Finite Group Databasebeta

← #28476284

Subgroups — #28476284

Order 15104.

206 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 41 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#21425257C211yesmaximal, characteristic
2#21422223C211yesmaximal, characteristic
3C59×#1272C211yesmaximal, characteristic
4#16838033C411yescharacteristic
5#16837411—21no—
6C2×#14273646—21no—
7#16837171C411yescharacteristic
8#16837162—21no—
9C59×#391C2211yescharacteristic
10C59×#336—21no—
11C2×#11745664—21no—
12C2×#11745664—41no—
13#14273726—41no—
14#14273718—41no—
15#14273706—41no—
16#14273686—21no—
17#14273651—41no—
18#14273651—41no—
19#14273646—22no—
20#14273646—41no—
21C22×Q8×C59D411yescharacteristic
22C22×C8×C59—41no—
23C2×C4⋊C4×C59C2×C411yescharacteristic
24C2×C42×C59D411yescharacteristic
25#95×C59—41no—
26C2×Q8×C59—21no—
27C2×Q8×C59—41no—
28C2×Q8×C59—41no—
29C2×Q8×C59SD1611yescharacteristic
30C2×Q8×C59Q1611yescharacteristic
31C22×C4×C59—21no—
32C22×C4×C59—21no—
33C22×C4×C59—21no—
34C22×C4×C59C22⋊C411yescharacteristic
35C2×Dic118—41no—
36C2×C8×C59—42no—
37C2×C8×C59—81no—
38C2×C8×C59—81no—
39C4⋊C4×C59—41no—
40C42×C59—41no—
41C22⋊Dic59—41no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59—41no—
45Dic59⋊C4—42no—
46C4×Dic59—41no—
47#11745664—42no—
48#11745664—41no—
49#11745664—41no—
50#11745664—81no—
51C2×C59⋊C8—41no—
52C2×C59⋊C8—81no—
53C23×C59#9911yescharacteristic
54Q8×C59—41no—
55Q8×C59—41no—
56Q8×C59—81no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—21no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59—81no—
69C2×C4×C59#10311yescharacteristic
70C2×C4×C59#10411yescharacteristic
71C2×Dic59—41no—
72C2×Dic59—41no—
73Dic118—161no—
74C8×C59—82no—
75C59⋊C8—81no—
76C59⋊C8—82no—
77#7431—591nomaximal, Sylow
78C22×C59—21no—
79C22×C59—21no—
80C22×C59#32811yescharacteristic
81C22×C59AΣL(1,𝔽16)11yescharacteristic
82C22×C59#35411yescharacteristic
83C4×C59—21no—
84C4×C59—21no—
85C4×C59—41no—
86C4×C59—41no—
87C4×C59—41no—
88C4×C59—41no—
89C4×C59—81no—
90Dic59—81no—
91Dic59—81no—
92#2028—591no—
93#1394—591no—
94#1272D5911yescharacteristic
95C2×C59—21no—
96C2×C59—21no—
97C2×C59#135111yescharacteristic
98C2×C59#140311yescharacteristic
99C2×C59#140511yescharacteristic
100#544—591no—
101#419—1181no—
102C2×#101—1181no—
103#391C2×D5911yescharacteristic
104#343—591no—
105#339—1181no—
106#336—21no—
107C59#743111yescharacteristic, complemented, Sylow
108C22×Q8D23611yescharacteristic
109C2×M16—1181no—
110C2×M16—2361no—
111C22×C8—41no—
112C4⋊Q8—2361no—
113#125—2361no—
114C22⋊Q8—2361no—
115#117—1181no—
116C2×C4⋊C4C4×D5911yescharacteristic
117C2×C42C22⋊D5911yescharacteristic
118#103—2361no—
119#103—2361no—
120#101—1182no—
121#101—2361no—
122#95—41no—
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—2361no—
127C2×Q8#1174566011yescharacteristic
128C2×Q8Dic23611yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4(C2×D59)⋊C411yescharacteristic
133M16—4721no—
134M16—2362no—
135M16—2361no—
136M16—2361no—
137C2×C8—42no—
138C2×C8—81no—
139C2×C8—81no—
140C2×C8—4721no—
141C2×C8—2361no—
142C4⋊C4—41no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—2361no—
146C4⋊C4—2362no—
147C22⋊C4—2361no—
148C42—41no—
149C42—2361no—
150C23#1427364111yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—9441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—2361no—
168C2×C4—2361no—
169C2×C4#1427365211yescharacteristic
170C2×C4#1427365311yescharacteristic
171C8—82no—
172C8—4721no—
173C8—4722no—
174C22—21no—
175C22—21no—
176C22#1683714011yescharacteristic
177C22#1683719011yescharacteristic
178C22#1683719611yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—4721no—
187C4—4721no—
188C2—21no—
189C2—21no—
190C2#2142211811yescharacteristic
191C2#2142224511yescharacteristic
192C2#2142225111yescharacteristic
subgroupG/H
centerC22#16837190
commutatorC2×C4⋊C4×C59C2×C4
Frattini#391C2×D59
FittingC59×#1272C2
socleC22×C59AΣL(1,𝔽16)
prime radicalC23×C59#99
cosocleC59×#391C22
hypercenter#1272D59
hypocenterC59#7431
LCSG ▷ C2×C4⋊C4×C59 ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
107. C59#7431semidirect

Maximal subgroups

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

subgroupindex
#214252572
#214222232
C59×#12722
#743159