Finite Group Databasebeta

← #364989

Subgroups — #364989

Order 512.

2256 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic
4C2×#1872C212yesmaximal, complemented
5C2×#1803C211yesmaximal, characteristic, complemented
6C2×C4×#103C211yesmaximal, characteristic, complemented
7#11200C212yesmaximal, complemented
8#10970C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10841C211yesmaximal, characteristic, complemented
11#10730C212yesmaximal, complemented
12C22×C22⋊Q8C2212yes—
13C22×C4×Q8C2211yescharacteristic
14C22×C4×D4—21no—
15C22×C4×D4C2211yescharacteristic
16C23×C4⋊C4C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×#103C2211yescharacteristic
19C22×#103C2212yes—
20C22×#103C2211yescharacteristic
21C22×C22⋊C8C2212yes—
22C22×C22⋊C8C2212yes—
23C22×C4×C8C2211yescharacteristic
24#2538—24no—
25#2538C418yescomplemented
26C2×#396—22no—
27D4×C4⋊C4—24no—
28D4×C4⋊C4—24no—
29C2×#390—21no—
30C2×#389—21no—
31C2×#389—21no—
32C2×#385—22no—
33C2×#384C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#380C2212yes—
36C2×#380C2212yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1954—24no—
39#1872—28no—
40#1803—24no—
41C4×#103—24no—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2212yes—
48C2×#340C2212yes—
49C23×Q8C2311yescharacteristic
50C23×D4D411yescharacteristic
51C24×C4—22no—
52C24×C4C2312yes—
53C23×C8C2312yes—
54C23×C8C2311yescharacteristic
55C23×C8C2311yescharacteristic
56C2×C22⋊Q8—24no—
57C2×C22⋊Q8—24no—
58C2×C22⋊Q8—24no—
59C2×C22⋊Q8—42no—
60C2×C22⋊Q8—42no—
61C2×C22⋊Q8C2×C418yescomplemented
62C2×C4×Q8—22no—
63C2×C4×Q8—22no—
64C2×C4×Q8—22no—
65C2×C4×Q8—22no—
66C2×C4×Q8—22no—
67C2×C4×Q8C2×C414yescomplemented
68C2×C4×D4—28no—
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—44no—
74C2×C4×D4—44no—
75C2×C4×D4C2×C414yes—
76C2×C4×D4D414yes—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—24no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—42no—
89C22×C4⋊C4—42no—
90C22×C4⋊C4D411yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—22no—
97C22×C22⋊C4—22no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4D412yes—
100C22×C42—21no—
101C22×C42—21no—
102C22×C42C2311yescharacteristic
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—24no—
112C2×#103—24no—
113C2×#103—42no—
114C2×#103D414yescomplemented
115C2×C22⋊C8—24no—
116C2×C22⋊C8—24no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—24no—
119C2×C22⋊C8—42no—
120C2×C22⋊C8—42no—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124#396—216no—
125#390—28no—
126#389—28no—
127#389—28no—
128#385—216no—
129#384—22no—
130#384—22no—
131#384C2×C414yescomplemented
132#384D414yes—
133#380—24no—
134#380—24no—
135#380—24no—
136#380C2×C418yescomplemented
137C4×C4⋊C4—22no—
138C4×C4⋊C4D414yes—
139C2×#95—22no—
140C2×#95—21no—
141C2×#95—22no—
142#340—24no—
143#340—24no—
144#340—24no—
145#340—22no—
146#340—22no—
147#340—42no—
148#340—42no—
149C25C2×D412yes—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8C22×C412yes—
162C22×Q8C2×D412yes—
163C22×Q8#4112yes—
164C22×D4—22no—
165C22×D4—22no—
166C22×D4—22no—
167C22×D4—22no—
168C22×D4C22⋊C414yes—
169C22×D4SD1614yes—
170C22×D4Q1614yes—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—22no—
189C23×C4—28no—
190C23×C4—44no—
191C23×C4—44no—
192C23×C4—44no—
193C23×C4—44no—
194C23×C4—82no—
195C23×C4—82no—
196C23×C4C22×C414yes—
197C23×C4C2×D412yes—
198C23×C4C2×D414yes—
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2411yescharacteristic
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8C2×D412yes—
222C22×C8#4112yes—
223C22⋊Q8—216no—
224C22⋊Q8—48no—
225C22⋊Q8—48no—
226C22⋊Q8—48no—
227C4×Q8—28no—
228C4×Q8—28no—
229C4×Q8—44no—
230C4×Q8—44no—
231C4×D4—28no—
232C4×D4—28no—
233C4×D4—28no—
234C4×D4—28no—
235C4×D4—432no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—28no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—48no—
269C2×C4⋊C4—48no—
270C2×C4⋊C4—48no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—48no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4C22⋊C414yes—
287C2×C4⋊C4C22×C412yes—
288C2×C4⋊C4C22×C414yes—
289C2×C4⋊C4C2×D414yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4#4112yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—82no—
304C2×C22⋊C4—82no—
305C2×C22⋊C4C22⋊C418yes—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—42no—
312C2×C42C22×C412yes—
313C2×C42C2×D412yes—
314C2×C42C2×D412yes—
315C2×C42C2×D412yes—
316C2×C42#4112yes—
317C2×C42#4112yes—
318C4⋊C8—44no—
319#103—28no—
320#103—28no—
321#103—48no—
322C22⋊C8—48no—
323C22⋊C8—48no—
324C4×C8—44no—
325#95—28no—
326#95—28no—
327#95—24no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24C2×C22⋊C414yes—
341C24C2×SD1614yes—
342C24C2×Q1614yes—
343C24C22×D411yescharacteristic
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8C4×D414yescomplemented
372C2×D4—28no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—28no—
376C2×D4—28no—
377C2×D4—28no—
378C2×D4#103116yescomplemented
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—416no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—416no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—42no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—41no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—88no—
462C22×C4—88no—
463C22×C4—88no—
464C22×C4—88no—
465C22×C4—88no—
466C22×C4C2×C22⋊C414yes—
467C22×C4C2×C22⋊C412yes—
468C22×C4C2×C22⋊C412yes—
469C22×C4#12012yes—
470C22×C4#12012yes—
471C22×C4#12312yes—
472C22×C4#12312yes—
473C22×C4C2×SD1612yes—
474C22×C4C2×Q1612yes—
475C22×C4AGL(1,ℤ/8)12yes—
476C22×C4#13712yes—
477C22×C4C23×C411yescharacteristic
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4C2×#4111yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4H(5,𝔽2)11yescharacteristic
488C22×C4H(5,𝔽2)11yescharacteristic
489C22×C4H(5,𝔽2)11yescharacteristic
490C22×C42−1+411yescharacteristic
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—42no—
508C2×C8—42no—
509C2×C8—42no—
510C2×C8—42no—
511C2×C8—42no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—28no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—416no—
525C4⋊C4—416no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—48no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—84no—
538C4⋊C4—84no—
539C4⋊C4#12114yes—
540C22⋊C4—216no—
541C22⋊C4—416no—
542C22⋊C4—416no—
543C22⋊C4—88no—
544C42—48no—
545C42—48no—
546C42C4×D414yes—
547C42C4×D414yes—
548C42#12114yes—
549C42#12114yes—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23C2×#10318yes—
585C23C22×C22⋊C411yescharacteristic
586C23C2×#12011yescharacteristic
587C23C2×#12311yescharacteristic
588C23D4211yescharacteristic
589C23#54611yescharacteristic
590C23#54611yescharacteristic
591C23#54711yescharacteristic
592C23C22×SD1611yescharacteristic
593C23C22×Q1611yescharacteristic
594C23C2×AGL(1,ℤ/8)11yescharacteristic
595C23C2×#13711yescharacteristic
596C23#57611yescharacteristic
597C23#57711yescharacteristic
598C23#57711yescharacteristic
599C23#57811yescharacteristic
600Q8—24no—
601Q8—24no—
602Q8—42no—
603Q8—42no—
604Q8—42no—
605Q8—42no—
606Q8—42no—
607Q8—42no—
608D4—232no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—42no—
647C2×C4—44no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—832no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—81no—
672C2×C4—82no—
673C2×C4#38614yes—
674C2×C4#38614yes—
675C2×C4C2×#10314yes—
676C2×C4#41714yes—
677C2×C4#45014yes—
678C2×C4#45114yes—
679C2×C4#48314yes—
680C2×C4#48414yes—
681C2×C4C2×C4×D411yescharacteristic
682C2×C4C2×C4×D411yescharacteristic
683C2×C4C2×C4×D411yescharacteristic
684C2×C4C4×#4111yescharacteristic
685C2×C4#51811yescharacteristic
686C2×C4#52011yescharacteristic
687C2×C4C2×#12111yescharacteristic
688C2×C4C2×#12111yescharacteristic
689C2×C4C2×#12111yescharacteristic
690C2×C4#52511yescharacteristic
691C2×C4#52911yescharacteristic
692C2×C4#53211yescharacteristic
693C2×C4#53511yescharacteristic
694C2×C4#53711yescharacteristic
695C2×C4#54011yescharacteristic
696C2×C4#54211yescharacteristic
697C2×C4D4211yescharacteristic
698C2×C4D4211yescharacteristic
699C2×C4#54611yescharacteristic
700C2×C4#54611yescharacteristic
701C2×C4#54611yescharacteristic
702C2×C4#54711yescharacteristic
703C2×C4#54711yescharacteristic
704C2×C4#54811yescharacteristic
705C2×C4#55011yescharacteristic
706C2×C4#55311yescharacteristic
707C2×C4#55311yescharacteristic
708C2×C4#55511yescharacteristic
709C8—42no—
710C8—42no—
711C8—82no—
712C22—28no—
713C22—28no—
714C22—28no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22C2×#38611yescharacteristic
728C22D4×C22⋊C411yescharacteristic
729C22#233911yescharacteristic
730C22#240711yescharacteristic
731C22#240811yescharacteristic
732C22#242011yescharacteristic
733C22#242211yescharacteristic
734C22C22×#10311yescharacteristic
735C22C2×#41711yescharacteristic
736C22#289711yescharacteristic
737C22#289811yescharacteristic
738C22C2×#45011yescharacteristic
739C22C2×#45111yescharacteristic
740C22#301211yescharacteristic
741C22#301311yescharacteristic
742C22C2×#48311yescharacteristic
743C22C2×#48411yescharacteristic
744C22#309811yescharacteristic
745C22#309911yescharacteristic
746C22#327411yescharacteristic
747C22#327811yescharacteristic
748C22D4×SD1611yescharacteristic
749C22D4×Q1611yescharacteristic
750C22#329511yescharacteristic
751C22#329811yescharacteristic
752C22#329911yescharacteristic
753C22#329911yescharacteristic
754C22#332411yescharacteristic
755C22#332811yescharacteristic
756C22#333211yescharacteristic
757C22#333311yescharacteristic
758C22#333511yescharacteristic
759C22#333811yescharacteristic
760C22#335311yescharacteristic
761C22#335611yescharacteristic
762C4—24no—
763C4—44no—
764C4—44no—
765C4—44no—
766C4—82no—
767C4—84no—
768C4—84no—
769C4—82no—
770C4#187218yescomplemented
771C4C4×#12111yescharacteristic
772C4#232411yescharacteristic
773C4#236111yescharacteristic
774C4#236311yescharacteristic
775C4#242711yescharacteristic
776C4#242811yescharacteristic
777C4#253511yescharacteristic
778C4#253711yescharacteristic
779C2—48no—
780C2#1397011yescharacteristic
781C2C2×#187211yescharacteristic
782C2#2091511yescharacteristic
783C2D4×#10311yescharacteristic
784C2#2243211yescharacteristic
785C2#2248711yescharacteristic
786C2#2250411yescharacteristic
787C2#2412011yescharacteristic
788C2#2412211yescharacteristic
789C2#2424011yescharacteristic
790C2#2424311yescharacteristic
791C2#2496911yescharacteristic
792C2#2497111yescharacteristic
793C2#2501411yescharacteristic
794C2#2501611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1872C2semidirect
5. C2×#1803C2semidirect
6. C2×C4×#103C2semidirect
7. #11200C2semidirect
8. #10970C2semidirect
9. #10849C2semidirect
10. #10841C2semidirect
11. #10730C2semidirect
25. #2538C4semidirect
61. C2×C22⋊Q8C2×C4semidirect
67. C2×C4×Q8C2×C4semidirect
114. C2×#103D4semidirect
131. #384C2×C4semidirect
136. #380C2×C4semidirect
371. C2×Q8C4×D4semidirect
378. C2×D4#103semidirect
770. C4#1872semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×D4×C4⋊C42
C2×#19542
C2×#18722
C2×#18032
C2×C4×#1032
#112002
#109702
#108492
#108412
#107302