Finite Group Databasebeta

← #376735

Subgroups — #376735

Order 512.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2361C211yesmaximal, characteristic
2C2×#2034C211yesmaximal, characteristic
3C2×#1944C211yesmaximal, characteristic, complemented
4C2×#1862C211yesmaximal, characteristic, complemented
5C2×#1852C211yesmaximal, characteristic, complemented
6C2×#1762C211yesmaximal, characteristic, complemented
7#13973C211yesmaximal, characteristic, complemented
8#11189C211yesmaximal, characteristic, complemented
9#11123C211yesmaximal, characteristic, complemented
10#10969C211yesmaximal, characteristic
11#10922C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10885C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×#97C2211yescharacteristic
30#2361—24no—
31#2361—24no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#388—21no—
36C2×#386—21no—
37C2×#385—21no—
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#2034C418yescomplemented
44#1944—24no—
45#1862—24no—
46#1852—24no—
47#1762—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1442—21no—
61#1439—21no—
62#1437—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65#1434—21no—
66C23×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121—22no—
80C2×#121C2×C414yes—
81C2×C4×D4—28no—
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×C4×D4D414yes—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—41no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4D411yescharacteristic
114C22×C42—21no—
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×#107—22no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107—22no—
122C2×#107—22no—
123C2×#107—41no—
124C2×#106—22no—
125C2×#106—22no—
126C2×#106C2×C414yescomplemented
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—41no—
136C2×#102—41no—
137C2×#102C2×C414yescomplemented
138C2×#102C2×C414yescomplemented
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—41no—
144C2×C22⋊C8C2×C414yescomplemented
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—41no—
148#390—22no—
149#390—22no—
150#389—22no—
151#389—22no—
152#389—22no—
153#389D414yes—
154#388—28no—
155#386—28no—
156#385—28no—
157#380—22no—
158#380—22no—
159#380—41no—
160#380C2×C414yescomplemented
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—41no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95D411yescharacteristic
178C2×#95D411yescharacteristic
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—41no—
186#340C2×C414yescomplemented
187#340D414yescomplemented
188#336—22no—
189#336—22no—
190#336—22no—
191C25—21no—
192C25C2×D411yescharacteristic
193C22×D4—24no—
194C22×D4—24no—
195C22×D4—24no—
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—21no—
206C22×D4—21no—
207C22×D4—42no—
208C22×D4—42no—
209C22×D4—42no—
210C22×D4—42no—
211C22×D4C22×C412yes—
212C22×D4C2×D412yes—
213C22×D4#4112yes—
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—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4—81no—
246C23×C4—81no—
247C23×C4C22×C412yes—
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4#4112yes—
254C23×C4C2411yescharacteristic
255C22×C8—21no—
256C22×C8—21no—
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×C8C22×C412yes—
279C22×C8C22×C412yes—
280C22×C8C2×D412yes—
281C22×C8#4112yes—
282C22×C8#4112yes—
283#121—28no—
284#121—28no—
285#121—28no—
286#121—28no—
287C4×D4—28no—
288C4×D4—44no—
289C4×D4—44no—
290C4×D4—44no—
291C4×D4—432no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
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—24no—
315C2×C4⋊C4—24no—
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—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4—81no—
337C2×C4⋊C4C22×C412yes—
338C2×C4⋊C4C22×C412yes—
339C2×C4⋊C4C22×C412yes—
340C2×C4⋊C4C2×D412yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4C2×D412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4#4112yes—
346C2×C4⋊C4#4112yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—41no—
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—81no—
367C2×C22⋊C4—81no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—24no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—81no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389#107—44no—
390#107—44no—
391#106—28no—
392#102—28no—
393#102—28no—
394#102—28no—
395#102—44no—
396C22⋊C8—28no—
397C22⋊C8—44no—
398#97—44no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—81no—
409#95—81no—
410#95—81no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24C4×D412yes—
439C24AGL(1,ℤ/8)12yes—
440C24#13712yes—
441C24C22×D411yescharacteristic
442C2×D4—216no—
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—22no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
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×D4—41no—
476C2×D4C4×D414yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
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—21no—
506C22×C4—21no—
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—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
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—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—48no—
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—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C4×D412yes—
600C22×C4#12012yes—
601C22×C4#12012yes—
602C22×C4AGL(1,ℤ/8)12yes—
603C22×C4C23×C411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C2×#4111yescharacteristic
608C22×C4C2×#4111yescharacteristic
609C22×C4C2×#4111yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4H(5,𝔽2)11yescharacteristic
614C22×C4H(5,𝔽2)11yescharacteristic
615C22×C42−1+411yescharacteristic
616C22×C42−1+411yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
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×C8C4×D414yescomplemented
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
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—48no—
660C4⋊C4—48no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—84no—
674C4⋊C4C4×D414yes—
675C4⋊C4#12114yes—
676C22⋊C4—28no—
677C22⋊C4—216no—
678C22⋊C4—48no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—84no—
682C22⋊C4—84no—
683C22⋊C4—84no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—48no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—84no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
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—24no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
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—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23—81no—
762C23—81no—
763C23#44014yes—
764C23C2×C4×D411yescharacteristic
765C23C2×#12011yescharacteristic
766C23#52511yescharacteristic
767C23D4211yescharacteristic
768C23#54611yescharacteristic
769C23#54711yescharacteristic
770C23#54711yescharacteristic
771C23C2×AGL(1,ℤ/8)11yescharacteristic
772C23C2×AGL(1,ℤ/8)11yescharacteristic
773C23C2×#13711yescharacteristic
774C23#57511yescharacteristic
775C23#57611yescharacteristic
776C23#57611yescharacteristic
777C23#57711yescharacteristic
778C23#57811yescharacteristic
779D4—24no—
780D4—24no—
781D4—432no—
782D4—42no—
783D4—42no—
784D4—42no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—816no—
858C2×C4—816no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
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×C4C2×C4×D411yescharacteristic
883C2×C4C2×C4×D411yescharacteristic
884C2×C4C2×C4×D411yescharacteristic
885C2×C4C4×#4111yescharacteristic
886C2×C4#52011yescharacteristic
887C2×C4#52011yescharacteristic
888C2×C4C2×#12111yescharacteristic
889C2×C4#52511yescharacteristic
890C2×C4#52511yescharacteristic
891C2×C4#52511yescharacteristic
892C2×C4#52911yescharacteristic
893C2×C4#53211yescharacteristic
894C2×C4#53411yescharacteristic
895C2×C4#53611yescharacteristic
896C2×C4#53911yescharacteristic
897C2×C4#53911yescharacteristic
898C2×C4D4211yescharacteristic
899C2×C4#54611yescharacteristic
900C2×C4#54711yescharacteristic
901C2×C4#54811yescharacteristic
902C2×C4#54811yescharacteristic
903C2×C4#54811yescharacteristic
904C2×C4#55111yescharacteristic
905C2×C4#55211yescharacteristic
906C2×C4#55311yescharacteristic
907C2×C4#55311yescharacteristic
908C2×C4#55611yescharacteristic
909C2×C4#55911yescharacteristic
910C8—24no—
911C8—42no—
912C8—42no—
913C8—81no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22—82no—
941C22—82no—
942C22—82no—
943C22—82no—
944C22C4×#12011yescharacteristic
945C22#235911yescharacteristic
946C22#236111yescharacteristic
947C22#241011yescharacteristic
948C22#243211yescharacteristic
949C22#245511yescharacteristic
950C22#246611yescharacteristic
951C22C2×#44011yescharacteristic
952C22C4×AGL(1,ℤ/8)11yescharacteristic
953C22#294611yescharacteristic
954C22#295111yescharacteristic
955C22#300311yescharacteristic
956C22#300711yescharacteristic
957C22#300811yescharacteristic
958C22#301311yescharacteristic
959C22#311011yescharacteristic
960C22#311411yescharacteristic
961C22#311911yescharacteristic
962C22#312411yescharacteristic
963C22#326411yescharacteristic
964C22#327011yescharacteristic
965C22#327411yescharacteristic
966C22#327511yescharacteristic
967C22#331611yescharacteristic
968C22#331811yescharacteristic
969C22#332511yescharacteristic
970C22#332711yescharacteristic
971C22#334311yescharacteristic
972C22#334311yescharacteristic
973C22#334511yescharacteristic
974C22#334511yescharacteristic
975C22#334611yescharacteristic
976C22#334611yescharacteristic
977C22#334711yescharacteristic
978C22#334711yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—44no—
983C4—42no—
984C4—44no—
985C4—81no—
986C4—82no—
987C4—82no—
988C4—82no—
989C4—82no—
990C4—161no—
991C4C4×#12111yescharacteristic
992C4#232211yescharacteristic
993C4#236111yescharacteristic
994C4#236711yescharacteristic
995C4#241511yescharacteristic
996C4#246011yescharacteristic
997C4#246311yescharacteristic
998C4#260211yescharacteristic
999C2—44no—
1000C2—84no—
1001C2#1418511yescharacteristic
1002C2#2145311yescharacteristic
1003C2#2146011yescharacteristic
1004C2#2293611yescharacteristic
1005C2#2294611yescharacteristic
1006C2#2303211yescharacteristic
1007C2#2303911yescharacteristic
1008C2#2444011yescharacteristic
1009C2#2444911yescharacteristic
1010C2#2570911yescharacteristic
1011C2#2571311yescharacteristic
1012C2#2656211yescharacteristic
1013C2#2657111yescharacteristic
1014C2#2704611yescharacteristic
1015C2#2704911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1944C2semidirect
4. C2×#1862C2semidirect
5. C2×#1852C2semidirect
6. C2×#1762C2semidirect
7. #13973C2semidirect
8. #11189C2semidirect
9. #11123C2semidirect
11. #10922C2semidirect
12. #10908C2semidirect
13. #10907C2semidirect
14. #10885C2semidirect
15. #10730C2semidirect
43. #2034C4semidirect
126. C2×#106C2×C4semidirect
137. C2×#102C2×C4semidirect
138. C2×#102C2×C4semidirect
144. C2×C22⋊C8C2×C4semidirect
160. #380C2×C4semidirect
186. #340C2×C4semidirect
187. #340D4semidirect
644. C2×C8C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23612
C2×#20342
C2×#19442
C2×#18622
C2×#18522
C2×#17622
#139732
#111892
#111232
#109692
#109222
#109082
#109072
#108852
#107302