Finite Group Databasebeta

← #16777408

Subgroups — #16777408

Order 3328.

286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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#13130716C211yesmaximal, characteristic
2#13130713C211yesmaximal, characteristic
3#13116446C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719136—21no—
6#11719127—21no—
7C2×#88104—21no—
8C2×#88102—21no—
9C2×C13×M32C411yescharacteristic, complemented
10C2×#88052C411yescharacteristic, complemented
11#11718268C412yescomplemented
12#11718265C412yes—
13#11718099—21no—
14#11718099—21no—
15C22×C4×D13D411yescharacteristic
16C2×C22⋊#261—41no—
17C2×C4⋊#261—22no—
18C2×#6118—22no—
19C22×C8×C13C2×C411yescharacteristic
20C22×#1055Q811yescharacteristic
21C2×C8×D13—41no—
22C2×C8×D13—41no—
23C2×C8×D13C2×C411yescharacteristic
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13D411yescharacteristic
27C22⋊#1057—41no—
28(C2×#261)⋊C4—41no—
29#88111—41no—
30#88104—41no—
31#88104—41no—
32#88102—41no—
33#88102—41no—
34C13×M32—41no—
35C2×C13×C16—21no—
36#88052—41no—
37C2×#6090—21no—
38#7235—131nomaximal, Sylow
39C23×D13SD1611yescharacteristic
40C22×#261—42no—
41C22×C4×C13C4⋊C411yescharacteristic
42C22×Dic13SD1611yescharacteristic
43C2×C4×D13—41no—
44C2×C4×D13—41no—
45C2×C4×D13C22⋊C411yescharacteristic
46C2×C4×D13C22⋊C411yescharacteristic
47C2×C4×D13D811yescharacteristic
48C2×C4×D13Q1611yescharacteristic
49C22⋊#261—82no—
50C2×#1057—42no—
51C4⋊#261—42no—
52C4⋊#261—42no—
53#6118—42no—
54#6118—42no—
55C2×C8×C13—21no—
56C2×C8×C13—21no—
57C2×C8×C13C4211yescharacteristic
58C2×C8×C13C22⋊C411yescharacteristic
59C2×#1055—41no—
60C2×#1055C4⋊C411yescharacteristic
61C2×#1055C4⋊C411yescharacteristic
62C8×D13—21no—
63C8×D13—21no—
64C8×D13—21no—
65C8×D13—21no—
66C8×D13—41no—
67C8×D13—41no—
68C13×C16—41no—
69#6090—41no—
70#2112—131no—
71#1810—131no—
72#1808—131no—
73C23×C13#10611yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—41no—
77C22×D13—41no—
78C22×D13#10211yescharacteristic
79C22×D13#10311yescharacteristic
80C2×#261—82no—
81C2×#261—82no—
82C2×#261—82no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13#9511yescharacteristic
86C2×C4×C13#10711yescharacteristic
87C2×Dic13—41no—
88C2×Dic13#10211yescharacteristic
89C2×Dic13#10311yescharacteristic
90C4×D13—21no—
91C4×D13—21no—
92C4×D13—21no—
93C4×D13—21no—
94C4×D13—41no—
95C4×D13—41no—
96#1057—82no—
97C8×C13—21no—
98C8×C13#9911yescharacteristic
99C8×C13#9911yescharacteristic
100#1055—21no—
101#1055—21no—
102C23×C8—131no—
103C2×M32—131no—
104C2×M32#26111yescharacteristic, complemented
105C2×#108—261no—
106C2×#107—261no—
107#407—261no—
108#380—261no—
109C22⋊C16—261no—
110C22⋊C16—261no—
111#341—132no—
112#340—132no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#34011yescharacteristic
117C2×D13—21no—
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—42no—
123C2×D13—42no—
124C2×D13#36111yescharacteristic
125C2×D13#36211yescharacteristic
126#261—162no—
127C4×C13—21no—
128C4×C13H(3,ℤ/4)11yescharacteristic
129C4×C13#34211yescharacteristic
130Dic13—21no—
131Dic13—21no—
132C23×C4—131no—
133C2×M16—262no—
134C22×C8—131no—
135C22×C8—131no—
136C22×C8—131no—
137C22×C8—131no—
138C22×C8—131no—
139C22×C8—521no—
140C22×C8—521no—
141C22×C8C2×#26111yescharacteristic
142C2×C4⋊C4—262no—
143C2×C22⋊C4—521no—
144M32—41no—
145M32—521no—
146C2×C16—21no—
147C2×C16—261no—
148#108—521no—
149#108—521no—
150#107—521no—
151#107—521no—
152C22⋊C8—521no—
153C22⋊C8—521no—
154#95—521no—
155C2×C13—41no—
156C2×C13#128911yescharacteristic
157C2×C13#138711yescharacteristic
158C2×C13#138911yescharacteristic
159D13—21no—
160D13—21no—
161D13—41no—
162C24—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—521no—
169C22×C4—521no—
170C22×C4—522no—
171C22×C4C4⋊#26111yescharacteristic
172M16—522no—
173M16—522no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—261no—
179C2×C8—261no—
180C2×C8—261no—
181C2×C8—261no—
182C2×C8—521no—
183C2×C8—521no—
184C2×C8—521no—
185C2×C8—522no—
186C2×C8C4×#26111yescharacteristic
187C2×C8C22⋊#26111yescharacteristic
188C4⋊C4—522no—
189C4⋊C4—522no—
190C22⋊C4—1042no—
191C16—41no—
192C16—521no—
193C13#723511yescharacteristic, complemented, Sylow
194C23—131no—
195C23—131no—
196C23—261no—
197C23—261no—
198C23—521no—
199C23—521no—
200C23#8810111yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—131no—
204C2×C4—131no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—521no—
210C2×C4—521no—
211C2×C4—521no—
212C2×C4—1042no—
213C2×C4—1042no—
214C2×C4—1042no—
215C2×C4#8810211yescharacteristic
216C2×C4(C2×#261)⋊C411yescharacteristic
217C8—21no—
218C8—261no—
219C8—261no—
220C8—1042no—
221C8#8810711yescharacteristic
222C8#8811911yescharacteristic
223C22—21no—
224C22—21no—
225C22—21no—
226C22—131no—
227C22—131no—
228C22—261no—
229C22—261no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—522no—
234C22—522no—
235C22#1171826511yescharacteristic
236C4—21no—
237C4—261no—
238C4—261no—
239C4—2082no—
240C4#1171826711yescharacteristic
241C4#1171828911yescharacteristic
242C2—41no—
243C2—261no—
244C2—261no—
245C2—521no—
246C2#1312969911yescharacteristic
247C2#1312991111yescharacteristic
248C2#1312991711yescharacteristic
subgroupG/H
centerC22#11718265
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC2×C13×M32C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC22×C8×D13C22
hypercenterC2×M32#261
hypocenterC13#7235
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
9. C2×C13×M32C4semidirect
10. C2×#88052C4semidirect
11. #11718268C4semidirect
104. C2×M32#261semidirect
193. C13#7235semidirect

Maximal subgroups

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

subgroupindex
#131307162
#131307132
#131164462
#723513