Finite Group Databasebeta

← #15777295

Subgroups — #15777295

Order 3328.

200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117111C211yesmaximal, characteristic
2#13114230C212yesmaximal
3#13112910C211yesmaximal, characteristic
4#13112890C212yesmaximal
5C13×#2183C211yesmaximal, characteristic
6C8×Q8×C13C2211yescharacteristic
7#11718692—22no—
8#11718343C2212yes—
9C13×C4⋊C16—21no—
10C13×C4⋊C16C2211yescharacteristic
11C13×#346—21no—
12C4×C13×C16C2211yescharacteristic
13#11718096—21no—
14#11718096—21no—
15#11718078—22no—
16#11718050C2212yes—
17C4×Q8×C13D411yescharacteristic
18C2×#6107—42no—
19#88123—22no—
20C2×C13×C16—21no—
21C2×C13×C16D411yescharacteristic
22C2×C13×C16D411yescharacteristic
23C13×C4⋊C8—21no—
24C13×C4⋊C8D411yescharacteristic
25C4×C8×C13—21no—
26C4×C8×C13C2311yescharacteristic
27#88058—22no—
28#88058—22no—
29#88050—42no—
30C4⋊#1055—22no—
31#12460—131nomaximal, Sylow
32C2×Q8×C13D811yescharacteristic
33C2×Dic26—42no—
34C2×C8×C13—21no—
35C2×C8×C13C2×D411yescharacteristic
36C2×C8×C13#4111yescharacteristic
37C13×C4⋊C4—21no—
38C13×C4⋊C4D811yescharacteristic
39C42×C13—21no—
40C42×C13C2×D411yescharacteristic
41#6107—84no—
42C4⋊Dic13—42no—
43C4⋊Dic13—42no—
44C2×#1055—42no—
45C13×C16—21no—
46C13×C16—41no—
47C13×C16Q1612yescomplemented
48#2252—131no—
49#2183D1311yescharacteristic
50#1674—132no—
51#1372—131no—
52#1364—132no—
53Q8×C13—22no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13#12111yescharacteristic
57C2×C4×C13C2×D811yescharacteristic
58C2×C4×C13#13511yescharacteristic
59C2×Dic13—82no—
60Dic26—82no—
61Dic26—82no—
62C8×C13—21no—
63C8×C13—41no—
64C8×C13C2×Q1611yescharacteristic
65C8×C13#13711yescharacteristic
66#1055—82no—
67#500—132no—
68#462—262no—
69C8×Q8C2×D1311yescharacteristic
70#366—261no—
71#366—261no—
72C4⋊C16—21no—
73C4⋊C16C2×D1311yescharacteristic
74#346—21no—
75C4×C16C2×D1311yescharacteristic
76#335—132no—
77#332—262no—
78C22×C13#46611yescharacteristic
79C4×C13—21no—
80C4×C13—41no—
81C4×C13—41no—
82C4×C13#46211yescharacteristic
83C4×C13#47311yescharacteristic
84C4×C13#50912yes—
85Dic13—162no—
86C2×Q16—522no—
87C4⋊Q8—262no—
88C4×Q8D5211yescharacteristic
89C2×C16—21no—
90C2×C16C22⋊D1311yescharacteristic
91C2×C16C22⋊D1311yescharacteristic
92#107—262no—
93#107—262no—
94C4⋊C8—21no—
95C4⋊C8—262no—
96C4⋊C8D5211yescharacteristic
97#103—522no—
98C4×C8—21no—
99C4×C8C22×D1311yescharacteristic
100C2×C13#167411yescharacteristic
101C2×C13#221811yescharacteristic
102C2×C13#222211yescharacteristic
103C2×Q8—522no—
104C2×Q8D10411yescharacteristic
105Q16—1044no—
106C2×C8—21no—
107C2×C8—522no—
108C2×C8#612711yescharacteristic
109C2×C8C2×C22⋊D1311yescharacteristic
110C4⋊C4—21no—
111C4⋊C4—522no—
112C4⋊C4—522no—
113C4⋊C4D10411yescharacteristic
114C42—21no—
115C42C2×D5211yescharacteristic
116C16—21no—
117C16—41no—
118C16#610712yescomplemented
119C13#1246011yescharacteristic, complemented, Sylow
120Q8—22no—
121Q8—1042no—
122Q8—1042no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—1042no—
126C2×C4C2×D10411yescharacteristic
127C2×C4#8815811yescharacteristic
128C2×C4#8818411yescharacteristic
129C8—21no—
130C8—41no—
131C8—1042no—
132C8C2×#610711yescharacteristic
133C8#8820511yescharacteristic
134C22#1171877611yescharacteristic
135C4—21no—
136C4—41no—
137C4—41no—
138C4—2082no—
139C4#1171856912yes—
140C4#1171869211yescharacteristic
141C4#1171880411yescharacteristic
142C2#1311423011yescharacteristic
143C2#1311693911yescharacteristic
144C2#1311696111yescharacteristic
subgroupG/H
centerC22#11718776
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2183C2
socle, prime radicalC22×C13#466
hypercenter#2183D13
hypocenterC13#12460
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
47. C13×C16Q16semidirect
118. C16#6107semidirect
119. C13#12460semidirect

Maximal subgroups

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

subgroupindex
#131171112
#131142302
#131129102
#131128902
C13×#21832
#1246013