Finite Group Databasebeta

← #11860272

Subgroups — #11860272

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63473C211yesmaximal, characteristic
2C4×D4×D9C211yesmaximal, characteristic, complemented
3C4×#3699C211yesmaximal, characteristic, complemented
4C9×#442C211yesmaximal, characteristic, complemented
5D8×Dic9C211yesmaximal, characteristic, complemented
6#10588697C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588541C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588451C211yesmaximal, characteristic, complemented
11#10588450C211yesmaximal, characteristic, complemented
12#10588438C211yesmaximal, characteristic, complemented
13#10588436C211yesmaximal, characteristic, complemented
14#10588391C211yesmaximal, characteristic, complemented
15#10588388C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17C2×#3699C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C22×C4×D9—21no—
20C2×C9×D8C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22C4×D4×C9C2211yescharacteristic, complemented
23D4×Dic9C2211yescharacteristic
24D4×Dic9C2211yescharacteristic, complemented
25C2×#3673C2211yescharacteristic
26C2×#3672C2211yescharacteristic
27C4×#611—21no—
28C4×#611—21no—
29C2×C4×Dic9—21no—
30#63473C418yescomplemented
31C2×#3664C2211yescharacteristic
32C2×#3663C2211yescharacteristic
33C2×#3663C2211yescharacteristic
34#63455C2211yescharacteristic
35#63454C2211yescharacteristic
36C4⋊C4×D9C2211yescharacteristic
37#63449C2211yescharacteristic, complemented
38#611⋊C4—21no—
39#611⋊C4—21no—
40C22⋊C4×D9—21no—
41#63439—21no—
42C4×D36C2211yescharacteristic
43C42×D9C2211yescharacteristic
44C4×Dic18C2211yescharacteristic, complemented
45C9×#106C2211yescharacteristic, complemented
46C9×#102C2211yescharacteristic
47C9×#102C2211yescharacteristic, complemented
48C9×#97C2211yescharacteristic, complemented
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic, complemented
51#63380C2211yescharacteristic
52#63378C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54C8×Dic9C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#63362C2211yescharacteristic, complemented
61C2×#911—31no—
62C4×D3×D4—31no—
63C4×#237—31no—
64C3×#442D311yescharacteristic
65Dic3×D8—31no—
66#5018—31no—
67#5014—31no—
68#4861—31no—
69#4852—31no—
70#4771—31no—
71#4770—31no—
72#4758—31no—
73#4756—31no—
74#4710—31no—
75#4707—31no—
76C23×D9—21no—
77C2×D4×C9C2311yescharacteristic
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9—21no—
80C22×C4×C9—21no—
81C2×#611—21no—
82C2×#611—21no—
83C22×Dic9—21no—
84C22×Dic9—21no—
85C22×Dic9—21no—
86#3699—22no—
87#3699C2×C414yescomplemented
88D4×D9—22no—
89D4×D9C2×C414yescomplemented
90C2×D36C2311yescharacteristic
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9—44no—
95C2×C4×D9D411yescharacteristic
96C2×C4×D9D411yescharacteristic
97C2×C4×D9C2311yescharacteristic
98C2×Dic18C2311yescharacteristic
99C9×D8C2×C414yescomplemented
100C2×C8×C9C2311yescharacteristic
101C2×C8×C9C2311yescharacteristic
102C9×C4⋊C4C2311yescharacteristic
103C9×C4⋊C4C2311yescharacteristic
104C9×C22⋊C4—21no—
105C9×C22⋊C4—21no—
106C42×C9C2311yescharacteristic
107#3676—21no—
108#3676—21no—
109#3673C2×C414yescomplemented
110#3672C2×C414yescomplemented
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9D411yescharacteristic
123C4×Dic9D411yescharacteristic
124C4×Dic9C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3664C2×C414yescomplemented
128#3663—22no—
129#3663C2×C414yescomplemented
130C4×AGL(1,ℤ/8)—91noSylow
131C2×#237—31no—
132C2×D3×D4—31no—
133C22×C4×D3—61no—
134C2×C3×D8C2×D311yescharacteristic
135C3×C4×D4C2×D311yescharacteristic
136C3×C4×D4C2×D311yescharacteristic
137D4×Dic3—31no—
138D4×Dic3—31no—
139C2×#214—31no—
140C2×#213—31no—
141C4×#67—61no—
142C4×#67—61no—
143C2×C4×Dic3—61no—
144#911—38no—
145C2×#204—31no—
146C2×ΓL(1,𝔽25)—31no—
147C2×ΓL(1,𝔽25)—31no—
148#893—31no—
149#892—31no—
150D3×C4⋊C4—31no—
151#887—31no—
152#67⋊C4—61no—
153#67⋊C4—61no—
154D3×C22⋊C4—61no—
155#877—61no—
156C4×D12—31no—
157C42×D3—31no—
158C4×Dic6—31no—
159C3×#106C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×#102C2×D311yescharacteristic
162C3×#97C2×D311yescharacteristic
163#832—31no—
164#832—31no—
165#821—31no—
166#818—31no—
167#816—31no—
168C8×Dic3—31no—
169C8×Dic3—31no—
170#810—31no—
171#809—31no—
172#808—31no—
173#807—31no—
174#803—31no—
175C23×C9—21no—
176C23×C9—21no—
177C22×D9—21no—
178C22×D9—24no—
179C22×D9—42no—
180C22×D9—42no—
181C22×D9C2×D411yescharacteristic
182D4×C9—21no—
183D4×C9—21no—
184D4×C9C22×C412yes—
185D4×C9C22×C412yescomplemented
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—42no—
189C2×C4×C9—42no—
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2411yescharacteristic
193#611—24no—
194#611—24no—
195C2×Dic9—21no—
196C2×Dic9—24no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—42no—
200C2×Dic9—42no—
201C2×Dic9C2×D411yescharacteristic
202C2×Dic9C2×D411yescharacteristic
203C2×Dic9C2×D411yescharacteristic
204D36—21no—
205D36C22×C412yes—
206C4×D9—22no—
207C4×D9—41no—
208C4×D9—42no—
209C4×D9—42no—
210C4×D9—42no—
211C4×D9C22×C412yes—
212C4×D9#4112yes—
213Dic18—21no—
214Dic18C22×C412yescomplemented
215C8×C9—21no—
216C8×C9C22×C412yescomplemented
217C9⋊C8—21no—
218C9⋊C8C22×C412yescomplemented
219C2×AGL(1,ℤ/8)—91no—
220C4×#41—91no—
221C2×C4×D4—91no—
222#442—91no—
223#442D911yescharacteristic, complemented
224#440—91no—
225#440—91no—
226C4×SD16—91no—
227C4×SD16—91no—
228C4×D8—91no—
229C4×D8—91no—
230#428—91no—
231#418—91no—
232#417—91no—
233C4×M16—91no—
234C23×D3—61no—
235C2×C3×D4C22×D311yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C2×#67—61no—
240C2×#67—61no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244#237—34no—
245#237—62no—
246D3×D4—34no—
247D3×D4—62no—
248C2×D12—31no—
249C2×C4×D3—31no—
250C2×C4×D3—31no—
251C2×C4×D3—31no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—124no—
256C2×Dic6—31no—
257C3×D8C4×D314yes—
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C42C22×D311yescharacteristic
265#217—61no—
266#217—61no—
267#214—34no—
268#213—34no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277C4×Dic3—31no—
278C4×Dic3—31no—
279C4×Dic3—31no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285#204—34no—
286ΓL(1,𝔽25)—34no—
287ΓL(1,𝔽25)—62no—
288C22×C9—22no—
289C22×C9—22no—
290C22×C9—41no—
291C22×C9—41no—
292C22×C9—41no—
293C22×C9—41no—
294C22×C9C22×D411yescharacteristic
295C2×D9—21no—
296C2×D9—21no—
297C2×D9—22no—
298C2×D9—48no—
299C2×D9—41no—
300C2×D9—41no—
301C2×D9C4×D412yes—
302C4×C9—21no—
303C4×C9—21no—
304C4×C9—41no—
305C4×C9—41no—
306C4×C9C23×C411yescharacteristic
307C4×C9C2×#4111yescharacteristic
308Dic9—22no—
309Dic9—21no—
310Dic9—41no—
311Dic9—41no—
312Dic9C4×D412yes—
313Dic9AGL(1,ℤ/8)12yescomplemented
314C2×#41—91no—
315C22×D4—91no—
316C23×C4—181no—
317AGL(1,ℤ/8)—98no—
318C2×SD16—91no—
319C2×SD16—91no—
320C2×D8—91no—
321C2×D8C2×D911yescharacteristic
322C2×M16—91no—
323C2×M16—91no—
324C4×Q8—91no—
325C4×Q8—91no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4—181no—
332C4×D4—181no—
333C4×D4—181no—
334C4×D4C2×D911yescharacteristic
335C4×D4C2×D911yescharacteristic, complemented
336#117—91no—
337#117—181no—
338C2×C4⋊C4—91no—
339C2×C22⋊C4—181no—
340C2×C42—91no—
341C2×C42—181no—
342#107—91no—
343#107—91no—
344#106—91no—
345#106C2×D911yescharacteristic, complemented
346#103—91no—
347#103—91no—
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102C2×D911yescharacteristic
353#102C2×D911yescharacteristic, complemented
354#97—91no—
355#97C2×D911yescharacteristic, complemented
356C4×C8—91no—
357C4×C8—91no—
358C23×C3—21no—
359C23×C3—21no—
360C22×D3—31no—
361C22×D3—64no—
362C22×D3—61no—
363C22×D3—122no—
364C22×D3—122no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4C2×C4×D312yes—
368C3×D4C2×C4×D312yes—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—64no—
377#67—64no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—64no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387D12—32no—
388D12—61no—
389C4×D3—32no—
390C4×D3—32no—
391C4×D3—62no—
392C4×D3—122no—
393C4×D3—121no—
394C4×D3—122no—
395C4×D3—122no—
396Dic6—32no—
397Dic6—61no—
398C3×C8—21no—
399C3×C8C2×C4×D312yes—
400C3⋊C8—32no—
401C3⋊C8—61no—
402C2×C9—42no—
403C2×C9—42no—
404C2×C9C2×C4×D411yescharacteristic
405C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C9#57511yescharacteristic
407D9—22no—
408D9—42no—
409C24—181no—
410#41—94no—
411#41—182no—
412C2×Q8—91no—
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—182no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4C22×D911yescharacteristic
419C2×D4C22×D911yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—364no—
432SD16—94no—
433SD16—94no—
434D8—94no—
435D8C4×D914yescomplemented
436M16—94no—
437M16—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×D911yescharacteristic
441C2×C8C22×D911yescharacteristic
442C4⋊C4—91no—
443C4⋊C4—91no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C4⋊C4C22×D911yescharacteristic
448C4⋊C4C22×D911yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—91no—
457C42—91no—
458C42—91no—
459C42—181no—
460C42—181no—
461C42—181no—
462C42C22×D911yescharacteristic
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3C2×D3×D411yescharacteristic
470C2×D3—32no—
471C2×D3—61no—
472C2×D3—61no—
473C2×D3—62no—
474C2×D3—128no—
475C2×D3—121no—
476C2×D3—121no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4C22×C4×D311yescharacteristic
482C3×C4D3×#4111yescharacteristic
483Dic3—32no—
484Dic3—32no—
485Dic3—61no—
486Dic3—62no—
487Dic3—121no—
488Dic3—121no—
489C9C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
490C23—21no—
491C23—21no—
492C23—91no—
493C23—184no—
494C23—181no—
495C23—362no—
496C23—362no—
497Q8—92no—
498Q8—181no—
499D4—21no—
500D4—21no—
501D4—92no—
502D4—184no—
503D4—184no—
504D4—181no—
505D4C2×C4×D912yes—
506D4C2×C4×D912yescomplemented
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—91no—
512C2×C4—91no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—91no—
516C2×C4—182no—
517C2×C4—184no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—361no—
522C2×C4—362no—
523C2×C4—362no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4—362no—
527C2×C4D4×D911yescharacteristic
528C2×C4D4×D911yescharacteristic
529C2×C4C23×D911yescharacteristic
530C8—21no—
531C8—92no—
532C8—181no—
533C8C2×C4×D912yescomplemented
534C2×C3—42no—
535C2×C3—42no—
536C2×C3C4×D3×D411yescharacteristic
537C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
538C2×C3#577311yescharacteristic
539D3—62no—
540D3—122no—
541C22—22no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—92no—
548C22—181no—
549C22—181no—
550C22—182no—
551C22—368no—
552C22—361no—
553C22—361no—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—92no—
560C4—92no—
561C4—181no—
562C4—182no—
563C4—361no—
564C4—361no—
565C4C22×C4×D911yescharacteristic
566C4#41×D911yescharacteristic
567C3#7986511yescharacteristic
568C2—42no—
569C2—42no—
570C2—182no—
571C2—362no—
572C2C4×D4×D911yescharacteristic
573C2D9×AGL(1,ℤ/8)11yescharacteristic
574C2#1058987511yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#442C2
socleC22×C3C2×D3×D4
prime radicalC2×#63473C2
cosocleC2×C4×C9C24
hypercenter#442D9
hypocenterC9C4×AGL(1,ℤ/8)
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D9C2semidirect
3. C4×#3699C2semidirect
4. C9×#442C2semidirect
5. D8×Dic9C2semidirect
6. #10588697C2semidirect
7. #10588694C2semidirect
8. #10588541C2semidirect
9. #10588532C2semidirect
10. #10588451C2semidirect
11. #10588450C2semidirect
12. #10588438C2semidirect
13. #10588436C2semidirect
14. #10588391C2semidirect
15. #10588388C2semidirect
22. C4×D4×C9C22semidirect
24. D4×Dic9C22semidirect
30. #63473C4semidirect
37. #63449C22semidirect
44. C4×Dic18C22semidirect
45. C9×#106C22semidirect
47. C9×#102C22semidirect
48. C9×#97C22semidirect
50. #63392C22semidirect
52. #63378C22semidirect
53. #63376C22semidirect
54. C8×Dic9C22semidirect
55. C8×Dic9C22semidirect
57. #63368C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
60. #63362C22semidirect
87. #3699C2×C4semidirect
89. D4×D9C2×C4semidirect
99. C9×D8C2×C4semidirect
109. #3673C2×C4semidirect
110. #3672C2×C4semidirect
127. #3664C2×C4semidirect
129. #3663C2×C4semidirect
185. D4×C9C22×C4semidirect
214. Dic18C22×C4semidirect
216. C8×C9C22×C4semidirect
218. C9⋊C8C22×C4semidirect
223. #442D9semidirect
313. Dic9AGL(1,ℤ/8)semidirect
335. C4×D4C2×D9semidirect
345. #106C2×D9semidirect
353. #102C2×D9semidirect
355. #97C2×D9semidirect
435. D8C4×D9semidirect
489. C9C4×AGL(1,ℤ/8)semidirect
506. D4C2×C4×D9semidirect
533. C8C2×C4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#634732
C4×D4×D92
C4×#36992
C9×#4422
D8×Dic92
#105886972
#105886942
#105885412
#105885322
#105884512
#105884502
#105884382
#105884362
#105883912
#105883882
#798653