Finite Group Databasebeta

← #16018734

Subgroups — #16018734

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124417C211yesmaximal, characteristic, complemented
2#13117044C211yesmaximal, characteristic, complemented
3#13117041C211yesmaximal, characteristic, complemented
4#13117027C211yesmaximal, characteristic, complemented
5#13117024C211yesmaximal, characteristic, complemented
6#13116951C211yesmaximal, characteristic, complemented
7#13116947C211yesmaximal, characteristic, complemented
8#13116942C211yesmaximal, characteristic, complemented
9#13116937C211yesmaximal, characteristic, complemented
10#13116776C211yesmaximal, characteristic, complemented
11#13116774C211yesmaximal, characteristic, complemented
12#13116759C211yesmaximal, characteristic, complemented
13#13116757C211yesmaximal, characteristic, complemented
14#13116447C211yesmaximal, characteristic, complemented
15C13×#3050C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C13×#525—21no—
19#11719496—21no—
20C2×#88158C2211yescharacteristic
21C13×#467C2211yescharacteristic
22C13×#467C2211yescharacteristic
23C13×#466C2211yescharacteristic
24C13×#466C2211yescharacteristic
25C13×#465—21no—
26C13×#465—21no—
27C13×#427C2211yescharacteristic
28C13×#416—21no—
29C2×#88069C2211yescharacteristic, complemented
30C2×#88068C2211yescharacteristic, complemented
31C2×#88067C2211yescharacteristic, complemented
32C2×#88066C2211yescharacteristic, complemented
33#11718777C2211yescharacteristic
34#11718777C2211yescharacteristic
35#11718776C2211yescharacteristic
36#11718776C2211yescharacteristic
37#11718775—21no—
38#11718775—21no—
39#11718774—21no—
40#11718767C2211yescharacteristic
41C2×#88052C2211yescharacteristic
42C2×#88052C2211yescharacteristic
43#11718156C2211yescharacteristic, complemented
44#11718156C2211yescharacteristic, complemented
45#11718154C2211yescharacteristic, complemented
46#11718154C2211yescharacteristic, complemented
47C22⋊#6090C2211yescharacteristic
48C22⋊#6090C2211yescharacteristic
49C22⋊#6090C2211yescharacteristic
50C22⋊#6090C2211yescharacteristic
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×C13×#41—21no—
60C23×C4×C13D411yescharacteristic
61C2×#6127—21no—
62C13×#135—41no—
63C13×#135—41no—
64C2×C13×Q16C2311yescharacteristic
65C2×C13×SD16—21no—
66C2×C13×D8C2311yescharacteristic
67C22×C8×C13—41no—
68C22×C8×C13—41no—
69C22×C8×C13D411yescharacteristic
70C22×C8×C13D411yescharacteristic
71C22×C8×C13D411yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×#123—41no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—21no—
78C13×#121—21no—
79C13×#121—21no—
80C13×#120—41no—
81C4×D4×C13—41no—
82C4×D4×C13—41no—
83C13×#117—21no—
84#88207—41no—
85#88184—21no—
86#88184—21no—
87#88183—41no—
88C4×C22⋊D13—41no—
89C4×C22⋊D13—41no—
90#88180—21no—
91#88178—21no—
92#88178—21no—
93C2×Dic52C2311yescharacteristic
94#88158—41no—
95#88158—41no—
96C2×D104C2311yescharacteristic
97C2×#6095—21no—
98C13×#107C2311yescharacteristic
99C13×#107C2311yescharacteristic
100C13×#106—21no—
101C13×#103—21no—
102C13×#103—21no—
103C13×#102—21no—
104C13×#102—21no—
105#88069—41no—
106#88068—41no—
107#88067—41no—
108#88066—41no—
109#88061—21no—
110#88061—21no—
111#88058C2311yescharacteristic
112#88058C2311yescharacteristic
113#88057—21no—
114#88056—21no—
115#88056—21no—
116#88052—41no—
117#88052—41no—
118C2×#6090C2311yescharacteristic
119C2×#6090C2311yescharacteristic
120C2×#6090C2311yescharacteristic
121C2×#6090C2311yescharacteristic
122#33763—131nomaximal, Sylow
123C24×C13D811yescharacteristic
124C13×#41—42no—
125C13×#41—42no—
126C2×Q8×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13D811yescharacteristic
135C22×C4×C13D811yescharacteristic
136C22×C4×C13D811yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C2×C22⋊D13—41no—
141C2×C22⋊D13—41no—
142C2×C22⋊D13—41no—
143#6127—42no—
144#6127—42no—
145C2×D52—21no—
146C2×C4×D13—41no—
147C2×Dic26—21no—
148C13×Q16—21no—
149C13×Q16—21no—
150C13×SD16—42no—
151C13×D8—21no—
152C13×D8—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—41no—
160C2×C8×C13—41no—
161C2×C8×C13—41no—
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C42×C13—41no—
176C22⋊Dic13—41no—
177C22⋊Dic13—41no—
178C22⋊Dic13—41no—
179#6103—41no—
180#6103—41no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183#6101—41no—
184#6101—41no—
185C4×Dic13—41no—
186Dic52—21no—
187Dic52—21no—
188D104—21no—
189D104—21no—
190#6095—42no—
191#6090—21no—
192#6090—21no—
193#6090—21no—
194#6090—21no—
195#3050—131no—
196#3050D1311yescharacteristic, complemented
197#2237—131no—
198#2237—131no—
199#2234—131no—
200#2234—131no—
201#2220—131no—
202#2220—131no—
203#2219—131no—
204#2218—131no—
205#2189—131no—
206#2189—131no—
207#2186—131no—
208#2186—131no—
209#2112—131no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13C2×D811yescharacteristic
215C23×C13C2×D811yescharacteristic
216C23×C13C2×D811yescharacteristic
217C22×D13—41no—
218Q8×C13—41no—
219Q8×C13—41no—
220D4×C13—41no—
221D4×C13—41no—
222D4×C13—82no—
223D4×C13—82no—
224D4×C13—82no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—82no—
238C2×C4×C13C2×D811yescharacteristic
239C2×C4×C13C2×D811yescharacteristic
240C2×C4×C13C2×D811yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C22⋊D13—82no—
243C22⋊D13—82no—
244C22⋊D13—82no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248D52—41no—
249D52—41no—
250C4×D13—82no—
251Dic26—41no—
252Dic26—41no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13H(5,𝔽2)11yescharacteristic
257C8×C13H(5,𝔽2)11yescharacteristic
258C2×#135—131no—
259C2×#135C2×D1311yescharacteristic
260C23×C8C2×D1311yescharacteristic
261#525—21no—
262#525—261no—
263C2×Q32—131no—
264C2×SD32—131no—
265C2×SD32—131no—
266C2×D16—131no—
267C2×M32—131no—
268C2×M32—131no—
269#467—131no—
270#467—131no—
271#467C2×D1311yescharacteristic
272#467C2×D1311yescharacteristic
273#466—131no—
274#466—131no—
275#466C2×D1311yescharacteristic
276#466C2×D1311yescharacteristic
277#465—21no—
278#465—21no—
279#465—261no—
280#465—261no—
281#427—131no—
282#427C2×D1311yescharacteristic
283#416—21no—
284#416—261no—
285#367—131no—
286#367—131no—
287#366—131no—
288#366—131no—
289#358—131no—
290#358—131no—
291#358—131no—
292#358—131no—
293#357—131no—
294#357—131no—
295#357—131no—
296#357—131no—
297C22⋊C16—131no—
298C22⋊C16—131no—
299C22⋊C16—131no—
300C22⋊C16—131no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—44no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13C22×D811yescharacteristic
315C2×D13—81no—
316C2×D13—81no—
317C2×D13—81no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—81no—
322C4×C13—81no—
323C4×C13—81no—
324C4×C13#53411yescharacteristic
325C4×C13#57511yescharacteristic
326Dic13—81no—
327Dic13—81no—
328Dic13—81no—
329C2×#41—21no—
330C2×#41—261no—
331C23×C4C22⋊D1311yescharacteristic
332#135—41no—
333#135—41no—
334#135—521no—
335#135—521no—
336C2×Q16—131no—
337C2×Q16C22×D1311yescharacteristic
338C2×SD16—21no—
339C2×SD16—261no—
340C2×D8—131no—
341C2×D8C22×D1311yescharacteristic
342C22×C8—41no—
343C22×C8—41no—
344C22×C8C22⋊D1311yescharacteristic
345C22×C8C22⋊D1311yescharacteristic
346C22×C8C22⋊D1311yescharacteristic
347C22×C8C22×D1311yescharacteristic
348C22×C8C22×D1311yescharacteristic
349C22×C8C22×D1311yescharacteristic
350#123—41no—
351#123—521no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—261no—
355C22⋊Q8—261no—
356#121—21no—
357#121—21no—
358#121—261no—
359#121—261no—
360#120—41no—
361#120—521no—
362C4×D4—41no—
363C4×D4—41no—
364C4×D4—521no—
365C4×D4—521no—
366#117—21no—
367#117—261no—
368Q32—521no—
369SD32—521no—
370SD32—521no—
371D16—521no—
372M32—521no—
373M32—521no—
374C2×C16—131no—
375C2×C16—131no—
376C2×C16—131no—
377C2×C16—131no—
378#107—131no—
379#107—131no—
380#107C22×D1311yescharacteristic
381#107C22×D1311yescharacteristic
382#106—21no—
383#106—261no—
384#103—21no—
385#103—21no—
386#103—261no—
387#103—261no—
388#102—21no—
389#102—21no—
390#102—261no—
391#102—261no—
392C2×C13—41no—
393C2×C13—41no—
394C2×C13—41no—
395C2×C13—161no—
396C2×C13#318611yescharacteristic
397C2×C13#341411yescharacteristic
398C2×C13#341411yescharacteristic
399D13—161no—
400C24#610411yescharacteristic
401#41—42no—
402#41—42no—
403#41—522no—
404#41—522no—
405C2×Q8—21no—
406C2×Q8—261no—
407C2×D4—21no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—261no—
412C2×D4—521no—
413C2×D4—521no—
414C2×D4—521no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—521no—
419C22×C4#610411yescharacteristic
420C22×C4#610411yescharacteristic
421C22×C4#610411yescharacteristic
422C22×C4C2×C22⋊D1311yescharacteristic
423C22×C4C2×C22⋊D1311yescharacteristic
424C22×C4C2×C22⋊D1311yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—261no—
428Q16—261no—
429SD16—42no—
430SD16—522no—
431D8—21no—
432D8—21no—
433D8—261no—
434D8—261no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8C2×C22⋊D1311yescharacteristic
445C2×C8C2×C22⋊D1311yescharacteristic
446C2×C8C2×C22⋊D1311yescharacteristic
447C2×C8C23×D1311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—521no—
455C4⋊C4—521no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—521no—
462C22⋊C4—521no—
463C22⋊C4—521no—
464C22⋊C4—521no—
465C22⋊C4—521no—
466C42—41no—
467C42—521no—
468C16—261no—
469C16—261no—
470C16—261no—
471C16—261no—
472C13#3376311yescharacteristic, complemented, Sylow
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—521no—
478C23C2×#610411yescharacteristic
479C23C2×#610411yescharacteristic
480C23C2×#610411yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—521no—
484Q8—521no—
485D4—41no—
486D4—41no—
487D4—82no—
488D4—82no—
489D4—82no—
490D4—521no—
491D4—521no—
492D4—1042no—
493D4—1042no—
494D4—1042no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—521no—
509C2×C4—521no—
510C2×C4—521no—
511C2×C4—1042no—
512C2×C4C2×#610411yescharacteristic
513C2×C4C2×#610411yescharacteristic
514C2×C4C2×#610411yescharacteristic
515C2×C4C22×C22⋊D1311yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8#8825111yescharacteristic
520C8#8825111yescharacteristic
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—44no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—1041no—
535C22—1041no—
536C22—1041no—
537C22C22×#610411yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—1041no—
545C4—1041no—
546C4—1041no—
547C4#1171950911yescharacteristic
548C4#1171952711yescharacteristic
549C2—41no—
550C2—41no—
551C2—41no—
552C2—161no—
553C2—2081no—
554C2#1312558411yescharacteristic
555C2#1312797011yescharacteristic
556C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3050C2
socleC22×C13C22×D8
hypercenter#3050D13
hypocenterC13#33763
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #13124417C2semidirect
2. #13117044C2semidirect
3. #13117041C2semidirect
4. #13117027C2semidirect
5. #13117024C2semidirect
6. #13116951C2semidirect
7. #13116947C2semidirect
8. #13116942C2semidirect
9. #13116937C2semidirect
10. #13116776C2semidirect
11. #13116774C2semidirect
12. #13116759C2semidirect
13. #13116757C2semidirect
14. #13116447C2semidirect
15. C13×#3050C2semidirect
29. C2×#88069C22semidirect
30. C2×#88068C22semidirect
31. C2×#88067C22semidirect
32. C2×#88066C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
45. #11718154C22semidirect
46. #11718154C22semidirect
51. #11718084C22semidirect
52. #11718084C22semidirect
53. #11718083C22semidirect
54. #11718083C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
196. #3050D13semidirect
472. C13#33763semidirect

Maximal subgroups

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

subgroupindex
#131244172
#131170442
#131170412
#131170272
#131170242
#131169512
#131169472
#131169422
#131169372
#131167762
#131167742
#131167592
#131167572
#131164472
C13×#30502
#3376313