Finite Group Databasebeta

← #13116506

Subgroups — #13116506

Order 1664.

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

normal subgroups only

This group has 270 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#11719420C211yesmaximal, characteristic
2#11718401C212yesmaximal, complemented
3C13×#353C211yesmaximal, characteristic, complemented
4#11718137C211yesmaximal, characteristic, complemented
5#11718066C212yesmaximal, complemented
6C2×#6129C2211yescharacteristic
7C2×D4×D13C411yescharacteristic, complemented
8C13×#127C2211yescharacteristic
9#88194C2211yescharacteristic
10#88193—22no—
11#88191—22no—
12#88190C411yescharacteristic, complemented
13#88131—22no—
14#88129C411yescharacteristic, complemented
15#88126C411yescharacteristic, complemented
16C13×#99C2212yescomplemented
17#88074C2212yescomplemented
18#88046—22no—
19C23×D13—21no—
20C2×D4×C13—22no—
21C2×D4×C13C2×C411yescharacteristic
22C2×D4×C13C2311yescharacteristic
23C2×C22⋊D13—22no—
24C2×C22⋊D13—21no—
25C2×C22⋊D13D412yes—
26C22×Dic13D412yes—
27#6129—42no—
28D4×D13—42no—
29C2×D52C2×C411yescharacteristic
30C2×C4×D13C2×C411yescharacteristic
31C2×Dic26C2×C411yescharacteristic
32C13×C22⋊C4—22no—
33C42×C13C2×C411yescharacteristic
34C22⋊Dic13—22no—
35C22⋊Dic13—22no—
36#6103—21no—
37#6103—22no—
38#6101—21no—
39#6101—42no—
40C4×Dic13—42no—
41C4×Dic13C2×C411yescharacteristic
42#2128—131nomaximal, Sylow
43C23×C13—21no—
44C23×C13C2×D412yes—
45C22×D13—21no—
46C22×D13—42no—
47C22×D13—82no—
48C22×D13C22⋊C411yescharacteristic
49D4×C13—41no—
50D4×C13—41no—
51D4×C13—82no—
52C2×C4×C13—21no—
53C2×C4×C13—42no—
54C2×C4×C13C22×C411yescharacteristic
55C22⋊D13—42no—
56C22⋊D13—42no—
57C22⋊D13—82no—
58C2×Dic13—22no—
59C2×Dic13—22no—
60C2×Dic13—21no—
61C2×Dic13—42no—
62C2×Dic13C22⋊C412yes—
63C2×Dic13C22⋊C411yescharacteristic
64D52—41no—
65C4×D13—22no—
66Dic26—41no—
67#535—131no—
68#410—132no—
69#353—131no—
70#353—132no—
71#353D1311yescharacteristic, complemented
72C22×C13—22no—
73C22×C13—42no—
74C22×C13—42no—
75C22×C13—41no—
76C22×C13C2×C22⋊C411yescharacteristic
77C2×D13—21no—
78C2×D13—41no—
79C2×D13—42no—
80C2×D13—41no—
81C2×D13—84no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—82no—
85Dic13—22no—
86Dic13—41no—
87Dic13—82no—
88Dic13#9912yes—
89C2×#41—131no—
90C22×D4—131no—
91#127—131no—
92#127C2×D1311yescharacteristic
93#124—131no—
94#124—131no—
95#121—262no—
96#120—262no—
97#117—131no—
98#117—262no—
99#99—132no—
100#99—262no—
101#99C2×D1312yescomplemented
102C2×C13—21no—
103C2×C13—42no—
104C2×C13—81no—
105C2×C13C2×#9911yescharacteristic
106D13—41no—
107D13—81no—
108C24—261no—
109#41—522no—
110C2×Q8—131no—
111C2×D4—22no—
112C2×D4—132no—
113C2×D4—131no—
114C2×D4—261no—
115C2×D4—262no—
116C2×D4—522no—
117C2×D4C4×D1311yescharacteristic
118C2×D4C22×D1311yescharacteristic
119C22×C4—132no—
120C22×C4—131no—
121C4⋊C4—261no—
122C4⋊C4—522no—
123C22⋊C4—22no—
124C22⋊C4—262no—
125C22⋊C4—261no—
126C22⋊C4—262no—
127C22⋊C4—262no—
128C42—131no—
129C42—522no—
130C42C4×D1311yescharacteristic
131C13#212811yescharacteristic, complemented, Sylow
132C23—21no—
133C23—131no—
134C23—261no—
135C23—522no—
136C23—1042no—
137C23D4×D1312yes—
138Q8—521no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—521no—
143D4—522no—
144D4—522no—
145D4—1042no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—131no—
149C2×C4—132no—
150C2×C4—262no—
151C2×C4—262no—
152C2×C4—262no—
153C2×C4—261no—
154C2×C4—522no—
155C2×C4C2×C4×D1311yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—261no—
161C22—521no—
162C22—522no—
163C22—521no—
164C22—1044no—
165C22C22⋊C4×D1311yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—132no—
170C4—262no—
171C4—521no—
172C4—1042no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—521no—
177C2—1041no—
178C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×D4C22×D13
FittingC13×#353C2
socleC2×C13C2×#99
prime radical#11719420C2
cosocleC2×D4×C13C23
hypercenter#353D13
hypocenterC13#2128
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #11718401C2semidirect
3. C13×#353C2semidirect
4. #11718137C2semidirect
5. #11718066C2semidirect
7. C2×D4×D13C4semidirect
12. #88190C4semidirect
14. #88129C4semidirect
15. #88126C4semidirect
16. C13×#99C22semidirect
17. #88074C22semidirect
71. #353D13semidirect
101. #99C2×D13semidirect
131. C13#2128semidirect

Maximal subgroups

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

subgroupindex
#117194202
#117184012
C13×#3532
#117181372
#117180662
#212813