Finite Group Databasebeta

← #11872781

Subgroups — #11872781

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589900C211yesmaximal, characteristic
2#10589727C211yesmaximal, characteristic, complemented
3C9×#450C211yesmaximal, characteristic
4#10588897C211yesmaximal, characteristic
5#10588844C211yesmaximal, characteristic, complemented
6#10588842C211yesmaximal, characteristic, complemented
7#10588842C211yesmaximal, characteristic, complemented
8SD16×Dic9C211yesmaximal, characteristic, complemented
9#10588725C211yesmaximal, characteristic, complemented
10#10588446C211yesmaximal, characteristic, complemented
11#10588443C211yesmaximal, characteristic, complemented
12#10588438C211yesmaximal, characteristic, complemented
13#10588437C211yesmaximal, characteristic, complemented
14#10588403C211yesmaximal, characteristic, complemented
15#10588400C211yesmaximal, characteristic, complemented
16#80137—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C2×C9×SD16C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C9×C22⋊Q8C2211yescharacteristic
21C2×#3676—21no—
22C2×#3676—21no—
23Q8×Dic9C2211yescharacteristic, complemented
24#63506C2211yescharacteristic, complemented
25D4×Dic9—21no—
26D4×Dic9—21no—
27D4×Dic9C2211yescharacteristic
28D4×Dic9C2211yescharacteristic
29D4×Dic9C2211yescharacteristic
30D4×Dic9C2211yescharacteristic
31C2×#3672C2211yescharacteristic
32C2×#3672C2211yescharacteristic
33#63488C2211yescharacteristic
34#63488C2211yescharacteristic
35#63486C2211yescharacteristic
36#63452—21no—
37#63452C2211yescharacteristic, complemented
38#63451—21no—
39#63449C2211yescharacteristic, complemented
40#63441—21no—
41#63441—21no—
42C9×#102C2211yescharacteristic
43C9×#102C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63389C2211yescharacteristic
50#63378C2211yescharacteristic, complemented
51#63377C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55Dic9⋊C8C2211yescharacteristic, complemented
56Dic9⋊C8C2211yescharacteristic, complemented
57C8×Dic9C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5798—31no—
61#5625—31no—
62C3×#450D311yescharacteristic
63#5218—31no—
64#5164—31no—
65#5162—31no—
66#5162—31no—
67Dic3×SD16—31no—
68#5045—31no—
69#4766—31no—
70#4763—31no—
71#4758—31no—
72#4757—31no—
73#4723—31no—
74#4720—31no—
75C24×C9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9—22no—
78C2×D4×C9—22no—
79C2×D4×C9—21no—
80C2×D4×C9C2311yescharacteristic
81C2×D4×C9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C22×Dic9—21no—
84C22×Dic9—21no—
85C22×Dic9—21no—
86C22×Dic9—21no—
87C2×Dic18C2311yescharacteristic
88C9×SD16—22no—
89C9×SD16—22no—
90C2×C8×C9C2311yescharacteristic
91C2×C8×C9C2311yescharacteristic
92C9×C4⋊C4—21no—
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95#3676—21no—
96#3676—21no—
97#3676—21no—
98#3676—21no—
99#3676—21no—
100#3676—21no—
101#3676D411yescharacteristic
102#3676D411yescharacteristic
103#3672—22no—
104#3672—22no—
105C4⋊Dic9—21no—
106C4⋊Dic9—21no—
107C4⋊Dic9D411yescharacteristic
108C4⋊Dic9D411yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3123—91noSylow
125C22×C3×D4C2×D311yescharacteristic
126C2×C3×SD16C2×D311yescharacteristic
127C2×C3×SD16C2×D311yescharacteristic
128C3×C22⋊Q8C2×D311yescharacteristic
129C2×#217—61no—
130C2×#217—61no—
131Q8×Dic3—31no—
132#944—31no—
133D4×Dic3—31no—
134D4×Dic3—31no—
135D4×Dic3—31no—
136D4×Dic3—31no—
137D4×Dic3—61no—
138D4×Dic3—61no—
139C2×#214—31no—
140C2×#214—31no—
141#926—31no—
142#926—31no—
143#924—31no—
144#890—31no—
145#890—61no—
146#889—61no—
147#887—31no—
148#879—61no—
149#879—61no—
150C3×#102C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#832—31no—
156#832—31no—
157#830—31no—
158#818—31no—
159#817—31no—
160#816—31no—
161#816—31no—
162#815—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166#808—31no—
167#807—31no—
168C23×C9—24no—
169C23×C9—21no—
170C23×C9—21no—
171C23×C9—81no—
172C23×C9—81no—
173C23×C9C2×D411yescharacteristic
174Q8×C9—21no—
175Q8×C9—21no—
176D4×C9—24no—
177D4×C9—21no—
178D4×C9—21no—
179D4×C9#4112yes—
180D4×C9#4112yes—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—81no—
192C2×Dic9—81no—
193C2×Dic9—81no—
194C2×Dic9—81no—
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199Dic18—21no—
200Dic18—21no—
201C8×C9—21no—
202C8×C9—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485—91no—
209#478—91no—
210#478—91no—
211#461—91no—
212#461—91no—
213#450—91no—
214#450D911yescharacteristic
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C24×C3—21no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—21no—
225C2×C3×D4C22×D311yescharacteristic
226C2×C3×D4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C2×Dic6—31no—
233C3×SD16—22no—
234C3×SD16—22no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C3×C4⋊C4—21no—
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240#217—31no—
241#217—31no—
242#217—61no—
243#217—61no—
244#217—61no—
245#217—61no—
246#217—61no—
247#217—61no—
248#214—62no—
249#214—62no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C22×C9—21no—
270C22×C9—22no—
271C22×C9—22no—
272C22×C9—21no—
273C22×C9—21no—
274C22×C9—41no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9—84no—
279C22×C9C22×D411yescharacteristic
280C4×C9—21no—
281C4×C9—41no—
282C4×C9—41no—
283C4×C9C2×#4111yescharacteristic
284C4×C9C2×#4111yescharacteristic
285Dic9—21no—
286Dic9—21no—
287Dic9—21no—
288Dic9—21no—
289Dic9—41no—
290Dic9—41no—
291Dic9—41no—
292Dic9—41no—
293C22×D4C2×D911yescharacteristic
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16C2×D911yescharacteristic
297C2×SD16C2×D911yescharacteristic
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×D911yescharacteristic
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—91no—
312C4×D4—181no—
313C4×D4—181no—
314#117—91no—
315#117—91no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107—91no—
320#106—91no—
321#106—91no—
322C4⋊C8—91no—
323C4⋊C8—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#103—91no—
328#102—91no—
329#102—91no—
330#102C2×D911yescharacteristic
331#102C2×D911yescharacteristic
332C22⋊C8—91no—
333C22⋊C8C2×D911yescharacteristic
334#97—91no—
335C4×C8—91no—
336C23×C3—24no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—81no—
340C23×C3—81no—
341C23×C3D3×D411yescharacteristic
342C3×Q8—21no—
343C3×Q8—21no—
344C3×D4—24no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4#23712yes—
348C3×D4#23712yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—241no—
364C2×Dic3—241no—
365C2×Dic3—241no—
366C2×Dic3—241no—
367Dic6—61no—
368Dic6—61no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C9—41no—
374C2×C9—42no—
375C2×C9—42no—
376C2×C9#52511yescharacteristic
377C2×C9#57711yescharacteristic
378C2×C9#57711yescharacteristic
379C24—21no—
380C2×Q8—91no—
381C2×Q8C22×D911yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4C22×D911yescharacteristic
386C2×D4C22×D911yescharacteristic
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C22×D911yescharacteristic
392SD16—22no—
393SD16—22no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×D911yescharacteristic
399C2×C8C22×D911yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4C22×D911yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—91no—
416C22⋊C4—91no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—91no—
424C42—91no—
425C42—181no—
426C42—181no—
427C42—181no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—84no—
438C22×C3C2×D3×D411yescharacteristic
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4C2×#23711yescharacteristic
443C3×C4C2×#23711yescharacteristic
444Dic3—61no—
445Dic3—61no—
446Dic3—61no—
447Dic3—61no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452C9#312311yescharacteristic, complemented, Sylow
453C23—24no—
454C23—21no—
455C23—21no—
456C23—81no—
457C23—81no—
458C23D4×D911yescharacteristic
459Q8—21no—
460Q8—21no—
461Q8—181no—
462Q8—181no—
463D4—24no—
464D4—21no—
465D4—21no—
466D4#369912yes—
467D4#369912yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4—721no—
484C2×C4D4×D911yescharacteristic
485C2×C4C23×D911yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—41no—
491C2×C3—42no—
492C2×C3—42no—
493C2×C3#558611yescharacteristic
494C2×C3#576211yescharacteristic
495C2×C3#577511yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—22no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—84no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—41no—
509C4—41no—
510C4—181no—
511C4—181no—
512C4—181no—
513C4—181no—
514C4—361no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#369911yescharacteristic
519C4C2×#369911yescharacteristic
520C3#8013711yescharacteristic
521C2—41no—
522C2—42no—
523C2—42no—
524C2#1058968811yescharacteristic
525C2#1058986411yescharacteristic
526C2#1058987711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#450C2
socleC22×C3C2×D3×D4
prime radicalC22×C3×D4C2×D3
hypercenter#450D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #10589727C2semidirect
5. #10588844C2semidirect
6. #10588842C2semidirect
7. #10588842C2semidirect
8. SD16×Dic9C2semidirect
9. #10588725C2semidirect
10. #10588446C2semidirect
11. #10588443C2semidirect
12. #10588438C2semidirect
13. #10588437C2semidirect
14. #10588403C2semidirect
15. #10588400C2semidirect
23. Q8×Dic9C22semidirect
24. #63506C22semidirect
37. #63452C22semidirect
39. #63449C22semidirect
45. #63395C22semidirect
46. #63395C22semidirect
50. #63378C22semidirect
51. #63377C22semidirect
52. #63376C22semidirect
53. #63376C22semidirect
54. #63375C22semidirect
55. Dic9⋊C8C22semidirect
56. Dic9⋊C8C22semidirect
57. C8×Dic9C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
452. C9#3123semidirect

Maximal subgroups

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

subgroupindex
#105899002
#105897272
C9×#4502
#105888972
#105888442
#105888422
SD16×Dic92
#105887252
#105884462
#105884432
#105884382
#105884372
#105884032
#105884002
#801373