Finite Group Databasebeta

← #13125585

Subgroups — #13125585

Order 1664.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#88192C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic, complemented
5#11718818C212yesmaximal, complemented
6#11718817C212yesmaximal, complemented
7#11718694C211yesmaximal, characteristic, complemented
8#11718436C212yesmaximal, complemented
9#11718435C212yesmaximal, complemented
10#11718397C211yesmaximal, characteristic, complemented
11D13×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic, complemented
13C22×C22⋊D13—21no—
14C2×D4×D13—21no—
15C2×D4×D13C2211yescharacteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C2×C13×D8C2212yescomplemented
18C13×#121C2211yescharacteristic
19C2×C22⋊Dic13—21no—
20#88193—21no—
21#88192—21no—
22#88192—21no—
23#88192C2212yes—
24#88192C2212yescomplemented
25#88192C2211yescharacteristic, complemented
26C2×#6104C2212yescomplemented
27#88184C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic, complemented
29C2×C8×D13C2212yescomplemented
30#88149C2211yescharacteristic, complemented
31C4⋊C4×D13C2211yescharacteristic, complemented
32#88138—21no—
33C22⋊C4×D13—21no—
34C13×#102C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic, complemented
36#88072C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic, complemented
39#88061C2212yescomplemented
40#88060C2212yescomplemented
41#88058C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13—21no—
44C23×D13—21no—
45C23×D13D411yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—42no—
49C2×D4×C13C2311yescharacteristic
50C2×D4×C13C2312yes—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—22no—
56C2×C22⋊D13—21no—
57C2×C22⋊D13—44no—
58C22×Dic13—21no—
59C22×Dic13D411yescharacteristic
60D4×D13—42no—
61D4×D13—44no—
62C2×D52—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—42no—
66C2×C4×D13D411yescharacteristic
67C2×C4×D13D411yescharacteristic
68C2×C4×D13C2311yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C13×D8—42no—
71C2×C8×C13C2312yes—
72C13×C4⋊C4C2311yescharacteristic
73C13×C22⋊C4—21no—
74C22⋊Dic13—21no—
75C22⋊Dic13—22no—
76C22⋊Dic13—22no—
77#6104—42no—
78#6103—21no—
79#6103—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13C2311yescharacteristic
82C4⋊Dic13C2312yes—
83#6101—21no—
84C2×#1055C2312yes—
85C8×D13—42no—
86#3186—131nomaximal, Sylow
87C23×C13—22no—
88C23×C13—21no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13C2×D411yescharacteristic
93C22×D13—21no—
94C22×D13—41no—
95C22×D13—41no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13—42no—
99C22×D13D814yescomplemented
100C22×D13C2×D411yescharacteristic
101C22×D13C2×D411yescharacteristic
102D4×C13—22no—
103D4×C13—22no—
104D4×C13—22no—
105D4×C13—42no—
106D4×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2411yescharacteristic
111C22⋊D13—42no—
112C22⋊D13—42no—
113C22⋊D13—42no—
114C22⋊D13—44no—
115C22⋊D13—44no—
116C2×Dic13—21no—
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122D52—22no—
123D52—42no—
124C4×D13—22no—
125C4×D13—22no—
126C4×D13—41no—
127C4×D13—41no—
128C4×D13—42no—
129C8×C13—22no—
130#1055—22no—
131C2×#121—131no—
132C2×#121—131no—
133#480—131no—
134#480—132no—
135#480—131no—
136#466—132no—
137#466—132no—
138#447—131no—
139#447—132no—
140#447D1311yescharacteristic, complemented
141C2×C22⋊C8—131no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—41no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—42no—
150C22×C13—84no—
151C22×C13C2×D812yes—
152C22×C13C22×D411yescharacteristic
153C2×D13—21no—
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—44no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—84no—
162C2×D13C2×D812yes—
163C2×D13C2×D812yes—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13H(5,𝔽2)12yes—
167Dic13—21no—
168Dic13—21no—
169Dic13—41no—
170Dic13—42no—
171C22×D4—131no—
172C22×D4—261no—
173C22×D4—261no—
174C22×D4C2×D1311yescharacteristic, complemented
175C23×C4—131no—
176C2×D8—132no—
177C2×D8C2×D1312yescomplemented
178C22×C8—132no—
179#121—132no—
180#121—131no—
181#121—132no—
182#121—131no—
183#121—131no—
184#121—261no—
185#121—261no—
186#121—261no—
187#121—261no—
188#121C2×D1311yescharacteristic
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C22⋊C4—261no—
192C2×C22⋊C4—261no—
193#107—132no—
194#107—132no—
195#102—132no—
196#102—132no—
197#102—132no—
198#102C2×D1312yescomplemented
199C22⋊C8—131no—
200C22⋊C8—132no—
201C22⋊C8C2×D1311yescharacteristic, complemented
202C2×C13—22no—
203C2×C13—81no—
204C2×C13—82no—
205C2×C13#53411yescharacteristic
206C2×C13C22×D811yescharacteristic
207C2×C13#57511yescharacteristic
208D13—22no—
209D13—22no—
210D13—81no—
211C24—21no—
212C24—131no—
213C24—261no—
214C2×D4—21no—
215C2×D4—21no—
216C2×D4—42no—
217C2×D4—131no—
218C2×D4—261no—
219C2×D4—261no—
220C2×D4—261no—
221C2×D4—262no—
222C2×D4—262no—
223C2×D4—261no—
224C2×D4—522no—
225C2×D4—524no—
226C2×D4—524no—
227C2×D4C22×D1311yescharacteristic
228C2×D4C22×D1312yes—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—522no—
237C22×C4C22×D1311yescharacteristic
238D8—42no—
239D8—522no—
240C2×C8—132no—
241C2×C8—522no—
242C2×C8C22×D1312yes—
243C4⋊C4—131no—
244C4⋊C4—132no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4C22×D1311yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—262no—
252C22⋊C4—262no—
253C22⋊C4—261no—
254C13#318611yescharacteristic, complemented, Sylow
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—131no—
261C23—131no—
262C23—134no—
263C23—261no—
264C23—521no—
265C23—521no—
266C23—522no—
267C23—522no—
268C23—522no—
269C23D4×D1311yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—262no—
276D4—522no—
277D4—522no—
278D4—522no—
279D4—524no—
280D4—524no—
281D4—522no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—262no—
287C2×C4—262no—
288C2×C4—262no—
289C2×C4—261no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—522no—
293C2×C4—521no—
294C2×C4—522no—
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—22no—
298C8—262no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—132no—
309C22—132no—
310C22—261no—
311C22—261no—
312C22—261no—
313C22—261no—
314C22—524no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22—1044no—
319C22D8×D1312yes—
320C22C2×D4×D1311yescharacteristic
321C4—21no—
322C4—41no—
323C4—261no—
324C4—261no—
325C4—521no—
326C4—522no—
327C4#8825112yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—262no—
332C2—262no—
333C2—1041no—
334C2#1171929411yescharacteristic
335C2C2×D8×D1311yescharacteristic
336C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3186
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#88192C2semidirect
2. D13×#121C2semidirect
3. C13×#447C2semidirect
4. #11718878C2semidirect
5. #11718818C2semidirect
6. #11718817C2semidirect
7. #11718694C2semidirect
8. #11718436C2semidirect
9. #11718435C2semidirect
10. #11718397C2semidirect
11. D13×C22⋊C8C2semidirect
12. C22×D4×C13C22semidirect
15. C2×D4×D13C22semidirect
17. C2×C13×D8C22semidirect
24. #88192C22semidirect
25. #88192C22semidirect
26. C2×#6104C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C2×C8×D13C22semidirect
30. #88149C22semidirect
31. C4⋊C4×D13C22semidirect
34. C13×#102C22semidirect
35. C13×C22⋊C8C22semidirect
36. #88072C22semidirect
37. #88072C22semidirect
38. C22⋊#1055C22semidirect
39. #88061C22semidirect
40. #88060C22semidirect
41. #88058C22semidirect
42. #88047C22semidirect
99. C22×D13D8semidirect
140. #447D13semidirect
174. C22×D4C2×D13semidirect
177. C2×D8C2×D13semidirect
198. #102C2×D13semidirect
201. C22⋊C8C2×D13semidirect
254. C13#3186semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
D13×#1212
C13×#4472
#117188782
#117188182
#117188172
#117186942
#117184362
#117184352
#117183972
D13×C22⋊C82
#318613