Finite Group Databasebeta

← #16787125

Subgroups — #16787125

Order 3328.

270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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#13131209C212yesmaximal
2#13129785C212yesmaximal
3#13129783C212yesmaximal
4#13123769C211yesmaximal, characteristic
5#11719222C411yescharacteristic
6C13×#424C411yescharacteristic
7#11718783C411yescharacteristic
8#11718779C2211yescharacteristic
9#11718763C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11#11718658C2211yescharacteristic
12#11718491—22no—
13#11718489—22no—
14#11718284C2214yes—
15#11718233—22no—
16#11718232—22no—
17C2×C13×M16C2×C411yescharacteristic
18C22×C8×C13C2×C411yescharacteristic
19C13×#117C2×C411yescharacteristic
20#88180C2×C411yescharacteristic
21C2×C4×Dic13C2×C411yescharacteristic
22C2×#6099C2311yescharacteristic
23C22×#1055C2×C411yescharacteristic
24#88144—21no—
25#88142—21no—
26#88132—22no—
27C4×Dic26—22no—
28#88106—24no—
29C13×C4⋊C8—22no—
30#88055—21no—
31#88054—22no—
32#88054—22no—
33C8×Dic13—21no—
34C8×Dic13—21no—
35C8×Dic13—21no—
36#88043D412yes—
37C4×#1055D412yes—
38#11539—131nomaximal, Sylow
39C22×C4×C13C22×C411yescharacteristic
40C22×Dic13—21no—
41C2×Dic26—22no—
42C13×M16—41no—
43C2×C8×C13—21no—
44C2×C8×C13—21no—
45C2×C8×C13—41no—
46C13×C4⋊C4—21no—
47C13×C22⋊C4—21no—
48C42×C13C22⋊C412yes—
49C22⋊Dic13M1612yes—
50C4⋊Dic13—22no—
51C4⋊Dic13—21no—
52#6101—22no—
53#6101—22no—
54C4×Dic13—21no—
55C4×Dic13—21no—
56C4×Dic13M1611yescharacteristic
57C4×Dic13M1611yescharacteristic
58#6099—41no—
59C2×#1055—22no—
60C2×#1055C22⋊C411yescharacteristic
61C2×#1055C22⋊C411yescharacteristic
62C2×#1055C2×D412yes—
63#6092—44no—
64#2960—131no—
65#2166—132no—
66#1328—132no—
67#1327—132no—
68C23×C13C2×M1611yescharacteristic
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—22no—
72C2×C4×C13C2×C22⋊C411yescharacteristic
73C2×C4×C13C2×M1611yescharacteristic
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—42no—
78Dic26—44no—
79C8×C13—41no—
80C8×C13—41no—
81#1055—22no—
82#1055—21no—
83#1055#10112yes—
84#533—131no—
85#446—262no—
86C8×Q8—262no—
87#424—131no—
88#424#26111yescharacteristic
89#423—131no—
90#405—131no—
91#405—131no—
92C2×C4×C8—131no—
93#364—262no—
94#349—134no—
95#347—262no—
96C22×C13—21no—
97C22×C13—41no—
98C22×C13#40711yescharacteristic
99C4×C13—21no—
100C4×C13—42no—
101C4×C13#41011yescharacteristic
102C4×C13C2×#10111yescharacteristic
103Dic13—22no—
104Dic13—42no—
105Dic13—41no—
106C2×M16—131no—
107C2×M16C2×#26111yescharacteristic
108C22×C8—131no—
109C22×C8C2×#26111yescharacteristic
110C4⋊Q8—261no—
111#125—261no—
112C22⋊Q8—262no—
113C4×Q8—262no—
114#117—131no—
115#117C2×#26111yescharacteristic
116C2×C42—131no—
117M32—264no—
118C4⋊C8—22no—
119C4⋊C8—262no—
120C4⋊C8—262no—
121#97—132no—
122#97—261no—
123C4×C8—132no—
124C4×C8—261no—
125C4×C8—261no—
126C4×C8—261no—
127C2×C13—21no—
128C2×C13—41no—
129C2×C13#146711yescharacteristic
130C2×Q8—262no—
131C22×C4—261no—
132C22×C4C22×#26111yescharacteristic
133M16—41no—
134M16—521no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—131no—
139C2×C8—132no—
140C2×C8—131no—
141C2×C8—262no—
142C4⋊C4—21no—
143C4⋊C4—262no—
144C4⋊C4—262no—
145C4⋊C4—262no—
146C4⋊C4—261no—
147C22⋊C4—21no—
148C22⋊C4—132no—
149C42—131no—
150C42—131no—
151C42—261no—
152C42—261no—
153C42C22⋊#26112yes—
154C16—524no—
155C13#1153911yescharacteristic, complemented, Sylow
156C23D13⋊M1611yescharacteristic
157Q8—524no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—261no—
162C2×C4—261no—
163C2×C4—262no—
164C2×C4—522no—
165C2×C4D13⋊M1611yescharacteristic
166C2×C4C2×C22⋊#26111yescharacteristic
167C8—41no—
168C8—41no—
169C8—132no—
170C8—262no—
171C8—261no—
172C22—21no—
173C22—41no—
174C22#1171912611yescharacteristic
175C4—21no—
176C4—42no—
177C4—262no—
178C4—521no—
179C4—522no—
180C4#1171914211yescharacteristic
181C4D13⋊#10111yescharacteristic
182C2—21no—
183C2—41no—
184C2#1313010011yescharacteristic
subgroupG/H
centerC4#11719142
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#424C4
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×#6099C23
hypercenter#424#261
hypocenterC13#11539
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
155. C13#11539semidirect

Maximal subgroups

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

subgroupindex
#131312092
#131297852
#131297832
#131237692
#1153913