Finite Group Databasebeta

← #11872710

Subgroups — #11872710

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#10589664C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic, complemented
3C9×#442C211yesmaximal, characteristic, complemented
4#10588836C211yesmaximal, characteristic, complemented
5#10588830C211yesmaximal, characteristic, complemented
6C4×#3673C211yesmaximal, characteristic, complemented
7C4×#3673C211yesmaximal, characteristic, complemented
8#10588551C211yesmaximal, characteristic, complemented
9#10588546C211yesmaximal, characteristic, complemented
10#10588466C211yesmaximal, characteristic, complemented
11#10588459C211yesmaximal, characteristic, complemented
12#10588453C211yesmaximal, characteristic, complemented
13#10588443C211yesmaximal, characteristic, complemented
14#10588392C211yesmaximal, characteristic, complemented
15#10588390C211yesmaximal, characteristic, complemented
16#79874—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×C9×D8C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic, complemented
21#63502C2211yescharacteristic, complemented
22#63500C2211yescharacteristic
23D4×Dic9C2211yescharacteristic
24C2×#3673C2211yescharacteristic
25C2×#3673C2211yescharacteristic
26#63492—21no—
27#63491—21no—
28C4×#611—21no—
29C2×(C2×D9)⋊C4—21no—
30C2×D72C2211yescharacteristic
31#63457C2211yescharacteristic
32#63455C2211yescharacteristic
33#63454C2211yescharacteristic
34#63452C2211yescharacteristic, complemented
35#63446—21no—
36#63445—21no—
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39C4×D36C2211yescharacteristic
40C4×D36C2211yescharacteristic, complemented
41#63434C2211yescharacteristic
42C9×#106C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic, complemented
45C9×#97C2211yescharacteristic, complemented
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic, complemented
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic, complemented
50(C2×D9)⋊C8C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63377C2211yescharacteristic, complemented
53Dic9⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63369C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4×C9⋊C8C2211yescharacteristic, complemented
60#5562—31no—
61#5545—31no—
62C3×#442D311yescharacteristic
63#5156—31no—
64#5150—31no—
65C4×#213—31no—
66C4×#213—31no—
67#4871—31no—
68#4866—31no—
69#4786—31no—
70#4779—31no—
71#4773—31no—
72#4763—31no—
73#4711—31no—
74#4709—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9—21no—
80C2×#611—21no—
81C2×#611—21no—
82C2×#611—21no—
83C2×#611—21no—
84C22×Dic9—21no—
85D4×D9—22no—
86D4×D9—22no—
87C2×D36—21no—
88C2×D36C2311yescharacteristic
89C2×D36C2311yescharacteristic
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9C2311yescharacteristic
94C9×D8—22no—
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C9×C22⋊C4—21no—
101C42×C9C2311yescharacteristic
102#3676—21no—
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)⋊C4D411yescharacteristic
112(C2×D9)⋊C4D411yescharacteristic
113C4⋊Dic9—21no—
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117Dic9⋊C4D411yescharacteristic
118Dic9⋊C4D411yescharacteristic
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123D72—22no—
124#3122—91noSylow
125C2×D3×D4—31no—
126C2×C3×D8C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128C3×C4×D4C2×D311yescharacteristic
129#940—31no—
130#938—31no—
131D4×Dic3—31no—
132C2×#213—31no—
133C2×#213—31no—
134#930—61no—
135#929—61no—
136C4×#67—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×D24—31no—
139#895—31no—
140#893—31no—
141#892—31no—
142#890—31no—
143#884—61no—
144#883—61no—
145#67⋊C4—61no—
146D3×C22⋊C4—61no—
147C4×D12—31no—
148C4×D12—31no—
149#872—31no—
150C3×#106C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×#102C2×D311yescharacteristic
153C3×#97C2×D311yescharacteristic
154#832—31no—
155#832—31no—
156#821—31no—
157#821—31no—
158(C2×D3)⋊C8—31no—
159(C2×D3)⋊C8—31no—
160#817—31no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163#809—31no—
164#809—31no—
165#807—31no—
166#807—31no—
167C4×C3⋊C8—31no—
168C23×C9—21no—
169C23×C9—21no—
170C22×D9—21no—
171C22×D9—24no—
172C22×D9—21no—
173C22×D9—81no—
174C22×D9—81no—
175C22×D9C2×D411yescharacteristic
176D4×C9—21no—
177D4×C9—21no—
178D4×C9—21no—
179D4×C9#4112yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—81no—
183C2×C4×C9—81no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187#611—24no—
188#611—81no—
189#611—81no—
190#611—81no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—81no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197D36—21no—
198D36—21no—
199D36—21no—
200D36—81no—
201D36#4112yes—
202C4×D9—21no—
203C4×D9—21no—
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#478—91no—
217#459—91no—
218#459—91no—
219#447—91no—
220#447—91no—
221#442—91no—
222#442D911yescharacteristic, complemented
223C4×D8—91no—
224C4×D8—91no—
225#433—91no—
226C23×D3—61no—
227C2×C3×D4C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C2×#67—61no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—61no—
235C22×Dic3—61no—
236D3×D4—62no—
237D3×D4—62no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—61no—
241C2×C4×D3—31no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C3×D8—22no—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—21no—
251C3×C22⋊C4—21no—
252C3×C42C22×D311yescharacteristic
253#217—61no—
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—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267Dic3⋊C4—31no—
268Dic3⋊C4—31no—
269Dic3⋊C4—61no—
270C4×Dic3—31no—
271C4×Dic3—61no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274D24—62no—
275C22×C9—22no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9—41no—
279C22×C9—41no—
280C22×C9—41no—
281C22×C9C22×D411yescharacteristic
282C2×D9—21no—
283C2×D9—22no—
284C2×D9—21no—
285C2×D9—21no—
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×C9C2×#4111yescharacteristic
297C4×C9C2×#4111yescharacteristic
298Dic9—21no—
299Dic9—21no—
300Dic9—21no—
301Dic9—41no—
302Dic9—41no—
303C22×D4—91no—
304C2×D8—91no—
305C2×D8—91no—
306C2×D8—91no—
307C2×D8C2×D911yescharacteristic
308#127—91no—
309#125—91no—
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—181no—
321C4×D4—181no—
322C4×D4C2×D911yescharacteristic
323C4×D4C2×D911yescharacteristic, complemented
324#117—91no—
325#117—91no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#107—91no—
329#107—91no—
330#106—91no—
331#106C2×D911yescharacteristic, complemented
332C4⋊C8—91no—
333C4⋊C8—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102C2×D911yescharacteristic
341#102C2×D911yescharacteristic, complemented
342C22⋊C8—91no—
343C22⋊C8—91no—
344#97C2×D911yescharacteristic, complemented
345C4×C8—91no—
346C23×C3—21no—
347C23×C3—21no—
348C22×D3—31no—
349C22×D3—61no—
350C22×D3—64no—
351C22×D3—61no—
352C22×D3—241no—
353C22×D3—241no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4#23512yes—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—81no—
361C2×C3×C4—81no—
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—64no—
366#67—241no—
367#67—241no—
368#67—241no—
369C2×Dic3—31no—
370C2×Dic3—31no—
371C2×Dic3—31no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—241no—
375D12—32no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—241no—
380C4×D3—61no—
381C4×D3—61no—
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—81no—
391C2×C9#52511yescharacteristic
392C2×C9#57611yescharacteristic
393C2×C9#57611yescharacteristic
394D9—41no—
395D9—42no—
396D9—81no—
397C24—181no—
398C2×D4—91no—
399C2×D4—91no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4C22×D911yescharacteristic
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—91no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4—181no—
416D8—22no—
417D8—182no—
418D8—182no—
419D8—182no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8C22×D911yescharacteristic
423C2×C8C22×D911yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4C22×D911yescharacteristic
431C4⋊C4C22×D911yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—91no—
435C22⋊C4—91no—
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×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3C2×D3×D411yescharacteristic
453C2×D3—61no—
454C2×D3—61no—
455C2×D3—61no—
456C2×D3—62no—
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×C4C2×#23511yescharacteristic
468C3×C4D3×#4111yescharacteristic
469Dic3—61no—
470Dic3—61no—
471Dic3—61no—
472Dic3—121no—
473Dic3—121no—
474C9#312211yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—91no—
478C23—184no—
479C23—181no—
480C23—181no—
481C23—721no—
482C23—721no—
483D4—21no—
484D4—21no—
485D4—21no—
486D4—92no—
487D4—184no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—721no—
492D4—721no—
493D4—721no—
494D4—721no—
495D4#369712yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
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—81no—
520C2×C3#554711yescharacteristic
521C2×C3#577411yescharacteristic
522C2×C3#577411yescharacteristic
523D3—121no—
524D3—122no—
525D3—241no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—181no—
533C22—181no—
534C22—181no—
535C22—182no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22—361no—
540C22—361no—
541C22—724no—
542C22C2×D4×D911yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—181no—
548C4—181no—
549C4—181no—
550C4—361no—
551C4—361no—
552C4C2×#369711yescharacteristic
553C4#41×D911yescharacteristic
554C3#7987411yescharacteristic
555C2—42no—
556C2—81no—
557C2—361no—
558C2—362no—
559C2—721no—
560C2#1058964911yescharacteristic
561C2#1058987611yescharacteristic
562C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#442C2
socleC22×C3C2×D3×D4
hypercenter#442D9
hypocenterC9#3122
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10589664C2semidirect
2. #10589647C2semidirect
3. C9×#442C2semidirect
4. #10588836C2semidirect
5. #10588830C2semidirect
6. C4×#3673C2semidirect
7. C4×#3673C2semidirect
8. #10588551C2semidirect
9. #10588546C2semidirect
10. #10588466C2semidirect
11. #10588459C2semidirect
12. #10588453C2semidirect
13. #10588443C2semidirect
14. #10588392C2semidirect
15. #10588390C2semidirect
20. C4×D4×C9C22semidirect
21. #63502C22semidirect
34. #63452C22semidirect
40. C4×D36C22semidirect
42. C9×#106C22semidirect
44. C9×#102C22semidirect
45. C9×#97C22semidirect
47. #63392C22semidirect
49. #63380C22semidirect
52. #63377C22semidirect
53. Dic9⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
56. #63369C22semidirect
57. #63366C22semidirect
58. #63366C22semidirect
59. C4×C9⋊C8C22semidirect
222. #442D9semidirect
323. C4×D4C2×D9semidirect
331. #106C2×D9semidirect
341. #102C2×D9semidirect
344. #97C2×D9semidirect
474. C9#3122semidirect

Maximal subgroups

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

subgroupindex
#105896642
#105896472
C9×#4422
#105888362
#105888302
C4×#36732
#105885512
#105885462
#105884662
#105884592
#105884532
#105884432
#105883922
#105883902
#798743