Finite Group Databasebeta

← #366847

Subgroups — #366847

Order 512.

1658 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic
2C2×#1894C211yesmaximal, characteristic
3C2×#1873C211yesmaximal, characteristic
4C2×#1823C211yesmaximal, characteristic
5C2×#1753C211yesmaximal, characteristic
6C2×#1736C211yesmaximal, characteristic
7#13879C211yesmaximal, characteristic
8#11373C211yesmaximal, characteristic, complemented
9#11371C211yesmaximal, characteristic, complemented
10#11052C211yesmaximal, characteristic, complemented
11#11050C211yesmaximal, characteristic, complemented
12#10928C211yesmaximal, characteristic, complemented
13#10926C211yesmaximal, characteristic, complemented
14#10843C211yesmaximal, characteristic, complemented
15#10841C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2502—24no—
28#2502C418yescomplemented
29C2×#398—22no—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#385—22no—
33C2×#384C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1894—24no—
40#1873—24no—
41#1823—24no—
42#1753—24no—
43#1736—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1439—22no—
59#1436—22no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C24×C4—21no—
64C24×C4C2311yescharacteristic
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16D414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C22⋊Q8—22no—
77C2×C22⋊Q8—22no—
78C2×C22⋊Q8—22no—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8C2×C414yes—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—41no—
87C2×#117—41no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4C2×C414yes—
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×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103—41no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8D414yes—
128C2×#97—22no—
129C2×#97—22no—
130C2×#97—41no—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—41no—
134#398—216no—
135#391—22no—
136#391—22no—
137#391C2×C414yes—
138#391C2×C414yes—
139#385—216no—
140#384—22no—
141#384—22no—
142#384—22no—
143#384—41no—
144#384C2×C414yes—
145#384C2×C414yes—
146#382—22no—
147#382—41no—
148#380—22no—
149#380—22no—
150C4×C22⋊C4C2×C414yes—
151C4×C22⋊C4D414yes—
152C2×#95—22no—
153C2×#95—22no—
154C2×#95—22no—
155C2×#95—21no—
156C2×#95—22no—
157C2×#95—22no—
158C2×#95D412yes—
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#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#336—22no—
172#336—22no—
173C25C2×D411yescharacteristic
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
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×Q8C22×C412yes—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
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—21no—
201C23×C4—21no—
202C23×C4—24no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—82no—
208C23×C4—82no—
209C23×C4C22×C412yes—
210C23×C4C2×D412yes—
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D412yes—
213C23×C4C2×D412yes—
214C23×C4C2×D412yes—
215C23×C4C2×D412yes—
216C23×C4#4112yes—
217C23×C4#4112yes—
218C23×C4C2411yescharacteristic
219C2×M16—28no—
220C2×M16—28no—
221C2×M16—44no—
222C2×M16—44no—
223C2×M16—44no—
224C2×M16—44no—
225C2×M16—44no—
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×C8#4112yes—
253C22×C8#4112yes—
254C22⋊Q8—28no—
255C22⋊Q8—28no—
256C22⋊Q8—44no—
257C22⋊Q8—44no—
258#117—28no—
259#117—44no—
260#117—44no—
261#117—44no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
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—24no—
285C2×C4⋊C4—24no—
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—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—82no—
314C2×C4⋊C4—82no—
315C2×C4⋊C4—82no—
316C2×C4⋊C4—82no—
317C2×C4⋊C4—82no—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C22×C412yes—
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4#4112yes—
322C2×C4⋊C4#4112yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—82no—
333C2×C22⋊C4C22⋊C418yes—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42C22×C412yes—
346C2×C42C22×C412yes—
347C2×C42C2×D412yes—
348C2×C42C2×D412yes—
349#103—44no—
350#103—44no—
351#103—44no—
352#103—44no—
353C22⋊C8—28no—
354#97—44no—
355C4×C8—44no—
356#95—28no—
357#95—28no—
358#95—44no—
359#95—42no—
360#95—44no—
361#95—82no—
362#95C22⋊C418yes—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24C2×C22⋊C412yes—
372C24#12412yes—
373C24#12712yes—
374C24C22×D411yescharacteristic
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
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—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
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—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
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—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—48no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—88no—
485C22×C4—88no—
486C22×C4—84no—
487C22×C4—84no—
488C22×C4C2×C22⋊C414yes—
489C22×C4C2×C22⋊C412yes—
490C22×C4C2×C22⋊C414yes—
491C22×C4C4×D414yes—
492C22×C4C4×D414yes—
493C22×C4#12114yes—
494C22×C4#12114yes—
495C22×C4#12412yes—
496C22×C4#12712yes—
497C22×C4#13714yes—
498C22×C4#13714yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C42−1+411yescharacteristic
512C22×C42−1+411yescharacteristic
513M16—416no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
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—41no—
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#12314yes—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—48no—
563C4⋊C4—48no—
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—88no—
573C4⋊C4—88no—
574C4⋊C4—88no—
575C22⋊C4—216no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—84no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—48no—
588C23—22no—
589C23—22no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23#39014yes—
611C23C22×C22⋊C411yescharacteristic
612C23C2×#12411yescharacteristic
613C23C2×#12711yescharacteristic
614C23#54611yescharacteristic
615C23#54611yescharacteristic
616C23#54711yescharacteristic
617C23#54711yescharacteristic
618C23C2×#13712yes—
619C23C2×#13712yes—
620C23#57612yes—
621C23#57712yes—
622Q8—42no—
623Q8—42no—
624Q8—42no—
625Q8—42no—
626Q8—81no—
627Q8—81no—
628Q8—81no—
629Q8—81no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
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—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—44no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—816no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4—82no—
675C2×C4—81no—
676C2×C4—81no—
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—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4#39014yes—
701C2×C4#41918yes—
702C2×C4C2×C4×D411yescharacteristic
703C2×C4C2×C4×D411yescharacteristic
704C2×C4C4×#4111yescharacteristic
705C2×C4C4×#4111yescharacteristic
706C2×C4#52011yescharacteristic
707C2×C4#52011yescharacteristic
708C2×C4C2×#12111yescharacteristic
709C2×C4C2×#12111yescharacteristic
710C2×C4C2×#12311yescharacteristic
711C2×C4#52511yescharacteristic
712C2×C4#52911yescharacteristic
713C2×C4#52911yescharacteristic
714C2×C4#53411yescharacteristic
715C2×C4#53611yescharacteristic
716C2×C4#53911yescharacteristic
717C2×C4#53911yescharacteristic
718C2×C4#54611yescharacteristic
719C2×C4#54611yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54611yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4#54711yescharacteristic
725C2×C4#54711yescharacteristic
726C2×C4#55111yescharacteristic
727C2×C4#55111yescharacteristic
728C2×C4#55211yescharacteristic
729C2×C4#55211yescharacteristic
730C8—24no—
731C8—42no—
732C8—42no—
733C8—42no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22C2×#39011yescharacteristic
746C22#233911yescharacteristic
747C22#233911yescharacteristic
748C22#248811yescharacteristic
749C22#248811yescharacteristic
750C22#250111yescharacteristic
751C22#253911yescharacteristic
752C22C2×#41912yes—
753C22#289712yes—
754C22#313612yes—
755C22#313912yes—
756C22#315211yescharacteristic
757C22#315211yescharacteristic
758C22#315411yescharacteristic
759C22#315511yescharacteristic
760C22#331412yes—
761C22#331612yes—
762C22#333112yes—
763C22#333312yes—
764C22#334412yes—
765C22#334612yes—
766C22#335612yes—
767C22#335712yes—
768C4—24no—
769C4—28no—
770C4—44no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—161no—
778C4—161no—
779C4C4×#12311yescharacteristic
780C4#232211yescharacteristic
781C4#235911yescharacteristic
782C4#235911yescharacteristic
783C4#241211yescharacteristic
784C4#241311yescharacteristic
785C4#242511yescharacteristic
786C4#242511yescharacteristic
787C2—44no—
788C2#1399611yescharacteristic
789C2#2120211yescharacteristic
790C2#2120611yescharacteristic
791C2#2249712yes—
792C2#2250212yes—
793C2#2770712yes—
794C2#2772112yes—
795C2#2794011yescharacteristic
796C2#2794511yescharacteristic
797C2#2836011yescharacteristic
798C2#2836211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11373C2semidirect
9. #11371C2semidirect
10. #11052C2semidirect
11. #11050C2semidirect
12. #10928C2semidirect
13. #10926C2semidirect
14. #10843C2semidirect
15. #10841C2semidirect
28. #2502C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#18942
C2×#18732
C2×#18232
C2×#17532
C2×#17362
#138792
#113732
#113712
#110522
#110502
#109282
#109262
#108432
#108412