Finite Group Databasebeta

← D3×SL(2,ℤ/4)⋊C4 #11922004

Subgroups — D3×SL(2,ℤ/4)⋊C4 #11922004

Order 1152.

1024 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×A4C211yesmaximal, characteristic
2C2×D3×SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×D3×SL(2,ℤ/4)C211yesmaximal, characteristic
4#10593645C211yesmaximal, characteristic, complemented
5C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic, complemented
7#10593238C211yesmaximal, characteristic, complemented
8C2×SL(2,ℤ/4)⋊C4—31nomaximal
9D3×#385—31nomaximal
10C22×D3×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13C4×D3×A4—22no—
14C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
15C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C2×C3×SL(2,ℤ/4)C2211yescharacteristic
18D3×SL(2,ℤ/4)—22no—
19D3×SL(2,ℤ/4)C414yescomplemented
20D3×Dic3⋊C4—41nomaximal
21C23×C4×D3D311yescharacteristic
22C22×C4×A4—31no—
23C22×SL(2,ℤ/4)—31no—
24C22×SL(2,ℤ/4)—31no—
25C2×D3×C4⋊C4—31no—
26C2×D3×C4⋊C4—31no—
27C2×D3×C22⋊C4—31no—
28C2×D3×C22⋊C4—31no—
29SL(2,ℤ/4)⋊C4—31no—
30SL(2,ℤ/4)⋊C4—31no—
31SL(2,ℤ/4)⋊C4—31no—
32SL(2,ℤ/4)⋊C4—61no—
33SL(2,ℤ/4)⋊C4D311yescharacteristic, direct product factor
34C3×#385—31no—
35#5210—31no—
36#4989—31no—
37#4989—31no—
38#4950—31no—
39#4946—31no—
40#4668—31no—
41#4668—31no—
42D3×#95—31no—
43D3×#95—31no—
44C22×C3×A4C2311yescharacteristic
45C2×D3×A4C2×C412yes—
46C2×D3×A4D412yes—
47C2×D3×A4Q812yes—
48C2×C3×C4×D3—41no—
49C3×C4×A4—21no—
50C2×D3×Dic3—41no—
51C2×D3×Dic3—41no—
52Dic3×A4—21no—
53C3⋊SL(2,ℤ/4)—21no—
54C3⋊SL(2,ℤ/4)C2×C412yescomplemented
55C3×SL(2,ℤ/4)—21no—
56C3×SL(2,ℤ/4)C2×C412yescomplemented
57#3750—41no—
58C3×Dic3⋊C4—41no—
59#3724—41no—
60Dic3⋊Dic3—41no—
61C2×#385—91noSylow
62C24×D3C2×D311yescharacteristic
63C23×A4—31no—
64C23×C3×C4C2×D311yescharacteristic
65C23×Dic3C2×D311yescharacteristic
66C22×C4×D3—22no—
67C22×C4×D3—31no—
68C22×C4×D3—31no—
69C22×C4×D3—31no—
70C22×C4×D3—31no—
71C22×C4×D3—31no—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—31no—
75C22×C4×D3—62no—
76C2×C4×A4—21no—
77C2×C4×A4—31no—
78C2×C4×A4—62no—
79C2×C4×A4C2×D311yescharacteristic
80C2×SL(2,ℤ/4)—31no—
81C2×SL(2,ℤ/4)—34no—
82C2×SL(2,ℤ/4)—31no—
83C2×SL(2,ℤ/4)—61no—
84C2×SL(2,ℤ/4)—61no—
85C2×SL(2,ℤ/4)—62no—
86C2×SL(2,ℤ/4)C2×D311yescharacteristic
87C2×SL(2,ℤ/4)C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—31no—
92C2×#217—31no—
93C2×#217—31no—
94C2×(C2×D3)⋊C4—31no—
95C2×(C2×D3)⋊C4—31no—
96C2×(C2×D3)⋊C4—31no—
97C2×(C2×D3)⋊C4—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×Dic3⋊C4—31no—
101C2×Dic3⋊C4—31no—
102C2×Dic3⋊C4—31no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—121no—
105D3×C4⋊C4—64no—
106D3×C4⋊C4—61no—
107D3×C4⋊C4—61no—
108D3×C4⋊C4—61no—
109D3×C4⋊C4—61no—
110D3×C22⋊C4—34no—
111D3×C22⋊C4—34no—
112D3×C22⋊C4—62no—
113D3×C22⋊C4—62no—
114C3×#95—31no—
115C3×#95—31no—
116C3⋊#95—31no—
117C3⋊#95—31no—
118C3⋊#95—31no—
119C3⋊#95—31no—
120C3⋊#95—31no—
121C3⋊#95—31no—
122C22×C3×D3—41no—
123C2×C3×A4C22×C411yescharacteristic
124C2×C3×A4C2×D411yescharacteristic
125C2×C3×A4C2×Q811yescharacteristic
126D3×A4C4⋊C414yescomplemented
127C2×C32×C4—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C3×C4×D3—82no—
134D3×Dic3—44no—
135D3×Dic3—82no—
136C24×C4—31no—
137C22×C4⋊C4—91no—
138C22×C4⋊C4—91no—
139C22×C22⋊C4—91no—
140C22×C22⋊C4—91no—
141#385—31no—
142#385—91no—
143#385—91no—
144#385—91no—
145#385—91no—
146#385—91no—
147#385—91no—
148#385—91no—
149C2×#95—91no—
150C2×#95—91no—
151C24×C3C22×D311yescharacteristic
152C23×D3—31no—
153C23×D3—32no—
154C23×D3—32no—
155C23×D3—31no—
156C23×D3—32no—
157C23×D3Dic612yes—
158C23×D3C4×D312yes—
159C23×D3#6712yes—
160C22×A4—21no—
161C22×A4—32no—
162C22×A4—32no—
163C22×A4—32no—
164C22×A4C22×D311yescharacteristic
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4—121no—
174C22×Dic3—21no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3—121no—
184C2×C4×D3—34no—
185C2×C4×D3—34no—
186C2×C4×D3—34no—
187C2×C4×D3—31no—
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—61no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3—61no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—61no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—61no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—61no—
210C2×C4×D3S411yescharacteristic
211C4×A4—21no—
212C4×A4—41no—
213C4×A4—61no—
214SL(2,ℤ/4)—21no—
215SL(2,ℤ/4)—32no—
216SL(2,ℤ/4)—62no—
217SL(2,ℤ/4)—61no—
218SL(2,ℤ/4)—121no—
219SL(2,ℤ/4)C4×D312yescomplemented
220C3×C4⋊C4—62no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—32no—
224C3×C22⋊C4—32no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227#217—32no—
228#217—32no—
229#217—61no—
230#217—61no—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238Dic3⋊C4—41no—
239Dic3⋊C4—62no—
240Dic3⋊C4—61no—
241Dic3⋊C4—62no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—121no—
246Dic3⋊C4—121no—
247Dic3⋊C4—121no—
248Dic3⋊C4—241no—
249C22×C32—41no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C3×A4C2×C4⋊C411yescharacteristic, complemented
254C32×C4—81no—
255C3⋊Dic3—42no—
256C3⋊Dic3—81no—
257C3×Dic3—42no—
258C3×Dic3—81no—
259C3×Dic3—81no—
260C25—31no—
261C23×C4—31no—
262C23×C4—62no—
263C23×C4—91no—
264C23×C4—91no—
265C23×C4—91no—
266C23×C4—91no—
267C23×C4—91no—
268C23×C4—91no—
269C23×C4—91no—
270C23×C4—91no—
271C23×C4—182no—
272C23×C4D3211yescharacteristic
273C2×C4⋊C4—31no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—181no—
282C2×C4⋊C4—181no—
283C2×C4⋊C4—181no—
284C2×C4⋊C4—184no—
285C2×C4⋊C4—181no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—94no—
289C2×C22⋊C4—94no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—182no—
297C2×C22⋊C4—182no—
298#95—31no—
299#95—31no—
300#95—91no—
301#95—91no—
302#95—91no—
303#95—91no—
304#95—91no—
305#95—91no—
306C23×C3—31no—
307C23×C3—31no—
308C23×C3—31no—
309C23×C3—31no—
310C23×C3—121no—
311C23×C3C2×Dic611yescharacteristic
312C23×C3C2×C4×D311yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C22×D3—31no—
315C22×D3—32no—
316C22×D3—32no—
317C22×D3—32no—
318C22×D3—32no—
319C22×D3—32no—
320C22×D3—32no—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—32no—
324C22×D3—34no—
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—64no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3Dic3⋊C414yescomplemented
332C22×D3C2×S411yescharacteristic
333C2×A4—21no—
334C2×A4—21no—
335C2×A4—21no—
336C2×A4—34no—
337C2×A4C2×C4×D311yescharacteristic
338C2×A4D3×D411yescharacteristic
339C2×A4D3×Q811yescharacteristic
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—31no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—81no—
359C2×C3×C4—121no—
360C2×C3×C4—242no—
361C2×C3×C4C2×S411yescharacteristic
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—31no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—124no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—241no—
385C2×Dic3—241no—
386C2×Dic3—242no—
387C2×Dic3C2×S411yescharacteristic
388C4×D3—22no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—68no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—64no—
395C4×D3—62no—
396C4×D3—124no—
397C4×D3—122no—
398C4×D3—122no—
399C2×C32—41no—
400C2×C32—41no—
401C2×C32—41no—
402C3×D3—44no—
403C24—32no—
404C24—32no—
405C24—32no—
406C24—91no—
407C24—91no—
408C24—92no—
409C24—92no—
410C24—92no—
411C24C2×D3211yescharacteristic
412C22×C4—21no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—94no—
426C22×C4—94no—
427C22×C4—94no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—181no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—181no—
440C22×C4—182no—
441C22×C4—181no—
442C22×C4—182no—
443C22×C4—182no—
444C22×C4—182no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—181no—
448C22×C4—182no—
449C22×C4—182no—
450C22×C4—182no—
451C22×C4—181no—
452C22×C4—182no—
453C22×C4—182no—
454C22×C4—181no—
455C4⋊C4—62no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—182no—
461C4⋊C4—181no—
462C4⋊C4—182no—
463C4⋊C4—181no—
464C4⋊C4—182no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C22⋊C4—32no—
468C22⋊C4—32no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—94no—
472C22⋊C4—94no—
473C22⋊C4—92no—
474C22⋊C4—92no—
475C22⋊C4—182no—
476C22⋊C4—182no—
477C22⋊C4—181no—
478C22⋊C4—181no—
479C22×C3—31no—
480C22×C3—31no—
481C22×C3—31no—
482C22×C3—31no—
483C22×C3—31no—
484C22×C3—31no—
485C22×C3—31no—
486C22×C3—31no—
487C22×C3—31no—
488C22×C3—41no—
489C22×C3—61no—
490C22×C3—81no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3C2×Dic3⋊C411yescharacteristic, complemented
495C22×C3C22×S411yescharacteristic
496C2×D3—32no—
497C2×D3—32no—
498C2×D3—32no—
499C2×D3—34no—
500C2×D3—34no—
501C2×D3—34no—
502C2×D3—34no—
503C2×D3—34no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3A4⋊Q812yes—
508C2×D3C4×S412yes—
509C2×D3GL(2,ℤ/4)12yes—
510A4—21no—
511A4D3×C4⋊C411yescharacteristic, complemented
512C3×C4—21no—
513C3×C4—62no—
514C3×C4—62no—
515C3×C4—61no—
516C3×C4—81no—
517C3×C4—121no—
518C3×C4—121no—
519C3×C4—161no—
520C3×C4—241no—
521Dic3—21no—
522Dic3—42no—
523Dic3—62no—
524Dic3—62no—
525Dic3—61no—
526Dic3—81no—
527Dic3—122no—
528Dic3—121no—
529Dic3—121no—
530Dic3—242no—
531Dic3—241no—
532Dic3—481no—
533C32—41noSylow
534C23—31no—
535C23—31no—
536C23—31no—
537C23—31no—
538C23—31no—
539C23—34no—
540C23—92no—
541C23—92no—
542C23—92no—
543C23—92no—
544C23—92no—
545C23—92no—
546C23—92no—
547C23—92no—
548C23—94no—
549C23—94no—
550C23—94no—
551C23—92no—
552C23—91no—
553C23—181no—
554C23—181no—
555C23—181no—
556C23—184no—
557C23D3×Dic611yescharacteristic
558C23C4×D3211yescharacteristic
559C23D3×#6711yescharacteristic
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—92no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—91no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—181no—
586C2×C4—182no—
587C2×C4—181no—
588C2×C4—184no—
589C2×C4—184no—
590C2×C4—188no—
591C2×C4—184no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—181no—
599C2×C4—181no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—181no—
603C2×C4—362no—
604C2×C4—364no—
605C2×C4—362no—
606C2×C4D3×S411yescharacteristic
607C2×C3—31no—
608C2×C3—31no—
609C2×C3—31no—
610C2×C3—31no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—41no—
614C2×C3—81no—
615C2×C3—81no—
616C2×C3—81no—
617C2×C3—124no—
618C2×C3C2×A4⋊Q811yescharacteristic
619C2×C3C2×C4×S411yescharacteristic
620C2×C3C2×GL(2,ℤ/4)11yescharacteristic
621D3—34no—
622D3SL(2,ℤ/4)⋊C414yesdirect product factor
623C22—31no—
624C22—31no—
625C22—31no—
626C22—31no—
627C22—31no—
628C22—32no—
629C22—31no—
630C22—31no—
631C22—32no—
632C22—31no—
633C22—31no—
634C22—32no—
635C22—61no—
636C22—94no—
637C22—94no—
638C22—94no—
639C22—94no—
640C22—94no—
641C22—92no—
642C22—92no—
643C22—92no—
644C22—182no—
645C22—182no—
646C22—182no—
647C22D3×Dic3⋊C411yescharacteristic, complemented
648C22C2×D3×S411yescharacteristic
649C4—21no—
650C4—62no—
651C4—62no—
652C4—61no—
653C4—61no—
654C4—121no—
655C4—121no—
656C4—182no—
657C4—182no—
658C4—181no—
659C4—361no—
660C4—361no—
661C3—41no—
662C3—81no—
663C3C2×SL(2,ℤ/4)⋊C411yescharacteristic, complemented
664C2—31no—
665C2—31no—
666C2—31no—
667C2—31no—
668C2—34no—
669C2—94no—
670C2D3×A4⋊Q811yescharacteristic
671C2C4×D3×S411yescharacteristic
672C2D3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×D3×A4C22
cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593645C2semidirect
5. C3×SL(2,ℤ/4)⋊C4C2semidirect
6. SL(2,ℤ/4)⋊Dic3C2semidirect
7. #10593238C2semidirect
19. D3×SL(2,ℤ/4)C4semidirect
33. SL(2,ℤ/4)⋊C4D3direct (N × H)
54. C3⋊SL(2,ℤ/4)C2×C4semidirect
56. C3×SL(2,ℤ/4)C2×C4semidirect
126. D3×A4C4⋊C4semidirect
219. SL(2,ℤ/4)C4×D3semidirect
253. C3×A4C2×C4⋊C4semidirect
331. C22×D3Dic3⋊C4semidirect
494. C22×C3C2×Dic3⋊C4semidirect
511. A4D3×C4⋊C4semidirect
622. D3SL(2,ℤ/4)⋊C4direct (N × H)
647. C22D3×Dic3⋊C4semidirect
663. C3C2×SL(2,ℤ/4)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
C2×D3×SL(2,ℤ/4)2
#105936452
C3×SL(2,ℤ/4)⋊C42
SL(2,ℤ/4)⋊Dic32
#105932382
C2×SL(2,ℤ/4)⋊C43
D3×#3853
D3×Dic3⋊C44