Finite Group Databasebeta

← #15766059

Subgroups — #15766059

Order 3328.

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

normal subgroups only

This group has 364 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
1#13115817C211yesmaximal, characteristic
2#13113334C212yesmaximal
3#13112739C212yesmaximal
4#13112665C211yesmaximal, characteristic
5C13×#2402C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C13×#400—22no—
8C13×#398—22no—
9C4×C13×C4⋊C4—22no—
10C4×C13×C4⋊C4C2212yes—
11C13×#376C2211yescharacteristic
12#11718586C2212yes—
13#11718585C2211yescharacteristic
14#11718115—22no—
15#11718044—22no—
16#11718044—22no—
17C2×C13×C4⋊C4—22no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C42×C13—22no—
21C2×C42×C13D412yes—
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24#88178—22no—
25C2×#6099—21no—
26#88124—21no—
27#88123Q812yes—
28C4×Dic26—22no—
29C13×#95—22no—
30C13×#95—22no—
31C13×#95—22no—
32C13×#95D412yes—
33C13×#95D412yes—
34C22⋊#1055—22no—
35C4⋊#1055—22no—
36C4⋊#1055—22no—
37C4×#1055—22no—
38#10373—131nomaximal, Sylow
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13C2×D412yes—
43C22×C4×C13C2×D411yescharacteristic
44C2×Dic26—22no—
45C13×C4⋊C4—44no—
46C13×C4⋊C4—44no—
47C13×C4⋊C4—44no—
48C42×C13—22no—
49C42×C13—22no—
50C42×C13—42no—
51C42×C13—42no—
52C42×C13C2×Q811yescharacteristic
53C42×C13#4112yes—
54C42×C13#4111yescharacteristic
55C22⋊Dic13—41no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58#6101—42no—
59C4×Dic13—41no—
60#6099—42no—
61C2×#1055—42no—
62C2×#1055—41no—
63#2402D1311yescharacteristic
64#1995—131no—
65#1503—132no—
66#1303—132no—
67#1274—131no—
68C23×C13#12011yescharacteristic
69C2×C4×C13—24no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13—42no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13C22⋊Q812yes—
80C2×C4×C13C22⋊Q811yescharacteristic
81C2×C4×C13#12412yes—
82C2×C4×C13#12411yescharacteristic
83C2×C4×C13#13512yes—
84C2×C4×C13#13712yes—
85C2×Dic13—42no—
86Dic26—82no—
87#1055—82no—
88#1055—81no—
89#533—131no—
90#431—132no—
91#423—131no—
92#400—22no—
93#398—22no—
94C4×C4⋊C4—22no—
95C4×C4⋊C4C2×D1312yes—
96#376C2×D1311yescharacteristic
97#339—262no—
98#328—262no—
99#328—262no—
100C22×C13—22no—
101C22×C13#39311yescharacteristic
102C22×C13#45212yes—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—44no—
106C4×C13—82no—
107C4×C13—82no—
108C4×C13#47912yes—
109C4×C13#48811yescharacteristic
110C4×C13#49111yescharacteristic
111Dic13—82no—
112C2×M16—261no—
113C4⋊Q8—132no—
114#125—261no—
115C22⋊Q8—262no—
116C4×Q8—262no—
117#117—261no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C42—22no—
122C2×C42C22⋊D1312yes—
123C2×C42C22×D1311yescharacteristic
124C4⋊C8—262no—
125C4⋊C8—262no—
126C22⋊C8—262no—
127C4×C8—262no—
128#95—22no—
129#95—22no—
130#95—22no—
131#95C22⋊D1312yes—
132#95C22⋊D1312yes—
133C2×C13—22no—
134C2×C13#202611yescharacteristic
135C2×C13#203112yes—
136C2×Q8—262no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4C2×C22⋊D1312yes—
141C22×C4C2×C22⋊D1311yescharacteristic
142M16—522no—
143C2×C8—522no—
144C2×C8—521no—
145C4⋊C4—44no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—262no—
149C4⋊C4—262no—
150C4⋊C4—522no—
151C22⋊C4—521no—
152C42—22no—
153C42—22no—
154C42—42no—
155C42—42no—
156C42—521no—
157C42Q8×D1311yescharacteristic
158C42#613111yescharacteristic
159C42#613112yes—
160C13#1037311yescharacteristic, complemented, Sylow
161C23#8820711yescharacteristic
162Q8—1042no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—522no—
174C2×C4#8820012yes—
175C2×C4#8820011yescharacteristic
176C2×C4#8820112yes—
177C2×C4#8820111yescharacteristic
178C2×C4#8820412yes—
179C2×C4#8820512yes—
180C8—1042no—
181C8—1041no—
182C22—22no—
183C22#1171889211yescharacteristic
184C22#1171890012yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—1042no—
191C4#1171872412yes—
192C4#1171872911yescharacteristic
193C4#1171873011yescharacteristic
194C2—22no—
195C2#1311598411yescharacteristic
196C2#1311600512yes—
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2402C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#2402D13
hypocenterC13#10373
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
160. C13#10373semidirect

Maximal subgroups

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

subgroupindex
#131158172
#131133342
#131127392
#131126652
C13×#24022
#1037313