Finite Group Databasebeta

← #16018743

Subgroups — #16018743

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124484C211yesmaximal, characteristic, complemented
2#13117041C211yesmaximal, characteristic, complemented
3#13117024C211yesmaximal, characteristic, complemented
4#13117021C211yesmaximal, characteristic, complemented
5#13117016C211yesmaximal, characteristic, complemented
6#13116951C211yesmaximal, characteristic, complemented
7#13116937C211yesmaximal, characteristic, complemented
8#13116934C211yesmaximal, characteristic, complemented
9#13116920C211yesmaximal, characteristic, complemented
10#13116764C211yesmaximal, characteristic, complemented
11#13116759C211yesmaximal, characteristic, complemented
12#13116759C211yesmaximal, characteristic, complemented
13#13116747C211yesmaximal, characteristic, complemented
14#13116450C211yesmaximal, characteristic, complemented
15C13×#3061C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic, complemented
17C2×C13×#131C2211yescharacteristic
18C13×#537—21no—
19#11719535—21no—
20C22×D104C2211yescharacteristic
21C13×#468—21no—
22C13×#468—21no—
23C13×#467C2211yescharacteristic
24C13×#467C2211yescharacteristic, complemented
25C13×#466C2211yescharacteristic
26C13×#466C2211yescharacteristic, complemented
27C2×C13×#107C2211yescharacteristic, complemented
28C13×#417—21no—
29C2×#88068C2211yescharacteristic
30C2×#88068C2211yescharacteristic
31C2×#88066C2211yescharacteristic
32C2×#88066C2211yescharacteristic
33#11718796—21no—
34#11718796—21no—
35#11718792—21no—
36#11718776C2211yescharacteristic
37#11718776C2211yescharacteristic
38#11718776C2211yescharacteristic
39#11718776C2211yescharacteristic
40#11718767C2211yescharacteristic
41C2×#88052C2211yescharacteristic, complemented
42C22×#6090C2211yescharacteristic, complemented
43#11718156C2211yescharacteristic, complemented
44#11718156C2211yescharacteristic, complemented
45#11718154C2211yescharacteristic, complemented
46#11718154C2211yescharacteristic, complemented
47C22⋊#6090C2211yescharacteristic
48C22⋊#6090C2211yescharacteristic
49C22⋊#6090C2211yescharacteristic, complemented
50C22⋊#6090C2211yescharacteristic, complemented
51#11718083C2211yescharacteristic
52#11718083C2211yescharacteristic
53#11718083C2211yescharacteristic
54#11718083C2211yescharacteristic
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C2×C13×#41D411yescharacteristic
61C22×D52—21no—
62C13×#135—41no—
63C13×#135—41no—
64C2×C13×Q16C2311yescharacteristic
65C2×C13×SD16—21no—
66C2×C13×D8C2311yescharacteristic
67C13×#131—41no—
68C13×#131—41no—
69C2×C13×M16D411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C2×C13×M16D411yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—41no—
78C13×#121—21no—
79C13×#121—21no—
80C13×#121—41no—
81C13×#121—41no—
82C13×#121—41no—
83C2×C13×C4⋊C4—21no—
84#88201—41no—
85#88194—41no—
86#88191—41no—
87#88191—41no—
88#88184—21no—
89#88184—21no—
90#88184—21no—
91#88184—21no—
92#88180—21no—
93C2×D104—21no—
94C2×D104—41no—
95C2×D104—41no—
96C2×D104C2311yescharacteristic
97C2×D104C2311yescharacteristic
98C13×#107—21no—
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#103—21no—
102C13×#103—21no—
103C13×#102—21no—
104C13×#102—21no—
105#88068—41no—
106#88068—41no—
107#88066—41no—
108#88066—41no—
109#88061—21no—
110#88061—21no—
111#88061—21no—
112#88061—21no—
113#88058C2311yescharacteristic
114#88058C2311yescharacteristic
115#88057—21no—
116#88052—41no—
117C2×#6090—41no—
118C2×#6090C2311yescharacteristic
119C2×#6090C2311yescharacteristic
120C2×#6090C2311yescharacteristic
121C2×#6090C2311yescharacteristic
122#33764—131nomaximal, Sylow
123C23×D13—41no—
124C13×#41—41no—
125C13×#41—41no—
126C13×#41—42no—
127C13×#41—42no—
128C2×Q8×C13—21no—
129C2×Q8×C13D811yescharacteristic
130C2×D4×C13—21no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13D811yescharacteristic
135C2×D4×C13D811yescharacteristic
136C2×D4×C13D811yescharacteristic
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C2×C22⋊D13—41no—
143C2×C22⋊D13—41no—
144C2×C22⋊D13—41no—
145C2×C22⋊D13—41no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—42no—
149C2×D52—42no—
150C2×D52—41no—
151C13×Q16—21no—
152C13×Q16—21no—
153C13×SD16—42no—
154C13×D8—21no—
155C13×D8—21no—
156C13×M16—41no—
157C13×M16—41no—
158C13×M16—41no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2411yescharacteristic
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—41no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C22⋊Dic13—41no—
179#6103—41no—
180#6103—41no—
181#6103—41no—
182#6103—41no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4×Dic13—41no—
186D104—21no—
187D104—21no—
188D104—21no—
189D104—21no—
190D104—42no—
191#6090—21no—
192#6090—21no—
193#6090—21no—
194#6090—21no—
195#3061D1311yescharacteristic, complemented
196#3058—131no—
197#2237—131no—
198#2234—131no—
199#2233—131no—
200#2232—131no—
201#2220—131no—
202#2218—131no—
203#2217—131no—
204#2215—131no—
205#2187—131no—
206#2186—131no—
207#2186—131no—
208#2184—131no—
209#2113—131no—
210C23×C13—41no—
211C23×C13C2×D811yescharacteristic
212C23×C13C2×D811yescharacteristic
213C23×C13C2×D811yescharacteristic
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—82no—
217C22×D13—161no—
218C22×D13—161no—
219Q8×C13—41no—
220Q8×C13—41no—
221Q8×C13—41no—
222D4×C13—41no—
223D4×C13—41no—
224D4×C13—41no—
225D4×C13—41no—
226D4×C13—41no—
227D4×C13—82no—
228D4×C13—161no—
229D4×C13—161no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—82no—
240C2×C4×C13—161no—
241C2×C4×C13C2×D811yescharacteristic
242C2×C4×C13C2×D811yescharacteristic
243C2×C4×C13C2×D811yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C22⋊D13—161no—
246C22⋊D13—161no—
247C22⋊D13—161no—
248C22⋊D13—161no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251D52—41no—
252D52—41no—
253D52—41no—
254D52—41no—
255D52—82no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13H(5,𝔽2)11yescharacteristic
260C8×C13H(5,𝔽2)11yescharacteristic
261C2×#135C2×D1311yescharacteristic, complemented
262C22×D8—131no—
263C2×#131C2×D1311yescharacteristic
264#537—21no—
265#535—261no—
266C2×SD32—131no—
267C2×SD32—131no—
268C2×D16—131no—
269C2×D16—131no—
270C2×M32—131no—
271C22×C16—131no—
272#469—261no—
273#469—261no—
274#468—21no—
275#468—21no—
276#467C2×D1311yescharacteristic
277#467C2×D1311yescharacteristic, complemented
278#466—131no—
279#466—131no—
280#466—131no—
281#466—131no—
282#466C2×D1311yescharacteristic
283#466C2×D1311yescharacteristic, complemented
284#427—131no—
285C2×#107C2×D1311yescharacteristic, complemented
286#418—261no—
287#417—21no—
288#367—131no—
289#367—131no—
290#366—131no—
291#366—131no—
292#358—131no—
293#358—131no—
294#357—131no—
295#357—131no—
296#357—131no—
297#357—131no—
298#357—131no—
299#357—131no—
300C22⋊C16—131no—
301C22⋊C16—131no—
302C22⋊C16—131no—
303C22⋊C16—131no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—21no—
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13C22×D811yescharacteristic
317C2×D13—81no—
318C2×D13—81no—
319C2×D13—81no—
320C2×D13—81no—
321C2×D13—81no—
322C2×D13—81no—
323C2×D13—164no—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—81no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13#53411yescharacteristic
331C4×C13#57511yescharacteristic
332Dic13—81no—
333Dic13—81no—
334C2×#41—21no—
335C2×#41C22⋊D1311yescharacteristic
336C22×D4—261no—
337#135—41no—
338#135—41no—
339C2×Q16C22×D1311yescharacteristic
340C2×SD16—21no—
341C2×D8—131no—
342C2×D8—131no—
343C2×D8—261no—
344C2×D8—521no—
345C2×D8—521no—
346C2×D8C22×D1311yescharacteristic
347#131—41no—
348#131—41no—
349C2×M16C22⋊D1311yescharacteristic
350C2×M16C22⋊D1311yescharacteristic
351C2×M16C22⋊D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355#127—521no—
356#124—521no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—41no—
360#121—21no—
361#121—21no—
362#121—41no—
363#121—41no—
364#121—41no—
365#121—261no—
366#121—261no—
367#121—261no—
368#121—261no—
369#120—521no—
370#120—521no—
371#117—261no—
372C2×C4⋊C4—21no—
373SD32—521no—
374SD32—521no—
375D16—521no—
376D16—521no—
377M32—521no—
378C2×C16—131no—
379C2×C16—131no—
380C2×C16—131no—
381C2×C16—131no—
382C2×C16—521no—
383#107—21no—
384#107—131no—
385#107—131no—
386#107C22×D1311yescharacteristic
387#107C22×D1311yescharacteristic
388#106—261no—
389#103—21no—
390#103—21no—
391#102—21no—
392#102—21no—
393#102—261no—
394#102—261no—
395#102—261no—
396#102—261no—
397C2×C13—41no—
398C2×C13—41no—
399C2×C13—41no—
400C2×C13—161no—
401C2×C13#318611yescharacteristic
402C2×C13#341511yescharacteristic
403C2×C13#341611yescharacteristic
404D13—161no—
405D13—161no—
406C24—521no—
407#41—41no—
408#41—41no—
409#41—42no—
410#41—42no—
411C2×Q8—21no—
412C2×Q8#610411yescharacteristic
413C2×D4—21no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—522no—
420C2×D4—522no—
421C2×D4—521no—
422C2×D4—521no—
423C2×D4—521no—
424C2×D4—521no—
425C2×D4—521no—
426C2×D4#610411yescharacteristic
427C2×D4#610411yescharacteristic
428C2×D4#610411yescharacteristic
429C22×C4—41no—
430C22×C4—41no—
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434Q16—21no—
435Q16—21no—
436SD16—42no—
437D8—21no—
438D8—21no—
439D8—261no—
440D8—261no—
441D8—261no—
442D8—261no—
443D8—522no—
444M16—41no—
445M16—41no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×C22⋊D1311yescharacteristic
454C2×C8C2×C22⋊D1311yescharacteristic
455C2×C8C2×C22⋊D1311yescharacteristic
456C2×C8C23×D1311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—521no—
469C22⋊C4—521no—
470C22⋊C4—521no—
471C22⋊C4—521no—
472C22⋊C4—521no—
473C42—521no—
474C16—261no—
475C16—261no—
476C16—261no—
477C16—261no—
478C13#3376411yescharacteristic, complemented, Sylow
479C23—41no—
480C23—521no—
481C23—521no—
482C23—1042no—
483C23—2081no—
484C23—2081no—
485C23C2×#610411yescharacteristic
486C23C2×#610411yescharacteristic
487C23C2×#610411yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—82no—
497D4—161no—
498D4—161no—
499D4—521no—
500D4—521no—
501D4—521no—
502D4—521no—
503D4—1042no—
504D4—2081no—
505D4—2081no—
506D4—2081no—
507D4—2081no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—161no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4C2×#610411yescharacteristic
522C2×C4C2×#610411yescharacteristic
523C2×C4C2×#610411yescharacteristic
524C2×C4C22×C22⋊D1311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8#8825111yescharacteristic
529C8#8825111yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—1041no—
543C22—1041no—
544C22—1041no—
545C22—1041no—
546C22—1041no—
547C22—1041no—
548C22—2084no—
549C22C22×#610411yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—1041no—
557C4—1041no—
558C4#1171950911yescharacteristic
559C4#1171952711yescharacteristic
560C2—41no—
561C2—41no—
562C2—41no—
563C2—161no—
564C2—2081no—
565C2—2081no—
566C2#1312558411yescharacteristic
567C2#1312797511yescharacteristic
568C2#1312798011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3061C2
socleC22×C13C22×D8
hypercenter#3061D13
hypocenterC13#33764
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. #13124484C2semidirect
2. #13117041C2semidirect
3. #13117024C2semidirect
4. #13117021C2semidirect
5. #13117016C2semidirect
6. #13116951C2semidirect
7. #13116937C2semidirect
8. #13116934C2semidirect
9. #13116920C2semidirect
10. #13116764C2semidirect
11. #13116759C2semidirect
12. #13116759C2semidirect
13. #13116747C2semidirect
14. #13116450C2semidirect
15. C13×#3061C2semidirect
16. C2×C13×#135C22semidirect
24. C13×#467C22semidirect
26. C13×#466C22semidirect
27. C2×C13×#107C22semidirect
41. C2×#88052C22semidirect
42. C22×#6090C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
45. #11718154C22semidirect
46. #11718154C22semidirect
49. C22⋊#6090C22semidirect
50. C22⋊#6090C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
195. #3061D13semidirect
261. C2×#135C2×D13semidirect
277. #467C2×D13semidirect
283. #466C2×D13semidirect
285. C2×#107C2×D13semidirect
478. C13#33764semidirect

Maximal subgroups

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

subgroupindex
#131244842
#131170412
#131170242
#131170212
#131170162
#131169512
#131169372
#131169342
#131169202
#131167642
#131167592
#131167472
#131164502
C13×#30612
#3376413