Finite Group Databasebeta

← #392877

Subgroups — #392877

Order 512.

1862 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#117C211yesmaximal, characteristic
2C2×#1948C211yesmaximal, characteristic, complemented
3C2×#1947C211yesmaximal, characteristic, complemented
4C2×#1854C212yesmaximal
5C2×#1797C211yesmaximal, characteristic
6#14686C211yesmaximal, characteristic
7#10908C212yesmaximal, complemented
8#10907C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10849C211yesmaximal, characteristic, complemented
11#10731C212yesmaximal
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C22×#107C2212yes—
16C22×#106C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2212yes—
20C2×#384C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×#380—21no—
23C2×#380—21no—
24C2×#380C2212yes—
25C4×#117—24no—
26C4×#117—24no—
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4—21no—
32C2×C4×C22⋊C4—21no—
33C2×#376—21no—
34C2×C43—21no—
35#1948—24no—
36#1947—24no—
37#1854—28no—
38#1797C418yescomplemented
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#336C2212yes—
46C4⋊#95—21no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C24×C4D411yescharacteristic
50C24×C4D411yescharacteristic
51C24×C4C2311yescharacteristic
52C23×C8C2312yes—
53C23×C8C2312yes—
54C2×#117—22no—
55C2×#117—22no—
56C2×#117—22no—
57C2×#117—22no—
58C2×#117—22no—
59C2×#117—22no—
60C2×#117—22no—
61C2×#117—22no—
62C2×#117—22no—
63C2×#117—22no—
64C2×#117D414yes—
65C2×#117Q814yes—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4C2312yes—
71C22×C4⋊C4C2312yes—
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C22⋊C4—21no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—22no—
79C22×C42—21no—
80C22×C42—21no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42—21no—
86C22×C42—21no—
87C22×C42—21no—
88C22×C42—21no—
89C22×C42C2×C414yes—
90C22×C42D411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42Q814yes—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#107—24no—
96C2×#107—24no—
97C2×#107—24no—
98C2×#106—24no—
99C2×#106—24no—
100C2×#106—24no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8C2×C414yes—
106C2×C4⋊C8C2×C414yes—
107C2×C22⋊C8—24no—
108C2×C22⋊C8—24no—
109C2×C22⋊C8C2×C418yes—
110#384—22no—
111#384—22no—
112#384—22no—
113#384—22no—
114#380—24no—
115#380—24no—
116#380—44no—
117#380—44no—
118C4×C4⋊C4—22no—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4D414yes—
125C4×C4⋊C4D414yes—
126C4×C22⋊C4—28no—
127C4×C22⋊C4—28no—
128#376—28no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95—22no—
136C43—28no—
137#340—24no—
138#340—24no—
139#340—24no—
140#340—24no—
141#340—24no—
142#340—24no—
143#336C2×C418yes—
144C25C2×D411yescharacteristic
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—22no—
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—22no—
169C23×C4—41no—
170C23×C4—41no—
171C23×C4C4⋊C414yes—
172C23×C4C4⋊C414yes—
173C23×C4C22×C412yes—
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D412yes—
179C23×C4C2×D411yescharacteristic
180C23×C4C2×Q812yes—
181C23×C4C2×Q812yes—
182C23×C4#4112yes—
183C23×C4#4112yes—
184C23×C4C2411yescharacteristic
185C22×C8—22no—
186C22×C8—22no—
187C22×C8—22no—
188C22×C8—22no—
189C22×C8—22no—
190C22×C8—22no—
191C22×C8—22no—
192C22×C8—22no—
193C22×C8—22no—
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8C22×C414yes—
198C22×C8C22×C414yes—
199#117—28no—
200#117—28no—
201#117—28no—
202#117—28no—
203#117—28no—
204#117—28no—
205#117—28no—
206#117—28no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—42no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4C2×D412yes—
244C2×C4⋊C4C2×D412yes—
245C2×C4⋊C4C2×D412yes—
246C2×C4⋊C4C2×D412yes—
247C2×C4⋊C4C2×D412yes—
248C2×C4⋊C4C2×D412yes—
249C2×C4⋊C4C2×Q812yes—
250C2×C4⋊C4C2×Q812yes—
251C2×C4⋊C4#4112yes—
252C2×C4⋊C4#4112yes—
253C2×C4⋊C4#4112yes—
254C2×C4⋊C4#4112yes—
255C2×C22⋊C4—24no—
256C2×C22⋊C4—24no—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—44no—
262C2×C22⋊C4—44no—
263C2×C22⋊C4—44no—
264C2×C42—24no—
265C2×C42—24no—
266C2×C42—24no—
267C2×C42—24no—
268C2×C42—22no—
269C2×C42—22no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—28no—
279C2×C42—28no—
280C2×C42—28no—
281C2×C42—28no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—42no—
287C2×C42—42no—
288C2×C42—42no—
289C2×C42—42no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42C4⋊C414yes—
295C2×C42C4⋊C414yes—
296C2×C42C22×C412yes—
297C2×C42C22×C412yes—
298C2×C42C2×D412yes—
299C2×C42C2×D412yes—
300C2×C42C2×Q812yes—
301C2×C42C2×Q812yes—
302C2×C42#4112yes—
303C2×C42#4112yes—
304#107—48no—
305#106—48no—
306C4⋊C8—28no—
307C4⋊C8—28no—
308C22⋊C8—216no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—44no—
314#95—44no—
315#95—44no—
316C24—21no—
317C24—21no—
318C24—21no—
319C24—21no—
320C24—21no—
321C24—21no—
322C24—21no—
323C24—21no—
324C24—21no—
325C24—21no—
326C24—21no—
327C24—21no—
328C24C2×C4⋊C412yes—
329C24#12112yes—
330C24C22⋊Q812yes—
331C24C22×D411yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×C4⋊C412yes—
431C22×C4C2×C4⋊C412yes—
432C22×C4C2×C4⋊C412yes—
433C22×C4C2×C4⋊C412yes—
434C22×C4C2×C4⋊C412yes—
435C22×C4C4×D414yes—
436C22×C4C4×Q814yes—
437C22×C4#12012yes—
438C22×C4#12012yes—
439C22×C4#12112yes—
440C22×C4C22⋊Q812yes—
441C22×C4#12312yes—
442C22×C4#12312yes—
443C22×C4#12514yes—
444C22×C4C4⋊Q814yes—
445C22×C4#13512yes—
446C22×C4#13512yes—
447C22×C4AGL(1,ℤ/8)12yes—
448C22×C4AGL(1,ℤ/8)12yes—
449C22×C4#13712yes—
450C22×C4#13712yes—
451C22×C4C23×C411yescharacteristic
452C22×C4C22×D411yescharacteristic
453C22×C4C22×D411yescharacteristic
454C22×C4C22×D411yescharacteristic
455C22×C4C22×Q811yescharacteristic
456C22×C4C22×Q811yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C2×C8—24no—
466C2×C8—24no—
467C2×C8—24no—
468C2×C8—24no—
469C2×C8—24no—
470C2×C8—24no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8—42no—
477C2×C8—42no—
478C2×C8—42no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—84no—
500C4⋊C4—84no—
501C4⋊C4—84no—
502C4⋊C4—84no—
503C4⋊C4#12114yes—
504C4⋊C4#12114yes—
505C4⋊C4C22⋊Q814yes—
506C4⋊C4C22⋊Q814yes—
507C22⋊C4—216no—
508C22⋊C4—216no—
509C22⋊C4—88no—
510C42—216no—
511C42—216no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—28no—
517C42—28no—
518C42—48no—
519C42—48no—
520C42—48no—
521C42—48no—
522C42C4×D414yes—
523C42C4×D414yes—
524C42C22⋊Q814yes—
525C42C22⋊Q814yes—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23#38914yes—
561C23C22×C4⋊C411yescharacteristic
562C23C2×#12011yescharacteristic
563C23C2×#12111yescharacteristic
564C23C2×C22⋊Q811yescharacteristic
565C23C2×#12311yescharacteristic
566C23#52511yescharacteristic
567C23#52511yescharacteristic
568C23C2×#13511yescharacteristic
569C23C2×#13511yescharacteristic
570C23C2×AGL(1,ℤ/8)11yescharacteristic
571C23C2×AGL(1,ℤ/8)11yescharacteristic
572C23C2×#13711yescharacteristic
573C23C2×#13711yescharacteristic
574C23#57511yescharacteristic
575C23#57511yescharacteristic
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—416no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—416no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4—82no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4—82no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—82no—
653C2×C4#38514yes—
654C2×C4#38514yes—
655C2×C4#38914yes—
656C2×C4#42714yes—
657C2×C4#42814yes—
658C2×C4#42814yes—
659C2×C4#44914yes—
660C2×C4#45214yes—
661C2×C4#48214yes—
662C2×C4#48514yes—
663C2×C4C2×C4×D411yescharacteristic
664C2×C4C2×C4×D411yescharacteristic
665C2×C4C2×C4×D411yescharacteristic
666C2×C4C2×C4×Q811yescharacteristic
667C2×C4C4×#4111yescharacteristic
668C2×C4C4×#4111yescharacteristic
669C2×C4C2×#12111yescharacteristic
670C2×C4C2×#12111yescharacteristic
671C2×C4C2×C22⋊Q811yescharacteristic
672C2×C4C2×C22⋊Q811yescharacteristic
673C2×C4C2×C22⋊Q811yescharacteristic
674C2×C4C2×C22⋊Q811yescharacteristic
675C2×C4#52511yescharacteristic
676C2×C4#52511yescharacteristic
677C2×C4#52511yescharacteristic
678C2×C4#52511yescharacteristic
679C2×C4C2×#12511yescharacteristic
680C2×C4#52911yescharacteristic
681C2×C4#52911yescharacteristic
682C2×C4#52911yescharacteristic
683C2×C4#52911yescharacteristic
684C2×C4C2×C4⋊Q811yescharacteristic
685C2×C4#53211yescharacteristic
686C2×C4#53211yescharacteristic
687C2×C4#53311yescharacteristic
688C2×C4#53311yescharacteristic
689C2×C4#53311yescharacteristic
690C2×C4#53311yescharacteristic
691C8—44no—
692C8—44no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22C2×#38511yescharacteristic
709C22C2×#38911yescharacteristic
710C22#229611yescharacteristic
711C22#284711yescharacteristic
712C22#284811yescharacteristic
713C22#285411yescharacteristic
714C22#285511yescharacteristic
715C22C2×#42711yescharacteristic
716C22C2×#42811yescharacteristic
717C22C2×#42811yescharacteristic
718C22#291111yescharacteristic
719C22C2×#44911yescharacteristic
720C22C2×#45211yescharacteristic
721C22#300611yescharacteristic
722C22#300711yescharacteristic
723C22#303511yescharacteristic
724C22#303511yescharacteristic
725C22#303811yescharacteristic
726C22#303911yescharacteristic
727C22#307611yescharacteristic
728C22#307611yescharacteristic
729C22#307911yescharacteristic
730C22#307911yescharacteristic
731C22C2×#48211yescharacteristic
732C22C2×#48511yescharacteristic
733C22#309411yescharacteristic
734C22#309511yescharacteristic
735C22#310611yescharacteristic
736C22#310611yescharacteristic
737C22#310711yescharacteristic
738C22#310711yescharacteristic
739C22#311511yescharacteristic
740C22#311511yescharacteristic
741C22#311611yescharacteristic
742C22#311611yescharacteristic
743C4—24no—
744C4—24no—
745C4—24no—
746C4—42no—
747C4—44no—
748C4—44no—
749C4—44no—
750C4—44no—
751C4—162no—
752C4—162no—
753C4#185418yescomplemented
754C4C4×#12111yescharacteristic
755C4C4×#12111yescharacteristic
756C4C4×C22⋊Q811yescharacteristic
757C4C4×C22⋊Q811yescharacteristic
758C4#285111yescharacteristic
759C4#285111yescharacteristic
760C4#285711yescharacteristic
761C4#285711yescharacteristic
762C2—44no—
763C2#1469711yescharacteristic
764C2C2×#185411yescharacteristic
765C2#2084611yescharacteristic
766C2#2116911yescharacteristic
767C2#2117111yescharacteristic
768C2#2136211yescharacteristic
769C2#2136411yescharacteristic
770C2#3290411yescharacteristic
771C2#3290711yescharacteristic
772C2#3295511yescharacteristic
773C2#3295811yescharacteristic
774C2#3311311yescharacteristic
775C2#3311411yescharacteristic
776C2#3315311yescharacteristic
777C2#3315411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
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
2. C2×#1948C2semidirect
3. C2×#1947C2semidirect
7. #10908C2semidirect
8. #10907C2semidirect
9. #10849C2semidirect
10. #10849C2semidirect
38. #1797C4semidirect
753. C4#1854semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1172
C2×#19482
C2×#19472
C2×#18542
C2×#17972
#146862
#109082
#109072
#108492
#107312