Finite Group Databasebeta

← #13113970

Subgroups — #13113970

Order 1664.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C13×#554C211yesmaximal, characteristic
2#11718753C211yesmaximal, characteristic, complemented
3#11718682C211yesmaximal, characteristic, complemented
4#11718669C211yesmaximal, characteristic
5#11718138C211yesmaximal, characteristic, complemented
6Q8⋊#1055C211yesmaximal, characteristic, complemented
7D4⋊#1055C211yesmaximal, characteristic
8C13×C4⋊Q8C2211yescharacteristic
9C13×#125—21no—
10C13×C22⋊Q8—21no—
11C13×C22⋊Q8—22no—
12C4×Q8×C13C2211yescharacteristic
13C4×D4×C13—21no—
14C4×D4×C13C2211yescharacteristic
15C2×C13×C4⋊C4—21no—
16C2×#6107—22no—
17#88123C2211yescharacteristic
18#88075—21no—
19#88072—21no—
20#88048—21no—
21#88047—21no—
22C4⋊#1055C2211yescharacteristic
23C4⋊#1055C2211yescharacteristic
24C4×#1055C2211yescharacteristic
25C2×Q8×C13D411yescharacteristic
26C2×Q8×C13D412yes—
27C2×D4×C13D411yescharacteristic
28C22×C4×C13—22no—
29C22×C4×C13—21no—
30C2×Dic26—21no—
31C13×C4⋊C4—22no—
32C13×C4⋊C4—22no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4D411yescharacteristic
37C13×C4⋊C4D411yescharacteristic
38C13×C22⋊C4—22no—
39C13×C22⋊C4—21no—
40C42×C13—21no—
41C42×C13C2311yescharacteristic
42#6107—44no—
43C4⋊Dic13—21no—
44C4⋊Dic13—21no—
45C2×#1055—21no—
46C2×#1055—21no—
47C2×#1055—21no—
48#1632—131nomaximal, Sylow
49C23×C13—21no—
50Q8×C13—21no—
51Q8×C13—21no—
52Q8×C13—42no—
53D4×C13—21no—
54D4×C13Q1612yescomplemented
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—22no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—82no—
62C2×C4×C13C2×D411yescharacteristic
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13C2×D411yescharacteristic
65C2×Dic13—41no—
66Dic26—42no—
67#1055—22no—
68#1055—41no—
69#1055—41no—
70#554D1311yescharacteristic
71#494—131no—
72#477—131no—
73#476—131no—
74#333—131no—
75Q8⋊C8—131no—
76D4⋊C8—131no—
77C22×C13—22no—
78C22×C13—41no—
79C22×C13—41no—
80C22×C13#12011yescharacteristic
81C4×C13—21no—
82C4×C13—41no—
83C4×C13—41no—
84C4×C13—41no—
85C4×C13—42no—
86C4×C13C2×Q1611yescharacteristic
87C4×C13#13511yescharacteristic
88C4×C13#13711yescharacteristic
89C4×C13#13711yescharacteristic
90Dic13—81no—
91C2×Q16—262no—
92C4⋊Q8—131no—
93C4⋊Q8C2×D1311yescharacteristic
94#125—21no—
95C22⋊Q8—21no—
96C22⋊Q8—22no—
97C4×Q8C2×D1311yescharacteristic
98C4×D4—21no—
99C4×D4C2×D1311yescharacteristic
100C2×C4⋊C4—21no—
101#107—261no—
102#106—261no—
103C4⋊C8—131no—
104C4⋊C8—131no—
105#103—261no—
106#102—261no—
107C4×C8—131no—
108C2×C13—42no—
109C2×C13#45111yescharacteristic
110C2×C13#45211yescharacteristic
111C2×C13#45311yescharacteristic
112C2×Q8—261no—
113C2×Q8C22⋊D1311yescharacteristic
114C2×Q8C22⋊D1312yes—
115C2×D4C22⋊D1311yescharacteristic
116C22×C4—22no—
117C22×C4—21no—
118Q16—524no—
119C2×C8—261no—
120C2×C8—261no—
121C2×C8—261no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—261no—
128C4⋊C4—261no—
129C4⋊C4C22⋊D1311yescharacteristic
130C4⋊C4C22⋊D1311yescharacteristic
131C22⋊C4—22no—
132C22⋊C4—21no—
133C42—21no—
134C42C22×D1311yescharacteristic
135C13#163211yescharacteristic, complemented, Sylow
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—522no—
141D4—21no—
142D4#610712yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—521no—
151C2×C4C2×C22⋊D1311yescharacteristic
152C2×C4C2×C22⋊D1311yescharacteristic
153C2×C4C2×C22⋊D1311yescharacteristic
154C8—262no—
155C8—521no—
156C8—521no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#8820711yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—41no—
165C4—42no—
166C4—1041no—
167C4#8819611yescharacteristic
168C4C2×#610711yescharacteristic
169C4#8820411yescharacteristic
170C4#8820511yescharacteristic
171C2—42no—
172C2#1171888911yescharacteristic
173C2#1171890011yescharacteristic
174C2#1171890211yescharacteristic
subgroupG/H
centerC22#88207
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#554C2
socleC22×C13#120
prime radicalC2×D4×C13D4
hypercenter#554D13
hypocenterC13#1632
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #11718753C2semidirect
3. #11718682C2semidirect
5. #11718138C2semidirect
6. Q8⋊#1055C2semidirect
54. D4×C13Q16semidirect
135. C13#1632semidirect
142. D4#6107semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
#117187532
#117186822
#117186692
#117181382
Q8⋊#10552
D4⋊#10552
#163213