Finite Group Databasebeta

← #15750471

Subgroups — #15750471

Order 3328.

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#13112782C211yesmaximal, characteristic, complemented
2#13112719C211yesmaximal, characteristic, complemented
3C13×#2039C211yesmaximal, characteristic
4C13×#537C411yescharacteristic
5C2×C13×#104—21no—
6C13×#417—21no—
7C13×#384C2211yescharacteristic
8C2×C4⋊#1055—21no—
9C13×#343C411yescharacteristic
10#11718120—21no—
11C2×C13×#41—21no—
12C2×C13×M16—21no—
13C13×C22⋊Q8—41no—
14C13×#121—41no—
15C13×#121—41no—
16C2×C13×C4⋊C4—41no—
17C2×C13×C4⋊C4C2×C411yescharacteristic
18C2×C13×C4⋊C4D411yescharacteristic
19C2×C42×C13D411yescharacteristic
20C22×#1055—41no—
21C13×#104—41no—
22C13×#104—41no—
23C13×#103—41no—
24C13×#102—41no—
25C22⋊#1055—41no—
26C4⋊#1055—22no—
27C4⋊#1055—41no—
28#7417—131nomaximal, Sylow
29C13×#41—41no—
30C13×#41—41no—
31C13×#41—41no—
32C13×#41—41no—
33C2×Q8×C13—21no—
34C2×D4×C13—21no—
35C2×D4×C13—41no—
36C2×D4×C13—41no—
37C22×C4×C13—21no—
38C22×C4×C13—21no—
39C22×C4×C13—21no—
40C22×C4×C13—41no—
41C22×C4×C13C22⋊C411yescharacteristic
42C13×M16—41no—
43C13×M16—41no—
44C2×C8×C13—41no—
45C13×C4⋊C4—41no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—41no—
48C13×C4⋊C4—81no—
49C13×C4⋊C4—81no—
50C13×C22⋊C4—42no—
51C42×C13—21no—
52C42×C13D811yescharacteristic
53C42×C13SD1611yescharacteristic
54C2×#1055—42no—
55C2×#1055—81no—
56C2×#1055—81no—
57C2×#1055—81no—
58#2039D1311yescharacteristic
59#1325—131no—
60#1296—131no—
61C23×C13—41no—
62C23×C13#9911yescharacteristic
63Q8×C13—41no—
64Q8×C13—41no—
65D4×C13—41no—
66D4×C13—41no—
67D4×C13—81no—
68D4×C13—81no—
69D4×C13—161no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13—81no—
82C2×C4×C13—81no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#10211yescharacteristic
86C2×C4×C13#10411yescharacteristic
87C8×C13—81no—
88#1055—82no—
89#1055—161no—
90#537Dic1311yescharacteristic
91C2×C4⋊C8—261no—
92C2×#104—21no—
93#417—21no—
94#384C2×D1311yescharacteristic
95#343Dic1311yescharacteristic
96#324—261no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13—81no—
100C22×C13—81no—
101C22×C13—81no—
102C22×C13#32711yescharacteristic
103C22×C13AΣL(1,𝔽16)11yescharacteristic
104C22×C13#35511yescharacteristic
105C4×C13—21no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—81no—
112C4×C13—81no—
113C4×C13—81no—
114C2×#41—21no—
115C2×M16—21no—
116C22×C8—521no—
117C22⋊Q8—41no—
118#121—41no—
119#121—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4C2×Dic1311yescharacteristic
122C2×C4⋊C4C22⋊D1311yescharacteristic
123C2×C42C22⋊D1311yescharacteristic
124C4⋊C8—262no—
125C4⋊C8—521no—
126#104—41no—
127#104—41no—
128#103—41no—
129#102—41no—
130C22⋊C8—521no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13—161no—
134C2×C13#134511yescharacteristic
135C2×C13#140211yescharacteristic
136C2×C13#140511yescharacteristic
137#41—41no—
138#41—41no—
139#41—41no—
140#41—41no—
141C2×Q8—21no—
142C2×D4—21no—
143C2×D4—41no—
144C2×D4—41no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4C22⋊Dic1311yescharacteristic
150M16—41no—
151M16—41no—
152C2×C8—41no—
153C2×C8—522no—
154C2×C8—1041no—
155C2×C8—1041no—
156C2×C8—1041no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—81no—
161C4⋊C4—81no—
162C22⋊C4—42no—
163C42—21no—
164C42#610411yescharacteristic
165C42#610511yescharacteristic
166C13#741711yescharacteristic, complemented, Sylow
167C23—41no—
168C23#8807411yescharacteristic
169Q8—41no—
170Q8—41no—
171D4—41no—
172D4—41no—
173D4—81no—
174D4—81no—
175D4—161no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#8807211yescharacteristic
192C2×C4#8807711yescharacteristic
193C8—81no—
194C8—1042no—
195C8—2081no—
196C22—21no—
197C22—21no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22#1171812811yescharacteristic
202C22#1171812911yescharacteristic
203C22#1171813411yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—21no—
210C4—81no—
211C4—81no—
212C4—81no—
213C2—21no—
214C2—21no—
215C2—161no—
216C2#1311283911yescharacteristic
217C2#1311298111yescharacteristic
218C2#1311299011yescharacteristic
subgroupG/H
centerC22#11718128
commutatorC2×C13×C4⋊C4C2×C4
Frattini#384C2×D13
FittingC13×#2039C2
socleC22×C13AΣL(1,𝔽16)
prime radicalC13×#537C4
cosocleC13×#384C22
hypercenter#2039D13
hypocenterC13#7417
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13112782C2semidirect
2. #13112719C2semidirect
166. C13#7417semidirect

Maximal subgroups

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

subgroupindex
#131127822
#131127192
C13×#20392
#741713