Finite Group Databasebeta

← #15766062

Subgroups — #15766062

Order 3328.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13118141C211yesmaximal, characteristic
2#13113335C212yesmaximal
3#13112737C212yesmaximal
4#13112665C211yesmaximal, characteristic
5C13×#1995C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C13×#423C2211yescharacteristic
8C13×#376C2211yescharacteristic
9C4×C4⋊Dic13C2212yes—
10C4×#6101—22no—
11#11718586C2212yes—
12#11718321—22no—
13#11718318—22no—
14C13×#339—22no—
15#11718130—22no—
16#11718130—22no—
17C2×C13×M16—21no—
18C13×C4⋊Q8Q812yes—
19C13×#125—21no—
20C13×C22⋊Q8—22no—
21C4×Q8×C13—22no—
22C13×#117—21no—
23C2×C42×C13D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—22no—
26C2×#6101—22no—
27C2×#6101—22no—
28C2×C4×Dic13—22no—
29C13×C4⋊C8—22no—
30C13×#95—22no—
31#88071—22no—
32#88071—22no—
33#88071D412yes—
34#88071D412yes—
35C22⋊#1055—22no—
36C4⋊#1055—22no—
37C4×#1055—22no—
38#10373—131nomaximal, Sylow
39C2×Q8×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13C2×D412yes—
42C22×C4×C13C2×D411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—22no—
45C13×M16—42no—
46C2×C8×C13—41no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—42no—
50C13×C22⋊C4—41no—
51C42×C13—22no—
52C42×C13—22no—
53C42×C13—41no—
54C42×C13C2×Q811yescharacteristic
55C42×C13#4111yescharacteristic
56C42×C13#4112yes—
57C4⋊Dic13—44no—
58#6101—44no—
59#6101—44no—
60C4×Dic13—42no—
61C4×Dic13—42no—
62C2×#1055—42no—
63#2402—131no—
64#1995D1311yescharacteristic
65#1503—132no—
66#1303—132no—
67#1274—131no—
68C23×C13#12011yescharacteristic
69Q8×C13—82no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13—42no—
74C2×C4×C13—42no—
75C2×C4×C13C22⋊Q812yes—
76C2×C4×C13C22⋊Q811yescharacteristic
77C2×C4×C13#12412yes—
78C2×C4×C13#12411yescharacteristic
79C2×C4×C13#13512yes—
80C2×C4×C13#13712yes—
81C2×Dic13—24no—
82C2×Dic13—42no—
83C2×Dic13—42no—
84C2×Dic13—42no—
85C2×Dic13—42no—
86C2×Dic13—42no—
87C8×C13—81no—
88#1055—82no—
89#533C2×D1311yescharacteristic
90#431—132no—
91#423C2×D1311yescharacteristic
92#400—262no—
93#398—262no—
94C4×C4⋊C4—132no—
95C4×C4⋊C4—262no—
96#376C2×D1311yescharacteristic
97#339—22no—
98#328—262no—
99#328—262no—
100C22×C13—22no—
101C22×C13#39311yescharacteristic
102C22×C13#45212yes—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—82no—
106C4×C13—82no—
107C4×C13#47912yes—
108C4×C13#48811yescharacteristic
109C4×C13#49111yescharacteristic
110Dic13—44no—
111Dic13—82no—
112C2×M16—21no—
113C4⋊Q8Dic2612yes—
114#125—21no—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117—21no—
118C2×C4⋊C4—262no—
119C2×C4⋊C4—262no—
120C2×C4⋊C4—262no—
121C2×C42—262no—
122C2×C42C22⋊D1312yes—
123C2×C42C22×D1311yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—262no—
126C22⋊C8—262no—
127C4×C8—262no—
128#95—22no—
129#95—132no—
130#95—132no—
131#95—262no—
132#95—262no—
133C2×C13—22no—
134C2×C13#202611yescharacteristic
135C2×C13#203112yes—
136C2×Q8—22no—
137C22×C4—22no—
138C22×C4—262no—
139C22×C4—262no—
140C22×C4D4×D1312yes—
141C22×C4C2×C22⋊D1311yescharacteristic
142M16—42no—
143C2×C8—41no—
144C2×C8—522no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—42no—
148C4⋊C4—524no—
149C4⋊C4—524no—
150C4⋊C4—524no—
151C22⋊C4—41no—
152C42—22no—
153C42—22no—
154C42—41no—
155C42—522no—
156C42—522no—
157C42C2×Dic2611yescharacteristic
158C42#612711yescharacteristic
159C42#612912yes—
160C13#1037311yescharacteristic, complemented, Sylow
161C23#8819111yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—264no—
169C2×C4—522no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4—522no—
174C2×C4#8813212yes—
175C2×C4#8813912yes—
176C2×C4#8817811yescharacteristic
177C2×C4#8819011yescharacteristic
178C2×C4#8819612yes—
179C2×C4#8820412yes—
180C8—81no—
181C8—1042no—
182C22—22no—
183C22#1171860811yescharacteristic
184C22#1171870812yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—524no—
190C4—1042no—
191C4#1171868312yes—
192C4#1171871711yescharacteristic
193C4#1171874311yescharacteristic
194C2—22no—
195C2#1311598711yescharacteristic
196C2#1311600612yes—
subgroupG/H
centerC2×C4#88190
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1995C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1995D13
hypocenterC13#10373
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

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
#131181412
#131133352
#131127372
#131126652
C13×#19952
#1037313