Finite Group Databasebeta

← #613961

Subgroups — #613961

Order 512.

4282 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×#2848C211yesmaximal, characteristic
3C2×#2283C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5#15236C212yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#14925C214yesmaximal, complemented
8#14919C212yesmaximal, complemented
9#14918C212yesmaximal
10#14702C211yesmaximal, characteristic, complemented
11#14697C211yesmaximal, characteristic, complemented
12#14680C211yesmaximal, characteristic
13#14080C214yesmaximal, complemented
14#14044C212yesmaximal, complemented
15#13997C212yesmaximal, complemented
16#13974C212yesmaximal, complemented
17#13971C212yesmaximal
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2855—28no—
26#2848—28no—
27C2×#391C2211yescharacteristic, complemented
28C2×#391C2211yescharacteristic, complemented
29C2×#391C2212yescomplemented
30C2×#389C2211yescharacteristic, complemented
31C2×#389C2211yescharacteristic, complemented
32C2×#389C2212yescomplemented
33C2×#388C2214yes—
34C2×#387C2212yescomplemented
35C2×#387C2212yescomplemented
36C2×#385C2214yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40#2283—28no—
41C2×#383C2212yescomplemented
42C2×#382C2212yescomplemented
43C2×#381C2212yes—
44C2×#381C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×C4×C4⋊C4C2212yescomplemented
54C2×C4×C22⋊C4—28no—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×#376C2212yescomplemented
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63#1445C2214yescomplemented
64#1443C2214yescomplemented
65#1443C2214yescomplemented
66#1442C2214yescomplemented
67#1442C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1437C2214yes—
76#1436C2214yescomplemented
77#1436C2214yescomplemented
78#1436C2214yescomplemented
79C4⋊#95C2214yescomplemented
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C22⋊#95C2214yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—28no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—44no—
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—44no—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—28no—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—44no—
139C22×C42D418yes—
140C22×C42C2312yes—
141C22×C42C2314yes—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147#391—24no—
148#391—24no—
149#391—44no—
150#389—24no—
151#389—24no—
152#389—44no—
153#388—216no—
154#387—28no—
155#387—28no—
156#385—28no—
157#385—28no—
158#385—28no—
159#385—216no—
160#383—28no—
161#382—28no—
162#381—28no—
163#381—28no—
164#380—24no—
165#380—24no—
166#380—28no—
167#380—28no—
168#380—44no—
169#380D418yes—
170#379—28no—
171#379—28no—
172C4×C4⋊C4—28no—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—28no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—28no—
178#376—28no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C25—22no—
208C25—24no—
209C25—22no—
210C25—24no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—42no—
216C25—42no—
217C25#4114yes—
218C25C2412yes—
219C25C2411yescharacteristic
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—24no—
224C22×Q8—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—232no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—432no—
266C23×C4—432no—
267C23×C4—416no—
268C23×C4—416no—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4#4118yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2414yes—
281C23×C4C2414yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C22⋊Q8—432no—
292C22⋊Q8—416no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4C2×D418yes—
319C2×C22⋊C4—232no—
320C2×C22⋊C4—232no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
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—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4C2×D418yes—
356C2×C22⋊C4#4118yes—
357C2×C42—232no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—28no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—28no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—44no—
375C2×C42—416no—
376C2×C42C2×D414yes—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95C2×D418yes—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—28no—
411C24—28no—
412C24—216no—
413C24—28no—
414C24—216no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—28no—
428C24—28no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—44no—
439C24—44no—
440C24—48no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24C22×D412yes—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24C2×#4114yes—
449C24C2×#4114yes—
450C24C2×#4112yes—
451C24C2×#4112yes—
452C24C2×#4112yes—
453C242−1+412yes—
454C242−1+412yes—
455C24C2511yescharacteristic
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—48no—
460C2×Q8—48no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—216no—
469C22×C4—216no—
470C22×C4—28no—
471C22×C4—216no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—216no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—4128no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4#121116yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D418yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4114yes—
596C22×C4H(5,𝔽2)14yes—
597C4⋊C4—216no—
598C4⋊C4—416no—
599C4⋊C4—48no—
600C4⋊C4—44no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—88no—
607C22⋊C4—216no—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—416no—
613C22⋊C4—416no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—88no—
619C42—28no—
620C42—28no—
621C42—28no—
622C42—28no—
623C42—416no—
624C42—48no—
625C42—48no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—232no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—432no—
662C23—432no—
663C23—416no—
664C23—416no—
665C23—432no—
666C23—432no—
667C23—416no—
668C23—416no—
669C23—416no—
670C23—42no—
671C23—416no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C2×#12114yes—
688C23#52514yes—
689C23#52918yes—
690C23#53614yes—
691C23#54714yes—
692C23#54814yes—
693C23#55214yes—
694C23#55614yes—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4112yes—
700C23C22×#4112yes—
701C23C22×#4111yescharacteristic
702C23C2×H(5,𝔽2)12yes—
703C23C2×2−1+411yescharacteristic
704C23C2×2−1+411yescharacteristic
705C23#58512yes—
706Q8—88no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—232no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—416no—
738C2×C4—432no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—42no—
743C2×C4—416no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—432no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4C2×#12114yes—
798C2×C4C2×#12114yes—
799C2×C4#52514yes—
800C2×C4#52514yes—
801C2×C4#53514yes—
802C2×C4#54618yes—
803C2×C4#55118yes—
804C22—28no—
805C22—24no—
806C22—24no—
807C22—28no—
808C22—28no—
809C22—28no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—28no—
815C22—28no—
816C22—28no—
817C22—464no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22#241518yes—
831C22C22×#12111yescharacteristic
832C22C2×#52511yescharacteristic
833C22C2×#52511yescharacteristic
834C22C2×#52511yescharacteristic
835C22C2×#52912yes—
836C22#344412yes—
837C22C2×#53511yescharacteristic
838C22C2×#53611yescharacteristic
839C22#344911yescharacteristic
840C22C2×#54612yes—
841C22C2×#54711yescharacteristic
842C22C2×#54811yescharacteristic
843C22D4×#4112yes—
844C22C2×#55112yes—
845C22C2×#55211yescharacteristic
846C22C2×#55611yescharacteristic
847C22#347512yes—
848C22#349512yes—
849C22#349512yes—
850C22#350512yes—
851C22#350512yes—
852C22#352012yes—
853C22#352012yes—
854C4—24no—
855C4—24no—
856C4—44no—
857C4—48no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—44no—
862C4—42no—
863C4—84no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4#241118yes—
869C2—28no—
870C2—48no—
871C2C2×#241511yescharacteristic
872C2C2×#241111yescharacteristic
873C2#3473711yescharacteristic
874C2#3510211yescharacteristic
875C2#3524011yescharacteristic
876C2#3532511yescharacteristic
877C2#3610812yes—
878C2#3614312yes—
879C2#3616712yes—
880C2#3620412yes—
881C2#3662111yescharacteristic
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
1. C2×#2855C2semidirect
3. C2×#2283C2semidirect
5. #15236C2semidirect
6. #15220C2semidirect
7. #14925C2semidirect
8. #14919C2semidirect
10. #14702C2semidirect
11. #14697C2semidirect
13. #14080C2semidirect
14. #14044C2semidirect
15. #13997C2semidirect
16. #13974C2semidirect
27. C2×#391C22semidirect
28. C2×#391C22semidirect
29. C2×#391C22semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
32. C2×#389C22semidirect
34. C2×#387C22semidirect
35. C2×#387C22semidirect
41. C2×#383C22semidirect
42. C2×#382C22semidirect
53. C2×C4×C4⋊C4C22semidirect
60. C2×#376C22semidirect
63. #1445C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1441C22semidirect
76. #1436C22semidirect
77. #1436C22semidirect
78. #1436C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×#28482
C2×#22832
C22×C4×C22⋊C42
#152362
#152202
#149252
#149192
#149182
#147022
#146972
#146802
#140802
#140442
#139972
#139742
#139712