Finite Group Databasebeta

← #393000

Subgroups — #393000

Order 512.

2096 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C22×#405C211yesmaximal, characteristic, complemented
3C2×#1973C211yesmaximal, characteristic, complemented
4C2×#1968C211yesmaximal, characteristic, complemented
5C2×#1893C211yesmaximal, characteristic
6C2×#1892C211yesmaximal, characteristic, complemented
7C2×#1809C211yesmaximal, characteristic, complemented
8#14258C211yesmaximal, characteristic, complemented
9#14257C211yesmaximal, characteristic
10#10928C211yesmaximal, characteristic, complemented
11#10927C211yesmaximal, characteristic, complemented
12#10926C211yesmaximal, characteristic, complemented
13#10925C211yesmaximal, characteristic, complemented
14#10863C211yesmaximal, characteristic, complemented
15#10862C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C2×#468—24no—
23C2×#468—24no—
24C2×#468C418yescomplemented
25C22×#107C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C2×#405—24no—
35C2×#405—24no—
36C2×#405—24no—
37C22×#97C2211yescharacteristic
38C22×#97C2211yescharacteristic
39C22×C4×C8C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47#1973—24no—
48#1968—24no—
49#1893—24no—
50#1892—24no—
51#1809—24no—
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58#1441—22no—
59#1440—22no—
60#1439—22no—
61#1438—22no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C22×SD16—22no—
71C22×SD16—22no—
72C22×SD16—22no—
73C22×SD16—22no—
74C22×SD16—22no—
75C22×SD16—22no—
76C22×SD16C2×C414yes—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16C2×C414yes—
82C22×M16D414yes—
83C22×M16D414yes—
84C23×C8—22no—
85C23×C8—22no—
86C23×C8—22no—
87C23×C8—22no—
88C23×C8—22no—
89C23×C8—22no—
90C23×C8D414yes—
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×C22⋊Q8—22no—
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8C2×C414yes—
101C2×#121—22no—
102C2×#121—22no—
103C2×#121—22no—
104C2×#121—22no—
105C2×#121—22no—
106C2×#121C2×C414yes—
107C2×#117—22no—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—22no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4D412yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—22no—
127C22×C22⋊C4D412yes—
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130#468—232no—
131C2×#107—22no—
132C2×#107—22no—
133C2×#107—22no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107C2×C414yes—
137C2×#106—22no—
138C2×#106—22no—
139C2×#106—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—22no—
148C2×#103C2×C414yes—
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—22no—
153C2×#102—22no—
154C2×#102—22no—
155C2×#102—22no—
156C2×#102—22no—
157C2×#102C2×C414yes—
158#405—232no—
159C2×#97—22no—
160C2×#97—22no—
161C2×#97—22no—
162C2×#97—22no—
163C2×#97—22no—
164C2×#97D414yescomplemented
165C2×C4×C8—22no—
166C2×C4×C8—22no—
167C2×C4×C8—22no—
168C2×C4×C8—22no—
169C2×C4×C8—22no—
170C2×C4×C8D414yescomplemented
171#391—22no—
172#391—22no—
173#391—22no—
174#391—22no—
175#390—22no—
176#390—22no—
177#390—22no—
178#390—22no—
179#380—22no—
180#380—22no—
181#380—22no—
182#380—22no—
183C2×#95—21no—
184C2×#95—22no—
185C2×#95—22no—
186C2×#95—21no—
187C2×#95—22no—
188C2×#95—22no—
189C2×#95—22no—
190C2×#95—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—22no—
197C25—21no—
198C25C2×D411yescharacteristic
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8C22×C412yes—
213C22×D4—24no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—82no—
230C22×D4—82no—
231C22×D4C22×C412yes—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4C22×C412yes—
248C23×C4C2×D412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D412yes—
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D412yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C2×SD16—28no—
258C2×SD16—28no—
259C2×SD16—28no—
260C2×SD16—44no—
261C2×SD16—44no—
262C2×SD16—44no—
263C2×SD16—44no—
264C2×M16—28no—
265C2×M16—28no—
266C2×M16—28no—
267C2×M16—28no—
268C2×M16—28no—
269C2×M16—28no—
270C2×M16C22⋊C4116yescomplemented
271C22×C8—28no—
272C22×C8—28no—
273C22×C8—28no—
274C22×C8—28no—
275C22×C8—28no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—28no—
289C22×C8—28no—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299C22×C8C2×D412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C22×C8#4112yes—
303C22×C8#4112yes—
304C22×C8#4112yes—
305C22×C8#4112yes—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308C22⋊Q8—44no—
309C22⋊Q8—44no—
310#121—28no—
311#121—28no—
312#121—44no—
313#121—44no—
314#117—28no—
315#117—28no—
316#117—28no—
317#117—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4C22×C412yes—
359C2×C4⋊C4C22×C412yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C22⋊C4—82no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42#4112yes—
390C2×C42#4112yes—
391#107—28no—
392#107—44no—
393#106—44no—
394#103—28no—
395#103—44no—
396#103—44no—
397#102—28no—
398#102—44no—
399#102—44no—
400#97—28no—
401#97—28no—
402C4×C8—28no—
403C4×C8—28no—
404#95—44no—
405#95—44no—
406#95—42no—
407#95—42no—
408#95—82no—
409#95—82no—
410#95—82no—
411#95—82no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24C4×D412yes—
432C24#12112yes—
433C24#12712yes—
434C24C22×D411yescharacteristic
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—48no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—88no—
493C2×D4—84no—
494C2×D4—84no—
495C2×D4—88no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4C2×C22⋊C414yes—
574C22×C4C4×D414yes—
575C22×C4C4×D412yes—
576C22×C4#12114yes—
577C22×C4#12114yes—
578C22×C4#12114yes—
579C22×C4#12112yes—
580C22×C4#12414yes—
581C22×C4#12712yes—
582C22×C4C23×C411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596SD16—416no—
597M16—232no—
598C2×C8—232no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8C2×C22⋊C414yes—
618C2×C8C2×C22⋊C414yes—
619C2×C8C4×D414yes—
620C2×C8C4×D414yes—
621C2×C8#12014yes—
622C2×C8#12114yes—
623C2×C8#12114yes—
624C2×C8#12114yes—
625C2×C8#12114yes—
626C2×C8#12314yes—
627C4⋊C4—216no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—48no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C22⋊C4—216no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—88no—
657C22⋊C4—88no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23—82no—
704C23—82no—
705C23—82no—
706C23—82no—
707C23—82no—
708C23—82no—
709C23—82no—
710C23—82no—
711C23—82no—
712C23—82no—
713C23#39014yes—
714C23C2×C4×D411yescharacteristic
715C23C2×#12111yescharacteristic
716C23C2×#12111yescharacteristic
717C23C2×#12111yescharacteristic
718C23C2×#12711yescharacteristic
719C23#53211yescharacteristic
720C23#53211yescharacteristic
721C23#57612yes—
722C23#57712yes—
723C23#57712yes—
724C23#57812yes—
725Q8—42no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—81no—
730Q8—81no—
731Q8—81no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—816no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—82no—
802C2×C4—82no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4#39014yes—
808C2×C4C22×C22⋊C411yescharacteristic
809C2×C4C2×C4×D411yescharacteristic
810C2×C4C2×C4×D411yescharacteristic
811C2×C4C2×C4×D411yescharacteristic
812C2×C4C4×#4111yescharacteristic
813C2×C4C4×#4111yescharacteristic
814C2×C4C2×#12011yescharacteristic
815C2×C4C2×#12111yescharacteristic
816C2×C4C2×#12111yescharacteristic
817C2×C4C2×#12111yescharacteristic
818C2×C4C2×#12111yescharacteristic
819C2×C4C2×#12111yescharacteristic
820C2×C4C2×#12311yescharacteristic
821C2×C4#52511yescharacteristic
822C2×C4#52511yescharacteristic
823C2×C4#52511yescharacteristic
824C2×C4#52511yescharacteristic
825C2×C4#52511yescharacteristic
826C2×C4#52511yescharacteristic
827C2×C4C2×#12411yescharacteristic
828C2×C4#52911yescharacteristic
829C2×C4#52911yescharacteristic
830C2×C4#52911yescharacteristic
831C2×C4#52911yescharacteristic
832C2×C4#53211yescharacteristic
833C2×C4#53211yescharacteristic
834C2×C4#53211yescharacteristic
835C2×C4#53211yescharacteristic
836C8—24no—
837C8—24no—
838C8—24no—
839C8#38618yes—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—84no—
852C22—84no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—162no—
857C22—161no—
858C22—161no—
859C22—161no—
860C22—161no—
861C22—162no—
862C22C2×#39011yescharacteristic
863C22C4×#12111yescharacteristic
864C22C4×#12111yescharacteristic
865C22#284711yescharacteristic
866C22#285411yescharacteristic
867C22#285611yescharacteristic
868C22#285611yescharacteristic
869C22#294612yes—
870C22#294712yes—
871C22#305712yes—
872C22#306112yes—
873C22#306212yes—
874C22#306212yes—
875C22#306312yes—
876C22#306312yes—
877C22#315411yescharacteristic
878C22#315411yescharacteristic
879C22#315511yescharacteristic
880C22#315611yescharacteristic
881C22#317412yes—
882C22#317512yes—
883C22#317812yes—
884C22#317912yes—
885C4—24no—
886C4—44no—
887C4—44no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—161no—
892C4—161no—
893C4—161no—
894C4—161no—
895C4C2×#38611yescharacteristic
896C4#229711yescharacteristic
897C4C4×#12111yescharacteristic
898C4C4×#12111yescharacteristic
899C4#284711yescharacteristic
900C4#285011yescharacteristic
901C4#285011yescharacteristic
902C4#285411yescharacteristic
903C2—44no—
904C2—162no—
905C2#1469811yescharacteristic
906C2#2123411yescharacteristic
907C2#2123511yescharacteristic
908C2#2153512yes—
909C2#2154312yes—
910C2#3293812yes—
911C2#3314212yes—
912C2#3317811yescharacteristic
913C2#3318211yescharacteristic
914C2#3318711yescharacteristic
915C2#3318811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#405C2semidirect
3. C2×#1973C2semidirect
4. C2×#1968C2semidirect
6. C2×#1892C2semidirect
7. C2×#1809C2semidirect
8. #14258C2semidirect
10. #10928C2semidirect
11. #10927C2semidirect
12. #10926C2semidirect
13. #10925C2semidirect
14. #10863C2semidirect
15. #10862C2semidirect
24. C2×#468C4semidirect
164. C2×#97D4semidirect
170. C2×C4×C8D4semidirect
270. C2×M16C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4052
C2×#19732
C2×#19682
C2×#18932
C2×#18922
C2×#18092
#142582
#142572
#109282
#109272
#109262
#109252
#108632
#108622