Finite Group Databasebeta

← #16784980

Subgroups — #16784980

Order 3328.

422 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 96 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#13131021C212yesmaximal
2#13130549C211yesmaximal, characteristic
3#13130395C211yesmaximal, characteristic
4#13130185C212yesmaximal
5#13125423C211yesmaximal, characteristic
6#11719433C2212yes—
7C42×#261C2211yescharacteristic
8#11719052C2212yes—
9C4×D13⋊C8C2211yescharacteristic
10C13×#500C411yescharacteristic, complemented
11#11718754C412yescomplemented
12#11718548—22no—
13#11718534—22no—
14#11718360C411yescharacteristic, complemented
15C4×C8×D13C2211yescharacteristic
16Q8⋊#1057—24no—
17(C2×#261)⋊C8—22no—
18#11718256—22no—
19#11718247—24no—
20C2×C4×#261—21no—
21C2×C4×#261—21no—
22C2×C4×#261D412yes—
23C2×#6118—22no—
24C2×D13⋊C8—21no—
25C13×C4⋊Q8C2×C412yes—
26#88200—22no—
27Q8×Dic13—22no—
28C2×Dic52—22no—
29C2×C8×D13D412yes—
30#88151—22no—
31#88146—22no—
32#88144—22no—
33#88141—22no—
34C42×D13C2311yescharacteristic
35#88123C2×C412yes—
36C4⋊#1057—22no—
37C4⋊#1057—22no—
38C4×#1057—21no—
39C4×#1057D412yes—
40C13×#107—22no—
41C4×C8×C13C2×C411yescharacteristic
42C8×Dic13D412yes—
43#88050—24no—
44C4×#1055C2×C411yescharacteristic
45#9848—131nomaximal, Sylow
46C22×#261—22no—
47C2×Q8×C13—22no—
48C2×C4×D13C2×D411yescharacteristic
49C2×C4×D13C2×D411yescharacteristic
50C2×C4×D13#4111yescharacteristic
51C2×Dic26—22no—
52C2×#1057—22no—
53C2×#1057—42no—
54C4×#261—22no—
55C4×#261—42no—
56C4×#261—42no—
57C4×#261Q1614yescomplemented
58#6118—44no—
59D13⋊C8—42no—
60C2×C8×C13C22⋊C412yes—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C42×C13C22×C411yescharacteristic
64#6103—42no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67C4⋊Dic13—42no—
68#6101—42no—
69C4×Dic13—42no—
70C4×Dic13C2×D411yescharacteristic
71C4×Dic13C2×D411yescharacteristic
72C4×Dic13#4111yescharacteristic
73C2×#1055C22⋊C412yes—
74Dic52—44no—
75C8×D13—42no—
76#3170—131no—
77#1994—132no—
78#1744—131no—
79#1567—131no—
80#1493—132no—
81C22×D13#12111yescharacteristic
82C2×#261—24no—
83C2×#261—42no—
84C2×#261—42no—
85Q8×C13—44no—
86C2×C4×C13—42no—
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×C4×C13C4×D411yescharacteristic
89C2×C4×C13C4×D411yescharacteristic
90C2×Dic13—42no—
91C2×Dic13#12111yescharacteristic
92C2×Dic13#12411yescharacteristic
93C2×Dic13#12711yescharacteristic
94C4×D13—22no—
95C4×D13—22no—
96C4×D13C2×Q1612yes—
97C4×D13#13512yes—
98Dic26—44no—
99#1057—42no—
100#1057—82no—
101C8×C13—22no—
102#1055—22no—
103#533—132no—
104#500#26111yescharacteristic, complemented
105#494—131no—
106#487—132no—
107#467—262no—
108C4×Q16—262no—
109#423—132no—
110C2×C4×C8—131no—
111C2×C4×C8—131no—
112C43—131no—
113#339—264no—
114#336—262no—
115#335—262no—
116Q8⋊C8—264no—
117C22×C13#39011yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13#46712yes—
121#261—44no—
122C4×C13—82no—
123C4×C13#42112yes—
124C4×C13C4×Q1612yes—
125C4×C13#44412yes—
126Dic13—21no—
127Dic13—21no—
128Dic13—82no—
129Dic13#49411yescharacteristic
130Dic13#49511yescharacteristic
131C2×Q16—262no—
132C2×M16—262no—
133C22×C8—132no—
134C22×C8—261no—
135C4⋊Q8—132no—
136C4⋊Q8C2×#26112yes—
137#125—262no—
138C22⋊Q8—262no—
139C22⋊Q8—262no—
140C4×Q8—262no—
141C4×Q8—262no—
142#117—262no—
143C2×C42—131no—
144C2×C42—132no—
145C2×C42—261no—
146C2×C42—261no—
147#107—22no—
148C4⋊C8—262no—
149C4⋊C8—262no—
150#103—264no—
151C4×C8—132no—
152C4×C8—132no—
153C4×C8—131no—
154C4×C8—261no—
155C4×C8C2×#26111yescharacteristic
156C2×C13#196311yescharacteristic
157C2×C13#196911yescharacteristic
158C2×C13#197511yescharacteristic
159D13—22no—
160C2×Q8—22no—
161C2×Q8—262no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—262no—
166Q16—524no—
167M16—524no—
168C2×C8—132no—
169C2×C8—262no—
170C2×C8—522no—
171C2×C8—522no—
172C2×C8—522no—
173C2×C8C22⋊#26112yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—522no—
179C4⋊C4—522no—
180C22⋊C4—522no—
181C42—131no—
182C42—131no—
183C42—131no—
184C42—134no—
185C42—262no—
186C42—522no—
187C42—522no—
188C42—522no—
189C42C22×#26111yescharacteristic
190C13#984811yescharacteristic, complemented, Sylow
191C23—131no—
192Q8—44no—
193Q8—524no—
194C2×C4—42no—
195C2×C4—131no—
196C2×C4—132no—
197C2×C4—132no—
198C2×C4—131no—
199C2×C4—131no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—264no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4D4×#26111yescharacteristic
207C2×C4D4×#26111yescharacteristic
208C2×C4C2×C22⋊#26111yescharacteristic
209C8—22no—
210C8—262no—
211C8—522no—
212C8—1042no—
213C22—132no—
214C22—261no—
215C22—261no—
216C22#1171915111yescharacteristic
217C4—82no—
218C4—131no—
219C4—131no—
220C4—261no—
221C4—261no—
222C4—524no—
223C4—1042no—
224C4#1171910412yes—
225C4Q16×#26112yes—
226C4#1171915512yes—
227C2—262no—
228C2#1313097211yescharacteristic
229C2#1313098211yescharacteristic
230C2#1313099111yescharacteristic
subgroupG/H
centerC22#11719151
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#500C4
socleC22×C13#390
prime radicalC22×D13#121
cosocleC42×D13C23
hypercenter#500#261
hypocenterC13#9848
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
10. C13×#500C4semidirect
11. #11718754C4semidirect
14. #11718360C4semidirect
57. C4×#261Q16semidirect
104. #500#261semidirect
190. C13#9848semidirect

Maximal subgroups

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

subgroupindex
#131310212
#131305492
#131303952
#131301852
#131254232
#984813