Finite Group Databasebeta

← #16788235

Subgroups — #16788235

Order 3328.

334 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 88 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#13131195C211yesmaximal, characteristic
2#13130757C211yesmaximal, characteristic
3#13129824C214yesmaximal
4#13125420C211yesmaximal, characteristic
5#11719433—21no—
6#11719059—21no—
7C13×#494C411yescharacteristic, complemented
8#11718849—21no—
9#11718849C2212yes—
10Q16×Dic13—21no—
11Q16×Dic13C412yescomplemented
12#11718742—21no—
13C4×C8×D13C2211yescharacteristic
14#11718343C411yescharacteristic, complemented
15#11718265—21no—
16#11718265C2212yes—
17#11718260—21no—
18#11718259C2212yes—
19C4×#6092—21no—
20C2×C4⋊#261—22no—
21C2×C4⋊#261—41no—
22C2×C4⋊#261—41no—
23C2×C13×Q16—21no—
24C2×C13×Q16C2×C412yes—
25C13×C4⋊Q8—21no—
26#88200—22no—
27Q8×Dic13—22no—
28C2×C8×D13D411yescharacteristic
29C2×C8×D13C2311yescharacteristic
30#88151—41no—
31#88146—41no—
32#88144—41no—
33#88141—41no—
34C42×D13D411yescharacteristic
35#88123—21no—
36C2×#6092—22no—
37C4×C8×C13C2×C411yescharacteristic
38#88075—22no—
39#88075—22no—
40#88058—21no—
41#88058C2×C412yes—
42C8×Dic13C2×C411yescharacteristic
43C8×Dic13D411yescharacteristic
44C4×#1055D411yescharacteristic
45#11857—131nomaximal, Sylow
46C22×#261—42no—
47C2×Q8×C13—22no—
48C2×C4×D13D811yescharacteristic
49C2×C4×D13D811yescharacteristic
50C2×C4×D13C2×D411yescharacteristic
51C2×Dic26—41no—
52C4⋊#261—42no—
53C4⋊#261—42no—
54C4⋊#261—82no—
55C4⋊#261—82no—
56C13×Q16—42no—
57C13×Q16—42no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C22×C411yescharacteristic
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C42×C13C22⋊C411yescharacteristic
63#6103—42no—
64C4⋊Dic13—22no—
65C4⋊Dic13—41no—
66C4⋊Dic13—42no—
67#6101—42no—
68C4×Dic13—42no—
69C4×Dic13C22⋊C411yescharacteristic
70C4×Dic13SD1611yescharacteristic
71C4×Dic13SD1611yescharacteristic
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D411yescharacteristic
74C8×D13—41no—
75C8×D13—41no—
76#6092—42no—
77#3170—131no—
78#2162—131no—
79#1834—131no—
80#1348—134no—
81C22×D13C2×D811yescharacteristic
82C2×#261—82no—
83C2×#261—82no—
84C2×#261—82no—
85Q8×C13—42no—
86Q8×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13#10211yescharacteristic
90C2×C4×C13C2×C22⋊C411yescharacteristic
91C2×Dic13—42no—
92C2×Dic13#10211yescharacteristic
93C2×Dic13#10211yescharacteristic
94C2×Dic13C2×SD1611yescharacteristic
95C4×D13—22no—
96C4×D13—21no—
97C4×D13—21no—
98C4×D13SD3212yes—
99C4×D13Q3212yes—
100Dic26—82no—
101C8×C13—21no—
102C8×C13—21no—
103#1055—21no—
104#1055—21no—
105#533—261no—
106#500—131no—
107#494#26111yescharacteristic, complemented
108#487—261no—
109#467—132no—
110#467—261no—
111C4×Q16—132no—
112C4×Q16—261no—
113C2×C4×C8—131no—
114#384—261no—
115C4⋊C16—261no—
116C22⋊C16—132no—
117C4×C16—261no—
118#340—132no—
119#340—261no—
120C22×C13C2×#10211yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13C2×SD3211yescharacteristic
124C2×D13C2×Q3211yescharacteristic
125#261—162no—
126C4×C13—82no—
127C4×C13#35812yes—
128C4×C13#36012yes—
129C4×C13#41011yescharacteristic
130C4×C13#42111yescharacteristic
131Dic13—21no—
132Dic13—21no—
133Dic13—82no—
134Dic13#35812yes—
135C2×Q16—21no—
136C2×Q16C2×#26112yes—
137C22×C8—131no—
138C22×C8—131no—
139C4⋊Q8—21no—
140C4⋊Q8—261no—
141#125—521no—
142C22⋊Q8—262no—
143C22⋊Q8—521no—
144C4×Q8—262no—
145C4×Q8—521no—
146#117—521no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—521no—
149C2×C4⋊C4—521no—
150C2×C42—131no—
151C2×C16—262no—
152#107—132no—
153#107—261no—
154#103—262no—
155#103—262no—
156C4×C8—131no—
157C4×C8—131no—
158C4×C8—131no—
159C4×C8C2×#26111yescharacteristic
160C2×C13#151711yescharacteristic
161C2×C13C2×#35811yescharacteristic
162C2×C13C2×#36011yescharacteristic
163D13—21no—
164D13—21no—
165C2×Q8—22no—
166C2×Q8—521no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—522no—
171Q16—42no—
172Q16—42no—
173C2×C8—131no—
174C2×C8—131no—
175C2×C8—521no—
176C2×C8—521no—
177C2×C8C22⋊#26111yescharacteristic
178C2×C8C22×#26111yescharacteristic
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—262no—
182C4⋊C4—522no—
183C4⋊C4—522no—
184C4⋊C4—522no—
185C4⋊C4—522no—
186C4⋊C4—521no—
187C4⋊C4—1042no—
188C4⋊C4—1042no—
189C22⋊C4—522no—
190C42—131no—
191C42—131no—
192C42—131no—
193C42—522no—
194C42C22⋊#26111yescharacteristic
195C16—522no—
196C13#1185711yescharacteristic, complemented, Sylow
197C23—131no—
198Q8—42no—
199Q8—42no—
200Q8—1042no—
201C2×C4—42no—
202C2×C4—131no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—131no—
206C2×C4—131no—
207C2×C4—262no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—522no—
211C2×C4—1042no—
212C2×C4—1042no—
213C2×C4—1042no—
214C2×C4#8811511yescharacteristic
215C2×C4#8811511yescharacteristic
216C2×C4C2×C22⋊#26111yescharacteristic
217C8—21no—
218C8—21no—
219C8—261no—
220C8—261no—
221C22—131no—
222C22—131no—
223C22—261no—
224C22—261no—
225C22C2×#8811511yescharacteristic
226C4—82no—
227C4—132no—
228C4—261no—
229C4—261no—
230C4—1042no—
231C4—2082no—
232C4#1171827912yes—
233C4#1171828012yes—
234C4#1171914011yescharacteristic
235C4#1171914211yescharacteristic
236C2—261no—
237C2—261no—
238C2#1313026511yescharacteristic
239C2C2×#1171828011yescharacteristic
240C2C2×#1171827911yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#494C4
socleC22×C13C2×#102
prime radicalC22×D13C2×D8
cosocleC2×C8×D13C23
hypercenter#494#261
hypocenterC13#11857
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
7. C13×#494C4semidirect
11. Q16×Dic13C4semidirect
14. #11718343C4semidirect
107. #494#261semidirect
196. C13#11857semidirect

Maximal subgroups

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

subgroupindex
#131311952
#131307572
#131298242
#131254202
#1185713