Finite Group Databasebeta

← #13116526

Subgroups — #13116526

Order 1664.

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

normal subgroups only

This group has 262 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#11719379C211yesmaximal, characteristic
2#11718412C212yesmaximal, complemented
3C13×#355C211yesmaximal, characteristic, complemented
4#11718134C211yesmaximal, characteristic, complemented
5#11718069C212yesmaximal, complemented
6C2×#6131C2211yescharacteristic
7C2×D4×D13C411yescharacteristic
8C13×#124C2211yescharacteristic
9#88201C2211yescharacteristic
10#88194C411yescharacteristic
11M16×D13—22no—
12#88138—22no—
13#88136—22no—
14#88128C411yescharacteristic
15#88126C411yescharacteristic
16C13×#101C2212yescomplemented
17#88076C2212yescomplemented
18#88063—22no—
19C23×D13—21no—
20C2×Q8×C13C2311yescharacteristic
21C2×D4×C13C2×C411yescharacteristic
22C2×C22⋊D13—22no—
23C2×C22⋊D13—21no—
24#6131—42no—
25D4×D13—42no—
26C2×D52—22no—
27C2×D52C2×C411yescharacteristic
28C2×D52C2×C411yescharacteristic
29C2×D52D412yes—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D412yes—
32C13×M16—22no—
33C13×C22⋊C4—22no—
34C42×C13C2×C411yescharacteristic
35#6103—21no—
36#6103—22no—
37#6101—21no—
38C4×Dic13C2×C411yescharacteristic
39#6099—22no—
40#6094—42no—
41C8×D13—42no—
42#2134—131nomaximal, Sylow
43C23×C13—21no—
44C22×D13—21no—
45C22×D13—42no—
46C22×D13—82no—
47C22×D13C22⋊C411yescharacteristic
48C22×D13C22⋊C412yes—
49Q8×C13—41no—
50D4×C13—41no—
51C2×C4×C13—21no—
52C2×C4×C13C22×C411yescharacteristic
53C2×C4×C13C2×D412yes—
54C22⋊D13—42no—
55C22⋊D13—82no—
56C2×Dic13—21no—
57C2×Dic13C22⋊C411yescharacteristic
58D52—41no—
59D52—42no—
60D52—41no—
61D52—82no—
62C4×D13—22no—
63C4×D13—22no—
64C4×D13—22no—
65C8×C13—42no—
66#1055—42no—
67#535—131no—
68#413—132no—
69#355—131no—
70#355—132no—
71#355D1311yescharacteristic, complemented
72C22×C13—42no—
73C22×C13—41no—
74C22×C13C2×C22⋊C411yescharacteristic
75C2×D13—21no—
76C2×D13—22no—
77C2×D13—42no—
78C2×D13—41no—
79C2×D13—42no—
80C2×D13—41no—
81C2×D13—84no—
82C4×C13—22no—
83C4×C13—21no—
84C4×C13—41no—
85Dic13—41no—
86Dic13#9912yes—
87C2×#41—131no—
88C22×D4—131no—
89C2×M16—262no—
90#127—131no—
91#127—131no—
92#124—131no—
93#124C2×D1311yescharacteristic
94#121—262no—
95#120—262no—
96#117—131no—
97#101—132no—
98#101C2×D1312yescomplemented
99#100—262no—
100C2×C13—21no—
101C2×C13—81no—
102C2×C13C2×#9911yescharacteristic
103D13—42no—
104D13—41no—
105D13—81no—
106C24—261no—
107#41—522no—
108C2×Q8C22×D1311yescharacteristic
109C2×D4—131no—
110C2×D4—131no—
111C2×D4—132no—
112C2×D4—262no—
113C2×D4—261no—
114C2×D4—262no—
115C2×D4—522no—
116C2×D4C4×D1311yescharacteristic
117C22×C4—131no—
118C22×C4—132no—
119M16—22no—
120M16—262no—
121M16—522no—
122C2×C8—522no—
123C4⋊C4—261no—
124C22⋊C4—22no—
125C22⋊C4—261no—
126C22⋊C4—262no—
127C42—131no—
128C42C4×D1311yescharacteristic
129C13#213411yescharacteristic, complemented, Sylow
130C23—21no—
131C23—131no—
132C23—132no—
133C23—261no—
134C23—522no—
135C23—1042no—
136Q8—41no—
137D4—41no—
138D4—522no—
139D4—521no—
140D4—521no—
141D4—522no—
142D4—1042no—
143D4—1042no—
144C2×C4—21no—
145C2×C4—131no—
146C2×C4—262no—
147C2×C4—262no—
148C2×C4—262no—
149C2×C4—261no—
150C2×C4C2×C4×D1311yescharacteristic
151C2×C4D4×D1312yes—
152C8—42no—
153C8—522no—
154C22—42no—
155C22—41no—
156C22—262no—
157C22—261no—
158C22—522no—
159C22—521no—
160C22—522no—
161C22—521no—
162C22—1044no—
163C22C22⋊C4×D1311yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—132no—
168C4—521no—
169C2—21no—
170C2—81no—
171C2—521no—
172C2—522no—
173C2—1041no—
174C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×Q8C22×D13
FittingC13×#355C2
socleC2×C13C2×#99
prime radical#11719379C2
cosocleC2×Q8×C13C23
hypercenter#355D13
hypocenterC13#2134
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. #11718412C2semidirect
3. C13×#355C2semidirect
4. #11718134C2semidirect
5. #11718069C2semidirect
16. C13×#101C22semidirect
17. #88076C22semidirect
71. #355D13semidirect
98. #101C2×D13semidirect
129. C13#2134semidirect

Maximal subgroups

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

subgroupindex
#117193792
#117184122
C13×#3552
#117181342
#117180692
#213413