Finite Group Databasebeta

← #375983

Subgroups — #375983

Order 512.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#2033C211yesmaximal, characteristic
3C2×#1925C211yesmaximal, characteristic, complemented
4C2×#1918C211yesmaximal, characteristic, complemented
5C4×#380C211yesmaximal, characteristic, complemented
6#11199C211yesmaximal, characteristic, complemented
7#11096C211yesmaximal, characteristic, complemented
8#10969C211yesmaximal, characteristic
9#10931C211yesmaximal, characteristic, complemented
10#10907C211yesmaximal, characteristic, complemented
11#10907C211yesmaximal, characteristic, complemented
12#10884C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C4×#121—24no—
29C4×#121—24no—
30C2×#390C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#388—21no—
33C2×#386—21no—
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4—21no—
41C2×C4×C22⋊C4—21no—
42#2033C418yescomplemented
43#1925—24no—
44#1918—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62C22⋊#95—21no—
63C4×#95—21no—
64C23×D4—21no—
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4D411yescharacteristic
68C24×C4D411yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#121—22no—
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121C2×C414yes—
80C2×C4×D4—28no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—44no—
88C2×C4×D4—44no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C42—21no—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42—41no—
112C22×C42—41no—
113C22×C42D411yescharacteristic
114C22×C42D411yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107—41no—
122C2×#107C2×C414yescomplemented
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—41no—
130C2×#102—41no—
131C2×#102—41no—
132C2×#102—41no—
133C2×#102C2×C414yescomplemented
134C2×#102C2×C414yescomplemented
135C2×C22⋊C8—22no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8—41no—
138C2×C22⋊C8—41no—
139C2×C22⋊C8—41no—
140C2×C22⋊C8C2×C414yescomplemented
141#390—22no—
142#390D414yes—
143#389—22no—
144#389D414yes—
145#388—28no—
146#386—28no—
147#380—22no—
148#380—22no—
149#380—22no—
150#380—22no—
151#380—22no—
152#380C2×C414yescomplemented
153C4×C4⋊C4—22no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—22no—
157C4×C4⋊C4—41no—
158C4×C4⋊C4—41no—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—44no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—41no—
179#340—41no—
180#340—41no—
181#340C2×C414yescomplemented
182#336—22no—
183#336—22no—
184#336—22no—
185#336—22no—
186C25—21no—
187C25C2×D411yescharacteristic
188C22×D4—24no—
189C22×D4—24no—
190C22×D4—24no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—42no—
203C22×D4—42no—
204C22×D4—42no—
205C22×D4—42no—
206C22×D4C22×C412yes—
207C22×D4C2×D412yes—
208C22×D4#4112yes—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—41no—
237C23×C4—41no—
238C23×C4—41no—
239C23×C4—41no—
240C23×C4—41no—
241C23×C4—41no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4D814yes—
249C23×C4C22×C412yes—
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8C22×C412yes—
284C22×C8C22×C412yes—
285#121—28no—
286#121—28no—
287#121—28no—
288#121—28no—
289C4×D4—44no—
290C4×D4—44no—
291C4×D4—44no—
292C4×D4—44no—
293C4×D4—432no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
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—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
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—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C22×C412yes—
333C2×C4⋊C4C2×D412yes—
334C2×C4⋊C4C2×D412yes—
335C2×C4⋊C4C2×D412yes—
336C2×C4⋊C4#4112yes—
337C2×C4⋊C4#4112yes—
338C2×C4⋊C4#4112yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—44no—
374C2×C42—44no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—41no—
378C2×C42—41no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42#4112yes—
390C2×C42#4112yes—
391#107—28no—
392#107—44no—
393#102—28no—
394#102—44no—
395#102—44no—
396#102—44no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24C4×D412yes—
438C24C2×D812yes—
439C24#13512yes—
440C24C22×D411yescharacteristic
441C2×D4—216no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C4×D414yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
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—28no—
518C22×C4—28no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—44no—
539C22×C4—44no—
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—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
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—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4C4×D412yes—
601C22×C4#12012yes—
602C22×C4#12012yes—
603C22×C4#12312yes—
604C22×C4#12312yes—
605C22×C4C2×D812yes—
606C22×C4C2×D812yes—
607C22×C4AGL(1,ℤ/8)12yes—
608C22×C4#13712yes—
609C22×C4C23×C411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4C2×#4111yescharacteristic
619C22×C4H(5,𝔽2)11yescharacteristic
620C22×C4H(5,𝔽2)11yescharacteristic
621C22×C4H(5,𝔽2)11yescharacteristic
622C22×C42−1+411yescharacteristic
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—48no—
679C4⋊C4C4×D414yes—
680C22⋊C4—216no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—44no—
696C42—44no—
697C42—48no—
698C42—84no—
699C42—84no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23—81no—
762C23—81no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23C4×D814yes—
770C23C2×C4×D411yescharacteristic
771C23C2×#12011yescharacteristic
772C23C2×#12311yescharacteristic
773C23#52511yescharacteristic
774C23#52511yescharacteristic
775C23#53411yescharacteristic
776C23#53711yescharacteristic
777C23C22×D811yescharacteristic
778C23C2×#13511yescharacteristic
779C23C2×AGL(1,ℤ/8)11yescharacteristic
780C23C2×#13711yescharacteristic
781C23#57511yescharacteristic
782C23#57511yescharacteristic
783C23#57511yescharacteristic
784C23#57511yescharacteristic
785D4—24no—
786D4—24no—
787D4—432no—
788D4—42no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—42no—
793D4—42no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—416no—
817C2×C4—416no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—816no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4#44714yes—
888C2×C4#48014yes—
889C2×C4C2×C4×D411yescharacteristic
890C2×C4C2×C4×D411yescharacteristic
891C2×C4C4×#4111yescharacteristic
892C2×C4C4×#4111yescharacteristic
893C2×C4#51811yescharacteristic
894C2×C4#52011yescharacteristic
895C2×C4#52511yescharacteristic
896C2×C4#52511yescharacteristic
897C2×C4#52911yescharacteristic
898C2×C4#52911yescharacteristic
899C2×C4#53811yescharacteristic
900C2×C4#53911yescharacteristic
901C2×C4#54611yescharacteristic
902C2×C4#54611yescharacteristic
903C2×C4#54611yescharacteristic
904C2×C4#54611yescharacteristic
905C2×C4#54611yescharacteristic
906C2×C4#54711yescharacteristic
907C2×C4#54811yescharacteristic
908C2×C4#55011yescharacteristic
909C2×C4#55111yescharacteristic
910C2×C4#55211yescharacteristic
911C2×C4#55311yescharacteristic
912C2×C4#55311yescharacteristic
913C2×C4#55311yescharacteristic
914C2×C4#55511yescharacteristic
915C2×C4#55611yescharacteristic
916C2×C4#55911yescharacteristic
917C8—42no—
918C8—42no—
919C8—81no—
920C8—81no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—82no—
940C22—82no—
941C22—82no—
942C22—82no—
943C22—82no—
944C22—82no—
945C22—82no—
946C22—82no—
947C22—82no—
948C22—82no—
949C22—82no—
950C22—82no—
951C22C4×#12011yescharacteristic
952C22C4×#12311yescharacteristic
953C22#232511yescharacteristic
954C22#240511yescharacteristic
955C22#240711yescharacteristic
956C22#248511yescharacteristic
957C22#260011yescharacteristic
958C22C2×C4×D811yescharacteristic
959C22#294311yescharacteristic
960C22C4×AGL(1,ℤ/8)11yescharacteristic
961C22C4×#13711yescharacteristic
962C22C2×#44711yescharacteristic
963C22#300211yescharacteristic
964C22#300511yescharacteristic
965C22#300711yescharacteristic
966C22C2×#48011yescharacteristic
967C22#309111yescharacteristic
968C22#309311yescharacteristic
969C22#309411yescharacteristic
970C22#310011yescharacteristic
971C22#310011yescharacteristic
972C22#310511yescharacteristic
973C22#310811yescharacteristic
974C22#311111yescharacteristic
975C22#311111yescharacteristic
976C22#311511yescharacteristic
977C22#311611yescharacteristic
978C22#318611yescharacteristic
979C22#319111yescharacteristic
980C22#319311yescharacteristic
981C22#319711yescharacteristic
982C22#324511yescharacteristic
983C22#325011yescharacteristic
984C22#325111yescharacteristic
985C22#325211yescharacteristic
986C4—24no—
987C4—24no—
988C4—42no—
989C4—44no—
990C4—42no—
991C4—42no—
992C4—82no—
993C4—82no—
994C4—82no—
995C4—82no—
996C4—82no—
997C4—82no—
998C4#235911yescharacteristic
999C4#236311yescharacteristic
1000C4#236411yescharacteristic
1001C4#236711yescharacteristic
1002C4#245911yescharacteristic
1003C4#246011yescharacteristic
1004C4#246611yescharacteristic
1005C4#246711yescharacteristic
1006C2—44no—
1007C2—84no—
1008C2#1417311yescharacteristic
1009C2C4×#44711yescharacteristic
1010C2#2145711yescharacteristic
1011C2C4×#48011yescharacteristic
1012C2#2158211yescharacteristic
1013C2#2218111yescharacteristic
1014C2#2218611yescharacteristic
1015C2#2400211yescharacteristic
1016C2#2400811yescharacteristic
1017C2#2415011yescharacteristic
1018C2#2416011yescharacteristic
1019C2#2762411yescharacteristic
1020C2#2763211yescharacteristic
1021C2#2940811yescharacteristic
1022C2#2941111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×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
3. C2×#1925C2semidirect
4. C2×#1918C2semidirect
5. C4×#380C2semidirect
6. #11199C2semidirect
7. #11096C2semidirect
9. #10931C2semidirect
10. #10907C2semidirect
11. #10907C2semidirect
12. #10884C2semidirect
13. #10788C2semidirect
14. #10788C2semidirect
15. #10712C2semidirect
42. #2033C4semidirect
122. C2×#107C2×C4semidirect
133. C2×#102C2×C4semidirect
134. C2×#102C2×C4semidirect
140. C2×C22⋊C8C2×C4semidirect
152. #380C2×C4semidirect
181. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#20332
C2×#19252
C2×#19182
C4×#3802
#111992
#110962
#109692
#109312
#109072
#108842
#107882
#107122