Finite Group Databasebeta

← #16777403

Subgroups — #16777403

Order 3328.

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

normal subgroups only

This group has 308 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#13131064C211yesmaximal, characteristic
2#13130712C211yesmaximal, characteristic
3#13114860C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719136—21no—
6C2×#88101—21no—
7C2×#88098C412yescomplemented
8#11718648—21no—
9C2×#88048—21no—
10C22⋊#6092—21no—
11#11718265C412yescomplemented
12#11718259—21no—
13C13×#340C411yescharacteristic, complemented
14#11718143C411yescharacteristic, complemented
15C22×C4×D13D411yescharacteristic
16C2×C22⋊#261—41no—
17C2×C4⋊#261—22no—
18C22×C8×C13C2×C411yescharacteristic
19C2×C13×C4⋊C4—21no—
20C2×#6103—41no—
21C2×C4⋊Dic13—21no—
22C22×#1055D411yescharacteristic
23C2×C8×D13—42no—
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13C2×C411yescharacteristic
26C2×C8×D13D411yescharacteristic
27C2×C8×D13Q811yescharacteristic
28(C2×#261)⋊C4—41no—
29C2×#6092—22no—
30#88101—42no—
31#88098—42no—
32#88071—41no—
33#88048—42no—
34#7233—131nomaximal, Sylow
35C23×D13D811yescharacteristic
36C22×#261—42no—
37C22×C4×C13—41no—
38C22×C4×C13C22⋊C411yescharacteristic
39C22×Dic13—41no—
40C22×Dic13SD1611yescharacteristic
41C2×C4×D13—41no—
42C2×C4×D13—41no—
43C2×C4×D13C22⋊C411yescharacteristic
44C2×C4×D13C4⋊C411yescharacteristic
45C2×C4×D13SD1611yescharacteristic
46C2×C4×D13Q1611yescharacteristic
47C22⋊#261—81no—
48C22⋊#261—81no—
49C4⋊#261—42no—
50C4⋊#261—42no—
51C2×C8×C13—41no—
52C2×C8×C13C4211yescharacteristic
53C2×C8×C13C4⋊C411yescharacteristic
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56#6103—82no—
57C4⋊Dic13—41no—
58C4⋊Dic13—41no—
59C2×#1055—22no—
60C2×#1055C22⋊C411yescharacteristic
61C2×#1055C4⋊C411yescharacteristic
62C8×D13—22no—
63C8×D13—22no—
64C8×D13—41no—
65C8×D13—41no—
66#6092—42no—
67#2112—131no—
68#1807—131no—
69#1807—131no—
70C23×C13#10211yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—22no—
74C22×D13—41no—
75C22×D13#10211yescharacteristic
76C22×D13#10711yescharacteristic
77C2×#261—82no—
78C2×#261—82no—
79C2×#261—82no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—81no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#9511yescharacteristic
86C2×C4×C13#10311yescharacteristic
87C2×Dic13—41no—
88C2×Dic13—81no—
89C2×Dic13—81no—
90C2×Dic13—81no—
91C2×Dic13#10311yescharacteristic
92C2×Dic13#10611yescharacteristic
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—21no—
96C4×D13—21no—
97C4×D13—41no—
98C4×D13—41no—
99C8×C13—21no—
100C8×C13—21no—
101#1055—21no—
102#1055#9912yes—
103C23×C8—131no—
104C2×M32—132no—
105C2×#106—261no—
106C2×#106—261no—
107#380—261no—
108#380—261no—
109C22⋊C16—261no—
110C22⋊C16—261no—
111#340—132no—
112#340—131no—
113#340#26111yescharacteristic, complemented
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#34011yescharacteristic
117C22×C13#36011yescharacteristic
118C22×C13#36011yescharacteristic
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13#36012yes—
127#261—162no—
128C4×C13—21no—
129C4×C13—161no—
130C4×C13H(3,ℤ/4)11yescharacteristic
131C4×C13#34211yescharacteristic
132Dic13—21no—
133Dic13—21no—
134Dic13—161no—
135C23×C4—131no—
136C22×C8—131no—
137C22×C8—131no—
138C22×C8—131no—
139C22×C8—131no—
140C22×C8—131no—
141C22×C8—522no—
142C22×C8C2×#26111yescharacteristic
143C2×C4⋊C4—21no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—261no—
146C2×C22⋊C4—521no—
147C2×C22⋊C4—521no—
148M32—522no—
149C2×C16—262no—
150#106—522no—
151#106—522no—
152#95—521no—
153#95—521no—
154C2×C13—21no—
155C2×C13—21no—
156C2×C13#128911yescharacteristic
157C2×C13#138611yescharacteristic
158C2×C13#138611yescharacteristic
159D13—22no—
160D13—41no—
161C24—131no—
162C22×C4—41no—
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×C4—521no—
172C22×C4C22⋊#26111yescharacteristic
173C2×C8—41no—
174C2×C8—131no—
175C2×C8—131no—
176C2×C8—262no—
177C2×C8—262no—
178C2×C8—262no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8C4×#26111yescharacteristic
182C2×C8C4⋊#26111yescharacteristic
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—521no—
186C4⋊C4—521no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C22⋊C4—1042no—
190C22⋊C4—1041no—
191C22⋊C4—1041no—
192C16—522no—
193C13#723311yescharacteristic, complemented, Sylow
194C23—131no—
195C23—131no—
196C23—262no—
197C23—261no—
198C23—261no—
199C23—521no—
200C23#8811511yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—131no—
207C2×C4—131no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—1041no—
216C2×C4—1041no—
217C2×C4—1042no—
218C2×C4—1042no—
219C2×C4—1042no—
220C2×C4—1041no—
221C2×C4(C2×#261)⋊C411yescharacteristic
222C2×C4#8811711yescharacteristic
223C8—21no—
224C8—21no—
225C8—132no—
226C8—261no—
227C22—21no—
228C22—21no—
229C22—132no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—261no—
234C22—261no—
235C22—522no—
236C22—522no—
237C22#1171824611yescharacteristic
238C22#1171827511yescharacteristic
239C22#1171827911yescharacteristic
240C4—21no—
241C4—161no—
242C4—261no—
243C4—261no—
244C4—2081no—
245C4—2082no—
246C4#1171823511yescharacteristic
247C4#1171823811yescharacteristic
248C2—21no—
249C2—21no—
250C2—262no—
251C2—521no—
252C2#1312969811yescharacteristic
253C2#1312990711yescharacteristic
254C2#1312990911yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC13×#340C4
socleC22×C13#340
prime radicalC23×D13D8
cosocleC22×C8×D13C22
hypercenter#340#261
hypocenterC13#7233
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
7. C2×#88098C4semidirect
11. #11718265C4semidirect
13. C13×#340C4semidirect
14. #11718143C4semidirect
113. #340#261semidirect
193. C13#7233semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131307122
#131148602
#723313