Finite Group Databasebeta

← #13116190

Subgroups — #13116190

Order 1664.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#11719188C211yesmaximal, characteristic
2#11718611C212yesmaximal
3#11718607C211yesmaximal, characteristic
4C13×#342C211yesmaximal, characteristic
5#11718119C212yesmaximal
6C23×Dic13C2211yescharacteristic
7C2×C13×C22⋊C4C2211yescharacteristic
8C2×C13×C22⋊C4C2212yes—
9C2×C22⋊Dic13C2212yes—
10C2×C22⋊Dic13C2211yescharacteristic
11C2×C4⋊Dic13—22no—
12#88178—21no—
13#88178—21no—
14C2×#6101—21no—
15#88132—22no—
16#88132—22no—
17#88071—21no—
18#88071—22no—
19C24×C13C2311yescharacteristic
20C22×C4×C13—22no—
21C22×C4×C13D411yescharacteristic
22C22×C4×C13D411yescharacteristic
23C22×Dic13—21no—
24C22×Dic13—21no—
25C22×Dic13—22no—
26C22×Dic13—42no—
27C22×Dic13D412yes—
28C22×Dic13D412yes—
29C2×Dic26—21no—
30C2×Dic26—21no—
31C13×C22⋊C4—22no—
32C13×C22⋊C4—22no—
33C13×C22⋊C4Q814yescomplemented
34C22⋊Dic13—22no—
35C22⋊Dic13—22no—
36C22⋊Dic13—21no—
37C22⋊Dic13Q812yescomplemented
38C4⋊Dic13—21no—
39C4⋊Dic13—21no—
40C4⋊Dic13—44no—
41#6101—22no—
42#6101—22no—
43#6101—42no—
44#2062—131nomaximal, Sylow
45C23×C13—41no—
46C23×C13—41no—
47C23×C13C2×D411yescharacteristic
48C23×C13C2×D412yes—
49C23×C13C2×Q812yes—
50C23×C13C2×Q811yescharacteristic
51C23×C13#4111yescharacteristic
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—24no—
55C2×C4×C13—42no—
56C2×C4×C13—42no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×Dic13—22no—
60C2×Dic13—24no—
61C2×Dic13—22no—
62C2×Dic13—22no—
63C2×Dic13—22no—
64C2×Dic13—41no—
65C2×Dic13—41no—
66C2×Dic13—41no—
67C2×Dic13—42no—
68C2×Dic13—41no—
69C2×Dic13—42no—
70C2×Dic13—42no—
71Dic26—81no—
72Dic26—81no—
73#543—131no—
74#385—131no—
75#385—132no—
76#342—132no—
77#342D1311yescharacteristic
78C22×C13—21no—
79C22×C13—22no—
80C22×C13—21no—
81C22×C13—22no—
82C22×C13—42no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13#12011yescharacteristic
86C22×C13C22⋊Q812yes—
87C22×C13C22⋊Q811yescharacteristic
88C22×C13C4⋊Q811yescharacteristic
89C22×C13C4⋊Q812yes—
90C4×C13—44no—
91C4×C13—41no—
92C4×C13—41no—
93Dic13—42no—
94Dic13—42no—
95Dic13—42no—
96Dic13—42no—
97C23×C4—131no—
98C22⋊Q8—262no—
99C22⋊Q8—262no—
100C22⋊Q8—261no—
101C22⋊Q8—261no—
102C2×C4⋊C4—262no—
103C2×C4⋊C4—261no—
104C2×C22⋊C4—131no—
105C2×C22⋊C4—132no—
106C2×C22⋊C4C2×D1311yescharacteristic
107C2×C22⋊C4C2×D1312yes—
108#95—262no—
109#95—261no—
110C2×C13—21no—
111C2×C13—22no—
112C2×C13—21no—
113C2×C13—22no—
114C2×C13#39511yescharacteristic
115C2×C13B(4,𝔽2)11yescharacteristic
116C2×C13#45811yescharacteristic
117C24C22×D1311yescharacteristic
118C2×Q8—261no—
119C2×Q8—261no—
120C22×C4—22no—
121C22×C4—132no—
122C22×C4—132no—
123C22×C4—261no—
124C22×C4—261no—
125C22×C4—262no—
126C22×C4—522no—
127C22×C4D5211yescharacteristic
128C22×C4D5211yescharacteristic
129C4⋊C4—262no—
130C4⋊C4—262no—
131C4⋊C4—261no—
132C4⋊C4—261no—
133C4⋊C4—522no—
134C4⋊C4—524no—
135C22⋊C4—22no—
136C22⋊C4—22no—
137C22⋊C4—132no—
138C22⋊C4—262no—
139C22⋊C4—262no—
140C22⋊C4—261no—
141C22⋊C4Dic2614yescomplemented
142C13#206211yescharacteristic, complemented, Sylow
143C23—41no—
144C23—41no—
145C23C2×Dic2612yes—
146C23C2×D5211yescharacteristic
147C23D4×D1312yes—
148C23#612911yescharacteristic
149C23Q8×D1311yescharacteristic
150Q8—1041no—
151Q8—1041no—
152C2×C4—24no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—262no—
160C2×C4—264no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—521no—
165C2×C4—521no—
166C2×C4—521no—
167C2×C4—522no—
168C2×C4—521no—
169C2×C4—522no—
170C2×C4—522no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22#8812311yescharacteristic
179C22#8813212yes—
180C22#8813611yescharacteristic
181C22#8814212yes—
182C22#8815111yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—522no—
187C4—522no—
188C4—522no—
189C4—522no—
190C2—22no—
191C2—21no—
192C2—21no—
193C2—22no—
194C2#1171831711yescharacteristic
195C2#1171840211yescharacteristic
196C2#1171840311yescharacteristic
subgroupG/H
centerC22#88136
commutator, prime radical, cosocleC24×C13C23
FrattiniC24C22×D13
FittingC13×#342C2
socleC22×C13#120
hypercenter#342D13
hypocenterC13#2062
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
33. C13×C22⋊C4Q8semidirect
37. C22⋊Dic13Q8semidirect
141. C22⋊C4Dic26semidirect
142. C13#2062semidirect

Maximal subgroups

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

subgroupindex
#117191882
#117186112
#117186072
C13×#3422
#117181192
#206213