Finite Group Databasebeta

← #15760523

Subgroups — #15760523

Order 3328.

400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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#13125218C211yesmaximal, characteristic
2#13113574C211yesmaximal, characteristic
3#13113520C212yesmaximal
4#13112727C212yesmaximal
5C13×#2986C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#446—22no—
9C8×Q8×C13—22no—
10C13×#433—22no—
11C13×#431C2212yes—
12#11718754—22no—
13#11718730C414yes—
14#11718665—22no—
15#11718585C2212yes—
16C4×#6099C2211yescharacteristic
17#11718139—22no—
18#11718074—22no—
19#11718074—22no—
20C22×Dic26—21no—
21C13×C4⋊Q8D412yes—
22C13×#125C2×C412yes—
23C13×C22⋊Q8—22no—
24C4×Q8×C13—22no—
25C13×#117D412yes—
26C2×C42×C13C2311yescharacteristic
27C2×C4⋊Dic13—22no—
28C2×#6099—21no—
29C2×#6099—22no—
30#88123—22no—
31#88123—21no—
32#88123C2×C412yes—
33C13×C4⋊C8—24no—
34C13×C4⋊C8D412yes—
35C13×C4⋊C8D412yes—
36C13×C22⋊C8—22no—
37C13×#97—22no—
38C4×C8×C13—22no—
39C4×C8×C13—22no—
40#88050—28no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43#88043C2×C412yes—
44C4×#1055—21no—
45#9436—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13#4112yes—
49C22×Dic13—41no—
50C2×Dic26—22no—
51C2×Dic26—44no—
52C2×Dic26—41no—
53C2×C8×C13—22no—
54C2×C8×C13—22no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C22⋊C414yes—
58C13×C22⋊C4—22no—
59C42×C13—22no—
60C42×C13C22×C411yescharacteristic
61C42×C13C2×D411yescharacteristic
62C42×C13C2×D412yes—
63C4⋊Dic13—24no—
64C4⋊Dic13—42no—
65#6099—42no—
66#6099—82no—
67C2×#1055—22no—
68C2×#1055—42no—
69#3139—131no—
70#2986D1311yescharacteristic
71#1561—131no—
72#1549—132no—
73#1299—132no—
74C23×C13#12311yescharacteristic
75Q8×C13—42no—
76Q8×C13—42no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—24no—
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13C4×D412yes—
83C2×C4×C13#12011yescharacteristic
84C2×C4×C13#12112yes—
85C2×Dic13—42no—
86C2×Dic13—82no—
87Dic26—44no—
88Dic26—82no—
89C8×C13—42no—
90C8×C13—42no—
91#1055—42no—
92#1055—82no—
93#533C2×D1311yescharacteristic
94C2×C4⋊Q8—131no—
95#491—134no—
96#487—262no—
97#446—22no—
98C8×Q8—22no—
99#433—22no—
100#431C2×D1312yes—
101#423—132no—
102#419—262no—
103C4×M16—131no—
104#332—262no—
105#332—262no—
106#332—262no—
107C22×C13—21no—
108C22×C13—22no—
109C22×C13#38611yescharacteristic
110C4×C13—21no—
111C4×C13—22no—
112C4×C13—44no—
113C4×C13#45412yes—
114C4×C13#47112yes—
115C4×C13#47312yes—
116Dic13—82no—
117C22×Q8—261no—
118C2×M16—261no—
119C2×M16—262no—
120C4⋊Q8—132no—
121C4⋊Q8—261no—
122C4⋊Q8—262no—
123C4⋊Q8D5212yes—
124#125C4×D1312yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117C22⋊D1312yes—
128C2×C4⋊C4—262no—
129C2×C42C22×D1311yescharacteristic
130C4⋊C8—24no—
131C4⋊C8—262no—
132C4⋊C8—262no—
133C4⋊C8C22⋊D1312yes—
134C4⋊C8C22⋊D1312yes—
135#103—268no—
136C22⋊C8—22no—
137#97—22no—
138#97—132no—
139C4×C8—22no—
140C4×C8—22no—
141C4×C8—261no—
142C2×C13—41no—
143C2×C13#188811yescharacteristic
144C2×C13#190812yes—
145C2×Q8—22no—
146C2×Q8—262no—
147C2×Q8—524no—
148C2×Q8—521no—
149C22×C4—521no—
150C22×C4#612712yes—
151C22×C4C2×C22⋊D1311yescharacteristic
152M16—522no—
153M16—1042no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—262no—
157C2×C8—522no—
158C4⋊C4—24no—
159C4⋊C4—22no—
160C4⋊C4—264no—
161C4⋊C4—522no—
162C4⋊C4#610314yes—
163C22⋊C4—22no—
164C42—22no—
165C42C2×C4×D1311yescharacteristic
166C42C2×D5211yescharacteristic
167C42C2×C22⋊D1312yes—
168C13#943611yescharacteristic, complemented, Sylow
169C23#8818311yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—524no—
173Q8—1042no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—522no—
179C2×C4—1042no—
180C2×C4C2×#610311yescharacteristic
181C2×C4C4×C22⋊D1312yes—
182C2×C4#8818412yes—
183C2×C4#8820711yescharacteristic
184C8—42no—
185C8—42no—
186C8—522no—
187C8—1042no—
188C22—21no—
189C22—22no—
190C22#1171887411yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—1042no—
195C4#1171880212yes—
196C4#1171880412yes—
197C4#1171890612yes—
198C2—41no—
199C2#1311523911yescharacteristic
200C2#1311535112yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2986C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#2986D13
hypocenterC13#9436
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
168. C13#9436semidirect

Maximal subgroups

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

subgroupindex
#131252182
#131135742
#131135202
#131127272
C13×#29862
#943613