Finite Group Databasebeta

← #16777357

Subgroups — #16777357

Order 3328.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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#13131196C211yesmaximal, characteristic
2#13130758C211yesmaximal, characteristic
3#13113596C211yesmaximal, characteristic
4#11719060—21no—
5#11718496—21no—
6C4×C8×D13C2211yescharacteristic
7#11718265—21no—
8#11718265C412yes—
9#11718259—21no—
10#11718257C412yescomplemented
11C4⋊#6092—21no—
12C13×#334C411yescharacteristic, complemented
13#11718071—21no—
14#11718049C411yescharacteristic, complemented
15C2×C4⋊#261—22no—
16C2×C8×D13C2×C411yescharacteristic
17C2×C8×D13D411yescharacteristic
18C42×D13D411yescharacteristic
19(C2×#261)⋊C4—41no—
20(C2×#261)⋊C4—41no—
21C2×#6092—22no—
22C13×C4⋊C8—21no—
23C4×C8×C13C2×C411yescharacteristic
24#88060—41no—
25#88055—41no—
26C8×Dic13C2×C411yescharacteristic
27C8×Dic13Q811yescharacteristic
28C4⋊#1055—21no—
29C4×#1055D411yescharacteristic
30#7218—131nomaximal, Sylow
31C22×#261—42no—
32C2×C4×D13C22⋊C411yescharacteristic
33C2×C4×D13D811yescharacteristic
34C2×C4×D13SD1611yescharacteristic
35C4⋊#261—42no—
36C4⋊#261—42no—
37C2×C8×C13—41no—
38C2×C8×C13C4211yescharacteristic
39C2×C8×C13C4⋊C411yescharacteristic
40C42×C13C22⋊C411yescharacteristic
41C4×Dic13C4⋊C411yescharacteristic
42C4×Dic13SD1611yescharacteristic
43C4×Dic13Q1611yescharacteristic
44C2×#1055—41no—
45C2×#1055C22⋊C411yescharacteristic
46C2×#1055C4⋊C411yescharacteristic
47C8×D13—41no—
48C8×D13—41no—
49#6092—42no—
50#2162—131no—
51#1835—131no—
52#1568—131no—
53C22×D13#10211yescharacteristic
54C2×#261—82no—
55C2×#261—82no—
56C2×#261—82no—
57C2×C4×C13#9511yescharacteristic
58C2×C4×C13#10211yescharacteristic
59C2×C4×C13#10311yescharacteristic
60C2×Dic13#10311yescharacteristic
61C2×Dic13#10611yescharacteristic
62C2×Dic13#10711yescharacteristic
63C4×D13—22no—
64C4×D13—21no—
65C4×D13—21no—
66C4×D13—41no—
67C8×C13—21no—
68C8×C13—21no—
69C8×C13—81no—
70#1055—21no—
71#1055—21no—
72#1055—81no—
73#432—261no—
74C2×C4×C8—131no—
75#382—261no—
76C4⋊C16—261no—
77C22⋊C16—261no—
78C4×C16—132no—
79#340—132no—
80#340—261no—
81#335—261no—
82#334—131no—
83#334#26111yescharacteristic, complemented
84C22×C13#34011yescharacteristic
85C2×D13—21no—
86C2×D13—21no—
87C2×D13#35912yes—
88#261—162no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13H(3,ℤ/4)11yescharacteristic
92C4×C13#34411yescharacteristic
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96C22×C8—131no—
97C22×C8—131no—
98C2×C4⋊C4—262no—
99C2×C42—131no—
100C2×C16—262no—
101C4⋊C8—21no—
102C4⋊C8—261no—
103C22⋊C8—521no—
104#97—521no—
105C4×C8—131no—
106C4×C8—131no—
107C4×C8—131no—
108C4×C8C2×#26111yescharacteristic
109#95—521no—
110#95—521no—
111C2×C13#128611yescharacteristic
112C2×C13#138211yescharacteristic
113C2×C13#138411yescharacteristic
114D13—22no—
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—522no—
119C2×C8—41no—
120C2×C8—131no—
121C2×C8—131no—
122C2×C8—521no—
123C2×C8—521no—
124C2×C8—521no—
125C2×C8C4×#26111yescharacteristic
126C2×C8C4⋊#26111yescharacteristic
127C4⋊C4—522no—
128C4⋊C4—522no—
129C42—131no—
130C42—131no—
131C42—131no—
132C42C22⋊#26111yescharacteristic
133C16—522no—
134C13#721811yescharacteristic, complemented, Sylow
135C23—131no—
136C2×C4—131no—
137C2×C4—131no—
138C2×C4—131no—
139C2×C4—262no—
140C2×C4—261no—
141C2×C4—261no—
142C2×C4—521no—
143C2×C4—1042no—
144C2×C4—1042no—
145C2×C4—1042no—
146C2×C4(C2×#261)⋊C411yescharacteristic
147C2×C4#8811511yescharacteristic
148C2×C4#8811711yescharacteristic
149C8—21no—
150C8—21no—
151C8—81no—
152C8—261no—
153C8—261no—
154C8—1041no—
155C22—132no—
156C22—261no—
157C22—261no—
158C22#1171824611yescharacteristic
159C4—21no—
160C4—21no—
161C4—261no—
162C4—261no—
163C4—261no—
164C4—2082no—
165C4#1171826711yescharacteristic
166C4#1171827411yescharacteristic
167C2—262no—
168C2#1312969111yescharacteristic
169C2#1312989911yescharacteristic
170C2#1312990311yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×#334C4
socleC22×C13#340
prime radicalC22×D13#102
cosocleC4×C8×D13C22
hypercenter#334#261
hypocenterC13#7218
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #334

Complements

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

NH ≅ G/Ntype
10. #11718257C4semidirect
12. C13×#334C4semidirect
14. #11718049C4semidirect
83. #334#261semidirect
134. C13#7218semidirect

Maximal subgroups

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

subgroupindex
#131311962
#131307582
#131135962
#721813