Finite Group Databasebeta

← #648052

Subgroups — #648052

Order 512.

5942 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2429C212yesmaximal, complemented
5C2×#2341C211yesmaximal, characteristic, complemented
6#15271C214yesmaximal, complemented
7#15268C214yesmaximal, complemented
8#15215C212yesmaximal, complemented
9#15126C212yesmaximal, complemented
10#14733C214yesmaximal, complemented
11#14185C214yesmaximal, complemented
12#14138C211yesmaximal, characteristic, complemented
13#14129C211yesmaximal, characteristic, complemented
14#13969C212yesmaximal, complemented
15C4×#379C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic, complemented
19C22×#124C2211yescharacteristic, complemented
20C2×#525—28no—
21C2×#525—216no—
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×#121C2212yes—
27C22×#120C2212yes—
28C22×C4×Q8C2212yescomplemented
29C22×C4×D4C2214yes—
30C22×#117C2211yescharacteristic
31#2848—28no—
32#2432—28no—
33#2429—216no—
34C2×#398C2214yescomplemented
35C2×#396C2214yes—
36C2×#394C2214yes—
37C2×#394C2214yes—
38#2341—28no—
39C2×#391C2212yescomplemented
40C2×#391C2211yescharacteristic, complemented
41C2×#390C2214yes—
42C2×#390C2211yescharacteristic, complemented
43C2×#390C2212yescomplemented
44C2×#389C2212yescomplemented
45C2×#389C2214yescomplemented
46C2×#388C2214yes—
47C2×#385C2214yes—
48C2×#385C2212yes—
49C2×#385C2214yescomplemented
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yescomplemented
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yescomplemented
60#1441C2214yescomplemented
61#1440C2214yes—
62#1440C2214yescomplemented
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1438C2214yes—
69#1438C2214yes—
70#1438C2214yes—
71#1437C2214yes—
72#1436C2214yescomplemented
73#1436C2212yescomplemented
74#1436C2212yescomplemented
75#1436C2214yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C26C2311yescharacteristic
82C22×#41—28no—
83C22×#41—24no—
84C22×#41—24no—
85C22×#41—44no—
86C22×#41D418yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2314yes—
91C23×D4C2312yes—
92C24×C4—28no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—44no—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C2×C4⋊Q8—28no—
103C2×C4⋊Q8—24no—
104C2×#124—24no—
105C2×#124—44no—
106#525—2128no—
107C2×#123—28no—
108C2×#123—216no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—44no—
117C2×C22⋊Q8D4116yes—
118C2×#121—28no—
119C2×#121—28no—
120C2×#121—28no—
121C2×#120—28no—
122C2×#120—216no—
123C2×C4×Q8—28no—
124C2×C4×Q8—28no—
125C2×C4×Q8—44no—
126C2×C4×D4—216no—
127C2×C4×D4—216no—
128C2×C4×D4—216no—
129C2×#117—24no—
130C2×#117—28no—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2314yes—
162#398—216no—
163#396—216no—
164#394—216no—
165#394—216no—
166#391—24no—
167#391—28no—
168#390—24no—
169#390—28no—
170#390—216no—
171#389—216no—
172#389—28no—
173#388—216no—
174#385—216no—
175#385—28no—
176#385—216no—
177#380—28no—
178#380—28no—
179#380D418yescomplemented
180#379—28no—
181#379—28no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—28no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—44no—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C25—24no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25C2412yes—
214C25C2411yescharacteristic
215C25C2412yes—
216C2×#41—232no—
217C2×#41—232no—
218C2×#41—416no—
219C2×#41—432no—
220C2×#41—432no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8C2×D418yes—
230C22×Q8C2×D414yes—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4C2×D414yes—
247C22×D4C2×D418yes—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—232no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—28no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—432no—
274C23×C4—432no—
275C23×C4—416no—
276C23×C4—416no—
277C23×C4C2×D418yes—
278C23×C4C2×D418yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2414yes—
287C23×C4C2414yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C4⋊Q8—416no—
295#124—416no—
296#123—264no—
297C22⋊Q8—264no—
298C22⋊Q8—432no—
299C22⋊Q8—416no—
300#121—264no—
301#120—264no—
302C4×Q8—432no—
303C4×D4—2128no—
304#117—232no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D4116yes—
331C2×C4⋊C4C2×D418yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D4116yes—
379C2×C22⋊C4C2×D418yes—
380C2×C22⋊C4#4118yescomplemented
381C2×C42—28no—
382C2×C42—24no—
383C2×C42—28no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—28no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—44no—
393#95—22no—
394#95—22no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—42no—
408#95—42no—
409#95C2×D418yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
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—22no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—44no—
456C24—48no—
457C24C22×D414yes—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C22×D414yes—
461C24C2×#4112yes—
462C24C2×#4114yes—
463C242−1+414yes—
464C24C2511yescharacteristic
465#41—4128no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—216no—
469C2×Q8—216no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—48no—
474C2×Q8—48no—
475C2×Q8#120116yes—
476C2×D4—232no—
477C2×D4—216no—
478C2×D4—216no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—48no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—416no—
491C2×D4—48no—
492C2×D4—48no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—28no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—216no—
535C22×C4—216no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—416no—
567C22×C4—416no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—4128no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4#121116yes—
582C22×C4C22×D418yes—
583C22×C4C22×D414yes—
584C22×C4C22×D418yes—
585C22×C4C22×D414yes—
586C22×C4C22×D418yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D412yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)14yes—
597C4⋊C4—216no—
598C4⋊C4—232no—
599C4⋊C4—216no—
600C4⋊C4—416no—
601C4⋊C4—416no—
602C4⋊C4—416no—
603C4⋊C4—416no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C22⋊C4—216no—
607C22⋊C4—232no—
608C22⋊C4—216no—
609C22⋊C4—232no—
610C22⋊C4—48no—
611C22⋊C4—416no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—416no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—88no—
623C42—216no—
624C42—416no—
625C42—44no—
626C42—44no—
627C42—48no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
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—28no—
662C23—28no—
663C23—416no—
664C23—416no—
665C23—432no—
666C23—432no—
667C23—432no—
668C23—416no—
669C23—432no—
670C23—432no—
671C23—432no—
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—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23C2×#12114yes—
713C23#54818yes—
714C23C23×D411yescharacteristic
715C23C23×D412yes—
716C23C23×D411yescharacteristic
717C23C22×#4111yescharacteristic
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+412yes—
721C23#58512yes—
722C23#58512yes—
723Q8—232no—
724Q8—88no—
725D4—432no—
726D4—464no—
727D4—416no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—232no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—432no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4C2×#12018yes—
801C2×C4C2×#12014yes—
802C2×C4C2×#12114yes—
803C2×C4C2×#12114yes—
804C2×C4#53414yes—
805C2×C4D4218yes—
806C2×C4#54618yes—
807C22—24no—
808C22—28no—
809C22—28no—
810C22—24no—
811C22—28no—
812C22—24no—
813C22—464no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
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—44no—
831C22—44no—
832C22—44no—
833C22—48no—
834C22—44no—
835C22—44no—
836C22—48no—
837C22—84no—
838C22—84no—
839C22—84no—
840C22—84no—
841C22C22×#12011yescharacteristic
842C22C22×#12111yescharacteristic
843C22#344411yescharacteristic
844C22C2×#53411yescharacteristic
845C22#345511yescharacteristic
846C22C2×D4212yes—
847C22C2×#54612yes—
848C22C2×#54812yes—
849C22D4×#4112yes—
850C22D4×#4112yes—
851C22D4×#4112yes—
852C22#348511yescharacteristic
853C22#348611yescharacteristic
854C22#348712yes—
855C22#348912yes—
856C22#348912yes—
857C22#349512yes—
858C22#350612yes—
859C22#352012yes—
860C22#353912yes—
861C22#354112yes—
862C4—24no—
863C4—28no—
864C4—44no—
865C4—48no—
866C4—44no—
867C4—48no—
868C4—44no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4#241018yes—
874C2—44no—
875C2—48no—
876C2—84no—
877C2C2×#241011yescharacteristic
878C2#3474311yescharacteristic
879C2#3563311yescharacteristic
880C2#3614812yes—
881C2#3642812yes—
882C2#3767112yes—
883C2#3988412yes—
884C2#5899912yes—
885C2#5900512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
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×#2848C2semidirect
3. C2×#2432C2semidirect
4. C2×#2429C2semidirect
5. C2×#2341C2semidirect
6. #15271C2semidirect
7. #15268C2semidirect
8. #15215C2semidirect
9. #15126C2semidirect
10. #14733C2semidirect
11. #14185C2semidirect
12. #14138C2semidirect
13. #14129C2semidirect
14. #13969C2semidirect
15. C4×#379C2semidirect
18. C22×C4⋊Q8C22semidirect
19. C22×#124C22semidirect
28. C22×C4×Q8C22semidirect
34. C2×#398C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
42. C2×#390C22semidirect
43. C2×#390C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
49. C2×#385C22semidirect
52. C2×#380C22semidirect
59. C2×C4×C22⋊C4C22semidirect
60. #1441C22semidirect
62. #1440C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
72. #1436C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. #1436C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
179. #380D4semidirect
380. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#28482
C2×#24322
C2×#24292
C2×#23412
#152712
#152682
#152152
#151262
#147332
#141852
#141382
#141292
#139692
C4×#3792