Finite Group Databasebeta

← #15773592

Subgroups — #15773592

Order 3328.

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

normal subgroups only

This group has 502 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#13113170C211yesmaximal, characteristic, complemented
3#13112832C214yesmaximal, complemented
4C13×#1820C211yesmaximal, characteristic, complemented
5C2×C13×#117C2211yescharacteristic
6C2×#88184—21no—
7C2×#88128C411yescharacteristic, complemented
8C13×#381—21no—
9#11718652—21no—
10#11718652C412yescomplemented
11#11718621—21no—
12#11718621C2212yes—
13#11718600—21no—
14#11718597C411yescharacteristic, complemented
15#11718587—21no—
16C13×#342—21no—
17C13×#342C2212yes—
18#11718120—21no—
19#11718117C2212yes—
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⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2311yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34#88184—44no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×C4⋊Dic13—21no—
39#88128—41no—
40#88128—41no—
41C13×#95—41no—
42C13×#95—41no—
43#88071—21no—
44#88071C2×C412yes—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47#88043—41no—
48#11800—131nomaximal, Sylow
49C24×C13C2×D411yescharacteristic
50C23×D13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—41no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C2×C22⋊D13—44no—
63C2×C22⋊D13—82no—
64C2×C22⋊D13—82no—
65C22×Dic13—22no—
66C2×D52—42no—
67C2×D52—42no—
68C2×D52—42no—
69C2×D52—42no—
70C2×D52—41no—
71C2×D52—41no—
72C2×D52—82no—
73C2×D52—82no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84#6103—44no—
85#6103—82no—
86#6103—82no—
87C4⋊Dic13—42no—
88C2×#1055—42no—
89#2619—131no—
90#1820D1311yescharacteristic, complemented
91#1464—131no—
92#1343—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13AGL(1,ℤ/8)12yes—
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—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—82no—
122C2×C4×C13—82no—
123C2×C4×C13—82no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C22⋊D13—88no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130D52—82no—
131D52—82no—
132D52—84no—
133D52—84no—
134#1055—82no—
135C2×#127—131no—
136C2×#121—261no—
137C2×#117C2×D1311yescharacteristic
138#432—261no—
139#394—132no—
140#394—261no—
141#392—132no—
142#392—261no—
143#390—261no—
144#382—131no—
145#381—21no—
146#342—21no—
147#342C2×D1312yes—
148#324—261no—
149#323—132no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13C2×#9911yescharacteristic
158C22×C13#41811yescharacteristic
159C22×C13#42111yescharacteristic
160C2×D13—82no—
161C2×D13—82no—
162C2×D13—82no—
163C2×D13—82no—
164C2×D13—82no—
165C2×D13—82no—
166C2×D13—82no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—162no—
175Dic13—82no—
176C22×D4—132no—
177C22×D4—262no—
178C22×D4—261no—
179C22×D4—261no—
180C23×C4C22⋊D1311yescharacteristic
181#127—521no—
182#127—521no—
183#121—524no—
184#117—41no—
185#117—41no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4C4×D1311yescharacteristic
188C2×C4⋊C4D5211yescharacteristic
189C2×C22⋊C4—22no—
190C2×C22⋊C4—262no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4C22×D1311yescharacteristic
195C2×C42C4×D1311yescharacteristic
196C2×C42D5211yescharacteristic
197C4⋊C8—521no—
198C22⋊C8—262no—
199#97—521no—
200#95—41no—
201#95—41no—
202#95—132no—
203#95—261no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13#151011yescharacteristic
208C2×C13#212211yescharacteristic
209C2×C13#212811yescharacteristic
210D13—162no—
211C24—262no—
212C24C2×C22⋊D1311yescharacteristic
213C2×D4—522no—
214C2×D4—522no—
215C2×D4—522no—
216C2×D4—522no—
217C2×D4—524no—
218C2×D4—521no—
219C2×D4—521no—
220C2×D4—1042no—
221C2×D4—1042no—
222C2×D4—1042no—
223C2×D4—1042no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—42no—
229C22×C4—262no—
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4C2×C4×D1311yescharacteristic
235C22×C4C2×D5211yescharacteristic
236C2×C8—522no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—522no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—524no—
245C22⋊C4—1042no—
246C22⋊C4—1042no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C13#1180011yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—522no—
257C23—522no—
258C23—522no—
259C23—522no—
260C23—522no—
261C23—522no—
262C23—522no—
263C23C2×#610311yescharacteristic
264C23#8820312yes—
265D4—1042no—
266D4—1042no—
267D4—1044no—
268D4—1044no—
269D4—1048no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4#8804611yescharacteristic
292C2×C4#8804611yescharacteristic
293C8—1042no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—81no—
301C22—1042no—
302C22—1042no—
303C22—1042no—
304C22—1042no—
305C22—1042no—
306C22—1042no—
307C22—1042no—
308C22C2×#8804611yescharacteristic
309C22#1171866211yescharacteristic
310C22#1171866611yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—162no—
319C4—1042no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—2082no—
324C2#1311336411yescharacteristic
325C2#1311648511yescharacteristic
326C2#1311650711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1820C2
socleC22×C13C2×#99
prime radical#13120586C2
cosocleC2×C13×C22⋊C4C23
hypercenter#1820D13
hypocenterC13#11800
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #13113170C2semidirect
3. #13112832C2semidirect
4. C13×#1820C2semidirect
7. C2×#88128C4semidirect
10. #11718652C4semidirect
14. #11718597C4semidirect
90. #1820D13semidirect
251. C13#11800semidirect

Maximal subgroups

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

subgroupindex
#131205862
#131131702
#131128322
C13×#18202
#1180013