Finite Group Databasebeta

← #16787122

Subgroups — #16787122

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#13131210C212yesmaximal
2#13129785C212yesmaximal
3#13129782C212yesmaximal
4#13123770C211yesmaximal, characteristic
5#11719175C411yescharacteristic
6C2×C4×C8×C13C411yescharacteristic
7#11718763C411yescharacteristic
8#11718763C2211yescharacteristic
9#11718762C411yescharacteristic
10#11718762C2211yescharacteristic
11#11718585C2211yescharacteristic
12#11718340—22no—
13C8×Dic26—22no—
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C22×C8×C13C2×C411yescharacteristic
18C22×C8×C13C2×C411yescharacteristic
19C2×C42×C13C2×C411yescharacteristic
20#88180C2×C411yescharacteristic
21#88180C2×C411yescharacteristic
22#88178—22no—
23C2×#6099C2×C411yescharacteristic
24C2×#6099C2311yescharacteristic
25#88124—21no—
26#88123—21no—
27C4×Dic26—22no—
28#88106—24no—
29C4×C8×C13—21no—
30C4×C8×C13—21no—
31#88055—21no—
32#88055D412yes—
33#88054—22no—
34#88054—22no—
35C8×Dic13—21no—
36C8×Dic13D412yes—
37C4⋊#1055—22no—
38#11539—131nomaximal, Sylow
39C22×C4×C13—21no—
40C22×C4×C13C22×C411yescharacteristic
41C2×Dic26—22no—
42C2×C8×C13—22no—
43C2×C8×C13—21no—
44C2×C8×C13—41no—
45C2×C8×C13C22⋊C411yescharacteristic
46C2×C8×C13C22⋊C411yescharacteristic
47C42×C13—21no—
48C42×C13M1611yescharacteristic
49C42×C13M1611yescharacteristic
50C22⋊Dic13—21no—
51C22⋊Dic13M1612yes—
52C4⋊Dic13—22no—
53C4⋊Dic13—21no—
54C4⋊Dic13—21no—
55#6101—24no—
56C4×Dic13—21no—
57C4×Dic13C22⋊C412yes—
58#6099—41no—
59#6099—41no—
60C2×#1055—21no—
61C2×#1055C2×D412yes—
62#6092—44no—
63#2960—131no—
64#2166—132no—
65#1328—132no—
66#1327—132no—
67C23×C13C2×M1611yescharacteristic
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—42no—
73C2×C4×C13C2×C22⋊C411yescharacteristic
74C2×C4×C13C2×M1611yescharacteristic
75C2×Dic13—22no—
76C2×Dic13—22no—
77Dic26—44no—
78C8×C13—21no—
79C8×C13—41no—
80C8×C13#10112yes—
81#1055—22no—
82#1055—41no—
83#533—131no—
84#446—262no—
85C8×Q8—262no—
86#424—131no—
87#424—131no—
88#423—131no—
89#405—131no—
90#405—131no—
91C2×C4×C8#26111yescharacteristic
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#41011yescharacteristic
102C4×C13C2×#10111yescharacteristic
103Dic13—42no—
104Dic13—42no—
105C2×M16—131no—
106C2×M16—131no—
107C22×C8C2×#26111yescharacteristic
108C22×C8C2×#26111yescharacteristic
109C4⋊Q8—261no—
110#125—261no—
111C22⋊Q8—262no—
112C4×Q8—262no—
113#117—131no—
114#117—131no—
115C2×C42C2×#26111yescharacteristic
116M32—264no—
117C4⋊C8—262no—
118C4⋊C8—262no—
119C4⋊C8—262no—
120#97—132no—
121#97—261no—
122C4×C8—21no—
123C4×C8—21no—
124C4×C8—132no—
125C4×C8—261no—
126C2×C13—21no—
127C2×C13—41no—
128C2×C13#146711yescharacteristic
129C2×Q8—262no—
130C22×C4—21no—
131C22×C4C22×#26111yescharacteristic
132M16—521no—
133M16—521no—
134C2×C8—22no—
135C2×C8—21no—
136C2×C8—41no—
137C2×C8—132no—
138C2×C8—261no—
139C2×C8C22⋊#26111yescharacteristic
140C2×C8C22⋊#26111yescharacteristic
141C4⋊C4—264no—
142C4⋊C4—262no—
143C4⋊C4—261no—
144C4⋊C4—261no—
145C22⋊C4—132no—
146C22⋊C4—261no—
147C42—21no—
148C42—132no—
149C42—261no—
150C42#611811yescharacteristic
151C42#611811yescharacteristic
152C16—524no—
153C13#1153911yescharacteristic, complemented, Sylow
154C23D13⋊M1611yescharacteristic
155Q8—524no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—42no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4C2×#611811yescharacteristic
164C2×C4C2×C22⋊#26111yescharacteristic
165C8—21no—
166C8—41no—
167C8—262no—
168C8—521no—
169C8#8811312yes—
170C22—21no—
171C22—41no—
172C22#1171912711yescharacteristic
173C4—22no—
174C4—21no—
175C4—41no—
176C4—522no—
177C4—522no—
178C4#1171911611yescharacteristic
179C4C2×#8811311yescharacteristic
180C2—21no—
181C2—41no—
182C2#1313009811yescharacteristic
subgroupG/H
centerC4#11719116
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×#6099C23
hypercenterC2×C4×C8#261
hypocenterC13#11539
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

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
#131312102
#131297852
#131297822
#131237702
#1153913