Finite Group Databasebeta

← #159154

Subgroups — #159154

Order 512.

3000 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C2×#1446C212yesmaximal
3C2×#1442C212yesmaximal
4C2×#1441C212yesmaximal
5C2×#1441C211yesmaximal, characteristic
6#7557C211yesmaximal, characteristic
7#7556C212yesmaximal
8#7556C212yesmaximal
9#7556C212yesmaximal
10C24×Q8C2211yescharacteristic
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C2×#395—24no—
15C2×#395—28no—
16C22×#95C2211yescharacteristic
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33#1446—28no—
34#1442—28no—
35#1441—28no—
36#1441—24no—
37C23×Q8—24no—
38C23×Q8—22no—
39C23×Q8—24no—
40C23×Q8—24no—
41C23×Q8—24no—
42C23×Q8—42no—
43C23×Q8—42no—
44C23×Q8—41no—
45C23×Q8—41no—
46C24×C4C2312yes—
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2312yes—
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—42no—
64C22×C4⋊C4—41no—
65C22×C4⋊C4—41no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4—41no—
69C22×C4⋊C4—41no—
70C22×C4⋊C4D414yes—
71C22×C4⋊C4D418yes—
72#395—232no—
73C2×#95—24no—
74C2×#95—24no—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—22no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—22no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
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—22no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—42no—
106C2×#95—42no—
107C2×#95—42no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—41no—
117C2×#95—41no—
118C2×#95—41no—
119C2×#95—41no—
120C2×#95D418yes—
121C2×#95Q818yescomplemented
122C25C2411yescharacteristic
123C22×Q8—216no—
124C22×Q8—28no—
125C22×Q8—44no—
126C22×Q8—48no—
127C22×Q8—48no—
128C22×Q8—48no—
129C22×Q8—48no—
130C22×Q8—48no—
131C22×Q8—48no—
132C22×Q8—48no—
133C22×Q8—48no—
134C22×Q8—44no—
135C22×Q8—48no—
136C22×Q8—44no—
137C22×Q8—48no—
138C22×Q8—48no—
139C22×Q8—48no—
140C22×Q8—44no—
141C22×Q8—44no—
142C22×Q8—48no—
143C22×Q8—44no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
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×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×D412yes—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D412yes—
254C23×C4C2×D412yes—
255C23×C4C2×Q814yes—
256C23×C4C2×Q814yes—
257C23×C4C2×Q814yes—
258C23×C4#4114yes—
259C23×C4#4114yes—
260C23×C4#4114yes—
261C23×C4#4112yes—
262C23×C4#4112yes—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—216no—
265C2×C4⋊C4—216no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—48no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—48no—
270C2×C4⋊C4—48no—
271C2×C4⋊C4—48no—
272C2×C4⋊C4—48no—
273C2×C4⋊C4—48no—
274C2×C4⋊C4—48no—
275C2×C4⋊C4—48no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—44no—
280#95—28no—
281#95—216no—
282#95—216no—
283#95—48no—
284#95—48no—
285#95—48no—
286#95—48no—
287#95—48no—
288#95—48no—
289#95—48no—
290#95—48no—
291#95—48no—
292#95—44no—
293#95—44no—
294#95—44no—
295#95—48no—
296#95—48no—
297C24C22×D412yes—
298C24C22×D411yescharacteristic
299C24C22×D412yes—
300C24C22×Q812yes—
301C24C2×#4112yes—
302C24C2×#4112yes—
303C24C2×#4112yes—
304C24C2×#4111yescharacteristic
305C24C2×#4111yescharacteristic
306C24H(5,𝔽2)11yescharacteristic
307C24H(5,𝔽2)12yes—
308C24H(5,𝔽2)11yescharacteristic
309C24H(5,𝔽2)12yes—
310C24H(5,𝔽2)11yescharacteristic
311C242−1+411yescharacteristic
312C242−1+412yes—
313C242−1+412yes—
314C242−1+412yes—
315C242−1+412yes—
316C2×Q8—416no—
317C2×Q8—432no—
318C2×Q8—432no—
319C2×Q8—432no—
320C2×Q8—432no—
321C2×Q8—432no—
322C2×Q8—416no—
323C2×Q8—432no—
324C2×Q8—416no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
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—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
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—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—41no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—42no—
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—42no—
517C22×C4—42no—
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—42no—
537C22×C4—42no—
538C22×C4—42no—
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#12014yes—
596C22×C4#12118yes—
597C22×C4C22⋊Q818yes—
598C22×C4#12314yes—
599C22×C4#12414yes—
600C4⋊C4—416no—
601C4⋊C4—432no—
602C4⋊C4—416no—
603C23C2×#12011yescharacteristic
604C23C2×#12112yes—
605C23C2×C22⋊Q812yes—
606C23C2×#12311yescharacteristic
607C23#52512yes—
608C23C2×#12411yescharacteristic
609C23#53212yes—
610C23#53312yes—
611C23#53312yes—
612C23#53411yescharacteristic
613C23#53412yes—
614C23#53412yes—
615C23#53612yes—
616C23#53611yescharacteristic
617C23#53611yescharacteristic
618C23#53612yes—
619C23#53612yes—
620C23#53612yes—
621C23#53612yes—
622C23#53711yescharacteristic
623C23#53712yes—
624C23#53811yescharacteristic
625C23#53812yes—
626C23#53811yescharacteristic
627C23#53812yes—
628C23#53912yes—
629C23#53912yes—
630C23#53911yescharacteristic
631C23#53911yescharacteristic
632C23#54112yes—
633C23#54112yes—
634C23#54112yes—
635C23#54112yes—
636C23#54112yes—
637C23#54212yes—
638C23#54212yes—
639C23#54212yes—
640C23#54212yes—
641C23#54212yes—
642C23#54412yes—
643C23#54412yes—
644C23#54412yes—
645C23#54412yes—
646C23D4212yes—
647C23D4212yes—
648C23D4211yescharacteristic
649C23#54612yes—
650C23#54612yes—
651C23#54612yes—
652C23#54612yes—
653C23#54612yes—
654C23#54612yes—
655C23#54712yes—
656C23#54812yes—
657C23#54812yes—
658C23#54812yes—
659C23#54812yes—
660C23D4×Q812yes—
661C23D4×Q812yes—
662C23D4×Q812yes—
663C23D4×Q812yes—
664C23#55111yescharacteristic
665C23#55112yes—
666C23#55212yes—
667C23#55212yes—
668C23#55212yes—
669C23#55412yes—
670C23#55412yes—
671C23#55512yes—
672C23#55511yescharacteristic
673C23#55612yes—
674C23#55612yes—
675C23#55612yes—
676C23#55712yes—
677C23Q8211yescharacteristic
678C23#56011yescharacteristic
679C23H(3,𝔽4)11yescharacteristic
680C23#56212yes—
681C23#56212yes—
682C23#56311yescharacteristic
683C23#56312yes—
684C23#56312yes—
685C23#56312yes—
686C23#56312yes—
687C23#56312yes—
688C23#56311yescharacteristic
689C23#56312yes—
690Q8—464no—
691C2×C4—28no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4—82no—
791C2×C4—82no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—82no—
802C2×C4—82no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C22#240511yescharacteristic
811C22#240912yes—
812C22#241012yes—
813C22#241712yes—
814C22#241812yes—
815C22#242412yes—
816C22#242912yes—
817C22#243611yescharacteristic
818C22#243912yes—
819C22#243912yes—
820C22#244612yes—
821C22#245112yes—
822C22#245212yes—
823C22#246212yes—
824C22#246512yes—
825C22#249112yes—
826C22#249212yes—
827C22#250311yescharacteristic
828C22#253412yes—
829C22#254512yes—
830C22#255511yescharacteristic
831C22#255612yes—
832C22#258611yescharacteristic
833C22#260412yes—
834C22#261212yes—
835C22#261611yescharacteristic
836C22#262112yes—
837C22#262511yescharacteristic
838C22#262712yes—
839C22#263412yes—
840C22#263911yescharacteristic
841C22#266312yes—
842C22#266612yes—
843C22#266612yes—
844C22#266812yes—
845C22#267412yes—
846C22#267712yes—
847C22#267712yes—
848C22#267712yes—
849C22#267712yes—
850C22#267911yescharacteristic
851C22#268011yescharacteristic
852C22#268112yes—
853C22#268112yes—
854C22#268412yes—
855C22#268612yes—
856C22#269012yes—
857C22#269012yes—
858C22#269012yes—
859C22#269012yes—
860C22#269711yescharacteristic
861C22#269812yes—
862C22#270012yes—
863C22#270212yes—
864C22#270212yes—
865C22#270412yes—
866C22#270412yes—
867C22#271312yes—
868C22#271312yes—
869C22#271612yes—
870C22#271612yes—
871C22#271612yes—
872C22#272912yes—
873C22#273112yes—
874C22#273111yescharacteristic
875C22#273411yescharacteristic
876C22#273412yes—
877C22#275512yes—
878C22#275812yes—
879C22#275812yes—
880C22#277412yes—
881C22#277512yes—
882C22#277512yes—
883C22#278511yescharacteristic
884C22#278812yes—
885C22#278912yes—
886C22#278911yescharacteristic
887C22#279211yescharacteristic
888C22#281412yes—
889C22#281712yes—
890C22#281711yescharacteristic
891C22#283011yescharacteristic
892C22#283112yes—
893C22#283211yescharacteristic
894C22#283312yes—
895C22#283812yes—
896C22#284412yes—
897C4—48no—
898C4—44no—
899C4—44no—
900C4—48no—
901C4—44no—
902C4—84no—
903C4—84no—
904C4—84no—
905C4—84no—
906C2#1526611yescharacteristic
907C2#1532212yes—
908C2#1563312yes—
909C2#1569912yes—
910C2#1586012yes—
911C2#1609311yescharacteristic
912C2#1626412yes—
913C2#1627912yes—
914C2#1629312yes—
915C2#1636611yescharacteristic
916C2#1655312yes—
917C2#1668612yes—
918C2#1680412yes—
919C2#1687811yescharacteristic
920C2#1700411yescharacteristic
921C2#1708511yescharacteristic
922C2#1712212yes—
923C2#1714411yescharacteristic
924C2#1721112yes—
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
121. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3952
C2×#14462
C2×#14422
C2×#14412
#75572
#75562