Finite Group Databasebeta

← #372312

Subgroups — #372312

Order 512.

1570 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic
2C2×#1921C211yesmaximal, characteristic, complemented
3C2×C4×#107C211yesmaximal, characteristic, complemented
4#13998C211yesmaximal, characteristic
5#13801C211yesmaximal, characteristic, complemented
6#11220C211yesmaximal, characteristic, complemented
7#11123C211yesmaximal, characteristic, complemented
8#11096C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10931C211yesmaximal, characteristic, complemented
12#10925C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10908C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C2×#482—24no—
19C2×#482—24no—
20C2×#482C418yescomplemented
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C2×#390—21no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1921—24no—
42C4×#107—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1439—21no—
56#1438—21no—
57#1437—21no—
58#1437—21no—
59#1437—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63C4×#95—21no—
64C23×D4—21no—
65C23×D4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#121—22no—
72C2×#121—22no—
73C2×#121—22no—
74C2×#121—41no—
75C2×#121—41no—
76C2×#121C2×C414yes—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—41no—
81C2×#117—41no—
82C2×#117C2×C414yes—
83C22×C4⋊C4—21no—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4D411yescharacteristic
100C22×C22⋊C4D411yescharacteristic
101C22×C42—21no—
102C22×C42—21no—
103C22×C42—21no—
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#482—232no—
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107C2×C414yes—
112C2×#107D414yes—
113C2×#107D414yes—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106C2×C414yes—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102—41no—
127C2×#102C2×C414yes—
128C2×#102C2×C414yes—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8C2×C414yes—
135C2×C4×C8—22no—
136C2×C4×C8—22no—
137C2×C4×C8—22no—
138#390—22no—
139#390—22no—
140#390—22no—
141#390—41no—
142#390—44no—
143#389—22no—
144#389—41no—
145#380—22no—
146#380—22no—
147#380—22no—
148#380—41no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4—41no—
153C4×C4⋊C4—41no—
154C4×C4⋊C4—41no—
155C4×C22⋊C4—22no—
156C4×C22⋊C4—22no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95D411yescharacteristic
168C2×#95D411yescharacteristic
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—41no—
176#340—41no—
177#340—41no—
178#336—22no—
179#336—22no—
180#336—41no—
181C25—21no—
182C25C2×D411yescharacteristic
183C22×D4—24no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—42no—
198C22×D4—42no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4—81no—
202C22×D4—81no—
203C22×D4C22×C412yes—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
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—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4C22×C412yes—
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4#4112yes—
230C23×C4C2411yescharacteristic
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8C22×C412yes—
255C22×C8C22×C412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8#4112yes—
259#121—28no—
260#121—44no—
261#121—44no—
262#121—44no—
263#117—28no—
264#117—44no—
265#117—44no—
266#117—44no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
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—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4C22×C412yes—
303C2×C4⋊C4C22×C412yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C4⋊C4#4112yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4—81no—
338C2×C22⋊C4—81no—
339C2×C22⋊C4—81no—
340C2×C22⋊C4—81no—
341C2×C22⋊C4—81no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—24no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—81no—
362C2×C42—81no—
363C2×C42—81no—
364C2×C42#4112yes—
365C2×C42#4112yes—
366#107—28no—
367#107C22⋊C4116yescomplemented
368#106—28no—
369#102—28no—
370#102—28no—
371#102—44no—
372#102—44no—
373C22⋊C8—28no—
374C22⋊C8—44no—
375C4×C8—28no—
376#95—24no—
377#95—22no—
378#95—22no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—81no—
387#95—81no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24C4×D412yes—
418C24C22×D411yescharacteristic
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—84no—
450C2×D4—84no—
451C2×D4—84no—
452C2×D4—84no—
453C2×D4—84no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
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×C4C4×D412yes—
561C22×C4#12312yes—
562C22×C4#12312yes—
563C22×C4#13512yes—
564C22×C4#13512yes—
565C22×C4AGL(1,ℤ/8)12yes—
566C22×C4C23×C411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C2×#4111yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4H(5,𝔽2)11yescharacteristic
577C22×C4H(5,𝔽2)11yescharacteristic
578C22×C4H(5,𝔽2)11yescharacteristic
579C22×C42−1+411yescharacteristic
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8C2×C22⋊C414yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—84no—
635C4⋊C4C2×C22⋊C414yes—
636C4⋊C4C2×C22⋊C414yes—
637C22⋊C4—44no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—44no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—48no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—84no—
657C42—84no—
658C42—84no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
705C23—81no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23C2×C4×D411yescharacteristic
730C23C2×#12311yescharacteristic
731C23#52511yescharacteristic
732C23D4211yescharacteristic
733C23D4211yescharacteristic
734C23#54611yescharacteristic
735C23#54711yescharacteristic
736C23C2×#13511yescharacteristic
737C23C2×#13511yescharacteristic
738C23C2×AGL(1,ℤ/8)11yescharacteristic
739C23#57511yescharacteristic
740C23#57611yescharacteristic
741C23#57611yescharacteristic
742C23#57711yescharacteristic
743C23#57811yescharacteristic
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—816no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4#48214yescomplemented
845C2×C4C22×C22⋊C411yescharacteristic
846C2×C4C4×#4111yescharacteristic
847C2×C4C4×#4111yescharacteristic
848C2×C4C4×#4111yescharacteristic
849C2×C4#51811yescharacteristic
850C2×C4#52011yescharacteristic
851C2×C4#52511yescharacteristic
852C2×C4#52511yescharacteristic
853C2×C4#52911yescharacteristic
854C2×C4#52911yescharacteristic
855C2×C4#53211yescharacteristic
856C2×C4#53211yescharacteristic
857C2×C4#53811yescharacteristic
858C2×C4#53911yescharacteristic
859C2×C4#54011yescharacteristic
860C2×C4#54211yescharacteristic
861C2×C4#54611yescharacteristic
862C2×C4#54611yescharacteristic
863C2×C4#54811yescharacteristic
864C2×C4#54811yescharacteristic
865C2×C4#55011yescharacteristic
866C2×C4#55011yescharacteristic
867C2×C4#55111yescharacteristic
868C2×C4#55111yescharacteristic
869C2×C4#55211yescharacteristic
870C2×C4#55311yescharacteristic
871C2×C4#55311yescharacteristic
872C2×C4#55911yescharacteristic
873C8—24no—
874C8—42no—
875C8—42no—
876C8—81no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—161no—
900C22—161no—
901C22—161no—
902C22—161no—
903C22—161no—
904C22—161no—
905C22—161no—
906C22—161no—
907C22C4×#12311yescharacteristic
908C22D4×C22⋊C411yescharacteristic
909C22#235911yescharacteristic
910C22#244311yescharacteristic
911C22#244511yescharacteristic
912C22#245611yescharacteristic
913C22#246111yescharacteristic
914C22C4×#13511yescharacteristic
915C22C4×AGL(1,ℤ/8)11yescharacteristic
916C22#294611yescharacteristic
917C22#295111yescharacteristic
918C22C2×#48211yescharacteristic
919C22#309111yescharacteristic
920C22#309611yescharacteristic
921C22#309811yescharacteristic
922C22#310211yescharacteristic
923C22#310611yescharacteristic
924C22#312111yescharacteristic
925C22#312211yescharacteristic
926C22#326411yescharacteristic
927C22#326711yescharacteristic
928C22#327211yescharacteristic
929C22#327311yescharacteristic
930C22#328511yescharacteristic
931C22#328511yescharacteristic
932C22#328711yescharacteristic
933C22#328711yescharacteristic
934C22#329711yescharacteristic
935C22#330411yescharacteristic
936C22#332511yescharacteristic
937C22#332711yescharacteristic
938C22#333911yescharacteristic
939C22#334011yescharacteristic
940C22#334311yescharacteristic
941C22#334711yescharacteristic
942C4—24no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—44no—
947C4—44no—
948C4—81no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4—161no—
954C4#229711yescharacteristic
955C4#233511yescharacteristic
956C4#234111yescharacteristic
957C4#237411yescharacteristic
958C4#245811yescharacteristic
959C4#247111yescharacteristic
960C4#255411yescharacteristic
961C4#255811yescharacteristic
962C2—82no—
963C2—162no—
964C2#1409511yescharacteristic
965C2C4×#48211yescharacteristic
966C2#2159011yescharacteristic
967C2#2244211yescharacteristic
968C2#2245111yescharacteristic
969C2#2292311yescharacteristic
970C2#2294611yescharacteristic
971C2#2613711yescharacteristic
972C2#2614011yescharacteristic
973C2#2623711yescharacteristic
974C2#2623811yescharacteristic
975C2#2661911yescharacteristic
976C2#2662311yescharacteristic
977C2#2679311yescharacteristic
978C2#2679811yescharacteristic
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
2. C2×#1921C2semidirect
3. C2×C4×#107C2semidirect
5. #13801C2semidirect
6. #11220C2semidirect
7. #11123C2semidirect
8. #11096C2semidirect
10. #10931C2semidirect
11. #10931C2semidirect
12. #10925C2semidirect
13. #10921C2semidirect
14. #10908C2semidirect
15. #10731C2semidirect
20. C2×#482C4semidirect
367. #107C22⋊C4semidirect
844. C2×C4#482semidirect

Maximal subgroups

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

subgroupindex
C22×#4822
C2×#19212
C2×C4×#1072
#139982
#138012
#112202
#111232
#110962
#109692
#109312
#109252
#109212
#109082
#107312