Finite Group Databasebeta

← #364885

Subgroups — #364885

Order 512.

2442 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D4C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic, complemented
4C2×#1869C212yesmaximal, complemented
5C2×#1797C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
7#11147C212yesmaximal, complemented
8#10964C212yesmaximal, complemented
9#10834C211yesmaximal, characteristic, complemented
10#10834C211yesmaximal, characteristic, complemented
11#10714C212yesmaximal, complemented
12C24×C8C2212yes—
13C22×#121C411yescharacteristic
14C22×C4×D4C2212yes—
15C22×C4×D4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×C8×D4—24no—
18C2×C8×D4—24no—
19C2×C8×D4—24no—
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2212yes—
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2212yes—
25C22×C22⋊C8C2212yes—
26C22×C22⋊C8C2212yes—
27C22×C22⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C4×#121—24no—
31C4×#121—24no—
32C2×#390C411yescharacteristic
33C2×#389C411yescharacteristic
34C2×#388C412yes—
35C2×#386C412yes—
36C2×#380C411yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2212yes—
39#1954—24no—
40#1869—28no—
41#1797—24no—
42C4×C22⋊C8—24no—
43C2×#336C2212yes—
44C2×#336C2212yes—
45C2×#336C2211yescharacteristic
46C2×#336C2212yes—
47C2×#336C2211yescharacteristic
48C2×#336C2212yes—
49C2×#336C2212yes—
50C23×D4C2×C412yes—
51C23×D4C2×C411yescharacteristic
52C24×C4C2×C411yescharacteristic
53C24×C4C2×C411yescharacteristic
54C24×C4C2312yes—
55C24×C4C2311yescharacteristic
56C23×C8—24no—
57C23×C8—24no—
58C23×C8—24no—
59C23×C8—24no—
60C23×C8—24no—
61C23×C8—42no—
62C23×C8—42no—
63C23×C8C2312yes—
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2312yes—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×#121—24no—
70C2×#121—24no—
71C2×#121C818yescomplemented
72C2×C4×D4—24no—
73C2×C4×D4—24no—
74C2×C4×D4—24no—
75C2×C4×D4—24no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—42no—
81C2×C4×D4—42no—
82C2×C4×D4D414yes—
83C2×C4×D4D414yes—
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C412yes—
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C412yes—
89C22×C22⋊C4C2×C412yes—
90C22×C22⋊C4C2×C412yes—
91C22×C22⋊C4C2×C412yes—
92C22×C22⋊C4C2×C412yes—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42C2×C411yescharacteristic
100C22×C42C2×C411yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2312yes—
103C22×C42C2311yescharacteristic
104C8×D4—232no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8D414yescomplemented
111C2×C22⋊C8—24no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—24no—
114C2×C22⋊C8—24no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
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—24no—
124C2×C22⋊C8—24no—
125C2×C22⋊C8—42no—
126C2×C22⋊C8—42no—
127C2×C22⋊C8—42no—
128C2×C22⋊C8D414yescomplemented
129C2×C4×C8—22no—
130C2×C4×C8—22no—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—22no—
134C2×C4×C8D414yescomplemented
135#390—24no—
136#389—24no—
137#388—28no—
138#386—28no—
139#380—24no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C4×C22⋊C4—24no—
143C4×C22⋊C4—24no—
144C2×#95C2×C412yes—
145C2×#95C2×C412yes—
146C2×#95C2×C412yes—
147#336—24no—
148#336—24no—
149#336—24no—
150#336—22no—
151#336—22no—
152#336—42no—
153#336—42no—
154C25C22×C412yes—
155C25C22×C411yescharacteristic
156C22×D4—24no—
157C22×D4—24no—
158C22×D4—24no—
159C22×D4—24no—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—22no—
163C22×D4—22no—
164C22×D4—42no—
165C22×D4—42no—
166C22×D4C22⋊C414yes—
167C22×D4C2×C814yes—
168C22×D4C2×C818yescomplemented
169C22×D4M1614yes—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—22no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—21no—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—41no—
206C23×C4—41no—
207C23×C4C2×C814yescomplemented
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C412yes—
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C2×D414yes—
217C23×C4C2×D414yes—
218C23×C4C2×D412yes—
219C23×C4#4112yes—
220C23×C4C2411yescharacteristic
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—216no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—22no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—22no—
243C22×C8—22no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8—22no—
257C22×C8—48no—
258C22×C8—48no—
259C22×C8—48no—
260C22×C8—48no—
261C22×C8—48no—
262C22×C8—48no—
263C22×C8C2×D414yes—
264C22×C8C2×D412yes—
265C22×C8C2×D412yes—
266C22×C8C2×D412yes—
267C22×C8C2×D412yes—
268C22×C8#4112yes—
269C22×C8#4112yes—
270#121—232no—
271C4×D4—28no—
272C4×D4—28no—
273C4×D4—28no—
274C4×D4—28no—
275C4×D4—48no—
276C4×D4—48no—
277C4×D4—48no—
278C4×D4—48no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4C22⋊C414yes—
290C2×C4⋊C4C2×C814yescomplemented
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4C22⋊C418yes—
305C2×C22⋊C4C2×C818yescomplemented
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—22no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—44no—
325C2×C42—44no—
326C2×C42—44no—
327C2×C42—44no—
328C2×C42C2×D412yes—
329C2×C42C2×D412yes—
330C2×C42C2×D412yes—
331C2×C42C2×D412yes—
332C2×C42#4112yes—
333C2×C42#4112yes—
334C4⋊C8—28no—
335C4⋊C8—44no—
336C22⋊C8—28no—
337C22⋊C8—216no—
338C22⋊C8—28no—
339C22⋊C8—48no—
340C22⋊C8—48no—
341C22⋊C8—48no—
342C4×C8—28no—
343C4×C8—44no—
344#95—24no—
345#95—24no—
346#95—24no—
347C24—21no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—21no—
352C24—21no—
353C24—22no—
354C24—21no—
355C24—21no—
356C24—22no—
357C24—22no—
358C24—21no—
359C24—21no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24C2×C22⋊C414yes—
372C24C4×D412yes—
373C24C22×C814yes—
374C24C22×C812yes—
375C24C2×M1614yes—
376C24#13112yes—
377C24C23×C411yescharacteristic
378C2×D4—216no—
379C2×D4—216no—
380C2×D4—28no—
381C2×D4—28no—
382C2×D4—28no—
383C2×D4—28no—
384C2×D4—28no—
385C2×D4—28no—
386C2×D4—48no—
387C2×D4—48no—
388C2×D4—48no—
389C2×D4—48no—
390C2×D4—48no—
391C2×D4C22⋊C8116yescomplemented
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—28no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4C2×C22⋊C414yes—
504C22×C4C2×C22⋊C412yes—
505C22×C4C2×C22⋊C412yes—
506C22×C4C4×D412yes—
507C22×C4C4×D412yes—
508C22×C4C4×D412yes—
509C22×C4C4×D412yes—
510C22×C4C4×D412yes—
511C22×C4C22×C812yes—
512C22×C4C22×C814yes—
513C22×C4C22×C812yes—
514C22×C4C2×M1612yes—
515C22×C4#13112yes—
516C22×C4#13112yes—
517C22×C4#13112yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C4H(5,𝔽2)11yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C42−1+411yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—24no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—24no—
546C2×C8—22no—
547C2×C8—24no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—432no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—42no—
554C2×C8—41no—
555C2×C8—42no—
556C2×C8—41no—
557C2×C8—42no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—42no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—42no—
568C2×C8—42no—
569C2×C8—42no—
570C2×C8—42no—
571C2×C8—42no—
572C2×C8—42no—
573C2×C8—42no—
574C2×C8#12114yescomplemented
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—48no—
578C4⋊C4—44no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—42no—
589C42—42no—
590C42—42no—
591C42—42no—
592C42—44no—
593C42—44no—
594C42#12014yes—
595C42#12114yes—
596C42#12114yes—
597C42#12314yes—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—41no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23C2×C22⋊C818yes—
667C23C8×D414yescomplemented
668C23C22×C22⋊C411yescharacteristic
669C23C2×C4×D411yescharacteristic
670C23C2×C4×D411yescharacteristic
671C23C2×C4×D411yescharacteristic
672C23C4×#4111yescharacteristic
673C23#51811yescharacteristic
674C23#52011yescharacteristic
675C23C23×C811yescharacteristic
676C23C22×M1611yescharacteristic
677C23C2×#13111yescharacteristic
678C23C2×#13111yescharacteristic
679C23C2×#13111yescharacteristic
680C23C2×#13111yescharacteristic
681C23#56811yescharacteristic
682C23#56811yescharacteristic
683D4—232no—
684D4—432no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—416no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—416no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4#38614yes—
752C2×C4#38614yes—
753C2×C4C2×C22⋊C814yes—
754C2×C4#40814yes—
755C2×C4C8×D414yes—
756C2×C4C8×D414yes—
757C2×C4#43514yes—
758C2×C4#43514yes—
759C2×C4C2×#12011yescharacteristic
760C2×C4C2×#12111yescharacteristic
761C2×C4C2×#12111yescharacteristic
762C2×C4C2×#12111yescharacteristic
763C2×C4C2×#12311yescharacteristic
764C2×C4#52511yescharacteristic
765C2×C4#52911yescharacteristic
766C2×C4#53211yescharacteristic
767C2×C4#53511yescharacteristic
768C2×C4#53711yescharacteristic
769C2×C4#54011yescharacteristic
770C2×C4#54211yescharacteristic
771C2×C4D4211yescharacteristic
772C2×C4D4211yescharacteristic
773C2×C4D4211yescharacteristic
774C2×C4#54611yescharacteristic
775C2×C4#54611yescharacteristic
776C2×C4#54611yescharacteristic
777C2×C4#54611yescharacteristic
778C2×C4#54611yescharacteristic
779C2×C4#54711yescharacteristic
780C2×C4#54711yescharacteristic
781C2×C4#54711yescharacteristic
782C2×C4#54811yescharacteristic
783C2×C4#55011yescharacteristic
784C2×C4#55311yescharacteristic
785C2×C4#55311yescharacteristic
786C2×C4#55511yescharacteristic
787C8—24no—
788C8—42no—
789C8—44no—
790C8—42no—
791C8—42no—
792C8—82no—
793C22—24no—
794C22—28no—
795C22—28no—
796C22—28no—
797C22—24no—
798C22—24no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—44no—
814C22—42no—
815C22—44no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22C2×#38611yescharacteristic
824C22C4×#12111yescharacteristic
825C22#232411yescharacteristic
826C22D4×C22⋊C411yescharacteristic
827C22#233911yescharacteristic
828C22#236111yescharacteristic
829C22#236311yescharacteristic
830C22C22×C22⋊C811yescharacteristic
831C22C2×#40811yescharacteristic
832C22#288011yescharacteristic
833C22#288011yescharacteristic
834C22C2×C8×D411yescharacteristic
835C22C2×C8×D411yescharacteristic
836C22C2×C8×D411yescharacteristic
837C22C2×#43511yescharacteristic
838C22C2×#43511yescharacteristic
839C22#292911yescharacteristic
840C22#293011yescharacteristic
841C22#293111yescharacteristic
842C22#293311yescharacteristic
843C22#293311yescharacteristic
844C22D4×M1611yescharacteristic
845C22#293511yescharacteristic
846C22C8×#4111yescharacteristic
847C22#296611yescharacteristic
848C22#296911yescharacteristic
849C22#297011yescharacteristic
850C22#297211yescharacteristic
851C22#297411yescharacteristic
852C22#297911yescharacteristic
853C22#298111yescharacteristic
854C22#298811yescharacteristic
855C22#299011yescharacteristic
856C22#299311yescharacteristic
857C22#299411yescharacteristic
858C4—24no—
859C4—44no—
860C4—42no—
861C4—44no—
862C4—42no—
863C4—42no—
864C4—82no—
865C4#186918yescomplemented
866C4#240711yescharacteristic
867C4#240811yescharacteristic
868C4#242011yescharacteristic
869C4#242211yescharacteristic
870C4#242711yescharacteristic
871C4#242811yescharacteristic
872C4#253511yescharacteristic
873C4#253711yescharacteristic
874C2—44no—
875C2—48no—
876C2#1397011yescharacteristic
877C2C2×#186911yescharacteristic
878C2#2089911yescharacteristic
879C2C8×#12111yescharacteristic
880C2#2148611yescharacteristic
881C2#2213311yescharacteristic
882C2#2213511yescharacteristic
883C2D4×C22⋊C811yescharacteristic
884C2#2240211yescharacteristic
885C2#2246911yescharacteristic
886C2#2247411yescharacteristic
887C2#2298511yescharacteristic
888C2#2298611yescharacteristic
889C2#2308311yescharacteristic
890C2#2308411yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC22×#121C4
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. C22×C8×D4C2semidirect
3. C2×#1954C2semidirect
4. C2×#1869C2semidirect
5. C2×#1797C2semidirect
6. C2×C4×C22⋊C8C2semidirect
7. #11147C2semidirect
8. #10964C2semidirect
9. #10834C2semidirect
10. #10834C2semidirect
11. #10714C2semidirect
71. C2×#121C8semidirect
110. C2×C4⋊C8D4semidirect
128. C2×C22⋊C8D4semidirect
134. C2×C4×C8D4semidirect
168. C22×D4C2×C8semidirect
207. C23×C4C2×C8semidirect
290. C2×C4⋊C4C2×C8semidirect
305. C2×C22⋊C4C2×C8semidirect
391. C2×D4C22⋊C8semidirect
574. C2×C8#121semidirect
667. C23C8×D4semidirect
865. C4#1869semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D42
C2×C4×#1212
C2×#19542
C2×#18692
C2×#17972
C2×C4×C22⋊C82
#111472
#109642
#108342
#107142