Finite Group Databasebeta

← #15750505

Subgroups — #15750505

Order 3328.

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

normal subgroups only

This group has 226 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#13115982C211yesmaximal, characteristic
2#13112961C211yesmaximal, characteristic
3C13×#1318C211yesmaximal, characteristic
4C2×#88124C411yescharacteristic, complemented
5C13×#390C2211yescharacteristic
6C2×#88074—21no—
7C2×#88072—21no—
8C13×#324—21no—
9#11718121—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×#6101—41no—
18C22×#1055—21no—
19#88124—42no—
20C13×C22⋊C8—41no—
21#88074—22no—
22#88074—41no—
23#88072—42no—
24#7428—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—22no—
43C4⋊Dic13—41no—
44#6101—42no—
45#6101—42no—
46C2×#1055—41no—
47C2×#1055—41no—
48C2×#1055—41no—
49#2025—131no—
50#1393—131no—
51#1318D1311yescharacteristic
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—41no—
55C23×C13—41no—
56C23×C13—81no—
57C23×C13—81no—
58C23×C13#9911yescharacteristic
59D4×C13—41no—
60D4×C13—41no—
61D4×C13—81no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—81no—
69C2×C4×C13#10311yescharacteristic
70C2×C4×C13#10411yescharacteristic
71C2×Dic13—42no—
72C2×Dic13—81no—
73C2×Dic13—81no—
74C2×Dic13—82no—
75C2×Dic13—161no—
76C2×Dic13—161no—
77C8×C13—161no—
78#1055—81no—
79C2×#125—131no—
80C2×#102—261no—
81C2×#99—261no—
82#390C2×D1311yescharacteristic
83#340—261no—
84#336—131no—
85#324—21no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13—81no—
91C22×C13—81no—
92C22×C13—81no—
93C22×C13—81no—
94C22×C13—161no—
95C22×C13#32811yescharacteristic
96C22×C13AΣL(1,𝔽16)11yescharacteristic
97C22×C13#35411yescharacteristic
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—81no—
101C4×C13—81no—
102Dic13—82no—
103Dic13—162no—
104C22×D4D5211yescharacteristic
105C22×C8—261no—
106#125—522no—
107C2×C4⋊C4—261no—
108C2×C4⋊C4—521no—
109C2×C4⋊C4C22⋊D1311yescharacteristic
110C2×C22⋊C4—41no—
111C2×C22⋊C4—521no—
112C2×C42C4×D1311yescharacteristic
113#102—522no—
114#99—262no—
115#99—521no—
116C22⋊C8—41no—
117C2×C13—21no—
118C2×C13—21no—
119C2×C13—81no—
120C2×C13—81no—
121C2×C13#135111yescharacteristic
122C2×C13#141211yescharacteristic
123C2×C13#141411yescharacteristic
124C24—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4#609511yescharacteristic
129C2×D4Dic5211yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—521no—
133C22×C4—1041no—
134C22×C4#610311yescharacteristic
135C2×C8—81no—
136C2×C8—521no—
137C2×C8—521no—
138C2×C8—521no—
139C4⋊C4—41no—
140C4⋊C4—262no—
141C4⋊C4—521no—
142C4⋊C4—522no—
143C4⋊C4—522no—
144C22⋊C4—82no—
145C22⋊C4—522no—
146C22⋊C4—1041no—
147C42—41no—
148C13#742811yescharacteristic, complemented, Sylow
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23#8804611yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—522no—
167C2×C4—1041no—
168C2×C4—1041no—
169C2×C4—1042no—
170C2×C4—2081no—
171C2×C4—2081no—
172C2×C4#8805611yescharacteristic
173C2×C4#8806511yescharacteristic
174C8—161no—
175C8—1041no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#1171805911yescharacteristic
186C22#1171806511yescharacteristic
187C22#1171806711yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—1042no—
193C4—2082no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1311285811yescharacteristic
199C2#1311300611yescharacteristic
200C2#1311301211yescharacteristic
subgroupG/H
centerC22#11718065
commutatorC2×C42×C13C2×C4
Frattini#390C2×D13
FittingC13×#1318C2
socleC22×C13#354
prime radicalC22×D4×C13D4
cosocleC13×#390C22
hypercenter#1318D13
hypocenterC13#7428
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
4. C2×#88124C4semidirect
10. #11718116C4semidirect
148. C13#7428semidirect

Maximal subgroups

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

subgroupindex
#131159822
#131129612
C13×#13182
#742813