Finite Group Databasebeta

← #533179

Subgroups — #533179

Order 512.

5022 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic
2C2×#2366C212yesmaximal, complemented
3C2×#2361C212yesmaximal, complemented
4C2×C4×#121C212yesmaximal, complemented
5#14521C212yesmaximal, complemented
6#14419C212yesmaximal, complemented
7#14187C214yesmaximal, complemented
8#14171C212yesmaximal, complemented
9#14036C214yesmaximal, complemented
10#14025C212yesmaximal, complemented
11#13998C212yesmaximal, complemented
12#13998C212yesmaximal, complemented
13#13872C211yesmaximal, characteristic, complemented
14#13821C212yesmaximal, complemented
15C4×#386C211yesmaximal, characteristic, complemented
16C22×#127C2212yes—
17C22×#127C2211yescharacteristic
18C22×#121C2212yes—
19C22×#121C2212yes—
20C22×C4×D4C2214yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2214yes—
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2541C4116yescomplemented
27C2×#392C2212yes—
28C2×#392C2212yes—
29#2366—216no—
30#2361—216no—
31C4×#121—216no—
32C2×#390C2212yes—
33C2×#390C2214yes—
34C2×#390C2214yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#388C2214yes—
41C2×#388C2214yes—
42C2×#386C2212yes—
43C2×#386C2211yescharacteristic
44C2×#386C2214yes—
45C2×#386C2214yes—
46C2×#386C2214yes—
47C2×#386C2214yes—
48C2×#386C2211yescharacteristic
49C2×#385C2214yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2214yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2214yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59#1441C2212yes—
60#1439C2212yes—
61#1439C2214yes—
62#1439C2214yes—
63#1438C2214yes—
64#1438C2214yes—
65#1438C2214yes—
66#1438C2214yes—
67#1437C2214yes—
68#1437C2212yes—
69#1437C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2212yes—
73C4⋊#95C2212yes—
74#1434C2214yes—
75C22⋊#95C2212yes—
76C22⋊#95C2211yescharacteristic
77C22⋊#95C2211yescharacteristic
78C4×#95C2212yes—
79C23×D4C2312yes—
80C23×D4C2314yes—
81C23×D4C2314yes—
82C23×D4C2312yes—
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2314yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C2×#127—28no—
92C2×#127—28no—
93C2×#127—42no—
94C2×#127—42no—
95C2×#127C2×C4116yescomplemented
96C2×#127C2×C418yescomplemented
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—28no—
101C2×#121C2×C4116yescomplemented
102C2×#121C2×C4116yescomplemented
103C2×C4×D4—216no—
104C2×C4×D4—216no—
105C2×C4×D4—28no—
106C2×C4×D4—216no—
107C2×C4×D4—216no—
108C2×C4×D4—28no—
109C2×C4×D4—44no—
110C2×C4×D4—42no—
111C2×C4×D4—42no—
112C2×C4×D4—48no—
113C2×C4×D4—48no—
114C2×C4×D4C2×C418yescomplemented
115C22×C4⋊C4—28no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C42—28no—
142C22×C42—42no—
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2314yes—
146C22×C42C2314yes—
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150#392C2×C4116yescomplemented
151#392C2×C4116yescomplemented
152#390—28no—
153#390—216no—
154#390—216no—
155#390—28no—
156#390—44no—
157#390C2×C4116yescomplemented
158#389—28no—
159#389D4116yescomplemented
160#388—216no—
161#388—216no—
162#386—28no—
163#386—24no—
164#386—216no—
165#386—216no—
166#386—216no—
167#386—48no—
168#386D418yescomplemented
169#385—216no—
170#380—28no—
171#380—42no—
172C4×C4⋊C4—28no—
173C4×C4⋊C4—28no—
174C4×C4⋊C4—216no—
175C4×C4⋊C4C2×C418yescomplemented
176C4×C22⋊C4—28no—
177C4×C22⋊C4—216no—
178C4×C22⋊C4—42no—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C25C2414yes—
196C25C2411yescharacteristic
197C25C2411yescharacteristic
198C22×D4—28no—
199C22×D4—28no—
200C22×D4—28no—
201C22×D4—28no—
202C22×D4—28no—
203C22×D4—28no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—28no—
208C22×D4—28no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—41no—
215C22×D4—41no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—42no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4C22×C418yes—
231C22×D4C22×C4116yes—
232C22×D4C22×C4116yes—
233C22×D4C22×C418yes—
234C22×D4C22×C418yes—
235C22×D4C22×C414yes—
236C22×D4C2×D414yes—
237C22×D4#4114yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—28no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—28no—
254C23×C4—28no—
255C23×C4—28no—
256C23×C4—41no—
257C23×C4—42no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—42no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—42no—
267C23×C4C22×C414yes—
268C23×C4C22×C414yes—
269C23×C4C2×D414yes—
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2414yes—
278C23×C4C2414yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282#127—264no—
283#127—416no—
284#121—264no—
285#121—264no—
286C4×D4—432no—
287C4×D4—416no—
288C4×D4—464no—
289C4×D4—464no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4C22×C414yes—
306C2×C4⋊C4C22×C418yes—
307C2×C4⋊C4C2×D418yes—
308C2×C4⋊C4C2×D4116yes—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4#4118yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C22×C4116yes—
357C2×C22⋊C4C22×C4116yes—
358C2×C22⋊C4C22×C414yes—
359C2×C22⋊C4C22×C414yes—
360C2×C22⋊C4C2×D418yes—
361C2×C22⋊C4C2×D414yes—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—28no—
371C2×C42—28no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—416no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42—42no—
381C2×C42C22×C414yes—
382C2×C42C22×C418yes—
383C2×C42C2×D418yes—
384#95—28no—
385#95—24no—
386#95—24no—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—28no—
392#95—24no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—44no—
397#95C22×C418yes—
398#95C2×D4116yes—
399#95C2×D418yes—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24C23×C418yes—
431C24C23×C412yes—
432C24C23×C412yes—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C2×#4112yes—
436C24C2×#4112yes—
437C24C2511yescharacteristic
438C2×D4—232no—
439C2×D4—232no—
440C2×D4—232no—
441C2×D4—232no—
442C2×D4—216no—
443C2×D4—216no—
444C2×D4—216no—
445C2×D4—216no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—416no—
449C2×D4—416no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—416no—
457C2×D4—416no—
458C2×D4—416no—
459C2×D4—416no—
460C2×D4—416no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—416no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—84no—
471C2×D4—84no—
472C2×D4—84no—
473C2×D4—84no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—88no—
477C2×D4C4×D4116yescomplemented
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—216no—
521C22×C4—216no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—416no—
546C22×C4—416no—
547C22×C4—416no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—88no—
561C22×C4—88no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4C23×C412yes—
567C22×C4C23×C412yes—
568C22×C4C23×C412yes—
569C22×C4C23×C418yes—
570C22×C4C23×C412yes—
571C22×C4C23×C412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D418yes—
574C22×C4C22×D414yes—
575C22×C4C22×D412yes—
576C22×C4C22×D418yes—
577C22×C4C22×D414yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4118yes—
582C22×C4C2×#4114yes—
583C22×C4H(5,𝔽2)14yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C4⋊C4—216no—
587C4⋊C4—232no—
588C4⋊C4—44no—
589C4⋊C4—416no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4C4×D4132yescomplemented
593C22⋊C4—232no—
594C22⋊C4—232no—
595C22⋊C4—216no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—416no—
600C22⋊C4—416no—
601C22⋊C4—48no—
602C22⋊C4—416no—
603C22⋊C4—416no—
604C22⋊C4—44no—
605C22⋊C4—416no—
606C22⋊C4—88no—
607C22⋊C4—88no—
608C22⋊C4—84no—
609C22⋊C4—88no—
610C42—216no—
611C42—28no—
612C42—216no—
613C42—48no—
614C42—416no—
615C42—416no—
616C42—48no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23C2×C4×D414yes—
697C23C2×C4×D414yes—
698C23C24×C411yescharacteristic
699C23C23×D412yes—
700C23C23×D411yescharacteristic
701C23C22×#4112yes—
702C23C22×#4111yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)12yes—
706C23#58511yescharacteristic
707C23#58511yescharacteristic
708C23#58512yes—
709D4—416no—
710D4—464no—
711D4—464no—
712D4—432no—
713D4—816no—
714D4—816no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—832no—
788C2×C4—816no—
789C2×C4C2×C4×D414yes—
790C2×C4C2×C4×D4116yes—
791C2×C4C2×C4×D418yes—
792C2×C4#51814yes—
793C2×C4D4218yes—
794C2×C4D4214yes—
795C2×C4#55018yes—
796C2×C4#55914yes—
797C22—28no—
798C22—28no—
799C22—24no—
800C22—24no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—48no—
820C22—48no—
821C22—48no—
822C22—48no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—84no—
827C22—84no—
828C22—84no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—84no—
833C22—84no—
834C22C22×C4×D412yes—
835C22C22×C4×D411yescharacteristic
836C22C2×#51811yescharacteristic
837C22#342811yescharacteristic
838C22C4×H(5,𝔽2)12yes—
839C22C2×D4211yescharacteristic
840C22C2×D4212yes—
841C22C2×#55012yes—
842C22D4×#4112yes—
843C22D4×#4112yes—
844C22C2×#55911yescharacteristic
845C22#348112yes—
846C22#348712yes—
847C22#348812yes—
848C22#349611yescharacteristic
849C22#349611yescharacteristic
850C22#350511yescharacteristic
851C22#350511yescharacteristic
852C22#351712yes—
853C22#352412yes—
854C22#353711yescharacteristic
855C22#354011yescharacteristic
856C22#354612yes—
857C4—216no—
858C4—28no—
859C4—24no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—48no—
864C4—44no—
865C4—44no—
866C4—84no—
867C4—82no—
868C4#236618yescomplemented
869C2—44no—
870C2—44no—
871C2—88no—
872C2C2×#236611yescharacteristic
873C2C4×D4212yes—
874C2#3420511yescharacteristic
875C2#3429512yes—
876C2#3441111yescharacteristic
877C2#5899711yescharacteristic
878C2#5900111yescharacteristic
879C2#5905112yes—
880C2#5905312yes—
881C2#5962811yescharacteristic
882C2#5963211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2541C2
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×#2366C2semidirect
3. C2×#2361C2semidirect
4. C2×C4×#121C2semidirect
5. #14521C2semidirect
6. #14419C2semidirect
7. #14187C2semidirect
8. #14171C2semidirect
9. #14036C2semidirect
10. #14025C2semidirect
11. #13998C2semidirect
12. #13998C2semidirect
13. #13872C2semidirect
14. #13821C2semidirect
15. C4×#386C2semidirect
26. #2541C4semidirect
95. C2×#127C2×C4semidirect
96. C2×#127C2×C4semidirect
101. C2×#121C2×C4semidirect
102. C2×#121C2×C4semidirect
114. C2×C4×D4C2×C4semidirect
150. #392C2×C4semidirect
151. #392C2×C4semidirect
157. #390C2×C4semidirect
159. #389D4semidirect
168. #386D4semidirect
175. C4×C4⋊C4C2×C4semidirect
477. C2×D4C4×D4semidirect
592. C4⋊C4C4×D4semidirect
868. C4#2366semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#23662
C2×#23612
C2×C4×#1212
#145212
#144192
#141872
#141712
#140362
#140252
#139982
#138722
#138212
C4×#3862