Finite Group Databasebeta

← #15773620

Subgroups — #15773620

Order 3328.

488 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120586C211yesmaximal, characteristic
2#13114919C211yesmaximal, characteristic, complemented
3#13112840C214yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic, complemented
5C2×C13×#117C2211yescharacteristic
6C2×#88184—21no—
7C2×#88128C411yescharacteristic
8C13×#432—21no—
9#11718868—21no—
10#11718652—21no—
11#11718652C2212yes—
12#11718621—21no—
13#11718621C412yes—
14#11718600—21no—
15#11718597C411yescharacteristic
16C13×#324C2212yes—
17C13×#323—21no—
18#11718122—21no—
19#11718122C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×C22⋊D13—22no—
22C22×D52—21no—
23C22×D52—21no—
24C22×D52C2×C412yes—
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33#88184—44no—
34C2×#6103—22no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×#6099—22no—
39#88128—41no—
40#88128—41no—
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×#97—41no—
44#88071—21no—
45#88071C2×C412yes—
46C22⋊#1055—41no—
47C22⋊#1055—41no—
48#11806—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C23×D13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—41no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C2×C22⋊D13—44no—
62C2×C22⋊D13—82no—
63C2×C22⋊D13—82no—
64C22×Dic13—22no—
65C2×D52—42no—
66C2×D52—42no—
67C2×D52—42no—
68C2×D52—42no—
69C2×D52—41no—
70C2×D52—41no—
71C2×D52—82no—
72C2×D52—82no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82#6103—44no—
83#6103—82no—
84#6103—82no—
85C4⋊Dic13—42no—
86#6099—42no—
87#6099—42no—
88C2×#1055—42no—
89#2619—131no—
90#1822—131no—
91#1464D1311yescharacteristic, complemented
92#1345—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C22×D13—42no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—42no—
105C22×D13—42no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)12yes—
123C22⋊D13—88no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127D52—82no—
128D52—82no—
129D52—84no—
130D52—84no—
131C8×C13—82no—
132#1055—82no—
133C2×#127—131no—
134C2×#121—261no—
135C2×#117C2×D1311yescharacteristic
136#432—21no—
137#407—261no—
138#394—132no—
139#394—261no—
140#392—132no—
141#392—261no—
142#390—261no—
143#382—131no—
144#343—132no—
145#343—261no—
146#324C2×D1312yes—
147#323—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—42no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—81no—
155C22×C13C2×#9911yescharacteristic
156C22×C13#41811yescharacteristic
157C22×C13#42111yescharacteristic
158C2×D13—82no—
159C2×D13—82no—
160C2×D13—82no—
161C2×D13—82no—
162C2×D13—82no—
163C2×D13—82no—
164C2×D13—82no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172Dic13—82no—
173C22×D4—132no—
174C22×D4—262no—
175C22×D4—261no—
176C22×D4—261no—
177C23×C4D5211yescharacteristic
178C2×M16—262no—
179#127—521no—
180#127—521no—
181#121—524no—
182#117—41no—
183#117—41no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4D5211yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—262no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4C4×D1311yescharacteristic
191C2×C22⋊C4C22⋊D1311yescharacteristic
192C2×C42C4×D1311yescharacteristic
193C2×C42C22⋊D1311yescharacteristic
194C4⋊C8—41no—
195C22⋊C8—22no—
196C22⋊C8—521no—
197C22⋊C8—521no—
198#97—41no—
199#95—132no—
200#95—261no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—81no—
204C2×C13#151011yescharacteristic
205C2×C13#212211yescharacteristic
206C2×C13#213411yescharacteristic
207D13—162no—
208C24—262no—
209C24#610311yescharacteristic
210C2×D4—522no—
211C2×D4—522no—
212C2×D4—522no—
213C2×D4—522no—
214C2×D4—524no—
215C2×D4—521no—
216C2×D4—521no—
217C2×D4—1042no—
218C2×D4—1042no—
219C2×D4—1042no—
220C2×D4—1042no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—262no—
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4C2×C4×D1311yescharacteristic
230C22×C4C2×D5211yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—522no—
233M16—522no—
234C2×C8—42no—
235C2×C8—522no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—522no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—524no—
242C22⋊C4—1042no—
243C22⋊C4—1042no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C13#1180611yescharacteristic, complemented, Sylow
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—522no—
255C23—522no—
256C23—522no—
257C23—522no—
258C23—522no—
259C23—522no—
260C23—522no—
261C23C2×#610311yescharacteristic
262D4—1042no—
263D4—1042no—
264D4—1044no—
265D4—1044no—
266D4—1048no—
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—522no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4#8804611yescharacteristic
285C2×C4#8804611yescharacteristic
286C2×C4#8816212yes—
287C8—82no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—1042no—
297C22—1042no—
298C22—1042no—
299C22—1042no—
300C22—1042no—
301C22—1042no—
302C22—1042no—
303C22C2×#8804611yescharacteristic
304C22#1171879211yescharacteristic
305C22#1171880011yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1042no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—2082no—
318C2#1311336611yescharacteristic
319C2#1311648511yescharacteristic
320C2#1311652711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
prime radical#13120586C2
cosocleC2×C13×C4⋊C4C23
hypercenter#1464D13
hypocenterC13#11806
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13114919C2semidirect
3. #13112840C2semidirect
4. C13×#1464C2semidirect
91. #1464D13semidirect
248. C13#11806semidirect

Maximal subgroups

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

subgroupindex
#131205862
#131149192
#131128402
C13×#14642
#1180613