Finite Group Databasebeta

← #11866305

Subgroups — #11866305

Order 1152.

1470 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64124C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596186C211yesmaximal, characteristic
4#10596043C211yesmaximal, characteristic, complemented
5C32×#460C211yesmaximal, characteristic, complemented
6#10592865C211yesmaximal, characteristic, complemented
7#10592862C211yesmaximal, characteristic, complemented
8#10592774C211yesmaximal, characteristic, complemented
9#10592727C211yesmaximal, characteristic, complemented
10#10592544C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592471C211yesmaximal, characteristic, complemented
13#10592469C211yesmaximal, characteristic, complemented
14#10592466C211yesmaximal, characteristic, complemented
15#10592461C211yesmaximal, characteristic, complemented
16#80385—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C32×#127C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic, complemented
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3756C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27#64149C2211yescharacteristic
28#64148—21no—
29#64148—21no—
30#64146—21no—
31#64146—21no—
32#64145C2211yescharacteristic
33C2×#3754C2211yescharacteristic
34C2×#3754C2211yescharacteristic, complemented
35#64124—24no—
36SD16×C3⋊D3—24no—
37C2×#3746C2211yescharacteristic, complemented
38C2×#3744C2211yescharacteristic
39C2×#3743C2211yescharacteristic
40C2×C8×C3⋊D3C2211yescharacteristic
41#64101—21no—
42#64101C2211yescharacteristic
43#64096—21no—
44#64096C2211yescharacteristic, complemented
45#64084C2211yescharacteristic
46#64081—21no—
47#64081C2211yescharacteristic
48C4×#634—21no—
49C4×#634C2211yescharacteristic, complemented
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#102C2211yescharacteristic
52C32×#102C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#915—34no—
63C2×D3×SD16—34no—
64#5715—34no—
65#5572—34no—
66C3×#460D314yescomplemented
67#5166—34no—
68#5163—34no—
69#5075—34no—
70#5028—34no—
71#4845—34no—
72#4839—34no—
73#4772—34no—
74#4770—34no—
75#4767—34no—
76#4762—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4C2311yescharacteristic
82C2×C32×D4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87C22×C3⋊Dic3—21no—
88Q8×C3⋊D3—22no—
89Q8×C3⋊D3D414yescomplemented
90#3830—22no—
91#3830—22no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3—22no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C32×SD16—22no—
101C32×SD16—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C42—21no—
107C32×C42C2311yescharacteristic
108#3757—21no—
109#3757—21no—
110#3756—22no—
111#3755—22no—
112#3754—22no—
113#3754—22no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123#3750D411yescharacteristic
124#3750D411yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3—21no—
128C4×C3⋊Dic3—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3746—22no—
133#3744—22no—
134#3743—22no—
135C8×C3⋊D3—22no—
136#3043—91noSylow
137C2×D3×Q8—34no—
138C2×#237—34no—
139C2×D3×D4—34no—
140C2×C3×SD16C2×D314yes—
141C2×C3×SD16C2×D314yescomplemented
142C3×#127C2×D314yes—
143C3×C4×Q8C2×D314yescomplemented
144Q8×Dic3—34no—
145C2×#216—34no—
146C2×#215—34no—
147#940—34no—
148#939—64no—
149#939—64no—
150#937—64no—
151#937—64no—
152#936—34no—
153C2×#214—34no—
154C2×#214—34no—
155#915—616no—
156D3×SD16—616no—
157C2×Dic12—34no—
158C2×#204—34no—
159C2×ΓL(1,𝔽25)—34no—
160C2×D3×C8—34no—
161#892—34no—
162#892—64no—
163#887—34no—
164#887—64no—
165#875—34no—
166#872—34no—
167#872—64no—
168C4×Dic6—34no—
169C4×Dic6—64no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#102C2×D314yes—
172C3×#102C2×D314yescomplemented
173#832—34no—
174#832—34no—
175#821—34no—
176#816—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#810—34no—
180#809—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C23×C32—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—42no—
186C22×C3⋊D3—81no—
187C22×C3⋊D3—81no—
188C22×C3⋊D3C2×D411yescharacteristic
189C32×Q8—21no—
190C32×Q8C2×D412yes—
191C32×D4—21no—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4—21no—
195C32×D4—81no—
196C32×D4—81no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2411yescharacteristic
202#638—42no—
203#638—42no—
204#638—81no—
205#638—81no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—42no—
210C2×C3⋊Dic3C2×D411yescharacteristic
211C2×C3⋊Dic3C2×D411yescharacteristic
212C2×C3⋊Dic3C2×D411yescharacteristic
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—21no—
215C4×C3⋊D3—24no—
216C4×C3⋊D3C2×D412yes—
217C4×C3⋊D3#4112yes—
218#634—21no—
219#634—24no—
220#634—21no—
221#634—21no—
222#634C2×D412yes—
223C32×C8—21no—
224C32×C8—21no—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C2×#137—91no—
228C22×SD16—91no—
229#535—91no—
230#519—91no—
231#464—91no—
232#464—91no—
233#464—91no—
234#464—91no—
235#460—91no—
236#460—91no—
237#460—91no—
238#460C3⋊D311yescharacteristic, complemented
239#424—91no—
240#418—91no—
241#416—91no—
242C23×D3—64no—
243C2×C3×Q8C22×D314yes—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4C22×D314yes—
247C2×C3×D4C22×D314yes—
248C2×#67—64no—
249C2×#67—64no—
250C2×#67—64no—
251C2×#67—64no—
252C22×Dic3—64no—
253D3×Q8—316no—
254D3×Q8—68no—
255#237—68no—
256#237—68no—
257D3×D4—68no—
258D3×D4—68no—
259C2×D12—34no—
260C2×C4×D3—34no—
261C2×C4×D3—64no—
262C2×Dic6—34no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C3×SD16—28no—
266C3×SD16—28no—
267C2×C3×C8C22×D314yes—
268C2×C3×C8C22×D314yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4C22×D314yes—
271C3×C42—24no—
272C3×C42C22×D314yes—
273#217—64no—
274#217—64no—
275#216—68no—
276#215—68no—
277#214—68no—
278#214—68no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284C4⋊Dic3—34no—
285C4⋊Dic3—64no—
286Dic3⋊C4—34no—
287Dic3⋊C4—34no—
288Dic3⋊C4—64no—
289Dic3⋊C4—64no—
290C4×Dic3—34no—
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C2×C3⋊C8—34no—
296C2×C3⋊C8—34no—
297Dic12—68no—
298#204—68no—
299ΓL(1,𝔽25)—68no—
300D3×C8—68no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—21no—
309C2×C3⋊D3—21no—
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—84no—
314C2×C3⋊D3#12112yes—
315C32×C4—22no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C22×D411yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3⋊Dic3—22no—
322C3⋊Dic3—21no—
323C3⋊Dic3—21no—
324C3⋊Dic3—41no—
325C3⋊Dic3—41no—
326C3⋊Dic3#12112yes—
327C2×#41—91no—
328C22×Q8—91no—
329C22×D4—91no—
330#137—184no—
331C2×Q16—91no—
332C2×Q16—91no—
333C2×SD16—91no—
334C2×SD16—91no—
335C2×SD16—91no—
336C2×SD16—91no—
337C2×SD16—184no—
338C2×SD16C2×C3⋊D311yescharacteristic
339C2×SD16C2×C3⋊D311yescharacteristic, complemented
340C2×M16—91no—
341C22×C8—91no—
342#127—91no—
343#127C2×C3⋊D311yescharacteristic
344#124—91no—
345#124—91no—
346#121—181no—
347#121—181no—
348#120—181no—
349#120—181no—
350C4×Q8—91no—
351C4×Q8—91no—
352C4×Q8—91no—
353C4×Q8—181no—
354C4×Q8—181no—
355C4×Q8C2×C3⋊D311yescharacteristic, complemented
356#117—91no—
357#117—91no—
358#117—181no—
359#117—181no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363C4⋊C8C2×C3⋊D311yescharacteristic, complemented
364#103—91no—
365#103—91no—
366#102—91no—
367#102—91no—
368#102—91no—
369#102—91no—
370#102C2×C3⋊D311yescharacteristic
371#102C2×C3⋊D311yescharacteristic, complemented
372C23×C3—24no—
373C23×C3—24no—
374C22×D3—34no—
375C22×D3—64no—
376C22×D3—128no—
377C22×D3—244no—
378C22×D3—244no—
379C3×Q8—24no—
380C3×Q8D3×D418yes—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—24no—
384C3×D4—24no—
385C3×D4—84no—
386C3×D4—84no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4D3×D414yes—
390C2×C3×C4D3×D414yes—
391C2×C3×C4C23×D314yes—
392#67—128no—
393#67—128no—
394#67—244no—
395#67—244no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—128no—
403D12—64no—
404D12—64no—
405C4×D3—38no—
406C4×D3—38no—
407C4×D3—616no—
408Dic6—38no—
409Dic6—616no—
410Dic6—64no—
411Dic6—64no—
412Dic6—64no—
413C3×C8—24no—
414C3×C8—24no—
415C3⋊C8—64no—
416C3⋊C8—64no—
417C2×C32—81no—
418C2×C32—81no—
419C2×C32C2×#12111yescharacteristic
420C2×C32#57711yescharacteristic
421C2×C32#57711yescharacteristic
422C3⋊D3—22no—
423C3⋊D3—81no—
424C24—181no—
425#41—182no—
426#41—182no—
427C2×Q8—94no—
428C2×Q8—91no—
429C2×Q8—91no—
430C2×Q8—181no—
431C2×Q8—182no—
432C2×Q8C22×C3⋊D311yescharacteristic
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—91no—
436C2×D4—182no—
437C2×D4—182no—
438C2×D4—181no—
439C2×D4—181no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4C22×C3⋊D311yescharacteristic
443C2×D4C22×C3⋊D311yescharacteristic
444C22×C4—91no—
445C22×C4—181no—
446C22×C4—181no—
447Q16—182no—
448Q16—182no—
449SD16—22no—
450SD16—22no—
451SD16—182no—
452SD16—182no—
453SD16—182no—
454SD16—182no—
455M16—182no—
456C2×C8—91no—
457C2×C8—91no—
458C2×C8—182no—
459C2×C8C22×C3⋊D311yescharacteristic
460C2×C8C22×C3⋊D311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—91no—
463C4⋊C4—91no—
464C4⋊C4—91no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4C22×C3⋊D311yescharacteristic
469C22⋊C4—91no—
470C22⋊C4—91no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C42—21no—
477C42—91no—
478C42—181no—
479C42—181no—
480C42—181no—
481C42—181no—
482C42C22×C3⋊D311yescharacteristic
483C22×C3—44no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—44no—
489C22×C3C2×D3×D414yes—
490C2×D3—38no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—124no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—2416no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—28no—
500C3×C4—44no—
501C3×C4C2×D3×D414yes—
502C3×C4D3×#4114yes—
503Dic3—38no—
504Dic3—64no—
505Dic3—64no—
506Dic3—68no—
507Dic3—124no—
508Dic3—124no—
509C32#304311yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—91no—
513C23—181no—
514C23—362no—
515C23—721no—
516C23—721no—
517Q8—21no—
518Q8—92no—
519Q8—184no—
520Q8—181no—
521Q8—181no—
522Q8—181no—
523Q8D4×C3⋊D312yes—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—81no—
529D4—81no—
530D4—181no—
531D4—181no—
532D4—362no—
533D4—362no—
534D4—721no—
535D4—721no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—91no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—91no—
542C2×C4—91no—
543C2×C4—184no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—362no—
548C2×C4D4×C3⋊D311yescharacteristic
549C2×C4D4×C3⋊D311yescharacteristic
550C2×C4C23×C3⋊D311yescharacteristic
551C8—21no—
552C8—21no—
553C8—181no—
554C8—181no—
555C2×C3—84no—
556C2×C3—84no—
557C2×C3D3×#12114yes—
558C2×C3#576214yes—
559C2×C3#577514yes—
560D3—68no—
561D3—244no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—92no—
569C22—181no—
570C22—181no—
571C22—361no—
572C22—361no—
573C22—361no—
574C22—724no—
575C22C2×D4×C3⋊D311yescharacteristic
576C4—21no—
577C4—21no—
578C4—22no—
579C4—41no—
580C4—92no—
581C4—181no—
582C4—181no—
583C4—182no—
584C4—361no—
585C4—361no—
586C4C2×D4×C3⋊D311yescharacteristic
587C4#41×C3⋊D311yescharacteristic
588C3#8038514yescomplemented
589C2—81no—
590C2—81no—
591C2—182no—
592C2—721no—
593C2C3⋊D3×#12111yescharacteristic
594C2#1059623311yescharacteristic
595C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radical#10596186C2
hypercenter#460C3⋊D3
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#64124C2semidirect
2. C2×SD16×C3⋊D3C2semidirect
4. #10596043C2semidirect
5. C32×#460C2semidirect
6. #10592865C2semidirect
7. #10592862C2semidirect
8. #10592774C2semidirect
9. #10592727C2semidirect
10. #10592544C2semidirect
11. #10592538C2semidirect
12. #10592471C2semidirect
13. #10592469C2semidirect
14. #10592466C2semidirect
15. #10592461C2semidirect
21. C2×C32×SD16C22semidirect
23. C32×C4×Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. C2×#3756C22semidirect
34. C2×#3754C22semidirect
37. C2×#3746C22semidirect
44. #64096C22semidirect
49. C4×#634C22semidirect
50. C32×C4⋊C8C22semidirect
52. C32×#102C22semidirect
54. #63659C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#460D3semidirect
89. Q8×C3⋊D3D4semidirect
141. C2×C3×SD16C2×D3semidirect
143. C3×C4×Q8C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
172. C3×#102C2×D3semidirect
238. #460C3⋊D3semidirect
339. C2×SD16C2×C3⋊D3semidirect
355. C4×Q8C2×C3⋊D3semidirect
363. C4⋊C8C2×C3⋊D3semidirect
371. #102C2×C3⋊D3semidirect
509. C32#3043semidirect
588. C3#80385semidirect

Maximal subgroups

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

subgroupindex
C2×#641242
C2×SD16×C3⋊D32
#105961862
#105960432
C32×#4602
#105928652
#105928622
#105927742
#105927272
#105925442
#105925382
#105924712
#105924692
#105924662
#105924612
#803853