Finite Group Databasebeta

← #15756442

Subgroups — #15756442

Order 3328.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117422C211yesmaximal, characteristic
2#13114760C211yesmaximal, characteristic
3#13112745C214yesmaximal
4C13×#1784C211yesmaximal, characteristic
5C23×Q8×C13C2211yescharacteristic
6C2×#88180C412yes—
7C2×C13×#101—22no—
8C13×#407C2212yes—
9#11718891—22no—
10#11718891—22no—
11C2×#88076—22no—
12#11718872C412yes—
13#11718872C2212yes—
14#11718868C2212yes—
15C22×Q8×C13—24no—
16C22×Q8×C13—44no—
17C22×Q8×C13D412yes—
18C22×Q8×C13D412yes—
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2311yescharacteristic
22C2×C13×M16—22no—
23C2×C22⋊Dic13C2×C414yes—
24#88180—44no—
25C2×C4⋊Dic13—22no—
26C2×C4×Dic13—22no—
27C2×#6099—22no—
28C13×#101—44no—
29C13×C22⋊C8—24no—
30#88076—44no—
31#88071—24no—
32#88071—22no—
33#88071—22no—
34C22⋊#1055—24no—
35#8754—131nomaximal, Sylow
36C24×C13C22×C411yescharacteristic
37C2×Q8×C13—24no—
38C2×Q8×C13—24no—
39C2×Q8×C13—24no—
40C2×Q8×C13—24no—
41C2×Q8×C13—42no—
42C2×Q8×C13—42no—
43C2×Q8×C13—416no—
44C22×C4×C13—22no—
45C22×C4×C13—24no—
46C22×C4×C13—22no—
47C22×C4×C13—42no—
48C22×C4×C13—42no—
49C22×C4×C13C22⋊C412yes—
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13#4114yes—
54C22×Dic13—24no—
55C13×M16—44no—
56C2×C8×C13—42no—
57C22⋊Dic13—44no—
58C4⋊Dic13—44no—
59C4×Dic13—44no—
60#6099—44no—
61C2×#1055—42no—
62#2310—131no—
63#1784—131no—
64#1784D1311yescharacteristic
65#1306—134no—
66C23×C13—22no—
67C23×C13—42no—
68C23×C13C2×C22⋊C411yescharacteristic
69C23×C13#11712yes—
70Q8×C13—48no—
71Q8×C13—48no—
72C2×C4×C13—28no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—44no—
81C2×C4×C13—44no—
82C2×C4×C13#9914yes—
83C2×C4×C13#12312yes—
84C2×C4×C13#12312yes—
85C2×Dic13—48no—
86C2×Dic13—44no—
87C8×C13—82no—
88#1055—82no—
89C23×Q8C2×D1311yescharacteristic
90C2×#117—132no—
91C2×#101—22no—
92C2×#101—262no—
93#407—132no—
94#407C2×D1312yes—
95#391—262no—
96#391—262no—
97#381—132no—
98#381—132no—
99C22×C13—22no—
100C22×C13—22no—
101C22×C13—24no—
102C22×C13—44no—
103C22×C13#38111yescharacteristic
104C22×C13C2×#9912yes—
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—24no—
108C4×C13—42no—
109Dic13—84no—
110C22×Q8—24no—
111C22×Q8—44no—
112C22×Q8D5212yes—
113C22×Q8C22⋊D1312yes—
114C23×C4C4×D1311yescharacteristic
115C23×C4C4×D1311yescharacteristic
116C23×C4C22×D1311yescharacteristic
117C2×M16—22no—
118C2×M16—262no—
119#117—524no—
120C2×C4⋊C4—262no—
121C2×C22⋊C4—134no—
122C2×C42—262no—
123#101—44no—
124#101—524no—
125C22⋊C8—24no—
126C22⋊C8—264no—
127#95—264no—
128#95—262no—
129#95—262no—
130C2×C13—22no—
131C2×C13—42no—
132C2×C13#181911yescharacteristic
133C2×C13#183012yes—
134C24C2×C4×D1311yescharacteristic
135C2×Q8—24no—
136C2×Q8—24no—
137C2×Q8—24no—
138C2×Q8—24no—
139C2×Q8—42no—
140C2×Q8—42no—
141C2×Q8—416no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—264no—
148C22×C4#610312yes—
149C22×C4#610312yes—
150C22×C4C2×D5211yescharacteristic
151C22×C4#612914yes—
152C22×C4C2×C22⋊D1311yescharacteristic
153M16—44no—
154M16—524no—
155C2×C8—42no—
156C2×C8—522no—
157C4⋊C4—524no—
158C22⋊C4—524no—
159C42—524no—
160C13#875411yescharacteristic, complemented, Sylow
161C23—22no—
162C23—42no—
163C23#8813112yes—
164C23C2×#610311yescharacteristic
165Q8—48no—
166Q8—48no—
167C2×C4—28no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—528no—
178C2×C4—524no—
179C2×C4#8804614yes—
180C2×C4#8814012yes—
181C2×C4#8818912yes—
182C8—82no—
183C8—1042no—
184C22—22no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22#1171860411yescharacteristic
189C22C2×#8804612yes—
190C4—22no—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—1044no—
195C2—22no—
196C2—42no—
197C2#1311490811yescharacteristic
198C2#1311494812yes—
subgroupG/H
centerC22#11718604
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1784C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1784D13
hypocenterC13#8754
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
160. C13#8754semidirect

Maximal subgroups

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

subgroupindex
#131174222
#131147602
#131127452
C13×#17842
#875413