Finite Group Databasebeta

← #15772208

Subgroups — #15772208

Order 3328.

440 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 87 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#13117544C211yesmaximal, characteristic
2#13113158C212yesmaximal, complemented
3#13112782C211yesmaximal, characteristic, complemented
4#13112767C212yesmaximal
5C13×#1325C211yesmaximal, characteristic, complemented
6C2×#88147C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×#88129C411yescharacteristic
9C13×#384C2211yescharacteristic
10#11718651—22no—
11#11718650—22no—
12#11718649C2211yescharacteristic
13#11718635C411yescharacteristic
14#11718593C411yescharacteristic
15#11718379—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×D52C2×C411yescharacteristic
20C22×C4×D13—21no—
21C22×Dic26C2×C411yescharacteristic
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C4⋊C4C2311yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×#6103—22no—
27C2×#6103—21no—
28C2×#6103—22no—
29C2×#6101D412yes—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D412yes—
33#88147—42no—
34#88141—42no—
35#88129—22no—
36#88129C814yescomplemented
37C13×C22⋊C8—22no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41C22⋊#1055—22no—
42#88054—42no—
43C8×Dic13—42no—
44#11480—131nomaximal, Sylow
45C23×D13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22×C411yescharacteristic
49C22×C4×C13C2×D412yes—
50C22×Dic13—21no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C411yescharacteristic
54C2×D52—21no—
55C2×D52—41no—
56C2×D52—41no—
57C2×D52C2×C812yes—
58C2×C4×D13—42no—
59C2×C4×D13—82no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C2×C812yes—
63C2×Dic26M1612yes—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—82no—
68C42×C13—21no—
69C42×C13C2×C812yes—
70#6103—28no—
71#6103—42no—
72#6103—82no—
73#6101—42no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—41no—
78C2×#1055—42no—
79#2326—131no—
80#1461—132no—
81#1325—131no—
82#1325D1311yescharacteristic, complemented
83#1318—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—42no—
88C22×D13—41no—
89C22×D13—41no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13C22×C811yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—41no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13C22⋊C814yes—
110C2×Dic13#9912yes—
111D52—42no—
112D52—42no—
113C4×D13—84no—
114Dic26—42no—
115Dic26—42no—
116C8×C13—82no—
117#1055—82no—
118C2×#124—131no—
119C2×C4×Q8—131no—
120C2×C4×D4—131no—
121#431—262no—
122#391—131no—
123#390—131no—
124#388—262no—
125#385—262no—
126#384C2×D1311yescharacteristic
127#376—131no—
128#324—132no—
129#324—262no—
130#324C2×D1312yes—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13C2×C22⋊C811yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13#41311yescharacteristic
136C2×D13—44no—
137C2×D13—42no—
138C2×D13—82no—
139C2×D13—81no—
140C2×D13—81no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—42no—
144C4×C13—42no—
145C4×C13—81no—
146Dic13—22no—
147Dic13—24no—
148Dic13—41no—
149Dic13—81no—
150C22×Q8—131no—
151C22×D4—131no—
152C23×C4—261no—
153#124—134no—
154#124—262no—
155C4×Q8—522no—
156C4×D4—522no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4C4×D1311yescharacteristic
160C2×C4⋊C4C22×D1311yescharacteristic
161C2×C22⋊C4—262no—
162C2×C22⋊C4—261no—
163C2×C22⋊C4—262no—
164C2×C42—131no—
165C2×C42—132no—
166C2×C42—131no—
167C2×C42C4×D1311yescharacteristic
168C4⋊C8—522no—
169C22⋊C8—22no—
170C22⋊C8—262no—
171C4×C8—522no—
172#95—261no—
173#95—261no—
174#95—262no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13#145911yescharacteristic
178C2×C13#212811yescharacteristic
179C2×C13#213311yescharacteristic
180D13—82no—
181C24—261no—
182C2×Q8—132no—
183C2×Q8—132no—
184C2×Q8—521no—
185C2×Q8—521no—
186C2×D4—132no—
187C2×D4—261no—
188C2×D4—521no—
189C2×D4—521no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—132no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—261no—
196C22×C4—522no—
197C22×C4—1042no—
198C22×C4C2×C4×D1311yescharacteristic
199C22×C4D4×D1312yes—
200C2×C8—42no—
201C2×C8—522no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—522no—
206C22⋊C4—268no—
207C22⋊C4—522no—
208C22⋊C4—1042no—
209C42—21no—
210C42—262no—
211C42—262no—
212C42—262no—
213C42—521no—
214C42C8×D1312yes—
215C13#1148011yescharacteristic, complemented, Sylow
216C23—262no—
217C23—522no—
218C23—522no—
219C23—521no—
220C23—521no—
221C23C22⋊C4×D1311yescharacteristic
222Q8—522no—
223Q8—522no—
224D4—522no—
225D4—522no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—132no—
236C2×C4—134no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—1044no—
246C2×C4C2×C8×D1311yescharacteristic
247C2×C4M16×D1311yescharacteristic
248C8—82no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22—524no—
253C22—522no—
254C22—1042no—
255C22—1041no—
256C22—1041no—
257C22D13×C22⋊C811yescharacteristic
258C22D13×#9911yescharacteristic
259C22#1171841211yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4—264no—
266C4—262no—
267C4—521no—
268C4—1041no—
269C2—21no—
270C2—21no—
271C2—1042no—
272C2#1311315311yescharacteristic
273C2#1311650611yescharacteristic
274C2#1311652411yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1325C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1325D13
hypocenterC13#11480
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #13113158C2semidirect
3. #13112782C2semidirect
5. C13×#1325C2semidirect
36. #88129C8semidirect
82. #1325D13semidirect
215. C13#11480semidirect

Maximal subgroups

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

subgroupindex
#131175442
#131131582
#131127822
#131127672
C13×#13252
#1148013