Finite Group Databasebeta

← #15750526

Subgroups — #15750526

Order 3328.

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

normal subgroups only

This group has 224 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#13116369C211yesmaximal, characteristic
2#13112961C211yesmaximal, characteristic
3C13×#1318C211yesmaximal, characteristic
4C13×#390C2211yescharacteristic
5C2×#88074—21no—
6C2×#88072—21no—
7C2×#88048—21no—
8#11718596C411yescharacteristic, complemented
9C13×#324—21no—
10#11718116C411yescharacteristic, complemented
11C22×D4×C13D411yescharacteristic
12C2×C13×C4⋊C4D411yescharacteristic
13C2×C13×C22⋊C4—41no—
14C2×C42×C13C2×C411yescharacteristic
15C2×C22⋊Dic13—41no—
16C2×C4⋊Dic13—21no—
17C2×C4⋊Dic13—41no—
18C22×#1055—21no—
19C13×C22⋊C8—41no—
20#88074—22no—
21#88074—41no—
22#88072—42no—
23#88048—42no—
24#7435—131nomaximal, Sylow
25C24×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13—41no—
28C2×D4×C13—41no—
29C2×D4×C13SD1611yescharacteristic
30C2×D4×C13Q1611yescharacteristic
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13C22⋊C411yescharacteristic
34C22×Dic13—41no—
35C22×Dic13—81no—
36C2×C8×C13—81no—
37C13×C4⋊C4—41no—
38C13×C22⋊C4—82no—
39C42×C13—41no—
40C22⋊Dic13—42no—
41C22⋊Dic13—81no—
42C4⋊Dic13—41no—
43C4⋊Dic13—41no—
44C4⋊Dic13—82no—
45C2×#1055—22no—
46C2×#1055—41no—
47C2×#1055—41no—
48#2094—131no—
49#1393—131no—
50#1318D1311yescharacteristic
51C23×C13—21no—
52C23×C13—21no—
53C23×C13—41no—
54C23×C13—41no—
55C23×C13—81no—
56C23×C13—81no—
57C23×C13#9911yescharacteristic
58D4×C13—41no—
59D4×C13—41no—
60D4×C13—81no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—81no—
68C2×C4×C13#10311yescharacteristic
69C2×C4×C13#10411yescharacteristic
70C2×Dic13—82no—
71C2×Dic13—82no—
72C2×Dic13—81no—
73C2×Dic13—161no—
74C2×Dic13—161no—
75C8×C13—161no—
76#1055—42no—
77C2×#106—261no—
78C2×#102—261no—
79C2×#99—261no—
80#390C2×D1311yescharacteristic
81#384—131no—
82#336—131no—
83#324—21no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—81no—
89C22×C13—81no—
90C22×C13—81no—
91C22×C13—81no—
92C22×C13—161no—
93C22×C13#32811yescharacteristic
94C22×C13#35211yescharacteristic
95C22×C13#35311yescharacteristic
96C4×C13—21no—
97C4×C13—21no—
98C4×C13—42no—
99C4×C13—81no—
100Dic13—162no—
101Dic13—161no—
102C22×D4D5211yescharacteristic
103C22×C8—261no—
104C2×C4⋊C4—261no—
105C2×C4⋊C4—521no—
106C2×C4⋊C4C22⋊D1311yescharacteristic
107C2×C22⋊C4—41no—
108C2×C22⋊C4—521no—
109C2×C42C4×D1311yescharacteristic
110#106—522no—
111#102—522no—
112#99—262no—
113#99—521no—
114C22⋊C8—41no—
115C2×C13—21no—
116C2×C13—21no—
117C2×C13—81no—
118C2×C13—81no—
119C2×C13#135211yescharacteristic
120C2×C13#140611yescharacteristic
121C2×C13#140911yescharacteristic
122C24—21no—
123C2×D4—21no—
124C2×D4—41no—
125C2×D4—41no—
126C2×D4#609511yescharacteristic
127C2×D4Dic5211yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—521no—
131C22×C4—1041no—
132C22×C4#610311yescharacteristic
133C2×C8—81no—
134C2×C8—262no—
135C2×C8—521no—
136C2×C8—521no—
137C4⋊C4—41no—
138C4⋊C4—521no—
139C4⋊C4—521no—
140C4⋊C4—1042no—
141C22⋊C4—82no—
142C22⋊C4—522no—
143C22⋊C4—1041no—
144C42—41no—
145C13#743511yescharacteristic, complemented, Sylow
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#8804611yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—1042no—
164C2×C4—1042no—
165C2×C4—1041no—
166C2×C4—2081no—
167C2×C4—2081no—
168C2×C4#8805611yescharacteristic
169C2×C4#8806511yescharacteristic
170C8—161no—
171C8—522no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1171805911yescharacteristic
182C22#1171806611yescharacteristic
183C22#1171806811yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—2082no—
189C4—2081no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1311286111yescharacteristic
195C2#1311299411yescharacteristic
196C2#1311300011yescharacteristic
subgroupG/H
centerC22#11718066
commutatorC2×C42×C13C2×C4
Frattini#390C2×D13
FittingC13×#1318C2
socleC22×C13#353
prime radicalC22×D4×C13D4
cosocleC13×#390C22
hypercenter#1318D13
hypocenterC13#7435
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
8. #11718596C4semidirect
10. #11718116C4semidirect
145. C13#7435semidirect

Maximal subgroups

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

subgroupindex
#131163692
#131129612
C13×#13182
#743513