Finite Group Databasebeta

← #376278

Subgroups — #376278

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2363C211yesmaximal, characteristic
2C2×#2034C211yesmaximal, characteristic
3C2×#1925C211yesmaximal, characteristic, complemented
4C2×#1864C211yesmaximal, characteristic, complemented
5C2×#1854C211yesmaximal, characteristic, complemented
6C2×C4×#106C211yesmaximal, characteristic, complemented
7#13994C211yesmaximal, characteristic, complemented
8#11328C211yesmaximal, characteristic, complemented
9#11220C211yesmaximal, characteristic, complemented
10#10969C211yesmaximal, characteristic
11#10925C211yesmaximal, characteristic, complemented
12#10921C211yesmaximal, characteristic, complemented
13#10807C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2363—24no—
30#2363—24no—
31C2×#390—21no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#388—21no—
36C2×#388—21no—
37C2×#386—21no—
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4—21no—
43C2×C4×C22⋊C4C2211yescharacteristic
44#2034C418yescomplemented
45#1925—24no—
46#1864—24no—
47#1854—24no—
48C4×#106—24no—
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1442—21no—
62#1440—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65#1434—21no—
66C23×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
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—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—41no—
91C2×#117—41no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4D411yescharacteristic
109C22×C22⋊C4D411yescharacteristic
110C22×C42—21no—
111C22×C42—21no—
112C22×C42—21no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—41no—
118C2×#106—22no—
119C2×#106—22no—
120C2×#106—22no—
121C2×#106—22no—
122C2×#106C2×C414yescomplemented
123C2×#106D414yescomplemented
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102C2×C414yes—
135C2×#102C2×C414yes—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8C2×C414yescomplemented
142C2×C4×C8—22no—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145#390—28no—
146#390—22no—
147#390D414yes—
148#389—22no—
149#389—22no—
150#389—22no—
151#389—41no—
152#388—28no—
153#388—44no—
154#386—28no—
155#380—22no—
156#380—22no—
157#380—41no—
158#380C2×C414yescomplemented
159C4×C4⋊C4—22no—
160C4×C4⋊C4—22no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4D414yes—
163C4×C22⋊C4—28no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
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—
175C2×#95—21no—
176C2×#95D411yescharacteristic
177C2×#95D411yescharacteristic
178#340—22no—
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#336—22no—
188#336—22no—
189#336—41no—
190C25—21no—
191C25C2×D411yescharacteristic
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—24no—
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—21no—
206C22×D4—81no—
207C22×D4—81no—
208C22×D4—81no—
209C22×D4—81no—
210C22×D4C22×C412yes—
211C22×D4C2×D412yes—
212C22×D4#4112yes—
213C23×C4—21no—
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—24no—
232C23×C4—21no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4C22×C412yes—
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4#4112yes—
246C23×C4C2411yescharacteristic
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
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×C8C22×C412yes—
271C22×C8C22×C412yes—
272C22×C8C2×D412yes—
273C22×C8#4112yes—
274C22×C8#4112yes—
275#121—28no—
276#121—28no—
277#121—28no—
278#121—28no—
279C4×D4—44no—
280C4×D4—44no—
281C4×D4—44no—
282C4×D4—44no—
283#117—44no—
284#117—44no—
285#117—44no—
286#117—44no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
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—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4C22×C412yes—
326C2×C4⋊C4C22×C412yes—
327C2×C4⋊C4C22×C412yes—
328C2×C4⋊C4C2×D412yes—
329C2×C4⋊C4C2×D412yes—
330C2×C4⋊C4C2×D412yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4C2×D412yes—
333C2×C4⋊C4#4112yes—
334C2×C4⋊C4#4112yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—41no—
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—81no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—24no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—24no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—81no—
380C2×C42—81no—
381C2×C42C2×D412yes—
382C2×C42C2×D412yes—
383#107—44no—
384#106—28no—
385#106—28no—
386#102—28no—
387#102—28no—
388#102—44no—
389#102—44no—
390C22⋊C8—28no—
391C22⋊C8—44no—
392C4×C8—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—22no—
397#95—22no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—81no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—21no—
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—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C4×D412yes—
435C24C22×D411yescharacteristic
436C2×D4—216no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
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—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4—84no—
467C2×D4—84no—
468C2×D4—84no—
469C2×D4—84no—
470C2×D4C4×D414yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
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—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
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—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
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—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—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4C4×D412yes—
585C22×C4#12012yes—
586C22×C4#12012yes—
587C22×C4#13512yes—
588C22×C4#13512yes—
589C22×C4AGL(1,ℤ/8)12yes—
590C22×C4C23×C411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4H(5,𝔽2)11yescharacteristic
601C22×C4H(5,𝔽2)11yescharacteristic
602C22×C42−1+411yescharacteristic
603C22×C42−1+411yescharacteristic
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—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8C4×D414yes—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C4⋊C4C4×D414yes—
661C4⋊C4#12114yes—
662C22⋊C4—216no—
663C22⋊C4—44no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—44no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—48no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—84no—
681C42—84no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23C2×C4×D411yescharacteristic
753C23C2×#12011yescharacteristic
754C23#52511yescharacteristic
755C23D4211yescharacteristic
756C23#54611yescharacteristic
757C23#54711yescharacteristic
758C23#54711yescharacteristic
759C23C2×#13511yescharacteristic
760C23C2×#13511yescharacteristic
761C23C2×AGL(1,ℤ/8)11yescharacteristic
762C23#57511yescharacteristic
763C23#57611yescharacteristic
764C23#57711yescharacteristic
765C23#57711yescharacteristic
766C23#57711yescharacteristic
767D4—24no—
768D4—24no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—816no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—816no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
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#44914yes—
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C2×C4×D411yescharacteristic
872C2×C4C4×#4111yescharacteristic
873C2×C4#52011yescharacteristic
874C2×C4#52011yescharacteristic
875C2×C4C2×#12111yescharacteristic
876C2×C4#52511yescharacteristic
877C2×C4#52511yescharacteristic
878C2×C4#52511yescharacteristic
879C2×C4#52911yescharacteristic
880C2×C4#53211yescharacteristic
881C2×C4#53511yescharacteristic
882C2×C4#53611yescharacteristic
883C2×C4#54211yescharacteristic
884C2×C4#54211yescharacteristic
885C2×C4D4211yescharacteristic
886C2×C4#54611yescharacteristic
887C2×C4#54711yescharacteristic
888C2×C4#54711yescharacteristic
889C2×C4#54811yescharacteristic
890C2×C4#54811yescharacteristic
891C2×C4#55111yescharacteristic
892C2×C4#55111yescharacteristic
893C2×C4#55211yescharacteristic
894C2×C4#55211yescharacteristic
895C2×C4#55311yescharacteristic
896C2×C4#55311yescharacteristic
897C8—24no—
898C8—42no—
899C8—42no—
900C8—81no—
901C22—42no—
902C22—44no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—42no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—82no—
913C22—81no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—81no—
918C22—82no—
919C22—81no—
920C22—82no—
921C22—81no—
922C22—82no—
923C22—82no—
924C22—81no—
925C22—81no—
926C22—82no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22C4×#12011yescharacteristic
932C22#235911yescharacteristic
933C22#236111yescharacteristic
934C22#240611yescharacteristic
935C22#240811yescharacteristic
936C22#246111yescharacteristic
937C22#246811yescharacteristic
938C22C4×#13511yescharacteristic
939C22C4×AGL(1,ℤ/8)11yescharacteristic
940C22#294611yescharacteristic
941C22#294911yescharacteristic
942C22C2×#44911yescharacteristic
943C22#300211yescharacteristic
944C22#300911yescharacteristic
945C22#301211yescharacteristic
946C22#310211yescharacteristic
947C22#310611yescharacteristic
948C22#311811yescharacteristic
949C22#312311yescharacteristic
950C22#327411yescharacteristic
951C22#327511yescharacteristic
952C22#328211yescharacteristic
953C22#328411yescharacteristic
954C22#329611yescharacteristic
955C22#330511yescharacteristic
956C22#332311yescharacteristic
957C22#333211yescharacteristic
958C22#333711yescharacteristic
959C22#333711yescharacteristic
960C22#334011yescharacteristic
961C22#334111yescharacteristic
962C22#334511yescharacteristic
963C22#334511yescharacteristic
964C22#334711yescharacteristic
965C22#334811yescharacteristic
966C4—24no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—44no—
971C4—44no—
972C4—81no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4—161no—
978C4C4×#12111yescharacteristic
979C4#232611yescharacteristic
980C4#235911yescharacteristic
981C4#236111yescharacteristic
982C4#246111yescharacteristic
983C4#246811yescharacteristic
984C4#253611yescharacteristic
985C4#259811yescharacteristic
986C2—82no—
987C2—84no—
988C2#1417611yescharacteristic
989C2C4×#44911yescharacteristic
990C2#2145911yescharacteristic
991C2#2292111yescharacteristic
992C2#2294311yescharacteristic
993C2#2302311yescharacteristic
994C2#2303911yescharacteristic
995C2#2409111yescharacteristic
996C2#2409311yescharacteristic
997C2#2423811yescharacteristic
998C2#2424711yescharacteristic
999C2#2679611yescharacteristic
1000C2#2679711yescharacteristic
1001C2#2710611yescharacteristic
1002C2#2710711yescharacteristic
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×#1925C2semidirect
4. C2×#1864C2semidirect
5. C2×#1854C2semidirect
6. C2×C4×#106C2semidirect
7. #13994C2semidirect
8. #11328C2semidirect
9. #11220C2semidirect
11. #10925C2semidirect
12. #10921C2semidirect
13. #10807C2semidirect
14. #10788C2semidirect
15. #10731C2semidirect
44. #2034C4semidirect
122. C2×#106C2×C4semidirect
123. C2×#106D4semidirect
141. C2×C22⋊C8C2×C4semidirect
158. #380C2×C4semidirect
186. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23632
C2×#20342
C2×#19252
C2×#18642
C2×#18542
C2×C4×#1062
#139942
#113282
#112202
#109692
#109252
#109212
#108072
#107882
#107312