Finite Group Databasebeta

← #626300

Subgroups — #626300

Order 512.

4224 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2501C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2431C211yesmaximal, characteristic
5C2×#2620C211yesmaximal, characteristic, complemented
6C2×#2311C211yesmaximal, characteristic, complemented
7#15505C218yesmaximal, complemented
8#15370C218yesmaximal, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15227C211yesmaximal, characteristic, complemented
11#15199C211yesmaximal, characteristic, complemented
12#15155C211yesmaximal, characteristic, complemented
13#14714C211yesmaximal, characteristic, complemented
14#14713C211yesmaximal, characteristic, complemented
15#14273C211yesmaximal, characteristic, complemented
16#14273C211yesmaximal, characteristic, complemented
17#13761C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×#127C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#123C2214yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2620—28no—
30#2502—28no—
31#2501—28no—
32#2432—28no—
33#2431—28no—
34C2×#399C2214yes—
35C2×#399C2218yes—
36C2×#398C2214yes—
37C2×#396C2214yes—
38C2×#394C2214yes—
39C2×#394C2214yes—
40C2×#392C2214yes—
41#2311—28no—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2218yes—
57C2×#386C2214yes—
58C2×#386C2214yes—
59C2×#385C2214yes—
60C2×#385C2214yes—
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C2×#380C2214yes—
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×#376C2211yescharacteristic
70C2×C43C2211yescharacteristic
71#1444C2218yes—
72#1439C2218yes—
73#1439C2218yes—
74#1439C2218yes—
75#1438C2218yes—
76#1437C2214yes—
77#1436C2214yes—
78C4⋊#95C2218yes—
79C4×#95C2211yescharacteristic
80C4×#95C2211yescharacteristic
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—24no—
85C22×#41—24no—
86C22×#41—42no—
87C22×#41—42no—
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C23×D4C2314yes—
94C23×D4C2312yes—
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—42no—
101C2×#127—24no—
102C2×#127—24no—
103C2×#127—42no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—42no—
110C2×#124—42no—
111C2×#124—42no—
112C2×#124—42no—
113C2×#123—216no—
114C2×#123—416no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#117—42no—
122C2×#117—42no—
123C2×#117D418yescomplemented
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C42C2314yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#399—216no—
163#399—416no—
164#398—216no—
165#396—216no—
166#394—216no—
167#394—216no—
168#392—216no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#390—24no—
177#390—24no—
178#390—24no—
179#390—24no—
180#390—24no—
181#390—24no—
182#390—24no—
183#390—416no—
184#386—216no—
185#386—216no—
186#385—216no—
187#385—216no—
188#384—24no—
189#384—24no—
190#384—24no—
191#384—24no—
192#384—24no—
193#380—216no—
194C4×C22⋊C4D418yes—
195C4×C22⋊C4D418yescomplemented
196#376—42no—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C43—42no—
210C25C2412yes—
211C25C2412yes—
212C25C2411yescharacteristic
213C2×#41—232no—
214C2×#41—416no—
215C2×#41—416no—
216C2×#41—416no—
217C2×#41—416no—
218C2×#41—416no—
219C2×#41—416no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8#4114yes—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—28no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—216no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—48no—
261C22×D4—44no—
262C22×D4—48no—
263C22×D4#4114yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—48no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C4⋊Q8—416no—
297#127—416no—
298#124—416no—
299#124—416no—
300#124—416no—
301#123—464no—
302C22⋊Q8—416no—
303#121—416no—
304#117—416no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—216no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—48no—
337C2×C4⋊C4—48no—
338C2×C4⋊C4—48no—
339C2×C4⋊C4C2×D418yes—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—216no—
357C2×C22⋊C4—216no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—48no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—48no—
370C2×C22⋊C4—48no—
371C2×C22⋊C4—48no—
372C2×C22⋊C4—48no—
373C2×C22⋊C4C2×D418yes—
374C2×C22⋊C4C2×D418yes—
375C2×C22⋊C4C2×D418yes—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—28no—
389C2×C42—28no—
390C2×C42—44no—
391C2×C42C2×D414yes—
392C2×C42C2×D414yes—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—44no—
407#95C2×D418yes—
408#95C2×D418yes—
409C24—21no—
410C24—21no—
411C24—24no—
412C24—21no—
413C24—21no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—28no—
420C24—22no—
421C24—22no—
422C24—28no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—28no—
429C24—22no—
430C24—22no—
431C24—28no—
432C24C22×D412yes—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C2×#4114yes—
436C24C2511yescharacteristic
437#41—4128no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×D4—216no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—416no—
459C2×D4—432no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—416no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—416no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—88no—
479C2×D4—816no—
480C2×D4—88no—
481C2×D4—88no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—88no—
553C22×C4—88no—
554C22×C4#127116yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D414yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D414yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)18yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C42−1+418yes—
574C4⋊C4—48no—
575C4⋊C4—416no—
576C4⋊C4—416no—
577C4⋊C4—48no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—48no—
583C4⋊C4—416no—
584C4⋊C4—88no—
585C4⋊C4—88no—
586C4⋊C4—88no—
587C22⋊C4—216no—
588C22⋊C4—216no—
589C22⋊C4—48no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—88no—
599C22⋊C4—88no—
600C22⋊C4—88no—
601C22⋊C4—88no—
602C42—28no—
603C42—28no—
604C42—28no—
605C42—28no—
606C42—28no—
607C42—28no—
608C42—416no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—216no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—42no—
630C23—42no—
631C23—44no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—48no—
640C23—48no—
641C23—48no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23—48no—
659C23C2×#12714yes—
660C23C23×D411yescharacteristic
661C23C23×D411yescharacteristic
662C23C23×D411yescharacteristic
663C23C22×#4111yescharacteristic
664C23C22×#4111yescharacteristic
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×H(5,𝔽2)11yescharacteristic
667C23C2×H(5,𝔽2)14yes—
668C23C2×2−1+414yes—
669Q8—416no—
670Q8—88no—
671D4—432no—
672D4—416no—
673D4—832no—
674D4—816no—
675D4—88no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—232no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—432no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—816no—
743C2×C4#52514yes—
744C2×C4C2×#12714yes—
745C2×C4C2×#12714yes—
746C2×C4#53414yes—
747C2×C4#53518yes—
748C2×C4#53618yes—
749C2×C4#54614yes—
750C2×C4#54614yes—
751C2×C4#54614yes—
752C2×C4#54614yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—48no—
764C22—48no—
765C22—48no—
766C22—84no—
767C22—84no—
768C22—84no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—84no—
773C22—84no—
774C22—84no—
775C22—84no—
776C22—84no—
777C22—82no—
778C22—84no—
779C22—82no—
780C22C2×#52511yescharacteristic
781C22C22×#12711yescharacteristic
782C22C2×#53411yescharacteristic
783C22C2×#53512yes—
784C22C2×#53612yes—
785C22C2×#54611yescharacteristic
786C22C2×#54611yescharacteristic
787C22C2×#54611yescharacteristic
788C22C2×#54611yescharacteristic
789C22#349812yes—
790C22#349812yes—
791C22#349912yes—
792C22#349912yes—
793C22#352014yes—
794C22#352214yes—
795C22#353614yes—
796C22#354814yes—
797C4—24no—
798C4—28no—
799C4—28no—
800C4—44no—
801C4—44no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4#253918yes—
811C2—44no—
812C2—84no—
813C2—162no—
814C2C2×#253911yescharacteristic
815C2#3527411yescharacteristic
816C2#3531711yescharacteristic
817C2#3553512yes—
818C2#3729612yes—
819C2#3807812yes—
820C2#3807912yes—
821C2#3895112yes—
822C2#3895212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2431C2
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×#2502C2semidirect
2. C2×#2501C2semidirect
3. C2×#2432C2semidirect
5. C2×#2620C2semidirect
6. C2×#2311C2semidirect
7. #15505C2semidirect
8. #15370C2semidirect
9. #15243C2semidirect
10. #15227C2semidirect
11. #15199C2semidirect
12. #15155C2semidirect
13. #14714C2semidirect
14. #14713C2semidirect
15. #14273C2semidirect
16. #14273C2semidirect
17. #13761C2semidirect
123. C2×#117D4semidirect
195. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#25012
C2×#24322
C2×#24312
C2×#26202
C2×#23112
#155052
#153702
#152432
#152272
#151992
#151552
#147142
#147132
#142732
#137612