Finite Group Databasebeta

← #28503212

Subgroups — #28503212

Order 15104.

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

normal subgroups only

This group has 200 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#21426324C211yesmaximal, characteristic
2#21426004C211yesmaximal, characteristic
3#21423491C211yesmaximal, characteristic
4#21423467C211yesmaximal, characteristic
5#21422152C211yesmaximal, characteristic
6#21422144C211yesmaximal, characteristic
7C59×#1371C211yesmaximal, characteristic
8#16837807C2211yescharacteristic
9#16837782C2211yescharacteristic
10#16837688—21no—
11#16837613—21no—
12C8×Dic118C2211yescharacteristic
13C4⋊(C59⋊C16)C2211yescharacteristic
14Dic59⋊C16—21no—
15#16837207—21no—
16#16837207—21no—
17#16837177—21no—
18#16837149—21no—
19#16837147—21no—
20C4×C16×C59C2211yescharacteristic
21C59×#335C2211yescharacteristic
22C59×#335C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25C2×Dic236—41no—
26#14273727—21no—
27#14273727—21no—
28C4×Dic118D411yescharacteristic
29C2×C59⋊C16—21no—
30#14273661—21no—
31#14273661—21no—
32#14273659—41no—
33C4⋊(C59⋊C8)D411yescharacteristic
34Dic59⋊C8—21no—
35#14273652—41no—
36#14273652—41no—
37C8×Dic59—21no—
38C2×C16×C59D411yescharacteristic
39C2×C16×C59D411yescharacteristic
40C4⋊C8×C59—21no—
41C4⋊C8×C59—21no—
42C4×C8×C59C2311yescharacteristic
43C2×Dic118—41no—
44C2×Dic118—41no—
45C2×Dic118D811yescharacteristic
46C2×C8×C59—41no—
47C2×C8×C59—41no—
48C2×C8×C59C2×D411yescharacteristic
49C2×C8×C59#4111yescharacteristic
50C42×C59C2×D411yescharacteristic
51C4⋊Dic59—41no—
52C4⋊Dic59—41no—
53C4⋊Dic59—41no—
54C4⋊Dic59—41no—
55C4⋊Dic59D811yescharacteristic
56Dic59⋊C4—21no—
57C4×Dic59—21no—
58C2×C59⋊C8—21no—
59Dic236—41no—
60Dic236—41no—
61Dic236—81no—
62Dic236—82no—
63C16×C59—21no—
64C16×C59—21no—
65C59⋊C16—41no—
66C2×C4×C59#12111yescharacteristic
67C2×C4×C59C2×D811yescharacteristic
68C2×C4×C59#13511yescharacteristic
69C2×Dic59—21no—
70C2×Dic59—21no—
71C2×Dic59—81no—
72C2×Dic59—81no—
73Dic118—21no—
74Dic118—21no—
75Dic118—81no—
76Dic118—81no—
77Dic118—81no—
78Dic118—81no—
79C8×C59—21no—
80C8×C59—81no—
81C8×C59—81no—
82C8×C59#13511yescharacteristic
83C8×C59#13711yescharacteristic
84C59⋊C8—41no—
85#12482—591nomaximal, Sylow
86C22×C59#46611yescharacteristic
87C4×C59—21no—
88C4×C59#46411yescharacteristic
89C4×C59#47111yescharacteristic
90C4×C59#50911yescharacteristic
91C4×C59#51011yescharacteristic
92Dic59—41no—
93Dic59—41no—
94Dic59—161no—
95Dic59—161no—
96#2241—591no—
97#2183—591no—
98#1674—591no—
99#1670—591no—
100#1371D5911yescharacteristic
101#1364—591no—
102#1362—591no—
103C2×C59#168211yescharacteristic
104C2×C59#222011yescharacteristic
105C2×C59#222211yescharacteristic
106#500—591no—
107#494—591no—
108#475—1181no—
109#462—1181no—
110C8×Q8—591no—
111C4⋊C16—591no—
112C4⋊C16—1181no—
113#358—1181no—
114#358—1181no—
115#346—1181no—
116C4×C16C2×D5911yescharacteristic
117#335C2×D5911yescharacteristic
118#335C2×D5911yescharacteristic
119#332—1181no—
120#332—1181no—
121C59#1248211yescharacteristic, complemented, Sylow
122C2×Q16—1181no—
123C2×Q16—1181no—
124C2×Q16—2361no—
125C4⋊Q8—1181no—
126C4⋊Q8—1181no—
127C4×Q8—591no—
128C2×C16—1181no—
129C2×C16D23611yescharacteristic
130C2×C16D23611yescharacteristic
131#107—1181no—
132#107—1181no—
133#106—2361no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—591no—
137C4⋊C8—1181no—
138#103—2361no—
139#103—2361no—
140C4×C8—1181no—
141C4×C8C22×D5911yescharacteristic
142C2×Q8—591no—
143C2×Q8—2361no—
144C2×Q8—2361no—
145Q16—4721no—
146Q16—4722no—
147Q16—2361no—
148Q16—2361no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—1181no—
152C2×C8C2×D23611yescharacteristic
153C2×C8#1174568911yescharacteristic
154C4⋊C4—591no—
155C4⋊C4—1181no—
156C4⋊C4—2361no—
157C4⋊C4—2361no—
158C4⋊C4—2361no—
159C4⋊C4—2361no—
160C42—1181no—
161C42D4×D5911yescharacteristic
162C16—21no—
163C16—21no—
164C16—2361no—
165Q8—1181no—
166Q8—1181no—
167Q8—4721no—
168Q8—4721no—
169Q8—4721no—
170Q8—4721no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—4721no—
174C2×C4—4721no—
175C2×C4#1427370211yescharacteristic
176C2×C4D8×D5911yescharacteristic
177C2×C4#1427375011yescharacteristic
178C8—21no—
179C8—81no—
180C8—81no—
181C8—2361no—
182C8#1427374911yescharacteristic
183C8#1427376011yescharacteristic
184C22#1683763911yescharacteristic
185C4—21no—
186C4—9441no—
187C4—9441no—
188C4—2361no—
189C4—2361no—
190C4#1683762511yescharacteristic
191C4#1683766611yescharacteristic
192C4#1683783611yescharacteristic
193C4#1683784411yescharacteristic
194C2#2142354111yescharacteristic
195C2#2142621011yescharacteristic
196C2#2142622211yescharacteristic
subgroupG/H
centerC22#16837639
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1371C2
socle, prime radicalC22×C59#466
hypercenter#1371D59
hypocenterC59#12482
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
121. C59#12482semidirect

Maximal subgroups

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

subgroupindex
#214263242
#214260042
#214234912
#214234672
#214221522
#214221442
C59×#13712
#1248259