Finite Group Databasebeta

← #15777937

Subgroups — #15777937

Order 3328.

310 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#11718058C211yesmaximal, characteristic
2#13114524C211yesmaximal, characteristic
3#13112919C212yesmaximal
4#13112917C212yesmaximal
5C2×C13×#347C211yesmaximal, characteristic
6C2×C13×M32C2212yes—
7C2×C13×#97C2211yescharacteristic
8C2×#88055C411yescharacteristic
9C2×#88055C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12C2×#88052C2212yes—
13#11718593C411yescharacteristic
14C2×C4×#1055C411yescharacteristic
15C13×#347C414yescomplemented
16#11718058C414yescomplemented
17C22×C8×C13C2×C411yescharacteristic
18C22×C8×C13C2311yescharacteristic
19C2×C42×C13C2×C411yescharacteristic
20C2×C4×Dic13C2×C411yescharacteristic
21C2×C4×Dic13C2×C411yescharacteristic
22C22×#1055C2×C411yescharacteristic
23C22×#1055C2×C411yescharacteristic
24C13×M32—22no—
25C13×M32C2×C414yes—
26C2×C13×C16—22no—
27C13×#97C2×C412yes—
28C13×#97C2×C412yes—
29#88071—22no—
30#88055—22no—
31#88055—22no—
32C8×Dic13—22no—
33C8×Dic13—22no—
34#88052—22no—
35#88052C2×C414yes—
36C2×#6090—22no—
37C4×#1055—22no—
38#12596—131nomaximal, Sylow
39C22×C4×C13—21no—
40C22×C4×C13C22×C411yescharacteristic
41C22×Dic13—21no—
42C22×Dic13M1612yes—
43C2×C8×C13—21no—
44C2×C8×C13—21no—
45C2×C8×C13C4212yes—
46C2×C8×C13C22×C411yescharacteristic
47C2×C8×C13C22×C411yescharacteristic
48C2×C8×C13#4112yes—
49C2×C8×C13#4112yes—
50C42×C13—21no—
51C42×C13C4212yes—
52C4×Dic13—21no—
53C4×Dic13—21no—
54C4×Dic13—21no—
55C4×Dic13M1612yes—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055—21no—
59C2×#1055—21no—
60C2×#1055M1612yes—
61C2×#1055M1612yes—
62C13×C16—24no—
63#6090—24no—
64C2×#347—131no—
65C2×#347D1311yescharacteristic
66#1726—131no—
67#1377—132no—
68#1376—132no—
69C23×C13C2×M1611yescharacteristic
70C2×C4×C13—22no—
71C2×C4×C13—42no—
72C2×C4×C13C2×C4211yescharacteristic
73C2×C4×C13#11711yescharacteristic
74C2×C4×C13#11711yescharacteristic
75C2×C4×C13C2×M1611yescharacteristic
76C2×C4×C13C2×M1611yescharacteristic
77C2×C4×C13C2×M1611yescharacteristic
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C8×C13—22no—
83C8×C13#11712yes—
84C8×C13#11712yes—
85#1055—22no—
86#1055—22no—
87C2×M32—132no—
88C2×M32C2×D1312yes—
89C2×#97—131no—
90C2×#97—131no—
91C2×#97C2×D1311yescharacteristic
92C2×C4×C8—131no—
93C2×C4×C8—131no—
94C2×C4×C8—131no—
95#376—131no—
96#347—134no—
97#347Dic1314yescomplemented
98C22×C13—22no—
99C22×C13C4×M1611yescharacteristic
100C22×C13#43211yescharacteristic
101C22×C13#43211yescharacteristic
102C4×C13—42no—
103C4×C13#37611yescharacteristic
104C4×C13C4×M1611yescharacteristic
105C4×C13#43211yescharacteristic
106C4×C13#43211yescharacteristic
107Dic13—42no—
108Dic13—42no—
109C22×C8—131no—
110C22×C8—131no—
111C22×C8C4×D1311yescharacteristic
112C22×C8C22×D1311yescharacteristic
113C2×C42—131no—
114C2×C42—131no—
115C2×C42C4×D1311yescharacteristic
116M32—22no—
117M32—134no—
118M32—262no—
119M32C2×Dic1314yes—
120C2×C16—22no—
121C2×C16—262no—
122#97—262no—
123#97—262no—
124#97C4×D1312yes—
125#97C2×Dic1312yes—
126C4×C8—262no—
127C4×C8—262no—
128C4×C8—262no—
129#95—262no—
130C2×C13—21no—
131C2×C13—21no—
132C2×C13#174511yescharacteristic
133C2×C13#216612yes—
134C22×C4—21no—
135C22×C4—132no—
136C22×C4—261no—
137C22×C4C2×C4×D1311yescharacteristic
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—132no—
141C2×C8—132no—
142C2×C8—261no—
143C2×C8—261no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8C4×Dic1312yes—
147C2×C8C2×C4×D1311yescharacteristic
148C2×C8#612712yes—
149C2×C8#612712yes—
150C2×C8C22×Dic1311yescharacteristic
151C42—21no—
152C42—132no—
153C42—261no—
154C42—261no—
155C42—261no—
156C42C4×Dic1312yes—
157C16—24no—
158C16—264no—
159C13#1259611yescharacteristic, complemented, Sylow
160C23M16×D1311yescharacteristic
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—522no—
166C2×C4—522no—
167C2×C4#8812611yescharacteristic
168C2×C4#8812611yescharacteristic
169C2×C4M16×D1311yescharacteristic
170C2×C4M16×D1311yescharacteristic
171C2×C4M16×D1311yescharacteristic
172C2×C4C2×C4×Dic1311yescharacteristic
173C8—22no—
174C8—262no—
175C8—262no—
176C8#8812612yes—
177C8#8818012yes—
178C22—22no—
179C22#1171836611yescharacteristic
180C22#1171836611yescharacteristic
181C22M16×Dic1311yescharacteristic
182C4—42no—
183C4—522no—
184C4—522no—
185C4#1171836611yescharacteristic
186C4#1171836611yescharacteristic
187C4#1171859311yescharacteristic
188C4M16×Dic1311yescharacteristic
189C2—21no—
190C2—21no—
191C2#1311458411yescharacteristic
192C2#1311665012yes—
subgroupG/H
centerC2×C4#88126
commutatorC2×C4×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#347C2
socleC22×C13#432
prime radicalC23×C13C2×M16
cosocleC22×C8×C13C23
hypercenterC2×#347D13
hypocenterC13#12596
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ C2×#347

Complements

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

NH ≅ G/Ntype
15. C13×#347C4semidirect
16. #11718058C4semidirect
97. #347Dic13semidirect
159. C13#12596semidirect

Maximal subgroups

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

subgroupindex
C2×#117180582
#131145242
#131129192
#131129172
C2×C13×#3472
#1259613