Finite Group Databasebeta

← #16784510

Subgroups — #16784510

Order 3328.

260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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#13130413C212yesmaximal
2#13130394C211yesmaximal, characteristic
3#13130046C211yesmaximal, characteristic
4#13129722C212yesmaximal
5#13113581C211yesmaximal, characteristic
6#11719052C2212yes—
7#11719051C2211yescharacteristic
8C4×#6118C2211yescharacteristic
9#11718494C2212yes—
10C4×C8×D13C2211yescharacteristic
11#11718256—22no—
12#11718254—21no—
13#11718254—21no—
14#11718253—22no—
15#1057⋊C8—21no—
16#11718251—21no—
17C13×#334C411yescharacteristic
18#11718071C412yes—
19#11718049C411yescharacteristic
20C2×#6118—21no—
21C2×#6118—22no—
22C2×C8×D13Q811yescharacteristic
23C2×C8×D13Q811yescharacteristic
24C42×D13C2311yescharacteristic
25#88111—21no—
26#88110Q812yes—
27C4⋊#1057—22no—
28C4⋊#1057—22no—
29C4⋊#1057D411yescharacteristic
30C4⋊#1057D411yescharacteristic
31C4×#1057—21no—
32C4×#1057—21no—
33C13×C4⋊C8C2×C412yes—
34C4×C8×C13C2×C411yescharacteristic
35#88060—22no—
36C8×Dic13—22no—
37C8×Dic13D411yescharacteristic
38C8×Dic13D411yescharacteristic
39C4⋊#1055C2×C412yes—
40C4×#1055C2×C411yescharacteristic
41#9636—131nomaximal, Sylow
42C2×C4×D13C2×Q811yescharacteristic
43C2×C4×D13#4111yescharacteristic
44C2×C4×D13#4111yescharacteristic
45C2×#1057—21no—
46C2×#1057—21no—
47C2×#1057—22no—
48C2×#1057—42no—
49#6118—42no—
50#6118—82no—
51C2×C8×C13—22no—
52C2×C8×C13C4⋊C411yescharacteristic
53C2×C8×C13C4⋊C411yescharacteristic
54C42×C13C22×C411yescharacteristic
55C4×Dic13C2×D411yescharacteristic
56C4×Dic13C2×D411yescharacteristic
57C4×Dic13C2×Q811yescharacteristic
58C2×#1055—22no—
59C2×#1055C4⋊C411yescharacteristic
60C2×#1055C4⋊C411yescharacteristic
61C8×D13—22no—
62C8×D13—41no—
63#1574—132no—
64#1567—131no—
65#1564—131no—
66#1451—131no—
67#1299—132no—
68C22×D13#12511yescharacteristic
69C2×C4×C13C2×C4⋊C411yescharacteristic
70C2×C4×C13C4×D411yescharacteristic
71C2×C4×C13C4×Q811yescharacteristic
72C2×Dic13#12111yescharacteristic
73C2×Dic13C22⋊Q811yescharacteristic
74C2×Dic13C4⋊Q811yescharacteristic
75C4×D13—21no—
76C4×D13—21no—
77C4×D13—22no—
78C4×D13—21no—
79C4×D13—21no—
80#1057—42no—
81#1057—41no—
82#1057—41no—
83#1057—82no—
84C8×C13—21no—
85C8×C13—42no—
86C8×C13#10812yes—
87#1055—21no—
88#1055—21no—
89#1055—42no—
90#431—131no—
91#431—132no—
92#423—132no—
93C4×M16—131no—
94C2×C4×C8—131no—
95#335—132no—
96#335—261no—
97#335—261no—
98#335—262no—
99#334—131no—
100#334—262no—
101#334#26111yescharacteristic
102#322—261no—
103#322—261no—
104C22×C13#38911yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C4×C13—21no—
109C4×C13C2×#10811yescharacteristic
110C4×C13#43011yescharacteristic
111C4×C13#44412yes—
112Dic13—21no—
113Dic13—21no—
114Dic13#47211yescharacteristic
115Dic13#47311yescharacteristic
116C2×M16—261no—
117C2×M16—262no—
118C22×C8—131no—
119C22×C8—131no—
120C2×C42—131no—
121C4⋊C8—131no—
122C4⋊C8—131no—
123C4⋊C8—132no—
124C4⋊C8—262no—
125C4⋊C8—262no—
126C4⋊C8C2×#26112yes—
127C22⋊C8—262no—
128C22⋊C8—261no—
129#97—132no—
130C4×C8—131no—
131C4×C8—131no—
132C4×C8—131no—
133C4×C8—262no—
134C4×C8—261no—
135C4×C8—261no—
136C4×C8C2×#26111yescharacteristic
137C2×C13#194611yescharacteristic
138C2×C13#195011yescharacteristic
139C2×C13#195211yescharacteristic
140D13—41no—
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144M16—522no—
145M16—1042no—
146C2×C8—22no—
147C2×C8—131no—
148C2×C8—131no—
149C2×C8—262no—
150C2×C8—262no—
151C2×C8—261no—
152C2×C8—261no—
153C2×C8—262no—
154C2×C8—521no—
155C2×C8—522no—
156C2×C8C4⋊#26111yescharacteristic
157C2×C8C4⋊#26111yescharacteristic
158C42—131no—
159C42—131no—
160C42—131no—
161C42C22×#26111yescharacteristic
162C13#963611yescharacteristic, complemented, Sylow
163C23—131no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—262no—
172C2×C4C2×C4⋊#26111yescharacteristic
173C2×C4D4×#26111yescharacteristic
174C2×C4Q8×#26111yescharacteristic
175C8—21no—
176C8—42no—
177C8—261no—
178C8—261no—
179C8—521no—
180C8—521no—
181C8—522no—
182C8—522no—
183C8—1042no—
184C8#8810312yes—
185C22—261no—
186C22—261no—
187C22—261no—
188C22#1171908311yescharacteristic
189C4—21no—
190C4—131no—
191C4—131no—
192C4—261no—
193C4—261no—
194C4C2×#8810311yescharacteristic
195C4#1171910011yescharacteristic
196C4#1171910812yes—
197C2—521no—
198C2#1313094611yescharacteristic
199C2#1313095111yescharacteristic
200C2#1313095411yescharacteristic
subgroupG/H
centerC22#11719083
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#334C4
socleC22×C13#389
prime radicalC22×D13#125
cosocleC42×D13C23
hypercenter#334#261
hypocenterC13#9636
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
162. C13#9636semidirect

Maximal subgroups

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

subgroupindex
#131304132
#131303942
#131300462
#131297222
#131135812
#963613