Finite Group Databasebeta

← #11884048

Subgroups — #11884048

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#137C211yesmaximal, characteristic, complemented
2#10589931C211yesmaximal, characteristic
3Q8×#611C211yesmaximal, characteristic, complemented
4C2×SD16×D9C211yesmaximal, characteristic, complemented
5#10588918C211yesmaximal, characteristic, complemented
6#10588908C211yesmaximal, characteristic, complemented
7#10588870C211yesmaximal, characteristic, complemented
8#10588868C211yesmaximal, characteristic, complemented
9#10588866C211yesmaximal, characteristic, complemented
10#10588865C211yesmaximal, characteristic, complemented
11#10588849C211yesmaximal, characteristic, complemented
12#10588844C211yesmaximal, characteristic, complemented
13#10588842C211yesmaximal, characteristic, complemented
14#10588816C211yesmaximal, characteristic, complemented
15#10588809C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic, complemented
19C2×Q8×D9C2211yescharacteristic
20C2×D4×D9C2211yescharacteristic
21C9×#137—24no—
22C2×C9×Q16C2211yescharacteristic, complemented
23C2×C9×Q16C2211yescharacteristic, complemented
24C2×C9×SD16C2211yescharacteristic
25C2×C9×SD16C2211yescharacteristic
26C2×C9×M16C2211yescharacteristic, complemented
27#63509C2211yescharacteristic
28#63508—21no—
29#63508C2211yescharacteristic
30#63508C2211yescharacteristic
31Q8×Dic9C2211yescharacteristic, complemented
32#63506—21no—
33#63506C2211yescharacteristic, complemented
34C2×#3675C2211yescharacteristic
35C2×#3675C2211yescharacteristic
36C2×#3674C2211yescharacteristic, complemented
37#63501—21no—
38#63499—21no—
39D4×Dic9C2211yescharacteristic
40C2×#3672C2211yescharacteristic
41#63492C2211yescharacteristic
42#63491—21no—
43C4×#611—21no—
44C4×#611C2211yescharacteristic
45C2×(C2×D9)⋊C4—21no—
46#63486—21no—
47#63486C2211yescharacteristic, complemented
48SD16×D9—24no—
49C2×#3664C2211yescharacteristic
50C2×C8×D9C2211yescharacteristic
51#63395C2211yescharacteristic, complemented
52#63395C2211yescharacteristic, complemented
53#63395C2211yescharacteristic, complemented
54#63392C2211yescharacteristic
55#63389C2211yescharacteristic, complemented
56#63380C2211yescharacteristic
57(C2×D9)⋊C8C2211yescharacteristic
58#63378C2211yescharacteristic, complemented
59#63376C2211yescharacteristic, complemented
60#63375C2211yescharacteristic, complemented
61Dic9⋊C8C2211yescharacteristic, complemented
62C2×C3×#137D311yescharacteristic
63#5829—31no—
64Q8×#67—31no—
65C2×D3×SD16—31no—
66#5239—31no—
67#5227—31no—
68#5190—31no—
69#5188—31no—
70#5186—31no—
71#5185—31no—
72#5169—31no—
73#5164—31no—
74#5162—31no—
75#5134—31no—
76#5127—31no—
77C23×D9—21no—
78C9×#41—22no—
79C9×#41—41no—
80C2×Q8×C9—21no—
81C2×Q8×C9—22no—
82C2×Q8×C9—41no—
83C2×Q8×C9C2311yescharacteristic
84C2×Q8×C9C2311yescharacteristic
85C2×Q8×C9C2311yescharacteristic
86C2×D4×C9—21no—
87C2×D4×C9C2311yescharacteristic
88C22×C4×C9—21no—
89C22×C4×C9—21no—
90C22×C4×C9C2311yescharacteristic
91C2×#611—21no—
92C2×#611—21no—
93C2×#611D411yescharacteristic
94C22×Dic9—21no—
95Q8×D9—22no—
96Q8×D9—41no—
97D4×D9—22no—
98D4×D9—41no—
99C2×D36C2311yescharacteristic
100C2×C4×D9—21no—
101C2×C4×D9C2311yescharacteristic
102C2×Dic18—21no—
103C2×Dic18C2311yescharacteristic
104C9×Q16—22no—
105C9×Q16—22no—
106C9×SD16—22no—
107C9×SD16D414yescomplemented
108C9×M16—22no—
109C2×C8×C9C2311yescharacteristic
110C2×C8×C9C2311yescharacteristic
111#3676—21no—
112#3676—21no—
113#3676D411yescharacteristic
114#3675—22no—
115#3675—41no—
116#3674—41no—
117#3672—22no—
118(C2×D9)⋊C4—21no—
119(C2×D9)⋊C4—21no—
120(C2×D9)⋊C4—21no—
121(C2×D9)⋊C4—21no—
122(C2×D9)⋊C4—21no—
123(C2×D9)⋊C4D411yescharacteristic
124C4⋊Dic9—21no—
125C4⋊Dic9C2311yescharacteristic
126C4⋊Dic9C2311yescharacteristic
127Dic9⋊C4—21no—
128Dic9⋊C4—21no—
129Dic9⋊C4—21no—
130Dic9⋊C4—21no—
131Dic9⋊C4—21no—
132Dic9⋊C4D411yescharacteristic
133C4×Dic9—21no—
134C4×Dic9C2311yescharacteristic
135C2×C9⋊C8C2311yescharacteristic
136C2×C9⋊C8C2311yescharacteristic
137#3664—22no—
138C8×D9—22no—
139#3266—91noSylow
140C2×C3×#41C2×D311yescharacteristic
141C22×C3×Q8C2×D311yescharacteristic
142C2×D3×Q8—31no—
143C2×D3×D4—31no—
144C3×#137—24no—
145C2×C3×Q16C2×D311yescharacteristic
146C2×C3×Q16C2×D311yescharacteristic
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×M16C2×D311yescharacteristic
150#947—31no—
151#946—31no—
152#946—31no—
153#946—61no—
154Q8×Dic3—31no—
155#944—31no—
156#944—61no—
157C2×#216—31no—
158C2×#215—31no—
159C2×#215—31no—
160#939—61no—
161#937—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164#930—31no—
165#929—61no—
166C4×#67—31no—
167C4×#67—61no—
168C2×(C2×D3)⋊C4—61no—
169#924—31no—
170#924—61no—
171D3×SD16—64no—
172C2×#204—31no—
173C2×D3×C8—31no—
174#835—31no—
175#835—31no—
176#835—31no—
177#832—31no—
178#830—31no—
179#821—31no—
180(C2×D3)⋊C8—31no—
181#818—31no—
182#816—31no—
183#815—31no—
184Dic3⋊C8—31no—
185C23×C9—21no—
186C23×C9C2×D411yescharacteristic
187C22×D9—21no—
188C22×D9—42no—
189C22×D9—42no—
190C22×D9—81no—
191C22×D9C2×D411yescharacteristic
192Q8×C9—21no—
193Q8×C9—21no—
194Q8×C9—21no—
195Q8×C9—21no—
196Q8×C9—21no—
197Q8×C9—42no—
198Q8×C9C2×D412yes—
199D4×C9—21no—
200D4×C9—42no—
201D4×C9C2×D412yes—
202C2×C4×C9—21no—
203C2×C4×C9—21no—
204C2×C4×C9—21no—
205C2×C4×C9—21no—
206C2×C4×C9—21no—
207C2×C4×C9—42no—
208C2×C4×C9—42no—
209C2×C4×C9C2×D411yescharacteristic
210C2×C4×C9C2411yescharacteristic
211#611—22no—
212#611—42no—
213#611—81no—
214C2×Dic9—21no—
215C2×Dic9—21no—
216C2×Dic9—21no—
217C2×Dic9—81no—
218C2×Dic9C2×D411yescharacteristic
219C2×Dic9C2×D411yescharacteristic
220C2×Dic9C2×D411yescharacteristic
221D36—21no—
222D36—21no—
223C4×D9—21no—
224C4×D9—21no—
225C4×D9—42no—
226Dic18—21no—
227Dic18—21no—
228Dic18—42no—
229C8×C9—21no—
230C8×C9C2×D412yes—
231C9⋊C8—21no—
232C9⋊C8—21no—
233C2×#137D911yescharacteristic, complemented
234C22×SD16—91no—
235D4×Q8—91no—
236#546—91no—
237#497—91no—
238#468—91no—
239#467—91no—
240#464—91no—
241#461—91no—
242#452—91no—
243#451—91no—
244#450—91no—
245#448—91no—
246#440—91no—
247#435—91no—
248C23×D3—61no—
249C3×#41—22no—
250C3×#41—41no—
251C2×C3×Q8—21no—
252C2×C3×Q8—22no—
253C2×C3×Q8—41no—
254C2×C3×Q8C22×D311yescharacteristic
255C2×C3×Q8C22×D311yescharacteristic
256C2×C3×Q8C22×D311yescharacteristic
257C2×C3×D4—21no—
258C2×C3×D4C22×D311yescharacteristic
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4C22×D311yescharacteristic
262C2×#67—31no—
263C2×#67—61no—
264C2×#67—61no—
265C22×Dic3—61no—
266D3×Q8—62no—
267D3×Q8—121no—
268D3×D4—62no—
269D3×D4—121no—
270C2×D12—31no—
271C2×C4×D3—31no—
272C2×C4×D3—61no—
273C2×Dic6—31no—
274C2×Dic6—61no—
275C3×Q16—22no—
276C3×Q16—22no—
277C3×SD16—22no—
278C3×SD16#6714yes—
279C3×M16—22no—
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282#217—31no—
283#217—61no—
284#217—61no—
285#216—121no—
286#215—62no—
287#215—121no—
288#214—62no—
289(C2×D3)⋊C4—31no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295C4⋊Dic3—31no—
296C4⋊Dic3—31no—
297C4⋊Dic3—61no—
298Dic3⋊C4—31no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304C4×Dic3—31no—
305C4×Dic3—61no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—31no—
308#204—62no—
309D3×C8—62no—
310C22×C9—22no—
311C22×C9—21no—
312C22×C9—21no—
313C22×C9—21no—
314C22×C9—41no—
315C22×C9—41no—
316C22×C9C22×D411yescharacteristic
317C2×D9—21no—
318C2×D9—21no—
319C2×D9—41no—
320C2×D9—41no—
321C2×D9—41no—
322C2×D9—84no—
323C2×D9#13712yescomplemented
324C4×C9—22no—
325C4×C9—21no—
326C4×C9—41no—
327C4×C9—41no—
328C4×C9C22×D411yescharacteristic
329C4×C9H(5,𝔽2)11yescharacteristic
330Dic9—21no—
331Dic9—21no—
332Dic9—21no—
333Dic9—41no—
334Dic9—41no—
335Dic9—41no—
336C2×#41C2×D911yescharacteristic
337C22×Q8—91no—
338C22×Q8C2×D911yescharacteristic, complemented
339C22×D4—91no—
340#137—24no—
341C2×Q16—91no—
342C2×Q16C2×D911yescharacteristic, complemented
343C2×Q16C2×D911yescharacteristic, complemented
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—184no—
349C2×SD16C2×D911yescharacteristic
350C2×SD16C2×D911yescharacteristic
351C2×M16C2×D911yescharacteristic, complemented
352C22×C8—91no—
353C4⋊Q8—91no—
354C4⋊Q8—181no—
355#124—91no—
356#123—181no—
357C22⋊Q8—91no—
358C22⋊Q8—91no—
359C22⋊Q8—91no—
360C22⋊Q8—181no—
361C22⋊Q8—181no—
362#121—91no—
363#121—181no—
364#120—181no—
365C4×Q8—91no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C2×C22⋊C4—181no—
370#107—91no—
371C4⋊C8—91no—
372#103—91no—
373#103—91no—
374#103—91no—
375#103—91no—
376#102—91no—
377#102—91no—
378C22⋊C8—91no—
379C22⋊C8—91no—
380#97—91no—
381C23×C3—21no—
382C23×C3D3×D411yescharacteristic
383C22×D3—31no—
384C22×D3—61no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—241no—
388C3×Q8—21no—
389C3×Q8—21no—
390C3×Q8—21no—
391C3×Q8—21no—
392C3×Q8—21no—
393C3×Q8—42no—
394C3×Q8C2×#6712yes—
395C3×D4—21no—
396C3×D4—42no—
397C3×D4C2×#6712yes—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—62no—
408#67—122no—
409#67—241no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—31no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—241no—
417D12—61no—
418D12—61no—
419C4×D3—61no—
420C4×D3—61no—
421C4×D3—122no—
422Dic6—61no—
423Dic6—61no—
424Dic6—122no—
425C3×C8—21no—
426C3×C8C2×#6712yes—
427C3⋊C8—61no—
428C3⋊C8—61no—
429C2×C9—42no—
430C2×C9—41no—
431C2×C9D4211yescharacteristic
432C2×C9C2×#13711yescharacteristic
433C2×C9#57711yescharacteristic
434D9—22no—
435D9—81no—
436C24—181no—
437#41—22no—
438#41—41no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—91no—
443C2×Q8—181no—
444C2×Q8—182no—
445C2×Q8—361no—
446C2×Q8C22×D911yescharacteristic
447C2×Q8C22×D911yescharacteristic
448C2×Q8C22×D911yescharacteristic
449C2×D4—21no—
450C2×D4—91no—
451C2×D4—91no—
452C2×D4—181no—
453C2×D4—182no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4C22×D911yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—91no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4C22×D911yescharacteristic
463Q16—22no—
464Q16—22no—
465Q16—361no—
466SD16—22no—
467SD16—182no—
468SD16—182no—
469SD16—182no—
470SD16—361no—
471SD16#61114yescomplemented
472M16—22no—
473C2×C8—91no—
474C2×C8—91no—
475C2×C8—182no—
476C2×C8C22×D911yescharacteristic
477C2×C8C22×D911yescharacteristic
478C4⋊C4—91no—
479C4⋊C4—91no—
480C4⋊C4—91no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C22⋊C4—91no—
488C22⋊C4—91no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C42—91no—
497C42—181no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3C2×D3×D411yescharacteristic
505C2×D3—32no—
506C2×D3—61no—
507C2×D3—61no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—244no—
512C3×C4—22no—
513C3×C4—21no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4#100411yescharacteristic
517C3×C4C22×#6711yescharacteristic
518Dic3—61no—
519Dic3—61no—
520Dic3—61no—
521Dic3—121no—
522Dic3—121no—
523Dic3—121no—
524C9#326611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—91no—
527C23—181no—
528C23—362no—
529C23—362no—
530C23—721no—
531C23D4×D911yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—42no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8C2×#61112yes—
542D4—21no—
543D4—42no—
544D4—182no—
545D4—181no—
546D4—181no—
547D4—362no—
548D4—721no—
549D4C2×#61112yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—91no—
558C2×C4—91no—
559C2×C4—91no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—362no—
566C2×C4—721no—
567C2×C4D4×D911yescharacteristic
568C2×C4C23×D911yescharacteristic
569C8—21no—
570C8—181no—
571C8—181no—
572C8C2×#61112yes—
573C2×C3—42no—
574C2×C3—41no—
575C2×C3D3×#13711yescharacteristic
576C2×C3#577811yescharacteristic
577C2×C3D4×#6711yescharacteristic
578D3—62no—
579D3—241no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—92no—
587C22—181no—
588C22—181no—
589C22—361no—
590C22—361no—
591C22—361no—
592C22—724no—
593C22C2×D4×D911yescharacteristic
594C4—21no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—181no—
599C4—181no—
600C4—181no—
601C4—361no—
602C4—361no—
603C4—361no—
604C4#6371011yescharacteristic
605C4C22×#61111yescharacteristic
606C3#8398711yescharacteristic
607C2—41no—
608C2—42no—
609C2—182no—
610C2—721no—
611C2D9×#13711yescharacteristic
612C2#1058988011yescharacteristic
613C2D4×#61111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#137C2
socleC22×C3C2×D3×D4
prime radical#10589931C2
hypercenterC2×#137D9
hypocenterC9#3266
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C9×#137C2semidirect
3. Q8×#611C2semidirect
4. C2×SD16×D9C2semidirect
5. #10588918C2semidirect
6. #10588908C2semidirect
7. #10588870C2semidirect
8. #10588868C2semidirect
9. #10588866C2semidirect
10. #10588865C2semidirect
11. #10588849C2semidirect
12. #10588844C2semidirect
13. #10588842C2semidirect
14. #10588816C2semidirect
15. #10588809C2semidirect
18. C22×Q8×C9C22semidirect
22. C2×C9×Q16C22semidirect
23. C2×C9×Q16C22semidirect
26. C2×C9×M16C22semidirect
31. Q8×Dic9C22semidirect
33. #63506C22semidirect
36. C2×#3674C22semidirect
47. #63486C22semidirect
51. #63395C22semidirect
52. #63395C22semidirect
53. #63395C22semidirect
55. #63389C22semidirect
58. #63378C22semidirect
59. #63376C22semidirect
60. #63375C22semidirect
61. Dic9⋊C8C22semidirect
107. C9×SD16D4semidirect
233. C2×#137D9semidirect
323. C2×D9#137semidirect
338. C22×Q8C2×D9semidirect
342. C2×Q16C2×D9semidirect
343. C2×Q16C2×D9semidirect
351. C2×M16C2×D9semidirect
471. SD16#611semidirect
524. C9#3266semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1372
#105899312
Q8×#6112
C2×SD16×D92
#105889182
#105889082
#105888702
#105888682
#105888662
#105888652
#105888492
#105888442
#105888422
#105888162
#105888092
#839873