Finite Group Databasebeta

← #360428

Subgroups — #360428

Order 512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1924C212yesmaximal
2C2×#1842C211yesmaximal, characteristic, complemented
3C2×#1797C211yesmaximal, characteristic
4C2×#1797C211yesmaximal, characteristic
5C2×#1767C211yesmaximal, characteristic, complemented
6C42×C22⋊C4C211yesmaximal, characteristic
7#11255C212yesmaximal, complemented
8#11042C212yesmaximal
9#10877C212yesmaximal, complemented
10#10832C211yesmaximal, characteristic, complemented
11#10832C211yesmaximal, characteristic, complemented
12C23×C42C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×C4⋊C8C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2212yes—
20C22×C22⋊C8C2212yes—
21C22×#97C2212yes—
22C2×C4×C22⋊C4C411yescharacteristic
23C2×C4×C22⋊C4C411yescharacteristic
24C2×C4×C22⋊C4C411yescharacteristic
25C2×C4×C22⋊C4C411yescharacteristic
26C2×C4×C22⋊C4C2211yescharacteristic
27C2×C4×C22⋊C4C2211yescharacteristic
28C2×C43C2211yescharacteristic
29C2×C43C2211yescharacteristic
30#1924—28no—
31#1842—24no—
32#1797—24no—
33#1797—24no—
34#1767—24no—
35C2×#336C2212yes—
36C2×#336C2212yes—
37C2×#336C2212yes—
38C2×#336C2212yes—
39C2×#336C2212yes—
40C2×#336C2212yes—
41C2×#336C2212yes—
42C4×#95C411yescharacteristic
43C4×#95C411yescharacteristic
44C4×#95C411yescharacteristic
45C4×#95C411yescharacteristic
46C4×#95C2211yescharacteristic
47C4×#95C2211yescharacteristic
48C24×C4C2×C411yescharacteristic
49C24×C4C2×C411yescharacteristic
50C24×C4C2311yescharacteristic
51C23×C8C2312yes—
52C23×C8C2312yes—
53C23×C8C2312yes—
54C23×C8C2312yes—
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4C2×C411yescharacteristic
57C22×C22⋊C4C2×C411yescharacteristic
58C22×C22⋊C4C2×C411yescharacteristic
59C22×C42—22no—
60C22×C42—22no—
61C22×C42—22no—
62C22×C42—22no—
63C22×C42—22no—
64C22×C42—22no—
65C22×C42C2×C411yescharacteristic
66C22×C42C2×C411yescharacteristic
67C22×C42C2×C411yescharacteristic
68C22×C42C2×C411yescharacteristic
69C22×C42C2×C411yescharacteristic
70C22×C42C2×C411yescharacteristic
71C22×C42C2×C411yescharacteristic
72C22×C42C2×C411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42C2×C411yescharacteristic
75C22×C42C2311yescharacteristic
76C22×C42C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C22×C42C2311yescharacteristic
79C22×C42C2311yescharacteristic
80C22×C42C2311yescharacteristic
81C2×C4⋊C8—22no—
82C2×C4⋊C8—22no—
83C2×C4⋊C8—22no—
84C2×C4⋊C8—22no—
85C2×C4⋊C8—24no—
86C2×C4⋊C8—24no—
87C2×C4⋊C8—22no—
88C2×C4⋊C8—22no—
89C2×C4⋊C8—22no—
90C2×C4⋊C8—24no—
91C2×C4⋊C8—24no—
92C2×C4⋊C8—22no—
93C2×C4⋊C8—22no—
94C2×C4⋊C8—22no—
95C2×C4⋊C8—42no—
96C2×C4⋊C8—42no—
97C2×C4⋊C8D414yes—
98C2×C4⋊C8D414yes—
99C2×C22⋊C8—24no—
100C2×C22⋊C8—24no—
101C2×C22⋊C8—24no—
102C2×C22⋊C8—24no—
103C2×C22⋊C8—42no—
104C2×C22⋊C8—42no—
105C2×#97—24no—
106C2×#97—24no—
107C2×#97—42no—
108C4×C22⋊C4—24no—
109C4×C22⋊C4—24no—
110C4×C22⋊C4—24no—
111C4×C22⋊C4—22no—
112C4×C22⋊C4—22no—
113C4×C22⋊C4—24no—
114C4×C22⋊C4D414yes—
115C4×C22⋊C4Q814yes—
116C2×#95C2×C411yescharacteristic
117C2×#95C2×C411yescharacteristic
118C2×#95C2×C411yescharacteristic
119C2×#95C2×C411yescharacteristic
120C2×#95C2×C411yescharacteristic
121C2×#95C2×C411yescharacteristic
122C2×#95C2×C411yescharacteristic
123C2×#95C2×C411yescharacteristic
124C2×#95C2×C411yescharacteristic
125C2×#95C2×C411yescharacteristic
126C2×#95C2×C411yescharacteristic
127C2×#95C2×C411yescharacteristic
128C43—22no—
129C43—22no—
130C43—22no—
131C43—22no—
132#336—24no—
133#336—24no—
134#336—24no—
135#336—24no—
136#336—24no—
137#336—24no—
138#336—42no—
139C25C22×C411yescharacteristic
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4M1614yes—
166C23×C4C22×C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C22×C411yescharacteristic
169C23×C4C22×C411yescharacteristic
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C22×C411yescharacteristic
173C23×C4C22×C411yescharacteristic
174C23×C4C22×C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C22×C411yescharacteristic
177C23×C4C22×C411yescharacteristic
178C23×C4C22×C411yescharacteristic
179C23×C4C2×D412yes—
180C23×C4C2×Q812yes—
181C23×C4C2411yescharacteristic
182C22×C8—22no—
183C22×C8—22no—
184C22×C8—22no—
185C22×C8—22no—
186C22×C8—22no—
187C22×C8—22no—
188C22×C8—22no—
189C22×C8—22no—
190C22×C8—22no—
191C22×C8—22no—
192C22×C8—22no—
193C22×C8—22no—
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—22no—
201C22×C8—22no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—22no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—22no—
208C22×C8C2×D414yes—
209C22×C8C2×D414yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4C4⋊C414yes—
220C2×C22⋊C4C4⋊C414yes—
221C2×C22⋊C4M1614yes—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—22no—
254C2×C42—22no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—22no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42—21no—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—41no—
272C2×C42—41no—
273C2×C42—41no—
274C2×C42—41no—
275C2×C42—44no—
276C2×C42—44no—
277C2×C42—44no—
278C2×C42—44no—
279C2×C42M1614yes—
280C2×C42C2×D412yes—
281C2×C42C2×D412yes—
282C2×C42C2×D412yes—
283C2×C42C2×D412yes—
284C2×C42C2×Q812yes—
285C2×C42C2×Q812yes—
286C2×C42#4112yes—
287C2×C42#4112yes—
288C2×C42#4112yes—
289C2×C42#4112yes—
290C2×C42#4112yes—
291C2×C42#4112yes—
292C4⋊C8—28no—
293C4⋊C8—28no—
294C4⋊C8—48no—
295C4⋊C8—48no—
296C4⋊C8—44no—
297C4⋊C8—44no—
298C22⋊C8—48no—
299C22⋊C8—48no—
300#97—48no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95—22no—
310#95C4⋊C414yes—
311#95C4⋊C414yes—
312#95M1614yes—
313C24—21no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—21no—
318C24—21no—
319C24—21no—
320C24—21no—
321C24—21no—
322C24—21no—
323C24—21no—
324C24—21no—
325C24C2×C4⋊C412yes—
326C24C2×M1612yes—
327C24C2×M1612yes—
328C24C23×C411yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—28no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
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—21no—
386C22×C4—21no—
387C22×C4—21no—
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—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4C2×C4⋊C412yes—
438C22×C4C2×C4⋊C412yes—
439C22×C4C2×C4⋊C412yes—
440C22×C4C2×C4⋊C412yes—
441C22×C4C2×C4⋊C412yes—
442C22×C4#11712yes—
443C22×C4#11712yes—
444C22×C4#11712yes—
445C22×C4#11712yes—
446C22×C4C4×D412yes—
447C22×C4C4×D412yes—
448C22×C4C4×D412yes—
449C22×C4C4×D412yes—
450C22×C4C2×M1612yes—
451C22×C4C2×M1612yes—
452C22×C4C2×M1612yes—
453C22×C4C2×M1612yes—
454C22×C4C2×M1612yes—
455C22×C4C2×M1612yes—
456C22×C4C2×M1612yes—
457C22×C4C2×M1612yes—
458C22×C4C2×M1612yes—
459C22×C4C2×M1612yes—
460C22×C4#13112yes—
461C22×C4#13112yes—
462C22×C4C22×D411yescharacteristic
463C22×C4C22×D411yescharacteristic
464C22×C4C22×D411yescharacteristic
465C22×C4C22×Q811yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4H(5,𝔽2)11yescharacteristic
473C22×C4H(5,𝔽2)11yescharacteristic
474C22×C42−1+411yescharacteristic
475C22×C42−1+411yescharacteristic
476C2×C8—24no—
477C2×C8—24no—
478C2×C8—24no—
479C2×C8—24no—
480C2×C8—24no—
481C2×C8—24no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—42no—
490C2×C8—42no—
491C2×C8—42no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8—42no—
500C2×C8—42no—
501C2×C8—42no—
502C2×C8—42no—
503C2×C8—42no—
504C22⋊C4—28no—
505C22⋊C4—28no—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—28no—
521C42—44no—
522C42—44no—
523C42—44no—
524C42—44no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—41no—
530C42—41no—
531C42—41no—
532C42—41no—
533C42—44no—
534C42—44no—
535C42—44no—
536C42—44no—
537C42—44no—
538C42#12114yes—
539C42#12314yes—
540C42#12414yes—
541C42#12614yes—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23#42314yes—
577C23C22×C4⋊C411yescharacteristic
578C23C2×#11711yescharacteristic
579C23C2×#11711yescharacteristic
580C23C2×C4×D411yescharacteristic
581C23C2×C4×D411yescharacteristic
582C23#52011yescharacteristic
583C23#52011yescharacteristic
584C23C22×M1611yescharacteristic
585C23C22×M1611yescharacteristic
586C23C22×M1611yescharacteristic
587C23C22×M1611yescharacteristic
588C23C2×#13111yescharacteristic
589C23C2×#13111yescharacteristic
590C23#56811yescharacteristic
591C23#56811yescharacteristic
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—416no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4#38814yes—
684C2×C4#38814yes—
685C2×C4#42314yes—
686C2×C4#43214yes—
687C2×C4#43214yes—
688C2×C4#43314yes—
689C2×C4#43514yes—
690C2×C4#43514yes—
691C2×C4#43514yes—
692C2×C4#43614yes—
693C2×C4C2×#12111yescharacteristic
694C2×C4C2×#12311yescharacteristic
695C2×C4C2×#12411yescharacteristic
696C2×C4C2×#12611yescharacteristic
697C2×C4#53211yescharacteristic
698C2×C4#53211yescharacteristic
699C2×C4#53311yescharacteristic
700C2×C4#53311yescharacteristic
701C2×C4#54011yescharacteristic
702C2×C4#54111yescharacteristic
703C2×C4#54211yescharacteristic
704C2×C4#54211yescharacteristic
705C2×C4D4211yescharacteristic
706C2×C4D4211yescharacteristic
707C2×C4#54611yescharacteristic
708C2×C4#54711yescharacteristic
709C2×C4#54711yescharacteristic
710C2×C4#54711yescharacteristic
711C2×C4#54811yescharacteristic
712C2×C4D4×Q811yescharacteristic
713C2×C4D4×Q811yescharacteristic
714C2×C4#55011yescharacteristic
715C2×C4#55211yescharacteristic
716C2×C4#55311yescharacteristic
717C2×C4#55411yescharacteristic
718C2×C4#55411yescharacteristic
719C2×C4#55511yescharacteristic
720C2×C4#55611yescharacteristic
721C8—44no—
722C8—44no—
723C8—82no—
724C8—82no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22#228511yescharacteristic
741C22C2×#38811yescharacteristic
742C22#231411yescharacteristic
743C22D4×C4⋊C411yescharacteristic
744C22D4×C4⋊C411yescharacteristic
745C22#235211yescharacteristic
746C22#235411yescharacteristic
747C22C2×#42311yescharacteristic
748C22C2×#42311yescharacteristic
749C22#290611yescharacteristic
750C22#290611yescharacteristic
751C22C2×#43211yescharacteristic
752C22C2×#43211yescharacteristic
753C22C2×#43311yescharacteristic
754C22#292011yescharacteristic
755C22#292011yescharacteristic
756C22#292111yescharacteristic
757C22#292511yescharacteristic
758C22#292511yescharacteristic
759C22C2×#43511yescharacteristic
760C22C2×#43511yescharacteristic
761C22C2×#43511yescharacteristic
762C22C2×#43611yescharacteristic
763C22D4×M1611yescharacteristic
764C22D4×M1611yescharacteristic
765C22D4×M1611yescharacteristic
766C22D4×M1611yescharacteristic
767C22#298911yescharacteristic
768C22#298911yescharacteristic
769C22#298911yescharacteristic
770C22#298911yescharacteristic
771C22#299011yescharacteristic
772C22#299011yescharacteristic
773C22#299011yescharacteristic
774C22#299111yescharacteristic
775C4—24no—
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4#192418yescomplemented
788C4#242211yescharacteristic
789C4#242311yescharacteristic
790C4#242811yescharacteristic
791C4#242911yescharacteristic
792C4#249111yescharacteristic
793C4#249211yescharacteristic
794C4#249611yescharacteristic
795C4#249711yescharacteristic
796C2—44no—
797C2#1387611yescharacteristic
798C2#2081011yescharacteristic
799C2#2081211yescharacteristic
800C2C2×#192411yescharacteristic
801C2#2104911yescharacteristic
802C2#2192411yescharacteristic
803C2#2192611yescharacteristic
804C2#2264811yescharacteristic
805C2#2264811yescharacteristic
806C2#2264811yescharacteristic
807C2#2265011yescharacteristic
808C2#2274911yescharacteristic
809C2#2275011yescharacteristic
810C2#2279711yescharacteristic
811C2#2279911yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC25C22×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×#1842C2semidirect
5. C2×#1767C2semidirect
7. #11255C2semidirect
9. #10877C2semidirect
10. #10832C2semidirect
11. #10832C2semidirect
787. C4#1924semidirect

Maximal subgroups

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

subgroupindex
C2×#19242
C2×#18422
C2×#17972
C2×#17672
C42×C22⋊C42
#112552
#110422
#108772
#108322