Finite Group Databasebeta

← #154124

Subgroups — #154124

Order 512.

5526 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#117C211yesmaximal, characteristic
2C2×#1441C212yesmaximal, complemented
3C2×#1439C212yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#1434C211yesmaximal, characteristic, complemented
6C2×C22⋊#95C212yesmaximal
7#7557C212yesmaximal, complemented
8#7555C212yesmaximal
9#7554C212yesmaximal, complemented
10C25×C4C2211yescharacteristic
11C22×#117—24no—
12C22×#117—24no—
13C22×#117—28no—
14C22×#117—28no—
15C22×#117C418yescomplemented
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2212yes—
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2214yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2214yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2214yes—
30C22×#95C2214yes—
31C22×#95C2212yes—
32#1441—28no—
33#1439—28no—
34C4⋊#95—24no—
35#1434—24no—
36C22⋊#95—28no—
37C26C2311yescharacteristic
38C24×C4—24no—
39C24×C4—24no—
40C24×C4—22no—
41C24×C4—22no—
42C24×C4—24no—
43C24×C4—22no—
44C24×C4—22no—
45C24×C4—24no—
46C24×C4C2×C414yes—
47C24×C4D414yes—
48C24×C4Q814yes—
49C24×C4C2314yes—
50C24×C4C2314yes—
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C24×C4C2311yescharacteristic
57C2×#117—264no—
58C2×#117—264no—
59C2×#117—232no—
60C2×#117—232no—
61C2×#117—232no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—28no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—44no—
74C22×C4⋊C4C2×C414yes—
75C22×C4⋊C4C2×C414yes—
76C22×C4⋊C4D418yes—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—22no—
79C22×C22⋊C4—22no—
80C22×C22⋊C4—24no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—24no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—28no—
85C22×C22⋊C4—28no—
86C22×C22⋊C4—28no—
87C22×C22⋊C4—28no—
88C22×C22⋊C4—28no—
89C22×C22⋊C4—44no—
90C22×C22⋊C4—44no—
91C22×C22⋊C4C2×C414yes—
92C22×C22⋊C4C2×C414yes—
93C22×C22⋊C4D418yes—
94C22×C42—24no—
95C22×C42—24no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—24no—
99C22×C42—24no—
100C22×C42C2×C414yes—
101C22×C42C2×C414yes—
102C22×C42D414yes—
103C22×C42D414yes—
104C2×#95—24no—
105C2×#95—28no—
106C2×#95—28no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—28no—
114C2×#95—24no—
115C2×#95—28no—
116C2×#95—24no—
117C2×#95—28no—
118C2×#95—28no—
119C2×#95—28no—
120C2×#95—28no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—44no—
124C2×#95—44no—
125C2×#95—44no—
126C25—21no—
127C25—21no—
128C25—22no—
129C25—24no—
130C25—24no—
131C25—21no—
132C25—21no—
133C25—22no—
134C25—22no—
135C25—22no—
136C25—22no—
137C25—22no—
138C25C22×C412yes—
139C25C2×D414yes—
140C25C2×D412yes—
141C25C2×Q812yes—
142C25#4114yes—
143C25C2411yescharacteristic
144C23×C4—216no—
145C23×C4—216no—
146C23×C4—216no—
147C23×C4—216no—
148C23×C4—216no—
149C23×C4—216no—
150C23×C4—216no—
151C23×C4—216no—
152C23×C4—28no—
153C23×C4—28no—
154C23×C4—216no—
155C23×C4—216no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—24no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—28no—
170C23×C4—28no—
171C23×C4—28no—
172C23×C4—28no—
173C23×C4—28no—
174C23×C4—28no—
175C23×C4—216no—
176C23×C4—28no—
177C23×C4—28no—
178C23×C4—216no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—24no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4C4⋊C4116yescomplemented
225C23×C4C22×C412yes—
226C23×C4C22×C412yes—
227C23×C4C22×C412yes—
228C23×C4C22×C412yes—
229C23×C4C22×C412yes—
230C23×C4C22×C412yes—
231C23×C4C2×D412yes—
232C23×C4C2×D412yes—
233C23×C4C2×D414yes—
234C23×C4C2×D414yes—
235C23×C4C2×D412yes—
236C23×C4C2×D414yes—
237C23×C4C2×D412yes—
238C23×C4C2×D414yes—
239C23×C4C2×D414yes—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×Q812yes—
245C23×C4C2×Q812yes—
246C23×C4#4118yes—
247C23×C4#4118yes—
248C23×C4#4112yes—
249C23×C4#4112yes—
250C23×C4#4114yes—
251#117—2256no—
252C2×C4⋊C4—216no—
253C2×C4⋊C4—216no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—28no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—216no—
260C2×C4⋊C4—216no—
261C2×C4⋊C4—216no—
262C2×C4⋊C4—416no—
263C2×C4⋊C4—416no—
264C2×C4⋊C4—48no—
265C2×C4⋊C4—48no—
266C2×C4⋊C4C22⋊C4116yescomplemented
267C2×C22⋊C4—216no—
268C2×C22⋊C4—216no—
269C2×C22⋊C4—28no—
270C2×C22⋊C4—28no—
271C2×C22⋊C4—28no—
272C2×C22⋊C4—28no—
273C2×C22⋊C4—28no—
274C2×C22⋊C4—216no—
275C2×C22⋊C4—216no—
276C2×C22⋊C4—232no—
277C2×C22⋊C4—416no—
278C2×C22⋊C4—416no—
279C2×C22⋊C4—416no—
280C2×C22⋊C4—416no—
281C2×C22⋊C4—416no—
282C2×C22⋊C4—416no—
283C2×C22⋊C4C22⋊C4116yes—
284C2×C42—216no—
285C2×C42—216no—
286C2×C42—28no—
287C2×C42—28no—
288C2×C42—28no—
289C2×C42—28no—
290C2×C42—28no—
291C2×C42—216no—
292C2×C42—216no—
293C2×C42C22⋊C4116yescomplemented
294#95—216no—
295#95—416no—
296#95—416no—
297#95—48no—
298#95—48no—
299#95—48no—
300#95—48no—
301#95—416no—
302C24—22no—
303C24—22no—
304C24—22no—
305C24—22no—
306C24—24no—
307C24—24no—
308C24—24no—
309C24—24no—
310C24—24no—
311C24—24no—
312C24—22no—
313C24—22no—
314C24—24no—
315C24—22no—
316C24—22no—
317C24—24no—
318C24—28no—
319C24—24no—
320C24—24no—
321C24—24no—
322C24—24no—
323C24—24no—
324C24—24no—
325C24—28no—
326C24—24no—
327C24—24no—
328C24—24no—
329C24—24no—
330C24—28no—
331C24—28no—
332C24—28no—
333C24—28no—
334C24—28no—
335C24—28no—
336C24—28no—
337C24—28no—
338C24—42no—
339C24—42no—
340C24—44no—
341C24—44no—
342C24—42no—
343C24—42no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—42no—
349C24—42no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—42no—
354C24—44no—
355C24—44no—
356C24—44no—
357C24—44no—
358C24—44no—
359C24—44no—
360C24—44no—
361C24—44no—
362C24C2×C22⋊C414yes—
363C24C2×C4⋊C414yes—
364C24#11714yes—
365C24#12118yes—
366C24C22⋊Q818yes—
367C24C23×C411yescharacteristic
368C24C22×D411yescharacteristic
369C24C22×D411yescharacteristic
370C24C22×D412yes—
371C24C22×D412yes—
372C24C22×D411yescharacteristic
373C24C22×Q811yescharacteristic
374C24C2×#4111yescharacteristic
375C24C2×#4111yescharacteristic
376C24C2×#4112yes—
377C24C2×#4112yes—
378C24C2×#4114yes—
379C24C2×#4114yes—
380C24H(5,𝔽2)12yes—
381C24H(5,𝔽2)12yes—
382C242−1+412yes—
383C242−1+412yes—
384C22×C4—232no—
385C22×C4—264no—
386C22×C4—264no—
387C22×C4—264no—
388C22×C4—264no—
389C22×C4—232no—
390C22×C4—232no—
391C22×C4—232no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—232no—
438C22×C4—232no—
439C22×C4—232no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
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—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4C2×C22⋊C414yes—
556C22×C4C2×C22⋊C414yes—
557C22×C4C2×C22⋊C414yes—
558C22×C4C2×C22⋊C414yes—
559C22×C4C2×C22⋊C414yes—
560C22×C4C2×C22⋊C414yes—
561C22×C4C2×C22⋊C414yes—
562C22×C4C2×C22⋊C414yes—
563C22×C4C2×C4⋊C414yes—
564C22×C4C2×C4⋊C414yes—
565C22×C4#11714yes—
566C22×C4#11714yes—
567C22×C4#12018yes—
568C22×C4#12018yes—
569C22×C4#12114yes—
570C22×C4#12114yes—
571C22×C4#12118yes—
572C22×C4C22⋊Q814yes—
573C22×C4C22⋊Q814yes—
574C22×C4C22⋊Q818yes—
575C4⋊C4—232no—
576C4⋊C4—232no—
577C4⋊C4—432no—
578C22⋊C4—232no—
579C22⋊C4—232no—
580C22⋊C4—464no—
581C42—232no—
582C42—232no—
583C23—28no—
584C23—28no—
585C23—28no—
586C23—28no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—28no—
591C23—28no—
592C23—216no—
593C23—216no—
594C23—216no—
595C23—216no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—28no—
603C23—42no—
604C23—42no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—48no—
611C23—44no—
612C23—44no—
613C23—48no—
614C23—44no—
615C23—44no—
616C23—42no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—48no—
629C23—48no—
630C23—48no—
631C23—48no—
632C23—44no—
633C23—44no—
634C23—48no—
635C23—48no—
636C23—48no—
637C23—48no—
638C23—48no—
639C23—48no—
640C23—48no—
641C23—48no—
642C23—48no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—44no—
647C23#38018yes—
648C23C22×C22⋊C411yescharacteristic
649C23C22×C22⋊C411yescharacteristic
650C23C22×C22⋊C411yescharacteristic
651C23C22×C4⋊C411yescharacteristic
652C23C2×#11711yescharacteristic
653C23C2×#11711yescharacteristic
654C23C2×#11711yescharacteristic
655C23C4×#4112yes—
656C23C4×#4112yes—
657C23#52012yes—
658C23#52012yes—
659C23C2×#12012yes—
660C23C2×#12012yes—
661C23C2×#12111yescharacteristic
662C23C2×#12111yescharacteristic
663C23C2×#12112yes—
664C23C2×#12112yes—
665C23C2×C22⋊Q811yescharacteristic
666C23C2×C22⋊Q811yescharacteristic
667C23C2×C22⋊Q812yes—
668C23C2×C22⋊Q812yes—
669C23#52512yes—
670C23#52512yes—
671C23#52512yes—
672C23#52512yes—
673C23#52512yes—
674C23#52512yes—
675C23#52512yes—
676C23#52512yes—
677C23#52514yes—
678C23#52914yes—
679C23#52914yes—
680C23#53212yes—
681C23#53212yes—
682C23#53314yes—
683C23#53511yescharacteristic
684C23#53511yescharacteristic
685C23#53512yes—
686C23#53611yescharacteristic
687C23#53611yescharacteristic
688C23#53612yes—
689C23#53712yes—
690C23#53712yes—
691C23#54012yes—
692C23#54112yes—
693C23#54212yes—
694C23#54212yes—
695C23#54412yes—
696C23#54412yes—
697C23#54614yes—
698C23#54614yes—
699C23#54614yes—
700C23#54714yes—
701C23#54714yes—
702C23#54714yes—
703C23#54814yes—
704C23#55014yes—
705C23#55114yes—
706C23#55114yes—
707C23#55214yes—
708C23#55214yes—
709C23#55214yes—
710C23#55314yes—
711C23#55514yes—
712C23#55614yes—
713C2×C4—2128no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—216no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4—84no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4—84no—
795C2×C4#37918yes—
796C2×C4#38018yes—
797C2×C4#38018yes—
798C22—28no—
799C22—216no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—48no—
804C22—416no—
805C22—416no—
806C22—48no—
807C22—48no—
808C22—44no—
809C22—44no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—44no—
814C22—44no—
815C22C2×#37911yescharacteristic
816C22C2×#38011yescharacteristic
817C22C2×#38011yescharacteristic
818C22C2×#38011yescharacteristic
819C22#228011yescharacteristic
820C22#228011yescharacteristic
821C22#228011yescharacteristic
822C22#229612yes—
823C22#229711yescharacteristic
824C22#229711yescharacteristic
825C22#229812yes—
826C22#231111yescharacteristic
827C22#231111yescharacteristic
828C22#231412yes—
829C22#231712yes—
830C22#233912yes—
831C22#233912yes—
832C22#233912yes—
833C22#234112yes—
834C22#234312yes—
835C22#234312yes—
836C22#234612yes—
837C22#234712yes—
838C22#239212yes—
839C22#239212yes—
840C22#239612yes—
841C22#239612yes—
842C22#240412yes—
843C22#240612yes—
844C22#240714yes—
845C22#241114yes—
846C22#241314yes—
847C22#241414yes—
848C22#241514yes—
849C22#243014yes—
850C22#243112yes—
851C22#243212yes—
852C22#243814yes—
853C22#243814yes—
854C22#243914yes—
855C22#244114yes—
856C22#247014yes—
857C22#247114yes—
858C22#247414yes—
859C22#247514yes—
860C22#247614yes—
861C22#247714yes—
862C22#247814yes—
863C22#247914yes—
864C22#259812yes—
865C22#259912yes—
866C22#260114yes—
867C22#260914yes—
868C22#261012yes—
869C22#261112yes—
870C22#261911yescharacteristic
871C22#262012yes—
872C22#262111yescharacteristic
873C22#262811yescharacteristic
874C22#262811yescharacteristic
875C22#262912yes—
876C22#284712yes—
877C22#284712yes—
878C22#284812yes—
879C22#284812yes—
880C4—28no—
881C4—28no—
882C4—28no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—88no—
887C4—88no—
888C2—48no—
889C2#1385211yescharacteristic
890C2#1393711yescharacteristic
891C2#1393811yescharacteristic
892C2#1394312yes—
893C2#1394412yes—
894C2#1395112yes—
895C2#1395611yescharacteristic
896C2#1395711yescharacteristic
897C2#1396212yes—
898C2#1434011yescharacteristic
899C2#1468011yescharacteristic
900C2#1488612yes—
901C2#1488712yes—
902C2#1489014yes—
903C2#1489114yes—
904C2#1489312yes—
905C2#1490712yes—
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1441C2semidirect
4. C2×C4⋊#95C2semidirect
5. C2×#1434C2semidirect
7. #7557C2semidirect
9. #7554C2semidirect
15. C22×#117C4semidirect
224. C23×C4C4⋊C4semidirect
266. C2×C4⋊C4C22⋊C4semidirect
293. C2×C42C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×#1172
C2×#14412
C2×#14392
C2×C4⋊#952
C2×#14342
C2×C22⋊#952
#75572
#75552
#75542