Finite Group Databasebeta

← #625929

Subgroups — #625929

Order 512.

4034 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2534C212yesmaximal, complemented
3C2×#2617C211yesmaximal, characteristic
4C2×#2325C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6#15780C214yesmaximal, complemented
7#15774C214yesmaximal, complemented
8#15307C214yesmaximal, complemented
9#15303C214yesmaximal, complemented
10#14927C212yesmaximal, complemented
11#14725C212yesmaximal, complemented
12#14685C211yesmaximal, characteristic, complemented
13#14353C211yesmaximal, characteristic, complemented
14#14338C211yesmaximal, characteristic, complemented
15#13872C212yesmaximal, complemented
16C22×#123C2212yes—
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C22×C4×D4C2212yes—
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2854—28no—
26#2617—28no—
27#2534—216no—
28C2×#397C2212yes—
29C2×#396C2214yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#392C2212yes—
34#2325—28no—
35C2×#390C2212yescomplemented
36C2×#389C2212yescomplemented
37C2×#388—28no—
38C2×#388C2214yes—
39C2×#388C2214yes—
40C2×#388C2214yes—
41C2×#388C2214yescomplemented
42C2×#388C2212yescomplemented
43C2×#387C2212yescomplemented
44C2×#386C2214yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yescomplemented
49C2×#385C2212yescomplemented
50C2×#381C2212yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2214yescomplemented
57C2×#379C2212yes—
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1444C2214yescomplemented
61#1444C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1440C2214yes—
66#1440C2214yescomplemented
67#1439C2214yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1438C2214yes—
74C4⋊#95C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77#1434C2214yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C26C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2314yes—
83C23×D4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C2×#123—28no—
92C2×#123—28no—
93C2×#123—44no—
94C2×#121—24no—
95C2×#121—24no—
96C2×#121D418yes—
97C2×#120—28no—
98C2×#120—28no—
99C2×#120—44no—
100C2×C4×D4—28no—
101C2×C4×D4—28no—
102C2×C4×D4—28no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4D418yescomplemented
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2312yes—
146#397—28no—
147#396—216no—
148#394—216no—
149#394—216no—
150#394—48no—
151#392—28no—
152#390—28no—
153#389—28no—
154#388—216no—
155#388—216no—
156#388—28no—
157#388—216no—
158#388—216no—
159#387—28no—
160#386—28no—
161#386—28no—
162#386—28no—
163#386—216no—
164#386—28no—
165#385—28no—
166#381—28no—
167#380—24no—
168#380—24no—
169#380—24no—
170#380—28no—
171#380—48no—
172#380—44no—
173#379—28no—
174C2×#95—24no—
175C2×#95D418yescomplemented
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—42no—
201C25—42no—
202C25—42no—
203C25—42no—
204C25C2×D414yes—
205C25C2412yes—
206C25C2412yes—
207C25C2411yescharacteristic
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—28no—
215C22×D4—28no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—44no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—44no—
225C22×D4C2×D418yes—
226C22×D4C2×D414yes—
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—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—44no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276#123—432no—
277#121—232no—
278#120—432no—
279C4×D4—432no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—416no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D414yes—
309C2×C22⋊C4—232no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—416no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4C2×D4116yes—
360C2×C22⋊C4C2×D418yes—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—416no—
371#95—28no—
372#95—24no—
373#95—28no—
374#95—24no—
375#95—24no—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D418yes—
388#95C2×D418yes—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—28no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—28no—
415C24—28no—
416C24—48no—
417C24—48no—
418C24—44no—
419C24—48no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24—84no—
429C24—84no—
430C24—84no—
431C24—84no—
432C24—84no—
433C24—84no—
434C24—84no—
435C24—84no—
436C24C22×D414yes—
437C24C22×D414yes—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C2×#4112yes—
442C24C2×#4112yes—
443C24H(5,𝔽2)12yes—
444C242−1+412yes—
445C24C2511yescharacteristic
446C2×D4—216no—
447C2×D4—216no—
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—416no—
456C2×D4—416no—
457C2×D4—82no—
458C2×D4—82no—
459C2×D4—84no—
460C2×D4—88no—
461C2×D4—88no—
462C2×D4—88no—
463C2×D4—88no—
464C2×D4—88no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—28no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—416no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—48no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—88no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4#121116yes—
558C22×C4#121116yes—
559C22×C4C22×D414yes—
560C22×C4C22×D414yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D414yes—
566C22×C4C22×D412yes—
567C22×C4C22×D414yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4114yes—
571C22×C4H(5,𝔽2)14yes—
572C4⋊C4—28no—
573C4⋊C4—416no—
574C4⋊C4—416no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—82no—
578C4⋊C4—82no—
579C4⋊C4—84no—
580C4⋊C4—88no—
581C4⋊C4—88no—
582C22⋊C4—232no—
583C22⋊C4—216no—
584C22⋊C4—416no—
585C22⋊C4—416no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—416no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C42—48no—
600C42—48no—
601C42—48no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—28no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—416no—
629C23—416no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—416no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—816no—
668C23—816no—
669C23—816no—
670C23—88no—
671C23—88no—
672C23—88no—
673C23—816no—
674C23—88no—
675C23C2×#12114yes—
676C23C2×#12114yes—
677C23#53714yes—
678C23D4214yes—
679C23#54714yes—
680C23#54714yes—
681C23#55514yes—
682C23C23×D411yescharacteristic
683C23C23×D411yescharacteristic
684C23C23×D411yescharacteristic
685C23C22×#4111yescharacteristic
686C23C22×#4111yescharacteristic
687C23C2×H(5,𝔽2)11yescharacteristic
688C23C2×H(5,𝔽2)12yes—
689C23C2×2−1+411yescharacteristic
690C23#58512yes—
691C23#58512yes—
692C23#58512yes—
693D4—432no—
694D4—88no—
695D4—832no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—416no—
721C2×C4—416no—
722C2×C4—416no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—42no—
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—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
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—816no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4C2×#12114yes—
771C2×C4C2×#12114yes—
772C2×C4C2×#12118yes—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—28no—
780C22—24no—
781C22—28no—
782C22—24no—
783C22—48no—
784C22—48no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—48no—
790C22—44no—
791C22—48no—
792C22—44no—
793C22—832no—
794C22—84no—
795C22—84no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—84no—
803C22—82no—
804C22—84no—
805C22—82no—
806C22#253718yes—
807C22C22×#12111yescharacteristic
808C22C22×#12111yescharacteristic
809C22C2×#53711yescharacteristic
810C22#344912yes—
811C22#345912yes—
812C22C2×D4211yescharacteristic
813C22C2×#54711yescharacteristic
814C22C2×#54711yescharacteristic
815C22C2×#55511yescharacteristic
816C22#348411yescharacteristic
817C22#348512yes—
818C22#348511yescharacteristic
819C22#348511yescharacteristic
820C22#348711yescharacteristic
821C22#348812yes—
822C22#349112yes—
823C22#349312yes—
824C22#349412yes—
825C22#349612yes—
826C22#355812yes—
827C22#356012yes—
828C22#356112yes—
829C22#356412yes—
830C4—24no—
831C4—24no—
832C4—28no—
833C4—44no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—84no—
838C4—84no—
839C4—82no—
840C4—82no—
841C4—82no—
842C2—28no—
843C2—84no—
844C2—84no—
845C2C2×#253711yescharacteristic
846C2#3498411yescharacteristic
847C2#3515011yescharacteristic
848C2#3544711yescharacteristic
849C2#3556311yescharacteristic
850C2#3695711yescharacteristic
851C2#3697111yescharacteristic
852C2#3767812yes—
853C2#3776212yes—
854C2#3786612yes—
855C2#3795012yes—
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×#2534C2semidirect
4. C2×#2325C2semidirect
5. C22×#388C2semidirect
6. #15780C2semidirect
7. #15774C2semidirect
8. #15307C2semidirect
9. #15303C2semidirect
10. #14927C2semidirect
11. #14725C2semidirect
12. #14685C2semidirect
13. #14353C2semidirect
14. #14338C2semidirect
15. #13872C2semidirect
35. C2×#390C22semidirect
36. C2×#389C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
43. C2×#387C22semidirect
48. C2×#386C22semidirect
49. C2×#385C22semidirect
56. C2×#380C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
66. #1440C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
77. #1434C22semidirect
122. C22×C22⋊C4D4semidirect
175. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#25342
C2×#26172
C2×#23252
C22×#3882
#157802
#157742
#153072
#153032
#149272
#147252
#146852
#143532
#143382
#138722