Finite Group Databasebeta

← #16784505

Subgroups — #16784505

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#13130414C212yesmaximal
2#13130391C211yesmaximal, characteristic
3#13130046C211yesmaximal, characteristic
4#13129722C212yesmaximal
5#13113583C211yesmaximal, characteristic
6#11719052C2212yes—
7#11719051C2211yescharacteristic
8C4×#6118C2211yescharacteristic
9#11718494C2212yes—
10C4×C8×D13C2211yescharacteristic
11#11718255—22no—
12#11718254—22no—
13#11718253—21no—
14#11718253—21no—
15#1057⋊C8—21no—
16#11718251—21no—
17C13×#335C411yescharacteristic
18#11718072C412yes—
19#11718050C411yescharacteristic
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⋊#1057D412yes—
30C4×#1057—21no—
31C4×#1057—21no—
32C13×C4⋊C8C2×C412yes—
33C4×C8×C13C2×C411yescharacteristic
34#88060—22no—
35C8×Dic13—22no—
36C8×Dic13D411yescharacteristic
37C8×Dic13D411yescharacteristic
38C4⋊#1055C2×C412yes—
39C4×#1055C2×C411yescharacteristic
40#9635—131nomaximal, Sylow
41C2×C4×D13C2×Q811yescharacteristic
42C2×C4×D13#4111yescharacteristic
43C2×C4×D13#4111yescharacteristic
44C2×#1057—22no—
45C2×#1057—22no—
46C2×#1057—42no—
47#6118—41no—
48#6118—41no—
49#6118—82no—
50C2×C8×C13—22no—
51C2×C8×C13C4⋊C411yescharacteristic
52C2×C8×C13C4⋊C411yescharacteristic
53C42×C13C22×C411yescharacteristic
54C4×Dic13C2×D411yescharacteristic
55C4×Dic13C2×D411yescharacteristic
56C4×Dic13C2×Q811yescharacteristic
57C2×#1055—22no—
58C2×#1055C4⋊C411yescharacteristic
59C2×#1055C4⋊C411yescharacteristic
60C8×D13—22no—
61C8×D13—41no—
62#1574—132no—
63#1566—131no—
64#1564—131no—
65#1451—131no—
66#1299—132no—
67C22×D13#12511yescharacteristic
68C2×C4×C13C2×C4⋊C411yescharacteristic
69C2×C4×C13C4×D411yescharacteristic
70C2×C4×C13C4×Q811yescharacteristic
71C2×Dic13#12111yescharacteristic
72C2×Dic13C22⋊Q811yescharacteristic
73C2×Dic13C4⋊Q811yescharacteristic
74C4×D13—21no—
75C4×D13—21no—
76C4×D13—21no—
77C4×D13—21no—
78C4×D13—22no—
79#1057—42no—
80#1057—42no—
81#1057—82no—
82C8×C13—21no—
83C8×C13—42no—
84C8×C13#10812yes—
85#1055—21no—
86#1055—21no—
87#1055—42no—
88#431—131no—
89#431—132no—
90#423—132no—
91C4×M16—131no—
92C2×C4×C8—131no—
93#335—131no—
94#335—262no—
95#335#26111yescharacteristic
96#334—132no—
97#334—261no—
98#334—261no—
99#334—262no—
100#322—261no—
101#322—261no—
102C22×C13#38911yescharacteristic
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C4×C13—21no—
107C4×C13C2×#10811yescharacteristic
108C4×C13#43011yescharacteristic
109C4×C13#44411yescharacteristic
110C4×C13#44411yescharacteristic
111Dic13—21no—
112Dic13—21no—
113Dic13#47112yes—
114C2×M16—261no—
115C2×M16—262no—
116C22×C8—131no—
117C22×C8—131no—
118C2×C42—131no—
119C4⋊C8—132no—
120C4⋊C8—132no—
121C4⋊C8—262no—
122C4⋊C8—262no—
123C4⋊C8C2×#26112yes—
124C22⋊C8—262no—
125C22⋊C8—261no—
126#97—132no—
127C4×C8—131no—
128C4×C8—131no—
129C4×C8—131no—
130C4×C8—262no—
131C4×C8—261no—
132C4×C8—261no—
133C4×C8C2×#26111yescharacteristic
134C2×C13#194611yescharacteristic
135C2×C13#195011yescharacteristic
136C2×C13#195111yescharacteristic
137D13—41no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—131no—
141M16—521no—
142M16—521no—
143M16—1042no—
144C2×C8—22no—
145C2×C8—131no—
146C2×C8—131no—
147C2×C8—262no—
148C2×C8—262no—
149C2×C8—262no—
150C2×C8—262no—
151C2×C8—521no—
152C2×C8—522no—
153C2×C8C4⋊#26111yescharacteristic
154C2×C8C4⋊#26111yescharacteristic
155C42—131no—
156C42—131no—
157C42—131no—
158C42C22×#26111yescharacteristic
159C13#963511yescharacteristic, complemented, Sylow
160C23—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—262no—
165C2×C4—261no—
166C2×C4—261no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4C2×C4⋊#26111yescharacteristic
170C2×C4D4×#26111yescharacteristic
171C2×C4Q8×#26111yescharacteristic
172C8—21no—
173C8—42no—
174C8—261no—
175C8—261no—
176C8—522no—
177C8—522no—
178C8—522no—
179C8—1042no—
180C8#8810412yes—
181C22—261no—
182C22—261no—
183C22—261no—
184C22#1171908311yescharacteristic
185C4—21no—
186C4—132no—
187C4—261no—
188C4—261no—
189C4C2×#8810411yescharacteristic
190C4#1171910011yescharacteristic
191C4#1171910411yescharacteristic
192C4#1171911211yescharacteristic
193C2—521no—
194C2#1313094511yescharacteristic
195C2#1313095011yescharacteristic
196C2#1313095311yescharacteristic
subgroupG/H
centerC22#11719083
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#335C4
socleC22×C13#389
prime radicalC22×D13#125
cosocleC42×D13C23
hypercenter#335#261
hypocenterC13#9635
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
159. C13#9635semidirect

Maximal subgroups

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

subgroupindex
#131304142
#131303912
#131300462
#131297222
#131135832
#963513