Finite Group Databasebeta

← C4×#63827 #11860415

Subgroups — C4×#63827 #11860415

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4C4×#3748C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic
8#10590381C212yesmaximal, complemented
9C4×#3718C212yesmaximal, complemented
10#10590358C212yesmaximal, complemented
11C4×#3715C212yesmaximal, complemented
12C4×#951—31nomaximal
13C4×#942—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×C4×#67—21no—
20C3×C4×#67—21no—
21C3×#926C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4—21no—
24C2×C3×C4×Dic3—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#872—21no—
28C3×C42×D3—21no—
29C3×C4×Dic6—21no—
30C3×C4×Dic6—21no—
31C3×C4×Dic6C2212yes—
32C3×C4×Dic6C2212yes—
33C3×C4×Dic6C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic
35C2×#3718C2212yes—
36#63827C418yesdirect product factor
37C2×#3715C2212yes—
38#63630C2212yes—
39C4×C3⋊(C3⋊C8)C2212yes—
40#63576C2212yes—
41#63574C2212yes—
42#63565C2212yes—
43#63565C2212yes—
44#63565C2212yes—
45#63562C2212yes—
46C3×C4×#41—31no—
47C2×C3×C4×Q8—31no—
48C2×#951—31no—
49C2×#942—31no—
50C4×#235D311yescharacteristic
51C2×C4×Dic6D311yescharacteristic, complemented
52#5232—31no—
53#5225—31no—
54#5030—32no—
55#5030—32no—
56C4×#216—32no—
57C4×#216—32no—
58#5026—32no—
59C4×#215—32no—
60#5018—32no—
61C4×#214—32no—
62#5004—31no—
63#4995—31no—
64#4966—31no—
65#4964—31no—
66C4×#208—31no—
67C4×#208—31no—
68C4×#208—61no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—21no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6C2×C414yescomplemented
84C2×C3×Dic6C2312yes—
85C2×C3×Dic6C2311yescharacteristic
86C32×C42D411yescharacteristic
87C32×C42D411yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2311yescharacteristic
90#3748—22no—
91#3748C2×C414yescomplemented
92C2×C3⋊(C3⋊C8)C2312yes—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#217—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—22no—
102C3×Dic3⋊C4—22no—
103C3×Dic3⋊C4—21no—
104C3×Dic3⋊C4—21no—
105C3×C4×Dic3—22no—
106C3×C4×Dic3—22no—
107C3×C4×Dic3—21no—
108C3×C4×Dic3—21no—
109C3×C4×Dic3—21no—
110#3718C2×C418yescomplemented
111#3715C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C22×C3×Q8—31no—
115C2×#235C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C3×C4×Q8—32no—
118C3×C4×Q8—32no—
119C3×C4×Q8—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—61no—
122C3×C4×Q8—61no—
123C3×C4×D4—31no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C3×#117—31no—
128C3×#117—61no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—61no—
131C2×C3×C42—21no—
132C2×C3×C42—61no—
133C2×C3×C42—61no—
134C2×C3×C42C2×D311yescharacteristic
135C2×C3×C42C2×D311yescharacteristic
136#951—38no—
137C2×#216—32no—
138C2×#216—32no—
139#942—38no—
140C2×#215—32no—
141C2×#214—32no—
142C4×#67—21no—
143C4×#67—21no—
144#926C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×Dic3⋊C4—21no—
147C2×C4×Dic3—21no—
148C2×#208—31no—
149C2×#208—31no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C2×#208—61no—
154C4×D12C2×D311yescharacteristic
155C4×D12C2×D311yescharacteristic
156#872—21no—
157C42×D3—21no—
158C4×Dic6—21no—
159C4×Dic6—21no—
160C4×Dic6C2×D312yes—
161C4×Dic6C2×D312yes—
162C4×Dic6C2×D311yescharacteristic
163C4×Dic6C2×D311yescharacteristic
164#835—32no—
165#835—32no—
166#835—32no—
167#832—32no—
168#810—32no—
169#810—32no—
170#810—32no—
171#809—32no—
172#808—32no—
173#808—32no—
174#807—32no—
175#807—32no—
176#803—32no—
177#803—32no—
178#803—62no—
179C4×C3⋊C8—32no—
180C4×C3⋊C8—32no—
181C4×C3⋊C8—62no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C2×C32×C4—22no—
185C2×C32×C4—41no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4#4112yes—
193C2×C32×C4C2411yescharacteristic
194C3×#67—24no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—42no—
202C3×D12—21no—
203C3×D12C22×C412yes—
204C3×C4×D3—24no—
205C3×C4×D3—42no—
206C3×C4×D3—42no—
207C3×Dic6—24no—
208C3×Dic6—22no—
209C3×Dic6—21no—
210C3×Dic6C22×C414yes—
211C3×Dic6C22×C412yes—
212C3⋊(C3⋊C8)—22no—
213C3⋊(C3⋊C8)C22×C414yes—
214C2×#137—91no—
215C4×#41—31no—
216C2×C4×Q8—31no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—91no—
222#419—91no—
223#417—91no—
224C4×M16—91no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—34no—
228C2×C3×Q8—32no—
229C2×C3×Q8—31no—
230C2×C3×Q8—62no—
231C2×C3×Q8—61no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4#6711yescharacteristic
244C22×C3×C4#6711yescharacteristic
245C22×C3×C4#6711yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251#235—22no—
252#235C4×D314yes—
253C2×D12C22×D311yescharacteristic
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×Dic6—22no—
258C2×Dic6—21no—
259C2×Dic6C4×D314yescomplemented
260C2×Dic6C22×D312yes—
261C2×Dic6C22×D311yescharacteristic
262C3×C4⋊C4—31no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—61no—
278C3×C42—61no—
279C3×C42—61no—
280C3×C42—62no—
281C3×C42—62no—
282C3×C42#6711yescharacteristic
283C3×C42#6711yescharacteristic
284C3×C42#6711yescharacteristic
285C3×C42#6711yescharacteristic
286C3×C42C22×D311yescharacteristic
287C3×C42C22×D311yescharacteristic
288C3×C42C22×D311yescharacteristic
289C3×C42C22×D311yescharacteristic
290#217—21no—
291#216—38no—
292#216—38no—
293#215—38no—
294#214—38no—
295(C2×D3)⋊C4—21no—
296(C2×D3)⋊C4—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3C22×D311yescharacteristic
299C4⋊Dic3C22×D312yes—
300C4⋊Dic3C22×D311yescharacteristic
301Dic3⋊C4—22no—
302Dic3⋊C4—22no—
303Dic3⋊C4—21no—
304Dic3⋊C4—21no—
305C4×Dic3—22no—
306C4×Dic3—22no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310#208—34no—
311#208—34no—
312#208—64no—
313#208—64no—
314#208—62no—
315#208—62no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—62no—
321C2×C3⋊C8—62no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32C4×D412yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4C4×D412yes—
333C32×C4#13712yescomplemented
334C32×C4C23×C411yescharacteristic
335C32×C4C2×#4111yescharacteristic
336C3×Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—41no—
339C3×Dic3—41no—
340C3×Dic3—42no—
341C2×#41—31no—
342C22×Q8—31no—
343#137—98no—
344C2×Q16—92no—
345C2×SD16—92no—
346C2×M16—91no—
347C2×M16—91no—
348C4×Q8—32no—
349C4×Q8—32no—
350C4×Q8—31no—
351C4×Q8—31no—
352C4×Q8—61no—
353C4×Q8—61no—
354C4×D4—31no—
355C4×D4—31no—
356C4×D4—61no—
357C4×D4—61no—
358#117—31no—
359#117—61no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C42—61no—
363C2×C42—61no—
364C2×C42D3211yescharacteristic
365#107—92no—
366#106—92no—
367#103—92no—
368#103—92no—
369#103—92no—
370#102—92no—
371#97—92no—
372C4×C8—92no—
373C23×C3—21no—
374C23×C3—61no—
375C23×C3C2×#6711yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—21no—
378C3×Q8—34no—
379C3×Q8—32no—
380C3×Q8—64no—
381C3×Q8—62no—
382C3×Q8—61no—
383C3×D4—32no—
384C3×D4—64no—
385C3×D4—61no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—64no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—64no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—62no—
407C2×C3×C4—122no—
408C2×C3×C4—122no—
409C2×C3×C4—122no—
410C2×C3×C4C2×C4×D312yes—
411C2×C3×C4C2×C4×D312yes—
412C2×C3×C4#23512yes—
413C2×C3×C4#23512yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—24no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—42no—
434D12—21no—
435D12C2×C4×D312yes—
436C4×D3—24no—
437C4×D3—42no—
438C4×D3—42no—
439Dic6—24no—
440Dic6—22no—
441Dic6—21no—
442Dic6C2×C4×D314yes—
443Dic6C2×C4×D312yes—
444C3⋊C8—34no—
445C3⋊C8—34no—
446C3⋊C8—64no—
447C3⋊C8—64no—
448C3⋊C8—62no—
449C3⋊C8—62no—
450C2×C32—22no—
451C2×C32C2×C4×D411yescharacteristic
452C2×C32C2×#13711yescharacteristic
453C2×C32#57511yescharacteristic
454C3×D3—42no—
455#41—34no—
456#41—62no—
457C2×Q8—32no—
458C2×Q8—31no—
459C2×Q8—34no—
460C2×Q8—62no—
461C2×Q8—61no—
462C2×D4—31no—
463C2×D4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4#62511yescharacteristic
470C22×C4#62511yescharacteristic
471C22×C4C2×D3211yescharacteristic
472Q16—98no—
473SD16—98no—
474M16—94no—
475M16—182no—
476C2×C8—92no—
477C2×C8—92no—
478C4⋊C4—32no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—61no—
482C4⋊C4—62no—
483C4⋊C4—62no—
484C4⋊C4—61no—
485C4⋊C4—61no—
486C22⋊C4—61no—
487C22⋊C4—61no—
488C22⋊C4—61no—
489C42—61no—
490C42—61no—
491C42—62no—
492C42—61no—
493C42—62no—
494C42#62511yescharacteristic
495C42#62511yescharacteristic
496C42C2×D3211yescharacteristic
497C42C2×D3211yescharacteristic
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—62no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3C4×#6712yes—
510C22×C3C4×#6712yes—
511C22×C3C22×#6711yescharacteristic
512C22×C3C22×#6711yescharacteristic
513C2×D3—22no—
514C2×D3—41no—
515C2×D3—41no—
516C3×C4—22no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—41no—
528C3×C4—41no—
529C3×C4—62no—
530C3×C4—64no—
531C3×C4—121no—
532C3×C4—122no—
533C3×C4—121no—
534C3×C4C4×#6712yes—
535C3×C4C4×#6712yes—
536C3×C4#94212yescomplemented
537C3×C4#95112yescomplemented
538C3×C4C22×C4×D311yescharacteristic
539C3×C4C22×C4×D311yescharacteristic
540C3×C4C2×#23511yescharacteristic
541C3×C4C2×#23511yescharacteristic
542Dic3—24no—
543Dic3—22no—
544Dic3—41no—
545Dic3—42no—
546Dic3—41no—
547C32C4×#13711yescharacteristic, complemented, Sylow
548C23—61no—
549C23C2×#62511yescharacteristic
550Q8—34no—
551Q8—32no—
552Q8—62no—
553Q8—61no—
554Q8—64no—
555D4—32no—
556D4—64no—
557D4—61no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—61no—
561C2×C4—62no—
562C2×C4—64no—
563C2×C4—64no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—122no—
568C2×C4—122no—
569C2×C4—122no—
570C2×C4#379812yes—
571C2×C4C4×D3212yes—
572C2×C4C2×#62511yescharacteristic
573C2×C4C2×#62511yescharacteristic
574C2×C4C2×#62511yescharacteristic
575C2×C4C2×#62511yescharacteristic
576C2×C4C2×#62511yescharacteristic
577C2×C4C22×D3211yescharacteristic
578C8—94no—
579C8—182no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—122no—
587C2×C3C2×C4×#6711yescharacteristic
588C2×C3C2×C4×#6711yescharacteristic
589C2×C3C2×#94211yescharacteristic
590C2×C3#582211yescharacteristic
591C2×C3#582211yescharacteristic
592C2×C3C2×#95111yescharacteristic
593D3—42no—
594C22—21no—
595C22—21no—
596C22—62no—
597C22—121no—
598C22—121no—
599C22C4×#62512yes—
600C22C22×#62511yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—62no—
605C4—64no—
606C4—121no—
607C4—122no—
608C4—121no—
609C4#6382712yesdirect product factor
610C4C4×#62512yes—
611C4C2×#379811yescharacteristic
612C4C2×C4×D3211yescharacteristic
613C3—21no—
614C3C4×#94211yescharacteristic, complemented
615C3C4×#95111yescharacteristic, complemented
616C2—22no—
617C2—122no—
618C2#1059478611yescharacteristic
619C2C2×#6382711yescharacteristic
620C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
4. C4×#3748C2semidirect
5. #10591139C2semidirect
6. #10591099C2semidirect
8. #10590381C2semidirect
9. C4×#3718C2semidirect
10. #10590358C2semidirect
11. C4×#3715C2semidirect
36. #63827C4direct (N × H)
51. C2×C4×Dic6D3semidirect
83. C2×C3×Dic6C2×C4semidirect
91. #3748C2×C4semidirect
110. #3718C2×C4semidirect
111. #3715C2×C4semidirect
259. C2×Dic6C4×D3semidirect
333. C32×C4#137semidirect
536. C3×C4#942semidirect
537. C3×C4#951semidirect
547. C32C4×#137semidirect
609. C4#63827direct (N × H)
614. C3C4×#942semidirect
615. C3C4×#951semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C2×C3×C4×Dic62
C2×#638272
C4×#37482
#105911392
#105910992
#105910872
#105903812
C4×#37182
#105903582
C4×#37152
C4×#9513
C4×#9423