8—591no—
167C4⋊C8—1181no—
168C4⋊C8—1181no—
169#103—21no—
170#103—1182no—
171#103—2361no—
172C4×C8—1181no—
173C4×C8C22×D5911yescharacteristic
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—591no—
177C2×Q8—2361no—
178Q16—21no—
179Q16—42no—
180Q16—41no—
181Q16—41no—
182Q16#1174567012yes—
183C2×C8—1181no—
184C2×C8—2361no—
185C2×C8D4×D5911yescharacteristic
186C2×C8C2×C22⋊D5911yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—591no—
192C4⋊C4—1181no—
193C4⋊C4—1182no—
194C4⋊C4—2362no—
195C4⋊C4—2362no—
196C4⋊C4—2362no—
197C4⋊C4—2361no—
198C42—41no—
199C42—1181no—
200C42—2362no—
201C42D4×D5911yescharacteristic
202C16—41no—
203C16—2361no—
204Q8—22no—
205Q8—41no—
206Q8—81no—
207Q8—81no—
208Q8—1181no—
209Q8—1181no—
210Q8—4721no—
211Q8—4721no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—2362no—
218C2×C4#1427369511yescharacteristic
219C2×C4D8×D5911yescharacteristic
220C2×C4#1427375111yescharacteristic
221C8—21no—
222C8—4721no—
223C8—2361no—
224C8C2×#1174567011yescharacteristic
225C8#1427375711yescharacteristic
226C22#1683753411yescharacteristic
227C4—21no—
228C4—42no—
229C4—81no—
230C4—161no—
231C4—4722no—
232C4—2361no—
233C4—2361no—
234C4#1683754011yescharacteristic
235C4#1683757311yescharacteristic
236C4#1683783511yescharacteristic
237C4#1683784411yescharacteristic
238C2#2142319811yescharacteristic
239C2#2142603511yescharacteristic
240C2#2142607111yescharacteristic
subgroupG/H
centerC22#16837534
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#2209C2
socle, prime radicalC22×C59#447
hypercenter#2209D59
hypocenterC59#12357
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
145. C59#12357semidirect

Maximal subgroups

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

subgroupindex
#214369852
#214263232
#214234632
#214221502
#214220742
#214220602
C59×#22092
#1235759