Finite Group Databasebeta

← #368182

Subgroups — #368182

Order 512.

2240 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1874C211yesmaximal, characteristic
3C2×#1874C211yesmaximal, characteristic
4C2×#1852C211yesmaximal, characteristic, complemented
5C2×C4⋊#95C211yesmaximal, characteristic, complemented
6#11292C212yesmaximal, complemented
7#11123C212yesmaximal, complemented
8#10907C212yesmaximal, complemented
9#10788C212yesmaximal, complemented
10#10730C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C22×#121C2211yescharacteristic
13C22×C4×D4—21no—
14C22×C4×D4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×#107C2212yes—
19C22×#102C2212yes—
20C22×#102C2212yes—
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C4×#121—24no—
24C4×#121—24no—
25C2×#390C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#388—21no—
28C2×#386—21no—
29C2×#380C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4—21no—
32C22×#95—21no—
33C22×#95—21no—
34#1874—24no—
35#1874C418yescomplemented
36#1852—24no—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44C4⋊#95—21no—
45C4⋊#95—21no—
46C4⋊#95C2212yes—
47C4⋊#95C2212yes—
48C23×D4—21no—
49C23×D4C2311yescharacteristic
50C24×C4—21no—
51C24×C4—21no—
52C24×C4—21no—
53C24×C4D411yescharacteristic
54C24×C4D411yescharacteristic
55C24×C4C2311yescharacteristic
56C23×C8C2312yes—
57C23×C8C2312yes—
58C2×#121—22no—
59C2×#121—22no—
60C2×#121—22no—
61C2×#121C2×C414yes—
62C2×#121D414yes—
63C2×#121Q814yes—
64C2×C4×D4—28no—
65C2×C4×D4—22no—
66C2×C4×D4—22no—
67C2×C4×D4—24no—
68C2×C4×D4—42no—
69C2×C4×D4—44no—
70C2×C4×D4—44no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—42no—
79C22×C4⋊C4—42no—
80C22×C4⋊C4—42no—
81C22×C4⋊C4C2×C414yescomplemented
82C22×C4⋊C4C2312yes—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2311yescharacteristic
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—21no—
95C22×C42—24no—
96C22×C42—42no—
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×#107—24no—
102C2×#107—24no—
103C2×#107—42no—
104C2×#102—24no—
105C2×#102—24no—
106C2×#102—42no—
107C2×#102—42no—
108C2×#102—42no—
109C2×#102C2×C418yescomplemented
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8C2×C414yescomplemented
116#390—22no—
117#390—22no—
118#389—22no—
119#389—22no—
120#388—28no—
121#386—28no—
122#380—22no—
123#380D414yes—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—22no—
126C4×C22⋊C4—28no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—22no—
131C2×#95—22no—
132C2×#95—22no—
133C2×#95—22no—
134C2×#95—44no—
135C2×#95—44no—
136#340—24no—
137#340—24no—
138#340—42no—
139#340—42no—
140#340C2×C418yescomplemented
141#336—24no—
142#336—42no—
143C25—21no—
144C25C2×D411yescharacteristic
145C22×D4—24no—
146C22×D4—24no—
147C22×D4—24no—
148C22×D4—21no—
149C22×D4—22no—
150C22×D4—22no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—22no—
154C22×D4—22no—
155C22×D4—42no—
156C22×D4—42no—
157C22×D4—42no—
158C22×D4—42no—
159C22×D4C22×C412yes—
160C22×D4C2×D412yes—
161C22×D4C2×Q812yes—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—24no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—41no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—41no—
187C23×C4—42no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4D814yes—
206C23×C4C22×C412yes—
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D412yes—
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D412yes—
213C23×C4C2×D411yescharacteristic
214C23×C4C2×Q812yes—
215C23×C4#4112yes—
216C23×C4#4112yes—
217C23×C4C2411yescharacteristic
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8C22×C414yes—
232#121—28no—
233#121—28no—
234#121—28no—
235#121C4⋊C4116yes—
236C4×D4—48no—
237C4×D4—48no—
238C4×D4—432no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—48no—
262C2×C4⋊C4—48no—
263C2×C4⋊C4—48no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—48no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4C22×C414yes—
272C2×C4⋊C4C22×C412yes—
273C2×C4⋊C4C2×D412yes—
274C2×C4⋊C4C2×D412yes—
275C2×C4⋊C4C2×D412yes—
276C2×C4⋊C4C2×Q812yes—
277C2×C4⋊C4#4114yes—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—22no—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—48no—
306C2×C42—48no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42#4114yes—
312#107—48no—
313#102—48no—
314#102—48no—
315C22⋊C8—28no—
316C22⋊C8—44no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—44no—
321#95—44no—
322#95—44no—
323#95—44no—
324C24—21no—
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24—41no—
339C24—41no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24C4×D412yes—
348C24#12012yes—
349C24C22⋊Q812yes—
350C24C2×D812yes—
351C24#13512yes—
352C24AGL(1,ℤ/8)12yes—
353C24#13712yes—
354C24C22×D411yescharacteristic
355C2×D4—216no—
356C2×D4—22no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—48no—
366C2×D4—48no—
367C2×D4—48no—
368C2×D4—48no—
369C2×D4—48no—
370C2×D4—48no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4C2×C4⋊C414yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
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—24no—
398C22×C4—28no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
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—28no—
421C22×C4—28no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—48no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—44no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—44no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—48no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—48no—
474C22×C4—84no—
475C22×C4—84no—
476C22×C4—84no—
477C22×C4—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—84no—
485C22×C4—84no—
486C22×C4C2×C4⋊C414yes—
487C22×C4C4×D414yes—
488C22×C4C4×D412yes—
489C22×C4#12012yes—
490C22×C4C22⋊Q814yes—
491C22×C4C22⋊Q812yes—
492C22×C4#12312yes—
493C22×C4#12314yes—
494C22×C4#12312yes—
495C22×C4C2×D812yes—
496C22×C4C2×D812yes—
497C22×C4AGL(1,ℤ/8)12yes—
498C22×C4#13712yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4112yes—
505C22×C4C2×#4112yes—
506C22×C4C2×#4111yescharacteristic
507C22×C4H(5,𝔽2)12yes—
508C22×C4H(5,𝔽2)12yes—
509C2×C8—24no—
510C2×C8—24no—
511C2×C8—24no—
512C2×C8—42no—
513C2×C8—42no—
514C2×C8—42no—
515C2×C8—42no—
516C2×C8—42no—
517C2×C8—42no—
518C2×C8—42no—
519C2×C8—42no—
520C2×C8—42no—
521C2×C8—42no—
522C2×C8—42no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4C2×C4⋊C414yes—
542C22⋊C4—216no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C42—24no—
548C42—24no—
549C42—44no—
550C42—44no—
551C42—48no—
552C42—42no—
553C42—42no—
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—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—81no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23#38514yes—
618C23C4×D814yes—
619C23#44014yes—
620C23#44714yes—
621C23#45214yes—
622C23#47414yes—
623C23#47814yes—
624C23C2×C4×D411yescharacteristic
625C23C2×#12011yescharacteristic
626C23C2×C22⋊Q811yescharacteristic
627C23C2×#12311yescharacteristic
628C23#52511yescharacteristic
629C23#53411yescharacteristic
630C23#53511yescharacteristic
631C23C22×D811yescharacteristic
632C23C2×#13511yescharacteristic
633C23C2×AGL(1,ℤ/8)11yescharacteristic
634C23C2×AGL(1,ℤ/8)11yescharacteristic
635C23C2×#13711yescharacteristic
636C23C2×#13711yescharacteristic
637C23#57511yescharacteristic
638C23#57511yescharacteristic
639D4—28no—
640D4—432no—
641D4—44no—
642D4—44no—
643D4—44no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—416no—
671C2×C4—416no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—816no—
703C2×C4—816no—
704C2×C4—816no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—82no—
710C2×C4—81no—
711C2×C4—82no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4#38514yes—
722C2×C4#48014yes—
723C2×C4C22×C4⋊C411yescharacteristic
724C2×C4C2×C4×D411yescharacteristic
725C2×C4C4×#4112yes—
726C2×C4#51812yes—
727C2×C4C2×C22⋊Q811yescharacteristic
728C2×C4C2×#12311yescharacteristic
729C2×C4#52912yes—
730C2×C4#53812yes—
731C2×C4#54612yes—
732C2×C4#54612yes—
733C2×C4#54612yes—
734C2×C4#54612yes—
735C2×C4#55312yes—
736C2×C4#55312yes—
737C2×C4#55412yes—
738C2×C4#55412yes—
739C8—44no—
740C8—82no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22#186218yes—
771C22C2×#38511yescharacteristic
772C22C4×#12311yescharacteristic
773C22#232111yescharacteristic
774C22#240411yescharacteristic
775C22#240511yescharacteristic
776C22#248711yescharacteristic
777C22#257911yescharacteristic
778C22C2×C4×D811yescharacteristic
779C22C2×#44011yescharacteristic
780C22C4×AGL(1,ℤ/8)11yescharacteristic
781C22C4×#13711yescharacteristic
782C22C2×#44711yescharacteristic
783C22C2×#45211yescharacteristic
784C22#300611yescharacteristic
785C22#300711yescharacteristic
786C22C2×#47411yescharacteristic
787C22C2×#47811yescharacteristic
788C22#307911yescharacteristic
789C22#308011yescharacteristic
790C22C2×#48011yescharacteristic
791C22#309111yescharacteristic
792C22#309211yescharacteristic
793C22#309411yescharacteristic
794C22#310011yescharacteristic
795C22#310811yescharacteristic
796C22#310911yescharacteristic
797C22#311711yescharacteristic
798C22#318611yescharacteristic
799C22#318811yescharacteristic
800C22#319311yescharacteristic
801C22#319611yescharacteristic
802C22#320511yescharacteristic
803C22#321111yescharacteristic
804C22#321311yescharacteristic
805C22#321811yescharacteristic
806C4—24no—
807C4—24no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—84no—
813C4—82no—
814C4—84no—
815C4—82no—
816C4#234912yes—
817C4#236412yes—
818C4#244412yes—
819C4#245012yes—
820C2—28no—
821C2—84no—
822C2#1401611yescharacteristic
823C2C2×#186211yescharacteristic
824C2#2087511yescharacteristic
825C2C4×#48011yescharacteristic
826C2#2158011yescharacteristic
827C2#2204011yescharacteristic
828C2#2204711yescharacteristic
829C2#2393011yescharacteristic
830C2#2393711yescharacteristic
831C2#2400211yescharacteristic
832C2#2400711yescharacteristic
833C2#2767711yescharacteristic
834C2#2768411yescharacteristic
835C2#2923411yescharacteristic
836C2#2923811yescharacteristic
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
4. C2×#1852C2semidirect
5. C2×C4⋊#95C2semidirect
6. #11292C2semidirect
7. #11123C2semidirect
8. #10907C2semidirect
9. #10788C2semidirect
10. #10730C2semidirect
11. #10712C2semidirect
35. #1874C4semidirect
81. C22×C4⋊C4C2×C4semidirect
109. C2×#102C2×C4semidirect
115. C2×C22⋊C8C2×C4semidirect
140. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#18742
C2×#18522
C2×C4⋊#952
#112922
#111232
#109072
#107882
#107302
#107122