Finite Group Databasebeta

← #16777287

Subgroups — #16777287

Order 3328.

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

normal subgroups only

This group has 286 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#13131064C211yesmaximal, characteristic
2#13130572C211yesmaximal, characteristic
3#13116446C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5C4×C22⋊#261C411yescharacteristic
6D13⋊(C22⋊C8)C411yescharacteristic
7C2×#88100—21no—
8C2×#88098—21no—
9C2×C13×M32C411yescharacteristic, complemented
10C2×#88052C411yescharacteristic, complemented
11C22⋊#6092C412yescomplemented
12(C2×#261)⋊C8—21no—
13#11718259—21no—
14#11718099—21no—
15#11718099—21no—
16C22×C4×D13C2×C411yescharacteristic
17C2×C22⋊#261C812yes—
18C2×C4×#261—21no—
19C2×D13⋊C8—21no—
20C22×C8×C13C2×C411yescharacteristic
21C22×#1055C2×C411yescharacteristic
22C2×C8×D13—41no—
23C2×C8×D13—41no—
24C2×C8×D13D411yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13D411yescharacteristic
27C2×C8×D13Q811yescharacteristic
28C22⋊#1057C812yes—
29(C2×#261)⋊C4—21no—
30#88111—21no—
31C2×#6092—22no—
32#88100—41no—
33#88100—41no—
34#88098—41no—
35#88098—41no—
36C13×M32—41no—
37C2×C13×C16—21no—
38#88052—41no—
39C2×#6090—21no—
40#7201—131nomaximal, Sylow
41C23×D13C2×C811yescharacteristic
42C22×#261—22no—
43C22×C4×C13C4211yescharacteristic
44C22×Dic13C2×C811yescharacteristic
45C2×C4×D13—41no—
46C2×C4×D13—41no—
47C2×C4×D13C22⋊C411yescharacteristic
48C2×C4×D13C4⋊C411yescharacteristic
49C2×C4×D13M1611yescharacteristic
50C2×C4×D13M1611yescharacteristic
51C22⋊#261—42no—
52C2×#1057—22no—
53C4×#261—41no—
54C4×#261—41no—
55D13⋊C8—41no—
56D13⋊C8—41no—
57C2×C8×C13—21no—
58C2×C8×C13—21no—
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C4⋊C411yescharacteristic
61C2×#1055—41no—
62C2×#1055C22⋊C411yescharacteristic
63C2×#1055C4⋊C411yescharacteristic
64C8×D13—21no—
65C8×D13—21no—
66C8×D13—21no—
67C8×D13—21no—
68C8×D13—41no—
69C8×D13—41no—
70#6092—42no—
71C13×C16—41no—
72#6090—41no—
73#2112—131no—
74#2112—131no—
75#1752—131no—
76C23×C13C4×C811yescharacteristic
77C22×D13—22no—
78C22×D13—41no—
79C22×D13—41no—
80C22×D13C22⋊C811yescharacteristic
81C22×D13C4⋊C811yescharacteristic
82C2×#261—42no—
83C2×#261—42no—
84C2×#261—42no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13#9511yescharacteristic
88C2×C4×C13#9711yescharacteristic
89C2×Dic13—41no—
90C2×Dic13C22⋊C811yescharacteristic
91C2×Dic13C4⋊C811yescharacteristic
92C4×D13—21no—
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—21no—
96C4×D13—41no—
97C4×D13—41no—
98#1057—42no—
99C8×C13—21no—
100C8×C13#9911yescharacteristic
101C8×C13#9911yescharacteristic
102#1055—21no—
103#1055—21no—
104C23×C8—131no—
105C2×M32—131no—
106C2×M32—261no—
107C2×M32#26111yescharacteristic, complemented
108C2×C22⋊C8—131no—
109C2×#97—261no—
110C4×C22⋊C4—131no—
111C22⋊C16—132no—
112C22⋊C16—261no—
113C22⋊C16—261no—
114C22⋊C16—261no—
115#336—261no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#33611yescharacteristic
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—21no—
125C2×D13—44no—
126C2×D13#34912yes—
127#261—82no—
128C4×C13—21no—
129C4×C13#34211yescharacteristic
130C4×C13#34411yescharacteristic
131Dic13—21no—
132Dic13—21no—
133C23×C4—131no—
134C22×C8—131no—
135C22×C8—131no—
136C22×C8—131no—
137C22×C8—131no—
138C22×C8—131no—
139C22×C8—261no—
140C22×C8—521no—
141C22×C8—521no—
142C22×C8C2×#26111yescharacteristic
143C2×C22⋊C4—132no—
144C2×C42—261no—
145M32—41no—
146M32—521no—
147M32—521no—
148M32—521no—
149C2×C16—21no—
150C2×C16—262no—
151C2×C16—261no—
152C22⋊C8—132no—
153C22⋊C8—261no—
154#97—521no—
155#97—521no—
156#95—261no—
157C2×C13—41no—
158C2×C13#128211yescharacteristic
159C2×C13#137711yescharacteristic
160C2×C13#137811yescharacteristic
161D13—22no—
162D13—41no—
163C24—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—262no—
170C22×C4—521no—
171C22×C4—521no—
172C22×C4C4×#26111yescharacteristic
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—261no—
178C2×C8—261no—
179C2×C8—261no—
180C2×C8—261no—
181C2×C8—262no—
182C2×C8—521no—
183C2×C8—521no—
184C2×C8—521no—
185C2×C8—521no—
186C2×C8—521no—
187C2×C8C4⋊#26111yescharacteristic
188C2×C8C22⋊#26111yescharacteristic
189C22⋊C4—522no—
190C42—521no—
191C42—521no—
192C16—41no—
193C16—522no—
194C16—521no—
195C13#720111yescharacteristic, complemented, Sylow
196C23—131no—
197C23—131no—
198C23—262no—
199C23—521no—
200C23—521no—
201C23C8×#26111yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—131no—
205C2×C4—131no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—521no—
211C2×C4—521no—
212C2×C4—521no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4#8810011yescharacteristic
217C2×C4(C2×#261)⋊C411yescharacteristic
218C8—21no—
219C8—261no—
220C8—261no—
221C8—522no—
222C8#8810711yescharacteristic
223C8#8811911yescharacteristic
224C22—21no—
225C22—21no—
226C22—21no—
227C22—132no—
228C22—261no—
229C22—261no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—524no—
234C22(C2×#261)⋊C811yescharacteristic
235C4—21no—
236C4—261no—
237C4—261no—
238C4—1042no—
239C4#1171826611yescharacteristic
240C4#1171828911yescharacteristic
241C2—41no—
242C2—262no—
243C2—521no—
244C2#1312967811yescharacteristic
245C2#1312988211yescharacteristic
246C2#1312988811yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutatorC23×C13C4×C8
FrattiniC22×C8C2×#261
FittingC2×C13×M32C4
socleC22×C13#336
prime radicalC23×D13C2×C8
cosocleC22×C8×D13C22
hypercenterC2×M32#261
hypocenterC13#7201
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×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. C22⋊#6092C4semidirect
107. C2×M32#261semidirect
195. C13#7201semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131305722
#131164462
#720113