Finite Group Databasebeta

← #657320

Subgroups — #657320

Order 512.

4190 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2360C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic
5#15512C214yesmaximal, complemented
6#15436C214yesmaximal, complemented
7#15179C212yesmaximal, complemented
8#15131C212yesmaximal, complemented
9#14955C212yesmaximal, complemented
10#14726C212yesmaximal
11#14149C212yesmaximal, complemented
12#13991C212yesmaximal
13#13969C212yesmaximal, complemented
14#13924C211yesmaximal, characteristic, complemented
15#13907C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic, complemented
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25#2848—28no—
26#2502—28no—
27C2×#398C2214yescomplemented
28C2×#396C2214yes—
29#2360—28no—
30C2×#391C2211yescharacteristic, complemented
31C2×#391C2212yescomplemented
32C2×#389C2211yescharacteristic, complemented
33C2×#389C2212yescomplemented
34C2×#389C2212yescomplemented
35C2×#388C2214yes—
36C2×#387C2212yescomplemented
37C2×#385C2212yes—
38C2×#385C2214yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#384C2212yescomplemented
43C2×#380—28no—
44C2×#380C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2214yes—
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C2×#379C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic, complemented
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2212yes—
60#1445C2212yescomplemented
61#1445C2212yescomplemented
62#1442C2214yescomplemented
63#1442C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1437C2214yes—
75#1436C2214yescomplemented
76#1436C2214yescomplemented
77C4⋊#95C2212yescomplemented
78C4⋊#95C2212yescomplemented
79C4⋊#95C2212yescomplemented
80C22⋊#95C2211yescharacteristic
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2211yescharacteristic
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—28no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—44no—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8D418yes—
106C2×C4×Q8—24no—
107C2×C4×Q8—44no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4D418yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—48no—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2312yes—
148#398—216no—
149#396—48no—
150#391—28no—
151#391—24no—
152#389—24no—
153#389—28no—
154#389—44no—
155#388—48no—
156#387—28no—
157#385—28no—
158#385—216no—
159#385—28no—
160#385—28no—
161#385—28no—
162#384—28no—
163#380—24no—
164#380—28no—
165#380—28no—
166#380—28no—
167#380—216no—
168#380—28no—
169#379—28no—
170#379—24no—
171#379Q818yescomplemented
172C4×C4⋊C4—24no—
173C4×C22⋊C4—24no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—44no—
178C2×#95—28no—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2311yescharacteristic
185C2×#95C2311yescharacteristic
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C25—22no—
204C25—24no—
205C25—24no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—42no—
212C25—42no—
213C25C2×Q814yes—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8C2×D414yes—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—232no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—432no—
248C23×C4—432no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—416no—
254C23×C4—416no—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D418yes—
258C23×C4#4118yes—
259C23×C4#4114yes—
260C23×C4C2411yescharacteristic
261C23×C4C2414yes—
262C23×C4C2411yescharacteristic
263C23×C4C2414yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C22⋊Q8—232no—
276C22⋊Q8—432no—
277C4×Q8—416no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4C2×D414yes—
313C2×C4⋊C4C2×D414yes—
314C2×C4⋊C4C2×D414yes—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D418yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—432no—
354C2×C22⋊C4C2×D418yes—
355C2×C22⋊C4C2×Q814yes—
356C2×C22⋊C4C2×Q814yes—
357C2×C22⋊C4C2×Q818yes—
358C2×C22⋊C4C2×Q818yes—
359C2×C22⋊C4#4114yes—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—44no—
370C2×C42—44no—
371#95—28no—
372#95—28no—
373#95—22no—
374#95—24no—
375#95—22no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—24no—
381#95—24no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—44no—
388#95—44no—
389#95—42no—
390#95—42no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—28no—
400C24—28no—
401C24—216no—
402C24—28no—
403C24—216no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—28no—
417C24—28no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—48no—
427C24—44no—
428C24—44no—
429C24—48no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24C22×D412yes—
435C24C22×D412yes—
436C24C22×Q814yes—
437C24C22×Q812yes—
438C24C2×#4114yes—
439C24C2×#4112yes—
440C24C2×#4112yes—
441C24H(5,𝔽2)14yes—
442C242−1+412yes—
443C242−1+412yes—
444C24C2511yescharacteristic
445C2×Q8—28no—
446C2×Q8—216no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—48no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—216no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—4128no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—88no—
549C22×C4—88no—
550C22×C4—88no—
551C22×C4—88no—
552C22×C4#121116yes—
553C22×C4C22×D414yes—
554C22×C4C22×D414yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×Q812yes—
562C22×C4C22×Q814yes—
563C22×C4C22×Q812yes—
564C22×C4C2×#4114yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4114yes—
569C22×C4H(5,𝔽2)14yes—
570C4⋊C4—28no—
571C4⋊C4—216no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—48no—
575C4⋊C4—416no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—84no—
581C4⋊C4—88no—
582C4⋊C4—88no—
583C4⋊C4—88no—
584C22⋊C4—216no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—216no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—416no—
592C22⋊C4—48no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—416no—
596C22⋊C4—44no—
597C22⋊C4—48no—
598C42—48no—
599C42—44no—
600C42—44no—
601C42—48no—
602C42—84no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—232no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—432no—
639C23—432no—
640C23—416no—
641C23—416no—
642C23—416no—
643C23—432no—
644C23—416no—
645C23—432no—
646C23—416no—
647C23—42no—
648C23—42no—
649C23—416no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C2×#12114yes—
665C23#53314yes—
666C23#54114yes—
667C23#54714yes—
668C23#54814yes—
669C23D4×Q814yes—
670C23D4×Q814yes—
671C23#55418yes—
672C23C23×D411yescharacteristic
673C23C23×D411yescharacteristic
674C23C23×Q811yescharacteristic
675C23C22×#4111yescharacteristic
676C23C22×#4112yes—
677C23C22×#4111yescharacteristic
678C23C2×H(5,𝔽2)12yes—
679C23C2×H(5,𝔽2)12yes—
680C23C2×2−1+411yescharacteristic
681C23C2×2−1+411yescharacteristic
682C23#58512yes—
683Q8—416no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—432no—
713C2×C4—416no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—432no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—816no—
768C2×C4—816no—
769C2×C4C2×#12114yes—
770C2×C4C2×#12114yes—
771C2×C4#52514yes—
772C2×C4#53414yes—
773C2×C4#54618yes—
774C2×C4#55118yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—464no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22#242918yes—
802C22C22×#12111yescharacteristic
803C22C2×#52511yescharacteristic
804C22C2×#53311yescharacteristic
805C22C2×#53411yescharacteristic
806C22C2×#54111yescharacteristic
807C22C2×#54612yes—
808C22C2×#54711yescharacteristic
809C22C2×#54811yescharacteristic
810C22C2×D4×Q811yescharacteristic
811C22C2×D4×Q811yescharacteristic
812C22C2×#55112yes—
813C22C2×#55412yes—
814C22#347512yes—
815C22#348411yescharacteristic
816C22#348711yescharacteristic
817C22#348812yes—
818C22#349212yes—
819C22#349412yes—
820C22#349512yes—
821C22#350112yes—
822C22#351912yes—
823C22#353612yes—
824C22#354112yes—
825C4—24no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—44no—
830C4—44no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—81no—
836C4—81no—
837C4—84no—
838C4—84no—
839C4#253418yes—
840C2—28no—
841C2—48no—
842C2C2×#242911yescharacteristic
843C2C2×#253411yescharacteristic
844C2#3556311yescharacteristic
845C2#3619012yes—
846C2#3642711yescharacteristic
847C2#3654611yescharacteristic
848C2#3785012yes—
849C2#3891611yescharacteristic
850C2#3959511yescharacteristic
851C2#5901612yes—
852C2#5902412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2502C2semidirect
3. C2×#2360C2semidirect
5. #15512C2semidirect
6. #15436C2semidirect
7. #15179C2semidirect
8. #15131C2semidirect
9. #14955C2semidirect
11. #14149C2semidirect
13. #13969C2semidirect
14. #13924C2semidirect
15. #13907C2semidirect
16. #13876C2semidirect
21. C22×C4×Q8C22semidirect
27. C2×#398C22semidirect
30. C2×#391C22semidirect
31. C2×#391C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
34. C2×#389C22semidirect
36. C2×#387C22semidirect
42. C2×#384C22semidirect
53. C2×C4×C4⋊C4C22semidirect
60. #1445C22semidirect
61. #1445C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
75. #1436C22semidirect
76. #1436C22semidirect
77. C4⋊#95C22semidirect
78. C4⋊#95C22semidirect
79. C4⋊#95C22semidirect
171. #379Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#25022
C2×#23602
C22×#3802
#155122
#154362
#151792
#151312
#149552
#147262
#141492
#139912
#139692
#139242
#139072
#138762
C4×#3792