Finite Group Databasebeta

← #13113971

Subgroups — #13113971

Order 1664.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#11719435C211yesmaximal, characteristic
2#11718753C211yesmaximal, characteristic, complemented
3#11718511C211yesmaximal, characteristic, complemented
4#11718503C211yesmaximal, characteristic
5C13×#333C211yesmaximal, characteristic, complemented
6#11718076C211yesmaximal, characteristic, complemented
7#11718075C211yesmaximal, characteristic
8C13×C4⋊Q8C2211yescharacteristic
9#88200—22no—
10C2×#6107—22no—
11#88151—21no—
12#88147—21no—
13C4⋊C4×D13—21no—
14#88144—21no—
15C4×D52C2211yescharacteristic
16#88123C2211yescharacteristic
17C4×Dic26C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20#88061—21no—
21#88058—21no—
22#88057—21no—
23#88056—21no—
24C4×#1055C2211yescharacteristic
25C2×Q8×C13D412yes—
26C2×D52D411yescharacteristic
27C2×C4×D13—21no—
28C2×C4×D13—22no—
29C2×Dic26—21no—
30C2×Dic26D411yescharacteristic
31C2×C8×C13—21no—
32C2×C8×C13—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C42×C13C2311yescharacteristic
36#6107—44no—
37#6103—22no—
38#6103—21no—
39C4⋊Dic13—22no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13D411yescharacteristic
43C4⋊Dic13D411yescharacteristic
44#6101—22no—
45#6101—21no—
46C4×Dic13—21no—
47C2×#1055—21no—
48#1632—131nomaximal, Sylow
49C22×D13—21no—
50Q8×C13—42no—
51C2×C4×C13—22no—
52C2×C4×C13C2×D411yescharacteristic
53C2×C4×C13C2×D411yescharacteristic
54C2×C4×C13C2×D411yescharacteristic
55C2×Dic13—21no—
56C2×Dic13—21no—
57C2×Dic13—21no—
58C2×Dic13—41no—
59D52—21no—
60D52Q1612yescomplemented
61C4×D13—41no—
62C4×D13—41no—
63C4×D13—82no—
64Dic26—21no—
65Dic26—21no—
66Dic26—42no—
67C8×C13—41no—
68C8×C13—41no—
69#1055—22no—
70#554—131no—
71#494—131no—
72#477—131no—
73#476—131no—
74#333D1311yescharacteristic, complemented
75Q8⋊C8—131no—
76D4⋊C8—131no—
77C22×C13#12011yescharacteristic
78C2×D13—22no—
79C2×D13—41no—
80C2×D13—41no—
81C4×C13—21no—
82C4×C13—42no—
83C4×C13C2×Q1611yescharacteristic
84C4×C13#13511yescharacteristic
85C4×C13#13711yescharacteristic
86C4×C13#13711yescharacteristic
87Dic13—41no—
88Dic13—41no—
89Dic13—41no—
90Dic13—81no—
91C2×Q16—262no—
92C4⋊Q8—131no—
93C4⋊Q8C2×D1311yescharacteristic
94#125—261no—
95C22⋊Q8—261no—
96C22⋊Q8—262no—
97C4×Q8—131no—
98C4×D4—131no—
99C4×D4—261no—
100C2×C4⋊C4—261no—
101#107—261no—
102#106—261no—
103C4⋊C8C2×D1311yescharacteristic
104C4⋊C8C2×D1311yescharacteristic
105#103—261no—
106#102—261no—
107C4×C8—131no—
108C2×C13#45111yescharacteristic
109C2×C13#45211yescharacteristic
110C2×C13#45311yescharacteristic
111D13—42no—
112C2×Q8—131no—
113C2×Q8—261no—
114C2×Q8D5212yes—
115C2×D4—131no—
116C22×C4—262no—
117C22×C4—261no—
118Q16—524no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—261no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—131no—
125C4⋊C4—131no—
126C4⋊C4—262no—
127C4⋊C4—262no—
128C4⋊C4—261no—
129C4⋊C4—261no—
130C4⋊C4—261no—
131C22⋊C4—262no—
132C22⋊C4—261no—
133C42—261no—
134C42C22×D1311yescharacteristic
135C13#163211yescharacteristic, complemented, Sylow
136C23—261no—
137Q8—42no—
138Q8—261no—
139Q8—261no—
140Q8—522no—
141D4—132no—
142D4—261no—
143C2×C4—22no—
144C2×C4—261no—
145C2×C4—261no—
146C2×C4—261no—
147C2×C4—521no—
148C2×C4—521no—
149C2×C4—521no—
150C2×C4—1042no—
151C2×C4C2×D5211yescharacteristic
152C2×C4D4×D1311yescharacteristic
153C2×C4D4×D1311yescharacteristic
154C8—41no—
155C8—41no—
156C8—262no—
157C22—262no—
158C22—521no—
159C22—521no—
160C22#8813611yescharacteristic
161C4—21no—
162C4—42no—
163C4—521no—
164C4—521no—
165C4—521no—
166C4—1041no—
167C4#8816911yescharacteristic
168C4#8817011yescharacteristic
169C4Q16×D1311yescharacteristic
170C4#8817211yescharacteristic
171C2—522no—
172C2#1171840811yescharacteristic
173C2#1171846911yescharacteristic
174C2#1171847111yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#333C2
socleC22×C13#120
prime radicalC2×D52D4
hypercenter#333D13
hypocenterC13#1632
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #11718753C2semidirect
3. #11718511C2semidirect
5. C13×#333C2semidirect
6. #11718076C2semidirect
60. D52Q16semidirect
74. #333D13semidirect
135. C13#1632semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117187532
#117185112
#117185032
C13×#3332
#117180762
#117180752
#163213