Finite Group Databasebeta

← #16017722

Subgroups — #16017722

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124418C211yesmaximal, characteristic
2D13×#427C211yesmaximal, characteristic, complemented
3#13117047C211yesmaximal, characteristic, complemented
4#13117046C211yesmaximal, characteristic, complemented
5#13117040C211yesmaximal, characteristic, complemented
6#13117035C211yesmaximal, characteristic, complemented
7#13117030C211yesmaximal, characteristic, complemented
8#13117029C211yesmaximal, characteristic, complemented
9#13117023C211yesmaximal, characteristic, complemented
10#13117018C211yesmaximal, characteristic, complemented
11#13116618C211yesmaximal, characteristic, complemented
12#13116544C211yesmaximal, characteristic, complemented
13#13116541C211yesmaximal, characteristic, complemented
14C2×#11718099C211yesmaximal, characteristic, complemented
15C13×#2158C211yesmaximal, characteristic, complemented
16C2×#88158C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18#11719229—21no—
19D13×#117—21no—
20C22×C13×C16C2211yescharacteristic
21C13×#427C2211yescharacteristic
22C13×#427C2211yescharacteristic
23#11718767C2211yescharacteristic
24C22×#6090C2211yescharacteristic
25#11718663—21no—
26#11718659—21no—
27#11718548C2211yescharacteristic
28#11718548C2211yescharacteristic
29#11718544C2211yescharacteristic
30#11718544C2211yescharacteristic
31#11718541C2211yescharacteristic
32#11718541C2211yescharacteristic
33D13×#107C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718525—21no—
36#11718525—21no—
37#11718521—21no—
38D13×#106—21no—
39C13×#367C2211yescharacteristic, complemented
40C13×#367C2211yescharacteristic, complemented
41C13×#366C2211yescharacteristic, complemented
42C13×#366C2211yescharacteristic, complemented
43#11718101C2211yescharacteristic, complemented
44#11718101C2211yescharacteristic, complemented
45#11718099C2211yescharacteristic
46#11718099C2211yescharacteristic
47#11718099C2211yescharacteristic
48#11718099C2211yescharacteristic
49#11718095C2211yescharacteristic, complemented
50#11718095C2211yescharacteristic, complemented
51#11718084C2211yescharacteristic, complemented
52#11718084C2211yescharacteristic, complemented
53#11718083C2211yescharacteristic, complemented
54#11718083C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C2×#6127—21no—
60C22×C4×D13D411yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C13×#117—21no—
63C13×#117—21no—
64#88180—21no—
65C22×#1055D411yescharacteristic
66C2×Dic52C2311yescharacteristic
67#88158—22no—
68#88158—22no—
69C2×D104C2311yescharacteristic
70C2×#6095—21no—
71C2×C8×D13—22no—
72C2×C8×D13—22no—
73C2×C8×D13D411yescharacteristic
74C2×C8×D13D411yescharacteristic
75C2×C8×D13C2311yescharacteristic
76C2×C8×D13C2311yescharacteristic
77#88151—21no—
78#88151—21no—
79#88149—21no—
80#88149—21no—
81#88146—21no—
82#88146—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13—21no—
85#88140—41no—
86#88136—41no—
87C22⋊C4×D13—41no—
88#88131—41no—
89C4×D52—41no—
90C4×D52—41no—
91#88126—41no—
92C42×D13—41no—
93C2×C13×C16—22no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#107C2311yescharacteristic
100C13×#106—21no—
101C13×#106—21no—
102#88058C2311yescharacteristic
103#88058C2311yescharacteristic
104#88057—21no—
105C2×#6090—22no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108#88050—21no—
109#88050—21no—
110#88049—21no—
111#88049—21no—
112#88048—21no—
113#88048—21no—
114#88047—21no—
115#88047—21no—
116#33645—131nomaximal, Sylow
117C23×D13D811yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C2×C22⋊D13—41no—
120C22×Dic13D811yescharacteristic
121#6127—42no—
122#6127—42no—
123C2×D52—21no—
124C2×D52—41no—
125C2×D52—41no—
126C2×C4×D13—22no—
127C2×C4×D13—22no—
128C2×C4×D13—41no—
129C2×C4×D13—41no—
130C2×C4×D13—41no—
131C2×C4×D13D811yescharacteristic
132C2×C4×D13D811yescharacteristic
133C2×C4×D13C2×D411yescharacteristic
134C2×C4×D13C2×D411yescharacteristic
135C2×Dic26—21no—
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13#4112yes—
138C2×C8×C13#4112yes—
139C2×C8×C13C2411yescharacteristic
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C42×C13—41no—
147C42×C13—41no—
148C22⋊Dic13—41no—
149#6103—41no—
150#6103—41no—
151#6103—41no—
152#6103—41no—
153#6103—41no—
154#6103—41no—
155C4⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13—41no—
158C4⋊Dic13—41no—
159#6101—41no—
160#6101—41no—
161C4×Dic13—41no—
162C4×Dic13—41no—
163C4×Dic13—41no—
164C2×#1055—22no—
165C2×#1055C2×D411yescharacteristic
166C2×#1055C2×D411yescharacteristic
167Dic52—21no—
168Dic52—21no—
169D104—21no—
170D104—21no—
171#6095—42no—
172C8×D13—22no—
173C8×D13—22no—
174C8×D13—21no—
175C8×D13—21no—
176C8×D13—21no—
177C8×D13—21no—
178C13×C16—21no—
179C13×C16—21no—
180#6090—21no—
181#6090—21no—
182#3050—131no—
183C2×#427—131no—
184#2237—131no—
185#2237—131no—
186#2236—131no—
187#2235—131no—
188#2234—131no—
189#2234—131no—
190#2233—131no—
191#2232—131no—
192#2158—131no—
193#2158D1311yescharacteristic, complemented
194#2138—131no—
195#2138—131no—
196C2×C22⋊C16—131no—
197C23×C13C2×D811yescharacteristic
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—41no—
201C22×D13—41no—
202C22×D13C2×D811yescharacteristic
203C22×D13C2×D811yescharacteristic
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13#12312yes—
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13#13712yes—
211C2×C4×C13C22×D411yescharacteristic
212C22⋊D13—82no—
213C2×Dic13—22no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13C2×D811yescharacteristic
218C2×Dic13C2×D811yescharacteristic
219D52—41no—
220D52—41no—
221D52—82no—
222D52—82no—
223C4×D13—21no—
224C4×D13—21no—
225C4×D13—21no—
226C4×D13—21no—
227C4×D13—22no—
228C4×D13—22no—
229C4×D13—82no—
230C4×D13—82no—
231C4×D13—82no—
232Dic26—41no—
233Dic26—41no—
234C8×C13#12312yes—
235C8×C13C2×#4111yescharacteristic
236C8×C13C2×#4111yescharacteristic
237#1055—21no—
238#1055—21no—
239C2×#135—131no—
240C23×C8—131no—
241#525—261no—
242C2×#117—261no—
243C22×C16—131no—
244C22×C16C2×D1311yescharacteristic
245#467—131no—
246#467—131no—
247#466—131no—
248#466—131no—
249#465—261no—
250#465—261no—
251#427—131no—
252#427—131no—
253#427—131no—
254#427—261no—
255#427—261no—
256#427C2×D1311yescharacteristic
257#427C2×D1311yescharacteristic
258C2×#107—131no—
259C2×#107—131no—
260C2×#106—261no—
261#416—261no—
262#367—131no—
263#367—131no—
264#367C2×D1311yescharacteristic, complemented
265#367C2×D1311yescharacteristic, complemented
266#366—131no—
267#366—131no—
268#366C2×D1311yescharacteristic, complemented
269#366C2×D1311yescharacteristic, complemented
270#358—131no—
271#358—131no—
272#358—131no—
273#358—131no—
274#357—131no—
275#357—131no—
276#357—131no—
277#357—131no—
278C22⋊C16—131no—
279C22⋊C16—131no—
280C22⋊C16—131no—
281C22⋊C16—131no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13#48012yes—
285C22×C13C22×D811yescharacteristic
286C2×D13—21no—
287C2×D13—21no—
288C2×D13—21no—
289C2×D13—21no—
290C2×D13—21no—
291C2×D13—44no—
292C2×D13—81no—
293C2×D13—81no—
294C2×D13—81no—
295C2×D13#50812yes—
296C4×C13—81no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13#48012yes—
301C4×C13C2×#12311yescharacteristic
302C4×C13C2×#13711yescharacteristic
303Dic13—21no—
304Dic13—21no—
305Dic13—81no—
306Dic13—81no—
307Dic13—81no—
308C2×#41—261no—
309C23×C4—131no—
310#135—262no—
311#135—262no—
312C2×Q16—131no—
313C2×SD16—261no—
314C2×D8—131no—
315C22×C8—131no—
316C22×C8—131no—
317C22×C8—131no—
318C22×C8—131no—
319C22×C8—131no—
320C22×C8—262no—
321C22×C8—262no—
322C22×C8C22×D1311yescharacteristic
323#123—521no—
324C22⋊Q8—261no—
325C22⋊Q8—261no—
326#121—261no—
327#121—261no—
328#120—521no—
329C4×D4—521no—
330C4×D4—521no—
331#117—21no—
332#117—21no—
333#117—261no—
334#117—261no—
335#117—261no—
336#117—521no—
337#117—521no—
338C2×C4⋊C4—261no—
339C2×C4⋊C4—261no—
340C2×C22⋊C4—521no—
341C2×C42—521no—
342C2×C16—22no—
343C2×C16—131no—
344C2×C16—131no—
345C2×C16—262no—
346C2×C16C22×D1311yescharacteristic
347C2×C16C22×D1311yescharacteristic
348#107—131no—
349#107—131no—
350#107—261no—
351#107—261no—
352#107C22×D1311yescharacteristic
353#107C22×D1311yescharacteristic
354#107C22×D1311yescharacteristic
355#107C22×D1311yescharacteristic
356#106—21no—
357#106—21no—
358#106—261no—
359#106—261no—
360#106—261no—
361#103—261no—
362#103—261no—
363#102—261no—
364#102—261no—
365C2×C13—22no—
366C2×C13C2×#48011yescharacteristic
367C2×C13C2×#50811yescharacteristic
368C2×C13#341411yescharacteristic
369D13—22no—
370D13—41no—
371D13—161no—
372C24—131no—
373#41—522no—
374#41—522no—
375C2×Q8—261no—
376C2×D4—261no—
377C2×D4—521no—
378C2×D4—521no—
379C2×D4—521no—
380C22×C4—131no—
381C22×C4—131no—
382C22×C4—131no—
383C22×C4—131no—
384C22×C4—131no—
385C22×C4—262no—
386C22×C4—262no—
387C22×C4—521no—
388C22×C4—521no—
389C22×C4—521no—
390C22×C4D4×D1311yescharacteristic
391Q16—261no—
392Q16—261no—
393SD16—522no—
394D8—261no—
395D8—261no—
396C2×C8—131no—
397C2×C8—131no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—262no—
401C2×C8—261no—
402C2×C8—261no—
403C2×C8—261no—
404C2×C8—261no—
405C2×C8#612712yes—
406C2×C8D4×D1311yescharacteristic
407C2×C8#613112yes—
408C2×C8C23×D1311yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—261no—
414C4⋊C4—261no—
415C4⋊C4—521no—
416C4⋊C4—521no—
417C4⋊C4—521no—
418C4⋊C4—521no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—521no—
422C22⋊C4—521no—
423C22⋊C4—521no—
424C22⋊C4—521no—
425C22⋊C4—521no—
426C22⋊C4—521no—
427C22⋊C4—521no—
428C42—41no—
429C42—41no—
430C42—521no—
431C42—521no—
432C42—521no—
433C16—21no—
434C16—21no—
435C16—261no—
436C16—261no—
437C13#3364511yescharacteristic, complemented, Sylow
438C23—131no—
439C23—131no—
440C23—262no—
441C23—262no—
442C23—521no—
443C23—521no—
444C23D8×D1311yescharacteristic
445Q8—521no—
446Q8—521no—
447D4—521no—
448D4—521no—
449D4—1042no—
450D4—1042no—
451D4—1042no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—131no—
457C2×C4—131no—
458C2×C4—262no—
459C2×C4—261no—
460C2×C4—261no—
461C2×C4—261no—
462C2×C4—261no—
463C2×C4—262no—
464C2×C4—262no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—521no—
468C2×C4—1042no—
469C2×C4—1042no—
470C2×C4—1042no—
471C2×C4#8814812yes—
472C2×C4D8×D1311yescharacteristic
473C2×C4#8817212yes—
474C2×C4C2×D4×D1311yescharacteristic
475C8—261no—
476C8—261no—
477C8#8814812yes—
478C8C2×#612711yescharacteristic
479C8C2×#613111yescharacteristic
480C22—21no—
481C22—21no—
482C22—132no—
483C22—261no—
484C22—261no—
485C22—261no—
486C22—261no—
487C22—261no—
488C22—524no—
489C22—1041no—
490C22—1041no—
491C22—1041no—
492C22#1171854312yes—
493C22C2×D8×D1311yescharacteristic
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—261no—
499C4—261no—
500C4—1041no—
501C4—1041no—
502C4—1041no—
503C4#1171854312yes—
504C4C2×#8814811yescharacteristic
505C4C2×#8817211yescharacteristic
506C2—22no—
507C2—262no—
508C2—521no—
509C2—2081no—
510C2C2×#1171854311yescharacteristic
511C2D13×#50811yescharacteristic
512C2#1312796911yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2158C2
socleC22×C13C22×D8
prime radical#13124418C2
hypercenter#2158D13
hypocenterC13#33645
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
2. D13×#427C2semidirect
3. #13117047C2semidirect
4. #13117046C2semidirect
5. #13117040C2semidirect
6. #13117035C2semidirect
7. #13117030C2semidirect
8. #13117029C2semidirect
9. #13117023C2semidirect
10. #13117018C2semidirect
11. #13116618C2semidirect
12. #13116544C2semidirect
13. #13116541C2semidirect
14. C2×#11718099C2semidirect
15. C13×#2158C2semidirect
39. C13×#367C22semidirect
40. C13×#367C22semidirect
41. C13×#366C22semidirect
42. C13×#366C22semidirect
43. #11718101C22semidirect
44. #11718101C22semidirect
49. #11718095C22semidirect
50. #11718095C22semidirect
51. #11718084C22semidirect
52. #11718084C22semidirect
53. #11718083C22semidirect
54. #11718083C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
193. #2158D13semidirect
264. #367C2×D13semidirect
265. #367C2×D13semidirect
268. #366C2×D13semidirect
269. #366C2×D13semidirect
437. C13#33645semidirect

Maximal subgroups

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

subgroupindex
#131244182
D13×#4272
#131170472
#131170462
#131170402
#131170352
#131170302
#131170292
#131170232
#131170182
#131166182
#131165442
#131165412
C2×#117180992
C13×#21582
#3364513