Finite Group Databasebeta

← #625768

Subgroups — #625768

Order 512.

4088 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2412C212yesmaximal, complemented
3C2×#2617C211yesmaximal, characteristic
4C2×#2315C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6#15419C214yesmaximal, complemented
7#15404C214yesmaximal, complemented
8#15303C214yesmaximal, complemented
9#15290C214yesmaximal, complemented
10#14927C212yesmaximal, complemented
11#14729C212yesmaximal, complemented
12#14685C211yesmaximal, characteristic, complemented
13#14275C211yesmaximal, characteristic, complemented
14#14271C211yesmaximal, characteristic, complemented
15#14134C212yesmaximal, complemented
16C22×#123C2212yes—
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2854—28no—
26#2617—28no—
27#2412—216no—
28C2×#397C2214yes—
29C2×#397C2212yes—
30C2×#396C2214yescomplemented
31C2×#394C2212yes—
32C2×#394C2214yes—
33C2×#394C2212yes—
34C2×#392C2212yes—
35#2315—28no—
36C2×#390C2212yescomplemented
37C2×#389C2212yescomplemented
38C2×#388—28no—
39C2×#388C2214yes—
40C2×#388C2214yes—
41C2×#388C2214yescomplemented
42C2×#386C2212yes—
43C2×#386C2214yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2214yes—
47C2×#386C2212yes—
48C2×#385C2214yes—
49C2×#385C2214yes—
50C2×#385C2212yes—
51C2×#381C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2214yes—
56C2×#380C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59#1445C2212yescomplemented
60#1444C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1440C2214yes—
68#1440C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1438C2214yes—
73#1438C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76#1434C2214yescomplemented
77C22⋊#95C2214yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C26C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2312yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2314yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×#123—28no—
93C2×#123—28no—
94C2×#123—44no—
95C2×#121—24no—
96C2×#121—24no—
97C2×#121—24no—
98C2×#120—28no—
99C2×#120—28no—
100C2×#120—28no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—44no—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—28no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—28no—
119C22×C22⋊C4—44no—
120C22×C22⋊C4—44no—
121C22×C22⋊C4D418yes—
122C22×C22⋊C4D418yescomplemented
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42C2312yes—
144C22×C42C2312yes—
145#397—28no—
146#397—216no—
147#396—48no—
148#394—28no—
149#394—28no—
150#394—216no—
151#392—28no—
152#390—28no—
153#389—28no—
154#388—216no—
155#388—216no—
156#388—216no—
157#386—28no—
158#386—28no—
159#386—28no—
160#386—216no—
161#386—48no—
162#386—44no—
163#385—28no—
164#385—216no—
165#385—216no—
166#381—28no—
167#380—24no—
168#380—24no—
169#380—28no—
170#380—216no—
171#380D418yescomplemented
172C2×#95—24no—
173C2×#95—24no—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—42no—
198C25—42no—
199C25—42no—
200C25—42no—
201C25C2×D414yes—
202C25C2×D414yes—
203C25#4114yes—
204C25C2412yes—
205C25C2412yes—
206C25C2411yescharacteristic
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
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—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—28no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—28no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—44no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4#4114yes—
268C23×C4C2414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2414yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280#123—432no—
281#121—416no—
282#120—432no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—416no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D418yes—
309C2×C22⋊C4—232no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—232no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—432no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4C2×D418yes—
359C2×C22⋊C4C2×D418yes—
360C2×C22⋊C4C2×D418yes—
361C2×C22⋊C4C2×D4116yes—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—416no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—28no—
376#95—24no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—24no—
381#95—24no—
382#95—28no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D418yes—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—22no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—28no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—44no—
418C24—48no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—84no—
426C24—84no—
427C24—84no—
428C24—84no—
429C24—84no—
430C24—84no—
431C24—84no—
432C24—84no—
433C24#121116yes—
434C24C22×D414yes—
435C24C22×D414yes—
436C24C22×D412yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24C2×#4114yes—
440C24C2×#4112yes—
441C24C2×#4112yes—
442C24H(5,𝔽2)12yes—
443C242−1+412yes—
444C24C2511yescharacteristic
445C2×D4—48no—
446C2×D4—416no—
447C2×D4—416no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—44no—
458C2×D4—82no—
459C2×D4—82no—
460C2×D4—84no—
461C2×D4—84no—
462C2×D4—84no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—88no—
466C2×D4—88no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—416no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—416no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—88no—
556C22×C4—88no—
557C22×C4—84no—
558C22×C4—84no—
559C22×C4—88no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4#121116yes—
565C22×C4C22×D414yes—
566C22×C4C22×D414yes—
567C22×C4C22×D414yes—
568C22×C4C22×D418yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4H(5,𝔽2)14yes—
576C4⋊C4—48no—
577C4⋊C4—416no—
578C4⋊C4—416no—
579C4⋊C4—44no—
580C4⋊C4—84no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—88no—
584C4⋊C4—88no—
585C22⋊C4—232no—
586C22⋊C4—216no—
587C22⋊C4—216no—
588C22⋊C4—216no—
589C22⋊C4—416no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C22⋊C4—88no—
601C22⋊C4—88no—
602C42—48no—
603C42—48no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—28no—
623C23—28no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—28no—
633C23—28no—
634C23—232no—
635C23—416no—
636C23—416no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—44no—
649C23—44no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—816no—
669C23—816no—
670C23—88no—
671C23—88no—
672C23—88no—
673C23—816no—
674C23—88no—
675C23—816no—
676C23C2×#12118yes—
677C23C2×#12114yes—
678C23C2×#12114yes—
679C23#53714yes—
680C23D4214yes—
681C23#54714yes—
682C23#54814yes—
683C23#55314yes—
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C23×D411yescharacteristic
687C23C22×#4111yescharacteristic
688C23C22×#4111yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)12yes—
691C23C2×2−1+411yescharacteristic
692C23#58512yes—
693C23#58512yes—
694C23#58512yes—
695D4—88no—
696D4—816no—
697D4—816no—
698D4—816no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—28no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—416no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
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—88no—
772C2×C4—832no—
773C2×C4—88no—
774C2×C4C2×#12114yes—
775C2×C4C2×#12114yes—
776C22—24no—
777C22—28no—
778C22—28no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—28no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—28no—
789C22—48no—
790C22—48no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—48no—
795C22—44no—
796C22—48no—
797C22—832no—
798C22—82no—
799C22—84no—
800C22—84no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—84no—
806C22—82no—
807C22—82no—
808C22—84no—
809C22#241618yes—
810C22C22×#12111yescharacteristic
811C22C22×#12111yescharacteristic
812C22C2×#53711yescharacteristic
813C22#344912yes—
814C22#345912yes—
815C22C2×D4211yescharacteristic
816C22C2×#54711yescharacteristic
817C22C2×#54811yescharacteristic
818C22C2×#55311yescharacteristic
819C22#348411yescharacteristic
820C22#348511yescharacteristic
821C22#348511yescharacteristic
822C22#348512yes—
823C22#348511yescharacteristic
824C22#348812yes—
825C22#349112yes—
826C22#349112yes—
827C22#349412yes—
828C22#349612yes—
829C22#355812yes—
830C22#356012yes—
831C22#356112yes—
832C22#356412yes—
833C4—24no—
834C4—24no—
835C4—48no—
836C4—44no—
837C4—44no—
838C4—44no—
839C4—44no—
840C4—82no—
841C4—84no—
842C4—82no—
843C4—82no—
844C4—82no—
845C2—28no—
846C2—48no—
847C2—162no—
848C2C2×#241611yescharacteristic
849C2#3498411yescharacteristic
850C2#3508911yescharacteristic
851C2#3544711yescharacteristic
852C2#3551411yescharacteristic
853C2#3695711yescharacteristic
854C2#3696011yescharacteristic
855C2#3767812yes—
856C2#3775412yes—
857C2#3786612yes—
858C2#3794212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2617C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2854C2semidirect
2. C2×#2412C2semidirect
4. C2×#2315C2semidirect
5. C22×#388C2semidirect
6. #15419C2semidirect
7. #15404C2semidirect
8. #15303C2semidirect
9. #15290C2semidirect
10. #14927C2semidirect
11. #14729C2semidirect
12. #14685C2semidirect
13. #14275C2semidirect
14. #14271C2semidirect
15. #14134C2semidirect
30. C2×#396C22semidirect
36. C2×#390C22semidirect
37. C2×#389C22semidirect
41. C2×#388C22semidirect
59. #1445C22semidirect
60. #1444C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
73. #1438C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. #1434C22semidirect
122. C22×C22⋊C4D4semidirect
171. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#24122
C2×#26172
C2×#23152
C22×#3882
#154192
#154042
#153032
#152902
#149272
#147292
#146852
#142752
#142712
#141342