Finite Group Databasebeta

← #15777349

Subgroups — #15777349

Order 3328.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117063C211yesmaximal, characteristic, complemented
2#13116655C211yesmaximal, characteristic
3#13114236C211yesmaximal, characteristic
4#13114198C211yesmaximal, characteristic
5#13112907C211yesmaximal, characteristic, complemented
6#13112893C211yesmaximal, characteristic, complemented
7C13×#1362C211yesmaximal, characteristic, complemented
8C13×#494C2211yescharacteristic
9#11718748—21no—
10C2×C16×D13—21no—
11#11718503—21no—
12C8×D52C2211yescharacteristic
13#11718343C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718156—21no—
17#11718156—21no—
18#11718139—21no—
19#11718099—21no—
20#11718073—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×C8×D13—21no—
27C4×D52D411yescharacteristic
28#88123—21no—
29C2×C13×C16—21no—
30C13×C4⋊C8—21no—
31C4×C8×C13C2311yescharacteristic
32#88061—41no—
33#88060—21no—
34#88058—21no—
35#88058—21no—
36#88057—41no—
37C2×#6090D411yescharacteristic
38C2×#6090D411yescharacteristic
39#88049—41no—
40#88047—41no—
41C4⋊#1055—21no—
42C4⋊#1055D411yescharacteristic
43C16×D13—42no—
44#12469—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×D52D811yescharacteristic
47C2×C4×D13—21no—
48C2×Dic26—41no—
49C13×Q16—41no—
50C13×Q16—41no—
51C13×Q16—81no—
52C2×C8×C13—41no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58#6103—21no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13D811yescharacteristic
62C2×#1055—21no—
63C2×#1055—41no—
64C8×D13—41no—
65C8×D13—41no—
66C13×C16—41no—
67#6090—21no—
68#6090—21no—
69#2241—131no—
70D4×C16—131no—
71#1675—131no—
72#1669—131no—
73#1371—131no—
74#1365—131no—
75#1362D1311yescharacteristic, complemented
76C22×D13—21no—
77Q8×C13—81no—
78Q8×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#12111yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13#13511yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—81no—
85D52—21no—
86D52Q3212yes—
87C4×D13—41no—
88C4×D13—41no—
89Dic26—161no—
90C8×C13—21no—
91C8×C13—81no—
92C8×C13#13511yescharacteristic
93C8×C13AGL(1,ℤ/8)11yescharacteristic
94#1055—41no—
95#1055—81no—
96C22×C16—261no—
97#500—131no—
98#494C2×D1311yescharacteristic
99#476—261no—
100#474—261no—
101C8×D4—131no—
102C4⋊C16C2×D1311yescharacteristic
103#358—261no—
104#358—261no—
105C22⋊C16—261no—
106C4×C16—131no—
107#335—131no—
108#335C2×D1311yescharacteristic
109#333—261no—
110#332—261no—
111C22×C13#46611yescharacteristic
112C2×D13—22no—
113C2×D13—41no—
114C2×D13—41no—
115C4×C13—21no—
116C4×C13—161no—
117C4×C13#46311yescharacteristic
118C4×C13#47111yescharacteristic
119C4×C13C2×Q3211yescharacteristic
120C4×C13#50811yescharacteristic
121Dic13—41no—
122Dic13—161no—
123C2×Q16—21no—
124C2×Q16—21no—
125C22×C8—261no—
126C4⋊Q8—21no—
127C4⋊Q8—261no—
128C4×D4—131no—
129C2×C16—21no—
130C2×C16—131no—
131C2×C16—131no—
132C2×C16—522no—
133#107—261no—
134#107—261no—
135#107—521no—
136#106—521no—
137C4⋊C8—21no—
138C4⋊C8—131no—
139C4⋊C8—261no—
140#102—521no—
141#102—521no—
142C22⋊C8—261no—
143C4×C8C22×D1311yescharacteristic
144C2×C13#168111yescharacteristic
145C2×C13#221611yescharacteristic
146C2×C13#222311yescharacteristic
147D13—42no—
148C2×Q8—41no—
149C2×Q8—521no—
150C2×D4—131no—
151C22×C4—261no—
152Q16—41no—
153Q16—41no—
154Q16—81no—
155C2×C8—41no—
156C2×C8—261no—
157C2×C8—521no—
158C2×C8—521no—
159C2×C8—521no—
160C2×C8#612711yescharacteristic
161C2×C8D4×D1311yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—131no—
165C4⋊C4—521no—
166C4⋊C4—521no—
167C22⋊C4—261no—
168C42D4×D1311yescharacteristic
169C16—41no—
170C16—261no—
171C16—261no—
172C13#1246911yescharacteristic, complemented, Sylow
173C23—261no—
174Q8—81no—
175Q8—81no—
176Q8—2081no—
177D4—132no—
178D4—261no—
179C2×C4—81no—
180C2×C4—261no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—1041no—
184C2×C4#8813811yescharacteristic
185C2×C4D8×D1311yescharacteristic
186C2×C4#8817011yescharacteristic
187C8—21no—
188C8—81no—
189C8—521no—
190C8—1041no—
191C8#8816511yescharacteristic
192C8#8817011yescharacteristic
193C22—262no—
194C22—521no—
195C22—521no—
196C22#1171843611yescharacteristic
197C4—21no—
198C4—161no—
199C4—521no—
200C4—2081no—
201C4#1171840911yescharacteristic
202C4#1171844811yescharacteristic
203C4#1171857711yescharacteristic
204C4D13×Q3211yescharacteristic
205C2—522no—
206C2#1311427211yescharacteristic
207C2#1311692611yescharacteristic
208C2#1311696911yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socleC22×C13#466
prime radicalC2×D52D8
hypercenter#1362D13
hypocenterC13#12469
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13117063C2semidirect
5. #13112907C2semidirect
6. #13112893C2semidirect
7. C13×#1362C2semidirect
75. #1362D13semidirect
172. C13#12469semidirect

Maximal subgroups

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

subgroupindex
#131170632
#131166552
#131142362
#131141982
#131129072
#131128932
C13×#13622
#1246913