Finite Group Databasebeta

← #366537

Subgroups — #366537

Order 512.

3424 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C8C211yesmaximal, characteristic, complemented
2C2×C4×#120C211yesmaximal, characteristic
3C2×#1954C212yesmaximal, complemented
4C2×#1869C211yesmaximal, characteristic, complemented
5C2×#1869C211yesmaximal, characteristic, complemented
6C2×#1850C211yesmaximal, characteristic, complemented
7C2×#1779C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
9#11042C212yesmaximal, complemented
10#10964C212yesmaximal, complemented
11#10921C212yesmaximal, complemented
12C25×C4C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C24×C8C2211yescharacteristic
15C22×#120C411yescharacteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2212yes—
18C22×C4⋊C8C2212yescomplemented
19C22×C22⋊C8—28no—
20C22×C22⋊C8—24no—
21C22×C22⋊C8C2212yes—
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2212yes—
24C22×C22⋊C8C2212yes—
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2212yes—
27C22×C22⋊C8C2211yescharacteristic, complemented
28C22×C22⋊C8C2212yescomplemented
29C22×C22⋊C8C2211yescharacteristic, complemented
30C22×C4×C8C2212yescomplemented
31C4×#120—24no—
32C4×#120—24no—
33C2×#386C412yes—
34C2×#386C411yescharacteristic
35C2×#385C411yescharacteristic
36C2×#385C412yes—
37C2×#379C411yescharacteristic
38C2×C4×C22⋊C4C2212yes—
39C2×C4×C22⋊C4C2211yescharacteristic
40#1954—28no—
41#1869—24no—
42#1869—24no—
43#1850—24no—
44#1779—24no—
45C8×C22⋊C4—24no—
46C2×#336C2211yescharacteristic, complemented
47C2×#336C2212yescomplemented
48C2×#336C2212yescomplemented
49C2×#336C2212yescomplemented
50C2×#336C2211yescharacteristic, complemented
51C26C2×C411yescharacteristic
52C23×D4C2×C411yescharacteristic
53C23×D4C2×C412yes—
54C24×C4—24no—
55C24×C4—22no—
56C24×C4—24no—
57C24×C4—22no—
58C24×C4—22no—
59C24×C4—22no—
60C24×C4—22no—
61C24×C4—22no—
62C24×C4—42no—
63C24×C4—42no—
64C24×C4C2×C411yescharacteristic
65C24×C4C2×C412yes—
66C24×C4C2311yescharacteristic
67C24×C4C2312yes—
68C24×C4C2311yescharacteristic
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—24no—
73C23×C8—24no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—42no—
77C23×C8—42no—
78C23×C8D414yescomplemented
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2312yes—
82C23×C8C2312yes—
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C2×#120—24no—
86C2×#120—24no—
87C2×#120C818yescomplemented
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—24no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4—24no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—24no—
97C2×C4×D4—24no—
98C2×C4×D4—42no—
99C2×C4×D4—42no—
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C4⋊C4C2×C412yes—
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C412yes—
105C22×C22⋊C4C2×C412yes—
106C22×C22⋊C4C2×C412yes—
107C22×C22⋊C4C2×C411yescharacteristic
108C22×C22⋊C4C2×C412yes—
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2312yes—
112C2×C4⋊C8—24no—
113C2×C4⋊C8—24no—
114C2×C4⋊C8—42no—
115C2×C22⋊C8—232no—
116C2×C22⋊C8—24no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—24no—
120C2×C22⋊C8—24no—
121C2×C22⋊C8—24no—
122C2×C22⋊C8—24no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—24no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—24no—
128C2×C22⋊C8—24no—
129C2×C22⋊C8—24no—
130C2×C22⋊C8—24no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—24no—
134C2×C22⋊C8—24no—
135C2×C22⋊C8—42no—
136C2×C22⋊C8—42no—
137C2×C22⋊C8—42no—
138C2×C22⋊C8—42no—
139C2×C22⋊C8D418yescomplemented
140C2×C22⋊C8D414yescomplemented
141C2×C4×C8—24no—
142C2×C4×C8—24no—
143C2×C4×C8—42no—
144#386—24no—
145#386—28no—
146#385—24no—
147#385—28no—
148#379—24no—
149C4×C22⋊C4—24no—
150C4×C22⋊C4—24no—
151C4×C22⋊C4D414yes—
152C4×C22⋊C4D414yes—
153C2×#95C2×C412yes—
154C2×#95C2×C412yes—
155C2×#95C2×C412yes—
156#336—24no—
157#336—22no—
158#336—22no—
159#336—24no—
160#336—24no—
161C25—24no—
162C25—22no—
163C25—24no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—22no—
169C25—42no—
170C25—42no—
171C25C2×C814yes—
172C25C22×C411yescharacteristic
173C25C22×C412yes—
174C25C22×C411yescharacteristic
175C22×D4—22no—
176C22×D4—24no—
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—24no—
181C22×D4—22no—
182C22×D4—22no—
183C22×D4—24no—
184C22×D4—24no—
185C22×D4—42no—
186C22×D4—42no—
187C22×D4C2×C814yes—
188C22×D4C2×C818yescomplemented
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—28no—
194C23×C4—216no—
195C23×C4—28no—
196C23×C4—24no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—48no—
231C23×C4—48no—
232C23×C4—48no—
233C23×C4—48no—
234C23×C4—48no—
235C23×C4—48no—
236C23×C4—48no—
237C23×C4—48no—
238C23×C4—44no—
239C23×C4—44no—
240C23×C4—48no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C22×C412yes—
252C23×C4C2×D414yes—
253C23×C4C2×D412yes—
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4#4114yes—
258C23×C4#4112yes—
259C23×C4#4112yes—
260C23×C4C2411yescharacteristic
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—22no—
264C22×C8—28no—
265C22×C8—28no—
266C22×C8—21no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—21no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—28no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—22no—
289C22×C8—21no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—44no—
294C22×C8—48no—
295C22×C8—48no—
296C22×C8—48no—
297C22×C8—48no—
298C22×C8—44no—
299C22×C8—44no—
300C22×C8C2×D414yes—
301C22×C8C2×D412yes—
302C22×C8C2×D414yes—
303C22×C8C2×D414yes—
304C22×C8C2×D412yes—
305#120—232no—
306C4×D4—48no—
307C4×D4—48no—
308C4×D4—48no—
309C4×D4—48no—
310C4×D4—44no—
311C4×D4—44no—
312C4×D4—44no—
313C4×D4—44no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—42no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4C22⋊C414yes—
340C2×C22⋊C4C22⋊C414yes—
341C2×C22⋊C4C2×C814yes—
342C2×C22⋊C4C2×C818yescomplemented
343C2×C22⋊C4M1614yes—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C2×D414yes—
355C2×C42C2×D414yes—
356C4⋊C8—48no—
357C22⋊C8—216no—
358C22⋊C8—28no—
359C22⋊C8—216no—
360C22⋊C8—48no—
361C22⋊C8—48no—
362C22⋊C8—48no—
363C22⋊C8—44no—
364C22⋊C8—44no—
365C22⋊C8—44no—
366C4×C8—48no—
367#95—24no—
368#95—24no—
369#95C22⋊C418yes—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—28no—
375C24—28no—
376C24—216no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—216no—
390C24—28no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—28no—
402C24—28no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—48no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—44no—
419C24C2×C22⋊C412yes—
420C24C4×D414yes—
421C24C4×D412yes—
422C24C4×D412yes—
423C24C22×C812yes—
424C24C22×C814yes—
425C24C22×C812yes—
426C24C2×M1612yes—
427C24#13114yes—
428C24#13112yes—
429C24#13112yes—
430C24C23×C411yescharacteristic
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—216no—
435C2×D4—216no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
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—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—216no—
466C22×C4—28no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—416no—
515C22×C4—416no—
516C22×C4—432no—
517C22×C4—416no—
518C22×C4—432no—
519C22×C4—416no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—48no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—42no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4C2×C22⋊C414yes—
558C22×C4C2×C22⋊C412yes—
559C22×C4C2×C22⋊C414yes—
560C22×C4C4×D414yes—
561C22×C4C4×D412yes—
562C22×C4C4×D412yes—
563C22×C4#12114yes—
564C22×C4#12114yes—
565C22×C4#12414yes—
566C22×C4#12714yes—
567C22×C4C22×C812yes—
568C22×C4C22×C814yes—
569C22×C4C2×M1614yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4C2×#4111yescharacteristic
577C22×C4C2×#4112yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—416no—
594C2×C8—416no—
595C2×C8—42no—
596C2×C8—42no—
597C2×C8—42no—
598C2×C8—42no—
599C2×C8—42no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—42no—
604C2×C8—42no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—42no—
612C2×C8—42no—
613C2×C8—42no—
614C2×C8—42no—
615C2×C8#12014yescomplemented
616C4⋊C4—48no—
617C4⋊C4—44no—
618C22⋊C4—28no—
619C22⋊C4—216no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4C22⋊C8116yescomplemented
626C42—24no—
627C42—24no—
628C42—24no—
629C42—24no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—232no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—432no—
675C23—432no—
676C23—416no—
677C23—416no—
678C23—416no—
679C23—432no—
680C23—432no—
681C23—416no—
682C23—416no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—416no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—41no—
718C23#39014yes—
719C23C2×C22⋊C814yes—
720C23#40814yes—
721C23C8×D418yes—
722C23C8×D414yes—
723C23C8×D414yes—
724C23#43614yes—
725C23#43614yes—
726C23C22×C22⋊C411yescharacteristic
727C23C2×C4×D411yescharacteristic
728C23C2×C4×D412yes—
729C23C2×C4×D411yescharacteristic
730C23#51812yes—
731C23C23×C811yescharacteristic
732C23C22×M1611yescharacteristic
733C23C2×#13111yescharacteristic
734C23C2×#13111yescharacteristic
735C23C2×#13112yes—
736C23#56812yes—
737D4—432no—
738D4—416no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—432no—
765C2×C4—416no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—82no—
799C2×C4—81no—
800C2×C4—82no—
801C2×C4—81no—
802C2×C4#39014yes—
803C2×C4C2×C22⋊C818yescomplemented
804C2×C4C2×#12011yescharacteristic
805C2×C4C2×#12111yescharacteristic
806C2×C4C2×#12111yescharacteristic
807C2×C4#52511yescharacteristic
808C2×C4#52512yes—
809C2×C4C2×#12411yescharacteristic
810C2×C4C2×#12711yescharacteristic
811C2×C4#53411yescharacteristic
812C2×C4#53511yescharacteristic
813C2×C4#53812yes—
814C2×C4D4212yes—
815C2×C4D4212yes—
816C2×C4D4212yes—
817C2×C4#54612yes—
818C2×C4#54612yes—
819C2×C4#54612yes—
820C2×C4#54612yes—
821C2×C4#55112yes—
822C8—24no—
823C8—42no—
824C8—44no—
825C8—44no—
826C8—81no—
827C8—81no—
828C22—24no—
829C22—24no—
830C22—28no—
831C22—28no—
832C22—28no—
833C22—28no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—464no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—81no—
860C22—82no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22#195418yescomplemented
866C22C2×#39011yescharacteristic
867C22C4×#12011yescharacteristic
868C22#232111yescharacteristic
869C22D4×C22⋊C412yes—
870C22#235812yes—
871C22C22×C22⋊C811yescharacteristic
872C22C2×#40811yescharacteristic
873C22#288012yes—
874C22C2×C8×D411yescharacteristic
875C22C2×C8×D411yescharacteristic
876C22C2×C8×D412yes—
877C22C2×#43611yescharacteristic
878C22C2×#43611yescharacteristic
879C22#292911yescharacteristic
880C22#292912yes—
881C22#293011yescharacteristic
882C22#293312yes—
883C22#293312yes—
884C22D4×M1612yes—
885C22#297212yes—
886C22#297412yes—
887C22#297612yes—
888C22#297712yes—
889C4—28no—
890C4—24no—
891C4—44no—
892C4—44no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4#241011yescharacteristic
897C4#241111yescharacteristic
898C4#242412yes—
899C4#243311yescharacteristic
900C4#247212yes—
901C4#253911yescharacteristic
902C2—28no—
903C2—48no—
904C2—82no—
905C2#1399511yescharacteristic
906C2C2×#195411yescharacteristic
907C2#2119111yescharacteristic
908C2C8×#12011yescharacteristic
909C2#2144111yescharacteristic
910C2#2202811yescharacteristic
911C2#2203211yescharacteristic
912C2D4×C22⋊C812yes—
913C2#2239812yes—
914C2#2284212yes—
915C2#2284812yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC22×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊C8C2semidirect
3. C2×#1954C2semidirect
4. C2×#1869C2semidirect
5. C2×#1869C2semidirect
6. C2×#1850C2semidirect
7. C2×#1779C2semidirect
8. C2×C8×C22⋊C4C2semidirect
9. #11042C2semidirect
10. #10964C2semidirect
11. #10921C2semidirect
18. C22×C4⋊C8C22semidirect
27. C22×C22⋊C8C22semidirect
28. C22×C22⋊C8C22semidirect
29. C22×C22⋊C8C22semidirect
30. C22×C4×C8C22semidirect
46. C2×#336C22semidirect
47. C2×#336C22semidirect
48. C2×#336C22semidirect
49. C2×#336C22semidirect
50. C2×#336C22semidirect
78. C23×C8D4semidirect
87. C2×#120C8semidirect
139. C2×C22⋊C8D4semidirect
140. C2×C22⋊C8D4semidirect
188. C22×D4C2×C8semidirect
342. C2×C22⋊C4C2×C8semidirect
615. C2×C8#120semidirect
625. C22⋊C4C22⋊C8semidirect
803. C2×C4C2×C22⋊C8semidirect
865. C22#1954semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C82
C2×C4×#1202
C2×#19542
C2×#18692
C2×#18502
C2×#17792
C2×C8×C22⋊C42
#110422
#109642
#109212