Finite Group Databasebeta

← #357733

Subgroups — #357733

Order 512.

3002 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#417C211yesmaximal, characteristic
2C22×#416C211yesmaximal, characteristic
3C2×#2317C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#11067C214yesmaximal, complemented
9#11066C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C24×C8C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C2×#417—24no—
18C2×#417—24no—
19C2×#417—24no—
20C2×#416—24no—
21C2×#416—24no—
22C2×#416C418yescomplemented
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×#102C2212yes—
26C22×#102C2212yes—
27#2317—24no—
28#2317—24no—
29#2311—24no—
30#2311—24no—
31C2×#391C2212yes—
32C2×#390C2212yes—
33C2×#389C2214yes—
34C2×#386—22no—
35C2×#385—22no—
36C2×#384—21no—
37C2×#382—21no—
38C2×#380—21no—
39C2×#380—21no—
40#1736—24no—
41C2×#340—24no—
42C2×#340C2214yes—
43C2×#340C2214yes—
44#1729—24no—
45C2×#336C2214yes—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41C2×C414yes—
58C22×#41D414yes—
59C22×#41Q814yes—
60C23×Q8C2311yescharacteristic
61C23×D4—21no—
62C23×D4C2311yescharacteristic
63C24×C4—21no—
64C24×C4—21no—
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16D414yes—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8C2×C414yes—
81C23×C8C2312yes—
82C23×C8C2312yes—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117C2×C414yes—
93C2×#117D414yes—
94C2×#117D414yes—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4D411yescharacteristic
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4D414yes—
111C22×C4⋊C4D414yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—22no—
117C22×C22⋊C4—22no—
118C22×C22⋊C4D412yes—
119C22×C42—21no—
120C22×C42C2312yes—
121#417—232no—
122#416—232no—
123C2×#103—24no—
124C2×#103—24no—
125C2×#103—24no—
126C2×#103—24no—
127C2×#103—24no—
128C2×#103C2×C418yescomplemented
129C2×#102—24no—
130C2×#102—24no—
131C2×#102—24no—
132C2×#102—24no—
133C2×#102—24no—
134C2×#102C2×C418yescomplemented
135#391—24no—
136#391—24no—
137#390—24no—
138#390—24no—
139#389—28no—
140#389—28no—
141#386—216no—
142#385—216no—
143#384—28no—
144#382—28no—
145#380—28no—
146#380—28no—
147C2×#95—22no—
148C2×#95—22no—
149C2×#95—24no—
150#340—28no—
151#340—28no—
152#336—28no—
153C25—21no—
154C25C2×D411yescharacteristic
155C2×#41—28no—
156C2×#41—28no—
157C2×#41—28no—
158C2×#41—28no—
159C2×#41—28no—
160C2×#41—28no—
161C2×#41—28no—
162C2×#41—28no—
163C2×#41—28no—
164C2×#41—28no—
165C2×#41—28no—
166C2×#41—28no—
167C2×#41—28no—
168C2×#41—28no—
169C2×#41—28no—
170C2×#41—44no—
171C2×#41—44no—
172C2×#41—44no—
173C2×#41—44no—
174C2×#41—44no—
175C2×#41—44no—
176C2×#41—44no—
177C2×#41—44no—
178C2×#41—44no—
179C2×#41—44no—
180C2×#41—44no—
181C2×#41—44no—
182C2×#41C4⋊C4116yescomplemented
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—24no—
198C22×D4—24no—
199C22×D4—24no—
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×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4C22×C412yes—
216C22×D4C2×D412yes—
217C22×D4C2×Q812yes—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—82no—
236C23×C4—82no—
237C23×C4—82no—
238C23×C4—82no—
239C23×C4C22×C412yes—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D412yes—
248C23×C4C2×D412yes—
249C23×C4C2×Q812yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4#4112yes—
253C23×C4#4112yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C2×M16—28no—
258C2×M16—28no—
259C2×M16—28no—
260C2×M16—44no—
261C2×M16—44no—
262C2×M16—44no—
263C2×M16—44no—
264C22×C8—28no—
265C22×C8—28no—
266C22×C8—28no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—44no—
280C22×C8—44no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8C22×C414yes—
284C22×C8C2×D414yes—
285#117—28no—
286#117—28no—
287#117—28no—
288#117—44no—
289#117—44no—
290#117—44no—
291#117—44no—
292#117C22⋊C4116yescomplemented
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—216no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—84no—
328C2×C4⋊C4—84no—
329C2×C4⋊C4C22×C414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—84no—
343C2×C22⋊C4—84no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353#103—216no—
354#103—216no—
355#102—216no—
356#102—216no—
357#95—28no—
358#95—28no—
359#95—216no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24C4×D412yes—
376C24#12012yes—
377C24#12012yes—
378C24#12112yes—
379C24#12112yes—
380C24C22⋊Q812yes—
381C24#12412yes—
382C24C22×D411yescharacteristic
383#41—232no—
384#41—232no—
385#41—416no—
386#41—416no—
387#41—416no—
388#41—416no—
389#41—416no—
390#41—416no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8C2×C4⋊C414yes—
419C2×D4—216no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×C4⋊C414yes—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—216no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—88no—
500C22×C4—88no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—88no—
504C22×C4—88no—
505C22×C4C2×C22⋊C414yes—
506C22×C4C2×C4⋊C414yes—
507C22×C4#11714yes—
508C22×C4C4×D414yes—
509C22×C4C4×D414yes—
510C22×C4C4×D414yes—
511C22×C4C4×D412yes—
512C22×C4#12014yes—
513C22×C4#12012yes—
514C22×C4#12012yes—
515C22×C4#12114yes—
516C22×C4#12114yes—
517C22×C4#12114yes—
518C22×C4#12114yes—
519C22×C4#12114yes—
520C22×C4#12114yes—
521C22×C4#12112yes—
522C22×C4#12112yes—
523C22×C4C22⋊Q814yes—
524C22×C4C22⋊Q814yes—
525C22×C4C22⋊Q814yes—
526C22×C4C22⋊Q814yes—
527C22×C4C22⋊Q814yes—
528C22×C4C22⋊Q812yes—
529C22×C4#12314yes—
530C22×C4#12314yes—
531C22×C4#12314yes—
532C22×C4#12314yes—
533C22×C4#12314yes—
534C22×C4#12414yes—
535C22×C4#12414yes—
536C22×C4#12412yes—
537C22×C4#12614yes—
538C22×C4#12614yes—
539C22×C4#12714yes—
540C22×C4C23×C411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×Q811yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554M16—416no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—42no—
564C2×C8—42no—
565C2×C8—42no—
566C2×C8—42no—
567C2×C8—42no—
568C2×C8—42no—
569C2×C8—416no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—48no—
585C4⋊C4—816no—
586C4⋊C4C2×C22⋊C418yes—
587C22⋊C4—216no—
588C22⋊C4—48no—
589C22⋊C4—88no—
590C22⋊C4—88no—
591C42—216no—
592C42—42no—
593C42—42no—
594C42—42no—
595C42—42no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—44no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—44no—
620C23—44no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—82no—
628C23—82no—
629C23—82no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23—82no—
635C23#38514yes—
636C23#38614yes—
637C23#38814yes—
638C23#39214yes—
639C23#39314yes—
640C23#39414yes—
641C23#39614yes—
642C23C2×C4×D411yescharacteristic
643C23C2×#12011yescharacteristic
644C23C2×#12011yescharacteristic
645C23C2×#12111yescharacteristic
646C23C2×#12111yescharacteristic
647C23C2×C22⋊Q811yescharacteristic
648C23C2×#12411yescharacteristic
649C23#57612yes—
650C23#57712yes—
651C23#57712yes—
652C23#57812yes—
653Q8—24no—
654Q8—24no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661D4—24no—
662D4—24no—
663D4—432no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—42no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—432no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—816no—
701C2×C4—816no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4#38018yes—
708C2×C4#38514yes—
709C2×C4#38518yes—
710C2×C4#38614yes—
711C2×C4#38814yes—
712C2×C4#38818yes—
713C2×C4#39018yes—
714C2×C4#39214yes—
715C2×C4#39314yes—
716C2×C4#39418yes—
717C2×C4#39414yes—
718C2×C4#39618yes—
719C2×C4#39614yes—
720C2×C4#39718yes—
721C2×C4#39918yes—
722C2×C4C22×C22⋊C411yescharacteristic
723C2×C4C22×C4⋊C411yescharacteristic
724C2×C4C2×#11711yescharacteristic
725C2×C4C2×C4×D411yescharacteristic
726C2×C4C2×C4×D411yescharacteristic
727C2×C4C2×C4×D411yescharacteristic
728C2×C4C2×#12011yescharacteristic
729C2×C4C2×#12111yescharacteristic
730C2×C4C2×#12111yescharacteristic
731C2×C4C2×#12111yescharacteristic
732C2×C4C2×#12111yescharacteristic
733C2×C4C2×#12111yescharacteristic
734C2×C4C2×#12111yescharacteristic
735C2×C4C2×C22⋊Q811yescharacteristic
736C2×C4C2×C22⋊Q811yescharacteristic
737C2×C4C2×C22⋊Q811yescharacteristic
738C2×C4C2×C22⋊Q811yescharacteristic
739C2×C4C2×C22⋊Q811yescharacteristic
740C2×C4C2×#12311yescharacteristic
741C2×C4C2×#12311yescharacteristic
742C2×C4C2×#12311yescharacteristic
743C2×C4C2×#12311yescharacteristic
744C2×C4C2×#12311yescharacteristic
745C2×C4C2×#12411yescharacteristic
746C2×C4C2×#12411yescharacteristic
747C2×C4C2×#12611yescharacteristic
748C2×C4C2×#12611yescharacteristic
749C2×C4C2×#12711yescharacteristic
750C8—44no—
751C8—44no—
752C22—28no—
753C22—28no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—28no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—84no—
766C22—84no—
767C22—82no—
768C22—82no—
769C22—84no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22#143918yes—
774C22C2×#38511yescharacteristic
775C22C2×#38611yescharacteristic
776C22C2×#38811yescharacteristic
777C22C2×#39211yescharacteristic
778C22C2×#39311yescharacteristic
779C22C2×#39411yescharacteristic
780C22C2×#39611yescharacteristic
781C22#295112yes—
782C22#295212yes—
783C22#300811yescharacteristic
784C22#300911yescharacteristic
785C22#301011yescharacteristic
786C22#301111yescharacteristic
787C22#301212yes—
788C22#301312yes—
789C22#304512yes—
790C22#304612yes—
791C22#306212yes—
792C22#306312yes—
793C22#308312yes—
794C22#308412yes—
795C22#313612yes—
796C22#313712yes—
797C4—44no—
798C4—48no—
799C4—82no—
800C4—84no—
801C4—82no—
802C4—84no—
803C4#143918yes—
804C4C2×#38011yescharacteristic
805C4C2×#38511yescharacteristic
806C4C2×#38811yescharacteristic
807C4C2×#39011yescharacteristic
808C4C2×#39411yescharacteristic
809C4C2×#39611yescharacteristic
810C4C2×#39711yescharacteristic
811C4C2×#39911yescharacteristic
812C2—28no—
813C2—84no—
814C2C2×#143911yescharacteristic
815C2#2088111yescharacteristic
816C2#2088211yescharacteristic
817C2#2093712yes—
818C2#2108712yes—
819C2#2339311yescharacteristic
820C2#2339411yescharacteristic
821C2#2345812yes—
822C2#2350911yescharacteristic
823C2#2351011yescharacteristic
824C2#2361612yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2317C2semidirect
5. C2×#1736C2semidirect
6. C22×#340C2semidirect
7. C2×#1729C2semidirect
8. #11067C2semidirect
9. #11066C2semidirect
22. C2×#416C4semidirect
128. C2×#103C2×C4semidirect
134. C2×#102C2×C4semidirect
182. C2×#41C4⋊C4semidirect
292. #117C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4172
C22×#4162
C2×#23172
C2×#23112
C2×#17362
C22×#3402
C2×#17292
#110672
#110662