Finite Group Databasebeta

← #15751231

Subgroups — #15751231

Order 3328.

468 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117383C211yesmaximal, characteristic
2#13114978C212yesmaximal, complemented
3#13112661C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#1270C211yesmaximal, characteristic
6C2×#88190C411yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8C2×#88141C411yescharacteristic
9C13×#390C2211yescharacteristic
10#11718638C411yescharacteristic
11#11718605—22no—
12C22⋊C4×Dic13—22no—
13C42×Dic13C2211yescharacteristic
14#11718590C2211yescharacteristic
15C13×#336C2212yes—
16#11718142—22no—
17#11718142—22no—
18#11718116C2212yes—
19C22×D4×C13C2×C411yescharacteristic
20C23×Dic13—21no—
21C22×Dic26C2×C411yescharacteristic
22C22×C8×C13—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4—22no—
25C2×C42×C13C2311yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—21no—
28#88190—22no—
29#88190—22no—
30D4×Dic13—42no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C2×C4×Dic13D412yes—
38C22×#1055—22no—
39#88141—42no—
40#88071—22no—
41#88071—22no—
42#7649—131nomaximal, Sylow
43C24×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13M1612yes—
48C22×C4×C13—21no—
49C22×C4×C13C22×C411yescharacteristic
50C22×C4×C13C2×D412yes—
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13—44no—
54C22×Dic13—42no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C2×Dic26—21no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×Dic26M1612yes—
62C2×C8×C13—42no—
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C42×C13—41no—
69C22⋊Dic13—28no—
70C22⋊Dic13—42no—
71C4⋊Dic13—41no—
72#6101—42no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—22no—
78C4×Dic13—42no—
79C4×Dic13—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83C4×#124—131no—
84#1839—132no—
85#1272—132no—
86#1270—131no—
87#1270D1311yescharacteristic
88C23×C13—22no—
89C23×C13—41no—
90C23×C13—41no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13C2×C22⋊C411yescharacteristic
94D4×C13—42no—
95D4×C13—42no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13C2×M1611yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C2×C4×C13#13512yes—
105C2×C4×C13#13512yes—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—42no—
117C2×Dic13—84no—
118C2×Dic13#10012yes—
119Dic26—42no—
120Dic26—42no—
121C8×C13—82no—
122#1055—82no—
123C2×#124—131no—
124C2×C4×Q8—131no—
125C2×C4×D4—131no—
126#391—131no—
127#390C2×D1311yescharacteristic
128#388—262no—
129#382—131no—
130C4×C22⋊C4—262no—
131C43—131no—
132#336—132no—
133#336—262no—
134#336—262no—
135#336C2×D1312yes—
136C22×C13—42no—
137C22×C13—44no—
138C22×C13—81no—
139C22×C13—82no—
140C22×C13—81no—
141C22×C13#40711yescharacteristic
142C22×C13#41011yescharacteristic
143C22×C13C2×#10011yescharacteristic
144C22×C13#41612yes—
145C22×C13#42112yes—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—22no—
149C4×C13—22no—
150C4×C13—81no—
151Dic13—22no—
152Dic13—41no—
153Dic13—42no—
154Dic13—42no—
155Dic13—81no—
156C22×Q8—131no—
157C22×D4C4×D1311yescharacteristic
158C23×C4—261no—
159C22×C8—22no—
160C22×C8—262no—
161#124—262no—
162#124—262no—
163C4×Q8—522no—
164C4×D4—522no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4C4×D1311yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4—262no—
170C2×C22⋊C4—261no—
171C2×C42—131no—
172C2×C42—131no—
173C2×C42—132no—
174C2×C42—132no—
175C2×C42—261no—
176C2×C42C22×D1311yescharacteristic
177#95—262no—
178#95—262no—
179C2×C13—82no—
180C2×C13#146611yescharacteristic
181C2×C13#148812yes—
182C2×C13#152112yes—
183C2×C13#153311yescharacteristic
184C2×C13#154311yescharacteristic
185C24—21no—
186C2×Q8—132no—
187C2×Q8—261no—
188C2×Q8—521no—
189C2×Q8—521no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4#609412yes—
194C22×C4—21no—
195C22×C4—131no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4—522no—
201C22×C4—524no—
202C22×C4C2×C4×D1311yescharacteristic
203C22×C4D4×D1312yes—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—522no—
208C2×C8—522no—
209C2×C8—522no—
210C4⋊C4—41no—
211C4⋊C4—521no—
212C4⋊C4—522no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—268no—
216C22⋊C4—522no—
217C42—41no—
218C42—262no—
219C42—261no—
220C42—261no—
221C42—262no—
222C42—262no—
223C42—522no—
224C42—522no—
225C13#764911yescharacteristic, complemented, Sylow
226C23—22no—
227C23—41no—
228C23—41no—
229C23—42no—
230C23—42no—
231C23C22⋊C4×D1311yescharacteristic
232Q8—522no—
233Q8—522no—
234D4—42no—
235D4—42no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—132no—
243C2×C4—262no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—522no—
254C2×C4—1044no—
255C2×C4C2×#609411yescharacteristic
256C2×C4M16×D1311yescharacteristic
257C2×C4#8816612yes—
258C2×C4#8817012yes—
259C8—82no—
260C8—1042no—
261C22—42no—
262C22—44no—
263C22—82no—
264C22—81no—
265C22—81no—
266C22#1171838711yescharacteristic
267C22#1171840111yescharacteristic
268C22D13×#10011yescharacteristic
269C22#1171843312yes—
270C22#1171848212yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—81no—
276C4—262no—
277C4—522no—
278C4—521no—
279C4—522no—
280C4—1041no—
281C2—82no—
282C2#1311317511yescharacteristic
283C2#1311326712yes—
284C2#1311341012yes—
285C2#1311345811yescharacteristic
286C2#1311349511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1270C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#1270D13
hypocenterC13#7649
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13114978C2semidirect
3. #13112661C2semidirect
225. C13#7649semidirect

Maximal subgroups

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

subgroupindex
#131173832
#131149782
#131126612
#131126572
C13×#12702
#764913