Finite Group Databasebeta

← D3×#548⋊C3 #11923244

Subgroups — D3×#548⋊C3 #11923244

Order 1152.

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

normal subgroups only

This group has 875 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×D3×#41⋊C3C211yesmaximal, characteristic, complemented
2C22×D3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C3×#548⋊C3C211yesmaximal, characteristic, complemented
4#5831⋊C3C211yesmaximal, characteristic, complemented
5#5817⋊C3C211yesmaximal, characteristic, complemented
6#5576⋊C3C211yesmaximal, characteristic, complemented
7C4×D3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
8D3×#548C311yesmaximal, characteristic, complemented
9C2×#548⋊C3—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic, complemented
11C22×C3×SL(2,𝔽3)C2211yescharacteristic, complemented
12D3×#41⋊C3—22no—
13C2×D3×SL(2,𝔽3)—22no—
14C2×D3×SL(2,𝔽3)C2211yescharacteristic
15C2×D3×SL(2,𝔽3)C2211yescharacteristic, complemented
16C2×C3⋊(#41⋊C3)C2211yescharacteristic, complemented
17C3×D3×C22⋊C4—41nomaximal
18C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
19Dic3×SL(2,𝔽3)C2211yescharacteristic, complemented
20C2×D3×#41C2×C311yescharacteristic, complemented
21C22×D3×Q8C2×C311yescharacteristic
22C22×#41⋊C3—31no—
23C23×SL(2,𝔽3)—31no—
24C3×#548C2×C311yescharacteristic, complemented
25#5831C2×C311yescharacteristic, complemented
26#5817C2×C311yescharacteristic, complemented
27#5677—31no—
28D3×#124—31no—
29#5633—31no—
30D3×C22⋊Q8—31no—
31D3×#121—31no—
32#5598—31no—
33#5576C2×C311yescharacteristic, complemented
34C4×D3×Q8C2×C311yescharacteristic, complemented
35#5552—31no—
36C4×D3×D4—31no—
37#548⋊C3—21no—
38#548⋊C3—31no—
39#548⋊C3—31no—
40#548⋊C3—31no—
41#548⋊C3D311yescharacteristic, direct product factor
42C2×C4×SL(2,𝔽3)—31no—
43C23×C3×D3—41no—
44C2×C3×C4×D3—41no—
45C2×C3×C4×D3—41no—
46C3×#41⋊C3—21no—
47C2×C3×SL(2,𝔽3)—21no—
48C2×C3×SL(2,𝔽3)C2311yescharacteristic
49D3×SL(2,𝔽3)—21no—
50D3×SL(2,𝔽3)D412yescomplemented
51C3⋊(#41⋊C3)—21no—
52C32×C22⋊C4—41no—
53C3×#217—41no—
54C3×(C2×D3)⋊C4—41no—
55C3×(C2×D3)⋊C4—41no—
56C2×#548—31noSylow
57C2×C3×#41C22×C311yescharacteristic, complemented
58C22×C3×Q8C22×C311yescharacteristic
59D3×#41—22no—
60D3×#41—62no—
61C2×#239C22×C311yescharacteristic, complemented
62C2×D3×Q8—22no—
63C2×D3×Q8—31no—
64C2×D3×Q8—31no—
65C2×D3×Q8—62no—
66C2×D3×Q8C22×C311yescharacteristic
67C2×D3×Q8C22×C311yescharacteristic
68C2×#237—31no—
69C2×D3×D4—31no—
70C2×D3×D4—31no—
71C2×#235—31no—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×Dic6—31no—
75C2×#41⋊C3—21no—
76C2×#41⋊C3—31no—
77C2×#41⋊C3—62no—
78C2×#41⋊C3C2×D311yescharacteristic, complemented
79C22×SL(2,𝔽3)—21no—
80C22×SL(2,𝔽3)—31no—
81C22×SL(2,𝔽3)—31no—
82C22×SL(2,𝔽3)—62no—
83C22×SL(2,𝔽3)C2×D311yescharacteristic, complemented
84C3×#124—31no—
85C3×C22⋊Q8—31no—
86C3×#121—31no—
87C3×C4×Q8C22×C311yescharacteristic, complemented
88C3×C4×D4—31no—
89C2×C3×C22⋊C4—121no—
90#947—31no—
91#946—31no—
92Q8×Dic3C22×C311yescharacteristic, complemented
93#939—32no—
94#938—31no—
95#936—31no—
96D4×Dic3—31no—
97#930—31no—
98C4×#67—31no—
99C4×#67—31no—
100#924—31no—
101#897—31no—
102#896—32no—
103#895—31no—
104#893—31no—
105D3×C4⋊C4—31no—
106D3×C4⋊C4—31no—
107#887—31no—
108#885—32no—
109#885—32no—
110#884—32no—
111#67⋊C4—31no—
112#67⋊C4—31no—
113D3×C22⋊C4—32no—
114D3×C22⋊C4—31no—
115D3×C22⋊C4A411yescharacteristic
116#878—32no—
117#875—31no—
118C4×D12—31no—
119C42×D3—31no—
120C4×Dic6—31no—
121C4×SL(2,𝔽3)—21no—
122C4×SL(2,𝔽3)—31no—
123C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
124C23×C32—41no—
125C22×C3×D3—44no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—82no—
129C22×C3×D3—82no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C3×C4×D3—82no—
135C3×C4×D3—82no—
136C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
137C22×#41—31no—
138C23×Q8—31no—
139#548—31no—
140#548—31no—
141#548—31no—
142#548—91no—
143#548—91no—
144#548—91no—
145#548—91no—
146#548C3×D311yescharacteristic, complemented
147C2×#124—91no—
148C2×C22⋊Q8—91no—
149C2×#121—91no—
150C2×C4×Q8—31no—
151C2×C4×D4—91no—
152C24×C3—121no—
153C23×D3—31no—
154C23×D3C2×A411yescharacteristic
155C3×#41—21no—
156C3×#41—61no—
157C2×C3×Q8—21no—
158C2×C3×Q8—31no—
159C2×C3×Q8—61no—
160C2×C3×Q8C23×C311yescharacteristic
161C2×C3×D4—31no—
162C2×C3×D4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—121no—
166C22×C3×C4—121no—
167C2×#67—32no—
168C2×#67—31no—
169C2×#67—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172#239—21no—
173#239—61no—
174D3×Q8—21no—
175D3×Q8—32no—
176D3×Q8—62no—
177D3×Q8—62no—
178D3×Q8—62no—
179D3×Q8—62no—
180D3×Q8—61no—
181D3×Q8C3×D412yes—
182#237—62no—
183#237—62no—
184D3×D4—62no—
185D3×D4—62no—
186D3×D4—64no—
187#235—62no—
188#235—62no—
189C2×D12—31no—
190C2×D12—31no—
191C2×C4×D3—31no—
192C2×C4×D3—31no—
193C2×C4×D3—31no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3C2×A411yescharacteristic
203C2×C4×D3C2×A411yescharacteristic
204C2×Dic6—31no—
205C2×Dic6—32no—
206C2×Dic6—31no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209#41⋊C3—21no—
210#41⋊C3—41no—
211#41⋊C3—61no—
212C2×SL(2,𝔽3)—21no—
213C2×SL(2,𝔽3)—21no—
214C2×SL(2,𝔽3)—32no—
215C2×SL(2,𝔽3)—41no—
216C2×SL(2,𝔽3)—61no—
217C2×SL(2,𝔽3)C22×D311yescharacteristic
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
220C3×C22⋊C4—32no—
221C3×C22⋊C4—31no—
222C3×C22⋊C4—41no—
223C3×C22⋊C4—81no—
224C3×C22⋊C4—121no—
225C3×C22⋊C4—121no—
226C3×C22⋊C4—121no—
227C3×C22⋊C4C2×A411yescharacteristic
228C3×C42—31no—
229#217—32no—
230#217—31no—
231#217C2×A411yescharacteristic
232(C2×D3)⋊C4—32no—
233(C2×D3)⋊C4—32no—
234(C2×D3)⋊C4—31no—
235(C2×D3)⋊C4—31no—
236(C2×D3)⋊C4C2×A411yescharacteristic
237(C2×D3)⋊C4C2×A411yescharacteristic
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240Dic3⋊C4—32no—
241Dic3⋊C4—31no—
242Dic3⋊C4—31no—
243C4×Dic3—31no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C22×C32—42no—
247C22×C32—41no—
248C22×C32—81no—
249C22×C32—81no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—88no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C32×C4—81no—
258C32×C4—81no—
259C3×Dic3—81no—
260C3×Dic3—81no—
261C2×#41—31no—
262C2×#41—62no—
263C2×#41—91no—
264C2×#41—91no—
265C2×#41—182no—
266C2×#41C2×C3×D311yescharacteristic, complemented
267C22×Q8—31no—
268C22×Q8—31no—
269C22×Q8—62no—
270C22×Q8—91no—
271C22×Q8—91no—
272C22×Q8—91no—
273C22×Q8—182no—
274C22×Q8C2×C3×D311yescharacteristic
275C22×D4—91no—
276C22×D4—91no—
277C23×C4—91no—
278C23×C4—91no—
279#124—31no—
280#124—91no—
281#124—92no—
282#124—92no—
283#124—91no—
284#124—91no—
285C22⋊Q8—31no—
286C22⋊Q8—92no—
287C22⋊Q8—92no—
288C22⋊Q8—91no—
289C22⋊Q8—91no—
290C22⋊Q8—91no—
291#121—31no—
292#121—92no—
293#121—91no—
294#121—91no—
295#121—91no—
296#121—92no—
297C4×Q8—31no—
298C4×Q8—91no—
299C4×Q8—91no—
300C4×Q8C2×C3×D311yescharacteristic, complemented
301C4×D4—31no—
302C4×D4—91no—
303C4×D4—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—91no—
313C2×C22⋊C4—92no—
314C2×C42—91no—
315C23×C3—31no—
316C23×C3—41no—
317C23×C3—81no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—124no—
321C23×C3—242no—
322C23×C3—242no—
323C23×C3C22×A411yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—31no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3#41⋊C314yescomplemented
331C22×D3C22×A411yescharacteristic
332C22×D3C22×A411yescharacteristic
333C3×Q8—31no—
334C3×Q8—61no—
335C3×Q8—61no—
336C3×Q8C2×C3×D411yescharacteristic
337C3×D4—61no—
338C3×D4—61no—
339C3×D4—62no—
340C2×C3×C4—31no—
341C2×C3×C4—31no—
342C2×C3×C4—31no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—81no—
350C2×C3×C4—81no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—242no—
354C2×C3×C4—242no—
355C2×C3×C4C22×A411yescharacteristic
356C2×C3×C4C22×A411yescharacteristic
357#67—64no—
358#67—62no—
359#67—62no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3C22×A411yescharacteristic
366C2×Dic3C22×A411yescharacteristic
367D12—61no—
368D12—61no—
369D12—62no—
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—32no—
373C4×D3—32no—
374C4×D3—61no—
375C4×D3—61no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—61no—
379C4×D3—61no—
380C4×D3—62no—
381C4×D3—62no—
382Dic6—32no—
383Dic6—32no—
384Dic6—64no—
385Dic6—61no—
386Dic6—61no—
387SL(2,𝔽3)—21no—
388SL(2,𝔽3)D3×D411yescharacteristic, complemented
389C2×C32—41no—
390C2×C32—41no—
391C2×C32—41no—
392C2×C32—82no—
393C3×D3—44no—
394C3×D3—82no—
395C24—31no—
396C24—91no—
397#41—21no—
398#41—61no—
399#41—61no—
400#41—182no—
401#41—182no—
402#41—182no—
403#41—182no—
404#41—181no—
405C2×Q8—21no—
406C2×Q8—31no—
407C2×Q8—32no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—92no—
411C2×Q8—91no—
412C2×Q8—91no—
413C2×Q8—92no—
414C2×Q8—182no—
415C2×Q8—182no—
416C2×Q8—182no—
417C2×Q8—182no—
418C2×Q8—182no—
419C2×Q8—181no—
420C2×Q8—182no—
421C2×Q8C22×C3×D311yescharacteristic
422C2×D4—31no—
423C2×D4—31no—
424C2×D4—91no—
425C2×D4—91no—
426C2×D4—91no—
427C2×D4—92no—
428C2×D4—91no—
429C2×D4—182no—
430C2×D4—182no—
431C2×D4—184no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—182no—
448C22×C4—182no—
449C4⋊C4—31no—
450C4⋊C4—31no—
451C4⋊C4—91no—
452C4⋊C4—91no—
453C4⋊C4—91no—
454C4⋊C4—92no—
455C4⋊C4—91no—
456C22⋊C4—32no—
457C22⋊C4—31no—
458C22⋊C4—31no—
459C22⋊C4—31no—
460C22⋊C4—31no—
461C22⋊C4—91no—
462C22⋊C4—91no—
463C22⋊C4—92no—
464C22⋊C4—92no—
465C22⋊C4—92no—
466C22⋊C4—91no—
467C22⋊C4D3×A411yescharacteristic
468C42—31no—
469C42—91no—
470C42—91no—
471C42—91no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—42no—
475C22×C3—41no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3—61no—
479C22×C3—81no—
480C22×C3—81no—
481C22×C3—82no—
482C22×C3—81no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—161no—
488C22×C3—161no—
489C22×C3—241no—
490C22×C3—241no—
491C22×C3—248no—
492C22×C3C2×#41⋊C312yescomplemented
493C22×C3C23×A411yescharacteristic
494C2×D3—21no—
495C2×D3—21no—
496C2×D3—28no—
497C2×D3—61no—
498C2×D3—61no—
499C2×D3—61no—
500C2×D3—124no—
501C2×D3D4×A412yes—
502C2×D3C2×#41⋊C312yes—
503C2×D3C2×#41⋊C312yescomplemented
504C2×D32−1+4⋊C312yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—31no—
508C3×C4—31no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—81no—
512C3×C4—81no—
513C3×C4—161no—
514C3×C4—161no—
515C3×C4—241no—
516C3×C4—241no—
517Dic3—21no—
518Dic3—21no—
519Dic3—32no—
520Dic3—61no—
521Dic3—61no—
522C32—41noSylow
523C23—31no—
524C23—34no—
525C23—31no—
526C23—31no—
527C23—62no—
528C23—62no—
529C23—91no—
530C23—182no—
531C23—182no—
532C23—182no—
533C23C2×D3×A411yescharacteristic
534Q8—31no—
535Q8—61no—
536Q8—61no—
537Q8—92no—
538Q8—92no—
539Q8—181no—
540Q8—181no—
541Q8—184no—
542Q8C3×D3×D411yescharacteristic
543D4—61no—
544D4—61no—
545D4—62no—
546D4—181no—
547D4—181no—
548D4—182no—
549D4—184no—
550D4—182no—
551D4—182no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—91no—
566C2×C4—91no—
567C2×C4—91no—
568C2×C4—182no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4C2×D3×A411yescharacteristic
579C2×C4C2×D3×A411yescharacteristic
580C2×C3—22no—
581C2×C3—41no—
582C2×C3—41no—
583C2×C3—41no—
584C2×C3—82no—
585C2×C3—81no—
586C2×C3—81no—
587C2×C3—81no—
588C2×C3—124no—
589C2×C3—121no—
590C2×C3—162no—
591C2×C3—242no—
592C2×C3C2×D4×A411yescharacteristic
593C2×C3C22×#41⋊C311yescharacteristic
594C2×C3C2×2−1+4⋊C311yescharacteristic
595D3—22no—
596D3—121no—
597D3#548⋊C314yesdirect product factor
598C22—21no—
599C22—21no—
600C22—32no—
601C22—32no—
602C22—32no—
603C22—32no—
604C22—68no—
605C22—61no—
606C22—61no—
607C22—61no—
608C22—61no—
609C22—61no—
610C22—181no—
611C22—181no—
612C22—181no—
613C22—364no—
614C22D3×#41⋊C312yescomplemented
615C22C22×D3×A411yescharacteristic
616C4—21no—
617C4—21no—
618C4—31no—
619C4—31no—
620C4—61no—
621C4—61no—
622C4—61no—
623C4—61no—
624C4—92no—
625C4—181no—
626C4—181no—
627C3—41no—
628C3—81no—
629C3C2×#548⋊C311yescharacteristic, complemented
630C2—22no—
631C2—34no—
632C2—62no—
633C2—121no—
634C2—361no—
635C2D3×D4×A411yescharacteristic
636C2C2×D3×#41⋊C311yescharacteristic
637C2D3×2−1+4⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, cosocleC2×C3×Q8C23×C3
FittingC3×#548C2×C3
socleC22×C3C23×A4
hypercenterC22⋊C4D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41⋊C3C2semidirect
2. C22×D3×SL(2,𝔽3)C2semidirect
3. C3×#548⋊C3C2semidirect
4. #5831⋊C3C2semidirect
5. #5817⋊C3C2semidirect
6. #5576⋊C3C2semidirect
7. C4×D3×SL(2,𝔽3)C2semidirect
8. D3×#548C3semidirect
10. C2×C3×#41⋊C3C22semidirect
11. C22×C3×SL(2,𝔽3)C22semidirect
15. C2×D3×SL(2,𝔽3)C22semidirect
16. C2×C3⋊(#41⋊C3)C22semidirect
18. C3×C4×SL(2,𝔽3)C22semidirect
19. Dic3×SL(2,𝔽3)C22semidirect
20. C2×D3×#41C2×C3semidirect
24. C3×#548C2×C3semidirect
25. #5831C2×C3semidirect
26. #5817C2×C3semidirect
33. #5576C2×C3semidirect
34. C4×D3×Q8C2×C3semidirect
41. #548⋊C3D3direct (N × H)
50. D3×SL(2,𝔽3)D4semidirect
57. C2×C3×#41C22×C3semidirect
61. C2×#239C22×C3semidirect
78. C2×#41⋊C3C2×D3semidirect
83. C22×SL(2,𝔽3)C2×D3semidirect
87. C3×C4×Q8C22×C3semidirect
92. Q8×Dic3C22×C3semidirect
123. C4×SL(2,𝔽3)C2×D3semidirect
136. C3×SL(2,𝔽3)C2×D4semidirect
146. #548C3×D3semidirect
266. C2×#41C2×C3×D3semidirect
300. C4×Q8C2×C3×D3semidirect
330. C22×D3#41⋊C3semidirect
388. SL(2,𝔽3)D3×D4semidirect
492. C22×C3C2×#41⋊C3semidirect
503. C2×D3C2×#41⋊C3semidirect
597. D3#548⋊C3direct (N × H)
614. C22D3×#41⋊C3semidirect
629. C3C2×#548⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
C22×D3×SL(2,𝔽3)2
C3×#548⋊C32
#5831⋊C32
#5817⋊C32
#5576⋊C32
C4×D3×SL(2,𝔽3)2
D3×#5483
C2×#548⋊C33
C3×D3×C22⋊C44