Finite Group Databasebeta

← C4×#64127 #11860370

Subgroups — C4×#64127 #11860370

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64127C211yesmaximal, characteristic
2C4×#3832C211yesmaximal, characteristic
3C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×C4×Q16C211yesmaximal, characteristic, complemented
5#10592883C211yesmaximal, characteristic, complemented
6C4×#3756C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592588C211yesmaximal, characteristic, complemented
9#10592580C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592502C211yesmaximal, characteristic
12#10592501C211yesmaximal, characteristic, complemented
13#10592488C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15C4×#3743C211yesmaximal, characteristic, complemented
16C4×#918—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26#64127C418yesdirect product factor
27C2×#3744C2211yescharacteristic
28C2×#3743C2211yescharacteristic
29C2×#3743C2211yescharacteristic
30#64102—21no—
31#64102C2211yescharacteristic
32#64101—21no—
33#64101C2211yescharacteristic
34C4⋊C4×C3⋊D3—21no—
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64096—21no—
37#64096C2211yescharacteristic
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C42×C3⋊D3—21no—
41C42×C3⋊D3—21no—
42C42×C3⋊D3C2211yescharacteristic
43C4×#634—21no—
44C4×#634C2211yescharacteristic
45C32×#107C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63648C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55#63642C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60C4×C3⋊(C3⋊C8)C2211yescharacteristic
61C2×#918—34no—
62C4×#239—34no—
63C4×D3×Q8—34no—
64C3×C4×Q16D314yescomplemented
65#5184—34no—
66C4×#216—34no—
67C4×#215—34no—
68#4889—34no—
69#4881—34no—
70#4817—34no—
71#4803—34no—
72#4802—34no—
73#4789—34no—
74C4×#204—34no—
75C4×ΓL(1,𝔽25)—34no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78#3832—22no—
79#3832C2×C414yes—
80Q8×C3⋊D3—22no—
81Q8×C3⋊D3C2×C414yescomplemented
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3D411yescharacteristic
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C32×Q16C2×C414yescomplemented
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C42—21no—
102C32×C42—21no—
103C32×C42C2311yescharacteristic
104#3756C2×C414yescomplemented
105#3755C2×C414yescomplemented
106#3752—21no—
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3D411yescharacteristic
122C4×C3⋊Dic3D411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744C2×C414yescomplemented
127#3743—22no—
128#3743C2×C414yescomplemented
129C4×#137—91noSylow
130C2×#239—34no—
131C2×D3×Q8—34no—
132C2×C3×Q16C2×D314yes—
133C3×C4×Q8C2×D314yes—
134C3×C4×Q8C2×D314yes—
135Q8×Dic3—34no—
136Q8×Dic3—34no—
137C2×#216—34no—
138C2×#215—34no—
139#918—332no—
140C2×#204—34no—
141C2×ΓL(1,𝔽25)—34no—
142C2×ΓL(1,𝔽25)—34no—
143#893—34no—
144#893—64no—
145#892—34no—
146#892—64no—
147D3×C4⋊C4—34no—
148D3×C4⋊C4—64no—
149#887—34no—
150#887—64no—
151C4×D12—34no—
152C4×D12—64no—
153C42×D3—34no—
154C42×D3—64no—
155C42×D3—64no—
156C4×Dic6—34no—
157C4×Dic6—64no—
158C3×#107C2×D314yes—
159C3×#103C2×D314yes—
160C3×#103C2×D314yes—
161C3×C4×C8C2×D314yes—
162#835—34no—
163#835—34no—
164#821—34no—
165#817—34no—
166#816—34no—
167#815—34no—
168#815—34no—
169#810—34no—
170#809—34no—
171#808—34no—
172#807—34no—
173C4×C3⋊C8—34no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8C22×C412yes—
179C32×Q8C22×C412yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—24no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)C22×C412yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—22no—
198C4×C3⋊D3—24no—
199C4×C3⋊D3—41no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3C22×C412yes—
204C4×C3⋊D3#4112yes—
205#634—21no—
206#634—24no—
207#634C22×C412yes—
208C32×C8—21no—
209C32×C8C22×C412yes—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)C22×C412yes—
212C2×#137—91no—
213C4×#41—91no—
214C2×C4×Q8—91no—
215#441—91no—
216#441—91no—
217#440—91no—
218#440—91no—
219C4×Q16—91no—
220C4×Q16C3⋊D311yescharacteristic, complemented
221C4×SD16—91no—
222C4×SD16—91no—
223#428—91no—
224#419—91no—
225#417—91no—
226C4×M16—91no—
227C2×C3×Q8C22×D314yes—
228C2×C3×Q8C22×D314yes—
229#239—316no—
230#239—68no—
231D3×Q8—316no—
232D3×Q8—68no—
233C2×D12—34no—
234C2×D12—64no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×Dic6—34no—
244C2×Dic6—64no—
245C3×Q16C4×D3116yescomplemented
246C2×C3×C8C22×D314yes—
247C2×C3×C8C22×D314yes—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—24no—
250C3×C4⋊C4C22×D314yes—
251C3×C4⋊C4C22×D314yes—
252C3×C42—24no—
253C3×C42—24no—
254C3×C42C22×D314yes—
255#216—316no—
256#215—316no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—34no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277#204—316no—
278ΓL(1,𝔽25)—316no—
279ΓL(1,𝔽25)—68no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3C4×D412yes—
287C32×C4—22no—
288C32×C4—22no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4—41no—
292C32×C4#13712yescomplemented
293C32×C4C23×C411yescharacteristic
294C32×C4C2×#4111yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—21no—
297C3⋊Dic3—21no—
298C3⋊Dic3—41no—
299C3⋊Dic3—41no—
300C3⋊Dic3C4×D412yes—
301C2×#41—91no—
302C22×Q8—91no—
303#137—98no—
304C2×Q16—91no—
305C2×Q16C2×C3⋊D311yescharacteristic
306C2×SD16—91no—
307C2×SD16—91no—
308C2×M16—91no—
309C2×M16—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—91no—
313C4×Q8—91no—
314C4×Q8—181no—
315C4×Q8—181no—
316C4×Q8C2×C3⋊D311yescharacteristic
317C4×Q8C2×C3⋊D311yescharacteristic
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—181no—
326C2×C42—91no—
327C2×C42—181no—
328C2×C42—181no—
329#107—91no—
330#107C2×C3⋊D311yescharacteristic
331#106—91no—
332#106—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103C2×C3⋊D311yescharacteristic
338#103C2×C3⋊D311yescharacteristic
339#102—91no—
340#102—91no—
341#97—91no—
342#97—91no—
343C4×C8—91no—
344C4×C8C2×C3⋊D311yescharacteristic
345C22×D3—34no—
346C22×D3—64no—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8C2×C4×D318yes—
350C3×Q8C2×C4×D318yes—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4D3×D414yes—
356C2×C3×C4D3×D414yes—
357C2×C3×C4C23×D314yes—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364D12—38no—
365D12—616no—
366D12—64no—
367C4×D3—38no—
368C4×D3—38no—
369C4×D3—616no—
370C4×D3—616no—
371C4×D3—68no—
372C4×D3—124no—
373C4×D3—128no—
374C4×D3—128no—
375C4×D3—128no—
376Dic6—38no—
377Dic6—616no—
378Dic6—64no—
379C3×C8—24no—
380C3×C8C2×C4×D318yes—
381C3⋊C8—38no—
382C3⋊C8—64no—
383C2×C32C2×C4×D411yescharacteristic
384C2×C32C2×#13711yescharacteristic
385C2×C32#57511yescharacteristic
386C3⋊D3—22no—
387C3⋊D3—42no—
388#41—94no—
389#41—182no—
390C2×Q8—94no—
391C2×Q8—91no—
392C2×Q8—181no—
393C2×Q8—182no—
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×Q8C22×C3⋊D311yescharacteristic
396C2×D4—91no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406Q16—94no—
407Q16C4×C3⋊D314yescomplemented
408SD16—94no—
409SD16—94no—
410M16—94no—
411M16—182no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8C22×C3⋊D311yescharacteristic
415C2×C8C22×C3⋊D311yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C22×C3⋊D311yescharacteristic
426C4⋊C4C22×C3⋊D311yescharacteristic
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C42—21no—
431C42—21no—
432C42—91no—
433C42—91no—
434C42—91no—
435C42—181no—
436C42—181no—
437C42—181no—
438C42—181no—
439C42—181no—
440C42C22×C3⋊D311yescharacteristic
441C22×C3C2×D3×D414yes—
442C2×D3—38no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—28no—
450C3×C4—28no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4#91818yescomplemented
454C3×C4C22×C4×D314yes—
455C3×C4D3×#4114yes—
456Dic3—38no—
457Dic3—64no—
458Dic3—64no—
459Dic3—68no—
460Dic3—124no—
461Dic3—124no—
462C32C4×#13711yescharacteristic, complemented, Sylow
463C23—91no—
464C23—181no—
465Q8—21no—
466Q8—21no—
467Q8—92no—
468Q8—184no—
469Q8—181no—
470Q8C2×C4×C3⋊D312yes—
471Q8C2×C4×C3⋊D312yes—
472D4—92no—
473D4—184no—
474D4—181no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—91no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—184no—
485C2×C4—184no—
486C2×C4—181no—
487C2×C4—182no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—361no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4D4×C3⋊D311yescharacteristic
496C2×C4C23×C3⋊D311yescharacteristic
497C8—21no—
498C8—92no—
499C8—181no—
500C8C2×C4×C3⋊D312yes—
501C2×C3C4×D3×D414yes—
502C2×C3C2×#91814yes—
503C2×C3#576814yes—
504D3—68no—
505D3—128no—
506C22—92no—
507C22—181no—
508C22—181no—
509C22—182no—
510C22—361no—
511C22—361no—
512C22C2×D4×C3⋊D311yescharacteristic
513C4—21no—
514C4—22no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—92no—
519C4—181no—
520C4—181no—
521C4—182no—
522C4—361no—
523C4—361no—
524C4#6412712yesdirect product factor
525C4C22×C4×C3⋊D311yescharacteristic
526C4#41×C3⋊D311yescharacteristic
527C3C4×#91814yescomplemented
528C2—182no—
529C2—362no—
530C2C4×D4×C3⋊D311yescharacteristic
531C2C2×#6412711yescharacteristic
532C2#1059623911yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×#3832C22
cosocleC2×C32×C4C24
hypercenterC4×Q16C3⋊D3
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×C3⋊D3C2semidirect
4. C32×C4×Q16C2semidirect
5. #10592883C2semidirect
6. C4×#3756C2semidirect
7. C4×#3755C2semidirect
8. #10592588C2semidirect
9. #10592580C2semidirect
10. #10592516C2semidirect
12. #10592501C2semidirect
13. #10592488C2semidirect
14. C4×#3744C2semidirect
15. C4×#3743C2semidirect
26. #64127C4direct (N × H)
64. C3×C4×Q16D3semidirect
81. Q8×C3⋊D3C2×C4semidirect
94. C32×Q16C2×C4semidirect
104. #3756C2×C4semidirect
105. #3755C2×C4semidirect
126. #3744C2×C4semidirect
128. #3743C2×C4semidirect
220. C4×Q16C3⋊D3semidirect
245. C3×Q16C4×D3semidirect
292. C32×C4#137semidirect
407. Q16C4×C3⋊D3semidirect
453. C3×C4#918semidirect
462. C32C4×#137semidirect
524. C4#64127direct (N × H)
527. C3C4×#918semidirect

Maximal subgroups

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

subgroupindex
C2×#641272
C4×#38322
C4×Q8×C3⋊D32
C32×C4×Q162
#105928832
C4×#37562
C4×#37552
#105925882
#105925802
#105925162
#105925022
#105925012
#105924882
C4×#37442
C4×#37432
C4×#9183