Finite Group Databasebeta

← #360976

Subgroups — #360976

Order 512.

2082 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D4C211yesmaximal, characteristic
2C2×#1924C212yesmaximal, complemented
3C2×#1817C211yesmaximal, characteristic, complemented
4C2×#1749C211yesmaximal, characteristic, complemented
5#11042C212yesmaximal, complemented
6#10964C212yesmaximal
7#10875C212yesmaximal, complemented
8#10832C211yesmaximal, characteristic, complemented
9#10795C211yesmaximal, characteristic, complemented
10#10712C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C22×C4×D4C411yescharacteristic
13C22×C4×D4C411yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×C4⋊C8C2212yes—
18C22×C22⋊C8C2212yes—
19C22×C22⋊C8C2212yes—
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×#97C2212yes—
23C42×D4—28no—
24C2×C4×C4⋊C4C411yescharacteristic
25C2×C4×C4⋊C4C411yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C4×C22⋊C4C411yescharacteristic
28C2×C4×C22⋊C4C411yescharacteristic
29C2×C4×C22⋊C4C411yescharacteristic
30C2×C4×C22⋊C4C411yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C43C2211yescharacteristic
34#1924—28no—
35#1817—24no—
36#1749—24no—
37C2×#336C2212yes—
38C2×#336C2212yes—
39C2×#336C2212yes—
40C2×#336C2211yescharacteristic
41C2×#336C2212yes—
42C2×#336C2212yes—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2212yes—
46C2×#336C2211yescharacteristic
47C23×D4C2×C411yescharacteristic
48C24×C4C2×C411yescharacteristic
49C24×C4C2×C411yescharacteristic
50C24×C4C2×C411yescharacteristic
51C24×C4C2×C411yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C23×C8C2312yes—
55C23×C8C2312yes—
56C23×C8C2312yes—
57C23×C8C2312yes—
58C2×C4×D4—24no—
59C2×C4×D4—24no—
60C2×C4×D4—24no—
61C2×C4×D4—24no—
62C2×C4×D4—24no—
63C2×C4×D4—24no—
64C2×C4×D4—24no—
65C2×C4×D4—24no—
66C2×C4×D4—22no—
67C2×C4×D4—22no—
68C22×C4⋊C4C2×C411yescharacteristic
69C22×C4⋊C4C2×C411yescharacteristic
70C22×C4⋊C4C2×C411yescharacteristic
71C22×C22⋊C4C2×C411yescharacteristic
72C22×C22⋊C4C2×C411yescharacteristic
73C22×C22⋊C4C2×C411yescharacteristic
74C22×C22⋊C4C2×C411yescharacteristic
75C22×C22⋊C4C2×C411yescharacteristic
76C22×C22⋊C4C2×C411yescharacteristic
77C22×C42—24no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—24no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—42no—
84C22×C42—42no—
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42C2×C411yescharacteristic
92C22×C42C2×C411yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×C4⋊C8—24no—
99C2×C4⋊C8—24no—
100C2×C4⋊C8—42no—
101C2×C22⋊C8—24no—
102C2×C22⋊C8—24no—
103C2×C22⋊C8—24no—
104C2×C22⋊C8—24no—
105C2×C22⋊C8—24no—
106C2×C22⋊C8—24no—
107C2×C22⋊C8—24no—
108C2×C22⋊C8—24no—
109C2×C22⋊C8—42no—
110C2×C22⋊C8—42no—
111C2×C22⋊C8—42no—
112C2×C22⋊C8—42no—
113C2×#97—24no—
114C2×#97—24no—
115C2×#97—42no—
116C4×C4⋊C4—24no—
117C4×C4⋊C4—24no—
118C4×C4⋊C4—24no—
119C4×C22⋊C4—24no—
120C4×C22⋊C4—24no—
121C4×C22⋊C4—24no—
122C4×C22⋊C4—24no—
123C4×C22⋊C4—24no—
124C4×C22⋊C4D418yes—
125C2×#95C2×C411yescharacteristic
126C2×#95C2×C411yescharacteristic
127C2×#95C2×C411yescharacteristic
128C2×#95C2×C411yescharacteristic
129C2×#95C2×C411yescharacteristic
130C2×#95C2×C411yescharacteristic
131C43—24no—
132#336—24no—
133#336—22no—
134#336—24no—
135#336—24no—
136#336—22no—
137#336—24no—
138#336—24no—
139#336—22no—
140#336—42no—
141#336D414yescomplemented
142C25C22×C411yescharacteristic
143C25C22×C411yescharacteristic
144C22×D4—22no—
145C22×D4—22no—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4—22no—
149C22×D4—22no—
150C22×D4M1614yes—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
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—21no—
166C23×C4—21no—
167C23×C4—22no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—41no—
189C23×C4—41no—
190C23×C4—41no—
191C23×C4—41no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4—41no—
195C23×C4—41no—
196C23×C4M1614yes—
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×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C2×D414yes—
210C23×C4#4114yes—
211C23×C4C2411yescharacteristic
212C22×C8—22no—
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×C8C2×D414yes—
239C22×C8#4114yes—
240C4×D4—232no—
241C4×D4—216no—
242C4×D4—216no—
243C4×D4—232no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
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⋊C4C22⋊C414yes—
269C2×C22⋊C4C22⋊C414yes—
270C2×C22⋊C4M1614yes—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—21no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42—21no—
284C2×C42—22no—
285C2×C42—21no—
286C2×C42—22no—
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—21no—
299C2×C42—22no—
300C2×C42—21no—
301C2×C42—22no—
302C2×C42—48no—
303C2×C42—48no—
304C2×C42—48no—
305C2×C42—48no—
306C2×C42—41no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42—41no—
312C2×C42M1614yes—
313C2×C42C2×D414yes—
314C2×C42C2×D414yes—
315C2×C42C2×D412yes—
316C2×C42#4112yes—
317C2×C42#4112yes—
318C2×C42#4112yes—
319C4⋊C8—48no—
320C22⋊C8—216no—
321C22⋊C8—48no—
322C22⋊C8—48no—
323C22⋊C8—48no—
324#97—48no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329#95C22⋊C414yes—
330#95C22⋊C414yes—
331C24—21no—
332C24—21no—
333C24—21no—
334C24—21no—
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—
356C24#11712yes—
357C24C2×M1612yes—
358C24C2×M1612yes—
359C24C2×M1612yes—
360C24C2×M1612yes—
361C24C23×C411yescharacteristic
362C2×D4—28no—
363C2×D4—28no—
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—28no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
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—28no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
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—28no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—28no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4C2×C22⋊C412yes—
494C22×C4C2×C22⋊C412yes—
495C22×C4C2×C22⋊C412yes—
496C22×C4C2×C22⋊C412yes—
497C22×C4C2×C22⋊C412yes—
498C22×C4#11712yes—
499C22×C4#11712yes—
500C22×C4#11712yes—
501C22×C4C4×D412yes—
502C22×C4C4×D412yes—
503C22×C4C2×M1612yes—
504C22×C4C2×M1612yes—
505C22×C4C2×M1612yes—
506C22×C4C2×M1612yes—
507C22×C4C2×M1612yes—
508C22×C4C2×M1612yes—
509C22×C4C2×M1612yes—
510C22×C4C2×M1612yes—
511C22×C4#13112yes—
512C22×C4#13112yes—
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D412yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4112yes—
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)12yes—
522C22×C42−1+411yescharacteristic
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—24no—
526C2×C8—24no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8—42no—
533C2×C8—42no—
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—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C22⋊C4—28no—
555C22⋊C4—28no—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C42—28no—
561C42—24no—
562C42—24no—
563C42—24no—
564C42—24no—
565C42—24no—
566C42—24no—
567C42—24no—
568C42—24no—
569C42—28no—
570C42—44no—
571C42—44no—
572C42—44no—
573C42—44no—
574C42—44no—
575C42—44no—
576C42—42no—
577C42—42no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
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—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
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—41no—
646C23#40714yes—
647C23#43214yes—
648C23C22×C22⋊C411yescharacteristic
649C23C2×#11711yescharacteristic
650C23C2×#11711yescharacteristic
651C23C2×C4×D411yescharacteristic
652C23C4×#4111yescharacteristic
653C23#51811yescharacteristic
654C23#52011yescharacteristic
655C23C22×M1611yescharacteristic
656C23C22×M1611yescharacteristic
657C23C22×M1611yescharacteristic
658C23C22×M1611yescharacteristic
659C23C2×#13111yescharacteristic
660C23C2×#13111yescharacteristic
661C23#56811yescharacteristic
662C23#56811yescharacteristic
663D4—232no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
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—416no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
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—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4#40714yes—
757C2×C4#43214yes—
758C2×C4#43514yes—
759C2×C4#43614yes—
760C2×C4#52512yes—
761C2×C4#52512yes—
762C2×C4#52512yes—
763C2×C4#52912yes—
764C2×C4#53812yes—
765C2×C4#53912yes—
766C2×C4D4212yes—
767C2×C4#54612yes—
768C2×C4#54612yes—
769C2×C4#54711yescharacteristic
770C2×C4#54712yes—
771C2×C4#55011yescharacteristic
772C2×C4#55312yes—
773C2×C4#55511yescharacteristic
774C2×C4#55611yescharacteristic
775C2×C4#55912yes—
776C8—44no—
777C8—44no—
778C8—82no—
779C8—82no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22#228011yescharacteristic
811C22#229011yescharacteristic
812C22#231811yescharacteristic
813C22D4×C22⋊C411yescharacteristic
814C22#233911yescharacteristic
815C22#235411yescharacteristic
816C22#235711yescharacteristic
817C22C2×#40711yescharacteristic
818C22C2×#40711yescharacteristic
819C22#288011yescharacteristic
820C22#288011yescharacteristic
821C22C2×#43211yescharacteristic
822C22C2×#43211yescharacteristic
823C22#292011yescharacteristic
824C22#292011yescharacteristic
825C22#292211yescharacteristic
826C22#292311yescharacteristic
827C22#292511yescharacteristic
828C22#292511yescharacteristic
829C22C2×#43511yescharacteristic
830C22C2×#43611yescharacteristic
831C22D4×M1611yescharacteristic
832C22D4×M1611yescharacteristic
833C22#296511yescharacteristic
834C22#296511yescharacteristic
835C22#297011yescharacteristic
836C22#297011yescharacteristic
837C22#297311yescharacteristic
838C22#297411yescharacteristic
839C22#297411yescharacteristic
840C22#297511yescharacteristic
841C22#298911yescharacteristic
842C22#298911yescharacteristic
843C22#299011yescharacteristic
844C22#299011yescharacteristic
845C4—24no—
846C4—24no—
847C4—24no—
848C4—24no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4#245512yes—
858C4#245612yes—
859C4#245912yes—
860C4#246612yes—
861C2—44no—
862C2—44no—
863C2#1388611yescharacteristic
864C2#2071511yescharacteristic
865C2#2072011yescharacteristic
866C2#2110211yescharacteristic
867C2#2110711yescharacteristic
868C2#2200011yescharacteristic
869C2#2200211yescharacteristic
870C2#2239911yescharacteristic
871C2#2240111yescharacteristic
872C2#2247111yescharacteristic
873C2#2247111yescharacteristic
874C2#2279711yescharacteristic
875C2#2279911yescharacteristic
876C2#2283711yescharacteristic
877C2#2283911yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1924C2semidirect
3. C2×#1817C2semidirect
4. C2×#1749C2semidirect
5. #11042C2semidirect
7. #10875C2semidirect
8. #10832C2semidirect
9. #10795C2semidirect
10. #10712C2semidirect
11. #10712C2semidirect
141. #336D4semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D42
C2×#19242
C2×#18172
C2×#17492
#110422
#109642
#108752
#108322
#107952
#107122