Finite Group Databasebeta

← #16787051

Subgroups — #16787051

Order 3328.

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

normal subgroups only

This group has 330 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#13131206C212yesmaximal, complemented
2#13129783C212yesmaximal, complemented
3#13129768C212yesmaximal
4#13123465C211yesmaximal, characteristic
5C22×C4×Dic13C411yescharacteristic
6C13×#407C411yescharacteristic
7#11718868C2211yescharacteristic
8#11718779C411yescharacteristic
9#11718779C2211yescharacteristic
10M16×Dic13C411yescharacteristic
11M16×Dic13C2211yescharacteristic
12#11718380—22no—
13#11718379—22no—
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13—21no—
19C2×C13×M16C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C4×Dic13—21no—
22C2×C4×Dic13—21no—
23C2×C4×Dic13—21no—
24C2×C4×Dic13—21no—
25C2×C4×Dic13—21no—
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C2×#6099C2×C411yescharacteristic
29C2×#6099C2311yescharacteristic
30#88106—24no—
31C13×C22⋊C8—22no—
32C22⋊#1055—22no—
33#88055—21no—
34#88055D412yes—
35#88054—22no—
36#88054—22no—
37C8×Dic13—21no—
38C8×Dic13D412yes—
39#11521—131nomaximal, Sylow
40C24×C13M1611yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—41no—
44C22×C4×C13—41no—
45C22×C4×C13M1611yescharacteristic
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—21no—
48C22×Dic13—21no—
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13—44no—
54C13×M16—41no—
55C13×M16—41no—
56C2×C8×C13—21no—
57C2×C8×C13C22⋊C412yes—
58C4×Dic13—21no—
59C4×Dic13—21no—
60C4×Dic13—21no—
61C4×Dic13—21no—
62C4×Dic13—21no—
63C4×Dic13—21no—
64C4×Dic13C22⋊C411yescharacteristic
65C4×Dic13C22⋊C411yescharacteristic
66C4×Dic13M1611yescharacteristic
67C4×Dic13M1611yescharacteristic
68#6099—41no—
69#6099—41no—
70C2×#1055—21no—
71C2×#1055C2×D412yes—
72#6092—44no—
73#2920—131no—
74#2165—132no—
75#1327—132no—
76#1320—132no—
77C23×C13—21no—
78C23×C13—42no—
79C23×C13—41no—
80C23×C13C2×M1611yescharacteristic
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13C2×M1611yescharacteristic
90C2×Dic13—24no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C8×C13—22no—
101C8×C13—41no—
102#1055—22no—
103#1055—41no—
104C22×C42—131no—
105#432—262no—
106#431—262no—
107#423—131no—
108#423—131no—
109#407—131no—
110#407#26111yescharacteristic
111C4×M16—131no—
112C4×M16—131no—
113#364—262no—
114#349—134no—
115#347—262no—
116C22×C13—22no—
117C22×C13—21no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13—41no—
123C22×C13#40711yescharacteristic
124C4×C13—21no—
125C4×C13—41no—
126C4×C13#41011yescharacteristic
127C4×C13#41311yescharacteristic
128Dic13—22no—
129Dic13—22no—
130Dic13—41no—
131Dic13—41no—
132C23×C4—261no—
133C23×C4C2×#26111yescharacteristic
134C2×M16—131no—
135C2×M16—131no—
136C2×M16C2×#26111yescharacteristic
137C2×M16C2×#26111yescharacteristic
138C2×C42—131no—
139C2×C42—131no—
140C2×C42—261no—
141C2×C42—261no—
142C2×C42—261no—
143C2×C42—261no—
144C2×C42—261no—
145M32—264no—
146C4⋊C8—262no—
147C4⋊C8—262no—
148C22⋊C8—22no—
149C22⋊C8—262no—
150#97—132no—
151#97—261no—
152C4×C8—132no—
153C4×C8—261no—
154C2×C13—21no—
155C2×C13—42no—
156C2×C13—41no—
157C2×C13#146411yescharacteristic
158C24#611811yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—261no—
164C22×C4—261no—
165C22×C4—261no—
166C22×C4—261no—
167C22×C4—261no—
168C22×C4—261no—
169C22×C4—524no—
170C22×C4#611811yescharacteristic
171C22×C4C22×#26111yescharacteristic
172M16—41no—
173M16—41no—
174M16—521no—
175M16—521no—
176C2×C8—21no—
177C2×C8—132no—
178C2×C8—261no—
179C2×C8C22⋊#26112yes—
180C42—131no—
181C42—131no—
182C42—131no—
183C42—131no—
184C42—261no—
185C42—261no—
186C42—261no—
187C42—261no—
188C42—261no—
189C42—261no—
190C16—524no—
191C13#1152111yescharacteristic, complemented, Sylow
192C23—21no—
193C23—41no—
194C23—42no—
195C23C2×#611811yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—264no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4D13⋊M1611yescharacteristic
214C2×C4C2×C22⋊#26111yescharacteristic
215C8—22no—
216C8—41no—
217C8—262no—
218C8—521no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22#1171912711yescharacteristic
227C4—21no—
228C4—41no—
229C4—262no—
230C4—262no—
231C4—521no—
232C4—521no—
233C4#1171914211yescharacteristic
234C4#1171914811yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2#1313008811yescharacteristic
subgroupG/H
centerC4#11719142
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#407C4
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×#6099C23
hypercenter#407#261
hypocenterC13#11521
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #13131206C2semidirect
2. #13129783C2semidirect
191. C13#11521semidirect

Maximal subgroups

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

subgroupindex
#131312062
#131297832
#131297682
#131234652
#1152113