Finite Group Databasebeta

← #13127053

Subgroups — #13127053

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719534C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718789C211yesmaximal, characteristic, complemented
7#11718629C211yesmaximal, characteristic, complemented
8#11718477C211yesmaximal, characteristic, complemented
9#11718475C211yesmaximal, characteristic, complemented
10#11718461C211yesmaximal, characteristic, complemented
11#11718459C211yesmaximal, characteristic, complemented
12#11718437C211yesmaximal, characteristic, complemented
13#11718431C211yesmaximal, characteristic, complemented
14#11718427C211yesmaximal, characteristic, complemented
15#11718419C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic, complemented
19C2×C13×C4⋊C4C2211yescharacteristic, complemented
20#88201C2211yescharacteristic
21#88200C2211yescharacteristic
22C2×#6107C2211yescharacteristic, complemented
23#88193—21no—
24#88191—21no—
25D4×Dic13C2211yescharacteristic
26C2×#6105C2211yescharacteristic
27#88184C2211yescharacteristic
28#88183—21no—
29#88183—21no—
30C4×C22⋊D13C2211yescharacteristic
31C2×#6103—21no—
32#88180—21no—
33#88178C2211yescharacteristic, complemented
34C2×#6095C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36#88152—21no—
37#88151C2211yescharacteristic
38#88146C2211yescharacteristic
39#88144C2211yescharacteristic, complemented
40#88143—21no—
41#88141C2211yescharacteristic, complemented
42C13×#103C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic, complemented
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic, complemented
52#88056C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54C8×Dic13C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C23×D13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13D411yescharacteristic
71C22×Dic13—21no—
72D4×D13—22no—
73D4×D13—41no—
74C2×D52C2311yescharacteristic
75C2×C4×D13C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C13×M16—41no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13D411yescharacteristic
86#6107—41no—
87#6105—22no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—41no—
110#6094—41no—
111#3323—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—42no—
116C22×D13—42no—
117C22×D13—81no—
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121D4×C13—21no—
122D4×C13—42no—
123D4×C13#4112yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—41no—
134C22⋊D13—42no—
135C22⋊D13—81no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—81no—
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143D52—21no—
144D52—21no—
145C4×D13—21no—
146C4×D13—21no—
147Dic26—21no—
148Dic26—21no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#552—131no—
154#546—131no—
155#488—131no—
156#485—131no—
157#481—131no—
158#478—131no—
159#470—131no—
160#468—131no—
161#464—131no—
162#452—131no—
163#450—131no—
164C4×SD16—131no—
165#436—131no—
166#418—131no—
167#417D1311yescharacteristic, complemented
168C22×C13—22no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—84no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13C2×#4111yescharacteristic
187C4×C13H(5,𝔽2)11yescharacteristic
188Dic13—21no—
189Dic13—21no—
190Dic13—21no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194C2×#41C2×D1311yescharacteristic
195C22×D4—131no—
196C2×Q16—131no—
197C2×SD16—131no—
198C2×SD16—131no—
199C2×M16—131no—
200C2×M16C2×D1311yescharacteristic, complemented
201#126—261no—
202#125—131no—
203#125—261no—
204#124—131no—
205#123—261no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—131no—
210#121—131no—
211#121—261no—
212#120—261no—
213C4×Q8—131no—
214C4×D4—131no—
215C4×D4—131no—
216#117—131no—
217#117—261no—
218C2×C4⋊C4C2×D1311yescharacteristic, complemented
219C2×C22⋊C4—261no—
220#107—131no—
221#106—131no—
222#106—131no—
223C4⋊C8—131no—
224#103—131no—
225#103—131no—
226#103C2×D1311yescharacteristic, complemented
227#103C2×D1311yescharacteristic, complemented
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102C2×D1311yescharacteristic
233#102C2×D1311yescharacteristic
234C22⋊C8—131no—
235C22⋊C8—131no—
236C4×C8—131no—
237C2×C13—42no—
238C2×C13—41no—
239C2×C13#54611yescharacteristic
240C2×C13#57511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—41no—
243D13—81no—
244C24—261no—
245#41—22no—
246#41—41no—
247C2×Q8—131no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—21no—
250C2×D4—131no—
251C2×D4—131no—
252C2×D4—261no—
253C2×D4—262no—
254C2×D4—261no—
255C2×D4—521no—
256C2×D4C22×D1311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—131no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262Q16—521no—
263SD16—262no—
264SD16—521no—
265M16—41no—
266M16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4C22×D1311yescharacteristic
282C4⋊C4C22×D1311yescharacteristic
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—261no—
295C42—261no—
296C13#332311yescharacteristic, complemented, Sylow
297C23—21no—
298C23—131no—
299C23—261no—
300C23—522no—
301C23—522no—
302C23—1041no—
303C23D4×D1311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—261no—
307Q8—261no—
308D4—21no—
309D4—42no—
310D4—261no—
311D4—261no—
312D4—521no—
313D4—522no—
314D4—1041no—
315D4#612712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—1041no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—261no—
345C22—261no—
346C22—261no—
347C22—521no—
348C22—521no—
349C22—521no—
350C22—1044no—
351C22C2×D4×D1311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—261no—
357C4—261no—
358C4—261no—
359C4—521no—
360C4—521no—
361C4—521no—
362C4C2×#612711yescharacteristic
363C4#8825111yescharacteristic
364C2—41no—
365C2—42no—
366C2—521no—
367C2—1041no—
368C2#1171919511yescharacteristic
369C2#1171947811yescharacteristic
370C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
prime radical#11719534C2
hypercenter#417D13
hypocenterC13#3323
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #11719218C2semidirect
3. C13×#417C2semidirect
4. #11718900C2semidirect
5. #11718795C2semidirect
6. #11718789C2semidirect
7. #11718629C2semidirect
8. #11718477C2semidirect
9. #11718475C2semidirect
10. #11718461C2semidirect
11. #11718459C2semidirect
12. #11718437C2semidirect
13. #11718431C2semidirect
14. #11718427C2semidirect
15. #11718419C2semidirect
18. C2×C13×M16C22semidirect
19. C2×C13×C4⋊C4C22semidirect
22. C2×#6107C22semidirect
33. #88178C22semidirect
39. #88144C22semidirect
41. #88141C22semidirect
42. C13×#103C22semidirect
43. C13×#103C22semidirect
46. #88075C22semidirect
48. C22⋊#1055C22semidirect
51. #88058C22semidirect
52. #88056C22semidirect
53. #88054C22semidirect
54. C8×Dic13C22semidirect
57. #88048C22semidirect
58. #88048C22semidirect
167. #417D13semidirect
200. C2×M16C2×D13semidirect
218. C2×C4⋊C4C2×D13semidirect
226. #103C2×D13semidirect
227. #103C2×D13semidirect
296. C13#3323semidirect

Maximal subgroups

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

subgroupindex
#117195342
#117192182
C13×#4172
#117189002
#117187952
#117187892
#117186292
#117184772
#117184752
#117184612
#117184592
#117184372
#117184312
#117184272
#117184192
#332313