Finite Group Databasebeta

← #10702079

Subgroups — #10702079

Order 768.

1252 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic
2C2×#5236C211yesmaximal, characteristic, complemented
3C2×#5237C211yesmaximal, characteristic, complemented
4#84074C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6#71998C211yesmaximal, characteristic, complemented
7C2×#4556C211yesmaximal, characteristic, complemented
8#11037—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×#41C2211yescharacteristic
11C3×#575—22no—
12C3×#575—22no—
13C3×#575—22no—
14C3×#575C414yescomplemented
15C2×C3×#137—21no—
16C2×C3×#137—21no—
17C2×C3×AGL(1,ℤ/8)—21no—
18C2×C3×AGL(1,ℤ/8)—21no—
19C2×C3×#135—22no—
20C22×C3×M16C2211yescharacteristic
21C2×#926C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C22×#208C2211yescharacteristic
25#5237—22no—
26#5237—22no—
27#5236—22no—
28#5236—22no—
29C2×#837—22no—
30#5234—22no—
31#5234—22no—
32#5233—22no—
33#5232—22no—
34C2×#836—21no—
35#5225—21no—
36C2×#833—21no—
37#5215—21no—
38#5207—22no—
39#4556—22no—
40#4552—22no—
41C2×#575D311yescharacteristic
42C2×#421—31no—
43#2896—31no—
44C2×#413—31no—
45#2879—31no—
46C2×#344—31no—
47#1738—31no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41—21no—
58C2×C3×#41—21no—
59C2×C3×#41—21no—
60C2×C3×#41—21no—
61C2×C3×#41—21no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×#41—21no—
65C2×C3×#41—21no—
66C2×C3×#41—21no—
67C2×C3×#41—21no—
68C2×C3×#41C2×C412yes—
69C2×C3×#41C2×C412yes—
70C2×C3×#41D412yes—
71C2×C3×#41D412yes—
72C22×C3×Q8D411yescharacteristic
73C22×C3×Q8D411yescharacteristic
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4D411yescharacteristic
77C22×C3×D4D411yescharacteristic
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C3×#137—24no—
82C3×#137—24no—
83C3×#137—24no—
84C3×#137—24no—
85C3×AGL(1,ℤ/8)—24no—
86C3×AGL(1,ℤ/8)—24no—
87C3×AGL(1,ℤ/8)—24no—
88C3×AGL(1,ℤ/8)—24no—
89C3×#135—28no—
90C3×#135—28no—
91C2×C3×Q16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×D8—22no—
95C2×C3×M16—21no—
96C2×C3×M16—21no—
97C2×C3×M16—21no—
98C2×C3×M16—21no—
99C2×C3×M16C2×C412yes—
100C2×C3×M16D412yes—
101C22×C3×C8D412yes—
102C2×#217—21no—
103#926—21no—
104#926—21no—
105#926—21no—
106#926D412yes—
107C2×C4⋊Dic3—21no—
108C2×C4×Dic3—21no—
109C2×#208—21no—
110C2×#208—21no—
111C2×#208—21no—
112C2×#208—21no—
113C2×#208—21no—
114C2×#208—21no—
115C2×#208—21no—
116C2×#208—21no—
117C2×#208—21no—
118C2×#208—21no—
119C2×#208—21no—
120C2×#208—21no—
121C2×#208—21no—
122C2×#208—21no—
123C2×#208—21no—
124C2×#208D412yes—
125C2×#208D412yes—
126C2×#208D412yes—
127C22×C3⋊C8—21no—
128C22×C3⋊C8—21no—
129C22×C3⋊C8—21no—
130#837—28no—
131#836—24no—
132#835—24no—
133#833—24no—
134#832—24no—
135#830—28no—
136C22×#41C2×D311yescharacteristic
137C22×#41C2×D311yescharacteristic
138#575—22no—
139#575—22no—
140#575—22no—
141#575Dic314yescomplemented
142C2×#137—21no—
143C2×#137—21no—
144C2×AGL(1,ℤ/8)—21no—
145C2×AGL(1,ℤ/8)—21no—
146C2×#135—22no—
147C22×M16—31no—
148C22×M16—31no—
149C22×M16—31no—
150C22×M16C2×D311yescharacteristic
151C2×#117—31no—
152#421—62no—
153#421—62no—
154C2×#104—62no—
155#419—61no—
156#418—61no—
157#417—62no—
158#416—62no—
159#413—62no—
160#413—62no—
161C2×#101—61no—
162C2×#100—61no—
163#408—62no—
164#408—62no—
165#407—62no—
166#344—62no—
167#341—62no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3#4111yescharacteristic
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—41no—
188C3×#41—41no—
189C3×#41—41no—
190C3×#41—41no—
191C3×#41—41no—
192C3×#41—41no—
193C3×#41—41no—
194C3×#41—41no—
195C3×#41—41no—
196C3×#41—41no—
197C3×#41—41no—
198C3×#41—41no—
199C3×#41—41no—
200C3×#41—41no—
201C3×#41—41no—
202C3×#41—41no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8C22⋊C412yes—
214C2×C3×Q8C22⋊C412yes—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—41no—
230C2×C3×D4—41no—
231C2×C3×D4—41no—
232C2×C3×D4—41no—
233C2×C3×D4—41no—
234C2×C3×D4—41no—
235C2×C3×D4—41no—
236C2×C3×D4—41no—
237C2×C3×D4C22⋊C412yes—
238C2×C3×D4C22⋊C412yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—41no—
246C22×C3×C4—41no—
247C22×C3×C4—41no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4—41no—
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4#4111yescharacteristic
265C22×C3×C4#4111yescharacteristic
266C22×C3×C4#4111yescharacteristic
267C22×Dic3—41no—
268C3×Q16—28no—
269C3×SD16—28no—
270C3×SD16—28no—
271C3×D8—28no—
272C3×M16—22no—
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—22no—
276C2×C3×C8—22no—
277C2×C3×C8—22no—
278C2×C3×C8C22⋊C414yes—
279#217—22no—
280#217—41no—
281C4⋊Dic3—22no—
282C4⋊Dic3—41no—
283C4×Dic3—22no—
284C4×Dic3—41no—
285#208—22no—
286#208—22no—
287#208—22no—
288#208—22no—
289#208—22no—
290#208—22no—
291#208—41no—
292#208—41no—
293#208—41no—
294#208—41no—
295#208—41no—
296#208—41no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—41no—
301C2×C3⋊C8—41no—
302C2×C3⋊C8—41no—
303C2×C3⋊C8—41no—
304C2×C3⋊C8—41no—
305C2×C3⋊C8—41no—
306C2×#41—21no—
307C2×#41—21no—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41C2×Dic312yes—
327C2×#41C2×Dic312yes—
328C2×#41#6712yes—
329C2×#41#6712yes—
330C22×Q8#6711yescharacteristic
331C22×Q8#6711yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4#6711yescharacteristic
335C22×D4#6711yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4C22×D311yescharacteristic
339#137—24no—
340#137—24no—
341#137—24no—
342#137—24no—
343AGL(1,ℤ/8)—24no—
344AGL(1,ℤ/8)—24no—
345AGL(1,ℤ/8)—24no—
346AGL(1,ℤ/8)—24no—
347#135—28no—
348#135—28no—
349C2×Q16—22no—
350C2×SD16—22no—
351C2×SD16—22no—
352C2×D8—22no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—32no—
358C2×M16—32no—
359C2×M16—32no—
360C2×M16—61no—
361C2×M16—61no—
362C2×M16—61no—
363C2×M16—61no—
364C2×M16—61no—
365C2×M16—61no—
366C2×M16—61no—
367C2×M16—61no—
368C2×M16—61no—
369C2×M16—61no—
370C2×M16—61no—
371C2×M16—61no—
372C2×M16—61no—
373C2×M16—61no—
374C2×M16—61no—
375C2×M16C2×Dic312yes—
376C2×M16#6712yes—
377C22×C8—61no—
378C22×C8—61no—
379C22×C8—61no—
380C22×C8#6712yes—
381#117—32no—
382#117—61no—
383#117—61no—
384#117—61no—
385C2×C4⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—61no—
388#104—68no—
389#103—64no—
390#102—64no—
391#101—64no—
392#100—64no—
393C22⋊C8—68no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—81no—
401C23×C3—82no—
402C23×C3—82no—
403C23×C3C4×D411yescharacteristic
404C23×C3#12111yescharacteristic
405C23×C3#12111yescharacteristic
406C23×C3#12111yescharacteristic
407C23×C3#12311yescharacteristic
408C23×C3#12311yescharacteristic
409C23×C3#12411yescharacteristic
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—22no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—42no—
423C3×D4—42no—
424C3×D4—42no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—42no—
428C3×D4—42no—
429C3×D4—42no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4C2×C22⋊C411yescharacteristic
449C2×C3×C4C2×C22⋊C411yescharacteristic
450C2×C3×C4C2×C22⋊C411yescharacteristic
451C2×C3×C4C4×D411yescharacteristic
452C2×C3×C4C4×D411yescharacteristic
453C2×C3×C4C4×D411yescharacteristic
454C2×C3×C4#12011yescharacteristic
455C2×C3×C4#12011yescharacteristic
456C2×C3×C4#12011yescharacteristic
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4#12011yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12111yescharacteristic
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4#12111yescharacteristic
469C2×C3×C4#12111yescharacteristic
470C2×C3×C4#12111yescharacteristic
471C2×C3×C4#12311yescharacteristic
472C2×C3×C4#12311yescharacteristic
473C2×C3×C4#12411yescharacteristic
474C2×C3×C4#12711yescharacteristic
475C2×C3×C4#12711yescharacteristic
476C2×Dic3—42no—
477C2×Dic3—82no—
478C3×C8—24no—
479C3⋊C8—42no—
480C3⋊C8—42no—
481C3⋊C8—42no—
482C24—21no—
483C24—21no—
484C24#23711yescharacteristic
485#41—22no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516#41—41no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#21712yes—
528C2×Q8#21712yes—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4#21712yes—
552C2×D4#21712yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—121no—
568C22×C4D3×D411yescharacteristic
569C22×C4D3×D411yescharacteristic
570C22×C4D3×D411yescharacteristic
571C22×C4D3×D411yescharacteristic
572C22×C4#23711yescharacteristic
573C22×C4#23711yescharacteristic
574C22×C4#23711yescharacteristic
575C22×C4C22×Dic311yescharacteristic
576C22×C4C2×#6711yescharacteristic
577C22×C4C2×#6711yescharacteristic
578C22×C4C2×#6711yescharacteristic
579C22×C4C2×#6711yescharacteristic
580C22×C4C2×#6711yescharacteristic
581C22×C4C2×#6711yescharacteristic
582Q16—28no—
583SD16—28no—
584SD16—28no—
585D8—28no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—22no—
590M16—62no—
591M16—62no—
592M16—62no—
593M16—62no—
594M16—62no—
595M16—62no—
596M16—121no—
597M16—121no—
598M16—121no—
599M16—121no—
600M16—121no—
601M16—121no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—62no—
605C2×C8—62no—
606C2×C8—62no—
607C2×C8—121no—
608C2×C8—121no—
609C2×C8—121no—
610C2×C8—121no—
611C2×C8—121no—
612C2×C8—121no—
613C2×C8#21714yes—
614C4⋊C4—62no—
615C4⋊C4—121no—
616C22⋊C4—62no—
617C22⋊C4—121no—
618C42—62no—
619C42—121no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—44no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—82no—
631C22×C3—82no—
632C22×C3—82no—
633C22×C3—82no—
634C22×C3—82no—
635C22×C3#38611yescharacteristic
636C22×C3#38611yescharacteristic
637C22×C3#39011yescharacteristic
638C22×C3#39211yescharacteristic
639C22×C3#39411yescharacteristic
640C22×C3#39411yescharacteristic
641C22×C3#39411yescharacteristic
642C3×C4—42no—
643C3×C4—42no—
644C3×C4#37911yescharacteristic
645C3×C4#38611yescharacteristic
646C3×C4#38611yescharacteristic
647C3×C4#39011yescharacteristic
648C3×C4#39211yescharacteristic
649C3×C4#39211yescharacteristic
650C3×C4#39211yescharacteristic
651C3×C4#39411yescharacteristic
652Dic3—82no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—81no—
660C23—82no—
661C23—82no—
662C23D4×Dic311yescharacteristic
663C23#93511yescharacteristic
664C23#93511yescharacteristic
665C23#93611yescharacteristic
666C23#93811yescharacteristic
667C23#93911yescharacteristic
668C23#93911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—122no—
708C2×C4—242no—
709C2×C4D4×Dic311yescharacteristic
710C2×C4D4×Dic311yescharacteristic
711C2×C4D4×Dic311yescharacteristic
712C2×C4#93511yescharacteristic
713C2×C4#93511yescharacteristic
714C2×C4#93611yescharacteristic
715C2×C4#93711yescharacteristic
716C2×C4#93711yescharacteristic
717C2×C4#93711yescharacteristic
718C2×C4#93711yescharacteristic
719C2×C4#93811yescharacteristic
720C2×C4#93811yescharacteristic
721C2×C4#93811yescharacteristic
722C2×C4#93911yescharacteristic
723C2×C4#93911yescharacteristic
724C2×C4#93911yescharacteristic
725C2×C4#93911yescharacteristic
726C2×C4#93911yescharacteristic
727C2×C4#93911yescharacteristic
728C2×C4#94011yescharacteristic
729C2×C4#94011yescharacteristic
730C2×C4C2×#21711yescharacteristic
731C2×C4C2×#21711yescharacteristic
732C2×C4C2×#21711yescharacteristic
733C2×C4#95311yescharacteristic
734C2×C4#95311yescharacteristic
735C2×C4#95311yescharacteristic
736C2×C4#95311yescharacteristic
737C8—24no—
738C8—122no—
739C8—122no—
740C8—122no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—82no—
749C2×C3—82no—
750C2×C3#143811yescharacteristic
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22#522011yescharacteristic
767C22#522011yescharacteristic
768C22#522111yescharacteristic
769C22#522211yescharacteristic
770C22#522211yescharacteristic
771C22#522211yescharacteristic
772C22#522311yescharacteristic
773C4—42no—
774C4—42no—
775C4—242no—
776C4#522011yescharacteristic
777C4#522011yescharacteristic
778C4#522111yescharacteristic
779C4#522211yescharacteristic
780C4#522311yescharacteristic
781C4#522311yescharacteristic
782C4#522311yescharacteristic
783C4#524711yescharacteristic
784C3#1103711yescharacteristic, complemented, Sylow
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—82no—
793C2—82no—
794C2#7213111yescharacteristic
subgroupG/H
centerC4#5223
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
Fitting, prime radicalC2×C3×#575C2
socleC2×C3#1438
cosocleC23×C3×C4C23
hypercenterC2×#575D3
hypocenterC3#11037
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. C2×#5236C2semidirect
3. C2×#5237C2semidirect
4. #84074C2semidirect
5. #84072C2semidirect
6. #71998C2semidirect
7. C2×#4556C2semidirect
14. C3×#575C4semidirect
141. #575Dic3semidirect
784. C3#11037semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×#52362
C2×#52372
#840742
#840722
#719982
C2×#45562
#110373