Finite Group Databasebeta

← #15774801

Subgroups — #15774801

Order 3328.

246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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#13116710C211yesmaximal, characteristic
2#13113660C211yesmaximal, characteristic, complemented
3#13113659C211yesmaximal, characteristic, complemented
4#13112901C211yesmaximal, characteristic, complemented
5#13112804C211yesmaximal, characteristic, complemented
6#13112758C211yesmaximal, characteristic, complemented
7C13×#1333C211yesmaximal, characteristic, complemented
8C4×C13×D8C2211yescharacteristic
9C2×#88066C411yescharacteristic
10D4×#1055—21no—
11#11718495—21no—
12C4×D104C2211yescharacteristic
13C13×#346C2211yescharacteristic
14C13×#334C2211yescharacteristic
15#11718154C411yescharacteristic
16D4⋊#1055—21no—
17#11718083C411yescharacteristic
18#11718082C411yescharacteristic
19#11718075—21no—
20#11718053C2211yescharacteristic
21#11718049C2211yescharacteristic
22#11718047C2211yescharacteristic
23C2×C13×D8C2×C411yescharacteristic
24C4×D4×C13—21no—
25C22×#1055—41no—
26C2×D104C2×C411yescharacteristic
27C2×C8×D13—41no—
28C4×D52—21no—
29C2×C13×C16—21no—
30C13×#107C2×C411yescharacteristic
31C13×C4⋊C8—21no—
32C13×#102—21no—
33C4×C8×C13C2311yescharacteristic
34C22⋊#1055—41no—
35#88066C814yescomplemented
36#88061—21no—
37#88060—41no—
38#88058C2×C411yescharacteristic
39C2×#6090C2×C411yescharacteristic
40C2×#6090C2×C411yescharacteristic
41C4⋊#1055—21no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#12067—131nomaximal, Sylow
45C2×D4×C13—21no—
46C22×C4×C13—41no—
47C2×D52—21no—
48C2×C4×D13—41no—
49C13×D8—21no—
50C13×D8C2×C812yescomplemented
51C2×C8×C13—41no—
52C2×C8×C13C22×C411yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C13×C4⋊C4—21no—
55C13×C22⋊C4—41no—
56C42×C13C2×D411yescharacteristic
57#6103—41no—
58C4⋊Dic13—21no—
59C2×#1055—21no—
60C2×#1055—21no—
61C2×#1055—41no—
62C2×#1055—82no—
63D104—21no—
64D104C2×C812yescomplemented
65C8×D13—82no—
66C13×C16—41no—
67#6090—21no—
68#6090C2×C812yescomplemented
69#2177—131no—
70#1580—131no—
71#1580—131no—
72#1368—131no—
73#1333—131no—
74#1333D1311yescharacteristic, complemented
75#1313—131no—
76C23×C13—41no—
77C22×D13—41no—
78D4×C13—22no—
79D4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13—81no—
82C2×C4×C13—81no—
83C2×C4×C13C4×D411yescharacteristic
84C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
85C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
86C2×Dic13—41no—
87D52—22no—
88D52—41no—
89C4×D13—81no—
90C4×D13—81no—
91C8×C13—21no—
92C8×C13—81no—
93C8×C13C22×C811yescharacteristic
94C8×C13#13111yescharacteristic
95#1055—41no—
96#1055—41no—
97#1055—81no—
98C2×D16—131no—
99C4×D8—131no—
100C4×D8C2×D1311yescharacteristic
101C8×D4—261no—
102C8×D4—261no—
103#367—131no—
104#357—131no—
105#357—131no—
106#346—131no—
107#346C2×D1311yescharacteristic
108#334—131no—
109#334C2×D1311yescharacteristic
110D4⋊C8—261no—
111D4⋊C8—261no—
112#322—131no—
113C22×C13—42no—
114C22×C13—81no—
115C22×C13—81no—
116C22×C13#44211yescharacteristic
117C2×D13—42no—
118C2×D13—81no—
119C2×D13—81no—
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—81no—
123C4×C13C8×D411yescharacteristic
124C4×C13#44411yescharacteristic
125Dic13—81no—
126C2×D8—131no—
127C2×D8C4×D1311yescharacteristic
128C22×C8—521no—
129C22×C8—521no—
130C4×D4—21no—
131C4×D4—261no—
132D16—134no—
133C2×C16—21no—
134C2×C16—131no—
135C2×C16—131no—
136#107—131no—
137#107C4×D1311yescharacteristic
138C4⋊C8—21no—
139C4⋊C8—261no—
140#102—21no—
141#102—261no—
142C22⋊C8—521no—
143C22⋊C8—521no—
144C4×C8—131no—
145C4×C8—131no—
146C4×C8C22×D1311yescharacteristic
147C2×C13—82no—
148C2×C13#158011yescharacteristic
149C2×C13AGL(1,ℤ/16)11yescharacteristic
150C2×C13AGL(1,ℤ/16)11yescharacteristic
151D13—82no—
152C2×D4—21no—
153C2×D4—261no—
154C22×C4—41no—
155C22×C4—521no—
156D8—21no—
157D8—132no—
158D8—261no—
159D8C8×D1312yescomplemented
160C2×C8—41no—
161C2×C8—261no—
162C2×C8—261no—
163C2×C8—521no—
164C2×C8—1042no—
165C2×C8—1042no—
166C2×C8C2×C4×D1311yescharacteristic
167C2×C8#612911yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—261no—
170C22⋊C4—41no—
171C22⋊C4—521no—
172C42D4×D1311yescharacteristic
173C16—41no—
174C16—132no—
175C16—261no—
176C13#1206711yescharacteristic, complemented, Sylow
177C23—41no—
178C23—521no—
179D4—22no—
180D4—41no—
181D4—262no—
182D4—521no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—521no—
187C2×C4—1041no—
188C2×C4—1041no—
189C2×C4#8813511yescharacteristic
190C2×C4#8816511yescharacteristic
191C2×C4#8816811yescharacteristic
192C8—21no—
193C8—81no—
194C8—521no—
195C8—521no—
196C8—1041no—
197C8C2×C8×D1311yescharacteristic
198C8#8816111yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22—522no—
203C22—1041no—
204C22—1041no—
205C22#1171844611yescharacteristic
206C4—21no—
207C4—21no—
208C4—81no—
209C4—1041no—
210C4#1171838611yescharacteristic
211C4#1171848411yescharacteristic
212C2—82no—
213C2—1042no—
214C2#1311365711yescharacteristic
215C2#1311673111yescharacteristic
216C2#1311673711yescharacteristic
subgroupG/H
centerC22#11718446
commutatorC8×C13C22×C8
FrattiniC4×C8C22×D13
FittingC13×#1333C2
socleC22×C13#442
prime radicalC2×#88066C4
cosocleC4×C8×C13C23
hypercenter#1333D13
hypocenterC13#12067
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
2. #13113660C2semidirect
3. #13113659C2semidirect
4. #13112901C2semidirect
5. #13112804C2semidirect
6. #13112758C2semidirect
7. C13×#1333C2semidirect
35. #88066C8semidirect
50. C13×D8C2×C8semidirect
64. D104C2×C8semidirect
68. #6090C2×C8semidirect
74. #1333D13semidirect
159. D8C8×D13semidirect
176. C13#12067semidirect

Maximal subgroups

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

subgroupindex
#131167102
#131136602
#131136592
#131129012
#131128042
#131127582
C13×#13332
#1206713