Finite Group Databasebeta

← #15750470

Subgroups — #15750470

Order 3328.

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

normal subgroups only

This group has 228 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#13116060C211yesmaximal, characteristic
2#13112782C211yesmaximal, characteristic, complemented
3C13×#1296C211yesmaximal, characteristic, complemented
4#11719215C411yescharacteristic
5C2×C13×C4⋊C8—21no—
6C13×#384C2211yescharacteristic
7#11718627—21no—
8C2×#88045—21no—
9#11718122C411yescharacteristic
10#11718120—21no—
11C2×#6127—21no—
12C22×C8×C13—41no—
13C2×C13×C4⋊C4—41no—
14C2×C13×C4⋊C4C2×C411yescharacteristic
15C2×C13×C4⋊C4D411yescharacteristic
16C2×C42×C13D411yescharacteristic
17#88184—41no—
18C2×#6099—21no—
19#88151—41no—
20#88149—41no—
21C13×C4⋊C8—22no—
22C13×C4⋊C8—41no—
23C22⋊#1055—41no—
24#88050—41no—
25#88049—41no—
26#88045—41no—
27#88045—41no—
28#7417—131nomaximal, Sylow
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13C22⋊C411yescharacteristic
33C2×C22⋊D13—41no—
34#6127—41no—
35#6127—41no—
36#6127—41no—
37#6127—41no—
38C2×D52—21no—
39C2×D52—41no—
40C2×C4×D13—41no—
41C2×Dic26—21no—
42C2×C8×C13—42no—
43C2×C8×C13—81no—
44C2×C8×C13—81no—
45C13×C4⋊C4—41no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—81no—
48C13×C4⋊C4—81no—
49C42×C13—21no—
50C42×C13D811yescharacteristic
51C42×C13SD1611yescharacteristic
52#6103—42no—
53C4⋊Dic13—41no—
54#6099—41no—
55#6099—41no—
56C2×#1055—41no—
57C2×#1055—81no—
58#2039—131no—
59#1325—131no—
60#1296D1311yescharacteristic, complemented
61C23×C13#9911yescharacteristic
62C22×D13—41no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—41no—
72C2×C4×C13—41no—
73C2×C4×C13—81no—
74C2×C4×C13—81no—
75C2×C4×C13#10211yescharacteristic
76C2×C4×C13#10411yescharacteristic
77C22⋊D13—81no—
78C22⋊D13—81no—
79C2×Dic13—41no—
80D52—41no—
81D52—41no—
82D52—161no—
83C4×D13—81no—
84C4×D13—81no—
85Dic26—41no—
86Dic26—41no—
87C8×C13—82no—
88#1055—81no—
89#1055—161no—
90#537—131no—
91C2×C4⋊C8—21no—
92C2×#104—261no—
93#417—261no—
94#384C2×D1311yescharacteristic
95#343—131no—
96#324—261no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13#32711yescharacteristic
100C22×C13AΣL(1,𝔽16)11yescharacteristic
101C22×C13#35511yescharacteristic
102C2×D13—81no—
103C2×D13—81no—
104C2×D13—81no—
105C4×C13—21no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—81no—
112C4×C13—81no—
113Dic13—81no—
114C2×#41—261no—
115C2×M16—261no—
116C22×C8—41no—
117C22⋊Q8—521no—
118#121—521no—
119#121—521no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4C4×D1311yescharacteristic
122C2×C4⋊C4D5211yescharacteristic
123C2×C42C22⋊D1311yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—41no—
126#104—521no—
127#104—521no—
128#103—521no—
129#102—521no—
130C22⋊C8—521no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13#134511yescharacteristic
134C2×C13#140211yescharacteristic
135C2×C13#140511yescharacteristic
136D13—161no—
137#41—521no—
138#41—521no—
139#41—521no—
140#41—521no—
141C2×Q8—261no—
142C2×D4—261no—
143C2×D4—521no—
144C2×D4—521no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—521no—
149C22×C4#610311yescharacteristic
150M16—521no—
151M16—521no—
152C2×C8—42no—
153C2×C8—81no—
154C2×C8—81no—
155C2×C8—521no—
156C2×C8—1041no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—81no—
160C4⋊C4—81no—
161C4⋊C4—521no—
162C22⋊C4—522no—
163C42—21no—
164C42#610411yescharacteristic
165C42#610611yescharacteristic
166C13#741711yescharacteristic, complemented, Sylow
167C23—521no—
168C23#8804611yescharacteristic
169Q8—521no—
170Q8—521no—
171D4—521no—
172D4—521no—
173D4—1041no—
174D4—1041no—
175D4—2081no—
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—81no—
187C2×C4—81no—
188C2×C4—521no—
189C2×C4—1041no—
190C2×C4—1041no—
191C2×C4#8804511yescharacteristic
192C2×C4#8804911yescharacteristic
193C8—82no—
194C8—1041no—
195C8—2081no—
196C22—21no—
197C22—21no—
198C22—1041no—
199C22—1041no—
200C22—1041no—
201C22#1171804311yescharacteristic
202C22#1171806711yescharacteristic
203C22#1171806911yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—21no—
210C4—81no—
211C4—81no—
212C4—1041no—
213C2—21no—
214C2—21no—
215C2—2081no—
216C2#1311283811yescharacteristic
217C2#1311298211yescharacteristic
218C2#1311299111yescharacteristic
subgroupG/H
centerC22#11718067
commutatorC2×C13×C4⋊C4C2×C4
Frattini#384C2×D13
FittingC13×#1296C2
socleC22×C13AΣL(1,𝔽16)
prime radical#11719215C4
cosocleC13×#384C22
hypercenter#1296D13
hypocenterC13#7417
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13112782C2semidirect
3. C13×#1296C2semidirect
60. #1296D13semidirect
166. C13#7417semidirect

Maximal subgroups

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

subgroupindex
#131160602
#131127822
C13×#12962
#741713