Finite Group Databasebeta

← #365603

Subgroups — #365603

Order 512.

1688 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×SD16C211yesmaximal, characteristic
2C2×#1973C211yesmaximal, characteristic
3C2×#1973C211yesmaximal, characteristic
4C2×#1942C211yesmaximal, characteristic, complemented
5C2×#1863C211yesmaximal, characteristic, complemented
6C2×#1864C211yesmaximal, characteristic
7C2×#1847C211yesmaximal, characteristic, complemented
8#13979C211yesmaximal, characteristic
9#13976C211yesmaximal, characteristic, complemented
10#11123C211yesmaximal, characteristic
11#11122C211yesmaximal, characteristic, complemented
12#11052C211yesmaximal, characteristic, complemented
13#11049C211yesmaximal, characteristic
14#10863C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×C4×SD16—24no—
20C2×C4×SD16—24no—
21C2×C4×SD16—24no—
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#382C2211yescharacteristic
44#1973—24no—
45#1973C418yescomplemented
46#1942—24no—
47#1864—24no—
48#1863—24no—
49#1847—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1444—22no—
58#1439—22no—
59#1436—22no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—22no—
63C4×#95C2211yescharacteristic
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16C2×C414yes—
72C22×SD16D414yes—
73C22×SD16Q814yes—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—41no—
83C2×C4×Q8—41no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—22no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—22no—
103C22×C42—21no—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C4×SD16—232no—
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—41no—
116C2×#107C2×C414yescomplemented
117C2×#106—22no—
118C2×#106—22no—
119C2×#106—22no—
120C2×#106—22no—
121C2×#106—41no—
122C2×#106D414yes—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—41no—
131C2×#103C2×C414yescomplemented
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—41no—
140C2×#102C2×C414yes—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97C2×C414yescomplemented
147C2×C4×C8—22no—
148C2×C4×C8—22no—
149C2×C4×C8D414yes—
150#391—22no—
151#391—22no—
152#391—41no—
153#391C2×C414yescomplemented
154#390—22no—
155#390—22no—
156#390—41no—
157#390C2×C414yes—
158#389—22no—
159#389—22no—
160#389—22no—
161#389—22no—
162#384—22no—
163#384—41no—
164#382—22no—
165#382—41no—
166C2×#95—22no—
167C2×#95—21no—
168C2×#95—22no—
169C2×#95—21no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95D412yes—
174C2×#95D412yes—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#336—22no—
180#336—22no—
181#336D414yes—
182C25—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8C22×C412yes—
195C22×Q8C2×D412yes—
196C22×Q8C2×Q812yes—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4C22×C412yes—
209C22×D4C2×D412yes—
210C22×D4C2×Q812yes—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—44no—
222C23×C4—82no—
223C23×C4C2×D412yes—
224C23×C4C2×D412yes—
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2411yescharacteristic
228C2×SD16—28no—
229C2×SD16—28no—
230C2×SD16—28no—
231C2×SD16—28no—
232C2×SD16—28no—
233C2×SD16—28no—
234C2×SD16C4⋊C4116yescomplemented
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8C22×C412yes—
252C22×C8C22×C412yes—
253C22×C8C2×D412yes—
254C22×C8C2×D412yes—
255C22×C8C2×D412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C22×C8C2×Q812yes—
260C22×C8#4112yes—
261C22×C8#4112yes—
262C22×C8#4112yes—
263C4×Q8—28no—
264C4×Q8—44no—
265C4×Q8—44no—
266C4×Q8—44no—
267C4×D4—28no—
268C4×D4—44no—
269C4×D4—44no—
270C4×D4—44no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—82no—
311C2×C4⋊C4—82no—
312C2×C4⋊C4—82no—
313C2×C4⋊C4C22×C412yes—
314C2×C4⋊C4C22×C412yes—
315C2×C4⋊C4C2×D412yes—
316C2×C4⋊C4C2×D412yes—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—82no—
324C2×C22⋊C4—82no—
325C2×C22⋊C4—82no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42C22×C412yes—
344C2×C42C2×D412yes—
345C2×C42C2×D412yes—
346C2×C42#4112yes—
347#107—28no—
348#107—44no—
349#107—44no—
350#106—28no—
351#106—44no—
352#103—28no—
353#103—28no—
354#103—44no—
355#102—28no—
356#102—28no—
357#102—44no—
358#97—28no—
359#97—44no—
360C4×C8—28no—
361#95—28no—
362#95—24no—
363#95—42no—
364#95—44no—
365#95—44no—
366#95—42no—
367#95—42no—
368#95—82no—
369#95—82no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24C22×D411yescharacteristic
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8C2×C4⋊C414yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4C2×C4⋊C414yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—48no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—88no—
497C22×C4—88no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4C4×D414yes—
501C22×C4#12712yes—
502C22×C4#12712yes—
503C22×C4#13714yes—
504C22×C4C23×C411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×Q811yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C42−1+411yescharacteristic
517C22×C42−1+411yescharacteristic
518SD16—232no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8C2×C4⋊C414yes—
540C2×C8C4×D414yes—
541C2×C8C4×D414yes—
542C2×C8C4×D414yes—
543C2×C8#12014yes—
544C2×C8C22⋊Q814yes—
545C2×C8C22⋊Q814yes—
546C2×C8#12314yes—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—48no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—84no—
573C4⋊C4—84no—
574C4⋊C4—88no—
575C22⋊C4—48no—
576C22⋊C4—88no—
577C22⋊C4—88no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—48no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C23—24no—
592C23—42no—
593C23—42no—
594C23—44no—
595C23—44no—
596C23—42no—
597C23—42no—
598C23—44no—
599C23—44no—
600C23—42no—
601C23—44no—
602C23—44no—
603C23—42no—
604C23—82no—
605C23—82no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—82no—
611C23—82no—
612C23—82no—
613C23—82no—
614C23C2×C4×D411yescharacteristic
615C23C2×#12711yescharacteristic
616C23#53211yescharacteristic
617C23D4211yescharacteristic
618C23D4211yescharacteristic
619C23#54711yescharacteristic
620C23D4×Q811yescharacteristic
621C23C2×#13712yes—
622C23#57512yes—
623C23#57612yes—
624C23#57712yes—
625Q8—24no—
626Q8—24no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—42no—
632Q8—42no—
633D4—24no—
634D4—24no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—42no—
639D4—42no—
640D4—42no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—816no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4#49714yes—
703C2×C4C22×C4⋊C411yescharacteristic
704C2×C4C2×C4×D411yescharacteristic
705C2×C4C2×C4×D411yescharacteristic
706C2×C4C2×C4×D411yescharacteristic
707C2×C4#52011yescharacteristic
708C2×C4#52011yescharacteristic
709C2×C4C2×#12011yescharacteristic
710C2×C4C2×C22⋊Q811yescharacteristic
711C2×C4C2×C22⋊Q811yescharacteristic
712C2×C4C2×#12311yescharacteristic
713C2×C4#53211yescharacteristic
714C2×C4#53211yescharacteristic
715C2×C4#53511yescharacteristic
716C2×C4#53611yescharacteristic
717C2×C4#54211yescharacteristic
718C2×C4#54211yescharacteristic
719C2×C4D4211yescharacteristic
720C2×C4D4211yescharacteristic
721C2×C4#54711yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4#54811yescharacteristic
725C2×C4#54811yescharacteristic
726C2×C4D4×Q811yescharacteristic
727C2×C4#55311yescharacteristic
728C2×C4#55311yescharacteristic
729C2×C4#55411yescharacteristic
730C2×C4#55411yescharacteristic
731C8—24no—
732C8—42no—
733C8—42no—
734C8#38518yes—
735C22—48no—
736C22—44no—
737C22—84no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—84no—
745C22—84no—
746C22C4×#12711yescharacteristic
747C22D4×C4⋊C411yescharacteristic
748C22#236111yescharacteristic
749C22#242211yescharacteristic
750C22#243311yescharacteristic
751C22#245211yescharacteristic
752C22#254211yescharacteristic
753C22C4×#13712yes—
754C22#294612yes—
755C22C2×#49711yescharacteristic
756C22#315011yescharacteristic
757C22#315411yescharacteristic
758C22#315511yescharacteristic
759C22#317212yes—
760C22#317912yes—
761C22#326612yes—
762C22#326612yes—
763C22#326812yes—
764C22#326812yes—
765C22#335112yes—
766C22#335712yes—
767C22#338512yes—
768C22#338812yes—
769C4—24no—
770C4—44no—
771C4—42no—
772C4—44no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—161no—
779C4—161no—
780C4C2×#38511yescharacteristic
781C4#232611yescharacteristic
782C4D4×C4⋊C411yescharacteristic
783C4#236111yescharacteristic
784C4#242211yescharacteristic
785C4#243211yescharacteristic
786C4#245211yescharacteristic
787C4#256611yescharacteristic
788C2—84no—
789C2#1397711yescharacteristic
790C2C4×#49711yescharacteristic
791C2#2170411yescharacteristic
792C2#2267812yes—
793C2#2303512yes—
794C2#2503712yes—
795C2#2578411yescharacteristic
796C2#2578511yescharacteristic
797C2#2648712yes—
798C2#2853711yescharacteristic
799C2#2853911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1942C2semidirect
5. C2×#1863C2semidirect
7. C2×#1847C2semidirect
9. #13976C2semidirect
11. #11122C2semidirect
12. #11052C2semidirect
14. #10863C2semidirect
15. #10696C2semidirect
45. #1973C4semidirect
116. C2×#107C2×C4semidirect
131. C2×#103C2×C4semidirect
146. C2×#97C2×C4semidirect
153. #391C2×C4semidirect
234. C2×SD16C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×SD162
C2×#19732
C2×#19422
C2×#18632
C2×#18642
C2×#18472
#139792
#139762
#111232
#111222
#110522
#110492
#108632
#106962