Finite Group Databasebeta

← #153900

Subgroups — #153900

Order 512.

3866 conjugacy classes of subgroups.

The subgroup lattice has 1129 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1440C211yesmaximal, characteristic
2C2×#1439C211yesmaximal, characteristic
3C2×#1437C212yesmaximal
4C2×#1437C212yesmaximal
5C2×#1437C211yesmaximal, characteristic
6C2×#1436C212yesmaximal, complemented
7C2×C4×#95C212yesmaximal, complemented
8#7556C212yesmaximal, complemented
9#7554C212yesmaximal, complemented
10C23×C4⋊C4C2211yescharacteristic
11C23×C22⋊C4C2212yes—
12C23×C22⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C42C2212yes—
17C23×C42C2212yes—
18C23×C42C2211yescharacteristic
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31#1440C418yescomplemented
32#1439C418yescomplemented
33#1437—28no—
34#1437—28no—
35#1437C418yescomplemented
36#1436—28no—
37C4×#95—28no—
38C26C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2311yescharacteristic
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2312yes—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—41no—
50C22×C4⋊C4—41no—
51C22×C4⋊C4C2×C414yes—
52C22×C22⋊C4—24no—
53C22×C22⋊C4—24no—
54C22×C22⋊C4—24no—
55C22×C22⋊C4—24no—
56C22×C22⋊C4—24no—
57C22×C22⋊C4—24no—
58C22×C22⋊C4—24no—
59C22×C22⋊C4—24no—
60C22×C22⋊C4—24no—
61C22×C22⋊C4—24no—
62C22×C22⋊C4—24no—
63C22×C22⋊C4—24no—
64C22×C22⋊C4—24no—
65C22×C22⋊C4—24no—
66C22×C22⋊C4—41no—
67C22×C22⋊C4—41no—
68C22×C22⋊C4—41no—
69C22×C22⋊C4—41no—
70C22×C22⋊C4—41no—
71C22×C22⋊C4—41no—
72C22×C22⋊C4—42no—
73C22×C22⋊C4—42no—
74C22×C22⋊C4—41no—
75C22×C22⋊C4—41no—
76C22×C22⋊C4C2×C418yes—
77C22×C22⋊C4C2×C418yes—
78C22×C22⋊C4C2×C414yes—
79C22×C22⋊C4C2×C414yes—
80C22×C22⋊C4C2×C414yes—
81C22×C22⋊C4C2×C414yes—
82C22×C22⋊C4C2×C414yes—
83C22×C42—24no—
84C22×C42—24no—
85C22×C42—24no—
86C22×C42—24no—
87C22×C42—24no—
88C22×C42—24no—
89C22×C42—24no—
90C22×C42—24no—
91C22×C42—24no—
92C22×C42—24no—
93C22×C42—24no—
94C22×C42—24no—
95C22×C42—41no—
96C22×C42—41no—
97C22×C42—42no—
98C22×C42—42no—
99C22×C42—42no—
100C22×C42—42no—
101C22×C42C2×C414yes—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—41no—
123C2×#95—41no—
124C2×#95—41no—
125C2×#95—41no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95C2×C418yes—
131C2×#95C2×C418yes—
132C2×#95C2×C418yes—
133C2×#95C2×C418yes—
134C2×#95C2×C414yes—
135C2×#95C2×C414yes—
136C2×#95D418yes—
137C2×#95D418yes—
138C25—22no—
139C25—22no—
140C25—22no—
141C25—22no—
142C25—22no—
143C25—22no—
144C25—22no—
145C25—22no—
146C25—22no—
147C25—22no—
148C25—21no—
149C25—21no—
150C25—21no—
151C25—21no—
152C25—22no—
153C25—22no—
154C25C22×C412yes—
155C25C22×C412yes—
156C25C22×C412yes—
157C25C2411yescharacteristic
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
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—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4C22×C414yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C22×C412yes—
250C23×C4C22×C412yes—
251C23×C4C22×C414yes—
252C23×C4C22×C414yes—
253C23×C4C22×C414yes—
254C23×C4C22×C414yes—
255C23×C4C22×C414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4#4114yes—
270C2×C4⋊C4—216no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—48no—
274C2×C4⋊C4—44no—
275C2×C22⋊C4—216no—
276C2×C22⋊C4—216no—
277C2×C22⋊C4—216no—
278C2×C22⋊C4—216no—
279C2×C22⋊C4—216no—
280C2×C22⋊C4—216no—
281C2×C22⋊C4—216no—
282C2×C22⋊C4—44no—
283C2×C22⋊C4—44no—
284C2×C22⋊C4—44no—
285C2×C22⋊C4—44no—
286C2×C22⋊C4—44no—
287C2×C22⋊C4—44no—
288C2×C22⋊C4—48no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4—48no—
293C2×C22⋊C4—44no—
294C2×C22⋊C4—48no—
295C2×C22⋊C4—48no—
296C2×C22⋊C4—48no—
297C2×C22⋊C4—48no—
298C2×C22⋊C4—44no—
299C2×C22⋊C4—48no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—48no—
302C2×C22⋊C4—48no—
303C2×C22⋊C4—48no—
304C2×C22⋊C4—48no—
305C2×C22⋊C4C42116yescomplemented
306C2×C42—216no—
307C2×C42—216no—
308C2×C42—216no—
309C2×C42—44no—
310C2×C42—44no—
311C2×C42—48no—
312C2×C42—44no—
313C2×C42—48no—
314C2×C42—48no—
315C2×C42—48no—
316C2×C42—48no—
317C2×C42—48no—
318C2×C42—48no—
319C2×C42—48no—
320C2×C42—48no—
321C2×C42—48no—
322C2×C42—48no—
323C2×C42—48no—
324C2×C42—48no—
325#95—216no—
326#95—216no—
327#95—216no—
328#95—216no—
329#95—216no—
330#95—216no—
331#95—44no—
332#95—44no—
333#95—48no—
334#95—48no—
335#95—48no—
336#95—48no—
337C24—24no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—24no—
342C24—24no—
343C24—24no—
344C24—22no—
345C24—24no—
346C24—22no—
347C24—24no—
348C24—24no—
349C24—24no—
350C24—24no—
351C24—24no—
352C24—24no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—24no—
362C24—24no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24—42no—
368C24—42no—
369C24—42no—
370C24—42no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24—42no—
387C24—41no—
388C24—41no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—41no—
403C24—41no—
404C24—42no—
405C24—41no—
406C24—41no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—41no—
421C24—41no—
422C24—42no—
423C24C2×C4214yes—
424C24C23×C411yescharacteristic
425C24C23×C411yescharacteristic
426C24C23×C411yescharacteristic
427C24C22×D412yes—
428C24C22×D412yes—
429C24C2×#4112yes—
430C24C2×#4112yes—
431C24C2×#4112yes—
432C24C2×#4112yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24C2×#4112yes—
436C24C2×#4112yes—
437C24H(5,𝔽2)11yescharacteristic
438C24H(5,𝔽2)11yescharacteristic
439C24H(5,𝔽2)11yescharacteristic
440C24H(5,𝔽2)11yescharacteristic
441C24H(5,𝔽2)12yes—
442C242−1+412yes—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
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—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—41no—
632C22×C4—42no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4C2×C4214yes—
687C22×C4C2×C4214yes—
688C22×C4#11718yes—
689C22×C4C4×D418yes—
690C22×C4C4×D418yes—
691C22×C4C4×D418yes—
692C22×C4C4×D418yes—
693C22×C4C4×D418yes—
694C22×C4C4×D418yes—
695C22×C4#12118yes—
696C22×C4#12318yes—
697C22×C4#12418yes—
698C22×C4#12618yes—
699C4⋊C4—416no—
700C22⋊C4—416no—
701C22⋊C4—416no—
702C22⋊C4—432no—
703C22⋊C4—416no—
704C22⋊C4—432no—
705C42—416no—
706C42—432no—
707C42—432no—
708C23—24no—
709C23—28no—
710C23—28no—
711C23—24no—
712C23—24no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—44no—
722C23—44no—
723C23—42no—
724C23—42no—
725C23—44no—
726C23—42no—
727C23—42no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—42no—
741C23—42no—
742C23—44no—
743C23—44no—
744C23—42no—
745C23—42no—
746C23—44no—
747C23—44no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—82no—
764C23—82no—
765C23—82no—
766C23—82no—
767C23—82no—
768C23—82no—
769C23—82no—
770C23—82no—
771C23—82no—
772C23—82no—
773C23—82no—
774C23—82no—
775C23—82no—
776C23—82no—
777C23—82no—
778C23—82no—
779C23—82no—
780C23—82no—
781C23—82no—
782C23—82no—
783C23—82no—
784C23—82no—
785C23—82no—
786C23—82no—
787C23—82no—
788C23—82no—
789C23—82no—
790C23—82no—
791C23—82no—
792C23—82no—
793C23—82no—
794C23—82no—
795C23C22×C4211yescharacteristic
796C23C2×#11712yes—
797C23C2×C4×D412yes—
798C23C2×C4×D412yes—
799C23C2×C4×D412yes—
800C23C2×C4×D412yes—
801C23C2×C4×D412yes—
802C23C2×C4×D412yes—
803C23C4×#4111yescharacteristic
804C23C4×#4112yes—
805C23C4×#4112yes—
806C23C4×#4112yes—
807C23C4×#4112yes—
808C23C4×#4112yes—
809C23C4×#4111yescharacteristic
810C23C4×#4112yes—
811C23C4×#4112yes—
812C23#51811yescharacteristic
813C23#51811yescharacteristic
814C23#51811yescharacteristic
815C23#51811yescharacteristic
816C23#51811yescharacteristic
817C23#51811yescharacteristic
818C23#51811yescharacteristic
819C23#51911yescharacteristic
820C23#52012yes—
821C23#52012yes—
822C23C2×#12112yes—
823C23C2×#12312yes—
824C23#52512yes—
825C23#52512yes—
826C23C2×#12412yes—
827C23C2×#12612yes—
828C23#52912yes—
829C23#52912yes—
830C23#52912yes—
831C23#52912yes—
832C23#52912yes—
833C23#52912yes—
834C23#52912yes—
835C23#52912yes—
836C23#53212yes—
837C23#53212yes—
838C23#53812yes—
839C23#53812yes—
840C23#53912yes—
841C23#53912yes—
842C23#54012yes—
843C23#54012yes—
844C23#54212yes—
845C23#54212yes—
846C23D4211yescharacteristic
847C23D4211yescharacteristic
848C23D4212yes—
849C23#54612yes—
850C23#54612yes—
851C23#54612yes—
852C23#54612yes—
853C23#54612yes—
854C23#54612yes—
855C23#54712yes—
856C23#54712yes—
857C23#54812yes—
858C23#54812yes—
859C23#55012yes—
860C23#55012yes—
861C23#55111yescharacteristic
862C23#55112yes—
863C23#55111yescharacteristic
864C23#55111yescharacteristic
865C23#55111yescharacteristic
866C23#55112yes—
867C23#55212yes—
868C23#55212yes—
869C23#55312yes—
870C23#55312yes—
871C23#55312yes—
872C23#55312yes—
873C23#55312yes—
874C23#55312yes—
875C23#55512yes—
876C23#55512yes—
877C23#55612yes—
878C23#55612yes—
879C23#55912yes—
880C23#55911yescharacteristic
881C23#55911yescharacteristic
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—44no—
937C2×C4—44no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—44no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—82no—
986C2×C4—82no—
987C2×C4—82no—
988C2×C4—82no—
989C2×C4—82no—
990C2×C4—82no—
991C2×C4—82no—
992C2×C4—82no—
993C2×C4#388116yes—
994C22—44no—
995C22—44no—
996C22—48no—
997C22—44no—
998C22—48no—
999C22—84no—
1000C22—84no—
1001C22—84no—
1002C22—84no—
1003C22—84no—
1004C22—82no—
1005C22—84no—
1006C22—84no—
1007C22—84no—
1008C22—84no—
1009C22—82no—
1010C22—82no—
1011C22—84no—
1012C22—82no—
1013C22C4×#11711yescharacteristic
1014C22C42×D412yes—
1015C22C42×D412yes—
1016C22#227311yescharacteristic
1017C22#227411yescharacteristic
1018C22C2×#38812yes—
1019C22#229012yes—
1020C22#229312yes—
1021C22#229812yes—
1022C22C4×#12112yes—
1023C22C4×#12112yes—
1024C22C4×#12312yes—
1025C22C4×#12312yes—
1026C22C4×#12412yes—
1027C22C4×#12412yes—
1028C22C4×#12612yes—
1029C22C4×#12612yes—
1030C22#231812yes—
1031C22#231912yes—
1032C22#233211yescharacteristic
1033C22#233211yescharacteristic
1034C22#233311yescharacteristic
1035C22#233311yescharacteristic
1036C22#233512yes—
1037C22#233512yes—
1038C22#235811yescharacteristic
1039C22#235811yescharacteristic
1040C22#235811yescharacteristic
1041C22#235811yescharacteristic
1042C22#235812yes—
1043C22#235912yes—
1044C22#235912yes—
1045C22#236112yes—
1046C22#236112yes—
1047C22#236212yes—
1048C22#236212yes—
1049C22#236312yes—
1050C22#236312yes—
1051C22#236312yes—
1052C22#236312yes—
1053C22#236412yes—
1054C22#236412yes—
1055C22#236611yescharacteristic
1056C22#236611yescharacteristic
1057C22#236712yes—
1058C22#236712yes—
1059C22#237211yescharacteristic
1060C22#237211yescharacteristic
1061C22#237312yes—
1062C22#237312yes—
1063C22#237411yescharacteristic
1064C22#237411yescharacteristic
1065C22#237411yescharacteristic
1066C22#237411yescharacteristic
1067C22#237412yes—
1068C22#242412yes—
1069C22#242512yes—
1070C22#242612yes—
1071C22#242812yes—
1072C22#244312yes—
1073C22#244412yes—
1074C22#244512yes—
1075C22#244812yes—
1076C22#247112yes—
1077C22#247212yes—
1078C22#247412yes—
1079C22#247612yes—
1080C22#247912yes—
1081C22#248112yes—
1082C22#248812yes—
1083C22#249012yes—
1084C22#249112yes—
1085C22#251012yes—
1086C22#251212yes—
1087C22#251312yes—
1088C22#252612yes—
1089C22#252912yes—
1090C22#253112yes—
1091C22#253212yes—
1092C22#255712yes—
1093C22#255812yes—
1094C22#255912yes—
1095C22#256012yes—
1096C22#259412yes—
1097C22#259512yes—
1098C22#259612yes—
1099C22#259712yes—
1100C4—216no—
1101C4—44no—
1102C4—44no—
1103C4—48no—
1104C4—48no—
1105C4—48no—
1106C4—48no—
1107C4—84no—
1108C2—84no—
1109C2C4×#38812yes—
1110C2#1378011yescharacteristic
1111C2#1382312yes—
1112C2#1382411yescharacteristic
1113C2#1382411yescharacteristic
1114C2#1414012yes—
1115C2#1414112yes—
1116C2#1414812yes—
1117C2#1415812yes—
1118C2#1419312yes—
1119C2#1419411yescharacteristic
1120C2#1419512yes—
1121C2#1419612yes—
1122C2#1420512yes—
1123C2#1420612yes—
1124C2#1420711yescharacteristic
1125C2#1423211yescharacteristic
1126C2#1423312yes—
1127C2#1425311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC23C22×C42
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C2×#1436C2semidirect
7. C2×C4×#95C2semidirect
8. #7556C2semidirect
9. #7554C2semidirect
31. #1440C4semidirect
32. #1439C4semidirect
35. #1437C4semidirect
305. C2×C22⋊C4C42semidirect

Maximal subgroups

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

subgroupindex
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×C4×#952
#75562
#75542