Finite Group Databasebeta

← #13116354

Subgroups — #13116354

Order 1664.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×C13×#107C211yesmaximal, characteristic, complemented
2C2×#88061C211yesmaximal, characteristic
3#11718649C211yesmaximal, characteristic
4#11718638C211yesmaximal, characteristic, complemented
5C2×#88049C211yesmaximal, characteristic
6C2×#88048C211yesmaximal, characteristic, complemented
7#11718142C211yesmaximal, characteristic, complemented
8C22×D52C2211yescharacteristic
9C22×C8×C13C2211yescharacteristic
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×#6103—22no—
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15C22×#1055C2211yescharacteristic
16C13×#107—22no—
17#88071—22no—
18#88061—22no—
19#88049—22no—
20#88048—22no—
21C23×D13—21no—
22C22×C4×C13—21no—
23C22×C4×C13—21no—
24C22×C4×C13C2311yescharacteristic
25C22×Dic13—21no—
26C22×Dic13D412yes—
27C2×D52—21no—
28C2×D52—21no—
29C2×D52—21no—
30C2×D52—21no—
31C2×D52—21no—
32C2×D52Q812yes—
33C2×C8×C13—21no—
34C2×C8×C13—21no—
35C2×C8×C13D412yes—
36C13×C4⋊C4—21no—
37C13×C4⋊C4—21no—
38C13×C4⋊C4—21no—
39C13×C4⋊C4—21no—
40#6103—44no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4×Dic13—21no—
44C4×Dic13—21no—
45C2×#1055—21no—
46C2×#1055—21no—
47C2×#1055D412yes—
48#2092—131nomaximal, Sylow
49C23×C13C2×D411yescharacteristic
50C22×D13—22no—
51C22×D13—41no—
52C22×D13—41no—
53C22×D13—42no—
54C22×D13—42no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13—42no—
58C2×C4×C13—42no—
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×Q811yescharacteristic
62C2×C4×C13#4111yescharacteristic
63C2×C4×C13#4111yescharacteristic
64C2×C4×C13#4111yescharacteristic
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—41no—
69C2×Dic13—42no—
70D52—22no—
71D52—22no—
72D52—41no—
73D52—41no—
74C8×C13—22no—
75#1055—22no—
76C2×#107D1311yescharacteristic, complemented
77C2×#106—131no—
78C2×#102—131no—
79C2×#102—131no—
80#390—131no—
81#382—131no—
82#336—131no—
83C22×C13C22⋊Q811yescharacteristic
84C22×C13#12311yescharacteristic
85C22×C13#12711yescharacteristic
86C22×C13#13512yes—
87C22×C13AGL(1,ℤ/8)12yes—
88C2×D13—42no—
89C2×D13—44no—
90C2×D13—82no—
91C2×D13—81no—
92C2×D13—81no—
93C4×C13—81no—
94C4×C13—81no—
95C4×C13C22⋊Q811yescharacteristic
96C4×C13C22⋊Q811yescharacteristic
97C4×C13#12311yescharacteristic
98C4×C13#12311yescharacteristic
99Dic13—42no—
100Dic13—81no—
101C22×D4—131no—
102C22×C8—131no—
103C22×C8C2×D1311yescharacteristic
104C2×C4⋊C4—131no—
105C2×C4⋊C4C2×D1311yescharacteristic
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C22⋊C4—262no—
108C2×C42—131no—
109#107—22no—
110#106—262no—
111#102—262no—
112#102—262no—
113#95—262no—
114C2×C13#39911yescharacteristic
115C2×C13#47812yes—
116C2×C13#48212yes—
117C2×C13#49511yescharacteristic
118C2×C13#49611yescharacteristic
119D13—82no—
120C24—261no—
121C2×D4—132no—
122C2×D4—261no—
123C2×D4—261no—
124C2×D4—261no—
125C2×D4—261no—
126C2×D4—261no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—132no—
130C22×C4—261no—
131C22×C4C22×D1311yescharacteristic
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—132no—
135C2×C8—261no—
136C2×C8—261no—
137C2×C8C22⋊D1312yes—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C22⋊C4—524no—
145C42—261no—
146C42—261no—
147C13#209211yescharacteristic, complemented, Sylow
148C23—262no—
149C23—521no—
150C23—522no—
151C23—522no—
152C23—521no—
153C23D4×D1311yescharacteristic
154D4—262no—
155D4—262no—
156D4—521no—
157D4—521no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—522no—
166C2×C4—521no—
167C2×C4#612711yescharacteristic
168C2×C4#612711yescharacteristic
169C2×C4D4×D1311yescharacteristic
170C2×C4Q8×D1311yescharacteristic
171C2×C4#613111yescharacteristic
172C2×C4C2×C22⋊D1311yescharacteristic
173C8—22no—
174C8—262no—
175C22—524no—
176C22—522no—
177C22—1042no—
178C22—1041no—
179C22—1041no—
180C22#8814811yescharacteristic
181C22#8815011yescharacteristic
182C22#8816512yes—
183C22#8817312yes—
184C22#8819411yescharacteristic
185C4—81no—
186C4—81no—
187C4—522no—
188C4—1041no—
189C4#8814811yescharacteristic
190C4#8815011yescharacteristic
191C4#8818311yescharacteristic
192C4#8820011yescharacteristic
193C2—1042no—
194C2#1171854612yes—
195C2#1171855212yes—
196C2#1171865311yescharacteristic
197C2#1171881511yescharacteristic
198C2#1171885211yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#107C2
socleC23×C13C2×D4
prime radicalC22×D52C22
hypercenterC2×#107D13
hypocenterC13#2092
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×C13×#107C2semidirect
4. #11718638C2semidirect
6. C2×#88048C2semidirect
7. #11718142C2semidirect
76. C2×#107D13semidirect
147. C13#2092semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1072
C2×#880612
#117186492
#117186382
C2×#880492
C2×#880482
#117181422
#209213