Finite Group Databasebeta

← #13126372

Subgroups — #13126372

Order 1664.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#546C211yesmaximal, characteristic, complemented
2C2×#88204C211yesmaximal, characteristic, complemented
3C2×#88186C211yesmaximal, characteristic, complemented
4#11719258C211yesmaximal, characteristic, complemented
5#11718899C211yesmaximal, characteristic, complemented
6#11718878C211yesmaximal, characteristic, complemented
7#11718719C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic, complemented
10#11718708C211yesmaximal, characteristic, complemented
11#11718699C211yesmaximal, characteristic, complemented
12#11718698C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718676C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C2×#6127C2211yescharacteristic, complemented
20C13×#124C2211yescharacteristic
21C13×#123—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121—21no—
24C13×#121C2211yescharacteristic
25C13×#120—21no—
26C4×D4×C13C2211yescharacteristic
27C4×D4×C13C2211yescharacteristic
28C2×C13×C22⋊C4—21no—
29#88204—24no—
30C2×#6107C2211yescharacteristic, complemented
31C2×#6106C2211yescharacteristic, complemented
32C2×#6106C2211yescharacteristic, complemented
33#88194—21no—
34C2×#6105C2211yescharacteristic
35C2×#6105C2211yescharacteristic
36#88186—24no—
37C2×#6104C2211yescharacteristic
38C2×#6104C2211yescharacteristic
39C2×#6104C2211yescharacteristic
40C2×#6104C2211yescharacteristic
41#88184C2211yescharacteristic
42#88184C2211yescharacteristic, complemented
43C2×#6099C2211yescharacteristic
44C22×#1055C2211yescharacteristic, complemented
45#88147—21no—
46#88138—21no—
47#88138—21no—
48#88128C2211yescharacteristic, complemented
49C4×Dic26C2211yescharacteristic, complemented
50#88075C2211yescharacteristic, complemented
51#88072C2211yescharacteristic
52#88072C2211yescharacteristic
53C22⋊#1055C2211yescharacteristic
54C22⋊#1055C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88049C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C4⋊#1055C2211yescharacteristic, complemented
60#88043C2211yescharacteristic, complemented
61C24×C13—21no—
62C13×#41—22no—
63C13×#41—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80C2×C22⋊D13—21no—
81#6127—22no—
82#6127—22no—
83#6127—41no—
84#6127—41no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52C2311yescharacteristic
88C2×D52C2311yescharacteristic
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×Dic26C2311yescharacteristic
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⋊C4—21no—
100C13×C22⋊C4D411yescharacteristic
101C13×C22⋊C4D411yescharacteristic
102C42×C13C2311yescharacteristic
103#6107—22no—
104#6106—22no—
105#6106—41no—
106#6105—22no—
107#6105D414yescomplemented
108#6104—22no—
109#6104—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#3268—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—81no—
129C23×C13C2×D411yescharacteristic
130C23×C13C2×D411yescharacteristic
131C22×D13—21no—
132C22×D13—21no—
133Q8×C13—21no—
134Q8×C13—21no—
135D4×C13—21no—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—41no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13—81no—
142D4×C13C2×D412yes—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—81no—
151C2×C4×C13C2×D411yescharacteristic
152C2×C4×C13C2×D411yescharacteristic
153C2×C4×C13C2×D411yescharacteristic
154C2×C4×C13C2×D411yescharacteristic
155C2×C4×C13C2411yescharacteristic
156C22⋊D13—42no—
157C22⋊D13—42no—
158C22⋊D13—81no—
159C22⋊D13—81no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162D52—21no—
163D52—21no—
164D52—21no—
165D52—21no—
166D52—42no—
167D52—81no—
168C4×D13—42no—
169C4×D13—42no—
170Dic26—21no—
171Dic26C2×D412yes—
172#1055—21no—
173#1055—21no—
174#1055—21no—
175#1055C2×D412yes—
176C2×AGL(1,ℤ/8)—131no—
177C2×#135—131no—
178#550—131no—
179#546D1311yescharacteristic, complemented
180#496—131no—
181#468—131no—
182#466—131no—
183#464—131no—
184#459—131no—
185#452—131no—
186#449—131no—
187#449—131no—
188#447—131no—
189#440—131no—
190#435—131no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—22no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—84no—
204C22×C13C22×D411yescharacteristic
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—41no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—41no—
216C4×C13—41no—
217C4×C13C22×D411yescharacteristic
218C4×C13H(5,𝔽2)11yescharacteristic
219Dic13—22no—
220Dic13—41no—
221C2×#41—131no—
222C2×#41—131no—
223C2×#41C2×D1311yescharacteristic
224C22×D4C2×D1311yescharacteristic
225AGL(1,ℤ/8)—264no—
226#135—264no—
227C2×Q16—131no—
228C2×SD16—131no—
229C2×SD16—131no—
230C2×SD16—131no—
231C2×SD16—131no—
232C2×D8—131no—
233C2×D8—131no—
234C2×D8—131no—
235C2×D8—131no—
236C2×M16—131no—
237C22×C8—131no—
238#127—131no—
239#127—261no—
240#124C2×D1311yescharacteristic
241#123—21no—
242C22⋊Q8C2×D1311yescharacteristic
243#121—21no—
244#121—131no—
245#121—131no—
246#121—261no—
247#121—261no—
248#121C2×D1311yescharacteristic
249#120—21no—
250C4×Q8—131no—
251C4×D4—261no—
252C4×D4C2×D1311yescharacteristic
253C4×D4C2×D1311yescharacteristic
254C2×C22⋊C4—21no—
255#107—131no—
256C4⋊C8—131no—
257#103—131no—
258#103—131no—
259#102—131no—
260#102—131no—
261#102—131no—
262#102—131no—
263C22⋊C8—131no—
264C22⋊C8—131no—
265#97—131no—
266C2×C13—41no—
267C2×C13—41no—
268C2×C13—42no—
269C2×C13—81no—
270C2×C13D4211yescharacteristic
271C2×C13#57511yescharacteristic
272C2×C13#57611yescharacteristic
273D13—81no—
274D13—81no—
275C24—21no—
276#41—22no—
277#41—41no—
278#41—262no—
279#41—262no—
280#41—521no—
281#41—521no—
282C2×Q8—131no—
283C2×Q8C22×D1311yescharacteristic
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—131no—
290C2×D4—131no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4C22⋊D1311yescharacteristic
298C2×D4C22×D1311yescharacteristic
299C2×D4C22×D1311yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—261no—
303C22×C4—261no—
304C22×C4C22×D1311yescharacteristic
305C22×C4C22×D1311yescharacteristic
306Q16—262no—
307SD16—134no—
308SD16—262no—
309SD16—262no—
310SD16—521no—
311D8—262no—
312D8—262no—
313D8—262no—
314D8—521no—
315M16—262no—
316C2×C8—131no—
317C2×C8—131no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—262no—
321C4⋊C4—21no—
322C4⋊C4—131no—
323C4⋊C4—261no—
324C4⋊C4C22⋊D1311yescharacteristic
325C4⋊C4C22×D1311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4C22⋊D1311yescharacteristic
334C22⋊C4C22⋊D1311yescharacteristic
335C42—261no—
336C42C22×D1311yescharacteristic
337C13#326811yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—261no—
344C23—261no—
345C23C2×C22⋊D1311yescharacteristic
346C23C2×C22⋊D1311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—132no—
350Q8—261no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—261no—
359D4—261no—
360D4—261no—
361D4—261no—
362D4—522no—
363D4—522no—
364D4—522no—
365D4—1041no—
366D4—1041no—
367D4—1041no—
368D4D4×D1312yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—522no—
380C2×C4—522no—
381C2×C4C2×C22⋊D1311yescharacteristic
382C2×C4C2×C22⋊D1311yescharacteristic
383C2×C4C2×C22⋊D1311yescharacteristic
384C2×C4C2×C22⋊D1311yescharacteristic
385C2×C4C23×D1311yescharacteristic
386C8—132no—
387C8—261no—
388C8—261no—
389C8—261no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—521no—
404C22—521no—
405C22—521no—
406C22—521no—
407C22—521no—
408C22—521no—
409C22C22×C22⋊D1311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—262no—
417C4—521no—
418C4C2×D4×D1311yescharacteristic
419C4#8825111yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—1041no—
425C2—1041no—
426C2D4×C22⋊D1311yescharacteristic
427C2#1171952711yescharacteristic
428C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#546C2
socleC22×C13C22×D4
hypercenter#546D13
hypocenterC13#3268
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C13×#546C2semidirect
2. C2×#88204C2semidirect
3. C2×#88186C2semidirect
4. #11719258C2semidirect
5. #11718899C2semidirect
6. #11718878C2semidirect
7. #11718719C2semidirect
8. #11718715C2semidirect
9. #11718710C2semidirect
10. #11718708C2semidirect
11. #11718699C2semidirect
12. #11718698C2semidirect
13. #11718679C2semidirect
14. #11718676C2semidirect
15. #11718672C2semidirect
19. C2×#6127C22semidirect
30. C2×#6107C22semidirect
31. C2×#6106C22semidirect
32. C2×#6106C22semidirect
42. #88184C22semidirect
44. C22×#1055C22semidirect
48. #88128C22semidirect
49. C4×Dic26C22semidirect
50. #88075C22semidirect
54. C22⋊#1055C22semidirect
55. #88050C22semidirect
56. #88049C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
59. C4⋊#1055C22semidirect
60. #88043C22semidirect
107. #6105D4semidirect
179. #546D13semidirect
337. C13#3268semidirect

Maximal subgroups

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

subgroupindex
C13×#5462
C2×#882042
C2×#881862
#117192582
#117188992
#117188782
#117187192
#117187152
#117187102
#117187082
#117186992
#117186982
#117186792
#117186762
#117186722
#326813