Finite Group Databasebeta

← #28502933

Subgroups — #28502933

Order 15104.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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, complemented
2#21426178C211yesmaximal, characteristic
3#21426174C211yesmaximal, characteristic
4#21425932C211yesmaximal, characteristic
5#21422171C211yesmaximal, characteristic, complemented
6#21422134C211yesmaximal, characteristic, complemented
7C59×#1358C211yesmaximal, characteristic, complemented
8#16837845—21no—
9#16837843—21no—
10C2×#14273673—21no—
11C2×#14273673—21no—
12#16837820—21no—
13#16837782C2211yescharacteristic
14#16837520C2211yescharacteristic
15#16837223C2211yescharacteristic
16#16837219—21no—
17#16837218—21no—
18#16837187—21no—
19C4×C59⋊C16C2211yescharacteristic
20C59×#494C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#364C2211yescharacteristic
23#14273749D411yescharacteristic
24C2×Dic236—21no—
25C2×Dic236—21no—
26#14273733—21no—
27#14273727—21no—
28Dic472—41no—
29#14273673—42no—
30#14273673—41no—
31#14273673—41no—
32#14273673—41no—
33#14273672—41no—
34#14273670—41no—
35#14273667—21no—
36#14273666—41no—
37C2×C59⋊C16D411yescharacteristic
38C2×C59⋊C16D411yescharacteristic
39C16×D59—41no—
40#14273663D411yescharacteristic
41#14273655—21no—
42C2×Q16×C59—21no—
43C2×Q16×C59—21no—
44C4⋊Q8×C59—21no—
45M32×C59—21no—
46M32×C59—21no—
47C4×C8×C59C2311yescharacteristic
48C2×Q8×C59—41no—
49#11745685—21no—
50C2×Dic118—41no—
51Q16×C59—41no—
52Q16×C59—41no—
53Q16×C59—41no—
54Q16×C59—41no—
55C2×C8×C59C2×D411yescharacteristic
56C2×C8×C59C2×D411yescharacteristic
57C4⋊C4×C59—81no—
58C42×C59#4111yescharacteristic
59C4⋊Dic59—81no—
60#11745664—21no—
61Dic236—41no—
62Dic236—41no—
63Dic236—41no—
64Dic236—41no—
65Dic236D811yescharacteristic
66D472D811yescharacteristic
67#11745660—21no—
68#11745659—41no—
69C8×D59—41no—
70C16×C59—41no—
71C16×C59—41no—
72C59⋊C16—21no—
73C59⋊C16—41no—
74C59⋊C16D811yescharacteristic
75C59⋊C16D811yescharacteristic
76Q8×C59—81no—
77Q8×C59—81no—
78C2×C4×C59—21no—
79C2×C4×C59—81no—
80C2×C4×C59#12111yescharacteristic
81C22⋊D59—41no—
82C2×Dic59—81no—
83D236—21no—
84C4×D59—41no—
85Dic118—21no—
86Dic118—81no—
87Dic118—81no—
88C8×C59C2×D811yescharacteristic
89C8×C59C2×D811yescharacteristic
90C8×C59#13511yescharacteristic
91C8×C59AGL(1,ℤ/8)11yescharacteristic
92C59⋊C8—41no—
93#12437—591nomaximal, Sylow
94C22×C59#47211yescharacteristic
95C2×D59—41no—
96C4×C59—22no—
97C4×C59—161no—
98C4×C59#45911yescharacteristic
99C4×C59#46611yescharacteristic
100Dic59—41no—
101Dic59—161no—
102#2247—591no—
103#2214—591no—
104#2214—591no—
105#2170—591no—
106#1373—591no—
107#1358—591no—
108#1358D5911yescharacteristic, complemented
109C2×C59—21no—
110C2×C59#166711yescharacteristic
111D59—81no—
112#510—1181no—
113#510—1181no—
114C2×Q32—1181no—
115C2×Q32—1181no—
116#504—1181no—
117#494—591no—
118#494C2×D5911yescharacteristic
119#443—591no—
120#364—591no—
121#364C2×D5911yescharacteristic
122#364C2×D5911yescharacteristic
123#362—1181no—
124#362—1181no—
125#350—1181no—
126C4×C16—591no—
127C59#1243711yescharacteristic, complemented, Sylow
128#135—591no—
129C2×Q16—21no—
130C2×Q16—21no—
131C2×Q16—1181no—
132C2×Q16—1181no—
133#131—1181no—
134C4⋊Q8—21no—
135C4⋊Q8—1181no—
136Q32—2361no—
137Q32—2361no—
138Q32—2361no—
139Q32—2362no—
140Q32—2361no—
141SD32—2361no—
142SD32—2361no—
143M32—21no—
144M32—21no—
145M32—1181no—
146M32—2361no—
147C2×C16—591no—
148C2×C16—591no—
149C2×C16—2361no—
150#108—591no—
151#104—1181no—
152C4×C8C22×D5911yescharacteristic
153#41—1181no—
154C2×Q8—41no—
155C2×Q8—2361no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—41no—
160Q16—591no—
161Q16—2361no—
162Q16—2361no—
163Q16—2361no—
164Q16—2361no—
165SD16—1181no—
166D8—591no—
167M16—1181no—
168M16—2361no—
169C2×C8—2361no—
170C2×C8D4×D5911yescharacteristic
171C2×C8D4×D5911yescharacteristic
172C4⋊C4—81no—
173C4⋊C4—4721no—
174C42#1174568511yescharacteristic
175C16—41no—
176C16—41no—
177C16—591no—
178C16—591no—
179C16—1181no—
180C16—2361no—
181Q8—81no—
182Q8—81no—
183Q8—1181no—
184Q8—4721no—
185Q8—4721no—
186D4—1181no—
187D4—2361no—
188C2×C4—21no—
189C2×C4—81no—
190C2×C4—4721no—
191C2×C4—2361no—
192C2×C4#1427370011yescharacteristic
193C8—2361no—
194C8D8×D5911yescharacteristic
195C8D8×D5911yescharacteristic
196C8#1427374811yescharacteristic
197C8#1427375411yescharacteristic
198C22—2361no—
199C22#1683767111yescharacteristic
200C4—22no—
201C4—161no—
202C4—9441no—
203C4—2361no—
204C4#1683759611yescharacteristic
205C4#1683763711yescharacteristic
206C2—21no—
207C2—4721no—
208C2#2142345011yescharacteristic
subgroupG/H
centerC2#21423450
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1358C2
socleC2×C59#1667
prime radical#14273749D4
hypercenter#1358D59
hypocenterC59#12437
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #21426348C2semidirect
5. #21422171C2semidirect
6. #21422134C2semidirect
7. C59×#1358C2semidirect
108. #1358D59semidirect
127. C59#12437semidirect

Maximal subgroups

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

subgroupindex
#214263482
#214261782
#214261742
#214259322
#214221712
#214221342
C59×#13582
#1243759