Finite Group Databasebeta

← C4×#63833 #11860413

Subgroups — C4×#63833 #11860413

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4C3×C4×#208C211yesmaximal, characteristic, complemented
5#10591130C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic
7#10591100C211yesmaximal, characteristic, complemented
8#10590383C212yesmaximal, complemented
9C4×#3719C212yesmaximal, complemented
10#10590362C212yesmaximal, complemented
11C4×#3717C212yesmaximal, complemented
12C4×#942—31nomaximal
13C4×#909—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C4×#638—21no—
18C4×#638—21no—
19#64135C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64081—21no—
23C42×C3⋊D3—21no—
24C4×#634C2211yescharacteristic
25C4×#634C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4—21no—
28C2×C3×C4×Dic3—21no—
29C2×C3×#208C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2212yes—
34C3×C4×Dic6C2212yes—
35C2×#3719C2212yes—
36#63833C418yesdirect product factor
37C2×#3717C2212yes—
38C3×#803C2212yes—
39C3×C4×C3⋊C8C2212yes—
40#63575C2212yes—
41#63573C2212yes—
42#63567C2212yes—
43#63566C2212yes—
44#63566C2212yes—
45#63564C2212yes—
46C2×C3×C4×Q8—31no—
47C2×#942—31no—
48C2×#909—31no—
49C4×#235—31no—
50C4×#235—31no—
51C4×#235—61no—
52C2×C4×Dic6D311yescharacteristic, complemented
53C3×C4×M16—31no—
54#5225—31no—
55#5133—31no—
56#5121—31no—
57#5120—31no—
58#5030—32no—
59C4×#216—32no—
60#5026—32no—
61C4×#215—32no—
62#4966—31no—
63#4964—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
72C2×#638—21no—
73#3828—22no—
74#3828C2×C414yes—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6C2×C414yescomplemented
85C2×C3×Dic6C2312yes—
86C32×C42D411yescharacteristic
87C32×C42D411yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2311yescharacteristic
90#3757—21no—
91#3752—21no—
92#3752—21no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95#3750—21no—
96#3750—21no—
97C4×C3⋊Dic3—21no—
98C4×C3⋊Dic3—21no—
99C4×C3⋊Dic3—21no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C3×Dic3⋊C4—22no—
103C3×Dic3⋊C4—22no—
104C3×C4×Dic3—22no—
105C3×C4×Dic3—22no—
106C3×#208—22no—
107C3×#208C2×C414yescomplemented
108C2×C3×C3⋊C8C2312yes—
109C2×C3×C3⋊C8C2312yes—
110#3719C2×C418yescomplemented
111#3717C2×C418yescomplemented
112C4×#137—91noSylow
113C22×C3×Q8—31no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C3×C4×Q8—32no—
121C3×C4×Q8—32no—
122C3×C4×Q8—61no—
123C3×C4×Q8—61no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—61no—
126C2×C3×C42—21no—
127C2×C3×C42—61no—
128C2×C3×C42C2×D311yescharacteristic
129C2×C3×C42C2×D311yescharacteristic
130C2×#216—32no—
131#942—38no—
132C2×#215—32no—
133C4×#67—62no—
134C4×#67—62no—
135C4×#67—61no—
136C4×#67—61no—
137C4×#67—61no—
138C4×#67—61no—
139#926—31no—
140#926—31no—
141#926—61no—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×Dic3⋊C4—21no—
144C2×C4×Dic3—21no—
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#909—38no—
148C2×Dic12—32no—
149C2×#204—32no—
150C4×D12—31no—
151C4×D12—31no—
152C4×D12—31no—
153C4×D12—31no—
154C4×D12—61no—
155C4×D12—61no—
156#872—62no—
157#872—61no—
158#872—61no—
159C42×D3—62no—
160C42×D3—61no—
161C42×D3—61no—
162C4×Dic6—21no—
163C4×Dic6—21no—
164C4×Dic6—31no—
165C4×Dic6—31no—
166C4×Dic6—31no—
167C4×Dic6—31no—
168C4×Dic6—61no—
169C4×Dic6—61no—
170C4×Dic6C2×D312yes—
171C4×Dic6C2×D312yes—
172C3×#97—32no—
173C3×C4×C8—32no—
174#835—32no—
175#835—32no—
176#821—32no—
177#818—32no—
178#817—32no—
179#816—32no—
180#816—32no—
181#816—32no—
182#810—32no—
183#809—32no—
184#808—32no—
185#807—32no—
186#803C2×D312yes—
187C4×C3⋊C8C2×D312yes—
188C23×C32C2×D411yescharacteristic
189C22×C3⋊D3—21no—
190C2×C32×C4—22no—
191C2×C32×C4—41no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4#4112yes—
199C2×C32×C4C2411yescharacteristic
200#638—24no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)C22×C412yes—
206C4×C3⋊D3—24no—
207C4×C3⋊D3—42no—
208C4×C3⋊D3—42no—
209#634—21no—
210#634C22×C412yes—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—42no—
215C3×Dic6—24no—
216C3×Dic6—22no—
217C3×Dic6C22×C414yes—
218C3×C3⋊C8—22no—
219C3×C3⋊C8C22×C414yes—
220C2×#137—91no—
221C4×#41—91no—
222C2×C4×Q8—31no—
223#441—92no—
224#440—92no—
225C4×Q16—92no—
226C4×SD16—92no—
227#428—91no—
228#419—91no—
229#417—91no—
230C4×M16—31no—
231C2×C3×Q8—34no—
232C2×C3×Q8—32no—
233C2×C3×Q8—61no—
234C2×C3×Q8—62no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
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—62no—
247C2×#67—61no—
248C2×#67—61no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251#235—34no—
252#235—34no—
253#235—64no—
254#235—64no—
255#235—62no—
256#235—62no—
257C2×D12—31no—
258C2×D12—31no—
259C2×D12—61no—
260C2×C4×D3—62no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×Dic6—22no—
270C2×Dic6—21no—
271C2×Dic6—31no—
272C2×Dic6—31no—
273C2×Dic6—61no—
274C2×Dic6C4×D314yescomplemented
275C2×Dic6C22×D312yes—
276C3×M16—34no—
277C3×M16—62no—
278C2×C3×C8—32no—
279C2×C3×C8—32no—
280C3×C4⋊C4—32no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4—61no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—62no—
289C3×C42—62no—
290C3×C42D1211yescharacteristic
291C3×C42D1211yescharacteristic
292C3×C42#6711yescharacteristic
293C3×C42#6711yescharacteristic
294C3×C42C22×D311yescharacteristic
295C3×C42C22×D311yescharacteristic
296C3×C42C22×D311yescharacteristic
297C3×C42C22×D311yescharacteristic
298#217—62no—
299#217—61no—
300#217—61no—
301#216—38no—
302#215—38no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—61no—
306(C2×D3)⋊C4—61no—
307(C2×D3)⋊C4—61no—
308(C2×D3)⋊C4—61no—
309C4⋊Dic3—21no—
310C4⋊Dic3—31no—
311C4⋊Dic3—31no—
312C4⋊Dic3—31no—
313C4⋊Dic3—31no—
314C4⋊Dic3—61no—
315C4⋊Dic3—61no—
316C4⋊Dic3C22×D312yes—
317Dic3⋊C4—22no—
318Dic3⋊C4—22no—
319Dic3⋊C4—62no—
320Dic3⋊C4—62no—
321Dic3⋊C4—61no—
322Dic3⋊C4—61no—
323Dic3⋊C4—61no—
324Dic3⋊C4—61no—
325C4×Dic3—22no—
326C4×Dic3—22no—
327C4×Dic3—62no—
328C4×Dic3—62no—
329C4×Dic3—62no—
330C4×Dic3—61no—
331C4×Dic3—61no—
332C4×Dic3—61no—
333C4×Dic3—61no—
334C4×Dic3—61no—
335C4×Dic3—61no—
336#208—22no—
337#208C4×D314yescomplemented
338C2×C3⋊C8C22×D312yes—
339C2×C3⋊C8C22×D312yes—
340Dic12—38no—
341#204—38no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32C4×D412yes—
345C22×C32C22×D411yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3⋊D3—41no—
348C2×C3⋊D3—41no—
349C32×C4—21no—
350C32×C4—21no—
351C32×C4—21no—
352C32×C4C4×D412yes—
353C32×C4#13712yescomplemented
354C32×C4C23×C411yescharacteristic
355C32×C4C2×#4111yescharacteristic
356C3⋊Dic3—22no—
357C3⋊Dic3—41no—
358C3⋊Dic3—41no—
359C3×Dic3—24no—
360C3×Dic3—42no—
361C2×#41—91no—
362C22×Q8—31no—
363#137—98no—
364C2×Q16—92no—
365C2×SD16—92no—
366C2×M16—31no—
367C2×M16—31no—
368C4×Q8—32no—
369C4×Q8—32no—
370C4×Q8—61no—
371C4×Q8—61no—
372C4×Q8—91no—
373C4×Q8—91no—
374C4×D4—91no—
375C4×D4—91no—
376C4×D4—181no—
377C4×D4—181no—
378#117—91no—
379#117—181no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—61no—
382C2×C42—61no—
383C2×C42—181no—
384C2×C42D3211yescharacteristic
385#107—92no—
386#106—92no—
387#103—92no—
388#103—92no—
389#103—92no—
390#102—92no—
391#97—32no—
392C4×C8—32no—
393C23×C3—21no—
394C23×C3C2×D1211yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C22×D3—62no—
397C22×D3—61no—
398C22×D3—61no—
399C3×Q8—34no—
400C3×Q8—64no—
401C3×Q8—62no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—42no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—64no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—122no—
420C2×C3×C4C2×C4×D312yes—
421C2×C3×C4C2×C4×D312yes—
422C2×C3×C4C2×D1211yescharacteristic
423C2×C3×C4C2×D1211yescharacteristic
424C2×C3×C4C2×D1211yescharacteristic
425C2×C3×C4C2×D1211yescharacteristic
426C2×C3×C4C2×D1211yescharacteristic
427C2×C3×C4#23512yes—
428C2×C3×C4#23512yes—
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C23×D311yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436#67—68no—
437#67—64no—
438#67—64no—
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—42no—
443C2×Dic3—62no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452D12—32no—
453D12—32no—
454D12—62no—
455D12—62no—
456D12—61no—
457D12—61no—
458C4×D3—68no—
459C4×D3—64no—
460C4×D3—64no—
461C4×D3—124no—
462C4×D3—122no—
463C4×D3—122no—
464C4×D3—124no—
465C4×D3—122no—
466C4×D3—122no—
467Dic6—24no—
468Dic6—22no—
469Dic6—32no—
470Dic6—32no—
471Dic6—62no—
472Dic6—62no—
473Dic6—61no—
474Dic6—61no—
475Dic6C2×C4×D314yes—
476C3×C8—34no—
477C3×C8—62no—
478C3⋊C8—22no—
479C3⋊C8C2×C4×D314yes—
480C2×C32—22no—
481C2×C32C2×C4×D411yescharacteristic
482C2×C32C2×#13711yescharacteristic
483C2×C32#57511yescharacteristic
484C3⋊D3—42no—
485#41—94no—
486#41—182no—
487C2×Q8—32no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—61no—
491C2×Q8—91no—
492C2×D4—91no—
493C2×D4—181no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—181no—
497C22×C4—181no—
498C22×C4—181no—
499C22×C4#62611yescharacteristic
500C22×C4#62611yescharacteristic
501C22×C4C2×D3211yescharacteristic
502Q16—98no—
503SD16—98no—
504M16—34no—
505M16—62no—
506C2×C8—32no—
507C2×C8—32no—
508C4⋊C4—32no—
509C4⋊C4—61no—
510C4⋊C4—62no—
511C4⋊C4—62no—
512C4⋊C4—91no—
513C4⋊C4—91no—
514C4⋊C4—181no—
515C4⋊C4—181no—
516C22⋊C4—181no—
517C22⋊C4—181no—
518C22⋊C4—181no—
519C42—62no—
520C42—62no—
521C42—181no—
522C42—181no—
523C42—181no—
524C42#62611yescharacteristic
525C42#62611yescharacteristic
526C42C2×D3211yescharacteristic
527C42C2×D3211yescharacteristic
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3C4×D1212yes—
537C22×C3C4×#6712yes—
538C22×C3C22×D1211yescharacteristic
539C22×C3C22×#6711yescharacteristic
540C2×D3—64no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C3×C4—22no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—64no—
563C3×C4—122no—
564C3×C4C4×D1212yes—
565C3×C4#90912yescomplemented
566C3×C4C4×#6712yes—
567C3×C4#94212yescomplemented
568C3×C4C22×C4×D311yescharacteristic
569C3×C4C22×C4×D311yescharacteristic
570C3×C4C2×#23511yescharacteristic
571C3×C4C2×#23511yescharacteristic
572Dic3—24no—
573Dic3—42no—
574Dic3—64no—
575Dic3—62no—
576Dic3—62no—
577Dic3—122no—
578Dic3—122no—
579Dic3—121no—
580Dic3—121no—
581Dic3—121no—
582Dic3—121no—
583C32C4×#13711yescharacteristic, complemented, Sylow
584C23—181no—
585C23C2×#62611yescharacteristic
586Q8—34no—
587Q8—62no—
588Q8—64no—
589Q8—92no—
590Q8—181no—
591D4—92no—
592D4—184no—
593D4—181no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—62no—
597C2×C4—64no—
598C2×C4—62no—
599C2×C4—122no—
600C2×C4—181no—
601C2×C4—184no—
602C2×C4—181no—
603C2×C4—181no—
604C2×C4—362no—
605C2×C4—362no—
606C2×C4#379812yes—
607C2×C4C4×D3212yes—
608C2×C4C2×#62611yescharacteristic
609C2×C4C2×#62611yescharacteristic
610C2×C4C2×#62611yescharacteristic
611C2×C4C2×#62611yescharacteristic
612C2×C4C2×#62611yescharacteristic
613C2×C4C22×D3211yescharacteristic
614C8—34no—
615C8—62no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—42no—
622C2×C3C2×C4×D1211yescharacteristic
623C2×C3C2×#90911yescharacteristic
624C2×C3#574811yescharacteristic
625C2×C3C2×C4×#6711yescharacteristic
626C2×C3C2×#94211yescharacteristic
627C2×C3#582211yescharacteristic
628D3—124no—
629D3—122no—
630D3—122no—
631C22—21no—
632C22—21no—
633C22—182no—
634C22—361no—
635C22—361no—
636C22C4×#62612yes—
637C22C22×#62611yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—64no—
642C4—122no—
643C4—182no—
644C4—361no—
645C4—361no—
646C4#6383312yesdirect product factor
647C4C4×#62612yes—
648C4C2×#379811yescharacteristic
649C4C2×C4×D3211yescharacteristic
650C3—21no—
651C3C4×#90911yescharacteristic, complemented
652C3C4×#94211yescharacteristic, complemented
653C2—22no—
654C2—362no—
655C2#1059479511yescharacteristic
656C2C2×#6383311yescharacteristic
657C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
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. C3×C4×#208C2semidirect
5. #10591130C2semidirect
7. #10591100C2semidirect
8. #10590383C2semidirect
9. C4×#3719C2semidirect
10. #10590362C2semidirect
11. C4×#3717C2semidirect
36. #63833C4direct (N × H)
52. C2×C4×Dic6D3semidirect
64. C4×#208D3semidirect
84. C2×C3×Dic6C2×C4semidirect
107. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3717C2×C4semidirect
274. C2×Dic6C4×D3semidirect
337. #208C4×D3semidirect
353. C32×C4#137semidirect
565. C3×C4#909semidirect
567. C3×C4#942semidirect
583. C32C4×#137semidirect
646. C4#63833direct (N × H)
651. C3C4×#909semidirect
652. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C2×C3×C4×Dic62
C2×#638332
C3×C4×#2082
#105911302
#105911062
#105911002
#105903832
C4×#37192
#105903622
C4×#37172
C4×#9423
C4×#9093