Finite Group Databasebeta

← #639835

Subgroups — #639835

Order 512.

4074 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×#2848C211yesmaximal, characteristic
2C2×#2625C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic
5#16400C212yesmaximal, complemented
6#16399C212yesmaximal, complemented
7#16396C214yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#14826C212yesmaximal, complemented
11#14820C214yesmaximal
12#14766C212yesmaximal, complemented
13#14343C211yesmaximal, characteristic, complemented
14#14264C211yesmaximal, characteristic, complemented
15#14258C211yesmaximal, characteristic, complemented
16#14139C212yesmaximal, complemented
17#13907C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C22⋊C4C2212yes—
26#2848—28no—
27#2625—28no—
28C2×#400C2212yescomplemented
29C2×#398C2212yescomplemented
30C2×#397C2214yes—
31C2×#397C2214yes—
32C2×#391C2212yescomplemented
33C2×#391C2212yescomplemented
34C2×#389C2212yescomplemented
35C2×#389C2212yescomplemented
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39#2280—28no—
40C2×#381C2212yes—
41C2×#380—28no—
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2214yes—
54C2×#380C2211yescharacteristic
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2212yes—
60#1445C2212yescomplemented
61#1445C2212yescomplemented
62#1444C2212yescomplemented
63#1443C2214yescomplemented
64#1442C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2212yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1440C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C22⋊#95C2214yes—
85C22⋊#95C2214yes—
86C22⋊#95C2214yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—28no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—44no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—44no—
113C22×C4⋊C4—28no—
114C22×C4⋊C4—28no—
115C22×C4⋊C4—44no—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—44no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151#400—28no—
152#398—28no—
153#397—216no—
154#397—48no—
155#391—28no—
156#391—44no—
157#389—28no—
158#389—44no—
159#385—28no—
160#385—28no—
161#385—28no—
162#381—28no—
163#380—24no—
164#380—24no—
165#380—24no—
166#380—24no—
167#380—24no—
168#380—24no—
169#380—24no—
170#380—24no—
171#380—28no—
172#380—28no—
173#380—28no—
174#380—48no—
175#380D418yes—
176#379—28no—
177#379—28no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—28no—
180C2×#95—28no—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—24no—
212C25—24no—
213C25—42no—
214C25—42no—
215C25C2×D414yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C25C2411yescharacteristic
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—24no—
223C22×Q8—24no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—232no—
233C23×C4—232no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—416no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—432no—
253C23×C4—432no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4#4114yes—
265C23×C4#4118yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2414yes—
275C23×C4C2414yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C22⋊Q8—416no—
281C22⋊Q8—416no—
282C22⋊Q8—416no—
283#117—416no—
284#117—416no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
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—432no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×D418yes—
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—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
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—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—432no—
367C2×C22⋊C4C2×D418yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374#95—28no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95C2×D418yes—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—21no—
403C24—22no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—28no—
408C24—28no—
409C24—28no—
410C24—28no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—28no—
428C24—28no—
429C24—44no—
430C24—44no—
431C24—48no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24C22×D412yes—
444C24C22×D412yes—
445C24C22×D412yes—
446C24C22×D412yes—
447C24C2×#4112yes—
448C24C2×#4114yes—
449C24H(5,𝔽2)12yes—
450C24H(5,𝔽2)12yes—
451C242−1+412yes—
452C242−1+414yes—
453C242−1+412yes—
454C24C2511yescharacteristic
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—48no—
459C2×Q8—48no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—216no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—4128no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—416no—
560C22×C4—416no—
561C22×C4—416no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—416no—
565C22×C4—88no—
566C22×C4—88no—
567C22×C4—88no—
568C22×C4#121116yes—
569C22×C4#123116yes—
570C22×C4C22×D412yes—
571C22×C4C22×D418yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4114yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4114yes—
581C22×C4H(5,𝔽2)14yes—
582C4⋊C4—216no—
583C4⋊C4—416no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—48no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C4⋊C4—48no—
595C4⋊C4—88no—
596C4⋊C4—88no—
597C22⋊C4—48no—
598C22⋊C4—416no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C42—48no—
613C42—48no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—232no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—416no—
662C23—416no—
663C23—416no—
664C23—416no—
665C23—432no—
666C23—432no—
667C23—416no—
668C23—432no—
669C23—432no—
670C23—416no—
671C23—42no—
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—
688C23C2×#12314yes—
689C23#53614yes—
690C23#53714yes—
691C23#53714yes—
692C23#54118yes—
693C23#54218yes—
694C23C23×D411yescharacteristic
695C23C23×D411yescharacteristic
696C23C22×#4111yescharacteristic
697C23C22×#4112yes—
698C23C2×H(5,𝔽2)12yes—
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×2−1+412yes—
702C23C2×2−1+411yescharacteristic
703C23C2×2−1+411yescharacteristic
704C23#58512yes—
705Q8—88no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—232no—
715C2×C4—232no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—416no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—416no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—832no—
790C2×C4C2×#12114yes—
791C2×C4C2×#12114yes—
792C2×C4C2×#12314yes—
793C2×C4C2×#12314yes—
794C2×C4#53414yes—
795C2×C4#54618yes—
796C2×C4#55118yes—
797C22—28no—
798C22—28no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—28no—
805C22—28no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—464no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22#262518yescomplemented
831C22C22×#12111yescharacteristic
832C22C22×#12311yescharacteristic
833C22C2×#53411yescharacteristic
834C22C2×#53611yescharacteristic
835C22C2×#53711yescharacteristic
836C22C2×#53711yescharacteristic
837C22#344911yescharacteristic
838C22C2×#54112yes—
839C22C2×#54212yes—
840C22C2×#54612yes—
841C22C2×#55112yes—
842C22#348411yescharacteristic
843C22#348611yescharacteristic
844C22#348912yes—
845C22#349211yescharacteristic
846C22#349211yescharacteristic
847C22#349412yes—
848C22#349512yes—
849C22#349512yes—
850C22#353612yes—
851C22#353812yes—
852C22#354112yes—
853C22#354212yes—
854C4—24no—
855C4—24no—
856C4—48no—
857C4—42no—
858C4—84no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4#241218yes—
868C2—28no—
869C2—44no—
870C2—44no—
871C2C2×#262511yescharacteristic
872C2C2×#241211yescharacteristic
873C2#3522311yescharacteristic
874C2#3526311yescharacteristic
875C2#3530611yescharacteristic
876C2#3744211yescharacteristic
877C2#3744411yescharacteristic
878C2#3766312yes—
879C2#3766412yes—
880C2#3785012yes—
881C2#3785312yes—
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×#2625C2semidirect
5. #16400C2semidirect
6. #16399C2semidirect
7. #16396C2semidirect
8. #15179C2semidirect
9. #15132C2semidirect
10. #14826C2semidirect
12. #14766C2semidirect
13. #14343C2semidirect
14. #14264C2semidirect
15. #14258C2semidirect
16. #14139C2semidirect
17. #13907C2semidirect
28. C2×#400C22semidirect
29. C2×#398C22semidirect
32. C2×#391C22semidirect
33. C2×#391C22semidirect
34. C2×#389C22semidirect
35. C2×#389C22semidirect
60. #1445C22semidirect
61. #1445C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
830. C22#2625semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26252
C2×#22802
C22×#3802
#164002
#163992
#163962
#151792
#151322
#148262
#148202
#147662
#143432
#142642
#142582
#141392
#139072