Finite Group Databasebeta

← #368187

Subgroups — #368187

Order 512.

2044 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1875C211yesmaximal, characteristic
3C2×#1875C211yesmaximal, characteristic
4C2×#1854C211yesmaximal, characteristic, complemented
5#13756C211yesmaximal, characteristic, complemented
6#11293C211yesmaximal, characteristic, complemented
7#11292C211yesmaximal, characteristic, complemented
8#11123C211yesmaximal, characteristic, complemented
9#11121C211yesmaximal, characteristic, complemented
10#10908C211yesmaximal, characteristic, complemented
11#10907C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C4×#121—24no—
31C4×#121—24no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#386—21no—
36C2×#380C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4—21no—
39#1875—24no—
40#1875C418yescomplemented
41#1854—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C4×#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×#121C2×C414yes—
78C2×#121D414yes—
79C2×#121Q814yes—
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—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—41no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117—41no—
98C2×#117—41no—
99C2×#117—41no—
100C2×#117C2×C414yescomplemented
101C22×C4⋊C4—21no—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C42—22no—
117C22×C42—22no—
118C22×C42—21no—
119C22×C42—21no—
120C22×C42—21no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—41no—
124C22×C42—41no—
125C22×C42D411yescharacteristic
126C22×C42D411yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C2×#107—22no—
130C2×#107—22no—
131C2×#107—41no—
132C2×#106—22no—
133C2×#106—22no—
134C2×#106—41no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—41no—
140C2×#102—41no—
141C2×#102—41no—
142C2×#102—41no—
143C2×#102—41no—
144C2×#102—41no—
145C2×#102C2×C414yescomplemented
146C2×#102C2×C414yescomplemented
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152C2×C22⋊C8C2×C414yescomplemented
153#390—22no—
154#390—22no—
155#389—22no—
156#389—22no—
157#388—28no—
158#386—28no—
159#380—22no—
160#380D414yes—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C22⋊C4—28no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340—41no—
183#340C2×C414yescomplemented
184#340C2×C414yescomplemented
185#336—22no—
186#336—22no—
187#336—41no—
188#336—41no—
189C25—21no—
190C25C2×D411yescharacteristic
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
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—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4—42no—
209C22×D4C22×C412yes—
210C22×D4C2×D412yes—
211C22×D4C2×Q812yes—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—22no—
233C23×C4—22no—
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×C4C22×C412yes—
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D412yes—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×Q812yes—
257C23×C4#4112yes—
258C23×C4#4112yes—
259C23×C4C2411yescharacteristic
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×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288#121—28no—
289#121—28no—
290#121—28no—
291#121C4⋊C4116yes—
292C4×D4—44no—
293C4×D4—44no—
294C4×D4—44no—
295C4×D4—44no—
296C4×D4—432no—
297#117—44no—
298#117—44no—
299#117—44no—
300#117—44no—
301#117—44no—
302#117—44no—
303#117—44no—
304#117—44no—
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—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—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
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—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4C22×C412yes—
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4C2×D412yes—
347C2×C4⋊C4C2×Q812yes—
348C2×C4⋊C4#4112yes—
349C2×C4⋊C4#4112yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
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×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42—44no—
392C2×C42—41no—
393C2×C42—41no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42#4112yes—
401C2×C42#4112yes—
402#107—44no—
403#106—44no—
404#102—44no—
405#102—44no—
406#102—44no—
407#102—44no—
408C22⋊C8—28no—
409C22⋊C8—44no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24—41no—
448C24C4×D412yes—
449C24#12012yes—
450C24C22⋊Q812yes—
451C24C22×D411yescharacteristic
452C2×D4—216no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
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×D4C2×C4⋊C414yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
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—28no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—44no—
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—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4C2×C4⋊C414yes—
608C22×C4C4×D414yes—
609C22×C4C4×D412yes—
610C22×C4#12012yes—
611C22×C4C22⋊Q814yes—
612C22×C4C22⋊Q812yes—
613C22×C4#12312yes—
614C22×C4#12314yes—
615C22×C4#12312yes—
616C22×C4#13512yes—
617C22×C4#13512yes—
618C22×C4AGL(1,ℤ/8)12yes—
619C22×C4AGL(1,ℤ/8)12yes—
620C22×C4C23×C411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×Q811yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4H(5,𝔽2)11yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C4H(5,𝔽2)11yescharacteristic
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
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—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—48no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4C2×C4⋊C414yes—
691C22⋊C4—216no—
692C22⋊C4—48no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—44no—
703C42—44no—
704C42—48no—
705C42—48no—
706C42—48no—
707C42—41no—
708C42—41no—
709C42—41no—
710C42—41no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23#38514yes—
781C23C2×C4×D411yescharacteristic
782C23C2×#12011yescharacteristic
783C23C2×C22⋊Q811yescharacteristic
784C23C2×#12311yescharacteristic
785C23#52511yescharacteristic
786C23#53411yescharacteristic
787C23#53511yescharacteristic
788C23C2×#13511yescharacteristic
789C23C2×#13511yescharacteristic
790C23C2×AGL(1,ℤ/8)11yescharacteristic
791C23C2×AGL(1,ℤ/8)11yescharacteristic
792C23#57511yescharacteristic
793C23#57511yescharacteristic
794C23#57511yescharacteristic
795C23#57511yescharacteristic
796D4—24no—
797D4—24no—
798D4—432no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—42no—
804D4—42no—
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—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—416no—
836C2×C4—416no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
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—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—816no—
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—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4#38514yes—
899C2×C4#48214yes—
900C2×C4C22×C4⋊C411yescharacteristic
901C2×C4C2×C4×D411yescharacteristic
902C2×C4C4×#4111yescharacteristic
903C2×C4C4×#4111yescharacteristic
904C2×C4#51811yescharacteristic
905C2×C4#51811yescharacteristic
906C2×C4C2×C22⋊Q811yescharacteristic
907C2×C4C2×#12311yescharacteristic
908C2×C4#52911yescharacteristic
909C2×C4#52911yescharacteristic
910C2×C4#53811yescharacteristic
911C2×C4#53811yescharacteristic
912C2×C4#54611yescharacteristic
913C2×C4#54611yescharacteristic
914C2×C4#54611yescharacteristic
915C2×C4#54611yescharacteristic
916C2×C4#54611yescharacteristic
917C2×C4#54611yescharacteristic
918C2×C4#54611yescharacteristic
919C2×C4#54611yescharacteristic
920C2×C4#55311yescharacteristic
921C2×C4#55311yescharacteristic
922C2×C4#55311yescharacteristic
923C2×C4#55311yescharacteristic
924C2×C4#55411yescharacteristic
925C2×C4#55411yescharacteristic
926C2×C4#55411yescharacteristic
927C2×C4#55411yescharacteristic
928C8—42no—
929C8—42no—
930C8—81no—
931C8—81no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—82no—
951C22—82no—
952C22—82no—
953C22—82no—
954C22—82no—
955C22—82no—
956C22—82no—
957C22—82no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22C2×#38511yescharacteristic
963C22C4×#12311yescharacteristic
964C22#232111yescharacteristic
965C22#240411yescharacteristic
966C22#240511yescharacteristic
967C22#248711yescharacteristic
968C22#257911yescharacteristic
969C22C4×#13511yescharacteristic
970C22#294311yescharacteristic
971C22C4×AGL(1,ℤ/8)11yescharacteristic
972C22C4×AGL(1,ℤ/8)11yescharacteristic
973C22#300211yescharacteristic
974C22#300211yescharacteristic
975C22#300311yescharacteristic
976C22#300511yescharacteristic
977C22#307611yescharacteristic
978C22#307611yescharacteristic
979C22#307711yescharacteristic
980C22#307711yescharacteristic
981C22C2×#48211yescharacteristic
982C22#309111yescharacteristic
983C22#309311yescharacteristic
984C22#309411yescharacteristic
985C22#310211yescharacteristic
986C22#310611yescharacteristic
987C22#311111yescharacteristic
988C22#311511yescharacteristic
989C22#318811yescharacteristic
990C22#319111yescharacteristic
991C22#319411yescharacteristic
992C22#319711yescharacteristic
993C22#320711yescharacteristic
994C22#321211yescharacteristic
995C22#321411yescharacteristic
996C22#321911yescharacteristic
997C4—24no—
998C4—24no—
999C4—44no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—82no—
1004C4—82no—
1005C4—82no—
1006C4—82no—
1007C4—82no—
1008C4—82no—
1009C4#234911yescharacteristic
1010C4#234911yescharacteristic
1011C4#236411yescharacteristic
1012C4#236411yescharacteristic
1013C4#244411yescharacteristic
1014C4#244411yescharacteristic
1015C4#245011yescharacteristic
1016C4#245011yescharacteristic
1017C2—44no—
1018C2—84no—
1019C2#1401611yescharacteristic
1020C2#2087211yescharacteristic
1021C2#2087311yescharacteristic
1022C2C4×#48211yescharacteristic
1023C2#2158211yescharacteristic
1024C2#2204511yescharacteristic
1025C2#2205111yescharacteristic
1026C2#2393211yescharacteristic
1027C2#2393811yescharacteristic
1028C2#2400811yescharacteristic
1029C2#2400911yescharacteristic
1030C2#2767911yescharacteristic
1031C2#2768311yescharacteristic
1032C2#2923611yescharacteristic
1033C2#2923911yescharacteristic
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
4. C2×#1854C2semidirect
5. #13756C2semidirect
6. #11293C2semidirect
7. #11292C2semidirect
8. #11123C2semidirect
9. #11121C2semidirect
10. #10908C2semidirect
11. #10907C2semidirect
12. #10788C2semidirect
13. #10788C2semidirect
14. #10731C2semidirect
15. #10712C2semidirect
40. #1875C4semidirect
100. C2×#117C2×C4semidirect
145. C2×#102C2×C4semidirect
146. C2×#102C2×C4semidirect
152. C2×C22⋊C8C2×C4semidirect
183. #340C2×C4semidirect
184. #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×#18752
C2×#18542
#137562
#112932
#112922
#111232
#111212
#109082
#109072
#107882
#107312
#107122