Finite Group Databasebeta

← #11872719

Subgroups — #11872719

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589799C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic, complemented
3C9×#478C211yesmaximal, characteristic, complemented
4#10588747C211yesmaximal, characteristic, complemented
5#10588698C211yesmaximal, characteristic, complemented
6#10588565C211yesmaximal, characteristic, complemented
7#10588552C211yesmaximal, characteristic, complemented
8#10588549C211yesmaximal, characteristic, complemented
9#10588546C211yesmaximal, characteristic, complemented
10#10588527C211yesmaximal, characteristic, complemented
11#10588524C211yesmaximal, characteristic, complemented
12#10588465C211yesmaximal, characteristic, complemented
13#10588453C211yesmaximal, characteristic, complemented
14#10588453C211yesmaximal, characteristic, complemented
15#10588436C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C9×#125C2211yescharacteristic, complemented
19C4×D4×C9C2211yescharacteristic
20D4×Dic9C2211yescharacteristic
21C2×#3673C2211yescharacteristic
22C2×#3673C2211yescharacteristic
23C4×#611—21no—
24C2×(C2×D9)⋊C4—21no—
25C2×D72C2211yescharacteristic
26C2×D72C2211yescharacteristic
27#63457—21no—
28#63457—21no—
29#63457C2211yescharacteristic
30#63457C2211yescharacteristic
31#63456—21no—
32#63456—21no—
33#63455C2211yescharacteristic
34#63455C2211yescharacteristic, complemented
35#63455C2211yescharacteristic, complemented
36#63454C2211yescharacteristic
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39#63436C2211yescharacteristic, complemented
40C4×D36C2211yescharacteristic
41#63434C2211yescharacteristic
42C9×#107C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×C4⋊C8C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47#63380C2211yescharacteristic, complemented
48#63380C2211yescharacteristic, complemented
49(C2×D9)⋊C8C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63375C2211yescharacteristic, complemented
52C8×Dic9C2211yescharacteristic, complemented
53#63369C2211yescharacteristic
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic, complemented
56#63369C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5697—31no—
61#5545—31no—
62C3×#478D311yescharacteristic
63#5066—31no—
64#5015—31no—
65#4885—31no—
66#4872—31no—
67#4869—31no—
68#4866—31no—
69#4843—31no—
70#4840—31no—
71#4785—31no—
72#4773—31no—
73#4773—31no—
74#4756—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C2×#611—21no—
79C22×Dic9—21no—
80D4×D9—22no—
81D4×D9—22no—
82C2×D36—21no—
83C2×D36—21no—
84C2×D36—21no—
85C2×D36—21no—
86C2×D36C2311yescharacteristic
87C2×D36C2311yescharacteristic
88C2×D36C2311yescharacteristic
89C2×C4×D9—21no—
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C42×C9C2311yescharacteristic
103#3676—21no—
104#3673—22no—
105#3673—22no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—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)⋊C4D411yescharacteristic
114(C2×D9)⋊C4D411yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122D72—22no—
123D72—22no—
124#3122—91noSylow
125C2×D3×D4—31no—
126C3×#125C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128D4×Dic3—31no—
129C2×#213—31no—
130C2×#213—31no—
131C4×#67—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×D24—31no—
134C2×D24—31no—
135#895—31no—
136#895—31no—
137#895—61no—
138#895—61no—
139#894—61no—
140#894—61no—
141#893—31no—
142#893—31no—
143#893—31no—
144#892—31no—
145#67⋊C4—61no—
146D3×C22⋊C4—61no—
147#874—31no—
148C4×D12—31no—
149#872—31no—
150C3×#107C2×D311yescharacteristic
151C3×#106C2×D311yescharacteristic
152C3×C4⋊C8C2×D311yescharacteristic
153C3×#102C2×D311yescharacteristic
154C3×#102C2×D311yescharacteristic
155#821—31no—
156#821—31no—
157(C2×D3)⋊C8—31no—
158(C2×D3)⋊C8—31no—
159#815—31no—
160C8×Dic3—31no—
161#809—31no—
162#809—31no—
163#809—31no—
164#809—31no—
165#808—31no—
166#807—31no—
167C4⋊(C3⋊C8)—31no—
168C23×C9—21no—
169C22×D9—21no—
170C22×D9—24no—
171C22×D9—21no—
172C22×D9—21no—
173C22×D9—81no—
174C22×D9—81no—
175C22×D9C2×D411yescharacteristic
176D4×C9—21no—
177D4×C9#4112yes—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—81no—
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185#611—24no—
186C2×Dic9—21no—
187C2×Dic9—81no—
188C2×Dic9C2×D411yescharacteristic
189C2×Dic9C2×D411yescharacteristic
190C2×Dic9C2×D411yescharacteristic
191D36—21no—
192D36—21no—
193D36—21no—
194D36—21no—
195D36—21no—
196D36—81no—
197D36—81no—
198D36—81no—
199D36—81no—
200D36#4112yes—
201C4×D9—21no—
202C4×D9—21no—
203C4×D9—81no—
204C4×D9—81no—
205C4×D9—81no—
206C4×D9—81no—
207C8×C9—21no—
208C8×C9—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211#540—91no—
212#518—91no—
213#482—91no—
214#482—91no—
215#478—91no—
216#478D911yescharacteristic, complemented
217#459—91no—
218#459—91no—
219#447—91no—
220#447—91no—
221#442—91no—
222#442—91no—
223C4×D8—91no—
224C4×D8—91no—
225#433—91no—
226C23×D3—61no—
227C2×C3×D4C22×D311yescharacteristic
228C22×C3×C4—21no—
229C2×#67—61no—
230C22×Dic3—61no—
231D3×D4—62no—
232D3×D4—62no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×C4×D3—31no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C22⋊C4—21no—
253C3×C42C22×D311yescharacteristic
254#217—61no—
255#213—62no—
256#213—62no—
257(C2×D3)⋊C4—31no—
258(C2×D3)⋊C4—31no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—61no—
266C4⋊Dic3—31no—
267Dic3⋊C4—31no—
268Dic3⋊C4—31no—
269C4×Dic3—31no—
270C4×Dic3—61no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273D24—62no—
274D24—62no—
275C22×C9—22no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9C22×D411yescharacteristic
279C2×D9—21no—
280C2×D9—22no—
281C2×D9—21no—
282C2×D9—21no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—41no—
286C2×D9—41no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—84no—
292C4×C9—21no—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9C2×#4111yescharacteristic
298C4×C9C2×#4111yescharacteristic
299Dic9—21no—
300Dic9—21no—
301Dic9—21no—
302Dic9—41no—
303C22×D4—91no—
304C2×D8—91no—
305C2×D8—91no—
306C2×D8—91no—
307C2×D8—91no—
308#127—91no—
309#125C2×D911yescharacteristic, complemented
310#123—181no—
311#123—181no—
312#121—91no—
313#121—91no—
314#121—181no—
315#121—181no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—91no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4C2×D911yescharacteristic
324#117—91no—
325#117—91no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#107—91no—
329#107C2×D911yescharacteristic, complemented
330#106—91no—
331#106C2×D911yescharacteristic, complemented
332C4⋊C8—91no—
333C4⋊C8C2×D911yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102C2×D911yescharacteristic
341#102C2×D911yescharacteristic
342C22⋊C8—91no—
343C22⋊C8—91no—
344#97—91no—
345C4×C8—91no—
346C23×C3—21no—
347C22×D3—31no—
348C22×D3—61no—
349C22×D3—64no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—241no—
353C22×D3—241no—
354C3×D4—21no—
355C3×D4#23912yes—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—81no—
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363#67—64no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—31no—
367C2×Dic3—61no—
368C2×Dic3—241no—
369D12—32no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—61no—
375D12—241no—
376D12—241no—
377D12—241no—
378D12—241no—
379C4×D3—61no—
380C4×D3—61no—
381C4×D3—241no—
382C4×D3—241no—
383C4×D3—241no—
384C4×D3—241no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—42no—
390C2×C9#52511yescharacteristic
391C2×C9#57611yescharacteristic
392C2×C9#57611yescharacteristic
393D9—41no—
394D9—42no—
395D9—81no—
396D9—81no—
397C24—181no—
398C2×D4—91no—
399C2×D4—91no—
400C2×D4—91no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4—181no—
416D8—182no—
417D8—182no—
418D8—182no—
419D8—182no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8C22×D911yescharacteristic
423C2×C8C22×D911yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—91no—
429C4⋊C4C22×D911yescharacteristic
430C4⋊C4C22×D911yescharacteristic
431C4⋊C4C22×D911yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—91no—
434C22⋊C4—91no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C42—91no—
444C42—181no—
445C42C22×D911yescharacteristic
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3C2×D3×D411yescharacteristic
450C2×D3—61no—
451C2×D3—61no—
452C2×D3—61no—
453C2×D3—62no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—244no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4C2×#23911yescharacteristic
469C3×C4D3×#4111yescharacteristic
470Dic3—61no—
471Dic3—61no—
472Dic3—61no—
473Dic3—121no—
474C9#312211yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—184no—
478C23—181no—
479C23—181no—
480C23—181no—
481C23—721no—
482C23—721no—
483D4—21no—
484D4—92no—
485D4—184no—
486D4—181no—
487D4—181no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—721no—
492D4—721no—
493D4—721no—
494D4—721no—
495D4#370112yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—81no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4—721no—
509C2×C4—721no—
510C2×C4—721no—
511C2×C4D4×D911yescharacteristic
512C2×C4D4×D911yescharacteristic
513C2×C4C23×D911yescharacteristic
514C8—21no—
515C8—21no—
516C8—181no—
517C8—181no—
518C2×C3—42no—
519C2×C3#562711yescharacteristic
520C2×C3#576911yescharacteristic
521C2×C3#577411yescharacteristic
522D3—121no—
523D3—122no—
524D3—241no—
525D3—241no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—181no—
530C22—182no—
531C22—181no—
532C22—181no—
533C22—361no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22—361no—
540C22—361no—
541C22—724no—
542C22C2×D4×D911yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—181no—
549C4—181no—
550C4—181no—
551C4—361no—
552C4C2×#370111yescharacteristic
553C4#41×D911yescharacteristic
554C3#8114611yescharacteristic
555C2—42no—
556C2—361no—
557C2—362no—
558C2—721no—
559C2—721no—
560C2#1058972911yescharacteristic
561C2#1058987111yescharacteristic
562C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#478C2
socleC22×C3C2×D3×D4
hypercenter#478D9
hypocenterC9#3122
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10589799C2semidirect
2. #10589647C2semidirect
3. C9×#478C2semidirect
4. #10588747C2semidirect
5. #10588698C2semidirect
6. #10588565C2semidirect
7. #10588552C2semidirect
8. #10588549C2semidirect
9. #10588546C2semidirect
10. #10588527C2semidirect
11. #10588524C2semidirect
12. #10588465C2semidirect
13. #10588453C2semidirect
14. #10588453C2semidirect
15. #10588436C2semidirect
18. C9×#125C22semidirect
34. #63455C22semidirect
35. #63455C22semidirect
39. #63436C22semidirect
42. C9×#107C22semidirect
43. C9×#106C22semidirect
44. C9×C4⋊C8C22semidirect
47. #63380C22semidirect
48. #63380C22semidirect
51. #63375C22semidirect
52. C8×Dic9C22semidirect
55. #63369C22semidirect
56. #63369C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
216. #478D9semidirect
309. #125C2×D9semidirect
329. #107C2×D9semidirect
331. #106C2×D9semidirect
333. C4⋊C8C2×D9semidirect
474. C9#3122semidirect

Maximal subgroups

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

subgroupindex
#105897992
#105896472
C9×#4782
#105887472
#105886982
#105885652
#105885522
#105885492
#105885462
#105885272
#105885242
#105884652
#105884532
#105884362
#811463