Finite Group Databasebeta

← #361250

Subgroups — #361250

Order 512.

2274 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D4C211yesmaximal, characteristic
2C2×#1869C212yesmaximal
3C2×#1817C211yesmaximal, characteristic, complemented
4C22×#336C211yesmaximal, characteristic, complemented
5#11346C212yesmaximal, complemented
6#11147C212yesmaximal, complemented
7#10795C211yesmaximal, characteristic, complemented
8#10795C211yesmaximal, characteristic, complemented
9#10714C212yesmaximal, complemented
10#10712C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C24×C8C2212yes—
13C22×C4×D4C411yescharacteristic
14C22×C4×D4C411yescharacteristic
15C22×C4×D4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×C22⋊C8C2212yes—
19C22×C22⋊C8C2212yes—
20C22×C22⋊C8C2212yes—
21C42×D4—28no—
22C2×C4×C4⋊C4C411yescharacteristic
23C2×C4×C4⋊C4C411yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C22⋊C4C411yescharacteristic
26C2×C4×C22⋊C4C411yescharacteristic
27C2×C4×C22⋊C4C411yescharacteristic
28C2×C4×C22⋊C4C411yescharacteristic
29C2×C4×C22⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C43C2211yescharacteristic
32#1869—28no—
33#1817—24no—
34C2×#336—24no—
35C2×#336C2212yes—
36C2×#336C2212yes—
37C2×#336C2211yescharacteristic
38C2×#336C2212yes—
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44C2×#336C2212yes—
45C2×#336C2212yes—
46C2×#336C2211yescharacteristic
47C23×D4C2×C411yescharacteristic
48C24×C4C2×C411yescharacteristic
49C24×C4C2×C411yescharacteristic
50C24×C4C2×C411yescharacteristic
51C24×C4C2×C411yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C23×C8—24no—
55C23×C8—24no—
56C23×C8—24no—
57C23×C8—24no—
58C23×C8—24no—
59C23×C8—42no—
60C23×C8—42no—
61C23×C8C2312yes—
62C23×C8C2312yes—
63C23×C8C2312yes—
64C23×C8C2312yes—
65C2×C4×D4—24no—
66C2×C4×D4—24no—
67C2×C4×D4—24no—
68C2×C4×D4—24no—
69C2×C4×D4—22no—
70C2×C4×D4—24no—
71C2×C4×D4—22no—
72C2×C4×D4—24no—
73C2×C4×D4C818yescomplemented
74C2×C4×D4D418yes—
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C22⋊C4C2×C411yescharacteristic
79C22×C22⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C42—24no—
85C22×C42—24no—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—42no—
91C22×C42—42no—
92C22×C42C2×C411yescharacteristic
93C22×C42C2×C411yescharacteristic
94C22×C42C2×C411yescharacteristic
95C22×C42C2×C411yescharacteristic
96C22×C42C2×C411yescharacteristic
97C22×C42C2×C411yescharacteristic
98C22×C42C2×C411yescharacteristic
99C22×C42C2×C411yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×C22⋊C8—24no—
106C2×C22⋊C8—24no—
107C2×C22⋊C8—24no—
108C2×C22⋊C8—24no—
109C2×C22⋊C8—24no—
110C2×C22⋊C8—24no—
111C2×C22⋊C8—24no—
112C2×C22⋊C8—42no—
113C2×C22⋊C8—42no—
114C4×C4⋊C4—24no—
115C4×C4⋊C4—24no—
116C4×C4⋊C4—24no—
117C4×C22⋊C4—24no—
118C4×C22⋊C4—24no—
119C4×C22⋊C4—24no—
120C4×C22⋊C4—24no—
121C4×C22⋊C4—24no—
122C4×C22⋊C4—24no—
123C2×#95C2×C411yescharacteristic
124C2×#95C2×C411yescharacteristic
125C2×#95C2×C411yescharacteristic
126C2×#95C2×C411yescharacteristic
127C2×#95C2×C411yescharacteristic
128C2×#95C2×C411yescharacteristic
129C43—24no—
130#336—24no—
131#336—24no—
132#336—24no—
133#336—22no—
134#336—24no—
135#336—24no—
136#336—22no—
137#336—22no—
138#336—42no—
139#336—42no—
140#336—42no—
141#336D414yescomplemented
142C25C22×C411yescharacteristic
143C25C22×C411yescharacteristic
144C22×D4—22no—
145C22×D4—22no—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4C22⋊C414yes—
149C22×D4C2×C814yes—
150C22×D4M1614yes—
151C23×C4—21no—
152C23×C4—22no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—22no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—41no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—41no—
187C23×C4—41no—
188C23×C4—41no—
189C23×C4—41no—
190C23×C4—41no—
191C23×C4C2×C814yes—
192C23×C4C2×C814yescomplemented
193C23×C4M1614yes—
194C23×C4C22×C411yescharacteristic
195C23×C4C22×C411yescharacteristic
196C23×C4C22×C411yescharacteristic
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C2×D414yes—
207C23×C4C2×D414yes—
208C23×C4#4112yes—
209C23×C4#4114yes—
210C23×C4#4112yes—
211C23×C4C2411yescharacteristic
212C22×C8—216no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—22no—
238C22×C8—22no—
239C22×C8—48no—
240C22×C8—48no—
241C22×C8—48no—
242C22×C8—48no—
243C22×C8—48no—
244C22×C8—48no—
245C22×C8C2×D414yes—
246C22×C8#4114yes—
247C4×D4—232no—
248C4×D4—232no—
249C4×D4—216no—
250C4×D4—216no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4C22⋊C414yes—
259C2×C4⋊C4C2×C814yescomplemented
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4C22⋊C414yes—
274C2×C22⋊C4C22⋊C414yes—
275C2×C22⋊C4C2×C814yes—
276C2×C22⋊C4C2×C814yescomplemented
277C2×C22⋊C4M1614yes—
278C2×C42—22no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—21no—
312C2×C42—48no—
313C2×C42—48no—
314C2×C42—48no—
315C2×C42—48no—
316C2×C42—41no—
317C2×C42—41no—
318C2×C42—41no—
319C2×C42—41no—
320C2×C42—41no—
321C2×C42—41no—
322C2×C42C2×C814yescomplemented
323C2×C42C2×D414yes—
324C2×C42C2×D412yes—
325C2×C42#4112yes—
326C22⋊C8—48no—
327C22⋊C8—48no—
328C22⋊C8—48no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95—22no—
334#95—22no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—21no—
339C24—21no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24C2×C22⋊C412yes—
356C24C2×C22⋊C412yes—
357C24#11712yes—
358C24#11712yes—
359C24C22×C812yes—
360C24C22×C812yes—
361C24C2×M1612yes—
362C24C2×M1612yes—
363C24C2×M1612yes—
364C24C2×M1612yes—
365C24C23×C411yescharacteristic
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—28no—
369C2×D4—28no—
370C2×D4—28no—
371C2×D4—28no—
372C2×D4C22⋊C8116yes—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—28no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—44no—
495C22×C4C2×C22⋊C412yes—
496C22×C4C2×C22⋊C412yes—
497C22×C4C2×C22⋊C412yes—
498C22×C4C2×C22⋊C412yes—
499C22×C4#11712yes—
500C22×C4#11712yes—
501C22×C4C4×D412yes—
502C22×C4C4×D412yes—
503C22×C4#12318yes—
504C22×C4#12318yes—
505C22×C4C22×C812yes—
506C22×C4C22×C812yes—
507C22×C4C22×C812yes—
508C22×C4C22×C812yes—
509C22×C4C22×C812yes—
510C22×C4C2×M1612yes—
511C22×C4C2×M1612yes—
512C22×C4C2×M1612yes—
513C22×C4C2×M1612yes—
514C22×C4C2×M1612yes—
515C22×C4#13112yes—
516C22×C4#13112yes—
517C22×C4C22×D412yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C2×#4112yes—
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4112yes—
523C22×C4C2×#4111yescharacteristic
524C22×C4H(5,𝔽2)11yescharacteristic
525C22×C4H(5,𝔽2)12yes—
526C22×C42−1+411yescharacteristic
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—24no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8—24no—
533C2×C8—432no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—42no—
537C2×C8—42no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8—42no—
552C2×C8—42no—
553C2×C8—42no—
554C2×C8—42no—
555C2×C8—42no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—28no—
561C22⋊C4—28no—
562C22⋊C4—28no—
563C22⋊C4—28no—
564C22⋊C4—28no—
565C42—28no—
566C42—24no—
567C42—24no—
568C42—24no—
569C42—24no—
570C42—28no—
571C42—44no—
572C42—44no—
573C42—44no—
574C42—44no—
575C42—44no—
576C42—44no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42—42no—
581C42—42no—
582C42—42no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#38114yes—
646C23C2×C22⋊C814yes—
647C23C2×C22⋊C814yes—
648C23#40714yes—
649C23#43114yes—
650C23#43114yes—
651C23#43214yes—
652C23#43214yes—
653C23C22×C22⋊C411yescharacteristic
654C23C2×#11711yescharacteristic
655C23C2×#11711yescharacteristic
656C23C2×C4×D411yescharacteristic
657C23C4×#4111yescharacteristic
658C23#51811yescharacteristic
659C23#52011yescharacteristic
660C23C23×C811yescharacteristic
661C23C22×M1611yescharacteristic
662C23C22×M1611yescharacteristic
663C23C22×M1611yescharacteristic
664C23C2×#13111yescharacteristic
665C23C2×#13111yescharacteristic
666C23#56811yescharacteristic
667C23#56811yescharacteristic
668D4—232no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—416no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—416no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4#38114yes—
762C2×C4C2×C22⋊C814yes—
763C2×C4C8×D414yes—
764C2×C4#43514yes—
765C2×C4C2×#12312yes—
766C2×C4C2×#12312yes—
767C2×C4#52512yes—
768C2×C4#52912yes—
769C2×C4#53812yes—
770C2×C4#53912yes—
771C2×C4D4212yes—
772C2×C4#54611yescharacteristic
773C2×C4#54612yes—
774C2×C4#54612yes—
775C2×C4#54712yes—
776C2×C4#54811yescharacteristic
777C2×C4#55112yes—
778C2×C4#55211yescharacteristic
779C2×C4#55312yes—
780C2×C4#55311yescharacteristic
781C8—44no—
782C8—44no—
783C8—82no—
784C8—82no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22#181718yescomplemented
815C22C2×#38111yescharacteristic
816C22#229011yescharacteristic
817C22#231811yescharacteristic
818C22D4×C22⋊C411yescharacteristic
819C22#233911yescharacteristic
820C22#235211yescharacteristic
821C22#235311yescharacteristic
822C22C22×C22⋊C811yescharacteristic
823C22C2×#40711yescharacteristic
824C22#288011yescharacteristic
825C22#288011yescharacteristic
826C22C2×#43111yescharacteristic
827C22C2×#43111yescharacteristic
828C22C2×#43211yescharacteristic
829C22C2×#43211yescharacteristic
830C22#292211yescharacteristic
831C22#292311yescharacteristic
832C22#292511yescharacteristic
833C22#292511yescharacteristic
834C22C2×C8×D411yescharacteristic
835C22C2×#43511yescharacteristic
836C22D4×M1611yescharacteristic
837C22D4×M1611yescharacteristic
838C22C8×#4111yescharacteristic
839C22#296511yescharacteristic
840C22#297011yescharacteristic
841C22#297011yescharacteristic
842C22#297211yescharacteristic
843C22#297311yescharacteristic
844C22#297411yescharacteristic
845C22#297411yescharacteristic
846C22#298811yescharacteristic
847C22#298911yescharacteristic
848C22#299011yescharacteristic
849C22#299011yescharacteristic
850C4—24no—
851C4—24no—
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4#241812yes—
863C4#241912yes—
864C4#244312yes—
865C4#244412yes—
866C2—28no—
867C2—44no—
868C2#1389411yescharacteristic
869C2C2×#181711yescharacteristic
870C2#2068411yescharacteristic
871C2#2110111yescharacteristic
872C2#2110711yescharacteristic
873C2#2199611yescharacteristic
874C2#2200011yescharacteristic
875C2D4×C22⋊C811yescharacteristic
876C2#2239911yescharacteristic
877C2#2246911yescharacteristic
878C2#2247111yescharacteristic
879C2#2274811yescharacteristic
880C2#2275011yescharacteristic
881C2#2278511yescharacteristic
882C2#2278711yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC23×D4C2×C4
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
3. C2×#1817C2semidirect
4. C22×#336C2semidirect
5. #11346C2semidirect
6. #11147C2semidirect
7. #10795C2semidirect
8. #10795C2semidirect
9. #10714C2semidirect
10. #10712C2semidirect
11. #10712C2semidirect
73. C2×C4×D4C8semidirect
141. #336D4semidirect
192. C23×C4C2×C8semidirect
259. C2×C4⋊C4C2×C8semidirect
276. C2×C22⋊C4C2×C8semidirect
322. C2×C42C2×C8semidirect
814. C22#1817semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D42
C2×#18692
C2×#18172
C22×#3362
#113462
#111472
#107952
#107142
#107122