Finite Group Databasebeta

← #15750374

Subgroups — #15750374

Order 3328.

136 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×D208C211yesmaximal, characteristic
2#13112970C211yesmaximal, characteristic, complemented
3C13×#1372C211yesmaximal, characteristic, complemented
4C2×D208C411yescharacteristic
5C4×D104—21no—
6C4×C13×C16C2211yescharacteristic
7C13×#335—21no—
8#11718101—21no—
9#11718096C411yescharacteristic
10C2×#88034—21no—
11C2×D104—21no—
12C4×D52—41no—
13C2×C13×C16C2×C411yescharacteristic
14C2×C13×C16D411yescharacteristic
15C13×C4⋊C8—41no—
16C4×C8×C13D411yescharacteristic
17#88061—41no—
18#88058—21no—
19D208—21no—
20D208C812yescomplemented
21#88034—22no—
22#7385—131nomaximal, Sylow
23C2×D52—41no—
24C2×C4×D13—81no—
25C2×C8×C13—81no—
26C2×C8×C13C22⋊C411yescharacteristic
27C2×C8×C13SD1611yescharacteristic
28C42×C13D811yescharacteristic
29#6103—81no—
30C4⋊Dic13—41no—
31D104—22no—
32D104—41no—
33C13×C16—21no—
34C13×C16C2×C811yescharacteristic
35C13×C16M1611yescharacteristic
36C4×D16—131no—
37#1397—131no—
38#1372D1311yescharacteristic, complemented
39C22×D13—81no—
40C2×C4×C13#10211yescharacteristic
41C2×C4×C13D1611yescharacteristic
42C2×C4×C13SD3211yescharacteristic
43C2×Dic13—81no—
44D52—42no—
45D52—81no—
46C4×D13—162no—
47C8×C13—21no—
48C8×C13—161no—
49C8×C13C22⋊C811yescharacteristic
50C8×C13#10411yescharacteristic
51C2×D16—131no—
52C4×D8—261no—
53C2×C32—261no—
54#366—131no—
55#357—261no—
56C4×C16C2×D1311yescharacteristic
57#335—21no—
58C22×C13#35711yescharacteristic
59C2×D13—82no—
60C2×D13—161no—
61C2×D13—161no—
62C4×C13—21no—
63C4×C13—21no—
64C4×C13D4⋊C811yescharacteristic
65C4×C13#35911yescharacteristic
66Dic13—161no—
67C2×D8—261no—
68C4×D4—521no—
69D16—132no—
70D16—261no—
71C2×C16C4×D1311yescharacteristic
72C2×C16D5211yescharacteristic
73#107—261no—
74C4⋊C8—41no—
75#102—521no—
76C4×C8C22⋊D1311yescharacteristic
77C32—262no—
78C2×C13#133111yescharacteristic
79C2×C13#141811yescharacteristic
80C2×C13#141911yescharacteristic
81D13—162no—
82C2×D4—521no—
83C22×C4—1041no—
84D8—262no—
85D8—521no—
86C2×C8—81no—
87C2×C8#610311yescharacteristic
88C2×C8#610611yescharacteristic
89C4⋊C4—521no—
90C22⋊C4—1041no—
91C42#610411yescharacteristic
92C16—21no—
93C16C8×D1311yescharacteristic
94C16#609411yescharacteristic
95C13#738511yescharacteristic, complemented, Sylow
96C23—1041no—
97D4—522no—
98D4—1041no—
99C2×C4—1041no—
100C2×C4—2082no—
101C2×C4#8804911yescharacteristic
102C2×C4#8806611yescharacteristic
103C2×C4#8806811yescharacteristic
104C8—21no—
105C8—161no—
106C8#8806011yescharacteristic
107C8#8806511yescharacteristic
108C22—1042no—
109C22—2081no—
110C22—2081no—
111C22#1171808311yescharacteristic
112C4—21no—
113C4—21no—
114C4—2081no—
115C4#1171807511yescharacteristic
116C4#1171808911yescharacteristic
117C2—2082no—
118C2#1311279611yescharacteristic
119C2#1311302211yescharacteristic
120C2#1311302511yescharacteristic
subgroupG/H
centerC22#11718083
commutatorC13×C16C2×C8
FrattiniC4×C16C2×D13
FittingC13×#1372C2
socleC22×C13#357
prime radicalC2×D208C4
cosocleC4×C13×C16C22
hypercenter#1372D13
hypocenterC13#7385
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #1372

Complements

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

NH ≅ G/Ntype
2. #13112970C2semidirect
3. C13×#1372C2semidirect
20. D208C8semidirect
38. #1372D13semidirect
95. C13#7385semidirect

Maximal subgroups

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

subgroupindex
C4×D2082
#131129702
C13×#13722
#738513