Finite Group Databasebeta

← #368338

Subgroups — #368338

Order 512.

2212 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#127C211yesmaximal, characteristic
2C2×#1982C211yesmaximal, characteristic
3C2×#1982C211yesmaximal, characteristic
4C2×#1947C211yesmaximal, characteristic, complemented
5C2×#1862C212yesmaximal, complemented
6C4×#389C211yesmaximal, characteristic, complemented
7#11123C212yesmaximal, complemented
8#11066C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10832C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal, complemented
12C22×#127C2211yescharacteristic
13C22×C4×D4—21no—
14C22×C4×D4—21no—
15C22×C4×D4C2212yes—
16C22×#107C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2212yes—
20C22×#102C2212yes—
21C22×#102C2212yes—
22C22×#102C2212yes—
23C4×#127—24no—
24C4×#127—24no—
25C2×#390—21no—
26C2×#390—21no—
27C2×#390C2212yes—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×C4×C4⋊C4—21no—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C43C2211yescharacteristic
35#1982—24no—
36#1982C418yescomplemented
37#1947—24no—
38#1862—28no—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44#1436—21no—
45#1436—21no—
46C4⋊#95C2211yescharacteristic
47C4⋊#95C2211yescharacteristic
48C4×#95—21no—
49C23×D4—21no—
50C23×D4—21no—
51C23×D4C2312yes—
52C24×C4—22no—
53C23×C8C2312yes—
54C23×C8C2312yes—
55C2×#127—22no—
56C2×#127—22no—
57C2×#127—22no—
58C2×#127C2×C414yes—
59C2×#127D414yes—
60C2×#127Q814yes—
61C2×C4×D4—28no—
62C2×C4×D4—28no—
63C2×C4×D4—24no—
64C2×C4×D4—24no—
65C2×C4×D4—24no—
66C2×C4×D4—24no—
67C2×C4×D4—42no—
68C2×C4×D4—42no—
69C2×C4×D4—44no—
70C2×C4×D4—44no—
71C2×C4×D4—44no—
72C2×C4×D4—44no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C22⋊C4—22no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—22no—
85C22×C42—21no—
86C22×C42—21no—
87C22×C42D411yescharacteristic
88C22×C42D411yescharacteristic
89C22×C42D411yescharacteristic
90C22×C42D411yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C2×#107—24no—
95C2×#107—24no—
96C2×#107—42no—
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8C2×C414yescomplemented
103C2×#102—24no—
104C2×#102—24no—
105C2×#102—24no—
106C2×#102—24no—
107C2×#102—24no—
108C2×#102—24no—
109C2×#102—42no—
110C2×#102—42no—
111C2×#102—42no—
112C2×#102—42no—
113C2×#102C2×C418yescomplemented
114C2×#102C2×C418yescomplemented
115#390—28no—
116#390—28no—
117#390—24no—
118#390—24no—
119#389—22no—
120#389—22no—
121#389—22no—
122#389D414yescomplemented
123#384—22no—
124#384D414yes—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—44no—
129C4×C4⋊C4C2×C414yescomplemented
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C43—22no—
139C43—22no—
140#340—24no—
141#340—24no—
142#340—42no—
143#336—24no—
144#336—42no—
145C25—22no—
146C22×D4—24no—
147C22×D4—24no—
148C22×D4—24no—
149C22×D4—24no—
150C22×D4—24no—
151C22×D4—24no—
152C22×D4—22no—
153C22×D4—22no—
154C22×D4—22no—
155C22×D4—22no—
156C22×D4—22no—
157C22×D4—22no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—22no—
163C22×D4—42no—
164C22×D4—42no—
165C22×D4—42no—
166C22×D4—42no—
167C22×D4—42no—
168C22×D4—42no—
169C22×D4—42no—
170C22×D4—42no—
171C22×D4C22×C414yes—
172C22×D4C2×D414yes—
173C22×D4C2×Q814yes—
174C23×C4—21no—
175C23×C4—28no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—44no—
181C23×C4—44no—
182C23×C4—44no—
183C23×C4—44no—
184C23×C4—44no—
185C23×C4—44no—
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2411yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—22no—
201C22×C8—22no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—22no—
205C22×C8—22no—
206C22×C8C22×C414yes—
207#127—28no—
208#127—28no—
209#127—28no—
210#127C4⋊C4116yescomplemented
211C4×D4—48no—
212C4×D4—48no—
213C4×D4—48no—
214C4×D4—48no—
215C4×D4—432no—
216C4×D4—432no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4C22×C412yes—
253C2×C4⋊C4C22×C412yes—
254C2×C4⋊C4C2×D414yes—
255C2×C4⋊C4C2×D412yes—
256C2×C4⋊C4C2×D412yes—
257C2×C4⋊C4#4112yes—
258C2×C4⋊C4#4112yes—
259C2×C22⋊C4—28no—
260C2×C22⋊C4—28no—
261C2×C22⋊C4—28no—
262C2×C22⋊C4—44no—
263C2×C22⋊C4—44no—
264C2×C22⋊C4—44no—
265C2×C22⋊C4—44no—
266C2×C22⋊C4—44no—
267C2×C22⋊C4—44no—
268C2×C42—22no—
269C2×C42—22no—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—24no—
278C2×C42—22no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—22no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—41no—
289C2×C42—41no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42D814yes—
296C2×C42C22×C412yes—
297C2×C42C2×D412yes—
298C2×C42C2×D412yes—
299C2×C42C2×D412yes—
300C2×C42C2×Q812yes—
301C2×C42#4112yes—
302C2×C42#4112yes—
303C2×C42#4112yes—
304#107—48no—
305C4⋊C8—28no—
306C4⋊C8—44no—
307#102—216no—
308#102—48no—
309#102—48no—
310#102—48no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—42no—
315#95—42no—
316#95—42no—
317#95—42no—
318#95—42no—
319C24—24no—
320C24—24no—
321C24—24no—
322C24—42no—
323C24—42no—
324C24—42no—
325C24—42no—
326C24—42no—
327C24—42no—
328C24—42no—
329C24—42no—
330C24—42no—
331C24—42no—
332C24—42no—
333C24—42no—
334C24C22×D411yescharacteristic
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—24no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—216no—
351C2×D4—216no—
352C2×D4—48no—
353C2×D4—48no—
354C2×D4—48no—
355C2×D4—48no—
356C2×D4—48no—
357C2×D4—48no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—48no—
371C2×D4—48no—
372C2×D4—48no—
373C2×D4—48no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4C2×C4⋊C418yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—416no—
411C22×C4—416no—
412C22×C4—416no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—88no—
442C22×C4—88no—
443C22×C4—88no—
444C22×C4—88no—
445C22×C4C4×D412yes—
446C22×C4C4×D412yes—
447C22×C4#12012yes—
448C22×C4#12012yes—
449C22×C4#12112yes—
450C22×C4#12112yes—
451C22×C4C22⋊Q812yes—
452C22×C4C22⋊Q812yes—
453C22×C4C2×D812yes—
454C22×C4C2×D812yes—
455C22×C4C2×D812yes—
456C22×C4#13512yes—
457C22×C4AGL(1,ℤ/8)12yes—
458C22×C4AGL(1,ℤ/8)12yes—
459C22×C4AGL(1,ℤ/8)12yes—
460C22×C4#13712yes—
461C22×C4C23×C411yescharacteristic
462C22×C4C22×D411yescharacteristic
463C22×C4C22×D411yescharacteristic
464C22×C4C22×D411yescharacteristic
465C22×C4C22×Q811yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4H(5,𝔽2)11yescharacteristic
472C22×C4H(5,𝔽2)11yescharacteristic
473C22×C4H(5,𝔽2)11yescharacteristic
474C22×C42−1+411yescharacteristic
475C2×C8—24no—
476C2×C8—24no—
477C2×C8—24no—
478C2×C8—42no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8—42no—
488C2×C8—42no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—48no—
501C4⋊C4—48no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—42no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—42no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—48no—
511C4⋊C4—48no—
512C4⋊C4C4×D414yescomplemented
513C22⋊C4—416no—
514C22⋊C4—416no—
515C22⋊C4—416no—
516C42—28no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—28no—
522C42—44no—
523C42—41no—
524C42—41no—
525C42—41no—
526C42—41no—
527C42—48no—
528C42—44no—
529C42—84no—
530C42C2×C4⋊C414yes—
531C42C4×D414yes—
532C42C22⋊Q814yes—
533C42#12314yes—
534C23—28no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—44no—
548C23—44no—
549C23—44no—
550C23—44no—
551C23—44no—
552C23—44no—
553C23—82no—
554C23—82no—
555C23—82no—
556C23—82no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23—82no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23—82no—
567C23—82no—
568C23—82no—
569C23C2×C4×D411yescharacteristic
570C23C2×#12011yescharacteristic
571C23C2×#12111yescharacteristic
572C23C2×C22⋊Q811yescharacteristic
573C23#52511yescharacteristic
574C23#53511yescharacteristic
575C23#53711yescharacteristic
576C23C22×D811yescharacteristic
577C23C2×#13511yescharacteristic
578C23C2×AGL(1,ℤ/8)11yescharacteristic
579C23C2×AGL(1,ℤ/8)11yescharacteristic
580C23C2×AGL(1,ℤ/8)11yescharacteristic
581C23C2×#13711yescharacteristic
582C23#57511yescharacteristic
583C23#57511yescharacteristic
584D4—28no—
585D4—28no—
586D4—432no—
587D4—44no—
588D4—44no—
589D4—432no—
590D4—44no—
591D4—44no—
592D4—44no—
593D4—44no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—832no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—82no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—82no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4#38514yes—
664C2×C4#38514yes—
665C2×C4C4×D814yes—
666C2×C4#44014yes—
667C2×C4#44714yes—
668C2×C4#45214yes—
669C2×C4#45914yes—
670C2×C4#47414yes—
671C2×C4#47814yes—
672C2×C4C22×C4⋊C411yescharacteristic
673C2×C4C2×C4×D411yescharacteristic
674C2×C4C2×C4×D411yescharacteristic
675C2×C4C4×#4111yescharacteristic
676C2×C4#51811yescharacteristic
677C2×C4#52011yescharacteristic
678C2×C4C2×C22⋊Q811yescharacteristic
679C2×C4C2×#12311yescharacteristic
680C2×C4#52911yescharacteristic
681C2×C4#53211yescharacteristic
682C2×C4#54011yescharacteristic
683C2×C4#54211yescharacteristic
684C2×C4D4211yescharacteristic
685C2×C4D4211yescharacteristic
686C2×C4#54611yescharacteristic
687C2×C4#54611yescharacteristic
688C2×C4#54611yescharacteristic
689C2×C4#54711yescharacteristic
690C2×C4#54811yescharacteristic
691C2×C4D4×Q811yescharacteristic
692C2×C4#55011yescharacteristic
693C2×C4#55011yescharacteristic
694C2×C4#55411yescharacteristic
695C2×C4#55411yescharacteristic
696C2×C4#55411yescharacteristic
697C2×C4#55611yescharacteristic
698C2×C4#55911yescharacteristic
699C2×C4#55911yescharacteristic
700C8—44no—
701C8—82no—
702C22—48no—
703C22—48no—
704C22—48no—
705C22—84no—
706C22—84no—
707C22—84no—
708C22—84no—
709C22—84no—
710C22—84no—
711C22—84no—
712C22—84no—
713C22—84no—
714C22—84no—
715C22—84no—
716C22—84no—
717C22C2×#38511yescharacteristic
718C22C4×#12111yescharacteristic
719C22#232411yescharacteristic
720C22#240711yescharacteristic
721C22#240811yescharacteristic
722C22#253811yescharacteristic
723C22#258011yescharacteristic
724C22C2×C4×D811yescharacteristic
725C22C2×#44011yescharacteristic
726C22C4×AGL(1,ℤ/8)11yescharacteristic
727C22C4×AGL(1,ℤ/8)11yescharacteristic
728C22C2×#44711yescharacteristic
729C22C2×#45211yescharacteristic
730C22#300311yescharacteristic
731C22#300511yescharacteristic
732C22C2×#45911yescharacteristic
733C22#303511yescharacteristic
734C22#303711yescharacteristic
735C22#303811yescharacteristic
736C22C2×#47411yescharacteristic
737C22C2×#47811yescharacteristic
738C22#307711yescharacteristic
739C22#307711yescharacteristic
740C22#310011yescharacteristic
741C22#310611yescharacteristic
742C22#311211yescharacteristic
743C22#311511yescharacteristic
744C22#320511yescharacteristic
745C22#321211yescharacteristic
746C22#321611yescharacteristic
747C22#321711yescharacteristic
748C22#324511yescharacteristic
749C22#324711yescharacteristic
750C22#325111yescharacteristic
751C22#325411yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—82no—
759C4—82no—
760C4—82no—
761C4—84no—
762C4#186218yescomplemented
763C4D4×C4⋊C411yescharacteristic
764C4#234911yescharacteristic
765C4#236611yescharacteristic
766C4#236711yescharacteristic
767C4#244511yescharacteristic
768C4#244711yescharacteristic
769C4#245211yescharacteristic
770C4#245411yescharacteristic
771C2—88no—
772C2#1401811yescharacteristic
773C2C2×#186211yescharacteristic
774C2#2087311yescharacteristic
775C2C4×#45911yescharacteristic
776C2#2150511yescharacteristic
777C2#2214511yescharacteristic
778C2#2215311yescharacteristic
779C2#2415011yescharacteristic
780C2#2415611yescharacteristic
781C2#2420811yescharacteristic
782C2#2421311yescharacteristic
783C2#2827911yescharacteristic
784C2#2828611yescharacteristic
785C2#2925411yescharacteristic
786C2#2925611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1947C2semidirect
5. C2×#1862C2semidirect
6. C4×#389C2semidirect
7. #11123C2semidirect
8. #11066C2semidirect
9. #10849C2semidirect
10. #10832C2semidirect
11. #10788C2semidirect
36. #1982C4semidirect
102. C2×C4⋊C8C2×C4semidirect
113. C2×#102C2×C4semidirect
114. C2×#102C2×C4semidirect
122. #389D4semidirect
129. C4×C4⋊C4C2×C4semidirect
210. #127C4⋊C4semidirect
512. C4⋊C4C4×D4semidirect
762. C4#1862semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1272
C2×#19822
C2×#19472
C2×#18622
C4×#3892
#111232
#110662
#108492
#108322
#107882