Finite Group Databasebeta

← #15766153

Subgroups — #15766153

Order 3328.

414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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#13114936C212yesmaximal
2#13114911C211yesmaximal, characteristic
3#13112744C211yesmaximal, characteristic
4#13112689C212yesmaximal
5C13×#2607C211yesmaximal, characteristic
6C2×#88180C2211yescharacteristic
7C13×#399—21no—
8C13×#393—21no—
9C13×#391—22no—
10C13×#387—22no—
11C13×#381C2211yescharacteristic
12C4×C13×C22⋊C4C2212yes—
13#11718872C2211yescharacteristic
14#11718868C2212yes—
15#11718119—21no—
16#11718119—21no—
17#11718115—22no—
18#11718115—22no—
19C22×Q8×C13—21no—
20C23×C4×C13C2311yescharacteristic
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C22⋊C4—22no—
24C2×C13×C22⋊C4D411yescharacteristic
25C2×C13×C22⋊C4D411yescharacteristic
26C2×C42×C13D412yes—
27C2×C42×C13D412yes—
28C2×C22⋊Dic13—21no—
29C2×C22⋊Dic13—21no—
30#88180—22no—
31#88180—22no—
32C2×C4⋊Dic13Q812yescomplemented
33C2×C4×Dic13—21no—
34C2×#6099—22no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95—22no—
40#88071—22no—
41C22⋊#1055—22no—
42C22⋊#1055—22no—
43#10387—131nomaximal, Sylow
44C24×C13C2×D411yescharacteristic
45C2×Q8×C13—44no—
46C2×Q8×C13—81no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13C2×D412yes—
54C22×C4×C13C2×Q811yescharacteristic
55C22×C4×C13#4112yes—
56C22×C4×C13#4111yescharacteristic
57C22×Dic13—22no—
58C22×Dic13—41no—
59C13×C4⋊C4—44no—
60C13×C4⋊C4—81no—
61C13×C22⋊C4—44no—
62C13×C22⋊C4—41no—
63C13×C22⋊C4—41no—
64C42×C13—42no—
65C42×C13—42no—
66C22⋊Dic13—41no—
67C22⋊Dic13—41no—
68C22⋊Dic13—41no—
69C22⋊Dic13—41no—
70C4⋊Dic13—24no—
71C4×Dic13—42no—
72#6099—42no—
73#6099—42no—
74C2×#1055—42no—
75#2607D1311yescharacteristic
76#1826—132no—
77#1820—131no—
78#1306—131no—
79#1284—132no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—42no—
83C23×C13#12011yescharacteristic
84C23×C13C22⋊Q811yescharacteristic
85C23×C13#12411yescharacteristic
86Q8×C13—84no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—24no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13C22⋊Q812yes—
103C2×C4×C13#12412yes—
104C2×Dic13—42no—
105C2×Dic13—82no—
106C2×Dic13—81no—
107C2×Dic13—82no—
108#1055—82no—
109C2×#117—131no—
110#407—132no—
111#399—21no—
112#393—21no—
113#391—22no—
114#387—22no—
115#381—131no—
116#381C2×D1311yescharacteristic
117C4×C22⋊C4C2×D1312yes—
118#342—261no—
119#342—261no—
120#339—262no—
121#339—262no—
122C22×C13—22no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—81no—
128C22×C13—81no—
129C22×C13#39311yescharacteristic
130C22×C13#45811yescharacteristic
131C22×C13#45811yescharacteristic
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—44no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—81no—
138Dic13—82no—
139Dic13—161no—
140C22×Q8—21no—
141C23×C4C22×D1311yescharacteristic
142C2×M16—262no—
143#117—262no—
144#117—262no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—132no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—261no—
150C2×C22⋊C4—261no—
151C2×C22⋊C4C22⋊D1311yescharacteristic
152C2×C22⋊C4C22⋊D1311yescharacteristic
153C2×C42—261no—
154C2×C42C22⋊D1312yes—
155C2×C42C22⋊D1312yes—
156C22⋊C8—262no—
157C22⋊C8—262no—
158#95—21no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—262no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—41no—
167C2×C13—41no—
168C2×C13#203011yescharacteristic
169C2×C13#203112yes—
170C24C2×C22⋊D1311yescharacteristic
171C2×Q8—44no—
172C2×Q8—81no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—262no—
180C22×C4—521no—
181C22×C4Q8×D1311yescharacteristic
182C22×C4#613112yes—
183C22×C4#613111yescharacteristic
184C22×C4C2×C22⋊D1312yes—
185M16—522no—
186M16—522no—
187C2×C8—522no—
188C4⋊C4—44no—
189C4⋊C4—81no—
190C4⋊C4—264no—
191C22⋊C4—44no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—521no—
195C22⋊C4—521no—
196C22⋊C4—521no—
197C22⋊C4—521no—
198C42—42no—
199C42—42no—
200C42—522no—
201C13#1038711yescharacteristic, complemented, Sylow
202C23—21no—
203C23—21no—
204C23—42no—
205C23#8820011yescharacteristic
206C23#8820111yescharacteristic
207C23#8820711yescharacteristic
208Q8—84no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—522no—
225C2×C4—1042no—
226C2×C4—1041no—
227C2×C4—1042no—
228C2×C4#8820012yes—
229C2×C4#8820112yes—
230C8—1042no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1171889211yescharacteristic
239C22#1171890411yescharacteristic
240C22#1171890411yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—82no—
245C4—81no—
246C4—81no—
247C4—1042no—
248C4—2081no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1311600211yescharacteristic
254C2#1311600512yes—
subgroupG/H
centerC22#11718892
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2607C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#2607D13
hypocenterC13#10387
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
32. C2×C4⋊Dic13Q8semidirect
201. C13#10387semidirect

Maximal subgroups

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

subgroupindex
#131149362
#131149112
#131127442
#131126892
C13×#26072
#1038713