Finite Group Databasebeta

← #11887357

Subgroups — #11887357

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#10589667C211yesmaximal, characteristic, complemented
2#10589652C211yesmaximal, characteristic, complemented
3C8×D4×C9C211yesmaximal, characteristic, complemented
4#10588796C211yesmaximal, characteristic, complemented
5#10588795C211yesmaximal, characteristic, complemented
6#10588794C211yesmaximal, characteristic, complemented
7C2×#63380C211yesmaximal, characteristic, complemented
8#10588531C211yesmaximal, characteristic, complemented
9#10588528C211yesmaximal, characteristic, complemented
10#10588419C211yesmaximal, characteristic, complemented
11#10588416C211yesmaximal, characteristic, complemented
12#10588414C211yesmaximal, characteristic, complemented
13#10588402C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C4×D72C211yesmaximal, characteristic, complemented
16#79441—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63501—21no—
23#63499—21no—
24#63492C2211yescharacteristic
25#63492C2211yescharacteristic
26#63492C2211yescharacteristic, complemented
27#63488C2211yescharacteristic, complemented
28C2×C4⋊Dic9C2211yescharacteristic
29#63486C2211yescharacteristic
30C2×D72C2211yescharacteristic
31C2×D72C2211yescharacteristic
32C2×#3664C2211yescharacteristic, complemented
33#63460—21no—
34#63456—21no—
35#63446—21no—
36#63445—21no—
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39#63437C2211yescharacteristic
40C4×D36C2211yescharacteristic
41C4×D36C2211yescharacteristic, complemented
42#63432C2211yescharacteristic, complemented
43C9×C4⋊C8C2211yescharacteristic, complemented
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic, complemented
46C4×C8×C9C2211yescharacteristic, complemented
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic
53#63380C2211yescharacteristic, complemented
54#63378C2211yescharacteristic, complemented
55#63378C2211yescharacteristic, complemented
56#63377C2211yescharacteristic, complemented
57#63376C2211yescharacteristic, complemented
58#63376C2211yescharacteristic, complemented
59#63376C2211yescharacteristic, complemented
60#5565—31no—
61#5550—31no—
62C3×C8×D4D311yescharacteristic
63#5115—31no—
64#5114—31no—
65#5113—31no—
66C2×#821—31no—
67#4847—31no—
68#4844—31no—
69#4737—31no—
70#4734—31no—
71#4732—31no—
72#4722—31no—
73#4697—31no—
74C4×D24—31no—
75C23×D9—21no—
76C2×D4×C9D411yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C2×#611—21no—
80C2×#611—21no—
81C2×#611—21no—
82C2×#611—21no—
83C22×Dic9—21no—
84#3697—22no—
85#3697—41no—
86C2×D36—22no—
87C2×D36—21no—
88C2×D36—41no—
89C2×D36C2311yescharacteristic
90C2×D36C2311yescharacteristic
91C2×D36C2311yescharacteristic
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9—21no—
95C2×Dic18C2311yescharacteristic
96C2×C8×C9—41no—
97C2×C8×C9—41no—
98C2×C8×C9C2311yescharacteristic
99C2×C8×C9C2311yescharacteristic
100C2×C8×C9C2311yescharacteristic
101C2×C8×C9C2311yescharacteristic
102C9×C4⋊C4D411yescharacteristic
103C9×C22⋊C4D411yescharacteristic
104C9×C22⋊C4D411yescharacteristic
105C42×C9C2311yescharacteristic
106#3676—21no—
107#3676—21no—
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)⋊C4—21no—
114(C2×D9)⋊C4—21no—
115C4⋊Dic9—21no—
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118C4⋊Dic9C2311yescharacteristic
119C4⋊Dic9C2311yescharacteristic
120Dic9⋊C4—21no—
121Dic9⋊C4—21no—
122Dic9⋊C4—21no—
123C4×Dic9—21no—
124D72—22no—
125D72—41no—
126#3664—41no—
127#3297—91noSylow
128C2×#235—31no—
129C22×D12—31no—
130C22×C3×C8C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#939—61no—
134#937—61no—
135#930—31no—
136#930—31no—
137#930—31no—
138#926—31no—
139C2×C4⋊Dic3—31no—
140#924—31no—
141C2×D24—31no—
142C2×D24—31no—
143C2×#204—31no—
144#898—61no—
145#894—61no—
146#884—61no—
147#883—61no—
148#67⋊C4—61no—
149D3×C22⋊C4—61no—
150#875—31no—
151C4×D12—31no—
152C4×D12—31no—
153#870—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C4×C8C2×D311yescharacteristic
158#821—31no—
159#821—31no—
160#821—31no—
161#821—31no—
162#821—31no—
163#821—31no—
164#821—31no—
165#818—31no—
166#818—31no—
167#817—31no—
168#816—31no—
169#816—31no—
170#816—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—21no—
176C22×D9—42no—
177C22×D9—42no—
178C22×D9—81no—
179D4×C9—22no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—42no—
190#611—42no—
191#611—81no—
192#611—81no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—81no—
199D36—21no—
200D36—21no—
201D36—21no—
202D36—21no—
203D36—21no—
204D36—42no—
205D36#4112yes—
206C4×D9—42no—
207C4×D9—81no—
208C4×D9—81no—
209Dic18—21no—
210Dic18—21no—
211C8×C9—21no—
212C8×C9—21no—
213C8×C9—21no—
214C8×C9—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×D8—91no—
227C8×D4D911yescharacteristic, complemented
228#416—91no—
229C2×#102—91no—
230C23×D3—61no—
231C2×C3×D4D1211yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—61no—
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—61no—
239#235—62no—
240#235—121no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—62no—
245C2×D12—61no—
246C2×D12—121no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×Dic6—31no—
251C2×C3×C8—41no—
252C2×C3×C8—41no—
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C2×C3×C8C22×D311yescharacteristic
257C3×C4⋊C4D1211yescharacteristic
258C3×C22⋊C4D1211yescharacteristic
259C3×C22⋊C4D1211yescharacteristic
260C3×C42C22×D311yescharacteristic
261#217—61no—
262#217—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
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—31no—
274C4⋊Dic3—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278C4×Dic3—61no—
279D24—62no—
280D24—121no—
281#204—121no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—21no—
285C22×C9—21no—
286C22×C9—21no—
287C22×C9#13512yes—
288C22×C9C22×D411yescharacteristic
289C2×D9—22no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—41no—
293C2×D9—41no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—41no—
297C2×D9—41no—
298C2×D9—84no—
299C4×C9—21no—
300C4×C9—21no—
301C4×C9—21no—
302C4×C9—21no—
303C4×C9C2×#4111yescharacteristic
304C4×C9H(5,𝔽2)11yescharacteristic
305Dic9—41no—
306Dic9—41no—
307Dic9—41no—
308Dic9—41no—
309Dic9—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8C2×D911yescharacteristic
316C22×C8C2×D911yescharacteristic, complemented
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—91no—
331C4×D4—181no—
332C4×D4C2×D911yescharacteristic
333#117—91no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107—91no—
338#106—91no—
339C4⋊C8C2×D911yescharacteristic, complemented
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#102—91no—
349#102—91no—
350C22⋊C8C2×D911yescharacteristic
351C22⋊C8C2×D911yescharacteristic, complemented
352C4×C8C2×D911yescharacteristic, complemented
353C23×C3C2×D1211yescharacteristic
354C23×C3C2×D1211yescharacteristic
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—241no—
361C3×D4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371#67—122no—
372#67—122no—
373#67—241no—
374#67—241no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—241no—
381D12—32no—
382D12—61no—
383D12—61no—
384D12—61no—
385D12—61no—
386D12—61no—
387D12—122no—
388C4×D3—122no—
389C4×D3—241no—
390C4×D3—241no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—21no—
396C3×C8—21no—
397C2×C9—22no—
398C2×C9—41no—
399C2×C9#54611yescharacteristic
400C2×C9C2×#13511yescharacteristic
401C2×C9#57611yescharacteristic
402D9—42no—
403D9—81no—
404D9—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—91no—
410C2×D4—91no—
411C2×D4—91no—
412C2×D4—182no—
413C2×D4—181no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—361no—
419C2×D4D3611yescharacteristic
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4C22×D911yescharacteristic
425C22×C4C22×D911yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8C22×D911yescharacteristic
432C2×C8C22×D911yescharacteristic
433C2×C8C22×D911yescharacteristic
434C2×C8C22×D911yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4—181no—
443C4⋊C4D3611yescharacteristic
444C22⋊C4—181no—
445C22⋊C4—181no—
446C22⋊C4—181no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4D3611yescharacteristic
454C22⋊C4D3611yescharacteristic
455C42—181no—
456C42C22×D911yescharacteristic
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3#90412yes—
463C22×C3C22×D1211yescharacteristic
464C2×D3—62no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—244no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4#100411yescharacteristic
479C3×C4D3×#4111yescharacteristic
480Dic3—121no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485C9#329711yescharacteristic, complemented, Sylow
486C23—181no—
487C23—181no—
488C23—181no—
489C23—362no—
490C23—362no—
491C23—721no—
492C23C2×D3611yescharacteristic
493C23C2×D3611yescharacteristic
494Q8—181no—
495Q8—181no—
496D4—22no—
497D4—92no—
498D4—181no—
499D4—181no—
500D4—181no—
501D4—181no—
502D4—181no—
503D4—362no—
504D4—362no—
505D4—362no—
506D4—721no—
507D4—721no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—362no—
518C2×C4—721no—
519C2×C4—721no—
520C2×C4—721no—
521C2×C4C2×D3611yescharacteristic
522C2×C4C2×D3611yescharacteristic
523C2×C4C2×D3611yescharacteristic
524C2×C4C2×D3611yescharacteristic
525C2×C4C23×D911yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C2×C3—22no—
531C2×C3—41no—
532C2×C3#555411yescharacteristic
533C2×C3C2×#90411yescharacteristic
534C2×C3#575211yescharacteristic
535D3—122no—
536D3—241no—
537D3—241no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—182no—
544C22—361no—
545C22—361no—
546C22—361no—
547C22—361no—
548C22—361no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—724no—
553C22#6346712yes—
554C22C22×D3611yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—361no—
560C4—361no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4#6371011yescharacteristic
565C4#41×D911yescharacteristic
566C3#7944111yescharacteristic
567C2—22no—
568C2—41no—
569C2—362no—
570C2—721no—
571C2—721no—
572C2#1058965611yescharacteristic
573C2C2×#6346711yescharacteristic
574C2#1058985411yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×D12
hypercenterC8×D4D9
hypocenterC9#3297
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #10589667C2semidirect
2. #10589652C2semidirect
3. C8×D4×C9C2semidirect
4. #10588796C2semidirect
5. #10588795C2semidirect
6. #10588794C2semidirect
7. C2×#63380C2semidirect
8. #10588531C2semidirect
9. #10588528C2semidirect
10. #10588419C2semidirect
11. #10588416C2semidirect
12. #10588414C2semidirect
13. #10588402C2semidirect
14. #10588379C2semidirect
15. C4×D72C2semidirect
20. C22×C8×C9C22semidirect
26. #63492C22semidirect
27. #63488C22semidirect
32. C2×#3664C22semidirect
41. C4×D36C22semidirect
42. #63432C22semidirect
43. C9×C4⋊C8C22semidirect
45. C9×C22⋊C8C22semidirect
46. C4×C8×C9C22semidirect
53. #63380C22semidirect
54. #63378C22semidirect
55. #63378C22semidirect
56. #63377C22semidirect
57. #63376C22semidirect
58. #63376C22semidirect
59. #63376C22semidirect
227. C8×D4D9semidirect
316. C22×C8C2×D9semidirect
339. C4⋊C8C2×D9semidirect
351. C22⋊C8C2×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
#105896672
#105896522
C8×D4×C92
#105887962
#105887952
#105887942
C2×#633802
#105885312
#105885282
#105884192
#105884162
#105884142
#105884022
#105883792
C4×D722
#794413