Finite Group Databasebeta

← #11887366

Subgroups — #11887366

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589660C211yesmaximal, characteristic, complemented
2#10589656C211yesmaximal, characteristic, complemented
3C4×C9×D8C211yesmaximal, characteristic, complemented
4#10588838C211yesmaximal, characteristic, complemented
5#10588836C211yesmaximal, characteristic, complemented
6#10588699C211yesmaximal, characteristic, complemented
7#10588692C211yesmaximal, characteristic, complemented
8#10588565C211yesmaximal, characteristic, complemented
9#10588564C211yesmaximal, characteristic, complemented
10#10588458C211yesmaximal, characteristic, complemented
11#10588455C211yesmaximal, characteristic, complemented
12#10588452C211yesmaximal, characteristic, complemented
13D9×#102C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C8×D36C211yesmaximal, characteristic, complemented
16#79609—31nomaximal
17C2×#3699C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C2×C9×D8C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic, complemented
22#63500C2211yescharacteristic
23#63500C2211yescharacteristic, complemented
24C2×#3673C2211yescharacteristic
25C2×#3672C2211yescharacteristic, complemented
26#63492—21no—
27#63491—21no—
28C4×#611—21no—
29C2×(C2×D9)⋊C4—21no—
30C2×C8×D9C2211yescharacteristic
31C2×C8×D9C2211yescharacteristic, complemented
32#63459C2211yescharacteristic
33#63457C2211yescharacteristic
34#63454C2211yescharacteristic, complemented
35C4⋊C4×D9C2211yescharacteristic
36#63448—21no—
37#63446—21no—
38#63444—21no—
39#63441—21no—
40#63437C2211yescharacteristic
41C4×D36C2211yescharacteristic
42#63432C2211yescharacteristic, complemented
43C9×#107C2211yescharacteristic, complemented
44C9×#102C2211yescharacteristic
45C9×#102C2211yescharacteristic, complemented
46C4×C8×C9C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52(C2×D9)⋊C8C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54#63376C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63368C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5558—31no—
61#5554—31no—
62C3×C4×D8D311yescharacteristic
63#5158—31no—
64#5156—31no—
65#5016—31no—
66#5009—31no—
67#4885—31no—
68#4884—31no—
69#4778—31no—
70#4775—31no—
71#4772—31no—
72D3×#102—31no—
73#4697—31no—
74C8×D12—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9—21no—
80C2×#611—21no—
81C2×#611—21no—
82C2×#611—21no—
83C2×#611—21no—
84C22×Dic9—21no—
85#3699—22no—
86#3699—41no—
87D4×D9—22no—
88D4×D9—41no—
89C2×D36—21no—
90C2×D36D411yescharacteristic
91C2×D36C2311yescharacteristic
92C2×C4×D9—21no—
93C2×C4×D9C2311yescharacteristic
94C2×C4×D9C2311yescharacteristic
95C2×Dic18C2311yescharacteristic
96C9×D8—22no—
97C2×C8×C9C2311yescharacteristic
98C2×C8×C9C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C9×C22⋊C4—21no—
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3676—21no—
106#3673—41no—
107#3672—41no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4D411yescharacteristic
114(C2×D9)⋊C4D411yescharacteristic
115C4⋊Dic9—21no—
116C4⋊Dic9D411yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118C4⋊Dic9C2311yescharacteristic
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121Dic9⋊C4—21no—
122C4×Dic9—21no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C8×D9—41no—
126C8×D9—41no—
127#3297—91noSylow
128C2×#237—31no—
129C2×D3×D4—31no—
130C2×C3×D8C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#938—31no—
134#938—31no—
135C2×#214—31no—
136C2×#213—31no—
137#930—61no—
138#929—61no—
139C4×#67—61no—
140C2×(C2×D3)⋊C4—61no—
141C2×D3×C8—31no—
142C2×D3×C8—31no—
143#897—31no—
144#895—31no—
145#892—31no—
146D3×C4⋊C4—31no—
147#886—61no—
148#884—61no—
149#882—61no—
150#879—61no—
151#875—31no—
152C4×D12—31no—
153#870—31no—
154C3×#107C2×D311yescharacteristic
155C3×#102C2×D311yescharacteristic
156C3×#102C2×D311yescharacteristic
157C3×C4×C8C2×D311yescharacteristic
158#832—31no—
159#832—31no—
160#821—31no—
161#821—31no—
162(C2×D3)⋊C8—31no—
163(C2×D3)⋊C8—31no—
164#816—31no—
165#816—31no—
166#810—31no—
167#809—31no—
168#808—31no—
169#807—31no—
170C4⋊(C3⋊C8)—31no—
171C23×C9—21no—
172C23×C9—21no—
173C22×D9—21no—
174C22×D9—42no—
175C22×D9—42no—
176C22×D9—81no—
177C22×D9C2×D411yescharacteristic
178C22×D9C2×D411yescharacteristic
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—21no—
182D4×C9#4112yes—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—81no—
186C2×C4×C9—81no—
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190#611—42no—
191#611—42no—
192#611—42no—
193#611—81no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—42no—
198C2×Dic9C2×D411yescharacteristic
199C2×Dic9C2×D411yescharacteristic
200D36—22no—
201D36—21no—
202D36—21no—
203D36—81no—
204C4×D9—21no—
205C4×D9—21no—
206C4×D9—21no—
207C4×D9—21no—
208C4×D9—81no—
209Dic18—21no—
210Dic18—21no—
211C8×C9—21no—
212C8×C9—21no—
213C9⋊C8—21no—
214C9⋊C8—21no—
215#553—91no—
216#546—91no—
217#488—91no—
218#484—91no—
219#482—91no—
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449—91no—
225#447—91no—
226C4×D8D911yescharacteristic, complemented
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—61no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—61no—
238C2×#67—61no—
239C22×Dic3—61no—
240#237—62no—
241#237—121no—
242D3×D4—62no—
243D3×D4—121no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—61no—
247C2×C4×D3—31no—
248C2×C4×D3—31no—
249C2×C4×D3—61no—
250C2×Dic6—31no—
251C3×D8—22no—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C42C22×D311yescharacteristic
259#217—61no—
260#217—61no—
261#214—121no—
262#213—121no—
263(C2×D3)⋊C4—31no—
264(C2×D3)⋊C4—31no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277C4×Dic3—61no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280D3×C8—121no—
281D3×C8—121no—
282C22×C9—22no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9C22×D411yescharacteristic
289C2×D9—21no—
290C2×D9—21no—
291C2×D9—21no—
292C2×D9—21no—
293C2×D9—21no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—41no—
297C2×D9—84no—
298C2×D9#13512yes—
299C4×C9—21no—
300C4×C9—21no—
301C4×C9—41no—
302C4×C9—41no—
303C4×C9C2×#4111yescharacteristic
304C4×C9H(5,𝔽2)11yescharacteristic
305Dic9—21no—
306Dic9—21no—
307Dic9—41no—
308Dic9—41no—
309Dic9—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8C2×D911yescharacteristic
315C22×C8—91no—
316C22×C8—91no—
317#126—181no—
318#125—91no—
319#124—91no—
320#123—181no—
321#123—181no—
322C22⋊Q8—91no—
323#121—91no—
324#121—91no—
325#121—91no—
326#121—181no—
327#121—181no—
328#120—181no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4C2×D911yescharacteristic
332C4×D4C2×D911yescharacteristic, complemented
333#117—91no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107C2×D911yescharacteristic, complemented
338#106—91no—
339C4⋊C8—91no—
340#103—91no—
341#103—91no—
342#103—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×D911yescharacteristic
349#102C2×D911yescharacteristic, complemented
350C22⋊C8—91no—
351C22⋊C8—91no—
352C4×C8C2×D911yescharacteristic, complemented
353C23×C3—21no—
354C23×C3—21no—
355C22×D3—31no—
356C22×D3—31no—
357C22×D3—61no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—241no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4#23512yes—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—81no—
368C2×C3×C4—81no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—122no—
373#67—122no—
374#67—122no—
375#67—241no—
376C2×Dic3—31no—
377C2×Dic3—31no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—122no—
382D12—62no—
383D12—61no—
384D12—61no—
385D12—241no—
386C4×D3—61no—
387C4×D3—61no—
388C4×D3—61no—
389C4×D3—61no—
390C4×D3—241no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—21no—
394C3×C8—21no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C2×C9—42no—
398C2×C9—81no—
399C2×C9#54611yescharacteristic
400C2×C9C2×#13511yescharacteristic
401C2×C9#57611yescharacteristic
402D9—22no—
403D9—41no—
404D9—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—91no—
410C2×D4—91no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—182no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—361no—
418C2×D4C22×D911yescharacteristic
419C2×D4C22×D911yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—181no—
425C22×C4—181no—
426SD16—361no—
427D8—22no—
428D8—361no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—361no—
432C2×C8—361no—
433C2×C8C22×D911yescharacteristic
434C2×C8C22×D911yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4C22×D911yescharacteristic
443C4⋊C4C22×D911yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—91no—
447C22⋊C4—91no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—181no—
456C42C22×D911yescharacteristic
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3C2×D3×D411yescharacteristic
464C2×D3—32no—
465C2×D3—61no—
466C2×D3—61no—
467C2×D3—61no—
468C2×D3—61no—
469C2×D3—61no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—244no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4C2×#23511yescharacteristic
479C3×C4#100911yescharacteristic
480Dic3—61no—
481Dic3—61no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485C9#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—91no—
489C23—91no—
490C23—181no—
491C23—362no—
492C23—362no—
493C23—721no—
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—182no—
500D4—181no—
501D4—181no—
502D4—362no—
503D4—362no—
504D4—362no—
505D4—721no—
506D4—721no—
507D4#369712yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—91no—
513C2×C4—91no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—362no—
522C2×C4—721no—
523C2×C4D4×D911yescharacteristic
524C2×C4D4×D911yescharacteristic
525C2×C4C23×D911yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—42no—
531C2×C3—81no—
532C2×C3#555011yescharacteristic
533C2×C3#575711yescharacteristic
534C2×C3D3×#13511yescharacteristic
535D3—62no—
536D3—121no—
537D3—241no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—181no—
548C22—181no—
549C22—181no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—724no—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—181no—
560C4—181no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4C2×#369711yescharacteristic
565C4#6371511yescharacteristic
566C3#7960911yescharacteristic
567C2—42no—
568C2—81no—
569C2—182no—
570C2—361no—
571C2—721no—
572C2#1058965211yescharacteristic
573C2#1058985911yescharacteristic
574C2D9×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×D8C2
socleC22×C3C2×D3×D4
hypercenterC4×D8D9
hypocenterC9#3297
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10589660C2semidirect
2. #10589656C2semidirect
3. C4×C9×D8C2semidirect
4. #10588838C2semidirect
5. #10588836C2semidirect
6. #10588699C2semidirect
7. #10588692C2semidirect
8. #10588565C2semidirect
9. #10588564C2semidirect
10. #10588458C2semidirect
11. #10588455C2semidirect
12. #10588452C2semidirect
13. D9×#102C2semidirect
14. #10588379C2semidirect
15. C8×D36C2semidirect
21. C4×D4×C9C22semidirect
23. #63500C22semidirect
25. C2×#3672C22semidirect
31. C2×C8×D9C22semidirect
34. #63454C22semidirect
42. #63432C22semidirect
43. C9×#107C22semidirect
45. C9×#102C22semidirect
46. C4×C8×C9C22semidirect
52. (C2×D9)⋊C8C22semidirect
53. #63376C22semidirect
54. #63376C22semidirect
56. #63368C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
226. C4×D8D9semidirect
332. C4×D4C2×D9semidirect
337. #107C2×D9semidirect
349. #102C2×D9semidirect
352. C4×C8C2×D9semidirect
485. C9#3297semidirect

Maximal subgroups

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

subgroupindex
#105896602
#105896562
C4×C9×D82
#105888382
#105888362
#105886992
#105886922
#105885652
#105885642
#105884582
#105884552
#105884522
D9×#1022
#105883792
C8×D362
#796093