Finite Group Databasebeta

← #13126422

Subgroups — #13126422

Order 1664.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#548C211yesmaximal, characteristic, complemented
2C2×#88204C211yesmaximal, characteristic, complemented
3C2×#88196C211yesmaximal, characteristic, complemented
4#11719258C211yesmaximal, characteristic, complemented
5#11718899C211yesmaximal, characteristic, complemented
6#11718888C211yesmaximal, characteristic, complemented
7#11718719C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718709C211yesmaximal, characteristic, complemented
10#11718708C211yesmaximal, characteristic, complemented
11#11718700C211yesmaximal, characteristic, complemented
12#11718698C211yesmaximal, characteristic, complemented
13#11718691C211yesmaximal, characteristic, complemented
14#11718688C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C2×#6127C2211yescharacteristic
20C13×#124—21no—
21C13×#124C2211yescharacteristic
22C13×C22⋊Q8—21no—
23C13×C22⋊Q8C2211yescharacteristic
24C13×#121—21no—
25C13×#121C2211yescharacteristic
26C4×Q8×C13C2211yescharacteristic
27C4×D4×C13—21no—
28C4×D4×C13C2211yescharacteristic
29#88204—24no—
30C2×#6107C2211yescharacteristic
31C2×#6107C2211yescharacteristic
32#88196—24no—
33C2×#6106C2211yescharacteristic
34C2×#6106C2211yescharacteristic
35C2×#6106C2211yescharacteristic
36C2×#6106C2211yescharacteristic
37#88194—21no—
38C2×#6105C2211yescharacteristic
39C2×#6104C2211yescharacteristic
40C2×#6104C2211yescharacteristic
41#88184C2211yescharacteristic
42#88184C2211yescharacteristic
43C2×#6099C2211yescharacteristic
44C22×#1055C2211yescharacteristic
45#88147—21no—
46#88138—21no—
47#88138—21no—
48#88128C2211yescharacteristic
49C4×Dic26C2211yescharacteristic
50#88075C2211yescharacteristic
51#88075C2211yescharacteristic
52#88072C2211yescharacteristic
53C22⋊#1055C2211yescharacteristic
54C22⋊#1055C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58#88048C2211yescharacteristic
59C4⋊#1055C2211yescharacteristic
60#88043C2211yescharacteristic
61C13×#41—22no—
62C13×#41—41no—
63C2×Q8×C13—21no—
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80#6127—22no—
81#6127—22no—
82#6127—41no—
83#6127—41no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52C2311yescharacteristic
87C2×D52C2311yescharacteristic
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×Dic26C2311yescharacteristic
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4D411yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4D411yescharacteristic
100C13×C22⋊C4D411yescharacteristic
101C42×C13—21no—
102C42×C13C2311yescharacteristic
103#6107—22no—
104#6107D414yescomplemented
105#6106—22no—
106#6106—22no—
107#6106—22no—
108#6106—41no—
109#6105—22no—
110#6104—22no—
111#6104—41no—
112#6103—21no—
113#6103—21no—
114C4⋊Dic13C2311yescharacteristic
115#6101—21no—
116C4×Dic13—21no—
117#6099—22no—
118C2×#1055—22no—
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122C2×#1055C2311yescharacteristic
123#3271—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13C2×D411yescharacteristic
126C23×C13C2×D411yescharacteristic
127C22×D13—21no—
128C22×D13—21no—
129Q8×C13—21no—
130Q8×C13—21no—
131Q8×C13—21no—
132Q8×C13—42no—
133Q8×C13C2×D412yes—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—41no—
137D4×C13—42no—
138D4×C13—42no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13C2×D411yescharacteristic
149C2×C4×C13C2×D411yescharacteristic
150C2×C4×C13C2×D411yescharacteristic
151C2×C4×C13C2×D411yescharacteristic
152C2×C4×C13C2411yescharacteristic
153C22⋊D13—42no—
154C22⋊D13—42no—
155C22⋊D13—81no—
156C22⋊D13—81no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159D52—21no—
160D52—21no—
161D52—21no—
162D52—21no—
163D52—42no—
164D52—81no—
165C4×D13—42no—
166C4×D13—42no—
167Dic26—21no—
168Dic26C2×D412yes—
169#1055—21no—
170#1055—21no—
171#1055—21no—
172#1055C2×D412yes—
173C2×#137—131no—
174C2×#135—131no—
175#550—131no—
176#548D1311yescharacteristic, complemented
177#496—131no—
178#469—131no—
179#465—131no—
180#464—131no—
181#460—131no—
182#452—131no—
183#449—131no—
184#449—131no—
185#448—131no—
186#441—131no—
187#435—131no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13C22×D411yescharacteristic
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—22no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13C22×D411yescharacteristic
212C4×C13H(5,𝔽2)11yescharacteristic
213Dic13—22no—
214Dic13—41no—
215C2×#41—131no—
216C2×#41—131no—
217C2×#41C2×D1311yescharacteristic
218C22×Q8C2×D1311yescharacteristic
219#137—264no—
220#135—264no—
221C2×Q16—131no—
222C2×Q16—131no—
223C2×SD16—131no—
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16—131no—
228C2×D8—131no—
229C2×D8—131no—
230C2×M16—131no—
231C22×C8—131no—
232#127—131no—
233#127—261no—
234#124—21no—
235#124C2×D1311yescharacteristic
236C22⋊Q8—21no—
237C22⋊Q8C2×D1311yescharacteristic
238#121—21no—
239#121—131no—
240#121—131no—
241#121—261no—
242#121—261no—
243#121C2×D1311yescharacteristic
244C4×Q8—131no—
245C4×Q8C2×D1311yescharacteristic
246C4×D4—21no—
247C4×D4—261no—
248C4×D4C2×D1311yescharacteristic
249#106—131no—
250C4⋊C8—131no—
251#103—131no—
252#103—131no—
253#103—131no—
254#102—131no—
255#102—131no—
256#102—131no—
257C22⋊C8—131no—
258C22⋊C8—131no—
259#97—131no—
260C2×C13—41no—
261C2×C13—41no—
262C2×C13—81no—
263C2×C13D4211yescharacteristic
264C2×C13#57511yescharacteristic
265C2×C13#57711yescharacteristic
266D13—81no—
267D13—81no—
268#41—22no—
269#41—41no—
270#41—262no—
271#41—262no—
272#41—521no—
273#41—521no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—131no—
278C2×Q8C22×D1311yescharacteristic
279C2×Q8C22×D1311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—131no—
283C2×D4—131no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4C22⋊D1311yescharacteristic
291C2×D4C22×D1311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4C22×D1311yescharacteristic
297C22×C4C22×D1311yescharacteristic
298Q16—134no—
299Q16—262no—
300SD16—262no—
301SD16—262no—
302SD16—262no—
303SD16—262no—
304SD16—521no—
305D8—262no—
306D8—521no—
307M16—262no—
308C2×C8—131no—
309C2×C8—131no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—262no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—131no—
316C4⋊C4—261no—
317C4⋊C4C22⋊D1311yescharacteristic
318C4⋊C4C22×D1311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4C22⋊D1311yescharacteristic
326C22⋊C4C22⋊D1311yescharacteristic
327C42—21no—
328C42—261no—
329C42C22×D1311yescharacteristic
330C13#327111yescharacteristic, complemented, Sylow
331C23—21no—
332C23—261no—
333C23—261no—
334C23C2×C22⋊D1311yescharacteristic
335C23C2×C22⋊D1311yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—42no—
340Q8—132no—
341Q8—261no—
342Q8D4×D1312yes—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—261no—
349D4—261no—
350D4—261no—
351D4—261no—
352D4—522no—
353D4—522no—
354D4—522no—
355D4—1041no—
356D4—1041no—
357D4—1041no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4C2×C22⋊D1311yescharacteristic
372C2×C4C2×C22⋊D1311yescharacteristic
373C2×C4C2×C22⋊D1311yescharacteristic
374C2×C4C2×C22⋊D1311yescharacteristic
375C2×C4C23×D1311yescharacteristic
376C8—132no—
377C8—261no—
378C8—261no—
379C8—261no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—521no—
395C22C22×C22⋊D1311yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—262no—
404C4—521no—
405C4C2×D4×D1311yescharacteristic
406C4#8825111yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—1041no—
411C2—1041no—
412C2D4×C22⋊D1311yescharacteristic
413C2#1171952711yescharacteristic
414C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#548C2
socleC22×C13C22×D4
hypercenter#548D13
hypocenterC13#3271
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C13×#548C2semidirect
2. C2×#88204C2semidirect
3. C2×#88196C2semidirect
4. #11719258C2semidirect
5. #11718899C2semidirect
6. #11718888C2semidirect
7. #11718719C2semidirect
8. #11718715C2semidirect
9. #11718709C2semidirect
10. #11718708C2semidirect
11. #11718700C2semidirect
12. #11718698C2semidirect
13. #11718691C2semidirect
14. #11718688C2semidirect
15. #11718672C2semidirect
104. #6107D4semidirect
176. #548D13semidirect
330. C13#3271semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
C2×#882042
C2×#881962
#117192582
#117188992
#117188882
#117187192
#117187152
#117187092
#117187082
#117187002
#117186982
#117186912
#117186882
#117186722
#327113