Finite Group Databasebeta

← #155184

Subgroups — #155184

Order 512.

2778 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1444C211yesmaximal, characteristic
2C2×#1441C212yesmaximal
3C2×#1436C212yesmaximal
4C2×#1436C212yesmaximal
5#7557C211yesmaximal, characteristic
6#7557C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2212yes—
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×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31#1444C418yescomplemented
32#1441—28no—
33#1436—28no—
34#1436—28no—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2311yescharacteristic
42C24×C4C2312yes—
43C24×C4C2312yes—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—24no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—42no—
55C22×C4⋊C4—42no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4—41no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—41no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—41no—
62C22×C4⋊C4—41no—
63C22×C4⋊C4—41no—
64C22×C4⋊C4C2×C414yes—
65C22×C4⋊C4C2×C418yes—
66C22×C42—24no—
67C22×C42—24no—
68C22×C42—24no—
69C22×C42—42no—
70C22×C42—42no—
71C22×C42—42no—
72C22×C42—42no—
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—22no—
84C2×#95—22no—
85C2×#95—24no—
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—41no—
99C2×#95—42no—
100C2×#95—42no—
101C2×#95—41no—
102C2×#95—41no—
103C2×#95—41no—
104C2×#95—42no—
105C2×#95—42no—
106C2×#95—41no—
107C2×#95—41no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95C2×C414yes—
115C2×#95C2×C414yes—
116C2×#95C2×C418yes—
117C2×#95D414yes—
118C2×#95D418yes—
119C2×#95Q818yes—
120C2×#95Q814yes—
121C25C2411yescharacteristic
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—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—21no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—22no—
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—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
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×C4C22×C412yes—
223C23×C4C22×C414yes—
224C23×C4C22×C412yes—
225C23×C4C22×C414yes—
226C23×C4C22×C412yes—
227C23×C4C2×D414yes—
228C23×C4C2×D412yes—
229C23×C4C2×D414yes—
230C23×C4C2×D414yes—
231C23×C4C2×D414yes—
232C23×C4C2×Q814yes—
233C23×C4C2×Q812yes—
234C23×C4C2×Q814yes—
235C23×C4C2×Q814yes—
236C23×C4C2×Q814yes—
237C23×C4#4114yes—
238C23×C4#4112yes—
239C23×C4#4112yes—
240C23×C4#4112yes—
241C23×C4#4114yes—
242C23×C4#4112yes—
243C23×C4#4114yes—
244C23×C4#4114yes—
245C2×C4⋊C4—216no—
246C2×C4⋊C4—216no—
247C2×C4⋊C4—216no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—48no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—48no—
252C2×C4⋊C4—48no—
253C2×C4⋊C4—48no—
254C2×C4⋊C4—48no—
255C2×C4⋊C4—48no—
256C2×C4⋊C4—44no—
257C2×C4⋊C4—48no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—48no—
264C2×C4⋊C4—48no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4—44no—
267C2×C42—48no—
268C2×C42—48no—
269C2×C42—48no—
270C2×C42—48no—
271C2×C42—48no—
272C2×C42—48no—
273C2×C42—48no—
274#95—216no—
275#95—216no—
276#95—216no—
277#95—28no—
278#95—216no—
279#95—44no—
280#95—48no—
281#95—44no—
282#95—48no—
283#95—44no—
284#95—48no—
285#95—48no—
286#95—48no—
287#95—48no—
288#95—48no—
289#95—48no—
290C24C23×C411yescharacteristic
291C24C22×D411yescharacteristic
292C24C22×D412yes—
293C24C22×Q812yes—
294C24C22×Q811yescharacteristic
295C24C2×#4111yescharacteristic
296C24C2×#4111yescharacteristic
297C24C2×#4112yes—
298C24C2×#4111yescharacteristic
299C24C2×#4112yes—
300C24C2×#4111yescharacteristic
301C24C2×#4112yes—
302C24C2×#4112yes—
303C24H(5,𝔽2)11yescharacteristic
304C24H(5,𝔽2)12yes—
305C24H(5,𝔽2)11yescharacteristic
306C24H(5,𝔽2)12yes—
307C24H(5,𝔽2)11yescharacteristic
308C24H(5,𝔽2)11yescharacteristic
309C242−1+411yescharacteristic
310C242−1+411yescharacteristic
311C242−1+411yescharacteristic
312C242−1+411yescharacteristic
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
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—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
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—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—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
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—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—41no—
478C22×C4—41no—
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—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—41no—
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—41no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—41no—
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#11714yes—
586C22×C4C4×D418yes—
587C22×C4C4×D414yes—
588C22×C4C4×Q814yes—
589C22×C4C4×Q818yes—
590C22×C4C22⋊Q818yes—
591C22×C4C4⋊Q818yes—
592C4⋊C4—416no—
593C4⋊C4—432no—
594C4⋊C4—416no—
595C4⋊C4—416no—
596C42—432no—
597C23C2×#11711yescharacteristic
598C23C2×C4×D412yes—
599C23C2×C4×D411yescharacteristic
600C23C2×C4×Q811yescharacteristic
601C23C2×C4×Q812yes—
602C23C4×#4112yes—
603C23#51811yescharacteristic
604C23#51812yes—
605C23#51911yescharacteristic
606C23#52011yescharacteristic
607C23#52011yescharacteristic
608C23C2×C22⋊Q812yes—
609C23#52512yes—
610C23#52512yes—
611C23#52512yes—
612C23#52912yes—
613C23#52912yes—
614C23#52912yes—
615C23C2×C4⋊Q812yes—
616C23#53212yes—
617C23#53312yes—
618C23#53312yes—
619C23#53312yes—
620C23#53411yescharacteristic
621C23#53412yes—
622C23#53711yescharacteristic
623C23#53712yes—
624C23#53812yes—
625C23#53811yescharacteristic
626C23#53812yes—
627C23#53811yescharacteristic
628C23#53911yescharacteristic
629C23#53911yescharacteristic
630C23#53911yescharacteristic
631C23#53911yescharacteristic
632C23#53912yes—
633C23#53911yescharacteristic
634C23#53912yes—
635C23#53911yescharacteristic
636C23#54012yes—
637C23#54212yes—
638C23#54212yes—
639C23#54212yes—
640C23#54311yescharacteristic
641C23#54411yescharacteristic
642C23#54412yes—
643C23#54412yes—
644C23D4212yes—
645C23D4211yescharacteristic
646C23#54612yes—
647C23#54612yes—
648C23#54612yes—
649C23#54612yes—
650C23#54711yescharacteristic
651C23#54712yes—
652C23#54711yescharacteristic
653C23#54812yes—
654C23D4×Q812yes—
655C23D4×Q811yescharacteristic
656C23#55011yescharacteristic
657C23#55112yes—
658C23#55111yescharacteristic
659C23#55111yescharacteristic
660C23#55112yes—
661C23#55112yes—
662C23#55212yes—
663C23#55212yes—
664C23#55212yes—
665C23#55312yes—
666C23#55312yes—
667C23#55312yes—
668C23#55312yes—
669C23#55412yes—
670C23#55412yes—
671C23#55412yes—
672C23#55412yes—
673C23#55411yescharacteristic
674C23#55412yes—
675C23#55412yes—
676C23#55412yes—
677C23#55511yescharacteristic
678C23#55511yescharacteristic
679C23#55611yescharacteristic
680C23#55611yescharacteristic
681C23#55611yescharacteristic
682C23#55612yes—
683C23#55712yes—
684C23#55711yescharacteristic
685C23#55711yescharacteristic
686C23Q8211yescharacteristic
687C23#55911yescharacteristic
688C23#55911yescharacteristic
689C23#56011yescharacteristic
690C23#56012yes—
691C23#56011yescharacteristic
692C23#56211yescharacteristic
693C23#56311yescharacteristic
694C23#56311yescharacteristic
695C23#56411yescharacteristic
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
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—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
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—42no—
755C2×C4—44no—
756C2×C4—44no—
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—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C22#229012yes—
820C22C4×C22⋊Q812yes—
821C22C4×C4⋊Q812yes—
822C22#231311yescharacteristic
823C22#232512yes—
824C22#232511yescharacteristic
825C22#232911yescharacteristic
826C22#233112yes—
827C22#233512yes—
828C22#234512yes—
829C22#235411yescharacteristic
830C22#235511yescharacteristic
831C22#235811yescharacteristic
832C22#235812yes—
833C22#236012yes—
834C22#236212yes—
835C22#236511yescharacteristic
836C22#236812yes—
837C22#236911yescharacteristic
838C22#237012yes—
839C22#237411yescharacteristic
840C22#238011yescharacteristic
841C22#238211yescharacteristic
842C22#243812yes—
843C22#244012yes—
844C22#244912yes—
845C22#245412yes—
846C22#245511yescharacteristic
847C22#245612yes—
848C22#246012yes—
849C22#246112yes—
850C22#246311yescharacteristic
851C22#246512yes—
852C22#246512yes—
853C22#246612yes—
854C22#246812yes—
855C22#247612yes—
856C22#251711yescharacteristic
857C22#252012yes—
858C22#252112yes—
859C22#252311yescharacteristic
860C22#254912yes—
861C22#255012yes—
862C22#255111yescharacteristic
863C22#255511yescharacteristic
864C22#255612yes—
865C22#257412yes—
866C22#257712yes—
867C22#257912yes—
868C22#258211yescharacteristic
869C22#258312yes—
870C22#258412yes—
871C22#258512yes—
872C22#258611yescharacteristic
873C22#258611yescharacteristic
874C22#258712yes—
875C22#258812yes—
876C22#258912yes—
877C22#259012yes—
878C22#259311yescharacteristic
879C22#260112yes—
880C22#260212yes—
881C22#260512yes—
882C22#260911yescharacteristic
883C22#261211yescharacteristic
884C22#266812yes—
885C22#266811yescharacteristic
886C22#267511yescharacteristic
887C22#269311yescharacteristic
888C22#269312yes—
889C22#270112yes—
890C22#270212yes—
891C22#272411yescharacteristic
892C22#272611yescharacteristic
893C22#272612yes—
894C22#272711yescharacteristic
895C22#272912yes—
896C22#273211yescharacteristic
897C22#273511yescharacteristic
898C22#274211yescharacteristic
899C22#274612yes—
900C22#275211yescharacteristic
901C22#276011yescharacteristic
902C22#276712yes—
903C22#277012yes—
904C22#278012yes—
905C22#278812yes—
906C22#279012yes—
907C22#279012yes—
908C22#279112yes—
909C22#279211yescharacteristic
910C22#279211yescharacteristic
911C22#279511yescharacteristic
912C22#279511yescharacteristic
913C22#280511yescharacteristic
914C22#280711yescharacteristic
915C22#280811yescharacteristic
916C22#280911yescharacteristic
917C22#281011yescharacteristic
918C4—44no—
919C4—48no—
920C4—44no—
921C4—48no—
922C4—48no—
923C4—44no—
924C4—48no—
925C4—84no—
926C4—84no—
927C2#1398712yes—
928C2#1408312yes—
929C2#1414311yescharacteristic
930C2#1421412yes—
931C2#1423611yescharacteristic
932C2#1423811yescharacteristic
933C2#1444611yescharacteristic
934C2#1445411yescharacteristic
935C2#1457211yescharacteristic
936C2#1458512yes—
937C2#1459211yescharacteristic
938C2#1535912yes—
939C2#1536311yescharacteristic
940C2#1541711yescharacteristic
941C2#1542112yes—
942C2#1558112yes—
943C2#1560112yes—
944C2#1577911yescharacteristic
945C2#1578211yescharacteristic
946C2#1608111yescharacteristic
947C2#1608811yescharacteristic
948C2#1621711yescharacteristic
949C2#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. #1444C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14442
C2×#14412
C2×#14362
#75572
#75562
#75542