Finite Group Databasebeta

← #16787123

Subgroups — #16787123

Order 3328.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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#13129784C212yesmaximal
3#13129782C212yesmaximal
4#13123771C211yesmaximal, characteristic
5C13×#533C411yescharacteristic
6#11718685—22no—
7Q8×#1055—22no—
8#11718660C411yescharacteristic
9#11718660C2211yescharacteristic
10#11718658C411yescharacteristic
11#11718658C2211yescharacteristic
12#11718585C2211yescharacteristic
13C2×C4×#1055C411yescharacteristic
14#11718284C2214yes—
15#11718233—22no—
16#11718232—22no—
17C13×C4⋊Q8—21no—
18C13×#125—21no—
19C13×C22⋊Q8—22no—
20C4×Q8×C13—22no—
21C13×#117C2×C411yescharacteristic
22C13×#117C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C2×#6099C2311yescharacteristic
26C22×#1055C2×C411yescharacteristic
27C22×#1055C2×C411yescharacteristic
28#88106—24no—
29C4⋊#1055—22no—
30C4⋊#1055—22no—
31C4⋊#1055—22no—
32#88043—21no—
33#88043D412yes—
34C4×#1055—21no—
35C4×#1055—21no—
36C4×#1055—21no—
37C4×#1055D412yes—
38#11539—131nomaximal, Sylow
39C2×Q8×C13—22no—
40C22×C4×C13—21no—
41C22×C4×C13C22×C411yescharacteristic
42C13×C4⋊C4—24no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C22⋊C4—21no—
47C13×C22⋊C4M1612yes—
48C42×C13—21no—
49C42×C13—21no—
50C42×C13C22⋊C412yes—
51C42×C13M1611yescharacteristic
52C42×C13M1611yescharacteristic
53#6099—41no—
54#6099—41no—
55C2×#1055—22no—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055—41no—
59C2×#1055C22⋊C411yescharacteristic
60C2×#1055C22⋊C411yescharacteristic
61C2×#1055C2×D412yes—
62#6092—44no—
63#2960—131no—
64#2166—132no—
65#1328—132no—
66#1327—132no—
67C23×C13C2×M1611yescharacteristic
68Q8×C13—44no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—42no—
76C2×C4×C13C2×C22⋊C411yescharacteristic
77C2×C4×C13C2×M1611yescharacteristic
78#1055—22no—
79#1055—21no—
80#1055—41no—
81#1055—41no—
82#1055#10112yes—
83#533#26111yescharacteristic
84#446—262no—
85C8×Q8—262no—
86#424—131no—
87#424—131no—
88#423—131no—
89#405—131no—
90#405—131no—
91C2×C4×C8—131no—
92#364—262no—
93#349—134no—
94#347—262no—
95C22×C13—21no—
96C22×C13—41no—
97C22×C13#40711yescharacteristic
98C4×C13—22no—
99C4×C13—21no—
100C4×C13—41no—
101C4×C13—42no—
102C4×C13—42no—
103C4×C13#41011yescharacteristic
104C4×C13C2×#10111yescharacteristic
105C2×M16—131no—
106C2×M16—131no—
107C22×C8—131no—
108C22×C8—131no—
109C4⋊Q8—21no—
110#125—21no—
111C22⋊Q8—22no—
112C4×Q8—22no—
113#117C2×#26111yescharacteristic
114#117C2×#26111yescharacteristic
115C2×C42C2×#26111yescharacteristic
116M32—264no—
117C4⋊C8—262no—
118C4⋊C8—262no—
119C4⋊C8—262no—
120#97—132no—
121#97—261no—
122C4×C8—132no—
123C4×C8—261no—
124C4×C8—261no—
125C4×C8—261no—
126C2×C13—21no—
127C2×C13—41no—
128C2×C13#146711yescharacteristic
129C2×Q8—22no—
130C22×C4—21no—
131C22×C4C22×#26111yescharacteristic
132M16—521no—
133M16—521no—
134C2×C8—131no—
135C2×C8—132no—
136C2×C8—131no—
137C2×C8—262no—
138C2×C8—261no—
139C2×C8—261no—
140C2×C8—521no—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4#612212yes—
147C42—21no—
148C42—21no—
149C42#612211yescharacteristic
150C42#612211yescharacteristic
151C42C22⋊#26112yes—
152C16—524no—
153C13#1153911yescharacteristic, complemented, Sylow
154C23C2×#612211yescharacteristic
155Q8—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4C2×#612211yescharacteristic
164C2×C4C2×C22⋊#26111yescharacteristic
165C8—132no—
166C8—262no—
167C8—261no—
168C8—521no—
169C8—521no—
170C22—21no—
171C22—41no—
172C22#1171916911yescharacteristic
173C4—22no—
174C4—21no—
175C4—41no—
176C4—42no—
177C4—42no—
178C4#1171915611yescharacteristic
179C4D13⋊#10111yescharacteristic
180C2—21no—
181C2—41no—
182C2#1313009911yescharacteristic
subgroupG/H
centerC4#11719156
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#533C4
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×#6099C23
hypercenter#533#261
hypocenterC13#11539
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ #117 ◁ #533

Complements

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

NH ≅ G/Ntype
153. C13#11539semidirect

Maximal subgroups

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

subgroupindex
#131312092
#131297842
#131297822
#131237712
#1153913