Finite Group Databasebeta

← #13115249

Subgroups — #13115249

Order 1664.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C13×#518C211yesmaximal, characteristic
2C2×#88189C211yesmaximal, characteristic
3C2×#88074C211yesmaximal, characteristic
4#11718604C212yesmaximal, complemented
5#11718118C212yesmaximal, complemented
6C22×D4×C13C2211yescharacteristic
7C23×Dic13C2211yescharacteristic
8C4×D4×C13—24no—
9C13×#117—21no—
10C2×C13×C22⋊C4—21no—
11C2×C13×C22⋊C4C2212yes—
12C2×C22⋊Dic13—21no—
13C2×C22⋊Dic13C2212yes—
14C2×C22⋊Dic13C2211yescharacteristic
15#88189—22no—
16#88189C414yescomplemented
17C2×#6101—21no—
18#88074—22no—
19#88071—24no—
20C24×C13D411yescharacteristic
21C24×C13C2311yescharacteristic
22C2×D4×C13—22no—
23C2×D4×C13—22no—
24C2×D4×C13C2×C412yes—
25C2×D4×C13D412yes—
26C22×C4×C13—22no—
27C22×C4×C13D411yescharacteristic
28C22×C4×C13D414yes—
29C22×Dic13—22no—
30C22×Dic13—21no—
31C22×Dic13—21no—
32C22×Dic13—21no—
33C22×Dic13—22no—
34C22×Dic13—22no—
35C22×Dic13C2×C412yescomplemented
36C13×C4⋊C4—22no—
37C13×C22⋊C4—22no—
38C13×C22⋊C4—22no—
39C13×C22⋊C4—22no—
40C42×C13—22no—
41C22⋊Dic13—24no—
42C22⋊Dic13—21no—
43C22⋊Dic13—22no—
44C22⋊Dic13—22no—
45C22⋊Dic13C2×C412yescomplemented
46#6101—24no—
47#1890—131nomaximal, Sylow
48C23×C13—21no—
49C23×C13—21no—
50C23×C13—42no—
51C23×C13—42no—
52C23×C13C22⋊C412yes—
53C23×C13C22×C411yescharacteristic
54C23×C13C2×D411yescharacteristic
55C23×C13C2×D412yes—
56C23×C13C2×D411yescharacteristic
57C23×C13#4112yes—
58D4×C13—24no—
59D4×C13—24no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—24no—
63C2×C4×C13—44no—
64C2×C4×C13—82no—
65C2×C4×C13C22⋊C412yes—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—24no—
69C2×Dic13—42no—
70C2×Dic13—41no—
71C2×Dic13—42no—
72C2×Dic13—41no—
73C2×Dic13—44no—
74C2×Dic13—42no—
75C2×#123—131no—
76#518D1311yescharacteristic
77C2×#99—131no—
78#381—132no—
79#342—132no—
80C22×C13—24no—
81C22×C13—22no—
82C22×C13—22no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13—42no—
86C22×C13—42no—
87C22×C13—42no—
88C22×C13—81no—
89C22×C13C2×C22⋊C411yescharacteristic
90C22×C13C4×D412yes—
91C22×C13#12011yescharacteristic
92C22×C13#12112yes—
93C22×C13#12311yescharacteristic
94C4×C13—22no—
95C4×C13—44no—
96Dic13—42no—
97Dic13—42no—
98Dic13—82no—
99C22×D4C2×D1311yescharacteristic
100C23×C4—131no—
101#123—134no—
102#123—262no—
103C4×D4—24no—
104#117—21no—
105C2×C4⋊C4—261no—
106C2×C22⋊C4—21no—
107C2×C22⋊C4—131no—
108C2×C22⋊C4—132no—
109C2×C22⋊C4—261no—
110C2×C22⋊C4C2×D1312yes—
111#99—262no—
112#95—264no—
113C2×C13—21no—
114C2×C13—22no—
115C2×C13—21no—
116C2×C13—22no—
117C2×C13—42no—
118C2×C13#38611yescharacteristic
119C2×C13#45812yes—
120C24C22⋊D1311yescharacteristic
121C24C22×D1311yescharacteristic
122C2×D4—22no—
123C2×D4—22no—
124C2×D4C4×D1312yes—
125C2×D4D5212yes—
126C22×C4—22no—
127C22×C4—132no—
128C22×C4—261no—
129C22×C4—262no—
130C22×C4—262no—
131C22×C4—261no—
132C22×C4—261no—
133C22×C4—262no—
134C22×C4C22⋊D1311yescharacteristic
135C22×C4C22⋊D1314yes—
136C4⋊C4—22no—
137C4⋊C4—264no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—132no—
142C22⋊C4—264no—
143C22⋊C4—261no—
144C22⋊C4—262no—
145C22⋊C4—262no—
146C42—22no—
147C13#189011yescharacteristic, complemented, Sylow
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23#610312yes—
153C23C2×C4×D1311yescharacteristic
154C23C2×D5211yescharacteristic
155C23#612712yes—
156C23C2×C22⋊D1311yescharacteristic
157C23C2×C22⋊D1312yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—264no—
168C2×C4—522no—
169C2×C4—521no—
170C2×C4—522no—
171C2×C4—521no—
172C2×C4—524no—
173C2×C4—522no—
174C2×C4#610312yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×#610311yescharacteristic
185C22C4×C22⋊D1312yes—
186C22#8818311yescharacteristic
187C22#8818412yes—
188C22#8820711yescharacteristic
189C4—22no—
190C4—44no—
191C4—522no—
192C4—522no—
193C4—1042no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1171887411yescharacteristic
200C2#1171890412yes—
subgroupG/H
centerC22#88207
commutatorC23×C13C22×C4
FrattiniC24C22×D13
FittingC13×#518C2
socleC22×C13#120
prime radicalC22×D4×C13C22
cosocleC24×C13C23
hypercenter#518D13
hypocenterC13#1890
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
4. #11718604C2semidirect
5. #11718118C2semidirect
16. #88189C4semidirect
35. C22×Dic13C2×C4semidirect
45. C22⋊Dic13C2×C4semidirect
147. C13#1890semidirect

Maximal subgroups

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

subgroupindex
C13×#5182
C2×#881892
C2×#880742
#117186042
#117181182
#189013