Finite Group Databasebeta

← #13126865

Subgroups — #13126865

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#11719511C211yesmaximal, characteristic
2#11719346C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718876C211yesmaximal, characteristic, complemented
5#11718834C211yesmaximal, characteristic, complemented
6#11718832C211yesmaximal, characteristic, complemented
7#11718827C211yesmaximal, characteristic, complemented
8#11718825C211yesmaximal, characteristic, complemented
9#11718713C211yesmaximal, characteristic, complemented
10#11718445C211yesmaximal, characteristic, complemented
11#11718433C211yesmaximal, characteristic, complemented
12#11718426C211yesmaximal, characteristic, complemented
13#11718422C211yesmaximal, characteristic, complemented
14#11718389C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88207—21no—
22C2×C22⋊Dic13—21no—
23#88200C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6107C2211yescharacteristic, complemented
26#88193—21no—
27#88192C2211yescharacteristic
28#88190C2211yescharacteristic
29#88189—21no—
30D4×Dic13C2211yescharacteristic
31C4×C22⋊D13C2211yescharacteristic
32#88180C2211yescharacteristic
33#88178C2211yescharacteristic
34C2×#6099C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic, complemented
36#88152—21no—
37#88146C2211yescharacteristic, complemented
38#88142C2211yescharacteristic, complemented
39#88141—21no—
40#88139—21no—
41#88133—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic, complemented
51#88058C2211yescharacteristic, complemented
52#88057C2211yescharacteristic, complemented
53#88056C2211yescharacteristic, complemented
54#88056C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—22no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72#6129—22no—
73#6129—41no—
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26C2311yescharacteristic
77C13×SD16—22no—
78C13×SD16—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6107—41no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107#6099—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3311—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—81no—
117C23×C13C2×D411yescharacteristic
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125D4×C13#4112yes—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C22⋊D13—41no—
133C22⋊D13—42no—
134C22⋊D13—81no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—42no—
140C2×Dic13—81no—
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C4×D13—21no—
145C4×D13—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—42no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#556—131no—
154#546—131no—
155#489—131no—
156#485—131no—
157#482—131no—
158#476—131no—
159#470—131no—
160#465—131no—
161#464—131no—
162#452—131no—
163#450D1311yescharacteristic, complemented
164#440—131no—
165#435—131no—
166#418—131no—
167#416—131no—
168C22×C13—22no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—84no—
178C22×C13C22×D411yescharacteristic
179C2×D13—21no—
180C2×D13—21no—
181C2×D13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—21no—
188Dic13—21no—
189Dic13—21no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194C2×#41—131no—
195C22×D4C2×D1311yescharacteristic
196C2×Q16—131no—
197C2×SD16C2×D1311yescharacteristic
198C2×SD16C2×D1311yescharacteristic
199C2×M16—131no—
200C22×C8—131no—
201C4⋊Q8—131no—
202#126—261no—
203#126—261no—
204#124—131no—
205#124—261no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8C2×D1311yescharacteristic
210#121—131no—
211#121—261no—
212#120—261no—
213C4×Q8—131no—
214C4×Q8—261no—
215C4×D4—131no—
216C4×D4—131no—
217#117—131no—
218#117—131no—
219C2×C22⋊C4—261no—
220#107—131no—
221#106—131no—
222#106—131no—
223C4⋊C8—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102C2×D1311yescharacteristic
233#102C2×D1311yescharacteristic
234C22⋊C8—131no—
235C22⋊C8C2×D1311yescharacteristic
236#97—131no—
237C2×C13—41no—
238C2×C13—42no—
239C2×C13—81no—
240C2×C13#54611yescharacteristic
241C2×C13#57511yescharacteristic
242C2×C13#57711yescharacteristic
243D13—41no—
244C24—21no—
245#41—262no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8—261no—
249C2×Q8C22×D1311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—131no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4C22×D1311yescharacteristic
257C2×D4C22×D1311yescharacteristic
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262Q16—521no—
263SD16—22no—
264SD16—41no—
265M16—521no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8—521no—
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4C22×D1311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—131no—
283C22⋊C4—131no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—131no—
293C42—261no—
294C42—261no—
295C42—261no—
296C13#331111yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—131no—
303C23D4×D1311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—261no—
307Q8—261no—
308Q8—522no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—521no—
314D4—522no—
315D4—1041no—
316D4#612912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—131no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—522no—
331C2×C4—1041no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—261no—
349C22—261no—
350C22—261no—
351C22C2×D4×D1311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—261no—
356C4—261no—
357C4—261no—
358C4—521no—
359C4—521no—
360C4—521no—
361C4—521no—
362C4C2×#612911yescharacteristic
363C4#8825111yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—521no—
368C2#1171929611yescharacteristic
369C2#1171946711yescharacteristic
370C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radical#11719511C2
hypercenter#450D13
hypocenterC13#3311
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #11719346C2semidirect
3. C13×#450C2semidirect
4. #11718876C2semidirect
5. #11718834C2semidirect
6. #11718832C2semidirect
7. #11718827C2semidirect
8. #11718825C2semidirect
9. #11718713C2semidirect
10. #11718445C2semidirect
11. #11718433C2semidirect
12. #11718426C2semidirect
13. #11718422C2semidirect
14. #11718389C2semidirect
15. #11718384C2semidirect
23. #88200C22semidirect
24. Q8×Dic13C22semidirect
25. C2×#6107C22semidirect
35. C2×C8×D13C22semidirect
37. #88146C22semidirect
38. #88142C22semidirect
45. #88075C22semidirect
50. #88060C22semidirect
51. #88058C22semidirect
52. #88057C22semidirect
53. #88056C22semidirect
54. #88056C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88050C22semidirect
58. #88048C22semidirect
163. #450D13semidirect
296. C13#3311semidirect

Maximal subgroups

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

subgroupindex
#117195112
#117193462
C13×#4502
#117188762
#117188342
#117188322
#117188272
#117188252
#117187132
#117184452
#117184332
#117184262
#117184222
#117183892
#117183842
#331113