Finite Group Databasebeta

← #11884081

Subgroups — #11884081

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×#63471C211yesmaximal, characteristic, complemented
2C22×#3664C211yesmaximal, characteristic, complemented
3#10589652C211yesmaximal, characteristic
4D4×Dic18C211yesmaximal, characteristic, complemented
5C9×#435C211yesmaximal, characteristic, complemented
6#10588816C211yesmaximal, characteristic, complemented
7#10588788C211yesmaximal, characteristic, complemented
8#10588529C211yesmaximal, characteristic, complemented
9#10588525C211yesmaximal, characteristic, complemented
10#10588415C211yesmaximal, characteristic, complemented
11#10588413C211yesmaximal, characteristic, complemented
12#10588405C211yesmaximal, characteristic, complemented
13#10588404C211yesmaximal, characteristic, complemented
14#10588396C211yesmaximal, characteristic, complemented
15#10588391C211yesmaximal, characteristic, complemented
16#79495—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C22×Dic18C2211yescharacteristic
20C22×Dic18C2211yescharacteristic, complemented
21C2×C9×M16C2211yescharacteristic, complemented
22C22×C8×C9C2211yescharacteristic
23C4×D4×C9C2211yescharacteristic
24#63499—21no—
25D4×Dic9—21no—
26#63492C2211yescharacteristic
27#63486C2211yescharacteristic
28#63486C2211yescharacteristic
29#63486C2211yescharacteristic, complemented
30#63471—24no—
31C2×#3664—24no—
32C2×#3664C2211yescharacteristic
33C2×#3664C2211yescharacteristic
34C2×#3664C2211yescharacteristic
35C2×#3664C2211yescharacteristic
36C2×#3664C2211yescharacteristic
37C2×#3664C2211yescharacteristic
38C2×Dic36C2211yescharacteristic, complemented
39C2×Dic36C2211yescharacteristic, complemented
40C2×Dic36C2211yescharacteristic, complemented
41#63456—21no—
42#63450—21no—
43#63446—21no—
44C22⋊C4×D9—21no—
45#63440—21no—
46#63440—21no—
47#63437C2211yescharacteristic
48C4×D36C2211yescharacteristic
49#63431C2211yescharacteristic, complemented
50C4×Dic18C2211yescharacteristic, complemented
51C9×C4⋊C8C2211yescharacteristic, complemented
52C9×C22⋊C8C2211yescharacteristic
53C9×C22⋊C8C2211yescharacteristic, complemented
54C9×#97C2211yescharacteristic, complemented
55#63380C2211yescharacteristic
56#63380C2211yescharacteristic
57#63378C2211yescharacteristic, complemented
58#63376C2211yescharacteristic, complemented
59#63376C2211yescharacteristic, complemented
60#63376C2211yescharacteristic, complemented
61#63376C2211yescharacteristic, complemented
62C2×#909—31no—
63C22×#204—31no—
64#5550—31no—
65D4×Dic6—31no—
66C3×#435D311yescharacteristic
67#5134—31no—
68#5116—31no—
69#4845—31no—
70#4841—31no—
71#4739—31no—
72#4738—31no—
73#4733—31no—
74#4731—31no—
75#4715—31no—
76#4710—31no—
77C23×D9—21no—
78C2×D4×C9D411yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C2×#611—21no—
82C2×#611—21no—
83C22×Dic9—21no—
84C22×Dic9—21no—
85#3697—22no—
86#3697—41no—
87C2×D36—22no—
88C2×D36—21no—
89C2×D36—41no—
90C2×D36C2311yescharacteristic
91C2×D36C2311yescharacteristic
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×Dic18—22no—
95C2×Dic18—22no—
96C2×Dic18—21no—
97C2×Dic18—21no—
98C2×Dic18—41no—
99C2×Dic18—41no—
100C2×Dic18C2311yescharacteristic
101C2×Dic18C2311yescharacteristic
102C2×Dic18C2311yescharacteristic
103C2×Dic18C2311yescharacteristic
104C9×M16—22no—
105C2×C8×C9—22no—
106C2×C8×C9C2311yescharacteristic
107C2×C8×C9C2311yescharacteristic
108C2×C8×C9C2311yescharacteristic
109C2×C8×C9C2311yescharacteristic
110C9×C4⋊C4D411yescharacteristic
111C9×C22⋊C4D411yescharacteristic
112C9×C22⋊C4D411yescharacteristic
113C42×C9C2311yescharacteristic
114#3676—21no—
115#3676—21no—
116#3676—21no—
117(C2×D9)⋊C4—21no—
118(C2×D9)⋊C4—21no—
119(C2×D9)⋊C4—21no—
120(C2×D9)⋊C4—21no—
121C4⋊Dic9—21no—
122C4⋊Dic9—21no—
123C4⋊Dic9C2311yescharacteristic
124C4⋊Dic9C2311yescharacteristic
125Dic9⋊C4—21no—
126Dic9⋊C4—21no—
127Dic9⋊C4—21no—
128Dic9⋊C4—21no—
129C4×Dic9—21no—
130#3664—22no—
131#3664—22no—
132#3664—22no—
133#3664—22no—
134#3664—41no—
135#3664D414yescomplemented
136Dic36—22no—
137Dic36—22no—
138Dic36—41no—
139#3266—91noSylow
140C2×#235—31no—
141C22×D12—31no—
142C22×Dic6—31no—
143C22×Dic6—31no—
144C2×C3×M16C2×D311yescharacteristic
145C22×C3×C8C2×D311yescharacteristic
146C3×C4×D4C2×D311yescharacteristic
147#937—61no—
148D4×Dic3—61no—
149#930—31no—
150#924—31no—
151#924—31no—
152#924—31no—
153#909—64no—
154C2×Dic12—31no—
155C2×Dic12—31no—
156C2×Dic12—31no—
157C2×#204—31no—
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—31no—
161C2×#204—31no—
162C2×#204—31no—
163C2×#204—64no—
164#894—61no—
165#888—61no—
166#884—61no—
167D3×C22⋊C4—61no—
168#878—61no—
169#878—61no—
170#875—31no—
171C4×D12—31no—
172#869—31no—
173C4×Dic6—31no—
174C3×C4⋊C8C2×D311yescharacteristic
175C3×C22⋊C8C2×D311yescharacteristic
176C3×C22⋊C8C2×D311yescharacteristic
177C3×#97C2×D311yescharacteristic
178#821—31no—
179#821—31no—
180#818—31no—
181#816—31no—
182#816—31no—
183#816—31no—
184#816—31no—
185C23×C9C2×D411yescharacteristic
186C23×C9C2×D411yescharacteristic
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—42no—
190C22×D9—42no—
191C22×D9—81no—
192D4×C9—22no—
193C2×C4×C9—21no—
194C2×C4×C9—21no—
195C2×C4×C9—21no—
196C2×C4×C9—21no—
197C2×C4×C9C2×D411yescharacteristic
198C2×C4×C9C2×D411yescharacteristic
199C2×C4×C9C2×D411yescharacteristic
200C2×C4×C9C2×D411yescharacteristic
201C2×C4×C9C2411yescharacteristic
202#611—42no—
203#611—81no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9—21no—
207C2×Dic9—21no—
208C2×Dic9—21no—
209C2×Dic9—21no—
210C2×Dic9—42no—
211C2×Dic9—42no—
212D36—21no—
213D36—21no—
214D36—21no—
215D36—42no—
216D36C2×D412yes—
217C4×D9—42no—
218C4×D9—81no—
219Dic18—21no—
220Dic18—21no—
221Dic18—21no—
222Dic18—21no—
223Dic18—21no—
224Dic18—21no—
225Dic18—21no—
226Dic18—42no—
227Dic18—42no—
228Dic18C2×D412yes—
229C8×C9—21no—
230C8×C9—21no—
231C8×C9—21no—
232C8×C9C2×D412yes—
233C2×#137—91no—
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#435D911yescharacteristic, complemented
248C23×D3—61no—
249C2×C3×D4D1211yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—61no—
253C2×#67—61no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256#235—62no—
257#235—121no—
258C2×D12—31no—
259C2×D12—31no—
260C2×D12—62no—
261C2×D12—61no—
262C2×D12—121no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×Dic6—31no—
266C2×Dic6—31no—
267C2×Dic6—31no—
268C2×Dic6—31no—
269C2×Dic6—62no—
270C2×Dic6—62no—
271C2×Dic6—61no—
272C2×Dic6—61no—
273C2×Dic6—121no—
274C2×Dic6—121no—
275C3×M16—22no—
276C2×C3×C8—22no—
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C3×C4⋊C4D1211yescharacteristic
282C3×C22⋊C4D1211yescharacteristic
283C3×C22⋊C4D1211yescharacteristic
284C3×C42C22×D311yescharacteristic
285#217—61no—
286#217—61no—
287#217—61no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292C4⋊Dic3—31no—
293C4⋊Dic3—31no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300C4×Dic3—61no—
301Dic12—62no—
302Dic12—62no—
303Dic12—121no—
304#204—34no—
305#204—62no—
306#204—62no—
307#204—62no—
308#204—62no—
309#204—121no—
310C22×C9—21no—
311C22×C9—21no—
312C22×C9—21no—
313C22×C9—21no—
314C22×C9—21no—
315C22×C9#13712yescomplemented
316C22×C9C22×D411yescharacteristic
317C2×D9—22no—
318C2×D9—41no—
319C2×D9—41no—
320C2×D9—41no—
321C2×D9—41no—
322C2×D9—41no—
323C2×D9—84no—
324C4×C9—21no—
325C4×C9—21no—
326C4×C9—21no—
327C4×C9—21no—
328C4×C9C22×D411yescharacteristic
329C4×C9H(5,𝔽2)11yescharacteristic
330Dic9—22no—
331Dic9—41no—
332Dic9—41no—
333Dic9—41no—
334Dic9—41no—
335Dic9—41no—
336C2×#41—91no—
337C22×Q8—91no—
338C22×Q8—91no—
339C22×D4—91no—
340#137—184no—
341C2×Q16—91no—
342C2×Q16—91no—
343C2×Q16—91no—
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—184no—
351C2×M16C2×D911yescharacteristic, complemented
352C22×C8C2×D911yescharacteristic
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—181no—
368C4×D4C2×D911yescharacteristic
369C2×C22⋊C4—181no—
370#107—91no—
371C4⋊C8C2×D911yescharacteristic, complemented
372#103—91no—
373#103—91no—
374#103—91no—
375#103—91no—
376#102—91no—
377#102—91no—
378C22⋊C8C2×D911yescharacteristic
379C22⋊C8C2×D911yescharacteristic, complemented
380#97C2×D911yescharacteristic, complemented
381C23×C3C2×D1211yescharacteristic
382C23×C3C2×D1211yescharacteristic
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—241no—
388C3×D4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4C2×D1211yescharacteristic
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4C2×D1211yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—122no—
399#67—241no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408D12—32no—
409D12—61no—
410D12—61no—
411D12—61no—
412D12—122no—
413C4×D3—122no—
414C4×D3—241no—
415Dic6—32no—
416Dic6—61no—
417Dic6—61no—
418Dic6—61no—
419Dic6—61no—
420Dic6—61no—
421Dic6—61no—
422Dic6—61no—
423Dic6—122no—
424Dic6—122no—
425C3×C8—21no—
426C3×C8—21no—
427C3×C8—21no—
428C3×C8D3×D412yes—
429C2×C9—22no—
430C2×C9—41no—
431C2×C9D4211yescharacteristic
432C2×C9C2×#13711yescharacteristic
433C2×C9#57711yescharacteristic
434D9—42no—
435D9—81no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—91no—
440C2×Q8—91no—
441C2×Q8—91no—
442C2×Q8—91no—
443C2×Q8—182no—
444C2×Q8—182no—
445C2×Q8—181no—
446C2×Q8—181no—
447C2×Q8—361no—
448C2×Q8—361no—
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—182no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4D3611yescharacteristic
457C22×C4—181no—
458C22×C4—181no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4C22×D911yescharacteristic
462C22×C4C22×D911yescharacteristic
463Q16—182no—
464Q16—182no—
465Q16—361no—
466SD16—94no—
467SD16—182no—
468SD16—182no—
469SD16—182no—
470SD16—182no—
471SD16—361no—
472M16—22no—
473C2×C8—22no—
474C2×C8C22×D911yescharacteristic
475C2×C8C22×D911yescharacteristic
476C2×C8C22×D911yescharacteristic
477C2×C8C22×D911yescharacteristic
478C4⋊C4—91no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4D3611yescharacteristic
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4D3611yescharacteristic
495C22⋊C4D3611yescharacteristic
496C42—181no—
497C42C22×D911yescharacteristic
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3#90912yes—
504C22×C3C22×D1211yescharacteristic
505C2×D3—62no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—244no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4C2×D3×D411yescharacteristic
517C3×C4#100911yescharacteristic
518Dic3—62no—
519Dic3—121no—
520Dic3—121no—
521Dic3—121no—
522Dic3—121no—
523Dic3—121no—
524C9#326611yescharacteristic, complemented, Sylow
525C23—181no—
526C23—181no—
527C23—362no—
528C23—362no—
529C23—721no—
530C23C2×D3611yescharacteristic
531C23C2×D3611yescharacteristic
532Q8—92no—
533Q8—181no—
534Q8—181no—
535Q8—181no—
536Q8—181no—
537Q8—181no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8—362no—
542D4—22no—
543D4—92no—
544D4—181no—
545D4—181no—
546D4—181no—
547D4—362no—
548D4—362no—
549D4—721no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—362no—
561C2×C4—362no—
562C2×C4—362no—
563C2×C4—721no—
564C2×C4C2×D3611yescharacteristic
565C2×C4C2×D3611yescharacteristic
566C2×C4C2×D3611yescharacteristic
567C2×C4C2×D3611yescharacteristic
568C2×C4C23×D911yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8D4×D912yes—
573C2×C3—22no—
574C2×C3—41no—
575C2×C3D4×D1211yescharacteristic
576C2×C3C2×#90911yescharacteristic
577C2×C3#575111yescharacteristic
578D3—122no—
579D3—241no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—182no—
586C22—361no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22—724no—
592C22#6347112yescomplemented
593C22C22×D3611yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—182no—
599C4—361no—
600C4—361no—
601C4—361no—
602C4—361no—
603C4—361no—
604C4C2×D4×D911yescharacteristic
605C4#6371511yescharacteristic
606C3#7949511yescharacteristic
607C2—22no—
608C2—41no—
609C2—362no—
610C2—721no—
611C2D4×D3611yescharacteristic
612C2C2×#6347111yescharacteristic
613C2#1058985311yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#435C2
socleC22×C3C22×D12
prime radical#10589652C2
hypercenter#435D9
hypocenterC9#3266
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#63471C2semidirect
2. C22×#3664C2semidirect
4. D4×Dic18C2semidirect
5. C9×#435C2semidirect
6. #10588816C2semidirect
7. #10588788C2semidirect
8. #10588529C2semidirect
9. #10588525C2semidirect
10. #10588415C2semidirect
11. #10588413C2semidirect
12. #10588405C2semidirect
13. #10588404C2semidirect
14. #10588396C2semidirect
15. #10588391C2semidirect
20. C22×Dic18C22semidirect
21. C2×C9×M16C22semidirect
29. #63486C22semidirect
38. C2×Dic36C22semidirect
39. C2×Dic36C22semidirect
40. C2×Dic36C22semidirect
49. #63431C22semidirect
50. C4×Dic18C22semidirect
51. C9×C4⋊C8C22semidirect
53. C9×C22⋊C8C22semidirect
54. C9×#97C22semidirect
57. #63378C22semidirect
58. #63376C22semidirect
59. #63376C22semidirect
60. #63376C22semidirect
61. #63376C22semidirect
135. #3664D4semidirect
247. #435D9semidirect
315. C22×C9#137semidirect
351. C2×M16C2×D9semidirect
371. C4⋊C8C2×D9semidirect
379. C22⋊C8C2×D9semidirect
380. #97C2×D9semidirect
524. C9#3266semidirect
592. C22#63471semidirect

Maximal subgroups

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

subgroupindex
C2×#634712
C22×#36642
#105896522
D4×Dic182
C9×#4352
#105888162
#105887882
#105885292
#105885252
#105884152
#105884132
#105884052
#105884042
#105883962
#105883912
#794953