Finite Group Databasebeta

← #13125673

Subgroups — #13125673

Order 1664.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#525C211yesmaximal, characteristic, complemented
2#11719496C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718868C211yesmaximal, characteristic, complemented
6#11718713C211yesmaximal, characteristic, complemented
7#11718710C211yesmaximal, characteristic, complemented
8#11718708C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718703C211yesmaximal, characteristic, complemented
11#11718700C211yesmaximal, characteristic, complemented
12#11718698C211yesmaximal, characteristic, complemented
13#11718696C211yesmaximal, characteristic, complemented
14#11718664C211yesmaximal, characteristic, complemented
15#11718657C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C13×#123—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C13×#120—21no—
25C4×D4×C13—21no—
26C4×D4×C13—21no—
27C13×#117C2211yescharacteristic
28#88207—21no—
29C2×#6107C2211yescharacteristic, complemented
30C2×#6106C2211yescharacteristic, complemented
31C2×#6105C2211yescharacteristic, complemented
32C2×#6104C2211yescharacteristic, complemented
33#88184C2211yescharacteristic
34#88184C2211yescharacteristic
35#88183—21no—
36C4×C22⋊D13—21no—
37C4×C22⋊D13—21no—
38#88180C2211yescharacteristic
39#88178C2211yescharacteristic
40#88178C2211yescharacteristic
41C2×#6099C2211yescharacteristic
42C2×#6099C2211yescharacteristic
43#88075C2211yescharacteristic, complemented
44#88075C2211yescharacteristic, complemented
45#88072C2211yescharacteristic, complemented
46#88072C2211yescharacteristic, complemented
47C22⋊#1055C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49C22⋊#1055C2211yescharacteristic
50C22⋊#1055C2211yescharacteristic
51#88050C2211yescharacteristic, complemented
52#88050C2211yescharacteristic, complemented
53#88049C2211yescharacteristic, complemented
54#88049C2211yescharacteristic, complemented
55#88048C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13D411yescharacteristic
60C13×#41—41no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13D411yescharacteristic
71C22×C4×C13D411yescharacteristic
72C22×C4×C13D411yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79#6127—41no—
80#6127—41no—
81C2×D52C2311yescharacteristic
82C2×C4×D13—21no—
83C2×Dic26C2311yescharacteristic
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C42×C13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97#6107—41no—
98#6106—41no—
99#6105—41no—
100#6104—41no—
101#6103—21no—
102#6103—21no—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108#6099—41no—
109#6099—41no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114#3197—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13C2×D411yescharacteristic
120C23×C13C2×D411yescharacteristic
121C23×C13C2×D411yescharacteristic
122C22×D13—21no—
123Q8×C13—21no—
124Q8×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—42no—
128D4×C13—42no—
129D4×C13—42no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13C2×D411yescharacteristic
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2411yescharacteristic
147C22⋊D13—42no—
148C22⋊D13—42no—
149C22⋊D13—42no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153D52—21no—
154D52—21no—
155C4×D13—42no—
156Dic26—21no—
157Dic26—21no—
158#1055—21no—
159#1055—21no—
160#1055—21no—
161#1055—21no—
162#525—131no—
163#525D1311yescharacteristic, complemented
164#485—131no—
165#485—131no—
166#482—131no—
167#482—131no—
168#470—131no—
169#469—131no—
170#468—131no—
171#468—131no—
172#452—131no—
173#452—131no—
174#449—131no—
175#449—131no—
176#407—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—44no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13C22×D411yescharacteristic
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13H(5,𝔽2)11yescharacteristic
201C4×C13H(5,𝔽2)11yescharacteristic
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205C2×#41—131no—
206C2×#41C2×D1311yescharacteristic
207C23×C4C2×D1311yescharacteristic
208C2×Q16—131no—
209C2×SD16—131no—
210C2×SD16—131no—
211C2×D8—131no—
212C2×M16—131no—
213C2×M16—131no—
214#123—21no—
215#123—261no—
216C22⋊Q8—131no—
217C22⋊Q8—131no—
218C22⋊Q8C2×D1311yescharacteristic
219C22⋊Q8C2×D1311yescharacteristic
220#121—131no—
221#121—131no—
222#121C2×D1311yescharacteristic
223#121C2×D1311yescharacteristic
224#120—21no—
225#120—261no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—261no—
229C4×D4—261no—
230#117—131no—
231#117C2×D1311yescharacteristic
232#107—131no—
233#107—131no—
234#106—131no—
235#106—131no—
236#103—131no—
237#103—131no—
238#103—131no—
239#103—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244C22⋊C8—131no—
245C22⋊C8—131no—
246C22⋊C8—131no—
247C22⋊C8—131no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13—41no—
251C2×C13—81no—
252C2×C13#53411yescharacteristic
253C2×C13#57511yescharacteristic
254C2×C13#57511yescharacteristic
255D13—81no—
256C24C22⋊D1311yescharacteristic
257#41—41no—
258#41—41no—
259#41—521no—
260#41—521no—
261C2×Q8—131no—
262C2×Q8C22×D1311yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—131no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4C22×D1311yescharacteristic
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—261no—
275C22×C4C22⋊D1311yescharacteristic
276C22×C4C22⋊D1311yescharacteristic
277C22×C4C22⋊D1311yescharacteristic
278C22×C4C22×D1311yescharacteristic
279C22×C4C22×D1311yescharacteristic
280C22×C4C22×D1311yescharacteristic
281Q16—521no—
282SD16—521no—
283SD16—521no—
284D8—521no—
285M16—521no—
286M16—521no—
287C2×C8—131no—
288C2×C8—131no—
289C2×C8—131no—
290C2×C8—131no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—131no—
294C4⋊C4—131no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4C22×D1311yescharacteristic
298C4⋊C4C22×D1311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C42—21no—
310C42—261no—
311C13#319711yescharacteristic, complemented, Sylow
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—261no—
317C23C2×C22⋊D1311yescharacteristic
318C23C2×C22⋊D1311yescharacteristic
319C23C2×C22⋊D1311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—261no—
323Q8—261no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—261no—
330D4—261no—
331D4—522no—
332D4—522no—
333D4—522no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—522no—
351C2×C4C2×C22⋊D1311yescharacteristic
352C2×C4C2×C22⋊D1311yescharacteristic
353C2×C4C2×C22⋊D1311yescharacteristic
354C2×C4C23×D1311yescharacteristic
355C8—261no—
356C8—261no—
357C8—261no—
358C8—261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—521no—
373C22—521no—
374C22—521no—
375C22C22×C22⋊D1311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—521no—
383C4—521no—
384C4—521no—
385C4#8825111yescharacteristic
386C4#8825111yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—1041no—
392C2#1171950911yescharacteristic
393C2#1171952711yescharacteristic
394C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#525C2
socleC22×C13C22×D4
hypercenter#525D13
hypocenterC13#3197
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C13×#525C2semidirect
2. #11719496C2semidirect
3. #11718900C2semidirect
4. #11718899C2semidirect
5. #11718868C2semidirect
6. #11718713C2semidirect
7. #11718710C2semidirect
8. #11718708C2semidirect
9. #11718706C2semidirect
10. #11718703C2semidirect
11. #11718700C2semidirect
12. #11718698C2semidirect
13. #11718696C2semidirect
14. #11718664C2semidirect
15. #11718657C2semidirect
29. C2×#6107C22semidirect
30. C2×#6106C22semidirect
31. C2×#6105C22semidirect
32. C2×#6104C22semidirect
43. #88075C22semidirect
44. #88075C22semidirect
45. #88072C22semidirect
46. #88072C22semidirect
51. #88050C22semidirect
52. #88050C22semidirect
53. #88049C22semidirect
54. #88049C22semidirect
55. #88048C22semidirect
56. #88048C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
163. #525D13semidirect
311. C13#3197semidirect

Maximal subgroups

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

subgroupindex
C13×#5252
#117194962
#117189002
#117188992
#117188682
#117187132
#117187102
#117187082
#117187062
#117187032
#117187002
#117186982
#117186962
#117186642
#117186572
#319713