Finite Group Databasebeta

← #10822702

Subgroups — #10822702

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5524C211yesmaximal, characteristic
2C2×#5133C211yesmaximal, characteristic, complemented
3C2×#5126C211yesmaximal, characteristic, complemented
4C2×#4995C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4966C211yesmaximal, characteristic, complemented
7C3×#1736C211yesmaximal, characteristic, complemented
8#68825C212yesmaximal, complemented
9#68824C212yesmaximal, complemented
10#68823C212yesmaximal, complemented
11#68822C212yesmaximal, complemented
12#23482—31nomaximal, Sylow
13C22×#235C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C2×C3×#117C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4—21no—
19C22×C4⋊Dic3C2211yescharacteristic
20C22×#208C2211yescharacteristic
21#5524—24no—
22#5524—24no—
23C2×#897C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#886—21no—
28C2×#882—21no—
29C2×C4×D12—21no—
30C2×C4×D12—21no—
31C2×C3⋊#95—21no—
32#5133—24no—
33#5126—24no—
34C2×#821C2212yescomplemented
35C2×(C2×D3)⋊C8C2212yes—
36C2×(C2×D3)⋊C8C2212yes—
37C2×#816C2212yescomplemented
38#4995—24no—
39#4987—21no—
40#4987—21no—
41#4987C2212yes—
42#4987C2212yes—
43C2×#810C2212yescomplemented
44#4966—24no—
45C2×#809C2212yescomplemented
46C2×#808C2212yescomplemented
47C2×#807C2212yescomplemented
48C3×#340C2212yescomplemented
49C3×#340C2212yescomplemented
50C2×#525—31no—
51C2×#428—31no—
52C2×#417—31no—
53C2×#417—31no—
54C2×#407—31no—
55C2×#380—31no—
56#2036—32no—
57#2035—32no—
58#2034—32no—
59#2033—32no—
60#1736D311yescharacteristic, complemented
61C24×D3D411yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4C2311yescharacteristic
64C22×#67—21no—
65C23×Dic3—21no—
66C23×Dic3D411yescharacteristic
67C2×#235—22no—
68C2×#235—22no—
69C2×#235—22no—
70C2×#235—22no—
71C2×#235—22no—
72C2×#235D414yes—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12C2311yescharacteristic
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—21no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×M16—22no—
89C2×C3×M16—22no—
90C2×C3×M16—22no—
91C22×C3×C8C2312yes—
92C3×#117—22no—
93C3×#117D414yes—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2312yes—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—44no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3C2312yes—
115C2×#208—22no—
116C2×#208—22no—
117C2×#208D414yescomplemented
118C22×C3⋊C8C2312yes—
119#897—22no—
120#897—22no—
121#897—22no—
122#897—22no—
123#895—22no—
124#895—22no—
125#895—22no—
126#895—22no—
127#886—28no—
128#882—28no—
129C4×D12—28no—
130C4×D12—28no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133#821—24no—
134(C2×D3)⋊C8—24no—
135(C2×D3)⋊C8—24no—
136#816—24no—
137#810—24no—
138#809—24no—
139#808—24no—
140#807—24no—
141C22×#41—31no—
142C24×C4—31no—
143C22×M16—31no—
144C22×M16C2×D311yescharacteristic
145#525—64no—
146#525—64no—
147C2×#123—61no—
148C2×C22⋊Q8—31no—
149C2×C22⋊Q8—31no—
150C2×#121—31no—
151C2×#121—31no—
152C2×#120—61no—
153C2×C4×D4—61no—
154C2×C4×D4—61no—
155C2×#117C2×D311yescharacteristic
156C22×C4⋊C4—31no—
157C22×C4⋊C4C2×D311yescharacteristic
158C22×C22⋊C4—61no—
159#428—64no—
160C2×#107—32no—
161C2×#106—32no—
162#417—64no—
163#417—64no—
164C2×#103—32no—
165C2×#103—32no—
166C2×#102—32no—
167C2×#102—32no—
168#407—64no—
169C2×C22⋊C8—32no—
170C2×C22⋊C8—32no—
171#380—32no—
172#380—32no—
173#380—61no—
174#380—61no—
175C2×#95—61no—
176#340C2×D312yescomplemented
177#340C2×D312yescomplemented
178C24×C3C2×D411yescharacteristic
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—21no—
185C23×D3—41no—
186C23×D3—41no—
187C23×D3C2×D411yescharacteristic
188C23×D3C2×D411yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D411yescharacteristic
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×C3×C4#4112yes—
202C22×C3×C4C2411yescharacteristic
203C2×#67—24no—
204C2×#67—42no—
205C2×#67—42no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—42no—
212C22×Dic3—42no—
213C22×Dic3—42no—
214C22×Dic3C2×D411yescharacteristic
215C22×Dic3C2×D411yescharacteristic
216#235—28no—
217#235—28no—
218#235—44no—
219#235—44no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—24no—
225C2×D12—24no—
226C2×D12—21no—
227C2×D12—42no—
228C2×D12—42no—
229C2×D12—42no—
230C2×D12—42no—
231C2×D12C2×D412yes—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—24no—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—44no—
252C2×C4×D3—44no—
253C2×C4×D3—42no—
254C2×C4×D3—44no—
255C2×C4×D3—42no—
256C2×C4×D3—44no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6C2×D412yes—
263C3×M16—44no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4C2×D412yes—
273C3×C4⋊C4C2×D412yes—
274C3×C22⋊C4—24no—
275C3×C42—24no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—44no—
281(C2×D3)⋊C4—44no—
282C4⋊Dic3—24no—
283C4⋊Dic3—24no—
284C4⋊Dic3—22no—
285C4⋊Dic3—22no—
286C4⋊Dic3—42no—
287#208—28no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8C2×D414yes—
291C25—31no—
292C2×#41—34no—
293C2×#41—62no—
294C2×#41—62no—
295C2×#41—62no—
296C2×#41—62no—
297C2×#41—62no—
298C22×Q8—31no—
299C22×D4—31no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4—61no—
303C23×C4—21no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—61no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—62no—
316C23×C4—61no—
317C23×C4C22×D311yescharacteristic
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—34no—
322C2×M16—62no—
323C2×M16—62no—
324C22×C8—32no—
325C22×C8C22×D312yes—
326#123—68no—
327C22⋊Q8—62no—
328C22⋊Q8—62no—
329C22⋊Q8—62no—
330C22⋊Q8—62no—
331#121—62no—
332#121—62no—
333#121—62no—
334#121—62no—
335#120—68no—
336C4×D4—68no—
337C4×D4—68no—
338#117—22no—
339#117D1214yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4C22×D312yes—
350C2×C4⋊C4C22×D311yescharacteristic
351C2×C4⋊C4C22×D311yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—124no—
360C2×C42—21no—
361#107—64no—
362#106—64no—
363#103—64no—
364#103—64no—
365#102—64no—
366#102—64no—
367C22⋊C8—64no—
368C22⋊C8—64no—
369#95—62no—
370#95—62no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3#12012yes—
376C23×C3#12112yes—
377C23×C3#12312yes—
378C23×C3C22×D411yescharacteristic
379C22×D3—28no—
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—21no—
383C22×D3—21no—
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—22no—
393C22×D3—44no—
394C22×D3—44no—
395C22×D3—44no—
396C22×D3—44no—
397C22×D3—44no—
398C22×D3—44no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3AGL(1,ℤ/8)12yes—
406C22×D3#13712yes—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—84no—
417C2×C3×C4#12012yes—
418C2×C3×C4#12114yes—
419C2×C3×C4#12112yes—
420C2×C3×C4#12114yes—
421C2×C3×C4#12314yes—
422C2×C3×C4#12312yes—
423C2×C3×C4#12414yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430#67—48no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—44no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—84no—
445D12—22no—
446D12—22no—
447D12—48no—
448D12—48no—
449D12—41no—
450D12—41no—
451C4×D3—41no—
452C4×D3—41no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—41no—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—44no—
460C4×D3—44no—
461C4×D3—48no—
462Dic6—22no—
463Dic6—22no—
464Dic6—41no—
465Dic6—41no—
466C3×C8—42no—
467C3⋊C8—24no—
468C24—31no—
469C24—31no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—61no—
476C24—121no—
477C24—121no—
478C24D3×D411yescharacteristic
479#41—68no—
480#41—68no—
481#41—124no—
482#41—124no—
483C2×Q8—32no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×D4—32no—
490C2×D4—64no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—122no—
499C2×D4—122no—
500C2×D4—122no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4—122no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—64no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—124no—
537C22×C4—124no—
538C22×C4—122no—
539C22×C4—124no—
540C22×C4—122no—
541C22×C4—124no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4—122no—
545C22×C4C2×D1212yes—
546C22×C4#23512yes—
547C22×C4#23512yes—
548C22×C4D3×D411yescharacteristic
549C22×C4D3×D412yes—
550C22×C4D3×D412yes—
551C22×C4#23912yes—
552C22×C4C23×D311yescharacteristic
553M16—44no—
554M16—68no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—34no—
559C2×C8—62no—
560C2×C8—62no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—42no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—122no—
571C4⋊C4C2×D1212yes—
572C4⋊C4C2×D1212yes—
573C22⋊C4—24no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C42—24no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3#39414yes—
588C22×C3C2×#12011yescharacteristic
589C22×C3C2×#12111yescharacteristic
590C22×C3C2×#12311yescharacteristic
591C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
592C22×C3C2×#13711yescharacteristic
593C22×C3#57511yescharacteristic
594C22×C3#57511yescharacteristic
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—416no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—82no—
620C3×C4#39414yes—
621C3×C4C2×#12111yescharacteristic
622C3×C4C2×#12111yescharacteristic
623C3×C4C2×#12311yescharacteristic
624C3×C4C2×#12411yescharacteristic
625Dic3—42no—
626Dic3—41no—
627Dic3—41no—
628Dic3—82no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—32no—
634C23—32no—
635C23—68no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—62no—
649C23—124no—
650C23—124no—
651C23—124no—
652C23—124no—
653C23—124no—
654C23—124no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23#88212yes—
662C23#88412yes—
663C23#89412yes—
664C23C2×D3×D411yescharacteristic
665Q8—62no—
666Q8—62no—
667Q8—121no—
668Q8—121no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—128no—
673D4—128no—
674D4—121no—
675D4—121no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—62no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—84no—
693C2×C4—124no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—124no—
697C2×C4—124no—
698C2×C4—128no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—244no—
711C2×C4#87514yes—
712C2×C4#88212yes—
713C2×C4#88412yes—
714C2×C4#88414yes—
715C2×C4#89412yes—
716C2×C4#89414yes—
717C2×C4#89514yes—
718C2×C4C22×D1211yescharacteristic
719C2×C4C2×#23511yescharacteristic
720C2×C4C2×#23511yescharacteristic
721C2×C4C2×D3×D411yescharacteristic
722C2×C4C2×D3×D411yescharacteristic
723C2×C4C2×#23911yescharacteristic
724C8—42no—
725C8—64no—
726C2×C3—24no—
727C2×C3C2×#39411yescharacteristic
728C2×C3#300611yescharacteristic
729C2×C3#300711yescharacteristic
730C2×C3#305511yescharacteristic
731C2×C3#305611yescharacteristic
732C2×C3#309211yescharacteristic
733C2×C3#309311yescharacteristic
734D3—42no—
735D3—42no—
736D3—82no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—62no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—1216no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22#467214yes—
766C22C2×#88211yescharacteristic
767C22C2×#88411yescharacteristic
768C22C2×#89411yescharacteristic
769C22D3×AGL(1,ℤ/8)11yescharacteristic
770C22#577311yescharacteristic
771C22D3×#13711yescharacteristic
772C22#577711yescharacteristic
773C4—42no—
774C4—42no—
775C4—82no—
776C4—121no—
777C4—121no—
778C4—122no—
779C4—242no—
780C4#467214yes—
781C4C2×#87511yescharacteristic
782C4C2×#88411yescharacteristic
783C4C2×#89411yescharacteristic
784C4C2×#89511yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—122no—
788C2—122no—
789C2—242no—
790C2C2×#467211yescharacteristic
791C2#7888411yescharacteristic
792C2#7888511yescharacteristic
793C2#7893011yescharacteristic
794C2#7896211yescharacteristic
795C2#7921511yescharacteristic
796C2#7921611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1736C2
socleC23×C3C22×D4
prime radicalC2×#5524C2
hypercenter#1736D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#5133C2semidirect
3. C2×#5126C2semidirect
4. C2×#4995C2semidirect
5. C2×#4987C2semidirect
6. C2×#4966C2semidirect
7. C3×#1736C2semidirect
8. #68825C2semidirect
9. #68824C2semidirect
10. #68823C2semidirect
11. #68822C2semidirect
34. C2×#821C22semidirect
37. C2×#816C22semidirect
43. C2×#810C22semidirect
45. C2×#809C22semidirect
46. C2×#808C22semidirect
47. C2×#807C22semidirect
48. C3×#340C22semidirect
49. C3×#340C22semidirect
60. #1736D3semidirect
117. C2×#208D4semidirect
176. #340C2×D3semidirect
177. #340C2×D3semidirect
785. C3#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#55242
C2×#51332
C2×#51262
C2×#49952
C2×#49872
C2×#49662
C3×#17362
#688252
#688242
#688232
#688222
#234823