Finite Group Databasebeta

← #156308

Subgroups — #156308

Order 512.

3762 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1439C211yesmaximal, characteristic
2C2×#1439C211yesmaximal, characteristic
3C2×C22⋊#95C212yesmaximal
4C2×C22⋊#95C211yesmaximal, characteristic
5#7557C212yesmaximal, complemented
6#7557C212yesmaximal, complemented
7#7556C212yesmaximal, complemented
8#7556C212yesmaximal, complemented
9#7555C212yesmaximal
10C25×C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C22⋊C4C2212yes—
14C23×C22⋊C4C2212yes—
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2211yescharacteristic
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31#1439—24no—
32#1439C418yescomplemented
33C22⋊#95—28no—
34C22⋊#95—24no—
35C26C2311yescharacteristic
36C24×C4—22no—
37C24×C4—22no—
38C24×C4—24no—
39C24×C4—24no—
40C24×C4—41no—
41C24×C4—41no—
42C24×C4—42no—
43C24×C4—42no—
44C24×C4—41no—
45C24×C4—41no—
46C24×C4D414yes—
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2312yes—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—41no—
58C22×C4⋊C4—41no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—41no—
62C22×C4⋊C4—42no—
63C22×C4⋊C4—41no—
64C22×C4⋊C4C2×C414yescomplemented
65C22×C22⋊C4—24no—
66C22×C22⋊C4—24no—
67C22×C22⋊C4—22no—
68C22×C22⋊C4—24no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—24no—
71C22×C22⋊C4—24no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—41no—
75C22×C22⋊C4—41no—
76C22×C22⋊C4—41no—
77C22×C22⋊C4—41no—
78C22×C22⋊C4—42no—
79C22×C22⋊C4—42no—
80C22×C22⋊C4—42no—
81C22×C22⋊C4—42no—
82C22×C22⋊C4—41no—
83C22×C22⋊C4—41no—
84C22×C22⋊C4—41no—
85C22×C22⋊C4—41no—
86C22×C22⋊C4—42no—
87C22×C22⋊C4—42no—
88C22×C22⋊C4C2×C418yes—
89C22×C22⋊C4C2×C414yes—
90C22×C22⋊C4D414yes—
91C22×C22⋊C4Q814yes—
92C22×C22⋊C4Q814yes—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—41no—
109C2×#95—41no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—41no—
116C2×#95—41no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95C2×C418yescomplemented
134C2×#95C2×C414yescomplemented
135C25—22no—
136C25—22no—
137C25—22no—
138C25—22no—
139C25—21no—
140C25—21no—
141C25—22no—
142C25—22no—
143C25—21no—
144C25—21no—
145C25—22no—
146C25—22no—
147C25—21no—
148C25—21no—
149C25—21no—
150C25—21no—
151C25C22×C412yes—
152C25C2×D412yes—
153C25C2×D412yes—
154C25C2×Q812yes—
155C25C2×Q812yes—
156C25#4112yes—
157C25#4112yes—
158C25C2411yescharacteristic
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—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
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—28no—
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—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
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×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—216no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—48no—
262C23×C4—44no—
263C23×C4—48no—
264C23×C4—44no—
265C23×C4—48no—
266C23×C4—48no—
267C23×C4—48no—
268C23×C4—48no—
269C23×C4—48no—
270C23×C4—48no—
271C23×C4—48no—
272C23×C4—48no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—48no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4C22×C414yes—
281C23×C4C22×C414yes—
282C23×C4C22×C412yes—
283C23×C4C22×C412yes—
284C23×C4C2×D412yes—
285C23×C4C2×D412yes—
286C23×C4C2×D414yes—
287C23×C4C2×Q814yes—
288C23×C4C2×Q812yes—
289C23×C4C2×Q812yes—
290C23×C4#4114yes—
291C23×C4#4114yes—
292C23×C4#4114yes—
293C23×C4#4114yes—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—48no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C22⋊C4—216no—
305C2×C22⋊C4—216no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—48no—
310C2×C22⋊C4—48no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—48no—
318C2×C22⋊C4—48no—
319C2×C22⋊C4—48no—
320C2×C22⋊C4—48no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—48no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—48no—
327C2×C22⋊C4—48no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—48no—
331C2×C22⋊C4C4⋊C4116yes—
332#95—44no—
333#95—48no—
334#95—48no—
335#95—48no—
336#95—48no—
337#95—44no—
338#95—48no—
339#95—48no—
340#95—48no—
341#95—48no—
342#95—48no—
343#95—48no—
344#95—48no—
345#95—48no—
346C24—24no—
347C24—24no—
348C24—22no—
349C24—22no—
350C24—24no—
351C24—24no—
352C24—22no—
353C24—22no—
354C24—24no—
355C24—24no—
356C24—24no—
357C24—24no—
358C24—22no—
359C24—22no—
360C24—24no—
361C24—22no—
362C24—22no—
363C24—24no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—24no—
369C24—24no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24—24no—
392C24—24no—
393C24—24no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—41no—
419C24—42no—
420C24—41no—
421C24—41no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—41no—
428C24—42no—
429C24—41no—
430C24—41no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—41no—
435C24—41no—
436C24—42no—
437C24—42no—
438C24C2×C4⋊C414yes—
439C24C4×D414yes—
440C24C4×Q814yes—
441C24#12114yes—
442C24C22⋊Q814yes—
443C24#12514yes—
444C24C4⋊Q814yes—
445C24C23×C411yescharacteristic
446C24C22×D411yescharacteristic
447C24C22×D411yescharacteristic
448C24C22×Q811yescharacteristic
449C24C22×Q811yescharacteristic
450C24C2×#4111yescharacteristic
451C24C2×#4111yescharacteristic
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4112yes—
456C24H(5,𝔽2)11yescharacteristic
457C24H(5,𝔽2)11yescharacteristic
458C24H(5,𝔽2)11yescharacteristic
459C24H(5,𝔽2)11yescharacteristic
460C24H(5,𝔽2)12yes—
461C24H(5,𝔽2)12yes—
462C24H(5,𝔽2)12yes—
463C24H(5,𝔽2)12yes—
464C24H(5,𝔽2)11yescharacteristic
465C24H(5,𝔽2)11yescharacteristic
466C242−1+411yescharacteristic
467C242−1+411yescharacteristic
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
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—416no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—416no—
549C22×C4—416no—
550C22×C4—432no—
551C22×C4—416no—
552C22×C4—416no—
553C22×C4—432no—
554C22×C4—416no—
555C22×C4—416no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—41no—
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—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
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—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
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—42no—
656C22×C4—42no—
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×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4C2×C4⋊C414yes—
733C22×C4C2×C4⋊C414yes—
734C22×C4#12318yes—
735C4⋊C4—416no—
736C4⋊C4—416no—
737C22⋊C4—416no—
738C22⋊C4—432no—
739C22⋊C4—416no—
740C22⋊C4—432no—
741C23—24no—
742C23—24no—
743C23—28no—
744C23—24no—
745C23—24no—
746C23—28no—
747C23—24no—
748C23—24no—
749C23—28no—
750C23—28no—
751C23—24no—
752C23—24no—
753C23—28no—
754C23—28no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—28no—
762C23—28no—
763C23—28no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—42no—
770C23—44no—
771C23—42no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—42no—
777C23—44no—
778C23—44no—
779C23—42no—
780C23—44no—
781C23—42no—
782C23—44no—
783C23—42no—
784C23—44no—
785C23—44no—
786C23—42no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—42no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—42no—
801C23—42no—
802C23—44no—
803C23—42no—
804C23—44no—
805C23—42no—
806C23—44no—
807C23—44no—
808C23—42no—
809C23—42no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—44no—
817C23—44no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—44no—
822C23—44no—
823C23—42no—
824C23—44no—
825C23—42no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—44no—
838C23—42no—
839C23#38918yes—
840C23C22×C4⋊C411yescharacteristic
841C23C2×C4×D411yescharacteristic
842C23C2×C4×Q811yescharacteristic
843C23C4×#4112yes—
844C23C4×#4112yes—
845C23#51811yescharacteristic
846C23#51811yescharacteristic
847C23#51812yes—
848C23#51812yes—
849C23#52011yescharacteristic
850C23#52011yescharacteristic
851C23C2×#12111yescharacteristic
852C23C2×C22⋊Q811yescharacteristic
853C23C2×#12312yes—
854C23#52512yes—
855C23C2×#12511yescharacteristic
856C23#52912yes—
857C23#52912yes—
858C23C2×C4⋊Q811yescharacteristic
859C23#53411yescharacteristic
860C23#53411yescharacteristic
861C23#53412yes—
862C23#53411yescharacteristic
863C23#53411yescharacteristic
864C23#53511yescharacteristic
865C23#53512yes—
866C23#53611yescharacteristic
867C23#53711yescharacteristic
868C23#53711yescharacteristic
869C23#53812yes—
870C23#53811yescharacteristic
871C23#53812yes—
872C23#53811yescharacteristic
873C23#53811yescharacteristic
874C23#53811yescharacteristic
875C23#53812yes—
876C23#53812yes—
877C23#53812yes—
878C23#53812yes—
879C23#53812yes—
880C23#53812yes—
881C23#53812yes—
882C23#53911yescharacteristic
883C23#53911yescharacteristic
884C23#53911yescharacteristic
885C23#53911yescharacteristic
886C23#53912yes—
887C23#54012yes—
888C23#54012yes—
889C23#54012yes—
890C23#54012yes—
891C23#54012yes—
892C23#54212yes—
893C23#54212yes—
894C23#54212yes—
895C23#54311yescharacteristic
896C23#54311yescharacteristic
897C23#54311yescharacteristic
898C23#54311yescharacteristic
899C23#54411yescharacteristic
900C23#54411yescharacteristic
901C23#54411yescharacteristic
902C23#54411yescharacteristic
903C23#54612yes—
904C23#54612yes—
905C23#54612yes—
906C23#54612yes—
907C23#55111yescharacteristic
908C23#55112yes—
909C23#55112yes—
910C23#55112yes—
911C23#55112yes—
912C23#55111yescharacteristic
913C23#55112yes—
914C23#55111yescharacteristic
915C23#55212yes—
916C23#55312yes—
917C23#55312yes—
918C23#55412yes—
919C23#55412yes—
920C23#55412yes—
921C23#55412yes—
922C23#55412yes—
923C23#55412yes—
924C23#55412yes—
925C23#55412yes—
926C23#55512yes—
927C23#55612yes—
928C23#55911yescharacteristic
929C23#56011yescharacteristic
930C23#56012yes—
931C23#56012yes—
932C23#56012yes—
933C23#56012yes—
934C23#56011yescharacteristic
935C23#56011yescharacteristic
936C23H(3,𝔽4)11yescharacteristic
937C23#56212yes—
938C23#56212yes—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—464no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—44no—
956C2×C4—42no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—42no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—42no—
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—44no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—44no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—82no—
1013C2×C4—82no—
1014C2×C4—82no—
1015C2×C4—82no—
1016C2×C4—82no—
1017C2×C4—82no—
1018C2×C4—82no—
1019C2×C4—82no—
1020C2×C4—82no—
1021C2×C4—82no—
1022C2×C4—82no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4—82no—
1026C2×C4—82no—
1027C2×C4—82no—
1028C2×C4—82no—
1029C2×C4—82no—
1030C2×C4—82no—
1031C2×C4—82no—
1032C2×C4—82no—
1033C2×C4—82no—
1034C2×C4—82no—
1035C2×C4—82no—
1036C2×C4—82no—
1037C2×C4—82no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4—82no—
1045C2×C4—82no—
1046C2×C4—82no—
1047C2×C4—82no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—82no—
1051C2×C4—82no—
1052C22—28no—
1053C22—216no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—48no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—48no—
1063C22—44no—
1064C22—48no—
1065C22—44no—
1066C22—48no—
1067C22—44no—
1068C22—44no—
1069C22—48no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—48no—
1074C22—48no—
1075C22C2×#38911yescharacteristic
1076C22C4×#12312yes—
1077C22#231511yescharacteristic
1078C22#231711yescharacteristic
1079C22#232112yes—
1080C22#232511yescharacteristic
1081C22#232511yescharacteristic
1082C22#232911yescharacteristic
1083C22#232911yescharacteristic
1084C22#233312yes—
1085C22#233312yes—
1086C22#233512yes—
1087C22#233712yes—
1088C22#234912yes—
1089C22#234912yes—
1090C22#236812yes—
1091C22#236812yes—
1092C22#237211yescharacteristic
1093C22#237312yes—
1094C22#237411yescharacteristic
1095C22#237511yescharacteristic
1096C22#237712yes—
1097C22#238011yescharacteristic
1098C22#241112yes—
1099C22#241212yes—
1100C22#245012yes—
1101C22#245012yes—
1102C22#248311yescharacteristic
1103C22#248512yes—
1104C22#250212yes—
1105C22#250512yes—
1106C22#250512yes—
1107C22#251711yescharacteristic
1108C22#251812yes—
1109C22#252311yescharacteristic
1110C22#258312yes—
1111C22#260011yescharacteristic
1112C22#261711yescharacteristic
1113C22#261811yescharacteristic
1114C22#262212yes—
1115C22#262412yes—
1116C22#262611yescharacteristic
1117C22#262711yescharacteristic
1118C22#263012yes—
1119C22#263512yes—
1120C22#264611yescharacteristic
1121C22#264611yescharacteristic
1122C22#264812yes—
1123C22#264812yes—
1124C22#264912yes—
1125C22#265312yes—
1126C22#265911yescharacteristic
1127C22#265911yescharacteristic
1128C22#268411yescharacteristic
1129C22#268512yes—
1130C22#268712yes—
1131C22#268812yes—
1132C22#269711yescharacteristic
1133C22#269711yescharacteristic
1134C22#269912yes—
1135C22#270012yes—
1136C22#270312yes—
1137C22#270911yescharacteristic
1138C22#273511yescharacteristic
1139C22#273512yes—
1140C22#273611yescharacteristic
1141C22#273712yes—
1142C22#274012yes—
1143C22#274211yescharacteristic
1144C22#274211yescharacteristic
1145C22#274212yes—
1146C22#274312yes—
1147C22#274612yes—
1148C22#274811yescharacteristic
1149C22#274811yescharacteristic
1150C22#274811yescharacteristic
1151C22#274812yes—
1152C22#274912yes—
1153C22#275211yescharacteristic
1154C22#276011yescharacteristic
1155C22#276311yescharacteristic
1156C22#276812yes—
1157C22#276812yes—
1158C22#278012yes—
1159C22#278012yes—
1160C22#278012yes—
1161C22#278412yes—
1162C22#278412yes—
1163C22#278812yes—
1164C22#278812yes—
1165C22#279012yes—
1166C22#280411yescharacteristic
1167C22#280711yescharacteristic
1168C22#281211yescharacteristic
1169C22#281312yes—
1170C22#281511yescharacteristic
1171C22#282411yescharacteristic
1172C22#282512yes—
1173C22#282611yescharacteristic
1174C4—48no—
1175C4—44no—
1176C4—44no—
1177C4—84no—
1178C4—84no—
1179C4—84no—
1180C4—84no—
1181C4—84no—
1182C2—48no—
1183C2#1404412yes—
1184C2#1424811yescharacteristic
1185C2#1427511yescharacteristic
1186C2#1430312yes—
1187C2#1448611yescharacteristic
1188C2#1448812yes—
1189C2#1451311yescharacteristic
1190C2#1459112yes—
1191C2#1459211yescharacteristic
1192C2#1459611yescharacteristic
1193C2#1462111yescharacteristic
1194C2#1639111yescharacteristic
1195C2#1639712yes—
1196C2#1647311yescharacteristic
1197C2#1647612yes—
1198C2#1648111yescharacteristic
1199C2#1666011yescharacteristic
1200C2#1670611yescharacteristic
1201C2#1670711yescharacteristic
1202C2#1670812yes—
1203C2#1698612yes—
1204C2#1698711yescharacteristic
1205C2#1705711yescharacteristic
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
5. #7557C2semidirect
6. #7557C2semidirect
7. #7556C2semidirect
8. #7556C2semidirect
32. #1439C4semidirect
64. C22×C4⋊C4C2×C4semidirect
133. C2×#95C2×C4semidirect
134. C2×#95C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14392
C2×C22⋊#952
#75572
#75562
#75552