Finite Group Databasebeta

← #357670

Subgroups — #357670

Order 512.

3642 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic, complemented
2C22×#407C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic, complemented
7C2×#1736C211yesmaximal, characteristic, complemented
8#11096C214yesmaximal, complemented
9#11095C214yesmaximal, complemented
10C25×C4C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C22⋊C4—21no—
18C2×#428—24no—
19C2×#428—24no—
20C2×#428—24no—
21C22×#107C2212yescomplemented
22C22×#106C2212yescomplemented
23C2×#407—24no—
24C2×#407—24no—
25C2×#407C418yescomplemented
26C22×C22⋊C8C2214yes—
27#2280—24no—
28#2280—24no—
29C2×#381—21no—
30C2×#380—22no—
31C2×#380—24no—
32C2×#380—24no—
33C2×#380C2212yes—
34C2×#380C2214yes—
35C2×#380C2212yes—
36C2×#379—21no—
37C2×C4×C22⋊C4—22no—
38C22×#95—21no—
39#1736—24no—
40#1736—24no—
41#1736—24no—
42C2×#340C2212yescomplemented
43C2×#340C2214yescomplemented
44C2×#340C2214yescomplemented
45C2×#340C2212yescomplemented
46C26D411yescharacteristic
47C24×C4—22no—
48C24×C4—22no—
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—22no—
52C24×C4—22no—
53C24×C4—22no—
54C24×C4—22no—
55C24×C4—22no—
56C24×C4—22no—
57C24×C4—22no—
58C24×C4—22no—
59C24×C4—21no—
60C24×C4—21no—
61C24×C4C2×C414yes—
62C24×C4D411yescharacteristic
63C24×C4D412yes—
64C24×C4Q814yes—
65C24×C4C2312yes—
66C24×C4C2311yescharacteristic
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16C2×C414yes—
78C22×M16C2×C414yes—
79C22×M16D414yes—
80C22×M16D414yes—
81C23×C8C2312yes—
82C23×C8C2312yes—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117D414yes—
94C2×#117D414yes—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—22no—
107C22×C4⋊C4D414yes—
108C22×C4⋊C4D414yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—22no—
119C22×C22⋊C4—22no—
120C22×C22⋊C4—48no—
121C22×C42—21no—
122C22×C42—21no—
123#428—232no—
124C2×#107—24no—
125C2×#107—24no—
126C2×#107—24no—
127C2×#106—24no—
128C2×#106—24no—
129C2×#106—24no—
130#407—232no—
131C2×C22⋊C8—28no—
132C2×C22⋊C8—28no—
133C2×C22⋊C8C2×C4116yescomplemented
134#381—28no—
135#380—216no—
136#380—28no—
137#380—28no—
138#380—24no—
139#380—24no—
140#380—24no—
141#380—24no—
142#379—28no—
143C4×C22⋊C4—216no—
144C2×#95—28no—
145C2×#95—24no—
146C2×#95—22no—
147C2×#95—22no—
148#340—28no—
149#340—28no—
150#340—24no—
151#340—24no—
152C25—22no—
153C25—22no—
154C25—24no—
155C25—24no—
156C25—22no—
157C25—22no—
158C25—22no—
159C25—22no—
160C25—42no—
161C25—42no—
162C25C4⋊C414yes—
163C25C2×D412yes—
164C25C2×D411yescharacteristic
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—28no—
172C23×C4—28no—
173C23×C4—28no—
174C23×C4—28no—
175C23×C4—28no—
176C23×C4—28no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—24no—
180C23×C4—24no—
181C23×C4—28no—
182C23×C4—28no—
183C23×C4—28no—
184C23×C4—28no—
185C23×C4—28no—
186C23×C4—28no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—44no—
209C23×C4—44no—
210C23×C4—44no—
211C23×C4—44no—
212C23×C4—44no—
213C23×C4—44no—
214C23×C4—44no—
215C23×C4—44no—
216C23×C4—44no—
217C23×C4—44no—
218C23×C4—44no—
219C23×C4—44no—
220C23×C4—44no—
221C23×C4—44no—
222C23×C4—44no—
223C23×C4—44no—
224C23×C4—44no—
225C23×C4—44no—
226C23×C4—44no—
227C23×C4—44no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4C4⋊C414yes—
233C23×C4C4⋊C418yes—
234C23×C4C22×C414yes—
235C23×C4C22×C412yes—
236C23×C4C2×D412yes—
237C23×C4C2×D412yes—
238C23×C4C2×D412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×Q814yes—
245C23×C4C2×Q812yes—
246C23×C4#4112yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4#4112yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4C2411yescharacteristic
253C2×M16—28no—
254C2×M16—28no—
255C2×M16—28no—
256C2×M16—28no—
257C2×M16—28no—
258C2×M16—28no—
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—44no—
263C2×M16—44no—
264C2×M16—44no—
265C2×M16—44no—
266C2×M16C22⋊C4116yescomplemented
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8C22×C414yes—
278C22×C8C22×C414yes—
279C22×C8C2×D414yes—
280C22×C8C2×D414yes—
281#117—28no—
282#117—28no—
283#117—28no—
284#117—28no—
285#117—44no—
286#117—44no—
287#117—44no—
288#117—44no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4C2×D412yes—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—432no—
341C2×C22⋊C4—48no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—48no—
348C2×C22⋊C4—44no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—42no—
355#107—216no—
356#106—216no—
357C22⋊C8—232no—
358#95—216no—
359#95—28no—
360#95—28no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—28no—
366C24—216no—
367C24—28no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—28no—
381C24—216no—
382C24—28no—
383C24—28no—
384C24—48no—
385C24—48no—
386C24—48no—
387C24—48no—
388C24—48no—
389C24—48no—
390C24—48no—
391C24—48no—
392C24—48no—
393C24—48no—
394C24—44no—
395C24—44no—
396C24—44no—
397C24—44no—
398C24—44no—
399C24—44no—
400C24C2×C4⋊C414yes—
401C24C2×C4⋊C412yes—
402C24#12012yes—
403C24#12012yes—
404C24#12112yes—
405C24#12112yes—
406C24#12312yes—
407C24#12312yes—
408C24AGL(1,ℤ/8)14yes—
409C24#13714yes—
410C24C22×D411yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—216no—
433C22×C4—216no—
434C22×C4—216no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—416no—
461C22×C4—416no—
462C22×C4—416no—
463C22×C4—416no—
464C22×C4—48no—
465C22×C4—416no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—416no—
469C22×C4—416no—
470C22×C4—48no—
471C22×C4—416no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—88no—
501C22×C4—88no—
502C22×C4—88no—
503C22×C4—88no—
504C22×C4C2×C22⋊C414yes—
505C22×C4C2×C4⋊C414yes—
506C22×C4C2×C4⋊C412yes—
507C22×C4#11714yes—
508C22×C4C4×D414yes—
509C22×C4C4×D414yes—
510C22×C4C4×D414yes—
511C22×C4C4×D414yes—
512C22×C4#12014yes—
513C22×C4#12012yes—
514C22×C4#12012yes—
515C22×C4#12114yes—
516C22×C4#12114yes—
517C22×C4#12114yes—
518C22×C4#12114yes—
519C22×C4#12114yes—
520C22×C4#12114yes—
521C22×C4#12112yes—
522C22×C4#12112yes—
523C22×C4C22⋊Q814yes—
524C22×C4C22⋊Q814yes—
525C22×C4C22⋊Q814yes—
526C22×C4C22⋊Q814yes—
527C22×C4C22⋊Q814yes—
528C22×C4C22⋊Q814yes—
529C22×C4#12314yes—
530C22×C4#12314yes—
531C22×C4#12314yes—
532C22×C4#12312yes—
533C22×C4#12312yes—
534C22×C4#12414yes—
535C22×C4#12414yes—
536C22×C4#12414yes—
537C22×C4#12614yes—
538C22×C4#12614yes—
539C22×C4#12714yes—
540C22×C4C23×C411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×Q811yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554M16—232no—
555M16—416no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—42no—
566C2×C8—42no—
567C2×C8—42no—
568C2×C8—42no—
569C2×C8C2×C22⋊C418yescomplemented
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—432no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C42—48no—
598C42—48no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—232no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—416no—
641C23—416no—
642C23—432no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—416no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23#38014yes—
661C23#38514yes—
662C23#38514yes—
663C23#39214yes—
664C23#39414yes—
665C23#39414yes—
666C23#39714yes—
667C23#42818yescomplemented
668C23C22×C4⋊C411yescharacteristic
669C23C2×#12011yescharacteristic
670C23C2×#12011yescharacteristic
671C23C2×#12111yescharacteristic
672C23C2×#12111yescharacteristic
673C23C2×#12311yescharacteristic
674C23C2×#12311yescharacteristic
675C23C2×AGL(1,ℤ/8)12yes—
676C23C2×#13712yes—
677C23#57512yes—
678C23#57512yes—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—432no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—816no—
710C2×C4—816no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—84no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—84no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#38014yes—
726C2×C4#38514yes—
727C2×C4#38514yes—
728C2×C4#38618yes—
729C2×C4#38818yes—
730C2×C4#38818yes—
731C2×C4#39018yes—
732C2×C4#39214yes—
733C2×C4#39318yes—
734C2×C4#39414yes—
735C2×C4#39414yes—
736C2×C4#39618yes—
737C2×C4#39618yes—
738C2×C4#39714yes—
739C2×C4#39918yes—
740C2×C4C22×C22⋊C411yescharacteristic
741C2×C4C2×#11711yescharacteristic
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C2×C4×D411yescharacteristic
746C2×C4C2×#12011yescharacteristic
747C2×C4C2×#12111yescharacteristic
748C2×C4C2×#12111yescharacteristic
749C2×C4C2×#12111yescharacteristic
750C2×C4C2×#12111yescharacteristic
751C2×C4C2×#12111yescharacteristic
752C2×C4C2×#12111yescharacteristic
753C2×C4C2×C22⋊Q811yescharacteristic
754C2×C4C2×C22⋊Q811yescharacteristic
755C2×C4C2×C22⋊Q811yescharacteristic
756C2×C4C2×C22⋊Q811yescharacteristic
757C2×C4C2×C22⋊Q811yescharacteristic
758C2×C4C2×C22⋊Q811yescharacteristic
759C2×C4C2×#12311yescharacteristic
760C2×C4C2×#12311yescharacteristic
761C2×C4C2×#12311yescharacteristic
762C2×C4C2×#12411yescharacteristic
763C2×C4C2×#12411yescharacteristic
764C2×C4C2×#12411yescharacteristic
765C2×C4C2×#12611yescharacteristic
766C2×C4C2×#12611yescharacteristic
767C2×C4C2×#12711yescharacteristic
768C8—28no—
769C8—44no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—28no—
776C22—28no—
777C22—24no—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—28no—
783C22—464no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22#143918yes—
797C22C2×#38011yescharacteristic
798C22C2×#38511yescharacteristic
799C22C2×#38511yescharacteristic
800C22C2×#39211yescharacteristic
801C22C2×#39411yescharacteristic
802C22C2×#39411yescharacteristic
803C22C2×#39711yescharacteristic
804C22C2×#42812yes—
805C22#291112yes—
806C22#300311yescharacteristic
807C22#300411yescharacteristic
808C22#300511yescharacteristic
809C22#300511yescharacteristic
810C22#300612yes—
811C22#300712yes—
812C22#305512yes—
813C22#305512yes—
814C22#305612yes—
815C22#305612yes—
816C22#309212yes—
817C22#309312yes—
818C22#309412yes—
819C22#309512yes—
820C4—44no—
821C4—82no—
822C4—84no—
823C4—82no—
824C4—84no—
825C4—84no—
826C4#143918yes—
827C4C2×#38611yescharacteristic
828C4C2×#38811yescharacteristic
829C4C2×#38811yescharacteristic
830C4C2×#39011yescharacteristic
831C4C2×#39311yescharacteristic
832C4C2×#39611yescharacteristic
833C4C2×#39611yescharacteristic
834C4C2×#39911yescharacteristic
835C2—28no—
836C2—48no—
837C2C2×#143911yescharacteristic
838C2#2066112yes—
839C2#2084411yescharacteristic
840C2#2084511yescharacteristic
841C2#2084612yes—
842C2#2339111yescharacteristic
843C2#2339211yescharacteristic
844C2#2348011yescharacteristic
845C2#2348111yescharacteristic
846C2#2348212yes—
847C2#2364212yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#428C2semidirect
5. C2×#1736C2semidirect
6. C2×#1736C2semidirect
7. C2×#1736C2semidirect
8. #11096C2semidirect
9. #11095C2semidirect
21. C22×#107C22semidirect
22. C22×#106C22semidirect
25. C2×#407C4semidirect
42. C2×#340C22semidirect
43. C2×#340C22semidirect
44. C2×#340C22semidirect
45. C2×#340C22semidirect
133. C2×C22⋊C8C2×C4semidirect
266. C2×M16C22⋊C4semidirect
569. C2×C8C2×C22⋊C4semidirect
667. C23#428semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C22×#4072
C2×#22802
C22×#3802
C2×#17362
#110962
#110952