Finite Group Databasebeta

← #15783789

Subgroups — #15783789

Order 3328.

180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×Dic208C211yesmaximal, characteristic, complemented
2#13116961C212yesmaximal
3#13113040C211yesmaximal, characteristic, complemented
4#13113030C212yesmaximal, complemented
5C13×#2258C211yesmaximal, characteristic
6C13×#504C2211yescharacteristic
7#11718804—22no—
8C2×Dic104C2212yes—
9C13×M64—21no—
10C13×M64C2211yescharacteristic
11C2×C13×C32—21no—
12C2×C13×C32C2211yescharacteristic
13#11718109—22no—
14#11718098C2212yes—
15Dic208—21no—
16Dic208—21no—
17C13×#131D411yescharacteristic
18#88205—42no—
19C2×Dic52—22no—
20C13×M32—21no—
21C13×M32D411yescharacteristic
22C2×C13×C16—21no—
23C2×C13×C16C2311yescharacteristic
24#88064—42no—
25#88059—22no—
26Dic104—22no—
27Dic104—22no—
28C13×C32—21no—
29C13×C32D411yescharacteristic
30C13×C32D411yescharacteristic
31#13701—131nomaximal, Sylow
32C13×#41D811yescharacteristic
33C2×Dic26—42no—
34C13×M16—21no—
35C13×M16D811yescharacteristic
36C2×C8×C13—21no—
37C2×C8×C13C2×D411yescharacteristic
38#6107—82no—
39#6105—82no—
40#6099—42no—
41Dic52—42no—
42Dic52—42no—
43C13×C16—21no—
44C13×C16C2×D411yescharacteristic
45C13×C16#4111yescharacteristic
46C2×Q64—131no—
47#2258D1311yescharacteristic
48#2222—132no—
49#1425—131no—
50#1420—132no—
51Q8×C13D1611yescharacteristic
52D4×C13—21no—
53D4×C13D1611yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13C2×D811yescharacteristic
56C2×Dic13—82no—
57Dic26—82no—
58Dic26—82no—
59C8×C13—21no—
60C8×C13#12111yescharacteristic
61C8×C13#13511yescharacteristic
62#1055—82no—
63C2×Q32—132no—
64#504C2×D1311yescharacteristic
65#473—262no—
66Q64—261no—
67Q64—261no—
68M64—21no—
69M64C2×D1311yescharacteristic
70C2×C32—21no—
71C2×C32C2×D1311yescharacteristic
72#368—132no—
73#362—262no—
74C22×C13—21no—
75C22×C13#50811yescharacteristic
76C4×C13—21no—
77C4×C13#46611yescharacteristic
78C4×C13C2×D1611yescharacteristic
79Dic13—162no—
80#137—522no—
81C2×Q16—262no—
82#131D5211yescharacteristic
83Q32—262no—
84Q32—262no—
85M32—21no—
86M32D5211yescharacteristic
87C2×C16—21no—
88C2×C16C22×D1311yescharacteristic
89#108—262no—
90#101—522no—
91C32—21no—
92C32C22⋊D1311yescharacteristic
93C32C22⋊D1311yescharacteristic
94C2×C13—21no—
95C2×C13—41no—
96C2×C13#221511yescharacteristic
97#41D10411yescharacteristic
98C2×Q8—522no—
99Q16—522no—
100Q16—522no—
101Q16—1042no—
102SD16—1042no—
103M16—21no—
104M16—522no—
105M16D10411yescharacteristic
106C2×C8—21no—
107C2×C8C2×D5211yescharacteristic
108C16—21no—
109C16#612711yescharacteristic
110C16C2×C22⋊D1311yescharacteristic
111C13#1370111yescharacteristic, complemented, Sylow
112Q8—1042no—
113Q8—1042no—
114Q8D20811yescharacteristic
115D4—21no—
116D4D20811yescharacteristic
117C2×C4—21no—
118C2×C4—1042no—
119C2×C4C2×D10411yescharacteristic
120C8—21no—
121C8—1042no—
122C8#8815811yescharacteristic
123C8#8818411yescharacteristic
124C22—21no—
125C22#1171856511yescharacteristic
126C4—21no—
127C4—2082no—
128C4C2×D20811yescharacteristic
129C4#1171877611yescharacteristic
130C2—21no—
131C2—41no—
132C2#1311692211yescharacteristic
subgroupG/H
centerC2#13116922
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#2258C2
socleC2×C13#2215
prime radicalC13×#41D8
hypercenter#2258D13
hypocenterC13#13701
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504 ◁ #2258

Complements

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

NH ≅ G/Ntype
1. C2×Dic208C2semidirect
3. #13113040C2semidirect
4. #13113030C2semidirect
111. C13#13701semidirect

Maximal subgroups

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

subgroupindex
C2×Dic2082
#131169612
#131130402
#131130302
C13×#22582
#1370113