Finite Group Databasebeta

← #399162

Subgroups — #399162

Order 512.

1614 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2317C211yesmaximal, characteristic
2C2×#2097C211yesmaximal, characteristic, complemented
3C2×#2095C211yesmaximal, characteristic, complemented
4C2×#1873C211yesmaximal, characteristic
5C2×#1872C211yesmaximal, characteristic
6C2×#1854C211yesmaximal, characteristic
7C2×#1852C211yesmaximal, characteristic
8#14258C211yesmaximal, characteristic
9#11373C211yesmaximal, characteristic, complemented
10#11372C211yesmaximal, characteristic, complemented
11#11325C211yesmaximal, characteristic, complemented
12#11324C211yesmaximal, characteristic, complemented
13#11052C211yesmaximal, characteristic, complemented
14#11050C211yesmaximal, characteristic, complemented
15#10713C211yesmaximal, characteristic
16C22×C22⋊Q8C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30#2317—24no—
31#2317—24no—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#389—22no—
35C2×#385—22no—
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#382C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#380C2211yescharacteristic
41#2097—24no—
42#2095—24no—
43#1873—24no—
44#1872—24no—
45#1854—24no—
46#1852—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1441—22no—
60#1440—22no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C23×Q8C2311yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C22⋊Q8—22no—
71C2×C22⋊Q8—22no—
72C2×C22⋊Q8—22no—
73C2×C22⋊Q8—22no—
74C2×C22⋊Q8—22no—
75C2×C22⋊Q8Q814yes—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—41no—
87C2×#117—41no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—41no—
97C22×C4⋊C4—41no—
98C22×C4⋊C4D412yes—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4D412yes—
110C22×C42—21no—
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—41no—
120C2×#107—41no—
121C2×#107—41no—
122C2×#106—22no—
123C2×#106—22no—
124C2×#106—41no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—41no—
134C2×#103—41no—
135C2×#103—41no—
136C2×#103—41no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8D414yes—
142C2×C22⋊C8D414yes—
143#391—22no—
144#391—22no—
145#391—22no—
146#391—22no—
147#389—216no—
148#385—216no—
149#384—22no—
150#384—22no—
151#384—22no—
152#384D414yes—
153#382—22no—
154#382—22no—
155#382—22no—
156#382D414yes—
157#380—22no—
158#380—22no—
159C2×#95—22no—
160C2×#95—22no—
161C2×#95—22no—
162C2×#95—22no—
163C2×#95—21no—
164C2×#95—22no—
165C2×#95—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178C25C2×D411yescharacteristic
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—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×Q8C2×Q812yes—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—24no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—82no—
213C23×C4—82no—
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—21no—
233C22×C8—21no—
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—21no—
247C22×C8—21no—
248C22×C8C2×D412yes—
249C22×C8C2×D412yes—
250C22×C8C2×D412yes—
251C22×C8C2×D412yes—
252C22⋊Q8—28no—
253C22⋊Q8—28no—
254C22⋊Q8—44no—
255C22⋊Q8—44no—
256#117—28no—
257#117—28no—
258#117—28no—
259#117—28no—
260#117—44no—
261#117—44no—
262#117—44no—
263#117—44no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
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—24no—
288C2×C4⋊C4—24no—
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—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—82no—
317C2×C4⋊C4—82no—
318C2×C4⋊C4—82no—
319C2×C4⋊C4—82no—
320C2×C4⋊C4C2×D412yes—
321C2×C4⋊C4C2×D412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4C2×D412yes—
324C2×C4⋊C4C2×Q812yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—82no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—24no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C2×D412yes—
348C2×C42C2×D412yes—
349C2×C42#4112yes—
350C2×C42#4112yes—
351#107—44no—
352#107—44no—
353#107—44no—
354#106—44no—
355#103—44no—
356#103—44no—
357#103—44no—
358#103—44no—
359C22⋊C8—28no—
360C22⋊C8—28no—
361#95—28no—
362#95—28no—
363#95—44no—
364#95—44no—
365#95—42no—
366#95—82no—
367#95—82no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24C22⋊Q812yes—
377C24#12312yes—
378C24#12712yes—
379C24C22×D411yescharacteristic
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
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—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
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—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—48no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—88no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—88no—
495C22×C4#12014yes—
496C22×C4C22⋊Q814yes—
497C22×C4C22⋊Q814yes—
498C22×C4C22⋊Q812yes—
499C22×C4#12314yes—
500C22×C4#12314yes—
501C22×C4#12314yes—
502C22×C4#12312yes—
503C22×C4#12712yes—
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C22×Q811yescharacteristic
509C22×C4C2×#4111yescharacteristic
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
518C2×C8—22no—
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—41no—
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×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C4⋊C4—216no—
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—22no—
556C4⋊C4—22no—
557C4⋊C4—48no—
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—48no—
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—88no—
578C4⋊C4—88no—
579C22⋊C4—216no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—84no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—48no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23#39914yes—
615C23C2×#12011yescharacteristic
616C23C2×C22⋊Q811yescharacteristic
617C23C2×#12311yescharacteristic
618C23C2×#12311yescharacteristic
619C23C2×#12711yescharacteristic
620C23#53511yescharacteristic
621C23#53611yescharacteristic
622C23#57612yes—
623C23#57712yes—
624C23#57812yes—
625C23#57812yes—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—81no—
631Q8—81no—
632Q8—81no—
633Q8—81no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
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—44no—
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—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—816no—
676C2×C4—82no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
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—81no—
689C2×C4—81no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—81no—
695C2×C4—82no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—81no—
705C2×C4#39914yes—
706C2×C4C2×C22⋊Q811yescharacteristic
707C2×C4C2×C22⋊Q811yescharacteristic
708C2×C4C2×#12311yescharacteristic
709C2×C4C2×#12311yescharacteristic
710C2×C4#52511yescharacteristic
711C2×C4#52511yescharacteristic
712C2×C4#52511yescharacteristic
713C2×C4#52511yescharacteristic
714C2×C4#53911yescharacteristic
715C2×C4#53911yescharacteristic
716C2×C4#53911yescharacteristic
717C2×C4#53911yescharacteristic
718C2×C4D4211yescharacteristic
719C2×C4D4211yescharacteristic
720C2×C4D4211yescharacteristic
721C2×C4D4211yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4#54711yescharacteristic
725C2×C4#54711yescharacteristic
726C2×C4#54811yescharacteristic
727C2×C4#54811yescharacteristic
728C2×C4D4×Q811yescharacteristic
729C2×C4D4×Q811yescharacteristic
730C2×C4#55311yescharacteristic
731C2×C4#55311yescharacteristic
732C2×C4#55411yescharacteristic
733C2×C4#55411yescharacteristic
734C8—42no—
735C8—42no—
736C8—42no—
737C8—42no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22C2×#39911yescharacteristic
750C22#240911yescharacteristic
751C22#243311yescharacteristic
752C22#248711yescharacteristic
753C22#250111yescharacteristic
754C22#262311yescharacteristic
755C22#284911yescharacteristic
756C22#301112yes—
757C22#301212yes—
758C22#308212yes—
759C22#308312yes—
760C22#309712yes—
761C22#309712yes—
762C22#309812yes—
763C22#309812yes—
764C22#315411yescharacteristic
765C22#315511yescharacteristic
766C22#315611yescharacteristic
767C22#315611yescharacteristic
768C22#322312yes—
769C22#322412yes—
770C22#324212yes—
771C22#324312yes—
772C4—24no—
773C4—44no—
774C4—44no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—161no—
782C4—161no—
783C4#244311yescharacteristic
784C4#244311yescharacteristic
785C4#244311yescharacteristic
786C4#244311yescharacteristic
787C4#244911yescharacteristic
788C4#244911yescharacteristic
789C4#244911yescharacteristic
790C4#244911yescharacteristic
791C2—44no—
792C2#1477711yescharacteristic
793C2#2373611yescharacteristic
794C2#2373711yescharacteristic
795C2#2431112yes—
796C2#2573511yescharacteristic
797C2#2573611yescharacteristic
798C2#2769012yes—
799C2#2792111yescharacteristic
800C2#2792211yescharacteristic
801C2#2991812yes—
802C2#3298912yes—
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×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
2. C2×#2097C2semidirect
3. C2×#2095C2semidirect
9. #11373C2semidirect
10. #11372C2semidirect
11. #11325C2semidirect
12. #11324C2semidirect
13. #11052C2semidirect
14. #11050C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23172
C2×#20972
C2×#20952
C2×#18732
C2×#18722
C2×#18542
C2×#18522
#142582
#113732
#113722
#113252
#113242
#110522
#110502
#107132