Finite Group Databasebeta

← #13125752

Subgroups — #13125752

Order 1664.

532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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×#88194C211yesmaximal, characteristic, complemented
2#11719301C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic, complemented
5#11718812C212yesmaximal, complemented
6#11718811C212yesmaximal, complemented
7#11718697C211yesmaximal, characteristic, complemented
8#11718447C212yesmaximal, complemented
9#11718421C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C22×C22⋊D13—21no—
15C2×#6129—21no—
16C22×D52C2211yescharacteristic
17C2×C13×D8C2212yescomplemented
18C13×#121C2211yescharacteristic
19#88194—21no—
20#88194—21no—
21#88194C2212yes—
22#88194C2212yes—
23#88194C2211yescharacteristic, complemented
24#88193—21no—
25D4×Dic13C2211yescharacteristic, complemented
26C2×#6104C2212yescomplemented
27C2×#6104C2212yescomplemented
28#88184C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30C2×D104C2212yescomplemented
31#88147C2211yescharacteristic, complemented
32#88142C2211yescharacteristic, complemented
33#88139—21no—
34#88135—21no—
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yescomplemented
40#88054C2212yescomplemented
41C8×Dic13C2212yescomplemented
42#88049C2212yescomplemented
43C24×C13—21no—
44C23×D13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13C2312yes—
49C2×D4×C13C2311yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—22no—
56C2×C22⋊D13—22no—
57C2×C22⋊D13—22no—
58C2×C22⋊D13—44no—
59C2×C22⋊D13—44no—
60C22×Dic13—21no—
61C22×Dic13D411yescharacteristic
62C22×Dic13D411yescharacteristic
63#6129—44no—
64C2×D52—21no—
65C2×D52—42no—
66C2×D52C2311yescharacteristic
67C2×D52C2312yes—
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C13×D8—42no—
71C2×C8×C13C2312yes—
72C13×C4⋊C4C2311yescharacteristic
73C13×C22⋊C4—21no—
74C22⋊Dic13—21no—
75#6104—42no—
76#6104—42no—
77#6103—21no—
78#6103—21no—
79C4⋊Dic13C2311yescharacteristic
80#6101—21no—
81C4×Dic13D411yescharacteristic
82C4×Dic13D411yescharacteristic
83C4×Dic13C2311yescharacteristic
84C4×Dic13C2311yescharacteristic
85C2×#1055C2312yes—
86D104—42no—
87#3205—131nomaximal, Sylow
88C23×C13—21no—
89C23×C13—22no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13C2×D411yescharacteristic
94C22×D13—21no—
95C22×D13—22no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13—42no—
99D4×C13—22no—
100D4×C13—22no—
101D4×C13—22no—
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—44no—
109C22⋊D13—42no—
110C22⋊D13—42no—
111C22⋊D13—44no—
112C22⋊D13—44no—
113C22⋊D13—42no—
114C22⋊D13—44no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—42no—
118C2×Dic13D814yescomplemented
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123D52—22no—
124D52—22no—
125D52—22no—
126D52—42no—
127C4×D13—42no—
128Dic26—42no—
129C8×C13—22no—
130#1055—22no—
131#532—131no—
132C2×#127—131no—
133#493—132no—
134#486—132no—
135#459—132no—
136#459—132no—
137#447—131no—
138#447—131no—
139#447—131no—
140#447D1311yescharacteristic, complemented
141#431—131no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—42no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—41no—
150C22×C13—84no—
151C22×C13C2×D812yes—
152C22×C13C22×D411yescharacteristic
153C2×D13—42no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—42no—
157C2×D13—42no—
158C2×D13—41no—
159C2×D13—84no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13H(5,𝔽2)12yes—
163Dic13—21no—
164Dic13—41no—
165Dic13C2×D812yes—
166Dic13C2×D812yes—
167Dic13AGL(1,ℤ/8)12yes—
168C2×#41—261no—
169C22×D4—131no—
170C22×D4—261no—
171C22×D4—261no—
172C22×D4C2×D1311yescharacteristic
173C2×D8—132no—
174C2×D8—132no—
175C2×D8—132no—
176C2×D8C2×D1312yescomplemented
177C4⋊Q8—131no—
178#127—132no—
179#127—132no—
180#127—131no—
181#127—261no—
182#127—261no—
183#124—261no—
184#121—131no—
185#121—261no—
186#121C2×D1311yescharacteristic
187C4×D4—131no—
188C4×D4—131no—
189C4×D4—261no—
190C2×C42—131no—
191C4⋊C8—132no—
192#102—132no—
193#102—132no—
194#102—132no—
195#102C2×D1312yescomplemented
196C22⋊C8—131no—
197C22⋊C8C2×D1311yescharacteristic
198C4×C8—132no—
199C2×C13—22no—
200C2×C13—81no—
201C2×C13—82no—
202C2×C13#53511yescharacteristic
203C2×C13C22×D811yescharacteristic
204C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
205D13—81no—
206D13—82no—
207C24—21no—
208C24—261no—
209#41—524no—
210C2×Q8—261no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—42no—
214C2×D4—132no—
215C2×D4—131no—
216C2×D4—261no—
217C2×D4—261no—
218C2×D4—262no—
219C2×D4—262no—
220C2×D4—262no—
221C2×D4—262no—
222C2×D4—261no—
223C2×D4—261no—
224C2×D4—522no—
225C2×D4—524no—
226C2×D4—524no—
227C2×D4C22×D1312yes—
228C2×D4C22×D1311yescharacteristic
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4C22×D1311yescharacteristic
234D8—42no—
235D8—522no—
236D8—522no—
237D8—522no—
238C2×C8—132no—
239C2×C8C22×D1312yes—
240C4⋊C4—131no—
241C4⋊C4—261no—
242C4⋊C4C22×D1311yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—261no—
245C22⋊C4—261no—
246C22⋊C4—261no—
247C42—131no—
248C42—131no—
249C42—131no—
250C42—131no—
251C13#320511yescharacteristic, complemented, Sylow
252C23—21no—
253C23—22no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—261no—
258C23—262no—
259C23—522no—
260C23—522no—
261C23—522no—
262C23D4×D1311yescharacteristic
263Q8—522no—
264D4—22no—
265D4—22no—
266D4—22no—
267D4—42no—
268D4—42no—
269D4—262no—
270D4—262no—
271D4—262no—
272D4—522no—
273D4—522no—
274D4—524no—
275D4—524no—
276D4—524no—
277D4—522no—
278D4—524no—
279D4—522no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—134no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—262no—
288C2×C4—261no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—22no—
294C8—262no—
295C22—21no—
296C22—21no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—41no—
303C22—84no—
304C22—521no—
305C22—522no—
306C22—522no—
307C22—521no—
308C22—522no—
309C22—521no—
310C22—1044no—
311C22D8×D1312yes—
312C22C2×D4×D1311yescharacteristic
313C4—21no—
314C4—41no—
315C4—132no—
316C4—132no—
317C4—132no—
318C4—261no—
319C4—521no—
320C4#8825112yes—
321C2—22no—
322C2—82no—
323C2—81no—
324C2—1042no—
325C2—1041no—
326C2#1171929711yescharacteristic
327C2C2×D8×D1311yescharacteristic
328C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3205
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×#88194C2semidirect
2. #11719301C2semidirect
3. C13×#447C2semidirect
4. #11718878C2semidirect
5. #11718812C2semidirect
6. #11718811C2semidirect
7. #11718697C2semidirect
8. #11718447C2semidirect
9. #11718421C2semidirect
10. #11718393C2semidirect
11. #11718379C2semidirect
17. C2×C13×D8C22semidirect
23. #88194C22semidirect
25. D4×Dic13C22semidirect
26. C2×#6104C22semidirect
27. C2×#6104C22semidirect
30. C2×D104C22semidirect
31. #88147C22semidirect
32. #88142C22semidirect
35. C13×#102C22semidirect
37. #88072C22semidirect
39. #88061C22semidirect
40. #88054C22semidirect
41. C8×Dic13C22semidirect
42. #88049C22semidirect
118. C2×Dic13D8semidirect
140. #447D13semidirect
176. C2×D8C2×D13semidirect
195. #102C2×D13semidirect
251. C13#3205semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
#117193012
C13×#4472
#117188782
#117188122
#117188112
#117186972
#117184472
#117184212
#117183932
#117183792
#320513