Finite Group Databasebeta

← #392784

Subgroups — #392784

Order 512.

2338 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#1925C212yesmaximal, complemented
3C2×#1874C211yesmaximal, characteristic
4C2×#1874C211yesmaximal, characteristic
5C2×#1852C211yesmaximal, characteristic, complemented
6#14698C211yesmaximal, characteristic
7#10931C212yesmaximal, complemented
8#10907C212yesmaximal, complemented
9#10806C212yesmaximal, complemented
10#10730C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C22×#121C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42—21no—
16C23×C42C2211yescharacteristic
17C22×#107C2212yes—
18C22×#102C2212yes—
19C22×#102C2212yes—
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C2×#390C2211yescharacteristic
23C2×#390C2211yescharacteristic
24C2×#386—21no—
25C2×#386—21no—
26C2×#380C2211yescharacteristic
27C2×C4×C4⋊C4—21no—
28C2×C4×C4⋊C4—21no—
29C2×C4×C4⋊C4—28no—
30C2×C4×C4⋊C4C2212yes—
31C2×C4×C4⋊C4C2212yes—
32C22×#95—21no—
33#1925—28no—
34#1874—24no—
35#1874C418yescomplemented
36#1852—24no—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44#1437—21no—
45#1437—21no—
46C4⋊#95C2211yescharacteristic
47C4⋊#95C2211yescharacteristic
48C23×D4—21no—
49C23×D4C2311yescharacteristic
50C24×C4—21no—
51C24×C4—21no—
52C24×C4D411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4C2311yescharacteristic
55C23×C8C2312yes—
56C23×C8C2312yes—
57C2×#121—22no—
58C2×#121—22no—
59C2×#121—22no—
60C2×#121—22no—
61C2×#121—22no—
62C2×#121C2×C414yes—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4C2×C414yes—
72C22×C4⋊C4D414yes—
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2312yes—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4—21no—
81C22×C22⋊C4—21no—
82C22×C22⋊C4—21no—
83C22×C22⋊C4—21no—
84C22×C42—22no—
85C22×C42—22no—
86C22×C42—24no—
87C22×C42—24no—
88C22×C42—28no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—44no—
92C22×C42—44no—
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×#107—24no—
98C2×#107—24no—
99C2×#107—24no—
100C2×#102—24no—
101C2×#102—24no—
102C2×#102—24no—
103C2×#102—24no—
104C2×#102—24no—
105C2×#102C2×C418yescomplemented
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8C2×C414yes—
112#390—24no—
113#390—24no—
114#386—44no—
115#386—44no—
116#380—22no—
117#380—22no—
118C4×C4⋊C4—28no—
119C4×C4⋊C4—28no—
120C4×C4⋊C4—24no—
121C4×C4⋊C4—24no—
122C4×C4⋊C4—24no—
123C4×C4⋊C4D418yescomplemented
124C2×#95—28no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132#340—24no—
133#340—24no—
134#340—24no—
135#340—24no—
136#340C2×C418yescomplemented
137#336—24no—
138#336—24no—
139C25—21no—
140C25C2×D411yescharacteristic
141C22×D4—24no—
142C22×D4—21no—
143C22×D4—22no—
144C22×D4—21no—
145C22×D4—21no—
146C22×D4—21no—
147C22×D4—22no—
148C22×D4—22no—
149C22×D4—22no—
150C22×D4—21no—
151C22×D4—42no—
152C22×D4—42no—
153C22×D4—42no—
154C22×D4—42no—
155C22×D4—42no—
156C22×D4—42no—
157C22×D4C22×C412yes—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—24no—
173C23×C4—24no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4D814yes—
195C23×C4C22×C412yes—
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D412yes—
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4#4112yes—
203C23×C4#4112yes—
204C23×C4#4112yes—
205C23×C4#4112yes—
206C23×C4C2411yescharacteristic
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8C22×C414yes—
221#121—28no—
222#121—28no—
223#121—44no—
224#121—44no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—216no—
228C2×C4⋊C4—216no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—216no—
240C2×C4⋊C4—216no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4C22×C412yes—
255C2×C4⋊C4C22×C414yes—
256C2×C4⋊C4C2×D414yes—
257C2×C4⋊C4C2×D414yes—
258C2×C4⋊C4C2×D414yes—
259C2×C4⋊C4#4114yes—
260C2×C4⋊C4#4114yes—
261C2×C22⋊C4—24no—
262C2×C22⋊C4—42no—
263C2×C22⋊C4—42no—
264C2×C22⋊C4—42no—
265C2×C22⋊C4—42no—
266C2×C22⋊C4—42no—
267C2×C22⋊C4—42no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C42—216no—
280C2×C42—216no—
281C2×C42—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—28no—
294C2×C42—28no—
295C2×C42—44no—
296C2×C42—432no—
297C2×C42—44no—
298C2×C42—44no—
299C2×C42—44no—
300C2×C42C2×D414yes—
301C2×C42#4114yes—
302#107—48no—
303#102—216no—
304#102—48no—
305C22⋊C8—28no—
306C22⋊C8—44no—
307#95—28no—
308#95—28no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—42no—
313#95—42no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—21no—
318C24—21no—
319C24—21no—
320C24—21no—
321C24—21no—
322C24—22no—
323C24—41no—
324C24—41no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24C4×D412yes—
338C24#12112yes—
339C24#12312yes—
340C24C2×D812yes—
341C24#13512yes—
342C24AGL(1,ℤ/8)12yes—
343C24#13712yes—
344C24C22×D411yescharacteristic
345C2×D4—22no—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—24no—
349C2×D4—48no—
350C2×D4—48no—
351C2×D4—48no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—84no—
365C2×D4—84no—
366C2×D4—84no—
367C2×D4—84no—
368C22×C4—28no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—28no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—28no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—216no—
401C22×C4—216no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—48no—
426C22×C4—48no—
427C22×C4—44no—
428C22×C4—48no—
429C22×C4—48no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—44no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4#11714yes—
468C22×C4C4×D414yes—
469C22×C4C4×D412yes—
470C22×C4#12012yes—
471C22×C4#12012yes—
472C22×C4#12112yes—
473C22×C4#12312yes—
474C22×C4#12312yes—
475C22×C4#12312yes—
476C22×C4#12414yes—
477C22×C4#12614yes—
478C22×C4C2×D812yes—
479C22×C4C2×D812yes—
480C22×C4AGL(1,ℤ/8)12yes—
481C22×C4#13712yes—
482C22×C4C23×C411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×D412yes—
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4112yes—
489C22×C4C2×#4112yes—
490C22×C4C2×#4112yes—
491C22×C4C2×#4111yescharacteristic
492C2×C8—24no—
493C2×C8—24no—
494C2×C8—24no—
495C2×C8—42no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8—42no—
500C2×C8—42no—
501C2×C8—42no—
502C2×C8—42no—
503C2×C8—42no—
504C2×C8—42no—
505C2×C8—42no—
506C4⋊C4—216no—
507C4⋊C4—216no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4C4×D418yes—
523C4⋊C4#12118yes—
524C22⋊C4—48no—
525C22⋊C4—84no—
526C22⋊C4—84no—
527C22⋊C4—84no—
528C22⋊C4—84no—
529C22⋊C4—84no—
530C42—28no—
531C42—28no—
532C42—24no—
533C42—24no—
534C42—24no—
535C42—24no—
536C42—416no—
537C42—416no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23—81no—
590C23—81no—
591C23—81no—
592C23—81no—
593C23—81no—
594C23—81no—
595C23—81no—
596C23—81no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23#38814yes—
602C23C4×D814yes—
603C23#44014yes—
604C23#45914yes—
605C23#46414yes—
606C23#48014yes—
607C23#48214yes—
608C23C2×C4×D411yescharacteristic
609C23C2×#12011yescharacteristic
610C23C2×#12111yescharacteristic
611C23C2×#12311yescharacteristic
612C23C2×#12311yescharacteristic
613C23#52511yescharacteristic
614C23#52511yescharacteristic
615C23C22×D811yescharacteristic
616C23C2×#13511yescharacteristic
617C23C2×AGL(1,ℤ/8)11yescharacteristic
618C23C2×AGL(1,ℤ/8)11yescharacteristic
619C23C2×#13711yescharacteristic
620C23C2×#13711yescharacteristic
621C23#57511yescharacteristic
622C23#57511yescharacteristic
623D4—44no—
624D4—44no—
625D4—816no—
626D4—82no—
627D4—82no—
628C2×C4—232no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—416no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—41no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4#38814yes—
704C2×C4#44714yes—
705C2×C4#48014yes—
706C2×C4C2×#11711yescharacteristic
707C2×C4C2×C4×D412yes—
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C4×#4112yes—
710C2×C4C2×#12112yes—
711C2×C4#52512yes—
712C2×C4#52512yes—
713C2×C4#52512yes—
714C2×C4#52512yes—
715C2×C4C2×#12411yescharacteristic
716C2×C4C2×#12611yescharacteristic
717C2×C4#52912yes—
718C2×C4#52912yes—
719C2×C4#52912yes—
720C2×C4#52912yes—
721C2×C4#53212yes—
722C8—44no—
723C8—82no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—161no—
746C22—161no—
747C22—161no—
748C22—161no—
749C22—161no—
750C22—161no—
751C22—161no—
752C22—161no—
753C22#192518yescomplemented
754C22C2×#38811yescharacteristic
755C22C4×#12011yescharacteristic
756C22C4×#12311yescharacteristic
757C22#284711yescharacteristic
758C22#284911yescharacteristic
759C22#285311yescharacteristic
760C22#285411yescharacteristic
761C22C2×C4×D811yescharacteristic
762C22C2×#44011yescharacteristic
763C22C4×AGL(1,ℤ/8)11yescharacteristic
764C22C4×#13711yescharacteristic
765C22C2×#44711yescharacteristic
766C22#300211yescharacteristic
767C22#300411yescharacteristic
768C22#300611yescharacteristic
769C22C2×#45911yescharacteristic
770C22C2×#46411yescharacteristic
771C22#303611yescharacteristic
772C22#303711yescharacteristic
773C22C2×#48011yescharacteristic
774C22C2×#48011yescharacteristic
775C22C2×#48211yescharacteristic
776C22#309111yescharacteristic
777C22#309211yescharacteristic
778C22#309211yescharacteristic
779C22#309311yescharacteristic
780C22#309411yescharacteristic
781C22#310011yescharacteristic
782C22#310011yescharacteristic
783C22#310511yescharacteristic
784C22#310811yescharacteristic
785C22#310911yescharacteristic
786C22#311211yescharacteristic
787C22#311711yescharacteristic
788C22#311711yescharacteristic
789C4—24no—
790C4—24no—
791C4—24no—
792C4—48no—
793C4—48no—
794C4—42no—
795C4—42no—
796C4—82no—
797C4—161no—
798C4—161no—
799C4#229012yes—
800C4C4×#12112yes—
801C4#285012yes—
802C4#285212yes—
803C2—28no—
804C2—162no—
805C2#1469611yescharacteristic
806C2C2×#192511yescharacteristic
807C2#2105911yescharacteristic
808C2C4×#44711yescharacteristic
809C2#2145411yescharacteristic
810C2C4×#48011yescharacteristic
811C2#2158011yescharacteristic
812C2#3290211yescharacteristic
813C2#3290911yescharacteristic
814C2#3297811yescharacteristic
815C2#3298111yescharacteristic
816C2#3309411yescharacteristic
817C2#3309611yescharacteristic
818C2#3310611yescharacteristic
819C2#3311011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×C4×C4⋊C4C2semidirect
2. C2×#1925C2semidirect
5. C2×#1852C2semidirect
7. #10931C2semidirect
8. #10907C2semidirect
9. #10806C2semidirect
10. #10730C2semidirect
11. #10712C2semidirect
35. #1874C4semidirect
105. C2×#102C2×C4semidirect
123. C4×C4⋊C4D4semidirect
136. #340C2×C4semidirect
753. C22#1925semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C4⋊C42
C2×#19252
C2×#18742
C2×#18522
#146982
#109312
#109072
#108062
#107302
#107122