Finite Group Databasebeta

← C2×C4×#1842⋊C3 #72212885

Subgroups — C2×C4×#1842⋊C3 #72212885

Order 3072.

4796 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1842C311yesmaximal, characteristic, complemented, Sylow
2C4×#1842⋊C3C214yesmaximal, direct product factor
3C22×#1842⋊C3C212yesmaximal
4C2×C42×C42⋊C3C211yesmaximal, characteristic
5C2×C4×C8×A4—41nomaximal
6C22×C4×C42⋊C3C412yes—
7C22×C4×C42⋊C3C2211yescharacteristic
8C2×#1842⋊C3C418yesdirect product factor
9C2×#1842⋊C3C2214yes—
10C42×C42⋊C3C412yes—
11C42×C42⋊C3C2212yes—
12C22×#1842C2×C312yes—
13C22×C4×C4⋊C8—31no—
14C22×C4×C4⋊C8—31no—
15C2×C44C2×C311yescharacteristic
16C4×#1842—34no—
17C4×#1842C2×C314yescomplemented
18C2×#10832—32no—
19C22×C8×A4—42no—
20C2×C42×A4—41no—
21C23×C42⋊C3C2×C411yescharacteristic
22C4×C8×A4—44no—
23C2×C4×C42⋊C3C818yescomplemented
24C2×C4×C42⋊C3C2×C411yescharacteristic
25C2×C4×C42⋊C3C2×C414yes—
26C2×C4×C42⋊C3C2×C414yes—
27C2×C4×C42⋊C3C2311yescharacteristic
28#1842⋊C3C2×C418yesdirect product factor
29C23×C4⋊C8—32no—
30C23×C4⋊C8—32no—
31C23×C4×C8—31no—
32C23×C4×C8A411yescharacteristic
33C22×C43—31no—
34C22×C43—32no—
35C22×C43—31no—
36C22×C43C3×C412yes—
37C22×C43C22×C311yescharacteristic
38C2×#1842—38no—
39C2×#1842—34no—
40C2×#1842C3×C418yescomplemented
41C2×#1842C22×C314yes—
42C2×C4×C4⋊C8—34no—
43C2×C4×C4⋊C8—34no—
44C2×C4×C4⋊C8—34no—
45C2×C4×C4⋊C8—34no—
46C2×C4×C4⋊C8—62no—
47C2×C4×C4⋊C8—64no—
48C2×C4×C4⋊C8—62no—
49C2×C4×C4⋊C8—62no—
50C2×C4×C4⋊C8—62no—
51C2×C4×C4⋊C8—64no—
52C22×#336—32no—
53C22×#336—32no—
54C44—32no—
55C44—32no—
56C44C3×C412yes—
57C44C22×C312yes—
58#10832—38no—
59#10832—38no—
60C22×C4×A4—42no—
61C22×C4×A4—41no—
62C2×C8×A4—48no—
63C2×C8×A4—44no—
64C42×A4—42no—
65C42×A4—42no—
66C22×C42⋊C3C4212yes—
67C22×C42⋊C3C2×C814yes—
68C22×C42⋊C3C22×C411yescharacteristic
69C2×C3×C4×C8—161no—
70C4×C42⋊C3C4212yes—
71C4×C42⋊C3C2×C818yescomplemented
72C4×C42⋊C3C22×C412yes—
73C24×C8—32no—
74C24×C8C2×A412yes—
75C23×C42—32no—
76C23×C42—32no—
77C23×C42—32no—
78C23×C42—31no—
79C23×C42—31no—
80C23×C42—32no—
81C23×C42—31no—
82C23×C42C2×C3×C411yescharacteristic
83C23×C42C2×A411yescharacteristic
84C22×C4⋊C8—34no—
85C22×C4⋊C8—38no—
86C22×C4⋊C8—38no—
87C22×C4⋊C8—38no—
88C22×C4⋊C8—34no—
89C22×C4⋊C8—34no—
90C22×C4⋊C8—38no—
91C22×C4⋊C8—34no—
92C22×C4⋊C8—68no—
93C22×C4⋊C8—68no—
94C22×C4⋊C8—64no—
95C22×C4⋊C8—64no—
96C22×C4⋊C8—64no—
97C22×C4⋊C8—64no—
98C22×C4×C8—34no—
99C22×C4×C8—61no—
100C22×C4×C8—64no—
101C22×C4×C8—62no—
102C22×C4×C8—62no—
103C22×C4×C8—61no—
104C22×C4×C8—61no—
105C22×C4×C8—62no—
106C22×C4×C8—61no—
107C22×C4×C8—62no—
108C22×C4×C8C2×A414yes—
109C2×C43—31no—
110C2×C43—34no—
111C2×C43—34no—
112C2×C43—31no—
113C2×C43—38no—
114C2×C43—34no—
115C2×C43—34no—
116C2×C43—32no—
117C2×C43—34no—
118C2×C43—32no—
119C2×C43—32no—
120C2×C43—32no—
121C2×C43—32no—
122C2×C43—32no—
123C2×C43—32no—
124C2×C43—32no—
125C2×C43—34no—
126C2×C43—34no—
127C2×C43—32no—
128C2×C43—32no—
129C2×C43—38no—
130C2×C43—68no—
131C2×C43—616no—
132C2×C43C3×C818yescomplemented
133C2×C43C2×C3×C411yescharacteristic
134C2×C43C2×C3×C414yes—
135C2×C43C2×C3×C414yes—
136C2×C43C23×C311yescharacteristic
137#1842—316no—
138#1842—38no—
139#1842—316no—
140#1842C2×C3×C418yescomplemented
141C4×C4⋊C8—68no—
142C4×C4⋊C8—68no—
143C4×C4⋊C8—68no—
144C4×C4⋊C8—68no—
145C4×C4⋊C8—68no—
146C4×C4⋊C8—68no—
147C4×C4⋊C8—68no—
148C4×C4⋊C8—68no—
149C2×#336—38no—
150C2×#336—38no—
151C2×#336—64no—
152C2×#336—64no—
153C2×#336—64no—
154C2×#336—64no—
155C23×A4—41no—
156C2×C4×A4—48no—
157C2×C4×A4—41no—
158C2×C4×A4—44no—
159C2×C4×A4—44no—
160C2×C4×A4—41no—
161C22×C3×C8—162no—
162C2×C3×C42—161no—
163C8×A4—48no—
164C2×C42⋊C3C4×C814yescomplemented
165C2×C42⋊C3C2×C4211yescharacteristic
166C2×C42⋊C3C22×C812yes—
167C3×C4×C8—164no—
168C24×C4—31no—
169C24×C4—31no—
170C24×C4—32no—
171C24×C4C4×A412yes—
172C24×C4C22×A411yescharacteristic
173C23×C8—38no—
174C23×C8—34no—
175C23×C8—62no—
176C23×C8—64no—
177C23×C8—62no—
178C23×C8—62no—
179C23×C8—64no—
180C23×C8—68no—
181C23×C8—64no—
182C23×C8—62no—
183C23×C8—64no—
184C23×C8C4×A418yes—
185C23×C8C22×A414yes—
186C22×C42—32no—
187C22×C42—34no—
188C22×C42—31no—
189C22×C42—32no—
190C22×C42—32no—
191C22×C42—38no—
192C22×C42—34no—
193C22×C42—38no—
194C22×C42—34no—
195C22×C42—32no—
196C22×C42—32no—
197C22×C42—316no—
198C22×C42—38no—
199C22×C42—38no—
200C22×C42—34no—
201C22×C42—34no—
202C22×C42—31no—
203C22×C42—34no—
204C22×C42—31no—
205C22×C42—34no—
206C22×C42—31no—
207C22×C42—31no—
208C22×C42—31no—
209C22×C42—31no—
210C22×C42—32no—
211C22×C42—32no—
212C22×C42—32no—
213C22×C42—31no—
214C22×C42—34no—
215C22×C42—31no—
216C22×C42—38no—
217C22×C42—34no—
218C22×C42—32no—
219C22×C42—32no—
220C22×C42—34no—
221C22×C42—38no—
222C22×C42—34no—
223C22×C42—38no—
224C22×C42—34no—
225C22×C42—32no—
226C22×C42—32no—
227C22×C42—34no—
228C22×C42—32no—
229C22×C42—32no—
230C22×C42—34no—
231C22×C42—34no—
232C22×C42—32no—
233C22×C42—34no—
234C22×C42—34no—
235C22×C42—68no—
236C22×C42—68no—
237C22×C42—68no—
238C22×C42—68no—
239C22×C42—616no—
240C22×C42—68no—
241C22×C42—616no—
242C22×C42C3×C4212yes—
243C22×C42C2×C3×C814yes—
244C22×C42C4×A412yes—
245C22×C42C22×C3×C411yescharacteristic
246C22×C42C22×A412yes—
247C2×C4⋊C8—38no—
248C2×C4⋊C8—316no—
249C2×C4⋊C8—38no—
250C2×C4⋊C8—38no—
251C2×C4⋊C8—316no—
252C2×C4⋊C8—38no—
253C2×C4⋊C8—68no—
254C2×C4⋊C8—68no—
255C2×C4⋊C8—68no—
256C2×C4⋊C8—68no—
257C2×C4⋊C8—616no—
258C2×C4⋊C8—616no—
259C2×C4⋊C8—616no—
260C2×C4⋊C8—616no—
261C2×C4⋊C8—616no—
262C2×C4⋊C8—616no—
263C2×C4⋊C8—616no—
264C2×C4⋊C8—616no—
265C2×C4⋊C8—68no—
266C2×C4⋊C8—68no—
267C2×C4⋊C8—68no—
268C2×C4⋊C8—68no—
269C2×C4×C8—41no—
270C2×C4×C8—64no—
271C2×C4×C8—68no—
272C2×C4×C8—64no—
273C2×C4×C8—64no—
274C2×C4×C8—68no—
275C2×C4×C8—64no—
276C2×C4×C8—122no—
277C2×C4×C8—121no—
278C2×C4×C8—122no—
279C2×C4×C8—122no—
280C2×C4×C8—124no—
281C2×C4×C8—121no—
282C2×C4×C8—122no—
283C2×C4×C8—122no—
284C2×C4×C8—124no—
285C2×C4×C8—121no—
286C43—34no—
287C43—32no—
288C43—316no—
289C43—34no—
290C43—32no—
291C43—38no—
292C43—34no—
293C43—34no—
294C43—34no—
295C43—34no—
296C43—38no—
297C43—34no—
298C43—38no—
299C43—38no—
300C43—38no—
301C43—34no—
302C43—316no—
303C43—34no—
304C43—34no—
305C43—34no—
306C43—34no—
307C43—68no—
308C43—68no—
309C43—68no—
310C43—616no—
311C43—616no—
312C43—68no—
313C43—632no—
314C43C3×C4212yes—
315C43C2×C3×C818yescomplemented
316C43C22×C3×C412yes—
317#336—616no—
318#336—616no—
319C22×A4—41no—
320C22×A4—42no—
321C22×A4—44no—
322C22×C3×C4—162no—
323C22×C3×C4—161no—
324C4×A4—42no—
325C4×A4—42no—
326C4×A4—48no—
327C2×C3×C8—164no—
328C2×C3×C8—168no—
329C3×C42—162no—
330C3×C42—162no—
331C42⋊C3C2×C4×C811yescharacteristic, complemented
332C25C2×C4×A411yescharacteristic
333C23×C4—32no—
334C23×C4—32no—
335C23×C4—34no—
336C23×C4—38no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—32no—
340C23×C4—32no—
341C23×C4—34no—
342C23×C4—34no—
343C23×C4—32no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—34no—
347C23×C4—32no—
348C23×C4—34no—
349C23×C4—38no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—32no—
353C23×C4—34no—
354C23×C4—32no—
355C23×C4—34no—
356C23×C4—34no—
357C23×C4—38no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—34no—
361C23×C4—34no—
362C23×C4—38no—
363C23×C4—68no—
364C23×C4—68no—
365C23×C4—68no—
366C23×C4C8×A418yes—
367C23×C4C2×C4×A414yes—
368C23×C4C2×C4×A411yescharacteristic
369C23×C4C2×C4×A414yes—
370C23×C4C23×A411yescharacteristic
371C22×C8—38no—
372C22×C8—42no—
373C22×C8—68no—
374C22×C8—64no—
375C22×C8—64no—
376C22×C8—68no—
377C22×C8—68no—
378C22×C8—64no—
379C22×C8—616no—
380C22×C8—68no—
381C22×C8—68no—
382C22×C8—616no—
383C22×C8—68no—
384C22×C8—64no—
385C22×C8—124no—
386C22×C8—122no—
387C22×C8—124no—
388C22×C8—128no—
389C22×C8—124no—
390C22×C8—124no—
391C22×C8—128no—
392C22×C8—122no—
393C22×C8—124no—
394C22×C8—122no—
395C22×C8C2×C4×A418yes—
396C2×C42—32no—
397C2×C42—34no—
398C2×C42—32no—
399C2×C42—31no—
400C2×C42—34no—
401C2×C42—38no—
402C2×C42—32no—
403C2×C42—32no—
404C2×C42—32no—
405C2×C42—32no—
406C2×C42—38no—
407C2×C42—38no—
408C2×C42—32no—
409C2×C42—32no—
410C2×C42—38no—
411C2×C42—38no—
412C2×C42—32no—
413C2×C42—32no—
414C2×C42—32no—
415C2×C42—34no—
416C2×C42—34no—
417C2×C42—34no—
418C2×C42—34no—
419C2×C42—34no—
420C2×C42—316no—
421C2×C42—316no—
422C2×C42—32no—
423C2×C42—38no—
424C2×C42—38no—
425C2×C42—38no—
426C2×C42—38no—
427C2×C42—316no—
428C2×C42—316no—
429C2×C42—332no—
430C2×C42—316no—
431C2×C42—332no—
432C2×C42—316no—
433C2×C42—38no—
434C2×C42—38no—
435C2×C42—38no—
436C2×C42—38no—
437C2×C42—38no—
438C2×C42—32no—
439C2×C42—38no—
440C2×C42—32no—
441C2×C42—32no—
442C2×C42—32no—
443C2×C42—34no—
444C2×C42—32no—
445C2×C42—32no—
446C2×C42—32no—
447C2×C42—34no—
448C2×C42—31no—
449C2×C42—38no—
450C2×C42—316no—
451C2×C42—38no—
452C2×C42—32no—
453C2×C42—32no—
454C2×C42—32no—
455C2×C42—32no—
456C2×C42—32no—
457C2×C42—32no—
458C2×C42—34no—
459C2×C42—34no—
460C2×C42—32no—
461C2×C42—38no—
462C2×C42—32no—
463C2×C42—34no—
464C2×C42—38no—
465C2×C42—32no—
466C2×C42—32no—
467C2×C42—316no—
468C2×C42—38no—
469C2×C42—34no—
470C2×C42—38no—
471C2×C42—38no—
472C2×C42—34no—
473C2×C42—38no—
474C2×C42—38no—
475C2×C42—34no—
476C2×C42—64no—
477C2×C42—68no—
478C2×C42—68no—
479C2×C42—64no—
480C2×C42—68no—
481C2×C42—68no—
482C2×C42—68no—
483C2×C42—68no—
484C2×C42—68no—
485C2×C42—616no—
486C2×C42—616no—
487C2×C42—68no—
488C2×C42—68no—
489C2×C42—616no—
490C2×C42—616no—
491C2×C42—68no—
492C2×C42—632no—
493C2×C42—616no—
494C2×C42—616no—
495C2×C42—632no—
496C2×C42—68no—
497C2×C42—616no—
498C2×C42—68no—
499C2×C42—632no—
500C2×C42—616no—
501C2×C42—68no—
502C2×C42—664no—
503C2×C42C3×C4×C814yescomplemented
504C2×C42#127⋊C311yescharacteristic
505C2×C42C2×C3×C4211yescharacteristic
506C2×C42C22×C3×C812yes—
507C4⋊C8—616no—
508C4⋊C8—632no—
509C4⋊C8—616no—
510C4⋊C8—616no—
511C4⋊C8—632no—
512C4⋊C8—616no—
513C4×C8—44no—
514C4×C8—124no—
515C4×C8—124no—
516C4×C8—128no—
517C4×C8—124no—
518C23×C3—161no—
519C2×A4—44no—
520C2×A4—41no—
521C2×A4—42no—
522C2×C3×C4—161no—
523C2×C3×C4—168no—
524C2×C3×C4—161no—
525C2×C3×C4—164no—
526C2×C3×C4—164no—
527C3×C8—168no—
528C24—31no—
529C24—32no—
530C24—34no—
531C24—31no—
532C24C42×A412yes—
533C24C2×C8×A414yes—
534C24C22×C4×A411yescharacteristic
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—34no—
543C22×C4—38no—
544C22×C4—38no—
545C22×C4—34no—
546C22×C4—34no—
547C22×C4—38no—
548C22×C4—38no—
549C22×C4—34no—
550C22×C4—32no—
551C22×C4—34no—
552C22×C4—38no—
553C22×C4—38no—
554C22×C4—316no—
555C22×C4—316no—
556C22×C4—34no—
557C22×C4—38no—
558C22×C4—34no—
559C22×C4—316no—
560C22×C4—34no—
561C22×C4—34no—
562C22×C4—38no—
563C22×C4—31no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—32no—
567C22×C4—34no—
568C22×C4—32no—
569C22×C4—31no—
570C22×C4—32no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—38no—
574C22×C4—38no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—31no—
578C22×C4—34no—
579C22×C4—34no—
580C22×C4—34no—
581C22×C4—31no—
582C22×C4—34no—
583C22×C4—31no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—38no—
587C22×C4—34no—
588C22×C4—38no—
589C22×C4—316no—
590C22×C4—34no—
591C22×C4—34no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—38no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—38no—
598C22×C4—38no—
599C22×C4—316no—
600C22×C4—38no—
601C22×C4—316no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—38no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—68no—
608C22×C4—68no—
609C22×C4—616no—
610C22×C4—632no—
611C22×C4—68no—
612C22×C4—68no—
613C22×C4—68no—
614C22×C4—616no—
615C22×C4—632no—
616C22×C4—68no—
617C22×C4—68no—
618C22×C4—68no—
619C22×C4#384⋊C312yes—
620C22×C4C42×A412yes—
621C22×C4C2×#127⋊C311yescharacteristic
622C22×C4C2×C8×A418yes—
623C22×C4C22×C4×A412yes—
624C2×C8—44no—
625C2×C8—48no—
626C2×C8—68no—
627C2×C8—68no—
628C2×C8—616no—
629C2×C8—124no—
630C2×C8—128no—
631C2×C8—124no—
632C2×C8—128no—
633C2×C8—128no—
634C2×C8—1216no—
635C2×C8—124no—
636C2×C8—128no—
637C42—34no—
638C42—31no—
639C42—32no—
640C42—34no—
641C42—38no—
642C42—34no—
643C42—34no—
644C42—38no—
645C42—34no—
646C42—316no—
647C42—332no—
648C42—316no—
649C42—34no—
650C42—38no—
651C42—34no—
652C42—34no—
653C42—38no—
654C42—34no—
655C42—316no—
656C42—332no—
657C42—316no—
658C42—34no—
659C42—34no—
660C42—34no—
661C42—38no—
662C42—32no—
663C42—32no—
664C42—32no—
665C42—34no—
666C42—34no—
667C42—64no—
668C42—616no—
669C42—64no—
670C42—616no—
671C42—64no—
672C42—64no—
673C42—632no—
674C42—616no—
675C42—68no—
676C42—68no—
677C42—616no—
678C42—616no—
679C42—68no—
680C42—616no—
681C42—616no—
682C42—68no—
683C42—632no—
684C42—632no—
685C42#384⋊C312yes—
686C42C2×C3×C4×C811yescharacteristic, complemented
687C42C2×#127⋊C312yes—
688C22×C3—162no—
689C22×C3—164no—
690C22×C3—161no—
691A4—41no—
692C3×C4—162no—
693C3×C4—168no—
694C3×C4—162no—
695C23—32no—
696C23—31no—
697C23—32no—
698C23—34no—
699C23—34no—
700C23—38no—
701C23—32no—
702C23—34no—
703C23—38no—
704C23—32no—
705C23—32no—
706C23—34no—
707C23—34no—
708C23—31no—
709C23—31no—
710C23C2×#384⋊C311yescharacteristic
711C23C4×C8×A414yes—
712C23C2×C42×A411yescharacteristic
713C23C22×C8×A412yes—
714C2×C4—32no—
715C2×C4—34no—
716C2×C4—32no—
717C2×C4—34no—
718C2×C4—38no—
719C2×C4—34no—
720C2×C4—32no—
721C2×C4—34no—
722C2×C4—32no—
723C2×C4—34no—
724C2×C4—38no—
725C2×C4—34no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—38no—
729C2×C4—38no—
730C2×C4—316no—
731C2×C4—38no—
732C2×C4—38no—
733C2×C4—316no—
734C2×C4—38no—
735C2×C4—38no—
736C2×C4—316no—
737C2×C4—34no—
738C2×C4—38no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—34no—
742C2×C4—31no—
743C2×C4—34no—
744C2×C4—31no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—32no—
748C2×C4—34no—
749C2×C4—38no—
750C2×C4—38no—
751C2×C4—316no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—34no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—38no—
758C2×C4—34no—
759C2×C4—34no—
760C2×C4—316no—
761C2×C4—64no—
762C2×C4—64no—
763C2×C4—616no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—616no—
767C2×C4—68no—
768C2×C4—64no—
769C2×C4—64no—
770C2×C4—68no—
771C2×C4—616no—
772C2×C4—632no—
773C2×C4—616no—
774C2×C4—632no—
775C2×C4#1842⋊C318yesdirect product factor
776C2×C4C2×#384⋊C311yescharacteristic
777C2×C4C2×#384⋊C314yes—
778C2×C4C4×#127⋊C314yes—
779C2×C4C22×#127⋊C311yescharacteristic
780C8—48no—
781C8—128no—
782C2×C3—161no—
783C2×C3—164no—
784C2×C3—162no—
785C22—31no—
786C22—32no—
787C22—34no—
788C22—32no—
789C22—34no—
790C22—38no—
791C22—31no—
792C22—31no—
793C22—32no—
794C22—34no—
795C22—34no—
796C22—38no—
797C22—32no—
798C22—32no—
799C22—34no—
800C22C4×#384⋊C312yes—
801C22C2×#1842⋊C314yes—
802C22C22×#384⋊C311yescharacteristic
803C22C2×C4×C8×A411yescharacteristic
804C4—32no—
805C4—32no—
806C4—34no—
807C4—38no—
808C4—32no—
809C4—32no—
810C4—38no—
811C4—64no—
812C4—64no—
813C4—616no—
814C4C4×#384⋊C312yes—
815C4C2×#1842⋊C318yesdirect product factor
816C4C2×C4×#127⋊C312yes—
817C3—161noSylow
818C2—31no—
819C2—31no—
820C2—32no—
821C2—34no—
822C2C22×#1842⋊C312yes—
823C2C4×#1842⋊C314yesdirect product factor
824C2C2×C4×#384⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C42#127⋊C3
commutator, hypocenterC42C2×C3×C4×C8
FrattiniC23×C4C23×A4
FittingC2×C4×#1842C3
socleC25C2×C4×A4
prime radicalC23×C42⋊C3C2×C4
cosocleC2×C43C23×C3
LCSG ▷ C42
UCSC1 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1842C3semidirect
2. C4×#1842⋊C3C2direct (N × H)
8. C2×#1842⋊C3C4direct (N × H)
17. C4×#1842C2×C3semidirect
23. C2×C4×C42⋊C3C8semidirect
28. #1842⋊C3C2×C4direct (N × H)
40. C2×#1842C3×C4semidirect
71. C4×C42⋊C3C2×C8semidirect
132. C2×C43C3×C8semidirect
140. #1842C2×C3×C4semidirect
164. C2×C42⋊C3C4×C8semidirect
315. C43C2×C3×C8semidirect
331. C42⋊C3C2×C4×C8semidirect
503. C2×C42C3×C4×C8semidirect
686. C42C2×C3×C4×C8semidirect
775. C2×C4#1842⋊C3direct (N × H)
815. C4C2×#1842⋊C3direct (N × H)
823. C2C4×#1842⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#18423
C4×#1842⋊C32
C22×#1842⋊C32
C2×C42×C42⋊C32
C2×C4×C8×A44