Finite Group Databasebeta

← #28502967

Subgroups — #28502967

Order 15104.

212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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#21426348C211yesmaximal, characteristic
2#21426001C211yesmaximal, characteristic
3#21423467C211yesmaximal, characteristic
4#21423463C211yesmaximal, characteristic
5#21422169C211yesmaximal, characteristic
6#21422146C211yesmaximal, characteristic
7C59×#1362C211yesmaximal, characteristic
8C2×#14273673—21no—
9C2×#14273673—21no—
10#16837782C2211yescharacteristic
11#16837688—21no—
12#16837684—21no—
13C8×Dic118C2211yescharacteristic
14Dic59⋊C16—21no—
15#16837177—21no—
16C4×C59⋊C16C2211yescharacteristic
17#16837155C2211yescharacteristic
18#16837148—21no—
19#16837147—21no—
20C59×#494C2211yescharacteristic
21C59×C4⋊C16C2211yescharacteristic
22C59×#335C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25#14273727—21no—
26C4×Dic118D411yescharacteristic
27#14273673—42no—
28#14273673—42no—
29C2×C59⋊C16D411yescharacteristic
30C2×C59⋊C16D411yescharacteristic
31#14273659—41no—
32#14273658—41no—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)D411yescharacteristic
35Dic59⋊C8—21no—
36#14273652—41no—
37#14273650—41no—
38C8×Dic59—21no—
39C2×Q16×C59—21no—
40C2×Q16×C59—21no—
41C4⋊Q8×C59—21no—
42C2×C16×C59—21no—
43C4⋊C8×C59—21no—
44C4×C8×C59C2311yescharacteristic
45C2×Q8×C59—41no—
46C2×Dic118—41no—
47C2×Dic118D811yescharacteristic
48Q16×C59—41no—
49Q16×C59—41no—
50Q16×C59—81no—
51C2×C8×C59—41no—
52C2×C8×C59C2×D411yescharacteristic
53C2×C8×C59#4111yescharacteristic
54C4⋊C4×C59—41no—
55C4⋊C4×C59—41no—
56C42×C59C2×D411yescharacteristic
57C4⋊Dic59—41no—
58C4⋊Dic59—41no—
59C4⋊Dic59D811yescharacteristic
60Dic59⋊C4—21no—
61C4×Dic59—21no—
62C2×C59⋊C8—21no—
63C2×C59⋊C8—41no—
64Dic236—41no—
65Dic236—41no—
66Dic236—81no—
67C16×C59—41no—
68C59⋊C16—21no—
69C59⋊C16SD1612yes—
70Q8×C59—81no—
71Q8×C59—81no—
72C2×C4×C59—81no—
73C2×C4×C59#12111yescharacteristic
74C2×C4×C59C2×D811yescharacteristic
75C2×C4×C59#13511yescharacteristic
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—81no—
79Dic118—21no—
80Dic118—21no—
81Dic118—81no—
82Dic118—81no—
83C8×C59—21no—
84C8×C59—81no—
85C8×C59C2×SD1611yescharacteristic
86C8×C59AGL(1,ℤ/8)11yescharacteristic
87C59⋊C8—41no—
88C59⋊C8—81no—
89#12443—591nomaximal, Sylow
90C22×C59#46611yescharacteristic
91C4×C59—21no—
92C4×C59—161no—
93C4×C59#46011yescharacteristic
94C4×C59#47211yescharacteristic
95C4×C59#51011yescharacteristic
96C4×C59#51011yescharacteristic
97Dic59—41no—
98Dic59—41no—
99Dic59—161no—
100#2247—591no—
101#2183—591no—
102#1670—591no—
103#1670—591no—
104#1372—591no—
105#1362—591no—
106#1362D5911yescharacteristic
107C2×C59#166811yescharacteristic
108C2×C59#221911yescharacteristic
109C2×C59#222211yescharacteristic
110C2×Q32—1181no—
111C2×Q32—1181no—
112#494—591no—
113#494C2×D5911yescharacteristic
114#475—1181no—
115#475—1181no—
116C8×Q8—591no—
117C4⋊C16—1181no—
118C4⋊C16C2×D5911yescharacteristic
119#346—1181no—
120C4×C16—591no—
121#335—591no—
122#335C2×D5911yescharacteristic
123#332—1181no—
124#332—1181no—
125C59#1244311yescharacteristic, complemented, Sylow
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—1181no—
129C2×Q16—1181no—
130C4⋊Q8—21no—
131C4⋊Q8—1181no—
132C4×Q8—591no—
133Q32—2362no—
134Q32—2362no—
135C2×C16—21no—
136C2×C16—591no—
137C2×C16—591no—
138#106—2361no—
139#106—2361no—
140C4⋊C8—21no—
141C4⋊C8—591no—
142C4⋊C8—1181no—
143C4⋊C8—1181no—
144#103—2361no—
145#103—2361no—
146C4×C8—1181no—
147C4×C8C22×D5911yescharacteristic
148C2×Q8—41no—
149C2×Q8—591no—
150C2×Q8—2361no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—4721no—
155Q16—2361no—
156Q16—2361no—
157C2×C8—41no—
158C2×C8—1181no—
159C2×C8—2361no—
160C2×C8#1174568511yescharacteristic
161C2×C8D4×D5911yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—591no—
165C4⋊C4—1181no—
166C4⋊C4—2361no—
167C4⋊C4—2361no—
168C42—1181no—
169C42D4×D5911yescharacteristic
170C16—41no—
171C16—592no—
172C16—1181no—
173Q8—81no—
174Q8—81no—
175Q8—1181no—
176Q8—1181no—
177Q8—4721no—
178Q8—4721no—
179C2×C4—81no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—4721no—
183C2×C4#1427370011yescharacteristic
184C2×C4D8×D5911yescharacteristic
185C2×C4#1427374811yescharacteristic
186C8—21no—
187C8—81no—
188C8—4721no—
189C8—2361no—
190C8SD16×D5911yescharacteristic
191C8#1427375111yescharacteristic
192C22#1683763711yescharacteristic
193C4—21no—
194C4—161no—
195C4—9441no—
196C4—2361no—
197C4—2361no—
198C4#1683760111yescharacteristic
199C4#1683767111yescharacteristic
200C4#1683784111yescharacteristic
201C4#1683784411yescharacteristic
202C2#2142345511yescharacteristic
203C2#2142620311yescharacteristic
204C2#2142622011yescharacteristic
subgroupG/H
centerC22#16837637
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1362C2
socle, prime radicalC22×C59#466
hypercenter#1362D59
hypocenterC59#12443
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
125. C59#12443semidirect

Maximal subgroups

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

subgroupindex
#214263482
#214260012
#214234672
#214234632
#214221692
#214221462
C59×#13622
#1244359