Finite Group Databasebeta

← C4×#63476 #11860266

Subgroups — C4×#63476 #11860266

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×#63476C211yesmaximal, characteristic
2C4×#3701C211yesmaximal, characteristic, complemented
3C4×D4×D9C211yesmaximal, characteristic, complemented
4C4×C9×SD16C211yesmaximal, characteristic, complemented
5#10588844C211yesmaximal, characteristic, complemented
6C4×#3675C211yesmaximal, characteristic, complemented
7C4×#3673C211yesmaximal, characteristic, complemented
8#10588549C211yesmaximal, characteristic, complemented
9#10588541C211yesmaximal, characteristic, complemented
10#10588497C211yesmaximal, characteristic, complemented
11#10588483C211yesmaximal, characteristic, complemented
12#10588465C211yesmaximal, characteristic, complemented
13#10588450C211yesmaximal, characteristic, complemented
14C4×D72C211yesmaximal, characteristic, complemented
15C4×#3663C211yesmaximal, characteristic, complemented
16C4×#914—31nomaximal
17C2×#3701C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C22×C4×D9—21no—
20C2×C9×SD16C2211yescharacteristic
21C4×Q8×C9C2211yescharacteristic, complemented
22C4×D4×C9C2211yescharacteristic
23Q8×Dic9C2211yescharacteristic, complemented
24C2×#3675C2211yescharacteristic
25D4×Dic9C2211yescharacteristic
26C2×#3673C2211yescharacteristic
27C4×#611—21no—
28#63476C418yesdirect product factor
29C2×D72C2211yescharacteristic
30C2×#3663C2211yescharacteristic
31C2×#3663C2211yescharacteristic
32#63455—21no—
33#63455C2211yescharacteristic
34#63455C2211yescharacteristic, complemented
35#63454—21no—
36#63454C2211yescharacteristic
37C4⋊C4×D9C2211yescharacteristic
38#611⋊C4—21no—
39C22⋊C4×D9—21no—
40C4×D36—21no—
41C4×D36C2211yescharacteristic
42C4×D36C2211yescharacteristic, complemented
43C42×D9—21no—
44C42×D9C2211yescharacteristic
45C9×#106C2211yescharacteristic, complemented
46C9×#103C2211yescharacteristic, complemented
47C9×#102C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic, complemented
49#63395C2211yescharacteristic, complemented
50#63392C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic, complemented
53#63378C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55#63375C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63369C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60C4×C9⋊C8C2211yescharacteristic, complemented
61C2×#914—31no—
62C4×#239—31no—
63C4×D3×D4—31no—
64C3×C4×SD16D311yescharacteristic
65#5164—31no—
66C4×#215—31no—
67C4×#213—31no—
68#4869—31no—
69#4861—31no—
70#4817—31no—
71#4803—31no—
72#4785—31no—
73#4770—31no—
74C4×D24—31no—
75C4×ΓL(1,𝔽25)—31no—
76C23×D9—21no—
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9—21no—
80C2×#611—21no—
81C22×Dic9—21no—
82#3701—22no—
83#3701C2×C414yescomplemented
84D4×D9—22no—
85D4×D9C2×C414yescomplemented
86C2×D36—21no—
87C2×D36C2311yescharacteristic
88C2×D36C2311yescharacteristic
89C2×C4×D9—21no—
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9—21no—
95C2×C4×D9—44no—
96C2×C4×D9D411yescharacteristic
97C2×C4×D9D411yescharacteristic
98C2×C4×D9C2311yescharacteristic
99C9×SD16C2×C414yescomplemented
100C2×C8×C9C2311yescharacteristic
101C2×C8×C9C2311yescharacteristic
102C9×C4⋊C4—21no—
103C9×C4⋊C4C2311yescharacteristic
104C9×C4⋊C4C2311yescharacteristic
105C9×C22⋊C4—21no—
106C42×C9—21no—
107C42×C9C2311yescharacteristic
108#3676—21no—
109#3675C2×C414yescomplemented
110#3673C2×C414yescomplemented
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114(C2×D9)⋊C4—21no—
115(C2×D9)⋊C4—21no—
116C4⋊Dic9—21no—
117C4⋊Dic9C2311yescharacteristic
118C4⋊Dic9C2311yescharacteristic
119Dic9⋊C4—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9D411yescharacteristic
123C4×Dic9D411yescharacteristic
124C4×Dic9C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127D72C2×C414yescomplemented
128#3663—22no—
129#3663C2×C414yescomplemented
130C4×AGL(1,ℤ/8)—91noSylow
131C2×#239—31no—
132C2×D3×D4—31no—
133C22×C4×D3—61no—
134C2×C3×SD16C2×D311yescharacteristic
135C3×C4×Q8C2×D311yescharacteristic
136C3×C4×D4C2×D311yescharacteristic
137Q8×Dic3—31no—
138C2×#215—31no—
139D4×Dic3—31no—
140C2×#213—31no—
141C4×#67—61no—
142#914—38no—
143C2×D24—31no—
144C2×ΓL(1,𝔽25)—31no—
145C2×ΓL(1,𝔽25)—31no—
146#893—31no—
147#893—31no—
148#893—61no—
149#892—31no—
150#892—61no—
151D3×C4⋊C4—31no—
152#67⋊C4—61no—
153D3×C22⋊C4—61no—
154C4×D12—31no—
155C4×D12—31no—
156C4×D12—61no—
157C42×D3—31no—
158C42×D3—61no—
159C3×#106C2×D311yescharacteristic
160C3×#103C2×D311yescharacteristic
161C3×#102C2×D311yescharacteristic
162C3×C4×C8C2×D311yescharacteristic
163#835—31no—
164#832—31no—
165#821—31no—
166#821—31no—
167#818—31no—
168#815—31no—
169#815—31no—
170#809—31no—
171#809—31no—
172#808—31no—
173#807—31no—
174C4×C3⋊C8—31no—
175C23×C9—21no—
176C22×D9—21no—
177C22×D9—21no—
178C22×D9—24no—
179C22×D9—42no—
180C22×D9—42no—
181C22×D9C2×D411yescharacteristic
182Q8×C9—21no—
183Q8×C9C22×C412yescomplemented
184D4×C9—21no—
185D4×C9C22×C412yes—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—42no—
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2411yescharacteristic
193#611—24no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—42no—
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199C2×Dic9C2×D411yescharacteristic
200D36—24no—
201D36—21no—
202D36—21no—
203D36C22×C412yes—
204D36C22×C412yescomplemented
205C4×D9—22no—
206C4×D9—24no—
207C4×D9—41no—
208C4×D9—42no—
209C4×D9—42no—
210C4×D9—42no—
211C4×D9—42no—
212C4×D9—42no—
213C4×D9C22×C412yes—
214C4×D9#4112yes—
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#442—91no—
224#440—91no—
225#440—91no—
226C4×SD16—91no—
227C4×SD16D911yescharacteristic, complemented
228C4×D8—91no—
229C4×D8—91no—
230#428—91no—
231#418—91no—
232#417—91no—
233C4×M16—91no—
234C23×D3—61no—
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C22×C3×C4—21no—
238C2×#67—61no—
239C22×Dic3—61no—
240#239—34no—
241#239—62no—
242D3×D4—34no—
243D3×D4—62no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—61no—
247C2×C4×D3—31no—
248C2×C4×D3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×C4×D3—124no—
257C3×SD16C4×D314yes—
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C3×C4⋊C4—21no—
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C22⋊C4—21no—
264C3×C42—21no—
265C3×C42C22×D311yescharacteristic
266#217—61no—
267#215—34no—
268#213—34no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277Dic3⋊C4—61no—
278C4×Dic3—31no—
279C4×Dic3—31no—
280C4×Dic3—31no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285D24—34no—
286ΓL(1,𝔽25)—34no—
287ΓL(1,𝔽25)—62no—
288C22×C9—22no—
289C22×C9—41no—
290C22×C9—41no—
291C22×C9C22×D411yescharacteristic
292C2×D9—21no—
293C2×D9—21no—
294C2×D9—22no—
295C2×D9—22no—
296C2×D9—48no—
297C2×D9—41no—
298C2×D9—41no—
299C2×D9—41no—
300C2×D9—41no—
301C2×D9C4×D412yes—
302C4×C9—22no—
303C4×C9—21no—
304C4×C9—41no—
305C4×C9—41no—
306C4×C9AGL(1,ℤ/8)12yescomplemented
307C4×C9C23×C411yescharacteristic
308C4×C9C2×#4111yescharacteristic
309Dic9—21no—
310Dic9—21no—
311Dic9—41no—
312Dic9—41no—
313Dic9C4×D412yes—
314C2×#41—91no—
315C22×D4—91no—
316C23×C4—181no—
317AGL(1,ℤ/8)—98no—
318C2×SD16—91no—
319C2×SD16C2×D911yescharacteristic
320C2×D8—91no—
321C2×D8—91no—
322C2×M16—91no—
323C2×M16—91no—
324C4×Q8—91no—
325C4×Q8C2×D911yescharacteristic, complemented
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—181no—
332C4×D4—181no—
333C4×D4—181no—
334C4×D4—181no—
335C4×D4C2×D911yescharacteristic
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#103C2×D911yescharacteristic, complemented
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102C2×D911yescharacteristic
354#97—91no—
355#97—91no—
356C4×C8—91no—
357C4×C8C2×D911yescharacteristic, complemented
358C23×C3—21no—
359C22×D3—31no—
360C22×D3—64no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—122no—
364C22×D3—122no—
365C3×Q8—21no—
366C3×Q8C2×C4×D312yes—
367C3×D4—21no—
368C3×D4C2×C4×D312yes—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—42no—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—64no—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—122no—
383D12—32no—
384D12—32no—
385D12—64no—
386D12—61no—
387D12—61no—
388C4×D3—32no—
389C4×D3—32no—
390C4×D3—64no—
391C4×D3—62no—
392C4×D3—121no—
393C4×D3—122no—
394C4×D3—122no—
395C4×D3—122no—
396C4×D3—122no—
397C4×D3—122no—
398C3×C8—21no—
399C3×C8C2×C4×D312yes—
400C3⋊C8—32no—
401C3⋊C8—61no—
402C2×C9—42no—
403C2×C9C2×C4×D411yescharacteristic
404C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C9#57511yescharacteristic
406D9—22no—
407D9—42no—
408D9—42no—
409C24—181no—
410#41—94no—
411#41—182no—
412C2×Q8C22×D911yescharacteristic
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—91no—
416C2×D4—181no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4C22×D911yescharacteristic
420C22×C4—21no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—181no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—364no—
432SD16—94no—
433SD16C4×D914yescomplemented
434D8—94no—
435D8—94no—
436M16—94no—
437M16—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×D911yescharacteristic
441C2×C8C22×D911yescharacteristic
442C4⋊C4—21no—
443C4⋊C4—91no—
444C4⋊C4—91no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C4⋊C4C22×D911yescharacteristic
448C4⋊C4C22×D911yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—21no—
457C42—91no—
458C42—91no—
459C42—91no—
460C42—181no—
461C42—181no—
462C42C22×D911yescharacteristic
463C22×C3—22no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—32no—
468C2×D3—61no—
469C2×D3—61no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—128no—
473C2×D3—121no—
474C2×D3—121no—
475C2×D3—121no—
476C2×D3—121no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4#91412yes—
482C3×C4C22×C4×D311yescharacteristic
483C3×C4D3×#4111yescharacteristic
484Dic3—32no—
485Dic3—61no—
486Dic3—61no—
487Dic3—121no—
488Dic3—121no—
489C9C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
490C23—21no—
491C23—91no—
492C23—184no—
493C23—181no—
494C23—181no—
495C23—362no—
496C23—362no—
497Q8—21no—
498Q8C2×C4×D912yescomplemented
499D4—21no—
500D4—92no—
501D4—92no—
502D4—184no—
503D4—184no—
504D4—181no—
505D4—181no—
506D4C2×C4×D912yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—42no—
511C2×C4—91no—
512C2×C4—92no—
513C2×C4—92no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—184no—
517C2×C4—182no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—361no—
521C2×C4—362no—
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×C3C4×D3×D411yescharacteristic
536C2×C3C2×#91411yescharacteristic
537C2×C3#576811yescharacteristic
538D3—62no—
539D3—122no—
540D3—122no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—182no—
548C22—182no—
549C22—368no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—361no—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—92no—
560C4—181no—
561C4—181no—
562C4—361no—
563C4—361no—
564C4#6347612yesdirect product factor
565C4C22×C4×D911yescharacteristic
566C4#41×D911yescharacteristic
567C3C4×#91411yescharacteristic
568C2—42no—
569C2—182no—
570C2—362no—
571C2—362no—
572C2C4×D4×D911yescharacteristic
573C2C2×#6347611yescharacteristic
574C2#1058987011yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×#63476C2
cosocleC2×C4×C9C24
hypercenterC4×SD16D9
hypocenterC9C4×AGL(1,ℤ/8)
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#3701C2semidirect
3. C4×D4×D9C2semidirect
4. C4×C9×SD16C2semidirect
5. #10588844C2semidirect
6. C4×#3675C2semidirect
7. C4×#3673C2semidirect
8. #10588549C2semidirect
9. #10588541C2semidirect
10. #10588497C2semidirect
11. #10588483C2semidirect
12. #10588465C2semidirect
13. #10588450C2semidirect
14. C4×D72C2semidirect
15. C4×#3663C2semidirect
21. C4×Q8×C9C22semidirect
23. Q8×Dic9C22semidirect
28. #63476C4direct (N × H)
34. #63455C22semidirect
42. C4×D36C22semidirect
45. C9×#106C22semidirect
46. C9×#103C22semidirect
48. C4×C8×C9C22semidirect
49. #63395C22semidirect
52. #63380C22semidirect
53. #63378C22semidirect
54. #63375C22semidirect
55. #63375C22semidirect
57. #63369C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
60. C4×C9⋊C8C22semidirect
83. #3701C2×C4semidirect
85. D4×D9C2×C4semidirect
99. C9×SD16C2×C4semidirect
109. #3675C2×C4semidirect
110. #3673C2×C4semidirect
127. D72C2×C4semidirect
129. #3663C2×C4semidirect
183. Q8×C9C22×C4semidirect
204. D36C22×C4semidirect
216. C8×C9C22×C4semidirect
218. C9⋊C8C22×C4semidirect
227. C4×SD16D9semidirect
306. C4×C9AGL(1,ℤ/8)semidirect
325. C4×Q8C2×D9semidirect
345. #106C2×D9semidirect
347. #103C2×D9semidirect
357. C4×C8C2×D9semidirect
433. SD16C4×D9semidirect
489. C9C4×AGL(1,ℤ/8)semidirect
498. Q8C2×C4×D9semidirect
533. C8C2×C4×D9semidirect
564. C4#63476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#634762
C4×#37012
C4×D4×D92
C4×C9×SD162
#105888442
C4×#36752
C4×#36732
#105885492
#105885412
#105884972
#105884832
#105884652
#105884502
C4×D722
C4×#36632
C4×#9143