Finite Group Databasebeta

← #157451

Subgroups — #157451

Order 512.

3012 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C212yesmaximal
3C2×#1445C211yesmaximal, characteristic
4C2×#1442C211yesmaximal, characteristic
5C2×#1441C211yesmaximal, characteristic
6#7557C211yesmaximal, characteristic
7#7556C212yesmaximal
8#7556C211yesmaximal, characteristic
9#7556C212yesmaximal
10#7556C211yesmaximal, characteristic
11#7554C212yesmaximal
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#391—24no—
17C2×#391—24no—
18C2×#391—24no—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2212yes—
37C22×#95C2212yes—
38#1446—28no—
39#1445—24no—
40#1442—24no—
41#1441—24no—
42C23×Q8—22no—
43C23×Q8—22no—
44C23×Q8—22no—
45C23×Q8—22no—
46C23×Q8—22no—
47C23×Q8—22no—
48C23×Q8—24no—
49C23×Q8—24no—
50C23×Q8—42no—
51C23×Q8—42no—
52C23×Q8D414yes—
53C24×C4C2311yescharacteristic
54C24×C4C2312yes—
55C24×C4C2312yes—
56C24×C4C2312yes—
57C24×C4C2312yes—
58C24×C4C2311yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4D414yes—
74C22×C42—22no—
75C22×C42—22no—
76C22×C42—22no—
77C22×C42—24no—
78C22×C42—42no—
79#391—232no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—22no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
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—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×#95D414yes—
132C2×#95D414yes—
133C2×#95Q818yescomplemented
134C25C2411yescharacteristic
135C22×Q8—28no—
136C22×Q8—28no—
137C22×Q8—28no—
138C22×Q8—28no—
139C22×Q8—28no—
140C22×Q8—28no—
141C22×Q8—28no—
142C22×Q8—216no—
143C22×Q8—48no—
144C22×Q8—48no—
145C22×Q8—48no—
146C22×Q8—48no—
147C22×Q8—48no—
148C22×Q8—48no—
149C22×Q8—48no—
150C22×Q8—48no—
151C22×Q8—48no—
152C22×Q8—44no—
153C22×Q8—44no—
154C22×Q8—48no—
155C22×Q8—44no—
156C22×Q8—44no—
157C22×Q8—48no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
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—21no—
201C23×C4—21no—
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—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2×D412yes—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×Q814yes—
277C23×C4C2×Q814yes—
278C23×C4C2×Q814yes—
279C23×C4#4114yes—
280C23×C4#4114yes—
281C23×C4#4112yes—
282C23×C4#4112yes—
283C23×C4#4114yes—
284C23×C4#4112yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—48no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C42—28no—
298C2×C42—48no—
299C2×C42—48no—
300C2×C42—44no—
301C2×C42—44no—
302#95—28no—
303#95—28no—
304#95—28no—
305#95—28no—
306#95—28no—
307#95—48no—
308#95—48no—
309#95—48no—
310#95—48no—
311#95—44no—
312#95—48no—
313#95—48no—
314#95—44no—
315#95—48no—
316#95—48no—
317#95—48no—
318#95—48no—
319#95—48no—
320#95—48no—
321C24C22×D411yescharacteristic
322C24C22×D411yescharacteristic
323C24C22×D411yescharacteristic
324C24C22×D411yescharacteristic
325C24C22×Q812yes—
326C24C2×#4111yescharacteristic
327C24C2×#4111yescharacteristic
328C24C2×#4111yescharacteristic
329C24C2×#4112yes—
330C24C2×#4112yes—
331C24C2×#4112yes—
332C24C2×#4112yes—
333C24C2×#4112yes—
334C24H(5,𝔽2)12yes—
335C24H(5,𝔽2)12yes—
336C24H(5,𝔽2)12yes—
337C242−1+412yes—
338C242−1+412yes—
339C242−1+412yes—
340C2×Q8—232no—
341C2×Q8—432no—
342C2×Q8—432no—
343C2×Q8—416no—
344C2×Q8—416no—
345C2×Q8—416no—
346C2×Q8—416no—
347C2×Q8—432no—
348C2×Q8—432no—
349C2×Q8—416no—
350C2×Q8—416no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
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—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
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—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
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—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—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#12014yes—
635C22×C4#12114yes—
636C22×C4#12114yes—
637C22×C4#12114yes—
638C22×C4#12318yes—
639C22×C4#12314yes—
640C22×C4#12414yes—
641C22×C4#12414yes—
642C22×C4#12618yes—
643C22×C4C4⋊Q814yes—
644C4⋊C4—416no—
645C4⋊C4—416no—
646C42—416no—
647C23C2×#12011yescharacteristic
648C23C2×#12111yescharacteristic
649C23C2×#12111yescharacteristic
650C23C2×#12111yescharacteristic
651C23C2×#12311yescharacteristic
652C23C2×#12312yes—
653C23#52511yescharacteristic
654C23#52511yescharacteristic
655C23#52511yescharacteristic
656C23#52511yescharacteristic
657C23#52511yescharacteristic
658C23C2×#12411yescharacteristic
659C23C2×#12411yescharacteristic
660C23C2×#12612yes—
661C23#52912yes—
662C23#52912yes—
663C23#52912yes—
664C23#52912yes—
665C23C2×C4⋊Q811yescharacteristic
666C23#53312yes—
667C23#53312yes—
668C23#53312yes—
669C23#53312yes—
670C23#53411yescharacteristic
671C23#53412yes—
672C23#53511yescharacteristic
673C23#53511yescharacteristic
674C23#53611yescharacteristic
675C23#53611yescharacteristic
676C23#53611yescharacteristic
677C23#53812yes—
678C23#53812yes—
679C23#53912yes—
680C23#54112yes—
681C23#54112yes—
682C23#54112yes—
683C23#54112yes—
684C23#54212yes—
685C23#54212yes—
686C23#54212yes—
687C23#54212yes—
688C23#54212yes—
689C23#54212yes—
690C23#54212yes—
691C23#54212yes—
692C23#54312yes—
693C23#54412yes—
694C23#54612yes—
695C23#54612yes—
696C23#54612yes—
697C23#54612yes—
698C23#54612yes—
699C23#54612yes—
700C23#54712yes—
701C23#54712yes—
702C23#54812yes—
703C23#54812yes—
704C23#54812yes—
705C23#54812yes—
706C23D4×Q812yes—
707C23D4×Q812yes—
708C23D4×Q812yes—
709C23#55012yes—
710C23#55112yes—
711C23#55112yes—
712C23#55112yes—
713C23#55112yes—
714C23#55112yes—
715C23#55212yes—
716C23#55212yes—
717C23#55212yes—
718C23#55212yes—
719C23#55412yes—
720C23#55412yes—
721C23#55412yes—
722C23#55512yes—
723C23#55612yes—
724C23#55612yes—
725C23#55612yes—
726C23#55712yes—
727C23#55712yes—
728C23#55912yes—
729C23#55912yes—
730C23#56212yes—
731C23#56212yes—
732C23#56312yes—
733C23#56312yes—
734Q8—464no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—82no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—82no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4—82no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—82no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4#39718yes—
864C22C2×#39711yescharacteristic
865C22#239811yescharacteristic
866C22#239911yescharacteristic
867C22#240411yescharacteristic
868C22#240511yescharacteristic
869C22#240611yescharacteristic
870C22#241212yes—
871C22#241212yes—
872C22#242112yes—
873C22#242312yes—
874C22#242612yes—
875C22#242612yes—
876C22#242912yes—
877C22#242912yes—
878C22#243411yescharacteristic
879C22#243511yescharacteristic
880C22#243611yescharacteristic
881C22#244612yes—
882C22#244612yes—
883C22#244712yes—
884C22#244812yes—
885C22#245812yes—
886C22#245812yes—
887C22#245912yes—
888C22#246212yes—
889C22#246212yes—
890C22#246512yes—
891C22#247412yes—
892C22#247712yes—
893C22#248012yes—
894C22#248012yes—
895C22#248211yescharacteristic
896C22#248812yes—
897C22#248912yes—
898C22#249212yes—
899C22#249212yes—
900C22#251112yes—
901C22#251412yes—
902C22#252012yes—
903C22#252012yes—
904C22#252712yes—
905C22#253212yes—
906C22#253611yescharacteristic
907C22#253611yescharacteristic
908C22#254611yescharacteristic
909C22#254811yescharacteristic
910C22#254912yes—
911C22#255012yes—
912C22#256111yescharacteristic
913C22#257412yes—
914C22#258812yes—
915C22#258912yes—
916C22#260712yes—
917C22#261212yes—
918C22#261711yescharacteristic
919C22#263211yescharacteristic
920C22#263411yescharacteristic
921C22#264512yes—
922C22#265012yes—
923C22#266512yes—
924C22#268612yes—
925C22#269012yes—
926C22#269212yes—
927C22#269212yes—
928C22#269812yes—
929C22#270012yes—
930C22#270012yes—
931C22#271012yes—
932C22#271312yes—
933C22#271612yes—
934C22#272312yes—
935C22#272912yes—
936C22#272912yes—
937C22#273012yes—
938C22#273112yes—
939C22#273212yes—
940C22#275412yes—
941C22#275412yes—
942C22#275512yes—
943C22#275812yes—
944C22#276212yes—
945C22#276412yes—
946C22#279812yes—
947C22#279912yes—
948C22#283112yes—
949C22#284711yescharacteristic
950C22#286312yes—
951C4—28no—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4—84no—
958C4—84no—
959C4—84no—
960C4—82no—
961C4—84no—
962C2#1482011yescharacteristic
963C2#1488011yescharacteristic
964C2#1488311yescharacteristic
965C2#1499212yes—
966C2#1501312yes—
967C2#1518612yes—
968C2#1549912yes—
969C2#1550012yes—
970C2#1567011yescharacteristic
971C2#1567111yescharacteristic
972C2#1578311yescharacteristic
973C2#1585312yes—
974C2#1585712yes—
975C2#1588312yes—
976C2#1603211yescharacteristic
977C2#1606612yes—
978C2#1638712yes—
979C2#1638812yes—
980C2#1662812yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
133. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3912
C2×#14462
C2×#14452
C2×#14422
C2×#14412
#75572
#75562
#75542