Finite Group Databasebeta

← #357694

Subgroups — #357694

Order 512.

2734 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic, complemented
2C2×#2896C211yesmaximal, characteristic
3C22×#417C211yesmaximal, characteristic
4C2×#2879C211yesmaximal, characteristic
5C2×#1742C211yesmaximal, characteristic, complemented
6C22×#343C211yesmaximal, characteristic, complemented
7C2×#1738C211yesmaximal, characteristic, complemented
8#11107C214yesmaximal, complemented
9#11106C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C2×#428—22no—
18C2×#428—22no—
19C2×#428—24no—
20C2×#428—24no—
21C22×#107C2212yescomplemented
22C22×#106C2212yescomplemented
23#2896—24no—
24#2896—24no—
25C2×#417—22no—
26C2×#417—24no—
27C2×#417—24no—
28C2×#417C2212yes—
29C2×#417C2214yes—
30C2×#417C2212yes—
31C2×#419—21no—
32C2×#418—21no—
33C2×#416—22no—
34C22×#103—21no—
35C22×#102—21no—
36#2879—24no—
37#2879C418yescomplemented
38C2×#408—22no—
39C2×#408C2214yes—
40C2×#407—22no—
41#1742—24no—
42C2×#343—24no—
43C2×#343C2212yescomplemented
44C2×#343C2214yescomplemented
45C2×#343C2212yescomplemented
46#1738—24no—
47C2×#341C2214yescomplemented
48C22×#41—21no—
49C22×#41—22no—
50C22×#41—21no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41C2×C414yes—
61C22×#41D412yes—
62C22×#41Q814yes—
63C22×#41C2312yes—
64C23×Q8D411yescharacteristic
65C23×D4—21no—
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—21no—
77C22×M16—22no—
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16C2×C414yes—
93C22×M16C2×C414yes—
94C22×M16D414yes—
95C22×M16D414yes—
96C22×M16D412yes—
97C22×M16D412yes—
98C22×M16D414yes—
99C22×M16C2312yes—
100C22×M16C2312yes—
101C22×M16C2312yes—
102C23×C8—21no—
103C23×C8—21no—
104C23×C8—21no—
105C23×C8C2312yes—
106C2×#117—22no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117D414yes—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—22no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4D414yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C42—21no—
128#428—216no—
129#428—216no—
130C2×#107—24no—
131C2×#107—24no—
132C2×#107—24no—
133C2×#106—24no—
134C2×#106—24no—
135C2×#106—24no—
136#419—28no—
137#418—28no—
138#417—216no—
139#417—28no—
140#417—24no—
141#417—24no—
142#417—28no—
143#417—24no—
144#417—24no—
145#416—216no—
146C2×#103—28no—
147C2×#103—24no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#102—28no—
151C2×#102—24no—
152C2×#102—22no—
153C2×#102—22no—
154#408—216no—
155#408—28no—
156#408C2×C4116yescomplemented
157#407—216no—
158C2×C22⋊C8—28no—
159#343—28no—
160#343—24no—
161#343—24no—
162#341—28no—
163C25—21no—
164C25#4111yescharacteristic
165C2×#41—24no—
166C2×#41—24no—
167C2×#41—24no—
168C2×#41—24no—
169C2×#41—24no—
170C2×#41—22no—
171C2×#41—22no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—24no—
183C2×#41—24no—
184C2×#41—22no—
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—22no—
188C2×#41—22no—
189C2×#41—22no—
190C2×#41—22no—
191C2×#41—22no—
192C2×#41—42no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41—44no—
196C2×#41—44no—
197C2×#41—42no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—44no—
201C2×#41—44no—
202C2×#41—42no—
203C2×#41—44no—
204C2×#41—44no—
205C2×#41—42no—
206C2×#41—42no—
207C2×#41—42no—
208C2×#41C4⋊C418yes—
209C2×#41C22×C414yes—
210C2×#41C2×Q814yes—
211C22×Q8—21no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8C4⋊C414yes—
218C22×Q8C2×D412yes—
219C22×D4—24no—
220C22×D4—22no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—21no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4C4⋊C414yes—
234C22×D4C2×D412yes—
235C23×C4—21no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—22no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4—84no—
252C23×C4C22×C412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D412yes—
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×Q812yes—
263C23×C4#4111yescharacteristic
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4C2411yescharacteristic
270C2×M16—28no—
271C2×M16—28no—
272C2×M16—24no—
273C2×M16—24no—
274C2×M16—28no—
275C2×M16—28no—
276C2×M16—24no—
277C2×M16—24no—
278C2×M16—24no—
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—22no—
282C2×M16—22no—
283C2×M16—22no—
284C2×M16—28no—
285C2×M16—28no—
286C2×M16—28no—
287C2×M16—28no—
288C2×M16—28no—
289C2×M16—28no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—42no—
303C2×M16—42no—
304C2×M16—44no—
305C2×M16—44no—
306C2×M16—44no—
307C2×M16—44no—
308C2×M16—42no—
309C2×M16—42no—
310C2×M16—42no—
311C2×M16—44no—
312C2×M16—44no—
313C2×M16—42no—
314C2×M16C22⋊C418yes—
315C2×M16C22⋊C418yes—
316C2×M16C22×C414yes—
317C2×M16C2×D414yes—
318C2×M16C2×D414yes—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—24no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—42no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8—42no—
333C22×C8—42no—
334C22×C8—42no—
335C22×C8C22×C414yes—
336C22×C8C2×D414yes—
337C22×C8C2×D414yes—
338#117—24no—
339#117—24no—
340#117—24no—
341#117—24no—
342#117—42no—
343#117—42no—
344#117—42no—
345#117—42no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4C2×D412yes—
375C2×C4⋊C4C2×D412yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C42—24no—
381C2×C42—42no—
382C2×C42—41no—
383C2×C42—41no—
384#107—216no—
385#106—216no—
386#103—216no—
387#103—28no—
388#103—28no—
389#102—216no—
390#102—28no—
391#102—28no—
392C22⋊C8—232no—
393C24—22no—
394C24—24no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—82no—
400C24—82no—
401C24#11712yes—
402C24#12111yescharacteristic
403C24#12111yescharacteristic
404C24#12112yes—
405C24#12112yes—
406C24C22⋊Q812yes—
407C24#12612yes—
408C24#12612yes—
409C24C2×#4111yescharacteristic
410#41—24no—
411#41—24no—
412#41—24no—
413#41—24no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—24no—
418#41—216no—
419#41—216no—
420#41—42no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—42no—
427#41—42no—
428#41—48no—
429#41—48no—
430#41—48no—
431#41—48no—
432#41—48no—
433#41—48no—
434#41—48no—
435#41—48no—
436#41—48no—
437#41—48no—
438C2×Q8—22no—
439C2×Q8—24no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—42no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—42no—
450C2×Q8C2×C4⋊C414yes—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—28no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4C2×C4⋊C414yes—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—44no—
496C22×C4—48no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—84no—
506C22×C4—84no—
507C22×C4—88no—
508C22×C4—82no—
509C22×C4—82no—
510C22×C4—84no—
511C22×C4—88no—
512C22×C4C2×C22⋊C412yes—
513C22×C4C2×C22⋊C412yes—
514C22×C4C2×C4⋊C412yes—
515C22×C4C2×C4⋊C412yes—
516C22×C4#11712yes—
517C22×C4C4×D414yes—
518C22×C4C4×D414yes—
519C22×C4C4×D414yes—
520C22×C4C4×D414yes—
521C22×C4#12012yes—
522C22×C4#12012yes—
523C22×C4#12012yes—
524C22×C4#12012yes—
525C22×C4#12012yes—
526C22×C4#12012yes—
527C22×C4#12112yes—
528C22×C4#12112yes—
529C22×C4#12114yes—
530C22×C4#12114yes—
531C22×C4#12114yes—
532C22×C4#12114yes—
533C22×C4#12111yescharacteristic
534C22×C4#12111yescharacteristic
535C22×C4#12112yes—
536C22×C4#12112yes—
537C22×C4C22⋊Q812yes—
538C22×C4C22⋊Q812yes—
539C22×C4C22⋊Q814yes—
540C22×C4C22⋊Q814yes—
541C22×C4C22⋊Q814yes—
542C22×C4C22⋊Q814yes—
543C22×C4C22⋊Q812yes—
544C22×C4#12312yes—
545C22×C4#12312yes—
546C22×C4#12312yes—
547C22×C4#12312yes—
548C22×C4#12312yes—
549C22×C4#12312yes—
550C22×C4#12314yes—
551C22×C4#12314yes—
552C22×C4#12414yes—
553C22×C4#12414yes—
554C22×C4#12412yes—
555C22×C4#12412yes—
556C22×C4#12612yes—
557C22×C4#12612yes—
558C22×C4#12712yes—
559C22×C4#12712yes—
560C22×C4C23×C411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×Q811yescharacteristic
569C22×C4C2×#4111yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574M16—216no—
575M16—216no—
576M16—24no—
577M16—24no—
578M16—24no—
579M16—24no—
580M16—24no—
581M16—24no—
582M16—42no—
583M16—42no—
584M16—42no—
585M16—42no—
586M16—42no—
587M16—42no—
588M16—48no—
589M16—48no—
590M16—48no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—42no—
604C2×C8—42no—
605C2×C8—42no—
606C2×C8—48no—
607C2×C8—48no—
608C2×C8—48no—
609C2×C8C2×C22⋊C418yes—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—42no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—42no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C42—44no—
627C42—44no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—42no—
639C23—42no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—48no—
646C23—44no—
647C23—44no—
648C23—88no—
649C23—88no—
650C23—84no—
651C23—84no—
652C23#38012yes—
653C23#38012yes—
654C23#38814yes—
655C23#38814yes—
656C23#39212yes—
657C23#39212yes—
658C23#39614yes—
659C23#39614yes—
660C23#39712yes—
661C23#39712yes—
662C23C2×#11711yescharacteristic
663C23C2×#12111yescharacteristic
664C23C2×#12111yescharacteristic
665C23C2×#12111yescharacteristic
666C23C2×C22⋊Q811yescharacteristic
667C23C2×#12611yescharacteristic
668C23C2×#12611yescharacteristic
669Q8—24no—
670Q8—24no—
671Q8—42no—
672Q8—42no—
673Q8—48no—
674D4—24no—
675D4—24no—
676D4—44no—
677D4—44no—
678D4—416no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—48no—
684C2×C4—24no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—416no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—88no—
699C2×C4—84no—
700C2×C4—88no—
701C2×C4—82no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—84no—
707C2×C4#38012yes—
708C2×C4#38012yes—
709C2×C4#38514yes—
710C2×C4#38514yes—
711C2×C4#38514yes—
712C2×C4#38514yes—
713C2×C4#38614yes—
714C2×C4#38614yes—
715C2×C4#38814yes—
716C2×C4#38814yes—
717C2×C4#39014yes—
718C2×C4#39014yes—
719C2×C4#39212yes—
720C2×C4#39212yes—
721C2×C4#39314yes—
722C2×C4#39314yes—
723C2×C4#39414yes—
724C2×C4#39414yes—
725C2×C4#39414yes—
726C2×C4#39414yes—
727C2×C4#39614yes—
728C2×C4#39614yes—
729C2×C4#39712yes—
730C2×C4#39712yes—
731C2×C4#39914yes—
732C2×C4#39914yes—
733C2×C4C22×C22⋊C411yescharacteristic
734C2×C4C22×C4⋊C411yescharacteristic
735C2×C4C2×C4×D411yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×#12011yescharacteristic
740C2×C4C2×#12011yescharacteristic
741C2×C4C2×#12011yescharacteristic
742C2×C4C2×#12111yescharacteristic
743C2×C4C2×#12111yescharacteristic
744C2×C4C2×#12111yescharacteristic
745C2×C4C2×#12111yescharacteristic
746C2×C4C2×#12111yescharacteristic
747C2×C4C2×C22⋊Q811yescharacteristic
748C2×C4C2×C22⋊Q811yescharacteristic
749C2×C4C2×C22⋊Q811yescharacteristic
750C2×C4C2×C22⋊Q811yescharacteristic
751C2×C4C2×C22⋊Q811yescharacteristic
752C2×C4C2×#12311yescharacteristic
753C2×C4C2×#12311yescharacteristic
754C2×C4C2×#12311yescharacteristic
755C2×C4C2×#12311yescharacteristic
756C2×C4C2×#12311yescharacteristic
757C2×C4C2×#12411yescharacteristic
758C2×C4C2×#12411yescharacteristic
759C2×C4C2×#12411yescharacteristic
760C2×C4C2×#12711yescharacteristic
761C8—28no—
762C8—44no—
763C8—44no—
764C8—44no—
765C22—24no—
766C22—22no—
767C22—22no—
768C22—24no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—22no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—24no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—48no—
787C22—816no—
788C22—84no—
789C22—82no—
790C22—82no—
791C22#143914yes—
792C22#143914yes—
793C22C2×#38011yescharacteristic
794C22C2×#38811yescharacteristic
795C22C2×#38811yescharacteristic
796C22C2×#39211yescharacteristic
797C22C2×#39611yescharacteristic
798C22C2×#39611yescharacteristic
799C22C2×#39711yescharacteristic
800C22#306812yes—
801C22#306912yes—
802C4—44no—
803C4—82no—
804C4—84no—
805C4—82no—
806C4#143914yes—
807C4#143914yes—
808C4C2×#38511yescharacteristic
809C4C2×#38511yescharacteristic
810C4C2×#38611yescharacteristic
811C4C2×#39011yescharacteristic
812C4C2×#39311yescharacteristic
813C4C2×#39411yescharacteristic
814C4C2×#39411yescharacteristic
815C4C2×#39911yescharacteristic
816C2—24no—
817C2—21no—
818C2—21no—
819C2—24no—
820C2—21no—
821C2—21no—
822C2—84no—
823C2C2×#143911yescharacteristic
824C2#2067912yes—
825C2#2343911yescharacteristic
826C2#2344011yescharacteristic
827C2#2364712yes—
subgroupG/H
center, socleC23C2×#121
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#428C2semidirect
5. C2×#1742C2semidirect
6. C22×#343C2semidirect
7. C2×#1738C2semidirect
8. #11107C2semidirect
9. #11106C2semidirect
21. C22×#107C22semidirect
22. C22×#106C22semidirect
37. #2879C4semidirect
43. C2×#343C22semidirect
44. C2×#343C22semidirect
45. C2×#343C22semidirect
47. C2×#341C22semidirect
156. #408C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#28962
C22×#4172
C2×#28792
C2×#17422
C22×#3432
C2×#17382
#111072
#111062