Finite Group Databasebeta

← #13124666

Subgroups — #13124666

Order 1664.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719394C211yesmaximal, characteristic, complemented
2#11719250C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic, complemented
4#11718727C211yesmaximal, characteristic, complemented
5#11718668C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718521C211yesmaximal, characteristic, complemented
10#11718503C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718431C211yesmaximal, characteristic
13D13×#102C211yesmaximal, characteristic
14#11718424C211yesmaximal, characteristic, complemented
15#11718422C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C13×#125C2211yescharacteristic, complemented
18C4×D4×C13C2211yescharacteristic
19D4×Dic13C2211yescharacteristic
20C4×C22⋊D13—21no—
21C2×#6103—21no—
22C2×#6094C2211yescharacteristic
23C2×C8×D13C2211yescharacteristic
24#88151—21no—
25#88150—21no—
26#88147C2211yescharacteristic
27#88146C2211yescharacteristic
28#88146C2211yescharacteristic
29C4⋊C4×D13C2211yescharacteristic
30#88144C2211yescharacteristic, complemented
31#88143—21no—
32#88142—21no—
33#88142C2211yescharacteristic, complemented
34#88135—21no—
35C22⋊C4×D13—21no—
36C4×D52C2211yescharacteristic
37#88126C2211yescharacteristic
38#88123C2211yescharacteristic, complemented
39C13×#107C2211yescharacteristic, complemented
40C13×#106C2211yescharacteristic, complemented
41C13×C4⋊C8C2211yescharacteristic, complemented
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88057C2211yescharacteristic, complemented
49#88057C2211yescharacteristic, complemented
50#88054C2211yescharacteristic, complemented
51#88054C2211yescharacteristic, complemented
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic, complemented
55#88047C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64D4×D13—22no—
65D4×D13Q814yescomplemented
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103D411yescharacteristic
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105C8×D13—22no—
106#3081—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13—21no—
109C22×D13—24no—
110C22×D13—81no—
111C22×D13—81no—
112C22×D13C2×D411yescharacteristic
113D4×C13—21no—
114D4×C13C2×Q812yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—24no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—81no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52C2×Q812yes—
132C4×D13—81no—
133C4×D13—81no—
134C4×D13—81no—
135C4×D13C2×Q812yes—
136C4×D13#4112yes—
137Dic26—81no—
138Dic26—81no—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#544—131no—
144#518—131no—
145#478—131no—
146#478—131no—
147#478—131no—
148#478D1311yescharacteristic, complemented
149#476—131no—
150#476—131no—
151#474—131no—
152#474—131no—
153#428—131no—
154#427—131no—
155#424—131no—
156#418—131no—
157C2×#102—131no—
158C22×C13—22no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—22no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—84no—
168C2×D13C22⋊Q812yes—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C22×Q811yescharacteristic
175C4×C13C2×#4111yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13C22⋊Q812yes—
182C22×D4—131no—
183C2×M16—131no—
184C22×C8—131no—
185C4⋊Q8—131no—
186C4⋊Q8—131no—
187C4⋊Q8—261no—
188#125—131no—
189#125—261no—
190#125C2×D1311yescharacteristic, complemented
191C22⋊Q8—261no—
192C22⋊Q8—261no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—131no—
196C4×D4—261no—
197C4×D4—261no—
198C4×D4C2×D1311yescharacteristic
199#117—131no—
200#117—131no—
201#117—131no—
202C2×C4⋊C4—131no—
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107C2×D1311yescharacteristic, complemented
209#106—131no—
210#106—131no—
211#106—131no—
212#106C2×D1311yescharacteristic, complemented
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8—131no—
216C4⋊C8C2×D1311yescharacteristic, complemented
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102C2×D1311yescharacteristic
224#102C2×D1311yescharacteristic
225C2×C13—42no—
226C2×C13C2×C22⋊Q811yescharacteristic
227C2×C13#57611yescharacteristic
228C2×C13#57711yescharacteristic
229D13—22no—
230D13—42no—
231C24—261no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×D4—134no—
235C2×D4—131no—
236C2×D4—262no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245M16—262no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—262no—
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C4⋊C4C22×D1311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—131no—
268C22⋊C4—131no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—131no—
275C42—261no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#308111yescharacteristic, complemented, Sylow
279C23—21no—
280C23—131no—
281C23—264no—
282C23—261no—
283C23—1041no—
284C23—1041no—
285Q8—1041no—
286Q8—1041no—
287D4—21no—
288D4—132no—
289D4—264no—
290D4—261no—
291D4Q8×D1312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—131no—
297C2×C4—132no—
298C2×C4—132no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4D4×D1311yescharacteristic
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—261no—
314C8—261no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—132no—
319C22—261no—
320C22—261no—
321C22—262no—
322C22—521no—
323C22—521no—
324C22—1044no—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—132no—
332C4—261no—
333C4—261no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4C2×Q8×D1311yescharacteristic
338C4#41×D1311yescharacteristic
339C2—42no—
340C2—262no—
341C2—522no—
342C2D13×C22⋊Q811yescharacteristic
343C2#1171947511yescharacteristic
344C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#478D13
hypocenterC13#3081
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11719394C2semidirect
3. C13×#478C2semidirect
4. #11718727C2semidirect
5. #11718668C2semidirect
6. #11718551C2semidirect
7. #11718542C2semidirect
8. #11718532C2semidirect
9. #11718521C2semidirect
10. #11718503C2semidirect
11. #11718500C2semidirect
14. #11718424C2semidirect
15. #11718422C2semidirect
17. C13×#125C22semidirect
30. #88144C22semidirect
33. #88142C22semidirect
38. #88123C22semidirect
39. C13×#107C22semidirect
40. C13×#106C22semidirect
41. C13×C4⋊C8C22semidirect
48. #88057C22semidirect
49. #88057C22semidirect
50. #88054C22semidirect
51. #88054C22semidirect
54. #88048C22semidirect
55. #88047C22semidirect
56. #88047C22semidirect
57. #88047C22semidirect
58. C4⋊#1055C22semidirect
65. D4×D13Q8semidirect
148. #478D13semidirect
190. #125C2×D13semidirect
208. #107C2×D13semidirect
212. #106C2×D13semidirect
216. C4⋊C8C2×D13semidirect
278. C13#3081semidirect

Maximal subgroups

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

subgroupindex
#117193942
#117192502
C13×#4782
#117187272
#117186682
#117185512
#117185422
#117185322
#117185212
#117185032
#117185002
#117184312
D13×#1022
#117184242
#117184222
#308113