Finite Group Databasebeta

← #16788435

Subgroups — #16788435

Order 3328.

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

normal subgroups only

This group has 326 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, complemented
2#13129838C214yesmaximal, complemented
3#13125210C211yesmaximal, characteristic
4C2×C13×#127C411yescharacteristic
5#11719175C411yescharacteristic
6#11718876—22no—
7#11718732C412yes—
8#11718732C2212yes—
9#11718731—22no—
10C4×#6099C2211yescharacteristic
11#11718284—22no—
12#11718233—22no—
13#11718232C2214yescomplemented
14C22×D4×C13—21no—
15C22×D4×C13—41no—
16C13×#127—21no—
17C13×#127—41no—
18C13×#127C2×C412yes—
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#88072—24no—
28#88072—24no—
29#88043C2×C411yescharacteristic
30#88043C2311yescharacteristic
31C4×#1055D412yes—
32#11915—131nomaximal, Sylow
33C24×C13—41no—
34C2×D4×C13—22no—
35C2×D4×C13—44no—
36C2×D4×C13—42no—
37C2×D4×C13—42no—
38C2×D4×C13—41no—
39C2×D4×C13—84no—
40C22×C4×C13—21no—
41C22×C4×C13C22⋊C411yescharacteristic
42C2×Dic26—41no—
43C42×C13—21no—
44C42×C13C22⋊C411yescharacteristic
45C42×C13C22×C411yescharacteristic
46C22⋊Dic13—41no—
47C4⋊Dic13—22no—
48C4⋊Dic13—41no—
49#6101—42no—
50C4×Dic13—41no—
51#6099—42no—
52C2×#1055C22⋊C412yes—
53C2×#1055C2×D412yes—
54#6092—44no—
55#3138—131no—
56#2165—132no—
57#1355—134no—
58C23×C13—42no—
59C23×C13—82no—
60C23×C13—84no—
61C23×C13#10011yescharacteristic
62D4×C13—44no—
63D4×C13—82no—
64D4×C13—84no—
65D4×C13—84no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—42no—
70C2×C4×C13#10011yescharacteristic
71C2×C4×C13C2×C22⋊C411yescharacteristic
72C2×Dic13—42no—
73Dic26—82no—
74#1055—22no—
75#1055—22no—
76#533—131no—
77C2×#127#26111yescharacteristic
78#490—132no—
79#490—132no—
80#486—262no—
81#418—262no—
82C4×M16—131no—
83#364—262no—
84#349—262no—
85#347—134no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13—84no—
89C22×C13—82no—
90C22×C13—164no—
91C22×C13C2×#10011yescharacteristic
92C4×C13—22no—
93C4×C13—21no—
94C4×C13—41no—
95C4×C13#42112yes—
96Dic13—82no—
97C22×D4—21no—
98C22×D4—41no—
99C2×M16—132no—
100C4⋊Q8—261no—
101#127—21no—
102#127—41no—
103#127C2×#26112yes—
104#125—132no—
105C22⋊Q8—521no—
106C4×Q8—521no—
107#117—261no—
108C2×C42C2×#26111yescharacteristic
109M32—264no—
110#102—264no—
111#102—264no—
112#97—131no—
113#97—131no—
114C4×C8—132no—
115C2×C13—21no—
116C2×C13—41no—
117C2×C13—162no—
118C2×C13#153311yescharacteristic
119C24—41no—
120C2×Q8—521no—
121C2×D4—22no—
122C2×D4—44no—
123C2×D4—42no—
124C2×D4—42no—
125C2×D4—41no—
126C2×D4—84no—
127C22×C4—21no—
128C22×C4C22⋊#26111yescharacteristic
129M16—522no—
130C2×C8—132no—
131C2×C8—132no—
132C4⋊C4—262no—
133C4⋊C4—522no—
134C4⋊C4—521no—
135C22⋊C4—521no—
136C42—21no—
137C42—521no—
138C42C22⋊#26111yescharacteristic
139C42C22×#26111yescharacteristic
140C16—524no—
141C13#1191511yescharacteristic, complemented, Sylow
142C23—42no—
143C23—82no—
144C23—84no—
145C23#8812111yescharacteristic
146Q8—1042no—
147D4—44no—
148D4—82no—
149D4—84no—
150D4—84no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—522no—
156C2×C4#8812111yescharacteristic
157C2×C4C2×C22⋊#26111yescharacteristic
158C8—262no—
159C8—262no—
160C22—21no—
161C22—41no—
162C22—84no—
163C22—82no—
164C22—164no—
165C22C2×#8812111yescharacteristic
166C4—22no—
167C4—21no—
168C4—41no—
169C4—1042no—
170C4#1171914012yes—
171C2—21no—
172C2—41no—
173C2—162no—
174C2#1313031511yescharacteristic
subgroupG/H
centerC2#13130315
commutatorC42×C13C22×C4
FrattiniC42C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC2×C13#1533
cosocle#88043C23
hypercenterC2×#127#261
hypocenterC13#11915
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #13131205C2semidirect
2. #13129838C2semidirect
13. #11718232C22semidirect
141. C13#11915semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298382
#131252102
#1191513