Finite Group Databasebeta

← #15766024

Subgroups — #15766024

Order 3328.

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

normal subgroups only

This group has 402 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#13115664C211yesmaximal, characteristic
2#13113395C212yesmaximal
3#13112694C212yesmaximal, complemented
4#13112669C211yesmaximal, characteristic, complemented
5C13×#2864C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C13×#389—22no—
8C13×#387—24no—
9C13×#382C2212yes—
10C43×C13C2211yescharacteristic
11C2×#88045—22no—
12#11718586C2212yes—
13#11718585C2211yescharacteristic
14#11718043—24no—
15C2×#6127—21no—
16C2×C13×C4⋊C4—24no—
17C2×C13×C4⋊C4—22no—
18C2×C42×C13—22no—
19C2×C42×C13D412yes—
20C2×C42×C13C2311yescharacteristic
21#88184—22no—
22C2×#6099—21no—
23#88129—21no—
24#88128Q811yescharacteristic
25C4×D52—22no—
26#88123Q811yescharacteristic
27C13×#95—24no—
28C13×#95—22no—
29C13×#95D414yes—
30C22⋊#1055—22no—
31#88045—44no—
32C4⋊#1055—22no—
33C4⋊#1055—22no—
34C4×#1055—22no—
35#10366—131nomaximal, Sylow
36C22×C4×C13—22no—
37C22×C4×C13—24no—
38C22×C4×C13C2×D412yes—
39C22×C4×C13C2×D411yescharacteristic
40C2×C22⋊D13—41no—
41#6127—42no—
42#6127—42no—
43C2×D52—21no—
44C2×D52—22no—
45C2×C4×D13—41no—
46C2×Dic26—21no—
47C13×C4⋊C4—48no—
48C13×C4⋊C4—42no—
49C13×C4⋊C4—42no—
50C42×C13—22no—
51C42×C13—22no—
52C42×C13—44no—
53C42×C13C2×Q811yescharacteristic
54C42×C13#4112yes—
55C42×C13#4111yescharacteristic
56#6103—42no—
57C4⋊Dic13—22no—
58#6099—42no—
59C2×#1055—42no—
60C2×#1055—41no—
61#2864D1311yescharacteristic, complemented
62#1962—131no—
63#1517—132no—
64#1286—132no—
65#1276—131no—
66C23×C13#12011yescharacteristic
67C22×D13—41no—
68C2×C4×C13—24no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—48no—
73C2×C4×C13—44no—
74C2×C4×C13C22⋊Q812yes—
75C2×C4×C13C22⋊Q811yescharacteristic
76C2×C4×C13#12412yes—
77C2×C4×C13#12411yescharacteristic
78C2×C4×C13#13512yes—
79C2×C4×C13AGL(1,ℤ/8)12yes—
80C22⋊D13—82no—
81C2×Dic13—41no—
82D52—42no—
83D52—82no—
84C4×D13—81no—
85C4×D13—81no—
86Dic26—42no—
87#1055—82no—
88#1055—81no—
89#532—131no—
90#431—132no—
91#423—131no—
92C2×#104—262no—
93#389—22no—
94#387—24no—
95#382C2×D1312yes—
96C43C2×D1311yescharacteristic
97#327—264no—
98C22×C13—22no—
99C22×C13#39311yescharacteristic
100C22×C13#44912yes—
101C2×D13—81no—
102C2×D13—82no—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—44no—
106C4×C13—84no—
107C4×C13#47812yes—
108C4×C13#48811yescharacteristic
109C4×C13#49011yescharacteristic
110Dic13—81no—
111C2×#41—261no—
112C2×M16—261no—
113C4⋊Q8—131no—
114#127—131no—
115#124—261no—
116#121—262no—
117C4×D4—262no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—22no—
120C2×C42—22no—
121C2×C42C22⋊D1312yes—
122C2×C42C22×D1311yescharacteristic
123C4⋊C8—262no—
124C4⋊C8—262no—
125#104—524no—
126C22⋊C8—262no—
127C4×C8—262no—
128#95—24no—
129#95—22no—
130#95C22⋊D1314yes—
131C2×C13—22no—
132C2×C13#202511yescharacteristic
133C2×C13#203112yes—
134D13—161no—
135#41—522no—
136#41—522no—
137C2×Q8—261no—
138C2×D4—261no—
139C2×D4—262no—
140C2×D4—521no—
141C22×C4—22no—
142C22×C4—24no—
143C22×C4—521no—
144C22×C4C2×C22⋊D1312yes—
145C22×C4C2×C22⋊D1311yescharacteristic
146M16—522no—
147C2×C8—522no—
148C2×C8—521no—
149C4⋊C4—48no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—262no—
153C22⋊C4—522no—
154C42—22no—
155C42—22no—
156C42—44no—
157C42Q8×D1311yescharacteristic
158C42#613111yescharacteristic
159C42#613112yes—
160C13#1036611yescharacteristic, complemented, Sylow
161C23—521no—
162C23#8820711yescharacteristic
163Q8—522no—
164D4—522no—
165D4—1042no—
166D4—1042no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—521no—
174C2×C4—1041no—
175C2×C4—1041no—
176C2×C4#8820012yes—
177C2×C4#8820011yescharacteristic
178C2×C4#8820112yes—
179C2×C4#8820111yescharacteristic
180C2×C4#8820312yes—
181C2×C4#8820412yes—
182C8—1042no—
183C8—1041no—
184C22—22no—
185C22—1041no—
186C22—1042no—
187C22#1171889211yescharacteristic
188C22#1171889912yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—1041no—
194C4#1171872712yes—
195C4#1171872811yescharacteristic
196C4#1171872911yescharacteristic
197C2—22no—
198C2—2081no—
199C2#1311597911yescharacteristic
200C2#1311600512yes—
subgroupG/H
centerC22#11718892
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2864C2
socleC22×C13#393
prime radical#11719182C22
hypercenter#2864D13
hypocenterC13#10366
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2864

Complements

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

NH ≅ G/Ntype
3. #13112694C2semidirect
4. #13112669C2semidirect
5. C13×#2864C2semidirect
61. #2864D13semidirect
160. C13#10366semidirect

Maximal subgroups

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

subgroupindex
#131156642
#131133952
#131126942
#131126692
C13×#28642
#1036613