Finite Group Databasebeta

← #5956082

Subgroups — #5956082

Order 512.

6162 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2316C211yesmaximal, characteristic, complemented
3C2×#2311C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5C2×#2280C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7#15181C214yesmaximal, complemented
8#15179C214yesmaximal, complemented
9#15129C214yesmaximal, complemented
10#15126C214yesmaximal, complemented
11#14927C214yesmaximal, complemented
12#14725C214yesmaximal, complemented
13#13795C211yesmaximal, characteristic, complemented
14C23×#41C2211yescharacteristic
15C25×C4C2211yescharacteristic
16C2×#525—28no—
17C2×#525—28no—
18C2×#525—28no—
19C22×#123C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×#121C2212yes—
22C22×#120C2212yes—
23C22×C4×D4C2214yes—
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C2×#394C2218yes—
31#2316—28no—
32#2311—28no—
33#2311—28no—
34C2×#391C2212yescomplemented
35C2×#391C2212yescomplemented
36C2×#390C2212yescomplemented
37C2×#390C2212yescomplemented
38C2×#389C2214yescomplemented
39C2×#389C2214yescomplemented
40C2×#386C2214yes—
41C2×#386C2214yes—
42#2280—28no—
43C2×#381C2212yes—
44C2×#380—28no—
45C2×#380C2214yes—
46C2×#380C2214yes—
47C2×#380C2212yes—
48C2×#380C2214yes—
49C2×#380C2212yes—
50C2×#380C2212yescomplemented
51C2×#380C2214yescomplemented
52C2×#380C2212yescomplemented
53C2×#379C2212yes—
54C2×C4×C22⋊C4C2214yes—
55C22×#95C2212yes—
56#1442C2218yescomplemented
57#1441C2218yescomplemented
58#1440C2218yes—
59#1440C2218yescomplemented
60#1439C2218yes—
61#1439C2218yescomplemented
62#1438C2218yes—
63C4⋊#95C2214yescomplemented
64C4⋊#95C2212yescomplemented
65C4⋊#95C2212yescomplemented
66C22⋊#95C2214yes—
67C26C2311yescharacteristic
68C22×#41—24no—
69C22×#41—24no—
70C22×#41—24no—
71C22×#41—24no—
72C22×#41—24no—
73C22×#41—24no—
74C22×#41D418yes—
75C23×Q8C2311yescharacteristic
76C23×D4C2312yes—
77C23×D4C2311yescharacteristic
78C23×D4C2314yes—
79C24×C4—24no—
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4D418yes—
86C24×C4C2312yes—
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93#525—2128no—
94C2×#123—28no—
95C2×#123—28no—
96C2×#123—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×#121—28no—
101C2×#121—28no—
102C2×#121—28no—
103C2×#120—28no—
104C2×#120—28no—
105C2×#120—28no—
106C2×C4×D4—216no—
107C2×C4×D4—216no—
108C2×C4×D4—216no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117D418yes—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4D418yescomplemented
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2318yes—
134C22×C22⋊C4—28no—
135C22×C22⋊C4—48no—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2318yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2318yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150#394—416no—
151#391—28no—
152#391—28no—
153#390—28no—
154#390—28no—
155#389—216no—
156#389—216no—
157#386—216no—
158#386—216no—
159#381—28no—
160#380—216no—
161#380—28no—
162#380—28no—
163#380—28no—
164#380—28no—
165#380—216no—
166#380—216no—
167#380—216no—
168#379—28no—
169C4×C22⋊C4—216no—
170C2×#95—28no—
171C2×#95C2318yes—
172C2×#95C2314yes—
173C2×#95C2318yes—
174C2×#95C2314yes—
175C2×#95C2318yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2318yes—
179C2×#95C2318yes—
180C25—22no—
181C25—22no—
182C25—24no—
183C25—24no—
184C25—22no—
185C25—22no—
186C25—22no—
187C25—22no—
188C25—42no—
189C25—42no—
190C25C2×D414yes—
191C25C2412yes—
192C25C2412yes—
193C25C2411yescharacteristic
194C2×#41—232no—
195C2×#41—232no—
196C2×#41—232no—
197C2×#41—416no—
198C2×#41—416no—
199C2×#41—416no—
200C2×#41—416no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8C2×D414yes—
208C22×D4—28no—
209C22×D4—28no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—28no—
217C22×D4—28no—
218C22×D4—28no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4C2×D418yes—
228C22×D4C2×D414yes—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—232no—
238C23×C4—232no—
239C23×C4—232no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4—416no—
266C23×C4—416no—
267C23×C4—416no—
268C23×C4—416no—
269C23×C4C2×D418yes—
270C23×C4C2×D418yes—
271C23×C4C2×D418yes—
272C23×C4C2×D414yes—
273C23×C4C2×D418yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4#4114yes—
280C23×C4#4114yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2414yes—
285C23×C4C2414yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291#123—264no—
292C22⋊Q8—264no—
293#121—264no—
294#120—264no—
295C4×D4—2128no—
296#117—232no—
297#117—416no—
298#117—416no—
299C2×C4⋊C4—232no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—216no—
325C2×C4⋊C4—416no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D418yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—216no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—216no—
351C2×C22⋊C4—216no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—48no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—432no—
358C2×C22⋊C4—48no—
359C2×C22⋊C4—48no—
360C2×C22⋊C4—48no—
361C2×C22⋊C4—48no—
362C2×C22⋊C4C2×D418yes—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42C2×D418yes—
372#95—216no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—216no—
378#95—216no—
379#95—48no—
380#95—48no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—28no—
386C24—28no—
387C24—216no—
388C24—28no—
389C24—216no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—28no—
403C24—28no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—48no—
423C24—44no—
424C24—44no—
425C24—48no—
426C24—44no—
427C24—44no—
428C24—44no—
429C24—44no—
430C24C22×D414yes—
431C24C22×D414yes—
432C24C22×D412yes—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C22×D412yes—
436C24C2×#4112yes—
437C24C2×#4112yes—
438C24C2×#4112yes—
439C24H(5,𝔽2)14yes—
440C242−1+414yes—
441C24C2511yescharacteristic
442#41—4128no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×D4—232no—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—216no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—416no—
458C2×D4—416no—
459C2×D4—416no—
460C2×D4—416no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—416no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—28no—
495C22×C4—24no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—216no—
505C22×C4—216no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—28no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—28no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—4128no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—88no—
551C22×C4—88no—
552C22×C4—88no—
553C22×C4—88no—
554C22×C4#120116yes—
555C22×C4#121116yes—
556C22×C4#121116yes—
557C22×C4#121116yes—
558C22×C4#123116yes—
559C22×C4#123116yes—
560C22×C4#124116yes—
561C22×C4C22×D418yes—
562C22×C4C22×D414yes—
563C22×C4C22×D414yes—
564C22×C4C22×D418yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4112yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C4⋊C4—232no—
580C4⋊C4—216no—
581C4⋊C4—216no—
582C4⋊C4—216no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—816no—
589C22⋊C4—232no—
590C22⋊C4—232no—
591C22⋊C4—216no—
592C22⋊C4—432no—
593C22⋊C4—416no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—416no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C22⋊C4—816no—
600C42—216no—
601C42—48no—
602C42—48no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—232no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—28no—
642C23—28no—
643C23—432no—
644C23—432no—
645C23—416no—
646C23—416no—
647C23—416no—
648C23—416no—
649C23—432no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23C2×#12014yes—
688C23C2×#12114yes—
689C23C2×#12114yes—
690C23C2×#12114yes—
691C23C2×#12314yes—
692C23C2×#12314yes—
693C23C2×#12414yes—
694C23#53718yes—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C23×D411yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C22×#4111yescharacteristic
702C23C2×H(5,𝔽2)12yes—
703C23C2×2−1+412yes—
704C23#58512yes—
705C23#58512yes—
706Q8—416no—
707D4—464no—
708D4—432no—
709D4—416no—
710C2×C4—28no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
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—44no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—432no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—48no—
762C2×C4—816no—
763C2×C4—816no—
764C2×C4#394164yescomplemented
765C2×C4C2×#12014yes—
766C2×C4C2×#12014yes—
767C2×C4C2×#12114yes—
768C2×C4C2×#12114yes—
769C2×C4C2×#12114yes—
770C2×C4C2×#12114yes—
771C2×C4C2×#12114yes—
772C2×C4C2×#12114yes—
773C2×C4C2×#12314yes—
774C2×C4C2×#12314yes—
775C2×C4C2×#12314yes—
776C2×C4C2×#12314yes—
777C2×C4C2×#12414yes—
778C2×C4C2×#12414yes—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—24no—
789C22—28no—
790C22—28no—
791C22—28no—
792C22—464no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—48no—
807C22—48no—
808C22—44no—
809C22—44no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—84no—
815C22—84no—
816C22C2×#39418yes—
817C22C22×#12011yescharacteristic
818C22C22×#12111yescharacteristic
819C22C22×#12111yescharacteristic
820C22C22×#12111yescharacteristic
821C22C22×#12311yescharacteristic
822C22C22×#12311yescharacteristic
823C22C22×#12411yescharacteristic
824C22C2×#53712yes—
825C22#344912yes—
826C22#348411yescharacteristic
827C22#348511yescharacteristic
828C22#348611yescharacteristic
829C22#348711yescharacteristic
830C22#348812yes—
831C22#348812yes—
832C22#348912yes—
833C22#348912yes—
834C22#349212yes—
835C22#349312yes—
836C22#349412yes—
837C22#349412yes—
838C22#349512yes—
839C22#349512yes—
840C4—48no—
841C4—48no—
842C4—44no—
843C4—44no—
844C4—82no—
845C4—82no—
846C4—84no—
847C4—84no—
848C4C2×#39418yes—
849C4C2×#39418yes—
850C2—28no—
851C2—48no—
852C2—84no—
853C2C22×#39411yescharacteristic
854C2#3515011yescharacteristic
855C2#3522311yescharacteristic
856C2#3525112yes—
857C2#3526312yes—
858C2#3551411yescharacteristic
859C2#3551612yes—
860C2#3554212yes—
861C2#3556311yescharacteristic
862C2#3563311yescharacteristic
863C2#3566111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2316C2semidirect
3. C2×#2311C2semidirect
4. C2×#2311C2semidirect
5. C2×#2280C2semidirect
6. C22×#380C2semidirect
7. #15181C2semidirect
8. #15179C2semidirect
9. #15129C2semidirect
10. #15126C2semidirect
11. #14927C2semidirect
12. #14725C2semidirect
13. #13795C2semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
36. C2×#390C22semidirect
37. C2×#390C22semidirect
38. C2×#389C22semidirect
39. C2×#389C22semidirect
50. C2×#380C22semidirect
51. C2×#380C22semidirect
52. C2×#380C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
59. #1440C22semidirect
61. #1439C22semidirect
63. C4⋊#95C22semidirect
64. C4⋊#95C22semidirect
65. C4⋊#95C22semidirect
123. C22×C4⋊C4D4semidirect
764. C2×C4#394semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#23162
C2×#23112
C2×#22802
C22×#3802
#151812
#151792
#151292
#151262
#149272
#147252
#137952