Finite Group Databasebeta

← #11872793

Subgroups — #11872793

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#10589833C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic
3C9×#461C211yesmaximal, characteristic, complemented
4#10588849C211yesmaximal, characteristic
5#10588849C211yesmaximal, characteristic
6#10588844C211yesmaximal, characteristic, complemented
7SD16×Dic9C211yesmaximal, characteristic, complemented
8#10588768C211yesmaximal, characteristic, complemented
9#10588692C211yesmaximal, characteristic, complemented
10#10588531C211yesmaximal, characteristic, complemented
11#10588524C211yesmaximal, characteristic, complemented
12#10588497C211yesmaximal, characteristic, complemented
13#10588495C211yesmaximal, characteristic, complemented
14#10588494C211yesmaximal, characteristic, complemented
15#10588468C211yesmaximal, characteristic, complemented
16#80413—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×C9×SD16C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C9×C4⋊Q8C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63508C2211yescharacteristic
23#63508C2211yescharacteristic
24Q8×Dic9C2211yescharacteristic, complemented
25Q8×Dic9C2211yescharacteristic, complemented
26C2×#3675C2211yescharacteristic
27C2×#3675C2211yescharacteristic
28D4×Dic9C2211yescharacteristic
29C4×#611—21no—
30C2×(C2×D9)⋊C4—21no—
31#63460—21no—
32#63460—21no—
33#63455C2211yescharacteristic
34#63454C2211yescharacteristic
35#63451—21no—
36#63451—21no—
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39C4×D36C2211yescharacteristic
40#63434C2211yescharacteristic
41#63432C2211yescharacteristic, complemented
42C9×C4⋊C8C2211yescharacteristic, complemented
43C9×#103C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45#63395C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52(C2×D9)⋊C8C2211yescharacteristic
53#63378C2211yescharacteristic, complemented
54#63377C2211yescharacteristic, complemented
55#63375C2211yescharacteristic, complemented
56C8×Dic9C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5731—31no—
61#5545—31no—
62C3×#461D311yescharacteristic
63#5169—31no—
64#5169—31no—
65#5164—31no—
66Dic3×SD16—31no—
67#5083—31no—
68#5009—31no—
69#4847—31no—
70#4840—31no—
71#4817—31no—
72#4815—31no—
73#4814—31no—
74#4788—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9—21no—
80C2×#611—21no—
81C22×Dic9—21no—
82D4×D9—22no—
83D4×D9—22no—
84C2×D36C2311yescharacteristic
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9C2311yescharacteristic
88C9×SD16—22no—
89C9×SD16—22no—
90C2×C8×C9C2311yescharacteristic
91C2×C8×C9C2311yescharacteristic
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4C2311yescharacteristic
95C9×C22⋊C4—21no—
96C42×C9C2311yescharacteristic
97#3676—21no—
98#3675—22no—
99#3675—22no—
100(C2×D9)⋊C4—21no—
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4D411yescharacteristic
106(C2×D9)⋊C4D411yescharacteristic
107C4⋊Dic9—21no—
108C4⋊Dic9—21no—
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3123—91noSylow
125C2×D3×D4—31no—
126C2×C3×SD16C2×D311yescharacteristic
127C2×C3×SD16C2×D311yescharacteristic
128C3×C4⋊Q8C2×D311yescharacteristic
129C3×C4×D4C2×D311yescharacteristic
130#946—31no—
131#946—31no—
132Q8×Dic3—31no—
133Q8×Dic3—31no—
134C2×#215—31no—
135C2×#215—31no—
136D4×Dic3—31no—
137C4×#67—61no—
138C2×(C2×D3)⋊C4—61no—
139#898—61no—
140#898—61no—
141#893—31no—
142#892—31no—
143#889—61no—
144#889—61no—
145#67⋊C4—61no—
146D3×C22⋊C4—61no—
147C4×D12—31no—
148#872—31no—
149#870—31no—
150C3×C4⋊C8C2×D311yescharacteristic
151C3×#103C2×D311yescharacteristic
152C3×#103C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#832—31no—
156#832—31no—
157#821—31no—
158#821—31no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161#818—31no—
162#817—31no—
163#815—31no—
164C8×Dic3—31no—
165#808—31no—
166#807—31no—
167C4⋊(C3⋊C8)—31no—
168C23×C9—21no—
169C22×D9—21no—
170C22×D9—24no—
171C22×D9—81no—
172C22×D9—81no—
173C22×D9C2×D411yescharacteristic
174Q8×C9—21no—
175Q8×C9—21no—
176Q8×C9—21no—
177Q8×C9—21no—
178D4×C9—21no—
179D4×C9#4112yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—81no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187#611—24no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—81no—
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195D36—21no—
196D36#4112yes—
197C4×D9—21no—
198C4×D9—21no—
199C4×D9—81no—
200C4×D9—81no—
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#461D911yescharacteristic, complemented
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×D4C22×D311yescharacteristic
224C22×C3×C4—21no—
225C2×#67—61no—
226C22×Dic3—61no—
227D3×D4—62no—
228D3×D4—62no—
229C2×D12—31no—
230C2×C4×D3—31no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C3×SD16—22no—
234C3×SD16—22no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C22⋊C4—21no—
241C3×C42C22×D311yescharacteristic
242#217—61no—
243#215—62no—
244#215—62no—
245(C2×D3)⋊C4—31no—
246(C2×D3)⋊C4—31no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257Dic3⋊C4—31no—
258Dic3⋊C4—31no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C22×C9—22no—
270C22×C9—41no—
271C22×C9—41no—
272C22×C9C22×D411yescharacteristic
273C2×D9—21no—
274C2×D9—22no—
275C2×D9—21no—
276C2×D9—21no—
277C2×D9—41no—
278C2×D9—41no—
279C2×D9—84no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—41no—
283C4×C9—41no—
284C4×C9—41no—
285C4×C9C2×#4111yescharacteristic
286C4×C9C2×#4111yescharacteristic
287Dic9—21no—
288Dic9—21no—
289Dic9—21no—
290Dic9—41no—
291Dic9—41no—
292Dic9—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16C2×D911yescharacteristic
297C2×SD16C2×D911yescharacteristic
298C4⋊Q8C2×D911yescharacteristic, complemented
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—181no—
312C4×D4—181no—
313C4×D4C2×D911yescharacteristic
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⋊C8C2×D911yescharacteristic, complemented
324#103—91no—
325#103—91no—
326#103C2×D911yescharacteristic, complemented
327#103C2×D911yescharacteristic, complemented
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332C22⋊C8—91no—
333C22⋊C8—91no—
334#97—91no—
335C4×C8—91no—
336C23×C3—21no—
337C22×D3—31no—
338C22×D3—61no—
339C22×D3—64no—
340C22×D3—241no—
341C22×D3—241no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×D4—21no—
347C3×D4#23712yes—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—81no—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—64no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—241no—
363D12—32no—
364D12—61no—
365C4×D3—61no—
366C4×D3—61no—
367C4×D3—241no—
368C4×D3—241no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C9—42no—
374C2×C9#52511yescharacteristic
375C2×C9#57711yescharacteristic
376C2×C9#57711yescharacteristic
377D9—41no—
378D9—42no—
379C24—181no—
380C2×Q8C22×D911yescharacteristic
381C2×Q8C22×D911yescharacteristic
382C2×D4—91no—
383C2×D4—181no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4C22×D911yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
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—21no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—91no—
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—181no—
425C42—181no—
426C42—181no—
427C42C22×D911yescharacteristic
428C22×C3—22no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—61no—
435C2×D3—62no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—244no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4C2×#23711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446Dic3—61no—
447Dic3—61no—
448Dic3—61no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452C9#312311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—91no—
455C23—184no—
456C23—181no—
457C23—721no—
458C23—721no—
459Q8—21no—
460Q8—21no—
461Q8—21no—
462Q8—21no—
463D4—21no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4#369912yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—81no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4D4×D911yescharacteristic
484C2×C4D4×D911yescharacteristic
485C2×C4C23×D911yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—42no—
491C2×C3#560611yescharacteristic
492C2×C3#576211yescharacteristic
493C2×C3#577811yescharacteristic
494D3—121no—
495D3—122no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—181no—
500C22—182no—
501C22—181no—
502C22—181no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#369911yescharacteristic
519C4#41×D911yescharacteristic
520C3#8041311yescharacteristic
521C2—42no—
522C2—361no—
523C2—362no—
524C2#1058970811yescharacteristic
525C2#1058986411yescharacteristic
526C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#461C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
hypercenter#461D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10589833C2semidirect
3. C9×#461C2semidirect
6. #10588844C2semidirect
7. SD16×Dic9C2semidirect
8. #10588768C2semidirect
9. #10588692C2semidirect
10. #10588531C2semidirect
11. #10588524C2semidirect
12. #10588497C2semidirect
13. #10588495C2semidirect
14. #10588494C2semidirect
15. #10588468C2semidirect
20. C9×C4⋊Q8C22semidirect
24. Q8×Dic9C22semidirect
25. Q8×Dic9C22semidirect
41. #63432C22semidirect
42. C9×C4⋊C8C22semidirect
43. C9×#103C22semidirect
44. C9×#103C22semidirect
45. #63395C22semidirect
46. #63395C22semidirect
53. #63378C22semidirect
54. #63377C22semidirect
55. #63375C22semidirect
56. C8×Dic9C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
212. #461D9semidirect
298. C4⋊Q8C2×D9semidirect
323. C4⋊C8C2×D9semidirect
326. #103C2×D9semidirect
327. #103C2×D9semidirect
452. C9#3123semidirect

Maximal subgroups

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

subgroupindex
#105898332
#105896472
C9×#4612
#105888492
#105888442
SD16×Dic92
#105887682
#105886922
#105885312
#105885242
#105884972
#105884952
#105884942
#105884682
#804133