Finite Group Databasebeta

← #154205

Subgroups — #154205

Order 512.

6170 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#385C212yesmaximal
2C22×#380C211yesmaximal, characteristic
3C23×#95C211yesmaximal, characteristic
4C2×#1444C212yesmaximal, complemented
5C2×C22⋊#95C212yesmaximal
6C2×C22⋊#95C211yesmaximal, characteristic
7#7557C214yesmaximal, complemented
8#7557C212yesmaximal, complemented
9C25×C4C2211yescharacteristic
10C25×C4C2211yescharacteristic
11C25×C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2214yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2212yes—
17C2×#385—28no—
18C2×#385—28no—
19C2×#385—28no—
20C2×#380—24no—
21C2×#380—28no—
22C22×#95—28no—
23C22×#95—24no—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2214yes—
27C22×#95C2214yes—
28C22×#95C2214yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32#1444—28no—
33C22⋊#95—28no—
34C22⋊#95C418yescomplemented
35C26C2311yescharacteristic
36C24×C4—22no—
37C24×C4—22no—
38C24×C4—24no—
39C24×C4—24no—
40C24×C4—22no—
41C24×C4—22no—
42C24×C4—24no—
43C24×C4—24no—
44C24×C4—24no—
45C24×C4—24no—
46C24×C4—24no—
47C24×C4—24no—
48C24×C4—24no—
49C24×C4—24no—
50C24×C4—24no—
51C24×C4—24no—
52C24×C4—42no—
53C24×C4—42no—
54C24×C4—42no—
55C24×C4—42no—
56C24×C4—42no—
57C24×C4—42no—
58C24×C4C2×C414yes—
59C24×C4D414yes—
60C24×C4D414yes—
61C24×C4Q814yes—
62C24×C4Q814yes—
63C24×C4C2312yes—
64C24×C4C2312yes—
65C24×C4C2311yescharacteristic
66C24×C4C2314yes—
67C24×C4C2312yes—
68C24×C4C2312yes—
69C24×C4C2311yescharacteristic
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—28no—
75C22×C4⋊C4—28no—
76C22×C4⋊C4—28no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—28no—
79C22×C4⋊C4—28no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—42no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4—44no—
84C22×C4⋊C4—44no—
85C22×C22⋊C4—24no—
86C22×C22⋊C4—24no—
87C22×C22⋊C4—24no—
88C22×C22⋊C4—24no—
89C22×C22⋊C4—24no—
90C22×C22⋊C4—24no—
91C22×C22⋊C4—24no—
92C22×C22⋊C4—24no—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—24no—
95C22×C22⋊C4C2×C418yes—
96C22×C22⋊C4D418yes—
97C22×C22⋊C4D418yes—
98C22×C22⋊C4Q818yes—
99#385—264no—
100#380—232no—
101C2×#95—232no—
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—28no—
112C2×#95—28no—
113C2×#95—28no—
114C2×#95—24no—
115C2×#95—28no—
116C2×#95—28no—
117C2×#95—28no—
118C2×#95—28no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—44no—
122C2×#95—44no—
123C2×#95C2×C418yescomplemented
124C2×#95C2×C418yescomplemented
125C2×#95D418yes—
126C25—22no—
127C25—22no—
128C25—22no—
129C25—22no—
130C25—22no—
131C25—22no—
132C25—22no—
133C25—22no—
134C25C22×C412yes—
135C25C2×D414yes—
136C25C2×D412yes—
137C25C2×D412yes—
138C25C2×D414yes—
139C25C2×Q814yes—
140C25C2×Q812yes—
141C25C2×Q812yes—
142C25#4112yes—
143C25#4114yes—
144C25#4112yes—
145C25C2411yescharacteristic
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—216no—
151C23×C4—216no—
152C23×C4—28no—
153C23×C4—28no—
154C23×C4—28no—
155C23×C4—28no—
156C23×C4—216no—
157C23×C4—28no—
158C23×C4—28no—
159C23×C4—216no—
160C23×C4—28no—
161C23×C4—28no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—24no—
166C23×C4—24no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—24no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—24no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—24no—
184C23×C4—24no—
185C23×C4—24no—
186C23×C4—24no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—24no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—216no—
197C23×C4—28no—
198C23×C4—216no—
199C23×C4—216no—
200C23×C4—216no—
201C23×C4—28no—
202C23×C4—216no—
203C23×C4—216no—
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—24no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—48no—
225C23×C4—44no—
226C23×C4—44no—
227C23×C4—48no—
228C23×C4—48no—
229C23×C4—48no—
230C23×C4—416no—
231C23×C4—416no—
232C23×C4—416no—
233C23×C4—416no—
234C23×C4—416no—
235C23×C4—416no—
236C23×C4—416no—
237C23×C4—416no—
238C23×C4—416no—
239C23×C4—416no—
240C23×C4—416no—
241C23×C4—416no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—48no—
247C23×C4—48no—
248C23×C4—44no—
249C23×C4—48no—
250C23×C4—48no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4C4⋊C4116yescomplemented
255C23×C4C22×C418yes—
256C23×C4C22×C412yes—
257C23×C4C22×C412yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D418yes—
261C23×C4C2×D412yes—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D412yes—
266C23×C4C2×D414yes—
267C23×C4C2×Q818yes—
268C23×C4C2×Q812yes—
269C23×C4C2×Q814yes—
270C23×C4C2×Q812yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—232no—
277C2×C4⋊C4—416no—
278C2×C4⋊C4—416no—
279C2×C4⋊C4—416no—
280C2×C4⋊C4—416no—
281C2×C4⋊C4—416no—
282C2×C4⋊C4—416no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—416no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—416no—
288C2×C4⋊C4—44no—
289C2×C22⋊C4—216no—
290C2×C22⋊C4—216no—
291C2×C22⋊C4—216no—
292C2×C22⋊C4—216no—
293C2×C22⋊C4—216no—
294C2×C22⋊C4—216no—
295C2×C22⋊C4—216no—
296C2×C22⋊C4—216no—
297C2×C22⋊C4—216no—
298C2×C22⋊C4—48no—
299C2×C22⋊C4—48no—
300C2×C22⋊C4—48no—
301C2×C22⋊C4—48no—
302C2×C22⋊C4C4⋊C4132yescomplemented
303#95—216no—
304#95—216no—
305#95—232no—
306#95—216no—
307#95—216no—
308#95—48no—
309#95—416no—
310#95—416no—
311C24—24no—
312C24—24no—
313C24—24no—
314C24—24no—
315C24—22no—
316C24—24no—
317C24—24no—
318C24—24no—
319C24—22no—
320C24—22no—
321C24—22no—
322C24—24no—
323C24—24no—
324C24—24no—
325C24—24no—
326C24—24no—
327C24—24no—
328C24—24no—
329C24—22no—
330C24—22no—
331C24—24no—
332C24—22no—
333C24—22no—
334C24—24no—
335C24—24no—
336C24—24no—
337C24—24no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—24no—
342C24—24no—
343C24—28no—
344C24—28no—
345C24—28no—
346C24—28no—
347C24—28no—
348C24—28no—
349C24—28no—
350C24—28no—
351C24—28no—
352C24—28no—
353C24—28no—
354C24—28no—
355C24—28no—
356C24—28no—
357C24—28no—
358C24—28no—
359C24C2×C4⋊C418yes—
360C24C2×C4⋊C414yes—
361C24C4×D414yes—
362C24C4×D418yes—
363C24C4×Q814yes—
364C24#12018yes—
365C24#12014yes—
366C24#12118yes—
367C24#12114yes—
368C24C22⋊Q818yes—
369C24C22⋊Q818yes—
370C24C22⋊Q818yes—
371C24C22⋊Q814yes—
372C24C22⋊Q818yes—
373C24#12318yes—
374C24#12314yes—
375C24#12514yes—
376C24#12518yes—
377C24#12714yes—
378C24C4⋊Q814yes—
379C24C4⋊Q818yes—
380C24C4⋊Q814yes—
381C24C4⋊Q818yes—
382C24C23×C411yescharacteristic
383C24C22×D411yescharacteristic
384C24C22×D412yes—
385C24C22×D411yescharacteristic
386C24C22×D412yes—
387C24C22×D412yes—
388C24C22×Q811yescharacteristic
389C24C22×Q812yes—
390C24C22×Q811yescharacteristic
391C24C2×#4111yescharacteristic
392C24C2×#4112yes—
393C24C2×#4112yes—
394C24C2×#4111yescharacteristic
395C24C2×#4112yes—
396C24C2×#4112yes—
397C24H(5,𝔽2)12yes—
398C24H(5,𝔽2)12yes—
399C24H(5,𝔽2)12yes—
400C242−1+412yes—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—232no—
414C22×C4—232no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—28no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—28no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—28no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—232no—
470C22×C4—232no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—416no—
482C22×C4—464no—
483C22×C4—416no—
484C22×C4—416no—
485C22×C4—416no—
486C22×C4—464no—
487C22×C4—416no—
488C22×C4—464no—
489C22×C4—464no—
490C22×C4—416no—
491C22×C4—416no—
492C22×C4—416no—
493C22×C4—416no—
494C22×C4—416no—
495C22×C4—464no—
496C22×C4—464no—
497C22×C4—416no—
498C22×C4—416no—
499C22×C4—416no—
500C22×C4—416no—
501C22×C4—416no—
502C22×C4—42no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—42no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—416no—
543C22×C4—416no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—44no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4C2×C4⋊C4116yes—
581C22×C4C2×C4⋊C414yes—
582C22×C4C2×C4⋊C414yes—
583C22×C4C4×D418yes—
584C22×C4#12014yes—
585C22×C4#12118yes—
586C22×C4C22⋊Q818yes—
587C22×C4C22⋊Q818yes—
588C22×C4#12314yes—
589C4⋊C4—416no—
590C4⋊C4—416no—
591C4⋊C4—464no—
592C22⋊C4—264no—
593C22⋊C4—432no—
594C23—216no—
595C23—24no—
596C23—24no—
597C23—28no—
598C23—24no—
599C23—24no—
600C23—28no—
601C23—24no—
602C23—24no—
603C23—28no—
604C23—24no—
605C23—24no—
606C23—28no—
607C23—216no—
608C23—216no—
609C23—216no—
610C23—216no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—28no—
616C23—24no—
617C23—28no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—216no—
623C23—216no—
624C23—216no—
625C23—216no—
626C23—216no—
627C23—216no—
628C23—216no—
629C23—24no—
630C23—24no—
631C23—216no—
632C23—216no—
633C23—216no—
634C23—216no—
635C23—216no—
636C23—216no—
637C23—216no—
638C23—216no—
639C23—216no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—216no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—216no—
650C23—216no—
651C23—24no—
652C23—28no—
653C23—28no—
654C23#38418yes—
655C23#385116yes—
656C23#38518yes—
657C23#38918yes—
658C23#389116yes—
659C23#39218yes—
660C23#39518yes—
661C23#395116yes—
662C23#398116yes—
663C23#39818yes—
664C23#39918yes—
665C23C22×C4⋊C411yescharacteristic
666C23C22×C4⋊C412yes—
667C23C2×C4×D411yescharacteristic
668C23C2×C4×D412yes—
669C23C2×C4×D412yes—
670C23C2×C4×Q811yescharacteristic
671C23C4×#4112yes—
672C23#51812yes—
673C23#52012yes—
674C23C2×#12011yescharacteristic
675C23C2×#12011yescharacteristic
676C23C2×#12012yes—
677C23C2×#12111yescharacteristic
678C23C2×#12112yes—
679C23C2×#12112yes—
680C23C2×C22⋊Q812yes—
681C23C2×C22⋊Q811yescharacteristic
682C23C2×C22⋊Q812yes—
683C23C2×C22⋊Q812yes—
684C23C2×C22⋊Q812yes—
685C23C2×C22⋊Q812yes—
686C23C2×C22⋊Q812yes—
687C23C2×#12311yescharacteristic
688C23C2×#12311yescharacteristic
689C23C2×#12312yes—
690C23#52511yescharacteristic
691C23#52511yescharacteristic
692C23#52512yes—
693C23#52512yes—
694C23C2×#12511yescharacteristic
695C23C2×#12512yes—
696C23#52912yes—
697C23#52912yes—
698C23C2×#12711yescharacteristic
699C23C2×C4⋊Q811yescharacteristic
700C23C2×C4⋊Q811yescharacteristic
701C23C2×C4⋊Q812yes—
702C23C2×C4⋊Q812yes—
703C23#53212yes—
704C23#53312yes—
705C23#53312yes—
706C23#53412yes—
707C23#53411yescharacteristic
708C23#53411yescharacteristic
709C23#53511yescharacteristic
710C23#53611yescharacteristic
711C23#53712yes—
712C23#53812yes—
713C23#53812yes—
714C23#53912yes—
715C23#53912yes—
716C23#54312yes—
717C23#54312yes—
718C23#54412yes—
719C23#54412yes—
720C23D4214yes—
721C23D4214yes—
722C23#54614yes—
723C23#54614yes—
724C23#54614yes—
725C23#54614yes—
726C23#54614yes—
727C23#54714yes—
728C23#54714yes—
729C23D4×Q814yes—
730C23#55114yes—
731C23#55114yes—
732C23#55214yes—
733C23#55414yes—
734C23#55414yes—
735C23#55414yes—
736C2×C4—24no—
737C2×C4—216no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—216no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—216no—
748C2×C4—216no—
749C2×C4—216no—
750C2×C4—216no—
751C2×C4—216no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—464no—
755C2×C4—464no—
756C2×C4—464no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4#38518yescomplemented
816C22—28no—
817C22—28no—
818C22—28no—
819C22—28no—
820C22—28no—
821C22—28no—
822C22—28no—
823C22—28no—
824C22—28no—
825C22—28no—
826C22—28no—
827C22—232no—
828C22—232no—
829C22—232no—
830C22—28no—
831C22—232no—
832C22—28no—
833C22—28no—
834C22#1444116yescomplemented
835C22C2×#38411yescharacteristic
836C22C2×#38511yescharacteristic
837C22C2×#38512yes—
838C22C2×#38511yescharacteristic
839C22C2×#38911yescharacteristic
840C22C2×#38912yes—
841C22#229611yescharacteristic
842C22C4×#12112yes—
843C22C4×C22⋊Q812yes—
844C22#231511yescharacteristic
845C22#231711yescharacteristic
846C22#232512yes—
847C22#232912yes—
848C22D4×C4⋊C414yes—
849C22#234914yes—
850C22#235814yes—
851C22#235914yes—
852C22C2×#39211yescharacteristic
853C22C2×#39511yescharacteristic
854C22C2×#39512yes—
855C22C2×#39812yes—
856C22C2×#39811yescharacteristic
857C22C2×#39911yescharacteristic
858C22#240311yescharacteristic
859C22#240411yescharacteristic
860C22#240511yescharacteristic
861C22#240511yescharacteristic
862C22#240611yescharacteristic
863C22#241014yes—
864C22#241714yes—
865C22#241814yes—
866C22#241914yes—
867C22#242414yes—
868C22#242514yes—
869C22#243014yes—
870C22#243311yescharacteristic
871C22#243411yescharacteristic
872C22#243714yes—
873C22#243714yes—
874C22#243814yes—
875C22#243814yes—
876C22#244014yes—
877C22#244014yes—
878C22#244914yes—
879C22#245014yes—
880C22#247314yes—
881C22#248211yescharacteristic
882C22#248311yescharacteristic
883C22#248411yescharacteristic
884C22#250111yescharacteristic
885C22#250211yescharacteristic
886C22#250514yes—
887C22#253911yescharacteristic
888C22#253911yescharacteristic
889C22#254914yes—
890C22#254914yes—
891C22#256414yes—
892C22#258311yescharacteristic
893C22#258311yescharacteristic
894C22#261711yescharacteristic
895C22#261811yescharacteristic
896C22#262611yescharacteristic
897C22#262711yescharacteristic
898C22#264612yes—
899C22#265912yes—
900C22#284711yescharacteristic
901C22#284811yescharacteristic
902C22#285112yes—
903C22#285411yescharacteristic
904C22#285511yescharacteristic
905C22#285712yes—
906C4—28no—
907C4—44no—
908C4—48no—
909C4—48no—
910C4—416no—
911C4—84no—
912C4—84no—
913C2—216no—
914C2C2×#144411yescharacteristic
915C2#1388011yescharacteristic
916C2#1396511yescharacteristic
917C2#1397514yes—
918C2#1400414yes—
919C2#1412711yescharacteristic
920C2#1412811yescharacteristic
921C2#1427511yescharacteristic
922C2#1469711yescharacteristic
923C2#1471611yescharacteristic
924C2#1472011yescharacteristic
925C2#1473411yescharacteristic
926C2#1473614yes—
927C2#1475814yes—
928C2#1482111yescharacteristic
929C2#1491411yescharacteristic
930C2#1492611yescharacteristic
931C2#1493611yescharacteristic
932C2#1501411yescharacteristic
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
4. C2×#1444C2semidirect
7. #7557C2semidirect
8. #7557C2semidirect
34. C22⋊#95C4semidirect
123. C2×#95C2×C4semidirect
124. C2×#95C2×C4semidirect
254. C23×C4C4⋊C4semidirect
302. C2×C22⋊C4C4⋊C4semidirect
815. C2×C4#385semidirect
834. C22#1444semidirect

Maximal subgroups

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

subgroupindex
C22×#3852
C22×#3802
C23×#952
C2×#14442
C2×C22⋊#952
#75572