Finite Group Databasebeta

← #16777282

Subgroups — #16777282

Order 3328.

292 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 70 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×#11718259C211yesmaximal, characteristic
2#13130572C211yesmaximal, characteristic
3#13116445C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5C4×C22⋊#261C411yescharacteristic
6D13⋊(C22⋊C8)C411yescharacteristic
7C22×#6092C412yescomplemented
8C2×#88100—21no—
9C2×#88038—21no—
10(C2×#261)⋊C8—21no—
11#11718259—21no—
12#11718259—21no—
13C13×C22⋊C16C411yescharacteristic, complemented
14C22⋊#6090C411yescharacteristic, complemented
15#11718099—21no—
16C22×C4×D13C2×C411yescharacteristic
17C2×C22⋊#261—21no—
18C2×C4×#261—21no—
19C2×D13⋊C8—21no—
20C22×C8×C13C2×C411yescharacteristic
21C22×#1055C2×C411yescharacteristic
22C2×C8×D13—42no—
23C2×C8×D13D411yescharacteristic
24C2×C8×D13D411yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13Q811yescharacteristic
27C22⋊#1057—21no—
28(C2×#261)⋊C4C812yes—
29#88111C812yes—
30C2×#6092—22no—
31C2×#6092—42no—
32#88100—42no—
33C2×C13×C16—21no—
34C2×#6090—21no—
35#88038—42no—
36#7200—131nomaximal, Sylow
37C23×D13M1611yescharacteristic
38C22×#261—22no—
39C22×C4×C13C4211yescharacteristic
40C22×Dic13M1611yescharacteristic
41C2×C4×D13—41no—
42C2×C4×D13—41no—
43C2×C4×D13C22⋊C411yescharacteristic
44C2×C4×D13C4⋊C411yescharacteristic
45C2×C4×D13C2×C811yescharacteristic
46C2×C4×D13C2×C811yescharacteristic
47C22⋊#261—41no—
48C22⋊#261—41no—
49C2×#1057—22no—
50C4×#261—41no—
51C4×#261—41no—
52D13⋊C8—41no—
53D13⋊C8—41no—
54C2×C8×C13—41no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C4⋊C411yescharacteristic
57C2×#1055—22no—
58C2×#1055C22⋊C411yescharacteristic
59C2×#1055C4⋊C411yescharacteristic
60C8×D13—22no—
61C8×D13—22no—
62C8×D13—41no—
63C8×D13—41no—
64#6092—42no—
65C13×C16—41no—
66#6090—41no—
67#2112—131no—
68C2×C22⋊C16—131no—
69#1752—131no—
70C23×C13#9711yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—22no—
74C22×D13—41no—
75C22×D13C22⋊C811yescharacteristic
76C22×D13C4⋊C811yescharacteristic
77C2×#261—42no—
78C2×#261—42no—
79C2×#261—42no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13#9511yescharacteristic
83C2×C4×C13C4×C811yescharacteristic
84C2×Dic13—41no—
85C2×Dic13C22⋊C811yescharacteristic
86C2×Dic13C4⋊C811yescharacteristic
87C4×D13—21no—
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—21no—
91C4×D13—41no—
92C4×D13—41no—
93#1057—42no—
94C8×C13—21no—
95C8×C13—21no—
96#1055—21no—
97#1055#9912yes—
98C23×C8—131no—
99C2×M32—261no—
100C22×C16—132no—
101C2×C22⋊C8—131no—
102C2×#97—261no—
103C4×C22⋊C4—131no—
104C22⋊C16—131no—
105C22⋊C16—261no—
106C22⋊C16—261no—
107C22⋊C16—261no—
108C22⋊C16#26111yescharacteristic, complemented
109#336—261no—
110C22×C13—21no—
111C22×C13—21no—
112C22×C13#33611yescharacteristic
113C22×C13#34711yescharacteristic
114C22×C13#34711yescharacteristic
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—42no—
121C2×D13—42no—
122C2×D13#35012yes—
123#261—82no—
124C4×C13—21no—
125C4×C13#34211yescharacteristic
126C4×C13#34411yescharacteristic
127Dic13—21no—
128Dic13—21no—
129C23×C4—131no—
130C22×C8—131no—
131C22×C8—131no—
132C22×C8—131no—
133C22×C8—131no—
134C22×C8—131no—
135C22×C8—261no—
136C22×C8—522no—
137C22×C8C2×#26111yescharacteristic
138C2×C22⋊C4—261no—
139C2×C42—261no—
140M32—522no—
141C2×C16—21no—
142C2×C16—262no—
143C2×C16—261no—
144C2×C16—522no—
145C22⋊C8—132no—
146C22⋊C8—261no—
147#97—522no—
148#95—132no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#128211yescharacteristic
152C2×C13#137511yescharacteristic
153C2×C13#137911yescharacteristic
154D13—22no—
155D13—41no—
156C24—131no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—262no—
163C22×C4—521no—
164C22×C4—521no—
165C22×C4C4×#26111yescharacteristic
166C2×C8—41no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—262no—
170C2×C8—262no—
171C2×C8—262no—
172C2×C8—262no—
173C2×C8—521no—
174C2×C8—521no—
175C2×C8—521no—
176C2×C8—521no—
177C2×C8C4⋊#26111yescharacteristic
178C2×C8C22⋊#26111yescharacteristic
179C22⋊C4—521no—
180C22⋊C4—521no—
181C42—521no—
182C42—521no—
183C16—41no—
184C16—521no—
185C16—522no—
186C13#720011yescharacteristic, complemented, Sylow
187C23—131no—
188C23—131no—
189C23—262no—
190C23—261no—
191C23—261no—
192C23—521no—
193C23#8810011yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—131no—
197C2×C4—131no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4C8×#26111yescharacteristic
209C2×C4(C2×#261)⋊C411yescharacteristic
210C8—21no—
211C8—21no—
212C8—132no—
213C8—261no—
214C8—522no—
215C22—21no—
216C22—21no—
217C22—132no—
218C22—261no—
219C22—261no—
220C22—261no—
221C22—261no—
222C22—261no—
223C22—522no—
224C22—522no—
225C22#1171821711yescharacteristic
226C22#1171821811yescharacteristic
227C22(C2×#261)⋊C811yescharacteristic
228C4—21no—
229C4—261no—
230C4—261no—
231C4—1042no—
232C4#1171823811yescharacteristic
233C4#1171827411yescharacteristic
234C2—21no—
235C2—21no—
236C2—262no—
237C2—521no—
238C2#1312967711yescharacteristic
239C2#1312987611yescharacteristic
240C2#1312989211yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutatorC2×C4×C13C4×C8
FrattiniC22×C8C2×#261
FittingC13×C22⋊C16C4
socleC22×C13#336
prime radicalC23×D13M16
cosocleC22×C8×D13C22
hypercenterC22⋊C16#261
hypocenterC13#7200
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
7. C22×#6092C4semidirect
13. C13×C22⋊C16C4semidirect
14. C22⋊#6090C4semidirect
108. C22⋊C16#261semidirect
186. C13#7200semidirect

Maximal subgroups

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

subgroupindex
C2×#117182592
#131305722
#131164452
#720013