Finite Group Databasebeta

← #16784996

Subgroups — #16784996

Order 3328.

422 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 92 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#13130392C211yesmaximal, 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#11718255—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#9853—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—24no—
55C4×#261—24no—
56C4×#261—42no—
57#6118—44no—
58D13⋊C8—42no—
59C2×C8×C13C22⋊C412yes—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C42×C13C22×C411yescharacteristic
63#6103—42no—
64C4⋊Dic13—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13—42no—
67#6101—42no—
68C4×Dic13—42no—
69C4×Dic13C2×D411yescharacteristic
70C4×Dic13C2×D411yescharacteristic
71C4×Dic13#4111yescharacteristic
72C2×#1055C22⋊C412yes—
73Dic52—44no—
74C8×D13—42no—
75#3170—131no—
76#1994—132no—
77#1744—131no—
78#1566—131no—
79#1493—132no—
80C22×D13#12111yescharacteristic
81C2×#261—24no—
82C2×#261—42no—
83C2×#261—42no—
84Q8×C13—44no—
85C2×C4×C13—42no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C4×D411yescharacteristic
88C2×C4×C13C4×D411yescharacteristic
89C2×Dic13—42no—
90C2×Dic13#12111yescharacteristic
91C2×Dic13#12411yescharacteristic
92C2×Dic13#12711yescharacteristic
93C4×D13—22no—
94C4×D13—22no—
95C4×D13#13714yes—
96Dic26—44no—
97#1057—42no—
98#1057—82no—
99C8×C13—22no—
100#1055—22no—
101#533—132no—
102#500#26111yescharacteristic, complemented
103#494—131no—
104#487—132no—
105#467—262no—
106C4×Q16—262no—
107#423—132no—
108C2×C4×C8—131no—
109C2×C4×C8—131no—
110C43—131no—
111#339—264no—
112#336—262no—
113#334—262no—
114Q8⋊C8—264no—
115C22×C13#39011yescharacteristic
116C2×D13—21no—
117C2×D13—21no—
118C2×D13#47012yes—
119#261—44no—
120C4×C13—82no—
121C4×C13#42112yes—
122C4×C13#44112yes—
123C4×C13#44312yes—
124Dic13—21no—
125Dic13—21no—
126Dic13—82no—
127Dic13#49712yes—
128C2×Q16—262no—
129C2×M16—262no—
130C22×C8—132no—
131C22×C8—261no—
132C4⋊Q8—132no—
133C4⋊Q8C2×#26112yes—
134#125—262no—
135C22⋊Q8—262no—
136C22⋊Q8—262no—
137C4×Q8—262no—
138C4×Q8—262no—
139#117—262no—
140C2×C42—131no—
141C2×C42—132no—
142C2×C42—261no—
143C2×C42—261no—
144#107—22no—
145C4⋊C8—262no—
146C4⋊C8—262no—
147#103—264no—
148C4×C8—132no—
149C4×C8—132no—
150C4×C8—131no—
151C4×C8—261no—
152C4×C8C2×#26111yescharacteristic
153C2×C13#196311yescharacteristic
154C2×C13#197111yescharacteristic
155C2×C13#197411yescharacteristic
156D13—22no—
157C2×Q8—22no—
158C2×Q8—262no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—262no—
163Q16—524no—
164M16—524no—
165C2×C8—132no—
166C2×C8—262no—
167C2×C8—522no—
168C2×C8—522no—
169C2×C8—522no—
170C2×C8C22⋊#26112yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—522no—
176C4⋊C4—522no—
177C22⋊C4—522no—
178C42—131no—
179C42—131no—
180C42—131no—
181C42—264no—
182C42—264no—
183C42—522no—
184C42—522no—
185C42C22×#26111yescharacteristic
186C13#985311yescharacteristic, complemented, Sylow
187C23—131no—
188Q8—44no—
189Q8—524no—
190C2×C4—42no—
191C2×C4—131no—
192C2×C4—134no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—264no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4D4×#26111yescharacteristic
202C2×C4D4×#26111yescharacteristic
203C2×C4C2×C22⋊#26111yescharacteristic
204C8—22no—
205C8—262no—
206C8—522no—
207C8—1042no—
208C22—132no—
209C22—261no—
210C22—261no—
211C22#1171915111yescharacteristic
212C4—82no—
213C4—132no—
214C4—261no—
215C4—261no—
216C4—524no—
217C4—1042no—
218C4#1171910312yes—
219C4#1171911012yes—
220C4#1171915512yes—
221C2—262no—
222C2#1313097211yescharacteristic
223C2#1313098411yescharacteristic
224C2#1313098911yescharacteristic
subgroupG/H
centerC22#11719151
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#500C4
socleC22×C13#390
prime radicalC22×D13#121
cosocleC42×D13C23
hypercenter#500#261
hypocenterC13#9853
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
102. #500#261semidirect
186. C13#9853semidirect

Maximal subgroups

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

subgroupindex
#131310212
#131305492
#131303922
#131301852
#131254232
#985313