Finite Group Databasebeta

← #402183

Subgroups — #402183

Order 512.

1766 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2092C211yesmaximal, characteristic, complemented
2C2×#1893C211yesmaximal, characteristic
3C2×#1893C211yesmaximal, characteristic
4C2×#1808C211yesmaximal, characteristic, complemented
5C2×#1807C211yesmaximal, characteristic, complemented
6C22×#336C211yesmaximal, characteristic, complemented
7#14698C211yesmaximal, characteristic
8#14682C211yesmaximal, characteristic, complemented
9#11378C211yesmaximal, characteristic, complemented
10#11377C211yesmaximal, characteristic, complemented
11#11372C211yesmaximal, characteristic, complemented
12#11325C211yesmaximal, characteristic, complemented
13#11123C211yesmaximal, characteristic, complemented
14#11121C211yesmaximal, characteristic, complemented
15#11051C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#386—22no—
31C2×#382C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36#2092—24no—
37#1893—24no—
38#1893—24no—
39#1808—24no—
40#1807—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336—24no—
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1437—22no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—22no—
60C22⋊#95—22no—
61C23×D4—21no—
62C23×D4C2311yescharacteristic
63C24×C4D412yes—
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8D414yes—
78C23×C8D414yes—
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C2×#121—22no—
84C2×#121—22no—
85C2×#121—22no—
86C2×#121—22no—
87C2×#121—22no—
88C2×#121Q814yes—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—22no—
106C22×C42—41no—
107C22×C42—41no—
108C22×C42D412yes—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—41no—
116C2×#107—41no—
117C2×#106—22no—
118C2×#106—22no—
119C2×#106—22no—
120C2×#106—22no—
121C2×#106—41no—
122C2×#106—41no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—41no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102—41no—
135#390—22no—
136#390—22no—
137#390—41no—
138#390—41no—
139#386—48no—
140#382—22no—
141#382—22no—
142#382—41no—
143#382—41no—
144#380—22no—
145#380—22no—
146#380—22no—
147#380—22no—
148#380—22no—
149#380—22no—
150C2×#95—22no—
151C2×#95—22no—
152C2×#95—22no—
153C2×#95—22no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—22no—
157C2×#95—22no—
158C2×#95—21no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336D414yescomplemented
171C25—21no—
172C25C2×D411yescharacteristic
173C22×D4—24no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—44no—
190C22×D4—44no—
191C22×D4C2×Q812yes—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4C2×D412yes—
215C23×C4C2×D412yes—
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D412yes—
218C23×C4C2×D412yes—
219C23×C4C2×Q812yes—
220C23×C4#4112yes—
221C23×C4#4112yes—
222C23×C4#4112yes—
223C23×C4C2411yescharacteristic
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—28no—
233C22×C8—28no—
234C22×C8—21no—
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—28no—
247C22×C8—28no—
248C22×C8—44no—
249C22×C8—44no—
250C22×C8—44no—
251C22×C8—44no—
252C22×C8—44no—
253C22×C8—44no—
254C22×C8—44no—
255C22×C8—44no—
256C22×C8—44no—
257C22×C8—44no—
258C22×C8C2×D412yes—
259C22×C8C2×D412yes—
260C22×C8C2×D412yes—
261C22×C8C2×D412yes—
262C22×C8C2×D412yes—
263C22×C8C2×D412yes—
264C22×C8#4112yes—
265C22×C8#4112yes—
266#121—28no—
267#121—28no—
268#121—44no—
269#121—44no—
270C2×C4⋊C4—21no—
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—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4C2×Q812yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—44no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42—42no—
344C2×C42C2×D412yes—
345C2×C42#4112yes—
346#107—44no—
347#107—44no—
348#106—44no—
349#106—44no—
350#102—44no—
351#102—44no—
352#102—44no—
353#102—44no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—44no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24C22⋊Q812yes—
381C24#12312yes—
382C24#12712yes—
383C24#13514yes—
384C24AGL(1,ℤ/8)14yes—
385C24C22×D411yescharacteristic
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—48no—
393C2×D4—416no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—88no—
417C2×D4—84no—
418C2×D4—84no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—216no—
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—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4#12114yes—
502C22×C4C22⋊Q814yes—
503C22×C4C22⋊Q814yes—
504C22×C4C22⋊Q812yes—
505C22×C4#12314yes—
506C22×C4#12314yes—
507C22×C4#12312yes—
508C22×C4#12712yes—
509C22×C4#13514yes—
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×Q811yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C42−1+411yescharacteristic
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—416no—
543C2×C8—416no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8#12114yes—
553C2×C8#12114yes—
554C4⋊C4—22no—
555C4⋊C4—22no—
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—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C22⋊C4—48no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—84no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—48no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—44no—
616C23—42no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—82no—
621C23—82no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—82no—
629C23—81no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23—82no—
635C23—81no—
636C23—82no—
637C23—82no—
638C23#39914yes—
639C23#47818yes—
640C23#48218yes—
641C23#49514yes—
642C23#49614yes—
643C23C2×#12111yescharacteristic
644C23C2×C22⋊Q811yescharacteristic
645C23C2×#12311yescharacteristic
646C23C2×#12711yescharacteristic
647C23#53211yescharacteristic
648C23#53411yescharacteristic
649C23#53711yescharacteristic
650C23C2×#13512yes—
651C23C2×#13512yes—
652C23C2×AGL(1,ℤ/8)12yes—
653C23#57512yes—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—816no—
659D4—81no—
660D4—81no—
661D4—81no—
662D4—81no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—432no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—82no—
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—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4#39914yes—
728C2×C4C2×#12111yescharacteristic
729C2×C4C2×#12111yescharacteristic
730C2×C4C2×C22⋊Q811yescharacteristic
731C2×C4C2×C22⋊Q811yescharacteristic
732C2×C4C2×#12311yescharacteristic
733C2×C4C2×#12311yescharacteristic
734C2×C4#53211yescharacteristic
735C2×C4#53211yescharacteristic
736C2×C4#53411yescharacteristic
737C2×C4#53411yescharacteristic
738C2×C4#53711yescharacteristic
739C2×C4#53711yescharacteristic
740C2×C4#54611yescharacteristic
741C2×C4#54611yescharacteristic
742C2×C4#54611yescharacteristic
743C2×C4D4×Q811yescharacteristic
744C2×C4#55111yescharacteristic
745C2×C4#55111yescharacteristic
746C2×C4#55111yescharacteristic
747C2×C4#55111yescharacteristic
748C2×C4#55111yescharacteristic
749C2×C4#55111yescharacteristic
750C2×C4#55211yescharacteristic
751C2×C4#55211yescharacteristic
752C2×C4#55211yescharacteristic
753C2×C4#55411yescharacteristic
754C2×C4#55411yescharacteristic
755C2×C4#55411yescharacteristic
756C8—24no—
757C8—24no—
758C8—42no—
759C8—42no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—84no—
774C22—82no—
775C22—161no—
776C22—161no—
777C22—161no—
778C22—161no—
779C22—162no—
780C22—162no—
781C22#209218yescomplemented
782C22C2×#39911yescharacteristic
783C22#241211yescharacteristic
784C22#241711yescharacteristic
785C22#249811yescharacteristic
786C22#256411yescharacteristic
787C22#265611yescharacteristic
788C22#285611yescharacteristic
789C22#305012yes—
790C22#305512yes—
791C22C2×#47812yes—
792C22#307612yes—
793C22C2×#48212yes—
794C22#309112yes—
795C22C2×#49511yescharacteristic
796C22#314711yescharacteristic
797C22C2×#49611yescharacteristic
798C22#315011yescharacteristic
799C22#316812yes—
800C22#318012yes—
801C22#318812yes—
802C22#319112yes—
803C22#324712yes—
804C22#325012yes—
805C4—24no—
806C4—44no—
807C4—44no—
808C4—82no—
809C4—161no—
810C4—161no—
811C4—161no—
812C4—161no—
813C4—161no—
814C4—161no—
815C4#241211yescharacteristic
816C4#241211yescharacteristic
817C4#241711yescharacteristic
818C4#241711yescharacteristic
819C4#249811yescharacteristic
820C4#249811yescharacteristic
821C4#256411yescharacteristic
822C4#256411yescharacteristic
823C2—28no—
824C2—162no—
825C2#1483611yescharacteristic
826C2C2×#209211yescharacteristic
827C2#2373011yescharacteristic
828C2#2455512yes—
829C2#2483912yes—
830C2#2785912yes—
831C2#2916112yes—
832C2#3024111yescharacteristic
833C2#3024311yescharacteristic
834C2#3317311yescharacteristic
835C2#3318311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C23×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. C2×#2092C2semidirect
4. C2×#1808C2semidirect
5. C2×#1807C2semidirect
6. C22×#336C2semidirect
8. #14682C2semidirect
9. #11378C2semidirect
10. #11377C2semidirect
11. #11372C2semidirect
12. #11325C2semidirect
13. #11123C2semidirect
14. #11121C2semidirect
15. #11051C2semidirect
170. #336D4semidirect
781. C22#2092semidirect

Maximal subgroups

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

subgroupindex
C2×#20922
C2×#18932
C2×#18082
C2×#18072
C22×#3362
#146982
#146822
#113782
#113772
#113722
#113252
#111232
#111212
#110512