Finite Group Databasebeta

← #13125742

Subgroups — #13125742

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#537C211yesmaximal, characteristic, complemented
2#11719538C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718895C211yesmaximal, characteristic, complemented
6#11718713C211yesmaximal, characteristic, complemented
7#11718709C211yesmaximal, characteristic, complemented
8#11718708C211yesmaximal, characteristic, complemented
9#11718704C211yesmaximal, characteristic, complemented
10#11718702C211yesmaximal, characteristic, complemented
11#11718700C211yesmaximal, characteristic, complemented
12#11718698C211yesmaximal, characteristic, complemented
13#11718695C211yesmaximal, characteristic, complemented
14#11718632C211yesmaximal, characteristic, complemented
15#11718629C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C13×C22⋊Q8—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121—21no—
23C13×#121—21no—
24C13×#121—21no—
25C13×#121C2211yescharacteristic
26C13×#121C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28#88200—21no—
29C2×#6107C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31#88193—21no—
32#88193—21no—
33#88192—21no—
34C2×#6105C2211yescharacteristic
35C2×#6104C2211yescharacteristic
36#88184C2211yescharacteristic
37#88184C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39#88178C2211yescharacteristic
40#88178C2211yescharacteristic
41C2×#6099C2211yescharacteristic
42C22×#1055C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49C22⋊#1055C2211yescharacteristic
50C22⋊#1055C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C13×#41—41no—
60C13×#41—41no—
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13D411yescharacteristic
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13D411yescharacteristic
69C2×D4×C13D411yescharacteristic
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80C22×Dic13—21no—
81#6127—41no—
82#6127—41no—
83C2×D52C2311yescharacteristic
84C2×C4×D13—21no—
85C2×Dic26C2311yescharacteristic
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2311yescharacteristic
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C13×C22⋊C4—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⋊Dic13—21no—
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108#6099—41no—
109C2×#1055—41no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114#3204—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C23×C13C2×D411yescharacteristic
118C23×C13C2×D411yescharacteristic
119C22×D13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—41no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—41no—
126D4×C13—41no—
127D4×C13—41no—
128D4×C13—42no—
129D4×C13—81no—
130D4×C13—81no—
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—21no—
140C2×C4×C13—42no—
141C2×C4×C13—81no—
142C2×C4×C13C2×D411yescharacteristic
143C2×C4×C13C2×D411yescharacteristic
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2411yescharacteristic
146C22⋊D13—42no—
147C22⋊D13—81no—
148C22⋊D13—81no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—81no—
153D52—21no—
154D52—21no—
155C4×D13—42no—
156Dic26—21no—
157Dic26—21no—
158#1055—21no—
159#1055—21no—
160#1055—21no—
161#1055—21no—
162#537—131no—
163#537D1311yescharacteristic, complemented
164#483—131no—
165#483—131no—
166#481—131no—
167#481—131no—
168#470—131no—
169#469—131no—
170#465—131no—
171#465—131no—
172#452—131no—
173#452—131no—
174#449—131no—
175#449—131no—
176#408—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—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13C22×D411yescharacteristic
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13H(5,𝔽2)11yescharacteristic
200C4×C13H(5,𝔽2)11yescharacteristic
201Dic13—41no—
202Dic13—41no—
203Dic13—41no—
204C2×#41—131no—
205C2×#41C2×D1311yescharacteristic
206C2×#41C2×D1311yescharacteristic
207C2×Q16—131no—
208C2×SD16—131no—
209C2×SD16—131no—
210C2×D8—131no—
211C2×M16—131no—
212C22×C8—131no—
213C22⋊Q8—21no—
214C22⋊Q8—131no—
215C22⋊Q8—131no—
216C22⋊Q8—261no—
217C22⋊Q8C2×D1311yescharacteristic
218C22⋊Q8C2×D1311yescharacteristic
219#121—21no—
220#121—21no—
221#121—21no—
222#121—131no—
223#121—131no—
224#121—261no—
225#121—261no—
226#121—261no—
227#121C2×D1311yescharacteristic
228#121C2×D1311yescharacteristic
229C2×C4⋊C4—131no—
230C2×C4⋊C4C2×D1311yescharacteristic
231#106—131no—
232#106—131no—
233#106—131no—
234#106—131no—
235#103—131no—
236#103—131no—
237#103—131no—
238#103—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243C22⋊C8—131no—
244C22⋊C8—131no—
245C22⋊C8—131no—
246C22⋊C8—131no—
247C2×C13—41no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13—81no—
251C2×C13#53411yescharacteristic
252C2×C13#57711yescharacteristic
253C2×C13#57711yescharacteristic
254D13—81no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—521no—
260#41—521no—
261C2×Q8—131no—
262C2×Q8C22⋊D1311yescharacteristic
263C2×Q8C22×D1311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—131no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4C22⋊D1311yescharacteristic
272C2×D4C22⋊D1311yescharacteristic
273C2×D4C22⋊D1311yescharacteristic
274C2×D4C22×D1311yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4C22×D1311yescharacteristic
280C22×C4C22×D1311yescharacteristic
281C22×C4C22×D1311yescharacteristic
282Q16—521no—
283SD16—521no—
284SD16—521no—
285D8—521no—
286M16—521no—
287C2×C8—131no—
288C2×C8—131no—
289C2×C8—131no—
290C2×C8—131no—
291C2×C8—521no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4C22×D1311yescharacteristic
301C4⋊C4C22×D1311yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C13#320411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—261no—
313C23C2×C22⋊D1311yescharacteristic
314C23C2×C22⋊D1311yescharacteristic
315C23C2×C22⋊D1311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—261no—
320Q8—261no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—261no—
330D4—261no—
331D4—522no—
332D4—1041no—
333D4—1041no—
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—42no—
344C2×C4—81no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—522no—
349C2×C4—1041no—
350C2×C4C2×C22⋊D1311yescharacteristic
351C2×C4C2×C22⋊D1311yescharacteristic
352C2×C4C2×C22⋊D1311yescharacteristic
353C2×C4C23×D1311yescharacteristic
354C8—261no—
355C8—261no—
356C8—261no—
357C8—261no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—521no—
371C22—521no—
372C22—521no—
373C22C22×C22⋊D1311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—521no—
381C4—521no—
382C4—521no—
383C4#8825111yescharacteristic
384C4#8825111yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—1041no—
390C2#1171950911yescharacteristic
391C2#1171954111yescharacteristic
392C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#537C2
socleC22×C13C22×D4
hypercenter#537D13
hypocenterC13#3204
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C13×#537C2semidirect
2. #11719538C2semidirect
3. #11718900C2semidirect
4. #11718899C2semidirect
5. #11718895C2semidirect
6. #11718713C2semidirect
7. #11718709C2semidirect
8. #11718708C2semidirect
9. #11718704C2semidirect
10. #11718702C2semidirect
11. #11718700C2semidirect
12. #11718698C2semidirect
13. #11718695C2semidirect
14. #11718632C2semidirect
15. #11718629C2semidirect
163. #537D13semidirect
310. C13#3204semidirect

Maximal subgroups

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

subgroupindex
C13×#5372
#117195382
#117189002
#117188992
#117188952
#117187132
#117187092
#117187082
#117187042
#117187022
#117187002
#117186982
#117186952
#117186322
#117186292
#320413