Finite Group Databasebeta

← C4×#64123 #11860267

Subgroups — C4×#64123 #11860267

Order 1152.

1644 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×#64123C211yesmaximal, characteristic
2C4×#3832C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5#10592863C211yesmaximal, characteristic, complemented
6C4×#3755C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic, complemented
8#10592568C211yesmaximal, characteristic, complemented
9#10592560C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592502C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic, complemented
13#10592469C211yesmaximal, characteristic, complemented
14C4×#3745C211yesmaximal, characteristic, complemented
15C4×#3743C211yesmaximal, characteristic, complemented
16C4×#914—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C4×#638—21no—
28#64123C418yesdirect product factor
29C2×#3745C2211yescharacteristic
30C2×#3743C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32#64102—21no—
33#64102C2211yescharacteristic
34#64102C2211yescharacteristic, complemented
35#64101—21no—
36#64101C2211yescharacteristic
37C4⋊C4×C3⋊D3C2211yescharacteristic
38#64090—21no—
39C22⋊C4×C3⋊D3—21no—
40C4×C4⋊(C3⋊D3)—21no—
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
43C42×C3⋊D3—21no—
44C42×C3⋊D3C2211yescharacteristic
45C32×#106C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63659C2211yescharacteristic
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic, complemented
53#63645C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic, complemented
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
61C2×#914—34no—
62C4×#239—34no—
63C4×D3×D4—34no—
64C3×C4×SD16D314yescomplemented
65#5164—34no—
66C4×#215—34no—
67C4×#213—34no—
68#4869—34no—
69#4861—34no—
70#4817—34no—
71#4803—34no—
72#4785—34no—
73#4770—34no—
74C4×D24—34no—
75C4×ΓL(1,𝔽25)—34no—
76C23×C3⋊D3—21no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C2×#638—21no—
81C22×C3⋊Dic3—21no—
82#3832—22no—
83#3832C2×C414yescomplemented
84D4×C3⋊D3—22no—
85D4×C3⋊D3C2×C414yescomplemented
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—44no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C32×SD16C2×C414yescomplemented
100C2×C32×C8C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C42—21no—
107C32×C42C2311yescharacteristic
108#3757—21no—
109#3755C2×C414yescomplemented
110#3753C2×C414yescomplemented
111#3752—21no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3D411yescharacteristic
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3745C2×C414yescomplemented
128#3743—22no—
129#3743C2×C414yescomplemented
130C4×AGL(1,ℤ/8)—91noSylow
131C2×#239—34no—
132C2×D3×D4—34no—
133C22×C4×D3—64no—
134C2×C3×SD16C2×D314yes—
135C3×C4×Q8C2×D314yescomplemented
136C3×C4×D4C2×D314yes—
137Q8×Dic3—34no—
138C2×#215—34no—
139D4×Dic3—34no—
140C2×#213—34no—
141C4×#67—64no—
142#914—332no—
143C2×D24—34no—
144C2×ΓL(1,𝔽25)—34no—
145C2×ΓL(1,𝔽25)—34no—
146#893—34no—
147#893—34no—
148#893—64no—
149#892—34no—
150#892—64no—
151D3×C4⋊C4—34no—
152#67⋊C4—64no—
153D3×C22⋊C4—64no—
154C4×D12—34no—
155C4×D12—34no—
156C4×D12—64no—
157C42×D3—34no—
158C42×D3—64no—
159C3×#106C2×D314yescomplemented
160C3×#103C2×D314yescomplemented
161C3×#102C2×D314yes—
162C3×C4×C8C2×D314yescomplemented
163#835—34no—
164#832—34no—
165#821—34no—
166#821—34no—
167#818—34no—
168#815—34no—
169#815—34no—
170#809—34no—
171#809—34no—
172#808—34no—
173#807—34no—
174C4×C3⋊C8—34no—
175C23×C32—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—24no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C22×C3⋊D3C2×D411yescharacteristic
182C32×Q8—21no—
183C32×Q8C22×C412yescomplemented
184C32×D4—21no—
185C32×D4C22×C412yes—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193#638—24no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—42no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C4⋊(C3⋊D3)—24no—
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)—21no—
203C4⋊(C3⋊D3)C22×C412yes—
204C4⋊(C3⋊D3)C22×C412yescomplemented
205C4×C3⋊D3—22no—
206C4×C3⋊D3—24no—
207C4×C3⋊D3—41no—
208C4×C3⋊D3—42no—
209C4×C3⋊D3—42no—
210C4×C3⋊D3—42no—
211C4×C3⋊D3—42no—
212C4×C3⋊D3—42no—
213C4×C3⋊D3C22×C412yes—
214C4×C3⋊D3#4112yes—
215C32×C8—21no—
216C32×C8C22×C412yescomplemented
217C3⋊(C3⋊C8)—21no—
218C3⋊(C3⋊C8)C22×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×SD16C3⋊D311yescharacteristic, complemented
228C4×D8—91no—
229C4×D8—91no—
230#428—91no—
231#418—91no—
232#417—91no—
233C4×M16—91no—
234C23×D3—64no—
235C2×C3×Q8C22×D314yes—
236C2×C3×D4C22×D314yes—
237C22×C3×C4—24no—
238C2×#67—64no—
239C22×Dic3—64no—
240#239—316no—
241#239—68no—
242D3×D4—316no—
243D3×D4—68no—
244C2×D12—34no—
245C2×D12—34no—
246C2×D12—64no—
247C2×C4×D3—34no—
248C2×C4×D3—34no—
249C2×C4×D3—34no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—1216no—
257C3×SD16C4×D3116yescomplemented
258C2×C3×C8C22×D314yes—
259C2×C3×C8C22×D314yes—
260C3×C4⋊C4—24no—
261C3×C4⋊C4C22×D314yes—
262C3×C4⋊C4C22×D314yes—
263C3×C22⋊C4—24no—
264C3×C42—24no—
265C3×C42C22×D314yes—
266#217—64no—
267#215—316no—
268#213—316no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274C4⋊Dic3—34no—
275C4⋊Dic3—34no—
276C4⋊Dic3—64no—
277Dic3⋊C4—64no—
278C4×Dic3—34no—
279C4×Dic3—34no—
280C4×Dic3—34no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C2×C3⋊C8—34no—
284C2×C3⋊C8—34no—
285D24—316no—
286ΓL(1,𝔽25)—316no—
287ΓL(1,𝔽25)—68no—
288C22×C32—22no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—22no—
295C2×C3⋊D3—22no—
296C2×C3⋊D3—48no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3C4×D412yes—
302C32×C4—22no—
303C32×C4—21no—
304C32×C4—41no—
305C32×C4—41no—
306C32×C4AGL(1,ℤ/8)12yescomplemented
307C32×C4C23×C411yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3⋊Dic3—21no—
310C3⋊Dic3—21no—
311C3⋊Dic3—41no—
312C3⋊Dic3—41no—
313C3⋊Dic3C4×D412yes—
314C2×#41—91no—
315C22×D4—91no—
316C23×C4—181no—
317AGL(1,ℤ/8)—98no—
318C2×SD16—91no—
319C2×SD16C2×C3⋊D311yescharacteristic
320C2×D8—91no—
321C2×D8—91no—
322C2×M16—91no—
323C2×M16—91no—
324C4×Q8—91no—
325C4×Q8C2×C3⋊D311yescharacteristic, 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×C3⋊D311yescharacteristic
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×C3⋊D311yescharacteristic, complemented
346#103—91no—
347#103C2×C3⋊D311yescharacteristic, complemented
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102C2×C3⋊D311yescharacteristic
354#97—91no—
355#97—91no—
356C4×C8—91no—
357C4×C8C2×C3⋊D311yescharacteristic, complemented
358C23×C3—24no—
359C22×D3—34no—
360C22×D3—616no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—128no—
364C22×D3—128no—
365C3×Q8—24no—
366C3×Q8C2×C4×D318yescomplemented
367C3×D4—24no—
368C3×D4C2×C4×D318yes—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—48no—
373C2×C3×C4D3×D414yes—
374C2×C3×C4D3×D414yes—
375C2×C3×C4C23×D314yes—
376#67—616no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—128no—
383D12—38no—
384D12—38no—
385D12—616no—
386D12—64no—
387D12—64no—
388C4×D3—38no—
389C4×D3—38no—
390C4×D3—616no—
391C4×D3—68no—
392C4×D3—124no—
393C4×D3—128no—
394C4×D3—128no—
395C4×D3—128no—
396C4×D3—128no—
397C4×D3—128no—
398C3×C8—24no—
399C3×C8C2×C4×D318yescomplemented
400C3⋊C8—38no—
401C3⋊C8—64no—
402C2×C32—42no—
403C2×C32C2×C4×D411yescharacteristic
404C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C32#57511yescharacteristic
406C3⋊D3—22no—
407C3⋊D3—42no—
408C3⋊D3—42no—
409C24—181no—
410#41—94no—
411#41—182no—
412C2×Q8C22×C3⋊D311yescharacteristic
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—91no—
416C2×D4—181no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4C22×C3⋊D311yescharacteristic
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×C3⋊D314yescomplemented
434D8—94no—
435D8—94no—
436M16—94no—
437M16—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×C3⋊D311yescharacteristic
441C2×C8C22×C3⋊D311yescharacteristic
442C4⋊C4—21no—
443C4⋊C4—91no—
444C4⋊C4—91no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C4⋊C4C22×C3⋊D311yescharacteristic
448C4⋊C4C22×C3⋊D311yescharacteristic
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×C3⋊D311yescharacteristic
463C22×C3—28no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3C2×D3×D414yes—
467C2×D3—38no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—68no—
471C2×D3—68no—
472C2×D3—1232no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—124no—
477C3×C4—24no—
478C3×C4—28no—
479C3×C4—44no—
480C3×C4—44no—
481C3×C4#91418yescomplemented
482C3×C4C22×C4×D314yes—
483C3×C4D3×#4114yes—
484Dic3—38no—
485Dic3—64no—
486Dic3—64no—
487Dic3—124no—
488Dic3—124no—
489C32C4×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×C3⋊D312yescomplemented
499D4—21no—
500D4—92no—
501D4—92no—
502D4—184no—
503D4—184no—
504D4—181no—
505D4—181no—
506D4C2×C4×C3⋊D312yes—
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×C3⋊D311yescharacteristic
528C2×C4D4×C3⋊D311yescharacteristic
529C2×C4C23×C3⋊D311yescharacteristic
530C8—21no—
531C8—92no—
532C8—181no—
533C8C2×C4×C3⋊D312yescomplemented
534C2×C3—48no—
535C2×C3C4×D3×D414yes—
536C2×C3C2×#91414yes—
537C2×C3#576814yes—
538D3—68no—
539D3—128no—
540D3—128no—
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×C3⋊D311yescharacteristic
555C4—21no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—92no—
560C4—181no—
561C4—181no—
562C4—361no—
563C4—361no—
564C4#6412312yesdirect product factor
565C4C22×C4×C3⋊D311yescharacteristic
566C4#41×C3⋊D311yescharacteristic
567C3C4×#91414yescomplemented
568C2—42no—
569C2—182no—
570C2—362no—
571C2—362no—
572C2C4×D4×C3⋊D311yescharacteristic
573C2C2×#6412311yescharacteristic
574C2#1059623911yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×#64123C2
cosocleC2×C32×C4C24
hypercenterC4×SD16C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#3832C2semidirect
3. C4×D4×C3⋊D3C2semidirect
4. C32×C4×SD16C2semidirect
5. #10592863C2semidirect
6. C4×#3755C2semidirect
7. C4×#3753C2semidirect
8. #10592568C2semidirect
9. #10592560C2semidirect
10. #10592516C2semidirect
11. #10592502C2semidirect
12. #10592484C2semidirect
13. #10592469C2semidirect
14. C4×#3745C2semidirect
15. C4×#3743C2semidirect
21. C32×C4×Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
28. #64123C4direct (N × H)
34. #64102C22semidirect
42. C4×C4⋊(C3⋊D3)C22semidirect
45. C32×#106C22semidirect
46. C32×#103C22semidirect
48. C32×C4×C8C22semidirect
49. #63662C22semidirect
52. #63648C22semidirect
53. #63645C22semidirect
54. #63642C22semidirect
55. #63642C22semidirect
57. #63636C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
60. C4×C3⋊(C3⋊C8)C22semidirect
64. C3×C4×SD16D3semidirect
83. #3832C2×C4semidirect
85. D4×C3⋊D3C2×C4semidirect
99. C32×SD16C2×C4semidirect
109. #3755C2×C4semidirect
110. #3753C2×C4semidirect
127. #3745C2×C4semidirect
129. #3743C2×C4semidirect
135. C3×C4×Q8C2×D3semidirect
159. C3×#106C2×D3semidirect
160. C3×#103C2×D3semidirect
162. C3×C4×C8C2×D3semidirect
183. C32×Q8C22×C4semidirect
204. C4⋊(C3⋊D3)C22×C4semidirect
216. C32×C8C22×C4semidirect
218. C3⋊(C3⋊C8)C22×C4semidirect
227. C4×SD16C3⋊D3semidirect
257. C3×SD16C4×D3semidirect
306. C32×C4AGL(1,ℤ/8)semidirect
325. C4×Q8C2×C3⋊D3semidirect
345. #106C2×C3⋊D3semidirect
347. #103C2×C3⋊D3semidirect
357. C4×C8C2×C3⋊D3semidirect
366. C3×Q8C2×C4×D3semidirect
399. C3×C8C2×C4×D3semidirect
433. SD16C4×C3⋊D3semidirect
481. C3×C4#914semidirect
489. C32C4×AGL(1,ℤ/8)semidirect
498. Q8C2×C4×C3⋊D3semidirect
533. C8C2×C4×C3⋊D3semidirect
564. C4#64123direct (N × H)
567. C3C4×#914semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C4×#38322
C4×D4×C3⋊D32
C32×C4×SD162
#105928632
C4×#37552
C4×#37532
#105925682
#105925602
#105925162
#105925022
#105924842
#105924692
C4×#37452
C4×#37432
C4×#9143