Finite Group Databasebeta

← #16788438

Subgroups — #16788438

Order 3328.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#13131205C212yesmaximal
2#13129841C214yesmaximal, complemented
3#13125216C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic
5#11719175C411yescharacteristic
6#11718886—22no—
7#11718743C412yes—
8#11718743C2212yes—
9#11718742—22no—
10C4×#6099C2211yescharacteristic
11#11718284—22no—
12#11718233—22no—
13#11718232C2214yes—
14C22×Q8×C13—21no—
15C13×C4⋊Q8—21no—
16C13×C4⋊Q8—41no—
17C13×C4⋊Q8C2×C412yes—
18C2×C13×C4⋊C4—41no—
19C2×C42×C13C2×C411yescharacteristic
20#88180—21no—
21#88178—41no—
22C2×#6099D412yes—
23#88124C2×C412yes—
24#88123—21no—
25C4×Dic26—41no—
26#88106—24no—
27#88075—24no—
28#88075—24no—
29#88043C2×C411yescharacteristic
30#88043C2311yescharacteristic
31C4×#1055D412yes—
32#11916—131nomaximal, Sylow
33C2×Q8×C13—22no—
34C2×Q8×C13—44no—
35C2×Q8×C13—41no—
36C22×C4×C13—21no—
37C22×C4×C13—41no—
38C22×C4×C13C22⋊C411yescharacteristic
39C2×Dic26—41no—
40C13×C4⋊C4—42no—
41C13×C4⋊C4—42no—
42C42×C13—21no—
43C42×C13C22⋊C411yescharacteristic
44C42×C13C22×C411yescharacteristic
45C22⋊Dic13—41no—
46C4⋊Dic13—22no—
47C4⋊Dic13—41no—
48#6101—42no—
49C4×Dic13—41no—
50#6099—42no—
51C2×#1055C22⋊C412yes—
52C2×#1055C2×D412yes—
53#6092—44no—
54#3139—131no—
55#2165—132no—
56#1356—134no—
57C23×C13#10011yescharacteristic
58Q8×C13—44no—
59Q8×C13—82no—
60C2×C4×C13—21no—
61C2×C4×C13—22no—
62C2×C4×C13—21no—
63C2×C4×C13—42no—
64C2×C4×C13—42no—
65C2×C4×C13—82no—
66C2×C4×C13#10011yescharacteristic
67C2×C4×C13C2×C22⋊C411yescharacteristic
68C2×Dic13—42no—
69Dic26—82no—
70#1055—22no—
71#1055—22no—
72#533—131no—
73C2×C4⋊Q8#26111yescharacteristic
74#491—132no—
75#491—132no—
76#487—262no—
77#419—262no—
78C4×M16—131no—
79#364—262no—
80#349—262no—
81#347—134no—
82C22×C13—21no—
83C22×C13—41no—
84C22×C13C2×#10011yescharacteristic
85C4×C13—22no—
86C4×C13—21no—
87C4×C13—41no—
88C4×C13—82no—
89C4×C13#42112yes—
90Dic13—82no—
91C22×Q8—21no—
92C2×M16—132no—
93C4⋊Q8—21no—
94C4⋊Q8—41no—
95C4⋊Q8—261no—
96C4⋊Q8C2×#26112yes—
97#125—132no—
98C22⋊Q8—521no—
99C4×Q8—521no—
100#117—261no—
101C2×C4⋊C4—41no—
102C2×C42C2×#26111yescharacteristic
103M32—264no—
104#103—264no—
105#103—264no—
106#97—131no—
107#97—131no—
108C4×C8—132no—
109C2×C13—21no—
110C2×C13—41no—
111C2×C13#153311yescharacteristic
112C2×Q8—22no—
113C2×Q8—44no—
114C2×Q8—41no—
115C2×Q8—521no—
116C22×C4—21no—
117C22×C4—41no—
118C22×C4C22⋊#26111yescharacteristic
119M16—522no—
120C2×C8—132no—
121C2×C8—132no—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C4⋊C4—262no—
125C4⋊C4—522no—
126C4⋊C4—521no—
127C22⋊C4—521no—
128C42—21no—
129C42—521no—
130C42C22⋊#26111yescharacteristic
131C42C22×#26111yescharacteristic
132C16—524no—
133C13#1191611yescharacteristic, complemented, Sylow
134C23#8812111yescharacteristic
135Q8—44no—
136Q8—82no—
137Q8—1042no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—82no—
144C2×C4—522no—
145C2×C4#8812111yescharacteristic
146C2×C4C2×C22⋊#26111yescharacteristic
147C8—262no—
148C8—262no—
149C22—21no—
150C22—41no—
151C22C2×#8812111yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—82no—
156C4—1042no—
157C4#1171914012yes—
158C2—21no—
159C2—41no—
160C2#1313031511yescharacteristic
subgroupG/H
centerC2#13130315
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×C4⋊Q8C4
socleC2×C13#1533
prime radicalC23×C13#100
cosocle#88043C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11916
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13129841C2semidirect
133. C13#11916semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298412
#131252162
#1191613