Finite Group Databasebeta

← #155424

Subgroups — #155424

Order 512.

2598 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1442C211yesmaximal, characteristic
2C2×#1436C212yesmaximal
3C2×#1434C212yesmaximal
4#7557C211yesmaximal, characteristic
5#7557C212yesmaximal
6#7557C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C42C2212yes—
14C22×#95C2212yes—
15C22×#95C2212yes—
16C22×#95C2212yes—
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31#1442C418yescomplemented
32#1436—28no—
33#1434—28no—
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2311yescharacteristic
39C24×C4C2311yescharacteristic
40C24×C4C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2312yes—
43C22×C4⋊C4—24no—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—24no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—41no—
48C22×C4⋊C4—41no—
49C22×C4⋊C4—42no—
50C22×C4⋊C4—42no—
51C22×C4⋊C4—41no—
52C22×C4⋊C4—41no—
53C22×C4⋊C4—42no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4C2×C414yes—
57C22×C4⋊C4D414yes—
58C22×C42—24no—
59C22×C42—24no—
60C22×C42—24no—
61C22×C42—24no—
62C22×C42—24no—
63C22×C42—42no—
64C22×C42—42no—
65C2×#95—24no—
66C2×#95—24no—
67C2×#95—24no—
68C2×#95—24no—
69C2×#95—24no—
70C2×#95—24no—
71C2×#95—24no—
72C2×#95—24no—
73C2×#95—24no—
74C2×#95—24no—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—22no—
90C2×#95—41no—
91C2×#95—41no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—41no—
95C2×#95—41no—
96C2×#95—42no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—42no—
100C2×#95—42no—
101C2×#95—42no—
102C2×#95—42no—
103C2×#95—42no—
104C2×#95—41no—
105C2×#95—42no—
106C2×#95—41no—
107C2×#95—42no—
108C2×#95—42no—
109C2×#95C2×C418yes—
110C2×#95C2×C418yes—
111C2×#95C2×C414yes—
112C2×#95C2×C414yes—
113C2×#95D414yes—
114C2×#95Q814yes—
115C2×#95Q814yes—
116C25C2411yescharacteristic
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—21no—
157C23×C4—21no—
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—21no—
170C23×C4—21no—
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—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—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×C4C22×C414yes—
220C23×C4C22×C412yes—
221C23×C4C22×C414yes—
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C2×D412yes—
225C23×C4C2×D414yes—
226C23×C4C2×D412yes—
227C23×C4C2×D414yes—
228C23×C4C2×Q814yes—
229C23×C4C2×Q812yes—
230C23×C4C2×Q812yes—
231C23×C4C2×Q814yes—
232C23×C4#4114yes—
233C23×C4#4114yes—
234C23×C4#4112yes—
235C23×C4#4112yes—
236C23×C4#4114yes—
237C23×C4#4114yes—
238C23×C4#4114yes—
239C23×C4#4114yes—
240C2×C4⋊C4—216no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4—48no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—44no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—48no—
247C2×C4⋊C4—48no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—48no—
251C2×C4⋊C4—48no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C42—216no—
256C2×C42—48no—
257C2×C42—48no—
258C2×C42—48no—
259C2×C42—48no—
260C2×C42—48no—
261C2×C42—48no—
262#95—216no—
263#95—216no—
264#95—216no—
265#95—44no—
266#95—48no—
267#95—44no—
268#95—48no—
269#95—48no—
270#95—48no—
271#95—48no—
272#95—48no—
273#95—48no—
274#95—48no—
275#95—48no—
276#95—44no—
277#95—48no—
278#95C4⋊C4116yescomplemented
279C24C23×C411yescharacteristic
280C24C22×D411yescharacteristic
281C24C22×D411yescharacteristic
282C24C22×Q811yescharacteristic
283C24C22×Q811yescharacteristic
284C24C2×#4111yescharacteristic
285C24C2×#4111yescharacteristic
286C24C2×#4112yes—
287C24C2×#4112yes—
288C24C2×#4112yes—
289C24C2×#4112yes—
290C24C2×#4112yes—
291C24C2×#4112yes—
292C24H(5,𝔽2)11yescharacteristic
293C24H(5,𝔽2)11yescharacteristic
294C24H(5,𝔽2)12yes—
295C24H(5,𝔽2)12yes—
296C24H(5,𝔽2)11yescharacteristic
297C24H(5,𝔽2)11yescharacteristic
298C242−1+411yescharacteristic
299C242−1+411yescharacteristic
300C242−1+411yescharacteristic
301C242−1+411yescharacteristic
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
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—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
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—41no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—41no—
488C22×C4—41no—
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×C4C2×C4⋊C414yes—
576C22×C4C2×C4⋊C418yes—
577C22×C4C4×D414yes—
578C22×C4C4×Q814yes—
579C22×C4#12318yes—
580C22×C4#12518yes—
581C4⋊C4—416no—
582C4⋊C4—416no—
583C4⋊C4—416no—
584C42—432no—
585C23C22×C4⋊C411yescharacteristic
586C23C2×C4×D411yescharacteristic
587C23C2×C4×Q811yescharacteristic
588C23C4×#4112yes—
589C23C4×#4112yes—
590C23C4×#4112yes—
591C23#51811yescharacteristic
592C23#51812yes—
593C23#51911yescharacteristic
594C23#52011yescharacteristic
595C23#52011yescharacteristic
596C23C2×#12312yes—
597C23#52512yes—
598C23#52512yes—
599C23#52512yes—
600C23C2×#12512yes—
601C23#52912yes—
602C23#52912yes—
603C23#52912yes—
604C23#52912yes—
605C23#53312yes—
606C23#53312yes—
607C23#53312yes—
608C23#53411yescharacteristic
609C23#53711yescharacteristic
610C23#53711yescharacteristic
611C23#53711yescharacteristic
612C23#53811yescharacteristic
613C23#53812yes—
614C23#53811yescharacteristic
615C23#53812yes—
616C23#53812yes—
617C23#53911yescharacteristic
618C23#53912yes—
619C23#53911yescharacteristic
620C23#53912yes—
621C23#53912yes—
622C23#54012yes—
623C23#54212yes—
624C23#54212yes—
625C23#54212yes—
626C23#54212yes—
627C23#54212yes—
628C23#54311yescharacteristic
629C23#54411yescharacteristic
630C23#54411yescharacteristic
631C23#54411yescharacteristic
632C23D4211yescharacteristic
633C23#54612yes—
634C23#54612yes—
635C23#54612yes—
636C23#54711yescharacteristic
637C23#54711yescharacteristic
638C23D4×Q811yescharacteristic
639C23D4×Q811yescharacteristic
640C23D4×Q811yescharacteristic
641C23#55011yescharacteristic
642C23#55012yes—
643C23#55112yes—
644C23#55112yes—
645C23#55111yescharacteristic
646C23#55112yes—
647C23#55112yes—
648C23#55112yes—
649C23#55111yescharacteristic
650C23#55111yescharacteristic
651C23#55212yes—
652C23#55212yes—
653C23#55212yes—
654C23#55212yes—
655C23#55212yes—
656C23#55212yes—
657C23#55312yes—
658C23#55312yes—
659C23#55312yes—
660C23#55312yes—
661C23#55411yescharacteristic
662C23#55412yes—
663C23#55412yes—
664C23#55412yes—
665C23#55412yes—
666C23#55511yescharacteristic
667C23#55512yes—
668C23#55511yescharacteristic
669C23#55512yes—
670C23#55612yes—
671C23#55611yescharacteristic
672C23#55612yes—
673C23#55711yescharacteristic
674C23#55711yescharacteristic
675C23Q8211yescharacteristic
676C23#55911yescharacteristic
677C23#56012yes—
678C23#56011yescharacteristic
679C23H(3,𝔽4)11yescharacteristic
680C23#56211yescharacteristic
681C23#56311yescharacteristic
682C23#56311yescharacteristic
683C23#56411yescharacteristic
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
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—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
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—
807C22#229612yes—
808C22C4×#12312yes—
809C22C4×#12512yes—
810C22#231611yescharacteristic
811C22#232511yescharacteristic
812C22#232911yescharacteristic
813C22#233212yes—
814C22#233512yes—
815C22#233712yes—
816C22D4×C4⋊C411yescharacteristic
817C22#234912yes—
818C22Q8×C4⋊C411yescharacteristic
819C22#236312yes—
820C22#236511yescharacteristic
821C22#236812yes—
822C22#237112yes—
823C22#237211yescharacteristic
824C22#237211yescharacteristic
825C22#237312yes—
826C22#237312yes—
827C22#237411yescharacteristic
828C22#237511yescharacteristic
829C22#238211yescharacteristic
830C22#241812yes—
831C22#241912yes—
832C22#242312yes—
833C22#242312yes—
834C22#245612yes—
835C22#246512yes—
836C22#246512yes—
837C22#246712yes—
838C22#246812yes—
839C22#247112yes—
840C22#247312yes—
841C22#247312yes—
842C22#247412yes—
843C22#247912yes—
844C22#248311yescharacteristic
845C22#248512yes—
846C22#250712yes—
847C22#250812yes—
848C22#251711yescharacteristic
849C22#251812yes—
850C22#252012yes—
851C22#252311yescharacteristic
852C22#253212yes—
853C22#256912yes—
854C22#257111yescharacteristic
855C22#257211yescharacteristic
856C22#257312yes—
857C22#257412yes—
858C22#257712yes—
859C22#258612yes—
860C22#258712yes—
861C22#258812yes—
862C22#259012yes—
863C22#259311yescharacteristic
864C22#260011yescharacteristic
865C22#260911yescharacteristic
866C22#260912yes—
867C22#260911yescharacteristic
868C22#261212yes—
869C22#261211yescharacteristic
870C22#261211yescharacteristic
871C22#261211yescharacteristic
872C22#268211yescharacteristic
873C22#268311yescharacteristic
874C22#269112yes—
875C22#269311yescharacteristic
876C22#269911yescharacteristic
877C22#270512yes—
878C22#271211yescharacteristic
879C22#272611yescharacteristic
880C22#272611yescharacteristic
881C22#272711yescharacteristic
882C22#273311yescharacteristic
883C22#273411yescharacteristic
884C22#273611yescharacteristic
885C22#273712yes—
886C22#274211yescharacteristic
887C22#274312yes—
888C22#274512yes—
889C22#275612yes—
890C22#276011yescharacteristic
891C22#276311yescharacteristic
892C22#276311yescharacteristic
893C22#276412yes—
894C22#276712yes—
895C22#276712yes—
896C22#277012yes—
897C22#277712yes—
898C22#277912yes—
899C22#278412yes—
900C22#278511yescharacteristic
901C22#279012yes—
902C22#279511yescharacteristic
903C22#280511yescharacteristic
904C22#280611yescharacteristic
905C22#280711yescharacteristic
906C4—44no—
907C4—48no—
908C4—48no—
909C4—48no—
910C4—44no—
911C4—44no—
912C4—84no—
913C4—84no—
914C4—84no—
915C2#1411512yes—
916C2#1411812yes—
917C2#1416811yescharacteristic
918C2#1417912yes—
919C2#1424811yescharacteristic
920C2#1425411yescharacteristic
921C2#1444111yescharacteristic
922C2#1451411yescharacteristic
923C2#1458911yescharacteristic
924C2#1459611yescharacteristic
925C2#1460812yes—
926C2#1595211yescharacteristic
927C2#1595912yes—
928C2#1597811yescharacteristic
929C2#1600211yescharacteristic
930C2#1602212yes—
931C2#1607812yes—
932C2#1608111yescharacteristic
933C2#1609611yescharacteristic
934C2#1611011yescharacteristic
935C2#1616812yes—
936C2#1618511yescharacteristic
937C2#1623611yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
31. #1442C4semidirect
278. #95C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14422
C2×#14362
C2×#14342
#75572
#75562
#75542