Finite Group Databasebeta

← #15774869

Subgroups — #15774869

Order 3328.

220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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#13113744C211yesmaximal, characteristic, complemented
3#13113659C211yesmaximal, characteristic
4#13112805C211yesmaximal, characteristic, complemented
5#13112802C211yesmaximal, characteristic
6#13112758C211yesmaximal, characteristic, complemented
7C13×#1368C211yesmaximal, characteristic, complemented
8C2×#88040C411yescharacteristic
9#11718495—21no—
10#11718492—21no—
11C4×Dic52C2211yescharacteristic
12C4×D104C2211yescharacteristic
13C13×#346C2211yescharacteristic
14C13×#334C2211yescharacteristic
15C13×#334C2211yescharacteristic
16#11718101C411yescharacteristic
17#11718096C411yescharacteristic
18#11718095C411yescharacteristic
19#11718076—21no—
20#11718075—21no—
21#11718053C2211yescharacteristic
22#11718047C2211yescharacteristic
23C2×Dic52C2×C411yescharacteristic
24C2×D104C2×C411yescharacteristic
25C2×C8×D13—41no—
26C4×D52—21no—
27C4×Dic26—21no—
28C2×C13×C16C2×C411yescharacteristic
29C2×C13×C16C2×C411yescharacteristic
30C13×C4⋊C8—21no—
31C13×C4⋊C8—21no—
32C4×C8×C13C2311yescharacteristic
33#88061—21no—
34#88060—41no—
35#88058C2×C411yescharacteristic
36#88058C2×C411yescharacteristic
37#88056—21no—
38#88055—41no—
39#88054—41no—
40C2×#6090—21no—
41C4×#1055D411yescharacteristic
42C4×#1055D411yescharacteristic
43#88040—22no—
44#12077—131nomaximal, Sylow
45C2×D52—21no—
46C2×C4×D13—41no—
47C2×Dic26—21no—
48C2×C8×C13—41no—
49C2×C8×C13—41no—
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—21no—
59C2×#1055—21no—
60Dic52—21no—
61Dic52—21no—
62D104—21no—
63D104M1612yes—
64C8×D13—82no—
65C13×C16—21no—
66C13×C16—21no—
67#6090—22no—
68#2175—131no—
69#1593—131no—
70#1580—131no—
71#1368D1311yescharacteristic, complemented
72#1334—131no—
73#1333—131no—
74#1313—131no—
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—41no—
87Dic26—41no—
88C8×C13—21no—
89C8×C13—81no—
90C8×C13—81no—
91C8×C13C2×M1611yescharacteristic
92C8×C13#13111yescharacteristic
93#1055—41no—
94#1055—41no—
95C2×SD32—131no—
96#446—261no—
97C4×Q16—131no—
98C4×D8—131no—
99C8×D4—261no—
100#366—131no—
101#358—131no—
102#357—131no—
103#346—131no—
104#346C2×D1311yescharacteristic
105#334C2×D1311yescharacteristic
106#334C2×D1311yescharacteristic
107Q8⋊C8—261no—
108D4⋊C8—261no—
109#322—131no—
110C22×C13#44211yescharacteristic
111C2×D13—42no—
112C2×D13—81no—
113C2×D13—81no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13#43511yescharacteristic
117C4×C13#44311yescharacteristic
118Dic13—81no—
119Dic13—81no—
120Dic13—81no—
121C2×Q16—131no—
122C2×D8—131no—
123C22×C8—521no—
124C4×Q8—261no—
125C4×D4—261no—
126SD32—262no—
127C2×C16—261no—
128C2×C16C4×D1311yescharacteristic
129C2×C16C4×D1311yescharacteristic
130#107—131no—
131#107—131no—
132C4⋊C8—21no—
133C4⋊C8—21no—
134C4⋊C8—521no—
135#103—261no—
136#102—261no—
137C22⋊C8—521no—
138#97—521no—
139C4×C8—131no—
140C4×C8—131no—
141C4×C8C22×D1311yescharacteristic
142C2×C13#158611yescharacteristic
143C2×C13#218011yescharacteristic
144C2×C13AGL(1,ℤ/16)11yescharacteristic
145D13—82no—
146C2×Q8—261no—
147C2×D4—261no—
148C22×C4—521no—
149Q16—261no—
150Q16—261no—
151D8—132no—
152D8—261no—
153C2×C8—41no—
154C2×C8—41no—
155C2×C8—261no—
156C2×C8—261no—
157C2×C8—1042no—
158C2×C8C2×C4×D1311yescharacteristic
159C2×C8#613111yescharacteristic
160C4⋊C4—261no—
161C4⋊C4—261no—
162C4⋊C4—521no—
163C22⋊C4—521no—
164C42—521no—
165C42D4×D1311yescharacteristic
166C16—21no—
167C16—21no—
168C16—262no—
169C13#1207711yescharacteristic, complemented, Sylow
170C23—521no—
171Q8—521no—
172Q8—521no—
173D4—262no—
174D4—521no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—1041no—
179C2×C4—1041no—
180C2×C4#8814711yescharacteristic
181C2×C4#8816811yescharacteristic
182C2×C4#8816811yescharacteristic
183C8—21no—
184C8—81no—
185C8—81no—
186C8—521no—
187C8—521no—
188C8#8815511yescharacteristic
189C8M16×D1311yescharacteristic
190C22—522no—
191C22—1041no—
192C22—1041no—
193C22#1171853011yescharacteristic
194C4—21no—
195C4—21no—
196C4—1041no—
197C4—1041no—
198C4—1041no—
199C4#1171849711yescharacteristic
200C4#1171855611yescharacteristic
201C2—1042no—
202C2#1311369911yescharacteristic
203C2#1311672611yescharacteristic
204C2#1311673311yescharacteristic
subgroupG/H
centerC22#11718530
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1368C2
socleC22×C13#442
prime radicalC2×D104C2×C4
cosocleC4×C8×C13C23
hypercenter#1368D13
hypocenterC13#12077
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1368

Complements

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

NH ≅ G/Ntype
2. #13113744C2semidirect
4. #13112805C2semidirect
6. #13112758C2semidirect
7. C13×#1368C2semidirect
71. #1368D13semidirect
169. C13#12077semidirect

Maximal subgroups

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

subgroupindex
#131167022
#131137442
#131136592
#131128052
#131128022
#131127582
C13×#13682
#1207713