Finite Group Databasebeta

← #16777401

Subgroups — #16777401

Order 3328.

292 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 68 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#13130715C211yesmaximal, characteristic
2#13130712C211yesmaximal, characteristic
3C2×#11718099C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719136—21no—
6#11719127—21no—
7C2×#88103—21no—
8C2×#88101—21no—
9C22×C13×C16C411yescharacteristic, complemented
10C22×#6090C411yescharacteristic, 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#88103—41no—
31#88103—41no—
32#88101—41no—
33#88101—41no—
34C2×C13×C16—21no—
35C2×C13×C16—41no—
36C2×#6090—21no—
37C2×#6090—41no—
38#7232—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—81no—
50C22⋊#261—81no—
51C2×#1057—42no—
52C4⋊#261—42no—
53C4⋊#261—42no—
54#6118—42no—
55#6118—42no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13C4211yescharacteristic
59C2×C8×C13C22⋊C411yescharacteristic
60C2×#1055—41no—
61C2×#1055C4⋊C411yescharacteristic
62C2×#1055C4⋊C411yescharacteristic
63C8×D13—21no—
64C8×D13—21no—
65C8×D13—21no—
66C8×D13—21no—
67C8×D13—41no—
68C8×D13—41no—
69C13×C16—41no—
70#6090—41no—
71C2×C22⋊C16—131no—
72#1810—131no—
73#1807—131no—
74C23×C13#10611yescharacteristic
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—22no—
78C22×D13—41no—
79C22×D13#10211yescharacteristic
80C22×D13#10311yescharacteristic
81C2×#261—82no—
82C2×#261—82no—
83C2×#261—82no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13#9511yescharacteristic
87C2×C4×C13#10711yescharacteristic
88C2×Dic13—41no—
89C2×Dic13#10211yescharacteristic
90C2×Dic13#10311yescharacteristic
91C4×D13—21no—
92C4×D13—21no—
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—41no—
96C4×D13—41no—
97#1057—82no—
98C8×C13—21no—
99C8×C13#9911yescharacteristic
100C8×C13#9911yescharacteristic
101#1055—21no—
102#1055—21no—
103C23×C8—131no—
104C22×C16—131no—
105C22×C16#26111yescharacteristic, complemented
106C2×#108—261no—
107C2×#106—261no—
108#407—261no—
109#380—261no—
110C22⋊C16—261no—
111C22⋊C16—261no—
112#341—132no—
113#340—132no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#34011yescharacteristic
117C22×C13#36511yescharacteristic
118C22×C13#36511yescharacteristic
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13#35912yes—
127#261—162no—
128C4×C13—21no—
129C4×C13H(3,ℤ/4)11yescharacteristic
130C4×C13#34211yescharacteristic
131Dic13—21no—
132Dic13—21no—
133C23×C4—131no—
134C2×M16—262no—
135C22×C8—131no—
136C22×C8—131no—
137C22×C8—131no—
138C22×C8—131no—
139C22×C8—131no—
140C22×C8—521no—
141C22×C8—521no—
142C22×C8C2×#26111yescharacteristic
143C2×C4⋊C4—262no—
144C2×C22⋊C4—521no—
145C2×C16—21no—
146C2×C16—41no—
147C2×C16—261no—
148C2×C16—521no—
149#108—521no—
150#108—521no—
151#106—521no—
152#106—521no—
153C22⋊C8—521no—
154C22⋊C8—521no—
155#95—521no—
156C2×C13—21no—
157C2×C13—21no—
158C2×C13#128911yescharacteristic
159C2×C13#138211yescharacteristic
160C2×C13#138311yescharacteristic
161D13—22no—
162D13—41no—
163C24—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—521no—
170C22×C4—521no—
171C22×C4—522no—
172C22×C4C4⋊#26111yescharacteristic
173M16—522no—
174M16—522no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—131no—
178C2×C8—131no—
179C2×C8—261no—
180C2×C8—261no—
181C2×C8—261no—
182C2×C8—261no—
183C2×C8—521no—
184C2×C8—521no—
185C2×C8—521no—
186C2×C8—522no—
187C2×C8C4×#26111yescharacteristic
188C2×C8C22⋊#26111yescharacteristic
189C4⋊C4—522no—
190C4⋊C4—522no—
191C22⋊C4—1041no—
192C22⋊C4—1041no—
193C16—41no—
194C16—521no—
195C13#723211yescharacteristic, complemented, Sylow
196C23—131no—
197C23—131no—
198C23—262no—
199C23—261no—
200C23—261no—
201C23—521no—
202C23#8810111yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—131no—
206C2×C4—131no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—521no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—1042no—
215C2×C4—1042no—
216C2×C4—1042no—
217C2×C4#8810211yescharacteristic
218C2×C4(C2×#261)⋊C411yescharacteristic
219C8—21no—
220C8—261no—
221C8—261no—
222C8—1042no—
223C8#8810711yescharacteristic
224C8#8811911yescharacteristic
225C22—21no—
226C22—21no—
227C22—132no—
228C22—261no—
229C22—261no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—522no—
234C22—522no—
235C22#1171821911yescharacteristic
236C22#1171822011yescharacteristic
237C22#1171826511yescharacteristic
238C4—21no—
239C4—261no—
240C4—261no—
241C4—2082no—
242C4#1171826711yescharacteristic
243C4#1171828911yescharacteristic
244C2—21no—
245C2—21no—
246C2—262no—
247C2—521no—
248C2#1312969911yescharacteristic
249C2#1312989811yescharacteristic
250C2#1312990111yescharacteristic
subgroupG/H
centerC22#11718265
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC22×C13×C16C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC22×C8×D13C22
hypercenterC22×C16#261
hypocenterC13#7232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
9. C22×C13×C16C4semidirect
10. C22×#6090C4semidirect
11. #11718268C4semidirect
105. C22×C16#261semidirect
195. C13#7232semidirect

Maximal subgroups

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

subgroupindex
#131307152
#131307122
C2×#117180992
#723213