Finite Group Databasebeta

← #28476114

Subgroups — #28476114

Order 15104.

228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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#21424305C211yesmaximal, characteristic
2#21421917C211yesmaximal, characteristic
3C59×#1318C211yesmaximal, characteristic
4#16837877C411yescharacteristic
5#16837442—21no—
6C2×#14273644C411yescharacteristic
7#16837162—21no—
8#16837157—21no—
9C59×#390C2211yescharacteristic
10C59×#324—21no—
11C2×#11745664—21no—
12C22×C59⋊C8—41no—
13D4×Dic59—41no—
14D4×Dic59—41no—
15#14273686—21no—
16C2×C22⋊Dic59—41no—
17#14273660—41no—
18#14273658—41no—
19#14273644—21no—
20#14273644C812yescomplemented
21C22×D4×C59C2×C411yescharacteristic
22C2×C4⋊C4×C59D411yescharacteristic
23C2×C22⋊C4×C59—41no—
24C2×C42×C59D411yescharacteristic
25C22⋊C8×C59—41no—
26C24×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59—41no—
29C2×D4×C59—41no—
30C2×D4×C59C2×C811yescharacteristic
31C2×D4×C59M1611yescharacteristic
32C22×C4×C59—21no—
33C22×C4×C59—21no—
34C22×C4×C59C22⋊C411yescharacteristic
35C22×Dic59—41no—
36C22×Dic59—41no—
37C2×C8×C59—81no—
38C4⋊C4×C59—41no—
39C22⋊C4×C59—81no—
40C22⋊C4×C59—81no—
41C42×C59—41no—
42C22⋊Dic59—42no—
43C22⋊Dic59—41no—
44C4⋊Dic59—21no—
45C4⋊Dic59—21no—
46C4×Dic59—41no—
47#11745664—22no—
48#11745664—41no—
49C2×C59⋊C8—41no—
50C2×C59⋊C8—42no—
51C2×C59⋊C8—81no—
52C2×C59⋊C8—81no—
53C23×C59—21no—
54C23×C59—21no—
55C23×C59—41no—
56C23×C59—41no—
57C23×C59—81no—
58C23×C59—81no—
59C23×C59#9911yescharacteristic
60D4×C59—41no—
61D4×C59—41no—
62D4×C59—42no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59—81no—
71C2×C4×C59C22⋊C811yescharacteristic
72C2×C4×C59#10111yescharacteristic
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—161no—
76C2×Dic59—161no—
77C8×C59—161no—
78C59⋊C8—42no—
79C59⋊C8—82no—
80#7375—591nomaximal, Sylow
81C22×C59—21no—
82C22×C59—21no—
83C22×C59—41no—
84C22×C59—41no—
85C22×C59—81no—
86C22×C59—81no—
87C22×C59—81no—
88C22×C59—81no—
89C22×C59—161no—
90C22×C59#32411yescharacteristic
91C22×C59AΣL(1,𝔽16)11yescharacteristic
92C22×C59#35211yescharacteristic
93C4×C59—21no—
94C4×C59—21no—
95C4×C59—41no—
96C4×C59—41no—
97C4×C59—81no—
98Dic59—81no—
99Dic59—81no—
100#1856—591no—
101#1318D5911yescharacteristic
102#1270—591no—
103C2×C59—21no—
104C2×C59—21no—
105C2×C59—81no—
106C2×C59—81no—
107C2×C59#132611yescharacteristic
108C2×C59#140211yescharacteristic
109C2×C59#140311yescharacteristic
110#518—591no—
111#428—1181no—
112C2×#100—591no—
113#390C2×D5911yescharacteristic
114#339—1181no—
115#336—1181no—
116#324—21no—
117C59#737511yescharacteristic, complemented, Sylow
118C22×D4C4×D5911yescharacteristic
119C2×M16—1181no—
120C22×C8—2361no—
121C4×D4—2361no—
122C4×D4—2361no—
123#117—1181no—
124C2×C4⋊C4C22⋊D5911yescharacteristic
125C2×C22⋊C4—41no—
126C2×C22⋊C4—2361no—
127C2×C42D23611yescharacteristic
128#107—2361no—
129#106—2361no—
130#100—592no—
131#100—1181no—
132C22⋊C8—41no—
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4C8×D5911yescharacteristic
138C2×D4#1174565911yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—2361no—
142C22×C4—2361no—
143C22×C4(C2×D59)⋊C411yescharacteristic
144M16—1182no—
145M16—2361no—
146C2×C8—81no—
147C2×C8—4721no—
148C2×C8—4721no—
149C2×C8—2362no—
150C2×C8—2361no—
151C4⋊C4—41no—
152C4⋊C4—1181no—
153C4⋊C4—1181no—
154C22⋊C4—81no—
155C22⋊C4—81no—
156C22⋊C4—2362no—
157C22⋊C4—2361no—
158C42—41no—
159C42—2361no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1427364111yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—9441no—
179C2×C4—9441no—
180C2×C4—2361no—
181C2×C4—2361no—
182C2×C4(C2×D59)⋊C811yescharacteristic
183C2×C4#1427364511yescharacteristic
184C8—161no—
185C8—4722no—
186C8—2362no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1683712711yescharacteristic
197C22#1683718811yescharacteristic
198C22#1683719311yescharacteristic
199C4—21no—
200C4—21no—
201C4—41no—
202C4—41no—
203C4—81no—
204C4—4721no—
205C4—4721no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#2142204311yescharacteristic
211C2#2142224011yescharacteristic
212C2#2142224311yescharacteristic
subgroupG/H
centerC22#16837188
commutatorC2×D4×C59C2×C8
Frattini#390C2×D59
FittingC59×#1318C2
socleC22×C59AΣL(1,𝔽16)
prime radicalC22×D4×C59C2×C4
cosocleC59×#390C22
hypercenter#1318D59
hypocenterC59#7375
LCSG ▷ C2×D4×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
20. #14273644C8semidirect
117. C59#7375semidirect

Maximal subgroups

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

subgroupindex
#214243052
#214219172
C59×#13182
#737559