Finite Group Databasebeta

← #11860454

Subgroups — #11860454

Order 1152.

759 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63473C211yesmaximal, characteristic
2#10589648C211yesmaximal, characteristic, complemented
3#10589647C211yesmaximal, characteristic, complemented
4C4×C9×D8C211yesmaximal, characteristic, complemented
5#10588832C211yesmaximal, characteristic, complemented
6#10588697C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588569C211yesmaximal, characteristic, complemented
9#10588561C211yesmaximal, characteristic, complemented
10#10588452C211yesmaximal, characteristic, complemented
11D9×#102C211yesmaximal, characteristic, complemented
12#10588438C211yesmaximal, characteristic, complemented
13#10588436C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15#10588371C211yesmaximal, characteristic, complemented
16#79587—31nomaximal
17C2×#3699C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C2×C9×D8C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic, complemented
22D4×Dic9C2211yescharacteristic
23D4×Dic9C2211yescharacteristic, complemented
24C2×#3673C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26C4×#611—21no—
27C4×#611—21no—
28C2×(C2×D9)⋊C4—21no—
29C2×Dic9⋊C4—21no—
30#63473C418yescomplemented
31C2×#3664C2211yescharacteristic
32C2×#3663C2211yescharacteristic
33C2×C8×D9C2211yescharacteristic
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
43#63434C2211yescharacteristic
44C4×Dic18C2211yescharacteristic, complemented
45C9×#107C2211yescharacteristic, complemented
46C9×#102C2211yescharacteristic
47C9×#102C2211yescharacteristic, complemented
48C4×C8×C9C2211yescharacteristic, complemented
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic, complemented
51#63380C2211yescharacteristic
52#63377C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#63362C2211yescharacteristic, complemented
61C2×#911—31no—
62#5546—31no—
63#5545—31no—
64C3×C4×D8D311yescharacteristic
65#5152—31no—
66#5018—31no—
67#5014—31no—
68#4889—31no—
69#4881—31no—
70#4772—31no—
71D3×#102—31no—
72#4758—31no—
73#4756—31no—
74C4×#204—31no—
75#4689—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×D9C2311yescharacteristic
95C2×Dic18C2311yescharacteristic
96C9×D8C2×C414yescomplemented
97C2×C8×C9C2311yescharacteristic
98C2×C8×C9C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C9×C22⋊C4—21no—
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3676—21no—
106#3673C2×C414yescomplemented
107#3672C2×C414yescomplemented
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4D411yescharacteristic
112(C2×D9)⋊C4D411yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4D411yescharacteristic
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3664C2×C414yescomplemented
127#3663C2×C414yescomplemented
128C8×D9—22no—
129#2946—91noSylow
130C2×#237—31no—
131C2×D3×D4—31no—
132C2×C3×D8C2×D311yescharacteristic
133C3×C4×D4C2×D311yescharacteristic
134C3×C4×D4C2×D311yescharacteristic
135D4×Dic3—31no—
136D4×Dic3—31no—
137C2×#214—31no—
138C2×#213—31no—
139C4×#67—61no—
140C4×#67—61no—
141C2×(C2×D3)⋊C4—61no—
142C2×Dic3⋊C4—61no—
143#911—38no—
144C2×#204—31no—
145C2×ΓL(1,𝔽25)—31no—
146C2×D3×C8—31no—
147#893—31no—
148#892—31no—
149D3×C4⋊C4—31no—
150#887—31no—
151#67⋊C4—61no—
152#67⋊C4—61no—
153D3×C22⋊C4—61no—
154#877—61no—
155C4×D12—31no—
156#872—31no—
157C4×Dic6—31no—
158C3×#107C2×D311yescharacteristic
159C3×#102C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#832—31no—
163#832—31no—
164#821—31no—
165#817—31no—
166#816—31no—
167#815—31no—
168C8×Dic3—31no—
169#810—31no—
170#809—31no—
171#808—31no—
172#807—31no—
173#803—31no—
174C23×C9—21no—
175C23×C9—21no—
176C22×D9—21no—
177C22×D9—24no—
178C22×D9—81no—
179C22×D9—81no—
180C22×D9C2×D411yescharacteristic
181D4×C9—21no—
182D4×C9—21no—
183D4×C9C22×C412yes—
184D4×C9C22×C412yes—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—81no—
188C2×C4×C9—81no—
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2411yescharacteristic
192#611—24no—
193#611—24no—
194C2×Dic9—21no—
195C2×Dic9—24no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—81no—
199C2×Dic9—81no—
200C2×Dic9C2×D411yescharacteristic
201C2×Dic9C2×D411yescharacteristic
202C2×Dic9C2×D411yescharacteristic
203D36—21no—
204D36C22×C412yes—
205C4×D9—81no—
206C4×D9—81no—
207C4×D9—81no—
208C4×D9C22×C412yes—
209C4×D9#4112yes—
210Dic18—21no—
211Dic18C22×C412yes—
212C8×C9—21no—
213C8×C9C22×C412yes—
214C9⋊C8—21no—
215C9⋊C8C22×C412yes—
216C2×AGL(1,ℤ/8)—91no—
217#520—91no—
218#518—91no—
219#442—91no—
220#442—91no—
221#440—91no—
222#440—91no—
223C4×SD16—91no—
224C4×SD16—91no—
225C4×D8—91no—
226C4×D8D911yescharacteristic, complemented
227#428—91no—
228#416—91no—
229C2×#102—91no—
230#405—91no—
231C23×D3—61no—
232C2×C3×D4C22×D311yescharacteristic
233C2×C3×D4C22×D311yescharacteristic
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241#237—34no—
242#237—62no—
243D3×D4—34no—
244D3×D4—62no—
245C2×D12—31no—
246C2×C4×D3—31no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×Dic6—31no—
251C3×D8C4×D314yes—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C42C22×D311yescharacteristic
259#217—61no—
260#217—61no—
261#214—34no—
262#213—34no—
263(C2×D3)⋊C4—31no—
264(C2×D3)⋊C4—31no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270Dic3⋊C4—31no—
271Dic3⋊C4—31no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275C4×Dic3—31no—
276C4×Dic3—61no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281#204—34no—
282ΓL(1,𝔽25)—34no—
283D3×C8—62no—
284C22×C9—22no—
285C22×C9—22no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9—41no—
289C22×C9—41no—
290C22×C9C22×D411yescharacteristic
291C2×D9—21no—
292C2×D9—21no—
293C2×D9—22no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—84no—
297C2×D9C4×D412yes—
298C4×C9—21no—
299C4×C9—21no—
300C4×C9—41no—
301C4×C9—41no—
302C4×C9C23×C411yescharacteristic
303C4×C9C2×#4111yescharacteristic
304Dic9—22no—
305Dic9—21no—
306Dic9—21no—
307Dic9—41no—
308Dic9—41no—
309Dic9C4×D412yes—
310C2×#41—91no—
311C22×D4—91no—
312AGL(1,ℤ/8)—98no—
313C2×SD16—91no—
314C2×SD16—91no—
315C2×D8—91no—
316C2×D8C2×D911yescharacteristic
317C2×M16—91no—
318C22×C8—91no—
319C4×Q8—91no—
320C4×Q8—91no—
321C4×D4—91no—
322C4×D4—91no—
323C4×D4—91no—
324C4×D4—91no—
325C4×D4—181no—
326C4×D4—181no—
327C4×D4—181no—
328C4×D4—181no—
329C4×D4C2×D911yescharacteristic
330C4×D4C2×D911yescharacteristic, complemented
331#117—91no—
332#117—91no—
333#117—181no—
334C2×C4⋊C4—91no—
335C2×C4⋊C4—181no—
336C2×C22⋊C4—181no—
337C2×C22⋊C4—181no—
338#107—91no—
339#107C2×D911yescharacteristic, complemented
340#106—91no—
341#106—91no—
342#103—91no—
343#103—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×D911yescharacteristic
349#102C2×D911yescharacteristic, complemented
350#97—91no—
351#97—91no—
352C4×C8—91no—
353C4×C8C2×D911yescharacteristic, complemented
354C23×C3—21no—
355C23×C3—21no—
356C22×D3—31no—
357C22×D3—64no—
358C22×D3—61no—
359C22×D3—241no—
360C22×D3—241no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4C2×C4×D312yes—
364C3×D4C2×C4×D312yes—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—81no—
368C2×C3×C4—81no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—64no—
373#67—64no—
374C2×Dic3—31no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—64no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—241no—
382C2×Dic3—241no—
383D12—32no—
384D12—61no—
385C4×D3—32no—
386C4×D3—32no—
387C4×D3—241no—
388C4×D3—241no—
389C4×D3—241no—
390Dic6—32no—
391Dic6—61no—
392C3×C8—21no—
393C3×C8C2×C4×D312yes—
394C3⋊C8—32no—
395C3⋊C8—61no—
396C2×C9—42no—
397C2×C9—42no—
398C2×C9C2×C4×D411yescharacteristic
399C2×C9#57611yescharacteristic
400C2×C9#57711yescharacteristic
401D9—22no—
402D9—42no—
403C24—181no—
404#41—94no—
405#41—182no—
406C2×Q8—91no—
407C2×D4—94no—
408C2×D4—91no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4C22×D911yescharacteristic
413C2×D4C22×D911yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—91no—
417C22×C4—181no—
418C22×C4—181no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423SD16—94no—
424SD16—94no—
425D8—94no—
426D8C4×D914yescomplemented
427M16—94no—
428C2×C8—91no—
429C2×C8—91no—
430C2×C8—182no—
431C2×C8C22×D911yescharacteristic
432C2×C8C22×D911yescharacteristic
433C4⋊C4—91no—
434C4⋊C4—91no—
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4C22×D911yescharacteristic
441C4⋊C4C22×D911yescharacteristic
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—91no—
445C22⋊C4—91no—
446C22⋊C4—181no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C42—91no—
452C42—181no—
453C42—181no—
454C42—181no—
455C42C22×D911yescharacteristic
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3C2×D3×D411yescharacteristic
463C2×D3—32no—
464C2×D3—61no—
465C2×D3—61no—
466C2×D3—62no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—244no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4C22×C4×D311yescharacteristic
475C3×C4D3×#4111yescharacteristic
476Dic3—32no—
477Dic3—61no—
478Dic3—61no—
479Dic3—62no—
480Dic3—121no—
481Dic3—121no—
482C9#294611yescharacteristic, complemented, Sylow
483C23—21no—
484C23—21no—
485C23—91no—
486C23—184no—
487C23—181no—
488C23—721no—
489C23—721no—
490Q8—92no—
491Q8—181no—
492D4—21no—
493D4—21no—
494D4—92no—
495D4—184no—
496D4—184no—
497D4—181no—
498D4C2×C4×D912yes—
499D4C2×C4×D912yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—91no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—91no—
508C2×C4—91no—
509C2×C4—184no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—721no—
514C2×C4—721no—
515C2×C4—721no—
516C2×C4—721no—
517C2×C4—721no—
518C2×C4D4×D911yescharacteristic
519C2×C4D4×D911yescharacteristic
520C2×C4C23×D911yescharacteristic
521C8—21no—
522C8—92no—
523C8—181no—
524C8C2×C4×D912yes—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3C4×D3×D411yescharacteristic
528C2×C3#575711yescharacteristic
529C2×C3#577011yescharacteristic
530D3—62no—
531D3—122no—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—92no—
539C22—181no—
540C22—181no—
541C22—182no—
542C22—361no—
543C22—361no—
544C22—724no—
545C22C2×D4×D911yescharacteristic
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—92no—
551C4—181no—
552C4—181no—
553C4—182no—
554C4—361no—
555C4—361no—
556C4C22×C4×D911yescharacteristic
557C4#41×D911yescharacteristic
558C3#7958711yescharacteristic
559C2—42no—
560C2—42no—
561C2—182no—
562C2—362no—
563C2C4×D4×D911yescharacteristic
564C2#1058985911yescharacteristic
565C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×D8C2
socleC22×C3C2×D3×D4
prime radicalC2×#63473C2
cosocleC2×C4×C9C24
hypercenterC4×D8D9
hypocenterC9#2946
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #10589648C2semidirect
3. #10589647C2semidirect
4. C4×C9×D8C2semidirect
5. #10588832C2semidirect
6. #10588697C2semidirect
7. #10588694C2semidirect
8. #10588569C2semidirect
9. #10588561C2semidirect
10. #10588452C2semidirect
11. D9×#102C2semidirect
12. #10588438C2semidirect
13. #10588436C2semidirect
14. C4×#3664C2semidirect
15. #10588371C2semidirect
21. C4×D4×C9C22semidirect
23. D4×Dic9C22semidirect
30. #63473C4semidirect
37. #63449C22semidirect
44. C4×Dic18C22semidirect
45. C9×#107C22semidirect
47. C9×#102C22semidirect
48. C4×C8×C9C22semidirect
50. #63392C22semidirect
52. #63377C22semidirect
53. #63376C22semidirect
54. #63375C22semidirect
55. C8×Dic9C22semidirect
57. #63368C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
60. #63362C22semidirect
87. #3699C2×C4semidirect
89. D4×D9C2×C4semidirect
96. C9×D8C2×C4semidirect
106. #3673C2×C4semidirect
107. #3672C2×C4semidirect
126. #3664C2×C4semidirect
127. #3663C2×C4semidirect
226. C4×D8D9semidirect
330. C4×D4C2×D9semidirect
339. #107C2×D9semidirect
349. #102C2×D9semidirect
353. C4×C8C2×D9semidirect
426. D8C4×D9semidirect
482. C9#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#634732
#105896482
#105896472
C4×C9×D82
#105888322
#105886972
#105886942
#105885692
#105885612
#105884522
D9×#1022
#105884382
#105884362
C4×#36642
#105883712
#795873