Finite Group Databasebeta

← #414626

Subgroups — #414626

Order 512.

2334 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#476C211yesmaximal, characteristic, complemented
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4C2×#1987C211yesmaximal, characteristic, complemented
5C2×#1802C211yesmaximal, characteristic, complemented
6C2×#1797C211yesmaximal, characteristic, complemented
7#11327C212yesmaximal, complemented
8#11095C212yesmaximal, complemented
9#11066C212yesmaximal, complemented
10#10969C212yesmaximal
11#10849C211yesmaximal, characteristic, complemented
12C22×C4⋊Q8C2211yescharacteristic
13C22×C22⋊Q8—21no—
14C22×#121C2211yescharacteristic
15C22×C4×D4—21no—
16C22×C4×D4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#476—24no—
19C2×#476—24no—
20C2×#476—24no—
21C22×#106C2212yes—
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×#102C2212yes—
25C22×#102C2212yes—
26C22×C22⋊C8C2212yes—
27#2857—24no—
28#2857—24no—
29C4×#121—24no—
30C4×#121—24no—
31C2×#391—21no—
32C2×#390C2211yescharacteristic
33C2×#389—21no—
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#388—21no—
37C2×#386—21no—
38C2×#384C2211yescharacteristic
39C2×#380—21no—
40C2×#380C2212yes—
41C2×#380C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4—21no—
44#1987—24no—
45#1802—24no—
46#1797—24no—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#340C2212yes—
50C2×#340C2212yes—
51C2×#340C2212yes—
52C2×#336C2212yes—
53C23×Q8—21no—
54C23×D4—21no—
55C23×D4C2311yescharacteristic
56C24×C4—21no—
57C24×C4D411yescharacteristic
58C24×C4D411yescharacteristic
59C24×C4C2311yescharacteristic
60C23×C8C2312yes—
61C23×C8C2312yes—
62C2×C4⋊Q8—22no—
63C2×C4⋊Q8—22no—
64C2×C4⋊Q8—22no—
65C2×C4⋊Q8—22no—
66C2×C4⋊Q8—22no—
67C2×C4⋊Q8D414yescomplemented
68C2×C22⋊Q8—28no—
69C2×C22⋊Q8—44no—
70C2×C22⋊Q8—44no—
71C2×#121—22no—
72C2×#121—22no—
73C2×#121—22no—
74C2×#121—22no—
75C2×#121—22no—
76C2×#121Q814yescomplemented
77C2×C4×D4—28no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—44no—
84C2×C4×D4—44no—
85C2×C4×D4D414yes—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C42—21no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42D411yescharacteristic
110C22×C42D411yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113#476—232no—
114C2×#106—24no—
115C2×#106—24no—
116C2×#106—24no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8D414yescomplemented
123C2×#102—24no—
124C2×#102—24no—
125C2×#102—24no—
126C2×#102—24no—
127C2×#102—24no—
128C2×#102—42no—
129C2×C22⋊C8—24no—
130C2×C22⋊C8—24no—
131C2×C22⋊C8—42no—
132#391—28no—
133#390—22no—
134#390—22no—
135#389—28no—
136#389—24no—
137#389—24no—
138#389—22no—
139#389—22no—
140#388—28no—
141#386—28no—
142#384—22no—
143#384D414yescomplemented
144#380—28no—
145#380—24no—
146#380—24no—
147#380—22no—
148#380—22no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4D414yes—
151C4×C22⋊C4—28no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—22no—
156C2×#95—22no—
157#340—24no—
158#340—24no—
159#340—24no—
160#340—24no—
161#340—42no—
162#336—24no—
163C25—21no—
164C25C2×D411yescharacteristic
165C22×Q8—24no—
166C22×Q8—42no—
167C22×Q8—42no—
168C22×Q8—42no—
169C22×Q8—42no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×D4—24no—
173C22×D4—24no—
174C22×D4—24no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—42no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—42no—
190C22×D4C2×D412yes—
191C22×D4C2×Q812yes—
192C22×D4#4112yes—
193C23×C4—22no—
194C23×C4—21no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—41no—
223C23×C4—41no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4SD1614yes—
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×Q812yes—
237C23×C4#4112yes—
238C23×C4C2411yescharacteristic
239C22×C8—22no—
240C22×C8—22no—
241C22×C8—22no—
242C22×C8—22no—
243C22×C8—22no—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—22no—
247C22×C8—22no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8C2×D414yes—
253C4⋊Q8—28no—
254C4⋊Q8—28no—
255C4⋊Q8—44no—
256C4⋊Q8—44no—
257C22⋊Q8—432no—
258#121—28no—
259#121—28no—
260#121—28no—
261#121—28no—
262C4×D4—28no—
263C4×D4—28no—
264C4×D4—432no—
265C4×D4—44no—
266C4×D4—44no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×Q812yes—
311C2×C4⋊C4#4112yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C42—24no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42—44no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349C2×C42C2×D412yes—
350C2×C42C2×D412yes—
351C2×C42C2×D412yes—
352C2×C42C2×D412yes—
353C2×C42C2×D412yes—
354C2×C42#4112yes—
355#106—216no—
356C4⋊C8—28no—
357C4⋊C8—44no—
358#102—216no—
359#102—48no—
360C22⋊C8—48no—
361#95—24no—
362#95—24no—
363#95—28no—
364#95—28no—
365#95—24no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24C22⋊Q812yes—
394C24C2×SD1612yes—
395C24AGL(1,ℤ/8)12yes—
396C24C22×D411yescharacteristic
397C2×Q8—48no—
398C2×Q8—48no—
399C2×Q8—48no—
400C2×Q8—84no—
401C2×Q8—84no—
402C2×Q8—84no—
403C2×Q8—84no—
404C2×D4—216no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4C22⋊Q814yescomplemented
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—28no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—42no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—41no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4#12012yes—
546C22×C4#12012yes—
547C22×C4#12012yes—
548C22×C4#12012yes—
549C22×C4#12112yes—
550C22×C4#12112yes—
551C22×C4C22⋊Q812yes—
552C22×C4C2×SD1612yes—
553C22×C4C2×SD1612yes—
554C22×C4#13512yes—
555C22×C4AGL(1,ℤ/8)12yes—
556C22×C4AGL(1,ℤ/8)12yes—
557C22×C4#13712yes—
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×Q811yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C42−1+411yescharacteristic
570C22×C42−1+411yescharacteristic
571C22×C42−1+411yescharacteristic
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—42no—
576C2×C8—42no—
577C2×C8—42no—
578C2×C8—42no—
579C2×C8—42no—
580C2×C8—42no—
581C2×C8—42no—
582C2×C8—42no—
583C2×C8—42no—
584C2×C8—42no—
585C2×C8—42no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—416no—
600C4⋊C4—41no—
601C4⋊C4—42no—
602C4⋊C4—41no—
603C4⋊C4—42no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4C22⋊Q814yescomplemented
611C22⋊C4—216no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—44no—
622C42—44no—
623C42—48no—
624C42#12014yes—
625C42#12114yes—
626C42#12114yes—
627C42#12714yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23#47614yescomplemented
698C23C2×#12011yescharacteristic
699C23C2×#12011yescharacteristic
700C23C2×#12111yescharacteristic
701C23C2×C22⋊Q811yescharacteristic
702C23#52511yescharacteristic
703C23#53611yescharacteristic
704C23#53711yescharacteristic
705C23C22×SD1611yescharacteristic
706C23C2×#13511yescharacteristic
707C23C2×AGL(1,ℤ/8)11yescharacteristic
708C23C2×AGL(1,ℤ/8)11yescharacteristic
709C23C2×AGL(1,ℤ/8)11yescharacteristic
710C23C2×#13711yescharacteristic
711C23#57511yescharacteristic
712C23#57511yescharacteristic
713Q8—816no—
714D4—24no—
715D4—24no—
716D4—432no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—416no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—416no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—82no—
790C2×C4—82no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—816no—
796C2×C4#39214yes—
797C2×C4#39214yes—
798C2×C4#44814yes—
799C2×C4#44914yes—
800C2×C4#45014yes—
801C2×C4#45214yes—
802C2×C4#46514yes—
803C2×C4#46814yes—
804C2×C4C2×#12011yescharacteristic
805C2×C4C2×#12111yescharacteristic
806C2×C4C2×#12111yescharacteristic
807C2×C4C2×C22⋊Q811yescharacteristic
808C2×C4C2×C22⋊Q811yescharacteristic
809C2×C4#52511yescharacteristic
810C2×C4#52511yescharacteristic
811C2×C4C2×#12711yescharacteristic
812C2×C4#53611yescharacteristic
813C2×C4#53611yescharacteristic
814C2×C4#53711yescharacteristic
815C2×C4#53711yescharacteristic
816C2×C4#54611yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54711yescharacteristic
819C2×C4#54711yescharacteristic
820C2×C4#54811yescharacteristic
821C2×C4#54811yescharacteristic
822C2×C4#54811yescharacteristic
823C2×C4#54811yescharacteristic
824C2×C4D4×Q811yescharacteristic
825C2×C4D4×Q811yescharacteristic
826C2×C4D4×Q811yescharacteristic
827C2×C4#55011yescharacteristic
828C2×C4#55211yescharacteristic
829C2×C4#55211yescharacteristic
830C2×C4#55411yescharacteristic
831C2×C4#55611yescharacteristic
832C8—44no—
833C8—82no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22C2×#39211yescharacteristic
865C22#240711yescharacteristic
866C22#240911yescharacteristic
867C22#241511yescharacteristic
868C22#241711yescharacteristic
869C22#261611yescharacteristic
870C22#284811yescharacteristic
871C22C2×#45011yescharacteristic
872C22C2×#44811yescharacteristic
873C22C2×#44911yescharacteristic
874C22C2×#45211yescharacteristic
875C22#300311yescharacteristic
876C22#300511yescharacteristic
877C22#300611yescharacteristic
878C22#300611yescharacteristic
879C22C2×#46511yescharacteristic
880C22C2×#46811yescharacteristic
881C22#305511yescharacteristic
882C22#305511yescharacteristic
883C22C2×#47611yescharacteristic
884C22#307611yescharacteristic
885C22#307711yescharacteristic
886C22#307911yescharacteristic
887C22#310111yescharacteristic
888C22#310611yescharacteristic
889C22#310911yescharacteristic
890C22#311611yescharacteristic
891C22#322711yescharacteristic
892C22#323311yescharacteristic
893C22#323511yescharacteristic
894C22#323811yescharacteristic
895C22#324611yescharacteristic
896C22#324711yescharacteristic
897C22#325211yescharacteristic
898C22#325311yescharacteristic
899C4—24no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—44no—
904C4—82no—
905C4—84no—
906C4—84no—
907C4—82no—
908C4#200018yes—
909C4#240711yescharacteristic
910C4#240911yescharacteristic
911C4#241511yescharacteristic
912C4#241711yescharacteristic
913C4#253611yescharacteristic
914C4#253811yescharacteristic
915C4#254011yescharacteristic
916C4#254211yescharacteristic
917C2—44no—
918C2—84no—
919C2#1517711yescharacteristic
920C2C2×#200011yescharacteristic
921C2#2339111yescharacteristic
922C2#2415111yescharacteristic
923C2#2415211yescharacteristic
924C2#2429911yescharacteristic
925C2#2430011yescharacteristic
926C2#2470111yescharacteristic
927C2#2470811yescharacteristic
928C2#2483611yescharacteristic
929C2#2484311yescharacteristic
930C2#2969011yescharacteristic
931C2#2969211yescharacteristic
932C2#3295611yescharacteristic
933C2#3295811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#476C2semidirect
2. C2×#2857C2semidirect
4. C2×#1987C2semidirect
5. C2×#1802C2semidirect
6. C2×#1797C2semidirect
7. #11327C2semidirect
8. #11095C2semidirect
9. #11066C2semidirect
11. #10849C2semidirect
67. C2×C4⋊Q8D4semidirect
76. C2×#121Q8semidirect
122. C2×C4⋊C8D4semidirect
143. #384D4semidirect
438. C2×D4C22⋊Q8semidirect
610. C4⋊C4C22⋊Q8semidirect
697. C23#476semidirect

Maximal subgroups

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

subgroupindex
C22×#4762
C2×#28572
C2×C4×#1212
C2×#19872
C2×#18022
C2×#17972
#113272
#110952
#110662
#109692
#108492