Finite Group Databasebeta

← #626075

Subgroups — #626075

Order 512.

3964 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×#2411C212yesmaximal, complemented
2C2×#2618C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic
4C2×#2316C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6#15621C214yesmaximal, complemented
7#15619C214yesmaximal, complemented
8#15617C214yesmaximal, complemented
9#15615C214yesmaximal, complemented
10#14921C212yesmaximal, complemented
11#14725C212yesmaximal, complemented
12#14698C211yesmaximal, characteristic, complemented
13#14697C211yesmaximal, characteristic, complemented
14#14338C211yesmaximal, characteristic, complemented
15#14135C212yesmaximal, complemented
16C22×#123C2212yes—
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C22×#117C2212yes—
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2618—28no—
26#2617—28no—
27#2411—216no—
28C2×#398C2212yescomplemented
29C2×#397C2212yes—
30C2×#396C2214yes—
31C2×#396C2212yescomplemented
32C2×#396C2212yescomplemented
33C2×#394C2214yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36C2×#394C2212yescomplemented
37C2×#392C2212yes—
38#2316—28no—
39C2×#390C2214yes—
40C2×#390C2212yescomplemented
41C2×#389C2214yescomplemented
42C2×#389C2214yescomplemented
43C2×#389C2212yescomplemented
44C2×#388—28no—
45C2×#388C2214yes—
46C2×#388C2214yes—
47C2×#388C2214yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#385C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#379C2212yes—
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1443C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1440C2214yes—
64#1439C2214yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2214yes—
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1438C2214yes—
72#1437C2214yescomplemented
73#1437C2214yescomplemented
74#1436C2214yescomplemented
75#1436C2214yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C26C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C23×D4C2314yes—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×#123—28no—
91C2×#123—28no—
92C2×#123—28no—
93C2×#121—24no—
94C2×#121—24no—
95C2×#121—24no—
96C2×#120—28no—
97C2×#120—28no—
98C2×#120—44no—
99C2×#117—28no—
100C2×#117—28no—
101C2×#117—44no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4D418yescomplemented
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—44no—
124C22×C22⋊C4D418yescomplemented
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C42—24no—
144C22×C42—44no—
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2314yes—
148#398—28no—
149#397—28no—
150#396—28no—
151#396—28no—
152#396—216no—
153#394—216no—
154#394—28no—
155#394—216no—
156#394—48no—
157#392—28no—
158#390—216no—
159#390—44no—
160#389—216no—
161#389—216no—
162#389—44no—
163#388—216no—
164#388—216no—
165#388—216no—
166#386—28no—
167#386—28no—
168#386—28no—
169#386—44no—
170#385—28no—
171#380—24no—
172#380—24no—
173#380—28no—
174#380D418yes—
175#379—28no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
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—24no—
215C22×D4—28no—
216C22×D4—28no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—44no—
221C22×D4—42no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—42no—
225C22×D4—44no—
226C22×D4—44no—
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—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2×D414yes—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4#4114yes—
258C23×C4#4114yes—
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271#123—432no—
272#121—416no—
273#120—432no—
274#117—432no—
275C2×C4⋊C4—232no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4C2×D418yes—
308C2×C4⋊C4C2×D418yes—
309C2×C4⋊C4C2×D418yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—232no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
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⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4C2×D4116yes—
364C2×C22⋊C4C2×D418yes—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—44no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—416no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—24no—
384#95—24no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95C2×D418yes—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—28no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—28no—
407C24—28no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—48no—
420C24—48no—
421C24—44no—
422C24—48no—
423C24—44no—
424C24—44no—
425C24—44no—
426C24—48no—
427C24—44no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—84no—
432C24—84no—
433C24—84no—
434C24—84no—
435C24—84no—
436C24—84no—
437C24—84no—
438C24—84no—
439C24C22×D414yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24H(5,𝔽2)12yes—
446C242−1+412yes—
447C24C2511yescharacteristic
448C2×D4—416no—
449C2×D4—48no—
450C2×D4—416no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—82no—
460C2×D4—82no—
461C2×D4—84no—
462C2×D4—88no—
463C2×D4—88no—
464C2×D4—88no—
465C2×D4—88no—
466C2×D4—88no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4#121116yes—
557C22×C4#121116yes—
558C22×C4C22×D414yes—
559C22×C4C22×D414yes—
560C22×C4C22×D418yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D414yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)14yes—
571C4⋊C4—216no—
572C4⋊C4—216no—
573C4⋊C4—48no—
574C4⋊C4—416no—
575C4⋊C4—44no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—82no—
579C4⋊C4—82no—
580C4⋊C4—84no—
581C4⋊C4—88no—
582C4⋊C4—88no—
583C22⋊C4—216no—
584C22⋊C4—232no—
585C22⋊C4—416no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—48no—
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—
599C22⋊C4—88no—
600C22⋊C4—88no—
601C42—48no—
602C42—48no—
603C42—416no—
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—28no—
622C23—24no—
623C23—24no—
624C23—28no—
625C23—416no—
626C23—416no—
627C23—42no—
628C23—416no—
629C23—42no—
630C23—44no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—44no—
650C23—44no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—816no—
670C23—816no—
671C23—88no—
672C23—88no—
673C23—88no—
674C23—88no—
675C23—816no—
676C23—816no—
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—832no—
697D4—816no—
698C2×C4—24no—
699C2×C4—232no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—416no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
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—42no—
760C2×C4—42no—
761C2×C4—42no—
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—88no—
772C2×C4—88no—
773C2×C4C2×#12118yes—
774C2×C4C2×#12114yes—
775C2×C4C2×#12114yes—
776C22—24no—
777C22—28no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—28no—
786C22—48no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—48no—
791C22—832no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—84no—
797C22—84no—
798C22—82no—
799C22—84no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—84no—
807C22—84no—
808C22—84no—
809C22#241618yes—
810C22C22×#12111yescharacteristic
811C22C22×#12111yescharacteristic
812C22C2×#53711yescharacteristic
813C22#344912yes—
814C22#346012yes—
815C22C2×D4211yescharacteristic
816C22C2×#54711yescharacteristic
817C22C2×#54811yescharacteristic
818C22C2×#55311yescharacteristic
819C22#348411yescharacteristic
820C22#348511yescharacteristic
821C22#348711yescharacteristic
822C22#348711yescharacteristic
823C22#349312yes—
824C22#349612yes—
825C22#349612yes—
826C22#350012yes—
827C22#350512yes—
828C22#351012yes—
829C22#353412yes—
830C22#353512yes—
831C22#356012yes—
832C22#356412yes—
833C4—24no—
834C4—24no—
835C4—28no—
836C4—44no—
837C4—44no—
838C4—44no—
839C4—48no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—84no—
845C2—28no—
846C2—84no—
847C2—162no—
848C2C2×#241611yescharacteristic
849C2#3515011yescharacteristic
850C2#3516811yescharacteristic
851C2#3535811yescharacteristic
852C2#3567711yescharacteristic
853C2#3672211yescharacteristic
854C2#3697111yescharacteristic
855C2#3935412yes—
856C2#3942312yes—
857C2#3948212yes—
858C2#3955112yes—
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×#2411C2semidirect
2. C2×#2618C2semidirect
4. C2×#2316C2semidirect
5. C22×#388C2semidirect
6. #15621C2semidirect
7. #15619C2semidirect
8. #15617C2semidirect
9. #15615C2semidirect
10. #14921C2semidirect
11. #14725C2semidirect
12. #14698C2semidirect
13. #14697C2semidirect
14. #14338C2semidirect
15. #14135C2semidirect
28. C2×#398C22semidirect
31. C2×#396C22semidirect
32. C2×#396C22semidirect
36. C2×#394C22semidirect
40. C2×#390C22semidirect
41. C2×#389C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
60. #1443C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
72. #1437C22semidirect
73. #1437C22semidirect
74. #1436C22semidirect
75. #1436C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
104. C22×C4⋊C4D4semidirect
124. C22×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24112
C2×#26182
C2×#26172
C2×#23162
C22×#3882
#156212
#156192
#156172
#156152
#149212
#147252
#146982
#146972
#143382
#141352