Finite Group Databasebeta

← #516588

Subgroups — #516588

Order 512.

7682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic
2C2×#2315C211yesmaximal, characteristic, complemented
3C2×#2308C211yesmaximal, characteristic
4C2×#2308C211yesmaximal, characteristic
5C22×#385C211yesmaximal, characteristic, complemented
6#14705C212yesmaximal, complemented
7#14693C212yesmaximal, complemented
8#14263C212yesmaximal, complemented
9#14262C212yesmaximal, complemented
10#14016C214yesmaximal, complemented
11#14015C214yesmaximal, complemented
12#13975C218yesmaximal, complemented
13#13794C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic, complemented
15C24×D4C2211yescharacteristic
16C25×C4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C4×D4—28no—
19C22×C4×D4—28no—
20C22×C4×D4—28no—
21C22×C4×D4C2214yes—
22C22×C4×D4C2214yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yescomplemented
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C42C2211yescharacteristic
32#2315—28no—
33#2308—28no—
34#2308C4116yescomplemented
35C2×#386C2214yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2214yes—
39C2×#386C2214yes—
40C2×#385—28no—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yescomplemented
46C2×#385C2212yescomplemented
47C2×#385C2214yescomplemented
48C2×#385C2218yescomplemented
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#380C2214yescomplemented
52C2×#379C2212yes—
53C2×#379C2212yes—
54C22×#95C2212yescomplemented
55C22×#95C2214yescomplemented
56#1444C2218yescomplemented
57#1442C2218yescomplemented
58#1439C2218yescomplemented
59#1439C2218yescomplemented
60#1436C2218yescomplemented
61#1436C2218yescomplemented
62C22⋊#95C2212yes—
63C22⋊#95C2212yes—
64C22⋊#95C2212yes—
65C22⋊#95C2212yes—
66C22⋊#95C2218yescomplemented
67C22⋊#95C2214yescomplemented
68C22⋊#95C2214yescomplemented
69C22⋊#95C2214yescomplemented
70C26C2311yescharacteristic
71C26C2311yescharacteristic
72C23×D4—24no—
73C23×D4—24no—
74C23×D4—24no—
75C23×D4—24no—
76C23×D4C2×C418yes—
77C23×D4D418yes—
78C23×D4Q818yes—
79C23×D4C2312yes—
80C23×D4C2312yes—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—48no—
87C24×C4—48no—
88C24×C4D418yes—
89C24×C4C2311yescharacteristic
90C24×C4C2314yes—
91C24×C4C2312yes—
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×C4×D4—2128no—
103C2×C4×D4—216no—
104C2×C4×D4—216no—
105C2×C4×D4—216no—
106C2×C4×D4—216no—
107C2×C4×D4—216no—
108C2×C4×D4—216no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—48no—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4C2×C418yescomplemented
135C22×C22⋊C4C2×C418yescomplemented
136C22×C22⋊C4D418yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2318yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42C2314yes—
155#386—28no—
156#386—28no—
157#386—216no—
158#386C2×C4132yescomplemented
159#386C2×C4132yescomplemented
160#385—28no—
161#385—28no—
162#385—28no—
163#385—28no—
164#385—216no—
165#385—28no—
166#385—28no—
167#385—416no—
168#381—28no—
169#381C2×C4116yescomplemented
170#380—216no—
171#379—28no—
172#379C2×C4116yescomplemented
173C2×#95—28no—
174C2×#95—48no—
175C2×#95C2318yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2318yes—
183C2×#95C2318yes—
184C2×#95C2318yes—
185C2×#95C2318yes—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—44no—
191C25—44no—
192C25—44no—
193C25—44no—
194C25C22×C414yes—
195C25C22×C414yes—
196C25C2×D414yes—
197C25C2×D414yes—
198C25C2×D414yes—
199C25C2×D414yes—
200C25C2×Q814yes—
201C25C2×Q814yes—
202C25#4114yes—
203C25#4114yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C22×D4—232no—
209C22×D4—232no—
210C22×D4—232no—
211C22×D4—232no—
212C22×D4—232no—
213C22×D4—232no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4C4⋊C4164yescomplemented
223C22×D4C22×C418yes—
224C22×D4C22×C418yes—
225C22×D4C2×D418yes—
226C22×D4C2×D418yes—
227C22×D4C2×Q818yes—
228C22×D4C2×Q818yes—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—28no—
236C23×C4—232no—
237C23×C4—232no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—28no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—28no—
254C23×C4—28no—
255C23×C4—28no—
256C23×C4—28no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—216no—
267C23×C4—432no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—48no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—432no—
283C23×C4—432no—
284C23×C4—432no—
285C23×C4—432no—
286C23×C4—432no—
287C23×C4C22×C414yes—
288C23×C4C22×C418yescomplemented
289C23×C4C22×C418yescomplemented
290C23×C4C2×D414yes—
291C23×C4C2×D418yes—
292C23×C4C2×D418yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×Q814yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2414yes—
301C23×C4C2414yes—
302C23×C4C2414yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C4×D4—2128no—
309C4×D4—2128no—
310C2×C4⋊C4—232no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—216no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—48no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—48no—
322C2×C4⋊C4—48no—
323C2×C22⋊C4—232no—
324C2×C22⋊C4—232no—
325C2×C22⋊C4—232no—
326C2×C22⋊C4—232no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—416no—
360C2×C22⋊C4—48no—
361C2×C22⋊C4—48no—
362C2×C22⋊C4C22×C418yes—
363C2×C22⋊C4C22×C418yes—
364C2×C22⋊C4C22×C418yescomplemented
365C2×C22⋊C4C22×C418yescomplemented
366C2×C22⋊C4C22×C4132yescomplemented
367C2×C22⋊C4C2×D418yes—
368C2×C22⋊C4C2×D418yes—
369C2×C42—232no—
370C2×C42—28no—
371C2×C42—28no—
372C2×C42—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—216no—
380#95—48no—
381#95—48no—
382#95—48no—
383#95C22×C4132yescomplemented
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24—28no—
391C24—28no—
392C24—28no—
393C24—28no—
394C24—28no—
395C24—28no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—28no—
401C24—28no—
402C24—48no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—416no—
407C24—416no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—416no—
413C24—416no—
414C24—416no—
415C24—416no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—416no—
420C24—48no—
421C24—416no—
422C24C2×C4⋊C4116yes—
423C24C2×C4⋊C4116yescomplemented
424C24C4×D4116yes—
425C24C4×D4116yes—
426C24#120116yes—
427C24C22⋊Q8116yes—
428C24C22⋊Q8116yes—
429C24#123116yes—
430C24C23×C414yes—
431C24C23×C412yes—
432C24C23×C412yes—
433C24C23×C412yes—
434C24C22×D414yes—
435C24C22×D412yes—
436C24C22×D412yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C22×D412yes—
444C24C22×Q814yes—
445C24C22×Q812yes—
446C24C22×Q812yes—
447C24C22×Q812yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C24C2×#4112yes—
451C24C2×#4112yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2511yescharacteristic
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—2256no—
468C2×D4C2×C4⋊C4132yes—
469C2×D4C2×C4⋊C4132yescomplemented
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—216no—
487C22×C4—232no—
488C22×C4—216no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—216no—
493C22×C4—216no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—24no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—24no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—216no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—416no—
533C22×C4—48no—
534C22×C4—432no—
535C22×C4—416no—
536C22×C4—416no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—432no—
541C22×C4—4128no—
542C22×C4—4128no—
543C22×C4—416no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—416no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—416no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—416no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—88no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—88no—
570C22×C4C2×C4⋊C4116yescomplemented
571C22×C4C23×C418yes—
572C22×C4C23×C418yes—
573C22×C4C23×C414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D414yes—
578C22×C4C22×D414yes—
579C22×C4C22×Q814yes—
580C22×C4H(5,𝔽2)18yes—
581C4⋊C4—232no—
582C4⋊C4—416no—
583C4⋊C4—416no—
584C4⋊C4—88no—
585C4⋊C4—88no—
586C22⋊C4—232no—
587C22⋊C4—216no—
588C22⋊C4—216no—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—216no—
593C22⋊C4—432no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—88no—
599C22⋊C4—88no—
600C42—232no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—28no—
611C23—28no—
612C23—28no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—24no—
632C23—24no—
633C23—216no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—28no—
639C23—28no—
640C23—216no—
641C23—232no—
642C23—416no—
643C23—432no—
644C23—432no—
645C23—432no—
646C23—432no—
647C23—416no—
648C23—432no—
649C23—432no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—432no—
654C23—432no—
655C23—432no—
656C23—432no—
657C23—432no—
658C23—44no—
659C23—44no—
660C23—48no—
661C23—44no—
662C23—44no—
663C23—48no—
664C23#385164yescomplemented
665C23C22×C4⋊C418yes—
666C23C22×C4⋊C414yes—
667C23C22×C4⋊C414yes—
668C23C22×C4⋊C414yes—
669C23C2×C4×D414yes—
670C23C2×C4×D414yes—
671C23C2×C4×D414yes—
672C23C2×C4×D414yes—
673C23C2×C4×D414yes—
674C23C2×C4×D414yes—
675C23C2×#12014yes—
676C23C2×#12014yes—
677C23C2×#12014yes—
678C23C2×C22⋊Q814yes—
679C23C2×C22⋊Q814yes—
680C23C2×C22⋊Q814yes—
681C23C2×C22⋊Q814yes—
682C23C2×C22⋊Q814yes—
683C23C2×C22⋊Q814yes—
684C23C2×#12314yes—
685C23C2×#12314yes—
686C23C2×#12314yes—
687C23C24×C411yescharacteristic
688C23C23×D411yescharacteristic
689C23C23×D411yescharacteristic
690C23C23×D411yescharacteristic
691C23C23×Q811yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C2×H(5,𝔽2)14yes—
695C23#58514yes—
696D4—264no—
697D4—264no—
698C2×C4—232no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—232no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—216no—
713C2×C4—216no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—432no—
722C2×C4—432no—
723C2×C4—464no—
724C2×C4—416no—
725C2×C4—432no—
726C2×C4—416no—
727C2×C4—416no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—48no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—48no—
753C2×C4—816no—
754C2×C4—88no—
755C2×C4—88no—
756C2×C4—816no—
757C2×C4C22×C4⋊C418yes—
758C2×C4#53418yes—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—28no—
763C22—28no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—28no—
769C22—28no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—28no—
777C22—28no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—28no—
783C22—216no—
784C22—28no—
785C22—464no—
786C22—464no—
787C22—44no—
788C22—48no—
789C22—44no—
790C22—48no—
791C22—48no—
792C22—48no—
793C22—48no—
794C22C2×#38518yes—
795C22C2×#38518yes—
796C22C2×#38518yes—
797C22C23×C4⋊C411yescharacteristic
798C22C22×C4×D411yescharacteristic
799C22C22×C4×D411yescharacteristic
800C22C4×H(5,𝔽2)14yes—
801C22C22×#12011yescharacteristic
802C22C22×C22⋊Q811yescharacteristic
803C22C22×C22⋊Q811yescharacteristic
804C22C22×#12311yescharacteristic
805C22C2×#53412yes—
806C22#344912yes—
807C22#345914yes—
808C22#348412yes—
809C22#348412yes—
810C22#348512yes—
811C22#348512yes—
812C22#350114yes—
813C22#350514yes—
814C4—28no—
815C4—28no—
816C4—44no—
817C4—48no—
818C4—44no—
819C4—44no—
820C4—48no—
821C4—82no—
822C4—82no—
823C4—84no—
824C2—28no—
825C2—28no—
826C2—28no—
827C2—48no—
828C2C22×#38511yescharacteristic
829C2C4×#53412yes—
830C2#3424812yes—
831C2#3426412yes—
832C2#3498011yescharacteristic
833C2#3498312yes—
834C2#3498512yes—
835C2#3501012yes—
836C2#3508811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2315C2semidirect
5. C22×#385C2semidirect
6. #14705C2semidirect
7. #14693C2semidirect
8. #14263C2semidirect
9. #14262C2semidirect
10. #14016C2semidirect
11. #14015C2semidirect
12. #13975C2semidirect
13. #13794C2semidirect
14. C2×C22⋊#95C2semidirect
24. C23×C4⋊C4C22semidirect
34. #2308C4semidirect
45. C2×#385C22semidirect
46. C2×#385C22semidirect
47. C2×#385C22semidirect
48. C2×#385C22semidirect
51. C2×#380C22semidirect
54. C22×#95C22semidirect
55. C22×#95C22semidirect
56. #1444C22semidirect
57. #1442C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1436C22semidirect
61. #1436C22semidirect
66. C22⋊#95C22semidirect
67. C22⋊#95C22semidirect
68. C22⋊#95C22semidirect
69. C22⋊#95C22semidirect
134. C22×C22⋊C4C2×C4semidirect
135. C22×C22⋊C4C2×C4semidirect
158. #386C2×C4semidirect
159. #386C2×C4semidirect
169. #381C2×C4semidirect
172. #379C2×C4semidirect
222. C22×D4C4⋊C4semidirect
288. C23×C4C22×C4semidirect
289. C23×C4C22×C4semidirect
364. C2×C22⋊C4C22×C4semidirect
365. C2×C22⋊C4C22×C4semidirect
366. C2×C22⋊C4C22×C4semidirect
383. #95C22×C4semidirect
423. C24C2×C4⋊C4semidirect
469. C2×D4C2×C4⋊C4semidirect
570. C22×C4C2×C4⋊C4semidirect
664. C23#385semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D42
C2×#23152
C2×#23082
C22×#3852
#147052
#146932
#142632
#142622
#140162
#140152
#139752
#137942
C2×C22⋊#952