Finite Group Databasebeta

← #13116522

Subgroups — #13116522

Order 1664.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#11719380C211yesmaximal, characteristic
2D13×#101C212yesmaximal, complemented
3C13×#355C211yesmaximal, characteristic, complemented
4#11718134C211yesmaximal, characteristic, complemented
5#11718070C212yesmaximal, complemented
6C2×Q8×D13C2211yescharacteristic
7C2×#6129C411yescharacteristic
8C13×#124C2211yescharacteristic
9#88198C2211yescharacteristic
10#88190C411yescharacteristic
11M16×D13—22no—
12#88137—22no—
13#88132—22no—
14#88126C411yescharacteristic
15#88123C411yescharacteristic
16C13×#101C2212yes—
17#88076C2212yes—
18#88064—22no—
19C2×Q8×C13C2311yescharacteristic
20C2×D4×C13C2×C411yescharacteristic
21C2×C22⋊D13—21no—
22C22×Dic13—21no—
23Q8×D13—42no—
24#6129—42no—
25C2×C4×D13C2×C411yescharacteristic
26C2×C4×D13D412yes—
27C2×Dic26C2×C411yescharacteristic
28C2×Dic26C2×C411yescharacteristic
29C2×Dic26D412yes—
30C13×M16—22no—
31C13×C22⋊C4—22no—
32C42×C13C2×C411yescharacteristic
33C22⋊Dic13—22no—
34#6103—21no—
35C4⋊Dic13—22no—
36#6101—22no—
37#6101—21no—
38C4×Dic13C2×C411yescharacteristic
39#6099—22no—
40#6094—42no—
41C8×D13—42no—
42#2133—131nomaximal, Sylow
43C23×C13—21no—
44C22×D13C22⋊C411yescharacteristic
45Q8×C13—41no—
46D4×C13—41no—
47C2×C4×C13—21no—
48C2×C4×C13C22×C411yescharacteristic
49C2×C4×C13C2×D412yes—
50C22⋊D13—42no—
51C2×Dic13—21no—
52C2×Dic13—21no—
53C2×Dic13—42no—
54C2×Dic13C22⋊C411yescharacteristic
55C2×Dic13C22⋊C412yes—
56C4×D13—22no—
57C4×D13—22no—
58C4×D13—22no—
59Dic26—41no—
60Dic26—42no—
61Dic26—41no—
62C8×C13—42no—
63#1055—42no—
64#536—131no—
65C2×#101—132no—
66#356—132no—
67#355—131no—
68#355D1311yescharacteristic, complemented
69C22×C13—42no—
70C22×C13—41no—
71C22×C13C2×C22⋊C411yescharacteristic
72C2×D13—41no—
73C2×D13#9912yes—
74C4×C13—22no—
75C4×C13—21no—
76C4×C13—41no—
77Dic13—21no—
78Dic13—22no—
79Dic13—41no—
80Dic13—41no—
81C2×#41—131no—
82C22×Q8—131no—
83C2×M16—262no—
84C4⋊Q8—131no—
85C4⋊Q8—131no—
86#124—131no—
87#124C2×D1311yescharacteristic
88#123—262no—
89C22⋊Q8—262no—
90#117—131no—
91#101—132no—
92#101—262no—
93#101C2×D1312yes—
94C2×C13—21no—
95C2×C13—81no—
96C2×C13C2×#9911yescharacteristic
97D13—22no—
98#41—522no—
99C2×Q8—131no—
100C2×Q8—132no—
101C2×Q8—131no—
102C2×Q8—522no—
103C2×Q8C22×D1311yescharacteristic
104C2×D4—261no—
105C2×D4C4×D1311yescharacteristic
106C22×C4—131no—
107C22×C4—132no—
108C22×C4—261no—
109M16—22no—
110M16—262no—
111M16—522no—
112C2×C8—522no—
113C4⋊C4—261no—
114C4⋊C4—262no—
115C4⋊C4—262no—
116C22⋊C4—22no—
117C22⋊C4—261no—
118C22⋊C4—262no—
119C42—131no—
120C42C4×D1311yescharacteristic
121C13#213311yescharacteristic, complemented, Sylow
122C23—21no—
123C23—131no—
124Q8—41no—
125Q8—522no—
126Q8—521no—
127Q8—521no—
128D4—41no—
129D4—522no—
130C2×C4—21no—
131C2×C4—132no—
132C2×C4—131no—
133C2×C4—262no—
134C2×C4—262no—
135C2×C4—262no—
136C2×C4—261no—
137C2×C4—261no—
138C2×C4—522no—
139C2×C4C2×C4×D1311yescharacteristic
140C2×C4D4×D1312yes—
141C8—42no—
142C8—522no—
143C22—42no—
144C22—41no—
145C22—132no—
146C22—521no—
147C22C22⋊C4×D1311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—261no—
152C4—262no—
153C4—521no—
154C4—521no—
155C2—21no—
156C2—81no—
157C2—262no—
158C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×Q8C22×D13
FittingC13×#355C2
socleC2×C13C2×#99
prime radicalC2×#6129C4
cosocleC2×Q8×C13C23
hypercenter#355D13
hypocenterC13#2133
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. D13×#101C2semidirect
3. C13×#355C2semidirect
4. #11718134C2semidirect
5. #11718070C2semidirect
68. #355D13semidirect
121. C13#2133semidirect

Maximal subgroups

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

subgroupindex
#117193802
D13×#1012
C13×#3552
#117181342
#117180702
#213313