Finite Group Databasebeta

← #364987

Subgroups — #364987

Order 512.

2548 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#1954C211yesmaximal, characteristic, complemented
4C2×#1874C212yesmaximal, complemented
5C2×#1802C211yesmaximal, characteristic, complemented
6C2×C4×#102C211yesmaximal, characteristic, complemented
7#11199C212yesmaximal, complemented
8#10969C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10841C211yesmaximal, characteristic, complemented
11#10730C212yesmaximal, complemented
12C22×#121—21no—
13C22×#121C2212yes—
14C22×C4×D4—21no—
15C22×C4×D4C2211yescharacteristic
16C22×C4×D4C2211yescharacteristic
17C23×C4⋊C4C2212yes—
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2212yes—
21C22×#102C2211yescharacteristic
22C22×C22⋊C8C2212yes—
23C22×C22⋊C8C2212yes—
24C22×C4×C8C2211yescharacteristic
25#2537—24no—
26#2537C418yescomplemented
27C2×#394—22no—
28D4×C4⋊C4—24no—
29D4×C4⋊C4—24no—
30C2×#389—21no—
31C2×#385—22no—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×#380C2212yes—
36C2×#380C2212yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1954—24no—
39#1874—28no—
40#1802—24no—
41C4×#102—24no—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2212yes—
48C2×#340C2212yes—
49C23×D4—22no—
50C23×D4D411yescharacteristic
51C23×D4C2311yescharacteristic
52C24×C4—22no—
53C24×C4—21no—
54C24×C4C2312yes—
55C23×C8C2312yes—
56C23×C8C2311yescharacteristic
57C23×C8C2311yescharacteristic
58C2×#121—28no—
59C2×#121—24no—
60C2×#121—24no—
61C2×#121—24no—
62C2×#121—42no—
63C2×#121—42no—
64C2×#121—44no—
65C2×#121—44no—
66C2×#121C2×C418yescomplemented
67C2×C4×D4—28no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—44no—
78C2×C4×D4—44no—
79C2×C4×D4C2×C414yes—
80C2×C4×D4C2×C414yescomplemented
81C2×C4×D4D414yes—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—42no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4D411yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—22no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—22no—
103C22×C22⋊C4D412yes—
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—24no—
115C2×#102—24no—
116C2×#102—42no—
117C2×#102D414yescomplemented
118C2×C22⋊C8—24no—
119C2×C22⋊C8—24no—
120C2×C22⋊C8—24no—
121C2×C22⋊C8—24no—
122C2×C22⋊C8—42no—
123C2×C22⋊C8—42no—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127#394—216no—
128#389—28no—
129#385—216no—
130#384—22no—
131#384—22no—
132#384C2×C414yescomplemented
133#384D414yescomplemented
134#380—24no—
135#380—28no—
136#380—24no—
137#380—24no—
138#380C2×C418yescomplemented
139C4×C4⋊C4—22no—
140C4×C4⋊C4D414yescomplemented
141C2×#95—22no—
142C2×#95—21no—
143C2×#95—22no—
144#340—24no—
145#340—24no—
146#340—24no—
147#340—22no—
148#340—22no—
149#340—42no—
150#340—42no—
151C25—21no—
152C25C2×D412yes—
153C22×D4—28no—
154C22×D4—22no—
155C22×D4—22no—
156C22×D4—22no—
157C22×D4—22no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—44no—
170C22×D4—44no—
171C22×D4—44no—
172C22×D4—44no—
173C22×D4—82no—
174C22×D4—82no—
175C22×D4C22⋊C414yes—
176C22×D4D814yes—
177C22×D4SD1614yes—
178C22×D4C22×C412yes—
179C22×D4C2×D412yes—
180C22×D4#4112yes—
181C23×C4—21no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—21no—
195C23×C4—22no—
196C23×C4—21no—
197C23×C4—22no—
198C23×C4—28no—
199C23×C4—24no—
200C23×C4—44no—
201C23×C4—44no—
202C23×C4—44no—
203C23×C4—44no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—82no—
211C23×C4—82no—
212C23×C4C22×C414yes—
213C23×C4C2×D412yes—
214C23×C4C2×D414yes—
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2411yescharacteristic
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8C2×D412yes—
238C22×C8#4112yes—
239#121—216no—
240#121—48no—
241#121—48no—
242#121—48no—
243#121—432no—
244C4×D4—28no—
245C4×D4—28no—
246C4×D4—28no—
247C4×D4—28no—
248C4×D4—28no—
249C4×D4—28no—
250C4×D4—432no—
251C4×D4—44no—
252C4×D4—44no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—81no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4—81no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4C22⋊C414yes—
298C2×C4⋊C4C22×C412yes—
299C2×C4⋊C4C22×C414yes—
300C2×C4⋊C4C2×D414yes—
301C2×C4⋊C4C2×D412yes—
302C2×C4⋊C4C2×D412yes—
303C2×C4⋊C4C2×D412yes—
304C2×C4⋊C4#4112yes—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4C22⋊C418yes—
320C2×C42—24no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42C22×C412yes—
324C2×C42C2×D412yes—
325C2×C42C2×D412yes—
326C2×C42C2×D412yes—
327C2×C42#4112yes—
328C2×C42#4112yes—
329C4⋊C8—44no—
330#102—28no—
331#102—28no—
332#102—48no—
333C22⋊C8—48no—
334C22⋊C8—48no—
335C4×C8—44no—
336#95—28no—
337#95—28no—
338#95—24no—
339C24—22no—
340C24—22no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—22no—
347C24—22no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24C2×C22⋊C414yes—
367C24C2×D814yes—
368C24C2×SD1614yes—
369C24C22×D411yescharacteristic
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—28no—
386C2×D4—28no—
387C2×D4—28no—
388C2×D4—28no—
389C2×D4—28no—
390C2×D4—28no—
391C2×D4—416no—
392C2×D4—416no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—88no—
406C2×D4—88no—
407C2×D4—88no—
408C2×D4—88no—
409C2×D4—88no—
410C2×D4#102116yescomplemented
411C2×D4C4×D414yescomplemented
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—416no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—416no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—88no—
491C22×C4—88no—
492C22×C4—88no—
493C22×C4—88no—
494C22×C4—88no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4C2×C22⋊C414yes—
500C22×C4C2×C22⋊C412yes—
501C22×C4C2×C22⋊C412yes—
502C22×C4#12012yes—
503C22×C4#12012yes—
504C22×C4#12312yes—
505C22×C4#12312yes—
506C22×C4C2×D812yes—
507C22×C4C2×SD1612yes—
508C22×C4AGL(1,ℤ/8)12yes—
509C22×C4#13712yes—
510C22×C4C23×C411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C42−1+411yescharacteristic
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—28no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—416no—
558C4⋊C4—42no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C4⋊C4#12114yescomplemented
571C22⋊C4—216no—
572C22⋊C4—416no—
573C22⋊C4—416no—
574C22⋊C4—416no—
575C22⋊C4—48no—
576C42—48no—
577C42C4×D414yes—
578C42C4×D414yes—
579C42#12114yes—
580C42#12114yes—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—81no—
650C23C2×#10218yes—
651C23C22×C22⋊C411yescharacteristic
652C23C2×#12011yescharacteristic
653C23C2×#12311yescharacteristic
654C23D4211yescharacteristic
655C23#54611yescharacteristic
656C23#54611yescharacteristic
657C23#54711yescharacteristic
658C23C22×D811yescharacteristic
659C23C22×SD1611yescharacteristic
660C23C2×AGL(1,ℤ/8)11yescharacteristic
661C23C2×#13711yescharacteristic
662C23#57611yescharacteristic
663C23#57711yescharacteristic
664C23#57711yescharacteristic
665C23#57811yescharacteristic
666D4—24no—
667D4—232no—
668D4—24no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—832no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—832no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—816no—
734C2×C4#38614yes—
735C2×C4#38614yes—
736C2×C4C2×#10214yes—
737C2×C4#41714yes—
738C2×C4#44714yes—
739C2×C4#44814yes—
740C2×C4#48014yes—
741C2×C4#48114yes—
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C4×#4111yescharacteristic
746C2×C4#51811yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4C2×#12111yescharacteristic
749C2×C4C2×#12111yescharacteristic
750C2×C4C2×#12111yescharacteristic
751C2×C4#52511yescharacteristic
752C2×C4#52911yescharacteristic
753C2×C4#53211yescharacteristic
754C2×C4#53511yescharacteristic
755C2×C4#53711yescharacteristic
756C2×C4#54011yescharacteristic
757C2×C4#54211yescharacteristic
758C2×C4D4211yescharacteristic
759C2×C4D4211yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4#54711yescharacteristic
764C2×C4#54711yescharacteristic
765C2×C4#54811yescharacteristic
766C2×C4#55011yescharacteristic
767C2×C4#55311yescharacteristic
768C2×C4#55311yescharacteristic
769C2×C4#55511yescharacteristic
770C8—42no—
771C8—42no—
772C8—82no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22C2×#38611yescharacteristic
804C22D4×C22⋊C411yescharacteristic
805C22#233911yescharacteristic
806C22#240711yescharacteristic
807C22#240811yescharacteristic
808C22#242011yescharacteristic
809C22#242211yescharacteristic
810C22C22×#10211yescharacteristic
811C22C2×#41711yescharacteristic
812C22#289711yescharacteristic
813C22#289811yescharacteristic
814C22C2×#44711yescharacteristic
815C22C2×#44811yescharacteristic
816C22#301211yescharacteristic
817C22#301311yescharacteristic
818C22C2×#48011yescharacteristic
819C22C2×#48111yescharacteristic
820C22#309811yescharacteristic
821C22#309911yescharacteristic
822C22#327211yescharacteristic
823C22#327611yescharacteristic
824C22D4×D811yescharacteristic
825C22D4×SD1611yescharacteristic
826C22#329411yescharacteristic
827C22#329411yescharacteristic
828C22#329511yescharacteristic
829C22#329811yescharacteristic
830C22#332511yescharacteristic
831C22#332911yescharacteristic
832C22#333011yescharacteristic
833C22#333111yescharacteristic
834C22#333411yescharacteristic
835C22#333511yescharacteristic
836C22#335411yescharacteristic
837C22#335711yescharacteristic
838C4—24no—
839C4—44no—
840C4—44no—
841C4—82no—
842C4—84no—
843C4—82no—
844C4—84no—
845C4#187418yescomplemented
846C4C4×#12111yescharacteristic
847C4#232411yescharacteristic
848C4#236111yescharacteristic
849C4#236311yescharacteristic
850C4#242711yescharacteristic
851C4#242811yescharacteristic
852C4#253511yescharacteristic
853C4#253711yescharacteristic
854C2—48no—
855C2—84no—
856C2#1397011yescharacteristic
857C2C2×#187411yescharacteristic
858C2#2091511yescharacteristic
859C2D4×#10211yescharacteristic
860C2#2243111yescharacteristic
861C2#2248511yescharacteristic
862C2#2250311yescharacteristic
863C2#2411611yescharacteristic
864C2#2411811yescharacteristic
865C2#2423611yescharacteristic
866C2#2423911yescharacteristic
867C2#2496511yescharacteristic
868C2#2496711yescharacteristic
869C2#2501011yescharacteristic
870C2#2501211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
3. C2×#1954C2semidirect
4. C2×#1874C2semidirect
5. C2×#1802C2semidirect
6. C2×C4×#102C2semidirect
7. #11199C2semidirect
8. #10969C2semidirect
9. #10849C2semidirect
10. #10841C2semidirect
11. #10730C2semidirect
26. #2537C4semidirect
66. C2×#121C2×C4semidirect
80. C2×C4×D4C2×C4semidirect
117. C2×#102D4semidirect
132. #384C2×C4semidirect
133. #384D4semidirect
138. #380C2×C4semidirect
140. C4×C4⋊C4D4semidirect
410. C2×D4#102semidirect
411. C2×D4C4×D4semidirect
570. C4⋊C4#121semidirect
845. C4#1874semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×D4×C4⋊C42
C2×#19542
C2×#18742
C2×#18022
C2×C4×#1022
#111992
#109692
#108492
#108412
#107302