Finite Group Databasebeta

← #15774794

Subgroups — #15774794

Order 3328.

230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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#13116702C211yesmaximal, characteristic
2#13113661C211yesmaximal, characteristic
3#13113656C211yesmaximal, characteristic, complemented
4#13112902C211yesmaximal, characteristic, complemented
5#13112807C211yesmaximal, characteristic, complemented
6#13112804C211yesmaximal, characteristic
7C13×#1313C211yesmaximal, characteristic, complemented
8C2×#88040C411yescharacteristic
9C4×Dic52C2211yescharacteristic
10C4×D104C2211yescharacteristic
11C8×D52—21no—
12C8×Dic26—21no—
13C13×#346C2211yescharacteristic
14C13×#346C2211yescharacteristic
15C13×#322C2211yescharacteristic
16#11718101C411yescharacteristic
17#11718096C411yescharacteristic
18#11718095C411yescharacteristic
19#11718051—21no—
20#11718049C2211yescharacteristic
21#11718049C2211yescharacteristic
22#11718048—21no—
23C2×Dic52C2×C411yescharacteristic
24C2×D104C2×C411yescharacteristic
25C2×C8×D13—41no—
26C4×D52—21no—
27C4×Dic26—21no—
28C2×C13×C16—21no—
29C2×C13×C16C2×C411yescharacteristic
30C2×C13×C16C2×C411yescharacteristic
31C4×C8×C13D411yescharacteristic
32C4×C8×C13D411yescharacteristic
33C4×C8×C13C2311yescharacteristic
34#88061—21no—
35#88060—41no—
36#88058C2×C411yescharacteristic
37#88058C2×C411yescharacteristic
38#88056—21no—
39#88054—41no—
40C8×Dic13—41no—
41C4⋊#1055—21no—
42C4⋊#1055—21no—
43#88040C814yescomplemented
44#12065—131nomaximal, Sylow
45C2×D52—21no—
46C2×C4×D13—41no—
47C2×Dic26—21no—
48C2×C8×C13—21no—
49C2×C8×C13—21no—
50C2×C8×C13C22×C411yescharacteristic
51C2×C8×C13#4111yescharacteristic
52C42×C13C2×D411yescharacteristic
53#6103—41no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56#6101—41no—
57C4×Dic13—41no—
58C2×#1055—41no—
59C2×#1055—41no—
60Dic52—21no—
61Dic52C2×C812yescomplemented
62D104—21no—
63D104C2×C812yes—
64C8×D13—82no—
65C13×C16—21no—
66C13×C16—41no—
67C13×C16C2×C812yescomplemented
68#2175—131no—
69#1580—131no—
70#1579—131no—
71#1368—131no—
72#1334—131no—
73#1333—131no—
74#1313D1311yescharacteristic, complemented
75C22×D13—41no—
76C2×C4×C13C4×D411yescharacteristic
77C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82D52—22no—
83D52—41no—
84C4×D13—81no—
85C4×D13—81no—
86Dic26—22no—
87Dic26—41no—
88C8×C13—21no—
89C8×C13—41no—
90C8×C13—41no—
91C8×C13C22×C811yescharacteristic
92C8×C13#13111yescharacteristic
93#1055—81no—
94#1055—81no—
95C2×SD32—131no—
96C8×Q8—261no—
97C4×Q16—131no—
98C4×D8—131no—
99C8×D4—261no—
100#366—131no—
101#358—131no—
102#357—131no—
103#346C2×D1311yescharacteristic
104#346C2×D1311yescharacteristic
105#334—131no—
106#334—131no—
107Q8⋊C8—261no—
108D4⋊C8—261no—
109#322C2×D1311yescharacteristic
110C22×C13#44211yescharacteristic
111C2×D13—42no—
112C2×D13—81no—
113C2×D13—81no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13C8×D411yescharacteristic
117C4×C13#44411yescharacteristic
118Dic13—42no—
119Dic13—81no—
120Dic13—81no—
121C2×Q16—131no—
122C2×D8—131no—
123C22×C8—521no—
124C4×Q8—261no—
125C4×D4—261no—
126SD32—134no—
127C2×C16—21no—
128C2×C16C4×D1311yescharacteristic
129C2×C16C4×D1311yescharacteristic
130#107—131no—
131#107—131no—
132C4⋊C8—261no—
133C4⋊C8—261no—
134C4⋊C8—521no—
135#103—261no—
136#102—261no—
137C22⋊C8—521no—
138C4×C8—521no—
139C4×C8D5211yescharacteristic
140C4×C8D5211yescharacteristic
141C4×C8C22×D1311yescharacteristic
142C2×C13#158011yescharacteristic
143C2×C13#218011yescharacteristic
144C2×C13AGL(1,ℤ/16)11yescharacteristic
145D13—82no—
146C2×Q8—261no—
147C2×D4—261no—
148C22×C4—521no—
149Q16—132no—
150Q16—261no—
151D8—132no—
152D8—261no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—521no—
156C2×C8—521no—
157C2×C8—1042no—
158C2×C8C2×C4×D1311yescharacteristic
159C2×C8#612711yescharacteristic
160C4⋊C4—261no—
161C4⋊C4—261no—
162C4⋊C4—521no—
163C22⋊C4—521no—
164C42—521no—
165C42C2×D5211yescharacteristic
166C16—21no—
167C16—41no—
168C16C8×D1312yescomplemented
169C13#1206511yescharacteristic, complemented, Sylow
170C23—521no—
171Q8—262no—
172Q8—521no—
173D4—262no—
174D4—521no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—1041no—
179C2×C4—1041no—
180C2×C4C4×D5211yescharacteristic
181C2×C4#8816211yescharacteristic
182C2×C4#8816211yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—1041no—
187C8—1041no—
188C8C2×C8×D1311yescharacteristic
189C8#8815511yescharacteristic
190C22—522no—
191C22—1041no—
192C22—1041no—
193C22#1171837211yescharacteristic
194C4—21no—
195C4—21no—
196C4—522no—
197C4—1041no—
198C4—1041no—
199C4C8×D5211yescharacteristic
200C4#1171837811yescharacteristic
201C2—1042no—
202C2#1311366111yescharacteristic
203C2#1311672911yescharacteristic
204C2#1311673611yescharacteristic
subgroupG/H
centerC22#11718372
commutatorC8×C13C22×C8
FrattiniC4×C8C22×D13
FittingC13×#1313C2
socleC22×C13#442
prime radicalC2×D104C2×C4
cosocleC4×C8×C13C23
hypercenter#1313D13
hypocenterC13#12065
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1313

Complements

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

NH ≅ G/Ntype
3. #13113656C2semidirect
4. #13112902C2semidirect
5. #13112807C2semidirect
7. C13×#1313C2semidirect
43. #88040C8semidirect
61. Dic52C2×C8semidirect
67. C13×C16C2×C8semidirect
74. #1313D13semidirect
168. C16C8×D13semidirect
169. C13#12065semidirect

Maximal subgroups

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

subgroupindex
#131167022
#131136612
#131136562
#131129022
#131128072
#131128042
C13×#13132
#1206513