Finite Group Databasebeta

← #11887363

Subgroups — #11887363

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#10589908C211yesmaximal, characteristic, complemented
2#10589720C211yesmaximal, characteristic, complemented
3C9×#447C211yesmaximal, characteristic, complemented
4C2×#63392C211yesmaximal, characteristic, complemented
5#10588838C211yesmaximal, characteristic, complemented
6#10588837C211yesmaximal, characteristic, complemented
7#10588833C211yesmaximal, characteristic, complemented
8D8×Dic9C211yesmaximal, characteristic, complemented
9#10588717C211yesmaximal, characteristic, complemented
10#10588464C211yesmaximal, characteristic, complemented
11#10588452C211yesmaximal, characteristic, complemented
12#10588448C211yesmaximal, characteristic, complemented
13#10588446C211yesmaximal, characteristic, complemented
14#611⋊C8C211yesmaximal, characteristic, complemented
15#10588402C211yesmaximal, characteristic, complemented
16#80015—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C2×#3699C2211yescharacteristic
19C2×C9×D8C2211yescharacteristic
20C2×C9×D8C2211yescharacteristic
21C9×#121C2211yescharacteristic
22#63515—21no—
23C2×#3676—21no—
24#63501—21no—
25#63501—21no—
26#63500C2211yescharacteristic
27#63500C2211yescharacteristic, complemented
28#63498C2211yescharacteristic
29#63497—21no—
30D4×Dic9—21no—
31D4×Dic9C2211yescharacteristic
32D4×Dic9C2211yescharacteristic, complemented
33C2×#3672C2211yescharacteristic, complemented
34C4×#611C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36#63486C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38C2×C8×D9C2211yescharacteristic, complemented
39#63454C2211yescharacteristic, complemented
40#63452C2211yescharacteristic, complemented
41#63448—21no—
42#63441—21no—
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic, complemented
51(C2×D9)⋊C8C2211yescharacteristic, complemented
52#63378C2211yescharacteristic, complemented
53#63378C2211yescharacteristic, complemented
54#63376C2211yescharacteristic, complemented
55#63376C2211yescharacteristic, complemented
56Dic9⋊C8C2211yescharacteristic, complemented
57C8×Dic9C2211yescharacteristic, complemented
58#63368C2211yescharacteristic, complemented
59#63367C2211yescharacteristic, complemented
60#5806—31no—
61#5618—31no—
62C3×#447D311yescharacteristic
63C2×#832—31no—
64#5158—31no—
65#5157—31no—
66#5153—31no—
67Dic3×D8—31no—
68#5041—31no—
69#4784—31no—
70#4772—31no—
71#4768—31no—
72#4766—31no—
73#67⋊C8—31no—
74#4722—31no—
75C24×C9—21no—
76C2×D4×C9—22no—
77C2×D4×C9—21no—
78C2×D4×C9—21no—
79C2×D4×C9—41no—
80C2×D4×C9C2311yescharacteristic
81C2×D4×C9C2311yescharacteristic
82C2×D4×C9C2311yescharacteristic
83C22×C4×C9C2311yescharacteristic
84C2×#611—21no—
85C2×#611—21no—
86C2×#611—21no—
87C2×#611D411yescharacteristic
88C22×Dic9—21no—
89C22×Dic9—21no—
90C22×Dic9—21no—
91C22×Dic9—21no—
92#3699—22no—
93#3699—41no—
94C2×C4×D9C2311yescharacteristic
95C2×Dic18C2311yescharacteristic
96C9×D8—22no—
97C9×D8—41no—
98C2×C8×C9C2311yescharacteristic
99C2×C8×C9C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676—21no—
106#3676—21no—
107#3676—21no—
108#3676—21no—
109#3676D411yescharacteristic
110#3672—41no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4D411yescharacteristic
113C4⋊Dic9—21no—
114C4⋊Dic9—21no—
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4D411yescharacteristic
121C4×Dic9—21no—
122C4×Dic9C2311yescharacteristic
123C2×C9⋊C8—41no—
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C8×D9—41no—
127#3297—91noSylow
128C22×C3×D4C2×D311yescharacteristic
129C2×#237—31no—
130C2×C3×D8C2×D311yescharacteristic
131C2×C3×D8C2×D311yescharacteristic
132C3×#121C2×D311yescharacteristic
133#953—61no—
134C2×#217—61no—
135#939—61no—
136#939—61no—
137#938—31no—
138#938—31no—
139#936—31no—
140#935—61no—
141D4×Dic3—31no—
142D4×Dic3—31no—
143D4×Dic3—61no—
144C2×#214—31no—
145C4×#67—31no—
146C2×C4⋊Dic3—31no—
147#924—31no—
148C22×C3⋊C8—31no—
149C2×D3×C8—31no—
150#892—31no—
151#890—31no—
152#886—61no—
153#879—61no—
154C3×#102C2×D311yescharacteristic
155C3×#102C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#832—31no—
158#832—31no—
159#832—31no—
160#832—31no—
161#832—31no—
162(C2×D3)⋊C8—31no—
163#818—31no—
164#818—31no—
165#816—31no—
166#816—31no—
167Dic3⋊C8—31no—
168C8×Dic3—31no—
169#810—31no—
170#808—31no—
171C23×C9—21no—
172C23×C9—21no—
173C23×C9—21no—
174C23×C9—42no—
175C23×C9—42no—
176C23×C9—81no—
177C23×C9C2×D411yescharacteristic
178C22×D9C2×D411yescharacteristic
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—21no—
182D4×C9—21no—
183D4×C9—21no—
184D4×C9—42no—
185D4×C9—42no—
186D4×C9#4112yes—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2411yescharacteristic
192#611—22no—
193#611—42no—
194#611—81no—
195#611—81no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—42no—
201C2×Dic9—81no—
202C2×Dic9—81no—
203C2×Dic9—81no—
204C2×Dic9C2×D411yescharacteristic
205C2×Dic9C2×D411yescharacteristic
206C2×Dic9C2×D411yescharacteristic
207C4×D9—21no—
208C4×D9—21no—
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#447D911yescharacteristic, complemented
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C24×C3—21no—
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—41no—
235C2×C3×D4C22×D311yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C2×C3×D4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—31no—
240C2×#67—61no—
241C2×#67—61no—
242C2×#67—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247#237—62no—
248#237—121no—
249C2×C4×D3—31no—
250C2×Dic6—31no—
251C3×D8—22no—
252C3×D8—41no—
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C22⋊C4—21no—
257#217—31no—
258#217—61no—
259#217—61no—
260#217—61no—
261#217—61no—
262#217—61no—
263#217—61no—
264#217—61no—
265#214—121no—
266(C2×D3)⋊C4—31no—
267(C2×D3)⋊C4—61no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273Dic3⋊C4—31no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276C4×Dic3—31no—
277C4×Dic3—61no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—121no—
281D3×C8—121no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—22no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9—41no—
289C22×C9—41no—
290C22×C9—41no—
291C22×C9—41no—
292C22×C9—41no—
293C22×C9—84no—
294C22×C9#13512yes—
295C22×C9C22×D411yescharacteristic
296C2×D9—21no—
297C2×D9—21no—
298C2×D9—21no—
299C4×C9—21no—
300C4×C9—41no—
301C4×C9C2×#4111yescharacteristic
302C4×C9H(5,𝔽2)11yescharacteristic
303Dic9—21no—
304Dic9—21no—
305Dic9—21no—
306Dic9—41no—
307Dic9—41no—
308Dic9—41no—
309Dic9—41no—
310C2×#41—91no—
311C22×D4C2×D911yescharacteristic
312C2×SD16—91no—
313C2×D8C2×D911yescharacteristic
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—181no—
326#121—181no—
327#121C2×D911yescharacteristic
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117—91no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107—91no—
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
350C22⋊C8—91no—
351C22⋊C8C2×D911yescharacteristic
352C4×C8—91no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—81no—
359C23×C3D3×D411yescharacteristic
360C22×D3—31no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4—21no—
365C3×D4—21no—
366C3×D4—42no—
367C3×D4—42no—
368C3×D4#23712yes—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—62no—
375#67—122no—
376#67—241no—
377#67—241no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—122no—
386C2×Dic3—241no—
387C2×Dic3—241no—
388C2×Dic3—241no—
389C4×D3—61no—
390C4×D3—61no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—21no—
394C3×C8—21no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C2×C9—22no—
398C2×C9—42no—
399C2×C9—81no—
400C2×C9—81no—
401C2×C9#54611yescharacteristic
402C2×C9C2×#13511yescharacteristic
403C2×C9#57611yescharacteristic
404D9—41no—
405C24—21no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—91no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4C22×D911yescharacteristic
418C2×D4C22×D911yescharacteristic
419C2×D4C22×D911yescharacteristic
420C22×C4—91no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×D911yescharacteristic
426SD16—361no—
427D8—22no—
428D8—41no—
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—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4—181no—
443C4⋊C4C22×D911yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—91no—
446C22⋊C4—91no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—91no—
456C42—181no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—84no—
469C22×C3#91212yes—
470C22×C3C2×D3×D411yescharacteristic
471C2×D3—61no—
472C2×D3—61no—
473C2×D3—61no—
474C3×C4—21no—
475C3×C4—41no—
476C3×C4C2×#23711yescharacteristic
477C3×C4#100411yescharacteristic
478Dic3—61no—
479Dic3—61no—
480Dic3—61no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485C9#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—42no—
490C23—42no—
491C23—81no—
492C23—91no—
493C23D4×D911yescharacteristic
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—42no—
503D4—182no—
504D4—362no—
505D4—721no—
506D4—721no—
507D4#369912yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—91no—
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—362no—
521C2×C4—721no—
522C2×C4—721no—
523C2×C4—721no—
524C2×C4D4×D911yescharacteristic
525C2×C4C23×D911yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—22no—
531C2×C3—42no—
532C2×C3—81no—
533C2×C3—81no—
534C2×C3#559111yescharacteristic
535C2×C3C2×#91211yescharacteristic
536C2×C3#577411yescharacteristic
537D3—121no—
538C22—21no—
539C22—21no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—84no—
550C22—181no—
551C22—181no—
552C22—181no—
553C22#6347412yes—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—41no—
557C4—181no—
558C4—181no—
559C4—181no—
560C4—361no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4C2×#369911yescharacteristic
565C4#6371011yescharacteristic
566C3#8001511yescharacteristic
567C2—22no—
568C2—42no—
569C2—81no—
570C2—81no—
571C2—361no—
572C2#1058969311yescharacteristic
573C2C2×#6347411yescharacteristic
574C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#447C2
socleC22×C3C2×D3×D4
hypercenter#447D9
hypocenterC9#3297
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10589908C2semidirect
2. #10589720C2semidirect
3. C9×#447C2semidirect
4. C2×#63392C2semidirect
5. #10588838C2semidirect
6. #10588837C2semidirect
7. #10588833C2semidirect
8. D8×Dic9C2semidirect
9. #10588717C2semidirect
10. #10588464C2semidirect
11. #10588452C2semidirect
12. #10588448C2semidirect
13. #10588446C2semidirect
14. #611⋊C8C2semidirect
15. #10588402C2semidirect
27. #63500C22semidirect
32. D4×Dic9C22semidirect
33. C2×#3672C22semidirect
38. C2×C8×D9C22semidirect
39. #63454C22semidirect
40. #63452C22semidirect
50. #63392C22semidirect
51. (C2×D9)⋊C8C22semidirect
52. #63378C22semidirect
53. #63378C22semidirect
54. #63376C22semidirect
55. #63376C22semidirect
56. Dic9⋊C8C22semidirect
57. C8×Dic9C22semidirect
58. #63368C22semidirect
59. #63367C22semidirect
225. #447D9semidirect
485. C9#3297semidirect

Maximal subgroups

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

subgroupindex
#105899082
#105897202
C9×#4472
C2×#633922
#105888382
#105888372
#105888332
D8×Dic92
#105887172
#105884642
#105884522
#105884482
#105884462
#611⋊C82
#105884022
#800153