Finite Group Databasebeta

← #15773619

Subgroups — #15773619

Order 3328.

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

normal subgroups only

This group has 488 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#13114919C211yesmaximal, characteristic, complemented
2#13113170C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2619C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#121—21no—
7C2×C13×#117C2211yescharacteristic
8C13×#394—21no—
9C13×#394C2212yes—
10C13×#392—21no—
11C13×#392C412yes—
12C13×#390—21no—
13C13×#382C411yescharacteristic
14#11718868—21no—
15#11718587—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13—22no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C23×C4×C13D411yescharacteristic
25C13×#127—41no—
26C13×#127—41no—
27C13×#121—44no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×#6099—22no—
41C13×#95—21no—
42C13×#95C2×C412yes—
43C22⋊#1055—22no—
44C22⋊#1055—41no—
45C22⋊#1055—41no—
46C4⋊#1055—41no—
47#88043—41no—
48#11806—131nomaximal, Sylow
49C24×C13—22no—
50C24×C13C22⋊C411yescharacteristic
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—42no—
55C2×D4×C13—44no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—82no—
59C2×D4×C13—82no—
60C2×D4×C13—82no—
61C2×D4×C13—82no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—82no—
80C13×C22⋊C4—82no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85#6099—42no—
86#6099—42no—
87C2×#1055—42no—
88C2×#1055—42no—
89#2619D1311yescharacteristic
90#1822—131no—
91#1464—131no—
92#1345—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13C2×C22⋊C411yescharacteristic
106D4×C13—82no—
107D4×C13—82no—
108D4×C13—84no—
109D4×C13—84no—
110D4×C13—88no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)12yes—
131#1055—82no—
132#1055—82no—
133C2×#127Dic1311yescharacteristic
134C2×#121—21no—
135C2×#117C2×D1311yescharacteristic
136#432—261no—
137#407—261no—
138#394—21no—
139#394C2×D1312yes—
140#392—21no—
141#392Dic1312yes—
142#390—21no—
143#382Dic1311yescharacteristic
144#343—132no—
145#343—261no—
146#324—132no—
147#323—261no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—42no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—81no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—82no—
160C22×C13—82no—
161C22×C13—82no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41811yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—82no—
173C22×D4—22no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4C2×Dic1312yes—
177C23×C4C22⋊D1311yescharacteristic
178C2×M16—262no—
179#127—41no—
180#127—41no—
181#121—44no—
182#117—41no—
183#117—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4C2×Dic1311yescharacteristic
191C2×C22⋊C4C22⋊D1311yescharacteristic
192C2×C42C2×Dic1311yescharacteristic
193C2×C42C22⋊D1311yescharacteristic
194C4⋊C8—521no—
195C22⋊C8—262no—
196C22⋊C8—521no—
197C22⋊C8—521no—
198#97—521no—
199#95—21no—
200#95C2×Dic1312yes—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—81no—
204C2×C13—162no—
205C2×C13#151011yescharacteristic
206C2×C13#212211yescharacteristic
207C2×C13#213411yescharacteristic
208C24—22no—
209C24C22⋊Dic1311yescharacteristic
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—44no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—82no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4—82no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—522no—
233M16—522no—
234C2×C8—522no—
235C2×C8—522no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—44no—
242C22⋊C4—82no—
243C22⋊C4—82no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C13#1180611yescharacteristic, complemented, Sylow
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23C2×C22⋊Dic1311yescharacteristic
262D4—82no—
263D4—82no—
264D4—84no—
265D4—84no—
266D4—88no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4#8807411yescharacteristic
285C2×C4#8807411yescharacteristic
286C2×C4#8818612yes—
287C8—1042no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—82no—
303C22#1171887611yescharacteristic
304C22C2×#8807411yescharacteristic
305C22#1171889711yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—162no—
318C2#1311336511yescharacteristic
319C2#1311648611yescharacteristic
320C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2619C2
socleC22×C13C2×#99
cosocleC2×C13×C4⋊C4C23
hypercenter#2619D13
hypocenterC13#11806
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. #13114919C2semidirect
2. #13113170C2semidirect
3. #13112839C2semidirect
248. C13#11806semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131131702
#131128392
C13×#26192
#1180613