Finite Group Databasebeta

← C4×#63831 #11860414

Subgroups — C4×#63831 #11860414

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic
4C3×C4×#208C211yesmaximal, characteristic, complemented
5#10591131C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic
8#10590383C212yesmaximal, complemented
9C4×#3719C212yesmaximal, complemented
10#10590360C212yesmaximal, complemented
11C4×#3716C212yesmaximal, complemented
12C4×#951—31nomaximal
13C4×#909—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—21no—
19C2×C4×C3⋊Dic3—21no—
20C4×#634—21no—
21C4×#634—21no—
22C4×#634C2212yes—
23C4×#634C2212yes—
24C3×C4×#67—21no—
25C3×C4×#67—21no—
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×C42×D3—21no—
33C3×C4×Dic6C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic
35C2×#3719C2212yes—
36#63831C418yesdirect product factor
37C2×#3716C2212yes—
38C3×#803C2212yes—
39C3×C4×C3⋊C8C2212yes—
40#63575C2212yes—
41#63573C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45#63563C2212yes—
46C3×C4×#41—31no—
47C2×#951—31no—
48C2×#909—31no—
49C4×#235D311yescharacteristic
50C2×C4×Dic6—31no—
51C2×C4×Dic6—31no—
52C2×C4×Dic6—61no—
53C3×C4×M16—31no—
54#5232—31no—
55#5133—31no—
56#5121—31no—
57#5120—31no—
58#5030—32no—
59C4×#216—32no—
60#5018—32no—
61C4×#214—32no—
62#5004—31no—
63#4995—31no—
64C4×#208D311yescharacteristic, complemented
65#4716—32no—
66#4710—32no—
67C4×Dic12—32no—
68C4×#204—32no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C2×#634—21no—
75C2×#634—22no—
76C2×#634C2×C414yescomplemented
77C2×#634C2312yes—
78C2×C3×#67—21no—
79C3×#235—22no—
80C3×#235C2×C414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—21no—
85C2×C3×Dic6C2311yescharacteristic
86C32×C42D411yescharacteristic
87C32×C42D411yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2311yescharacteristic
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2312yes—
92#3750—22no—
93#3750—22no—
94C4×C3⋊Dic3—22no—
95C4×C3⋊Dic3—22no—
96C3×#217—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—21no—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3—21no—
106C3×#208—22no—
107C3×#208C2×C414yescomplemented
108C2×C3×C3⋊C8C2312yes—
109C2×C3×C3⋊C8C2312yes—
110#3719C2×C418yescomplemented
111#3716C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C2×#235C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×#117—31no—
127C3×#117—61no—
128C2×C3×C42—21no—
129C2×C3×C42—61no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132#951—38no—
133C2×#216—32no—
134C2×#214—32no—
135C4×#67—21no—
136C4×#67—21no—
137#926C2×D311yescharacteristic
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—61no—
141C2×Dic3⋊C4—62no—
142C2×Dic3⋊C4—61no—
143C2×Dic3⋊C4—61no—
144C2×C4×Dic3—62no—
145C2×C4×Dic3—61no—
146C2×C4×Dic3—61no—
147C2×#208C2×D311yescharacteristic
148C2×#208C2×D311yescharacteristic
149#909—38no—
150C2×Dic12—32no—
151C2×#204—32no—
152C4×D12C2×D311yescharacteristic
153C4×D12C2×D311yescharacteristic
154#872—21no—
155C42×D3—21no—
156C4×Dic6—32no—
157C4×Dic6—32no—
158C4×Dic6—32no—
159C4×Dic6—32no—
160C4×Dic6—62no—
161C4×Dic6—62no—
162C4×Dic6—62no—
163C4×Dic6—62no—
164C4×Dic6—61no—
165C4×Dic6—61no—
166C4×Dic6—61no—
167C4×Dic6—61no—
168C4×Dic6C2×D311yescharacteristic
169C4×Dic6C2×D311yescharacteristic
170C3×#97—32no—
171C3×C4×C8—32no—
172#835—32no—
173#832—32no—
174#821—32no—
175#818—32no—
176#817—32no—
177#816—32no—
178#816—32no—
179#816—32no—
180#810—32no—
181#810—32no—
182#808—32no—
183#807—32no—
184#803C2×D312yes—
185C4×C3⋊C8C2×D312yes—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C2×C32×C4—22no—
189C2×C32×C4—41no—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4#4112yes—
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—24no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—42no—
202#634—24no—
203#634—22no—
204#634C22×C414yes—
205C3×#67—24no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C3×D12—21no—
210C3×D12C22×C412yes—
211C3×C4×D3—24no—
212C3×C4×D3—42no—
213C3×C4×D3—42no—
214C3×Dic6—21no—
215C3×Dic6C22×C412yes—
216C3×C3⋊C8—22no—
217C3×C3⋊C8C22×C414yes—
218C2×#137—91no—
219C4×#41—31no—
220C2×C4×Q8—91no—
221#441—92no—
222#440—92no—
223C4×Q16—92no—
224C4×SD16—92no—
225#428—91no—
226#419—91no—
227#417—91no—
228C4×M16—31no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—31no—
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×C4D1211yescharacteristic
241C22×C3×C4D1211yescharacteristic
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4#6711yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C22×Dic3—62no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253#235—22no—
254#235C4×D314yes—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×Dic6—34no—
260C2×Dic6—34no—
261C2×Dic6—32no—
262C2×Dic6—32no—
263C2×Dic6—62no—
264C2×Dic6—64no—
265C2×Dic6—62no—
266C2×Dic6—64no—
267C2×Dic6—61no—
268C2×Dic6—62no—
269C2×Dic6—62no—
270C2×Dic6—61no—
271C2×Dic6C22×D311yescharacteristic
272C3×M16—34no—
273C3×M16—62no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—61no—
288C3×C42—61no—
289C3×C42—61no—
290C3×C42D1211yescharacteristic
291C3×C42D1211yescharacteristic
292C3×C42#6711yescharacteristic
293C3×C42#6711yescharacteristic
294C3×C42C22×D311yescharacteristic
295C3×C42C22×D311yescharacteristic
296C3×C42C22×D311yescharacteristic
297C3×C42C22×D311yescharacteristic
298#217—21no—
299#216—38no—
300#214—38no—
301(C2×D3)⋊C4—21no—
302(C2×D3)⋊C4—21no—
303C4⋊Dic3—32no—
304C4⋊Dic3—32no—
305C4⋊Dic3—62no—
306C4⋊Dic3—62no—
307C4⋊Dic3—61no—
308C4⋊Dic3—61no—
309C4⋊Dic3C22×D311yescharacteristic
310C4⋊Dic3C22×D311yescharacteristic
311Dic3⋊C4—21no—
312Dic3⋊C4—21no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—62no—
318Dic3⋊C4—62no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3—21no—
322C4×Dic3—64no—
323C4×Dic3—64no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328#208—22no—
329#208C4×D314yescomplemented
330C2×C3⋊C8C22×D312yes—
331C2×C3⋊C8C22×D312yes—
332Dic12—38no—
333#204—38no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32C4×D412yes—
337C22×C32C22×D411yescharacteristic
338C2×C3×D3—22no—
339C2×C3×D3—41no—
340C2×C3×D3—41no—
341C32×C4—21no—
342C32×C4—21no—
343C32×C4—21no—
344C32×C4C4×D412yes—
345C32×C4#13712yescomplemented
346C32×C4C23×C411yescharacteristic
347C32×C4C2×#4111yescharacteristic
348C3⋊Dic3—24no—
349C3⋊Dic3—42no—
350C3×Dic3—22no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C2×#41—31no—
354C22×Q8—91no—
355#137—98no—
356C2×Q16—92no—
357C2×SD16—92no—
358C2×M16—31no—
359C2×M16—31no—
360C4×Q8—31no—
361C4×Q8—31no—
362C4×Q8—92no—
363C4×Q8—92no—
364C4×Q8—181no—
365C4×Q8—181no—
366C4×D4—31no—
367C4×D4—31no—
368C4×D4—61no—
369C4×D4—61no—
370#117—31no—
371#117—61no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—181no—
374C2×C42—61no—
375C2×C42—181no—
376C2×C42D3211yescharacteristic
377#107—92no—
378#106—92no—
379#103—92no—
380#103—92no—
381#103—92no—
382#102—92no—
383#97—32no—
384C4×C8—32no—
385C23×C3—21no—
386C23×C3—61no—
387C23×C3C2×D1211yescharacteristic
388C23×C3C2×#6711yescharacteristic
389C22×D3—21no—
390C3×Q8—32no—
391C3×Q8—61no—
392C3×D4—32no—
393C3×D4—64no—
394C3×D4—61no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409C2×C3×C4—61no—
410C2×C3×C4—64no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—122no—
414C2×C3×C4—122no—
415C2×C3×C4C2×C4×D312yes—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4C2×D1211yescharacteristic
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4C2×D1211yescharacteristic
421C2×C3×C4C2×D1211yescharacteristic
422C2×C3×C4#23512yes—
423C2×C3×C4#23512yes—
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—24no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—64no—
436C2×Dic3—68no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—64no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—124no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447D12—21no—
448D12C2×C4×D312yes—
449C4×D3—24no—
450C4×D3—42no—
451C4×D3—42no—
452Dic6—21no—
453Dic6—34no—
454Dic6—34no—
455Dic6—64no—
456Dic6—64no—
457Dic6—68no—
458Dic6—64no—
459Dic6—64no—
460Dic6—62no—
461Dic6—62no—
462Dic6C2×C4×D312yes—
463C3×C8—34no—
464C3×C8—62no—
465C3⋊C8—22no—
466C3⋊C8C2×C4×D314yes—
467C2×C32—22no—
468C2×C32C2×C4×D411yescharacteristic
469C2×C32C2×#13711yescharacteristic
470C2×C32#57511yescharacteristic
471C3×D3—42no—
472#41—34no—
473#41—62no—
474C2×Q8—31no—
475C2×Q8—92no—
476C2×Q8—94no—
477C2×Q8—182no—
478C2×Q8—181no—
479C2×D4—31no—
480C2×D4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—181no—
485C22×C4—181no—
486C22×C4#62611yescharacteristic
487C22×C4#62611yescharacteristic
488C22×C4C2×D3211yescharacteristic
489Q16—98no—
490SD16—98no—
491M16—34no—
492M16—62no—
493C2×C8—32no—
494C2×C8—32no—
495C4⋊C4—31no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—92no—
500C4⋊C4—181no—
501C4⋊C4—182no—
502C4⋊C4—182no—
503C22⋊C4—61no—
504C22⋊C4—61no—
505C22⋊C4—61no—
506C42—61no—
507C42—61no—
508C42—61no—
509C42—182no—
510C42—182no—
511C42#62611yescharacteristic
512C42#62611yescharacteristic
513C42C2×D3211yescharacteristic
514C42C2×D3211yescharacteristic
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—62no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3C4×D1212yes—
527C22×C3C4×#6712yes—
528C22×C3C22×D1211yescharacteristic
529C22×C3C22×#6711yescharacteristic
530C2×D3—22no—
531C2×D3—41no—
532C2×D3—41no—
533C3×C4—22no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—62no—
547C3×C4—121no—
548C3×C4—121no—
549C3×C4C4×D1212yes—
550C3×C4#90912yescomplemented
551C3×C4C4×#6712yes—
552C3×C4#95112yescomplemented
553C3×C4C22×C4×D311yescharacteristic
554C3×C4C22×C4×D311yescharacteristic
555C3×C4C2×#23511yescharacteristic
556C3×C4C2×#23511yescharacteristic
557Dic3—22no—
558Dic3—41no—
559Dic3—41no—
560Dic3—68no—
561Dic3—64no—
562Dic3—64no—
563Dic3—124no—
564Dic3—122no—
565Dic3—122no—
566C32C4×#13711yescharacteristic, complemented, Sylow
567C23—61no—
568C23C2×#62611yescharacteristic
569Q8—32no—
570Q8—61no—
571Q8—94no—
572Q8—182no—
573Q8—184no—
574D4—32no—
575D4—64no—
576D4—61no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—61no—
580C2×C4—64no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—122no—
584C2×C4—122no—
585C2×C4—182no—
586C2×C4—184no—
587C2×C4—182no—
588C2×C4—362no—
589C2×C4#379812yes—
590C2×C4C4×D3212yes—
591C2×C4C2×#62611yescharacteristic
592C2×C4C2×#62611yescharacteristic
593C2×C4C2×#62611yescharacteristic
594C2×C4C2×#62611yescharacteristic
595C2×C4C2×#62611yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—34no—
598C8—62no—
599C2×C3—24no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—122no—
606C2×C3C2×C4×D1211yescharacteristic
607C2×C3C2×#90911yescharacteristic
608C2×C3#574811yescharacteristic
609C2×C3C2×C4×#6711yescharacteristic
610C2×C3#582211yescharacteristic
611C2×C3C2×#95111yescharacteristic
612D3—42no—
613C22—21no—
614C22—21no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22C4×#62612yes—
619C22C22×#62611yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—62no—
624C4—121no—
625C4—121no—
626C4—184no—
627C4—362no—
628C4#6383112yesdirect product factor
629C4C4×#62612yes—
630C4C2×#379811yescharacteristic
631C4C2×C4×D3211yescharacteristic
632C3—21no—
633C3C4×#90911yescharacteristic, complemented
634C3C4×#95111yescharacteristic, complemented
635C2—22no—
636C2—122no—
637C2C2×#6383111yescharacteristic
638C2#1059479511yescharacteristic
639C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
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
1. C2×C4×#634C2semidirect
4. C3×C4×#208C2semidirect
5. #10591131C2semidirect
6. #10591107C2semidirect
8. #10590383C2semidirect
9. C4×#3719C2semidirect
10. #10590360C2semidirect
11. C4×#3716C2semidirect
36. #63831C4direct (N × H)
64. C4×#208D3semidirect
76. C2×#634C2×C4semidirect
107. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3716C2×C4semidirect
329. #208C4×D3semidirect
345. C32×C4#137semidirect
550. C3×C4#909semidirect
552. C3×C4#951semidirect
566. C32C4×#137semidirect
628. C4#63831direct (N × H)
633. C3C4×#909semidirect
634. C3C4×#951semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×C4×#2352
C2×#638312
C3×C4×#2082
#105911312
#105911072
#105910882
#105903832
C4×#37192
#105903602
C4×#37162
C4×#9513
C4×#9093