Finite Group Databasebeta

← #6627177

Subgroups — #6627177

Order 512.

3292 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#3360C212yesmaximal, complemented
3#36579C211yesmaximal, characteristic, complemented
4#32908C212yesmaximal
5#32905C211yesmaximal, characteristic, complemented
6#25938C214yesmaximal, complemented
7#25934C212yesmaximal, complemented
8#25907C212yesmaximal, complemented
9#25902C211yesmaximal, characteristic, complemented
10#24337C214yesmaximal, complemented
11#24327C212yesmaximal, complemented
12#24307C212yesmaximal, complemented
13#24299C211yesmaximal, characteristic, complemented
14#22519C212yesmaximal, complemented
15Q8×C22⋊C8C211yesmaximal, characteristic, complemented
16C4×#450C212yesmaximal, complemented
17C4×#447C211yesmaximal, characteristic
18C2×#556C2211yescharacteristic, complemented
19C2×#554—216no—
20C2×#554—21no—
21C2×#554—21no—
22C2×#554—22no—
23C2×#554C2212yes—
24C2×#554C2214yes—
25C2×#554C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125C2212yes—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8—22no—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yes—
33C23×C4⋊C4—21no—
34#3360—216no—
35C2×#488C2214yescomplemented
36C2×#487C2212yescomplemented
37C2×#479C2214yescomplemented
38C2×#476C2212yescomplemented
39C2×#463C2214yes—
40C2×#461C2212yes—
41C2×#450C2212yes—
42C2×#447C2211yescharacteristic
43C2×C8×Q8C2212yescomplemented
44C2×C4×SD16C2214yes—
45C2×C4×D8C2212yes—
46#2857C2211yescharacteristic
47#2850C2212yes—
48#2592C2212yescomplemented
49#2581C2212yescomplemented
50#2568C2211yescharacteristic, complemented
51#2538C2211yescharacteristic, complemented
52#2481—22no—
53#2469—22no—
54#2421—21no—
55#2409—21no—
56#2362—21no—
57#2355C2211yescharacteristic, complemented
58#2352—21no—
59C4×C22⋊Q8C2212yes—
60C4×#121C2211yescharacteristic
61#2059C2214yescomplemented
62#2058C2212yescomplemented
63#2026C2214yescomplemented
64#2026C2214yescomplemented
65#2025C2214yescomplemented
66#2024C2214yescomplemented
67#2023C2212yescomplemented
68#1991C2214yescomplemented
69#1990C2212yescomplemented
70#1989C2214yescomplemented
71#1987C2212yescomplemented
72#1984C2212yescomplemented
73#1984C2214yescomplemented
74#1879C2214yes—
75#1879C2212yes—
76#1877C2214yes—
77#1877C2214yes—
78#1877C2214yes—
79#1874C2211yescharacteristic
80#1874C2212yes—
81#1872C2212yes—
82#1872C2212yes—
83#1872C2212yes—
84#1864C2214yes—
85#1862C2212yes—
86#1853C2212yes—
87#1852C2211yescharacteristic
88#1804C2214yes—
89#1802C2212yes—
90#1797C2211yescharacteristic
91#1797C2212yes—
92#1786C2211yescharacteristic
93C4×#102C2212yes—
94C4×#102C2214yes—
95C4×C22⋊C8C2211yescharacteristic
96C4×C22⋊C8C2212yes—
97C23×Q8—21no—
98C23×Q8D411yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C24×C4—22no—
102C22×SD16C2314yes—
103C22×D8C2312yes—
104#556—28no—
105#554—216no—
106#554—232no—
107#554—216no—
108#554—28no—
109#554—216no—
110#554—28no—
111#554—28no—
112#554—216no—
113#554D4116yescomplemented
114C2×C4⋊Q8—28no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2312yes—
120C2×#126—22no—
121C2×#125—216no—
122C2×#125—22no—
123C2×#125—22no—
124C2×#125C2314yes—
125C2×#125C2314yes—
126C2×#124C2312yes—
127C2×C22⋊Q8—232no—
128C2×C22⋊Q8—216no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8C2312yes—
139C2×#121C2311yescharacteristic
140C2×C4×Q8—28no—
141C2×C4×Q8D411yescharacteristic
142C2×C4×Q8D411yescharacteristic
143C2×C4×Q8D412yes—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2311yescharacteristic
148C2×C4×D4—216no—
149C2×C4×D4—28no—
150C2×C4×D4—21no—
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4C2312yes—
156C2×C4×D4C2314yes—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2312yes—
159C2×C4×D4C2314yes—
160C2×#117—21no—
161C22×C4⋊C4—216no—
162C22×C4⋊C4—22no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—22no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—22no—
168C22×C4⋊C4D411yescharacteristic
169C22×C4⋊C4D412yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—22no—
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176#488—216no—
177#487—28no—
178#479—216no—
179#476—28no—
180#463—216no—
181#461—28no—
182#450—28no—
183#447—24no—
184C8×Q8—28no—
185C4×SD16—216no—
186C4×D8—28no—
187C2×#107C2312yes—
188C2×#106C2314yes—
189C2×C4⋊C8C2314yes—
190C2×C4⋊C8C2312yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2314yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2314yes—
205#400—22no—
206#400—22no—
207#397—22no—
208#396—22no—
209#395—22no—
210#393—22no—
211#391—21no—
212#391—21no—
213#391C2312yes—
214#391C2312yes—
215#391C2312yes—
216#390C2311yescharacteristic
217#390C2312yes—
218#389—21no—
219#389—21no—
220#389C2311yescharacteristic
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—21no—
227#387—22no—
228#387—22no—
229#387—22no—
230#387—22no—
231#386—22no—
232#386—22no—
233#386—21no—
234#385—22no—
235#384C2311yescharacteristic
236#382—21no—
237#382C2312yes—
238#380—21no—
239#380—21no—
240#380—21no—
241#380C2311yescharacteristic
242C4×C4⋊C4—21no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4C2311yescharacteristic
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—21no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2312yes—
252#340C2314yes—
253#340C2312yes—
254#340C2314yes—
255#336C2312yes—
256#336C2314yes—
257#336C2312yes—
258#336C2314yes—
259C25—21no—
260C22×Q8—28no—
261C22×Q8—24no—
262C22×Q8—24no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—42no—
266C22×Q8—82no—
267C22×Q8—82no—
268C22×Q8C2×D411yescharacteristic
269C22×Q8C2×D412yes—
270C22×Q8C2×D411yescharacteristic
271C22×Q8C2412yes—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4#4114yes—
278C22×D4C2411yescharacteristic
279C22×D4C2412yes—
280C23×C4—28no—
281C23×C4—21no—
282C23×C4—22no—
283C23×C4—216no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—21no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—84no—
292C23×C4—84no—
293C23×C4C2×D412yes—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D412yes—
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×SD16—28no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×D8—24no—
302C2×D8—24no—
303C2×D8—24no—
304C22×C8C2412yes—
305C22×C8C2414yes—
306C22×C8C2412yes—
307C4⋊Q8—28no—
308C4⋊Q8—28no—
309C4⋊Q8—28no—
310C4⋊Q8—24no—
311C4⋊Q8—24no—
312C4⋊Q8C2×D418yes—
313#126—48no—
314#125—216no—
315#125—216no—
316#125—28no—
317#125—28no—
318#125—28no—
319#125C2×D4116yes—
320#124—28no—
321C22⋊Q8—216no—
322C22⋊Q8—232no—
323C22⋊Q8—232no—
324C22⋊Q8—232no—
325C22⋊Q8—232no—
326C22⋊Q8—216no—
327C22⋊Q8—232no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332#121—22no—
333#121—22no—
334C4×Q8—24no—
335C4×Q8—28no—
336C4×Q8—24no—
337C4×Q8—24no—
338C4×Q8—28no—
339C4×Q8—28no—
340C4×Q8C2×D418yes—
341C4×D4—216no—
342C4×D4—216no—
343C4×D4—28no—
344C4×D4—28no—
345C4×D4—28no—
346C4×D4—24no—
347C4×D4—28no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—28no—
351C4×D4—24no—
352C4×D4—44no—
353C4×D4C2×D418yes—
354C4×D4C2×D4116yes—
355#117—44no—
356C2×C4⋊C4—216no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—216no—
359C2×C4⋊C4—232no—
360C2×C4⋊C4—216no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—216no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2414yes—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—216no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—22no—
411C2×C42—28no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—21no—
415C2×C42—22no—
416C2×C42C2×D412yes—
417C2×C42C2×D412yes—
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2412yes—
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2412yes—
424#107—24no—
425#106—28no—
426C4⋊C8—24no—
427C4⋊C8—28no—
428#103—28no—
429#103—28no—
430#103—28no—
431#102—24no—
432#102—24no—
433#102—28no—
434#102—24no—
435#102—24no—
436#102—28no—
437C22⋊C8—22no—
438C22⋊C8—24no—
439C22⋊C8—22no—
440C4×C8—24no—
441C4×C8—28no—
442#95—21no—
443#95—22no—
444#95—22no—
445#95—21no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—21no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—22no—
459C24—21no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24C22×D411yescharacteristic
465C2×Q8—28no—
466C2×Q8—24no—
467C2×Q8—22no—
468C2×Q8—28no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—42no—
479C2×Q8—416no—
480C2×Q8—82no—
481C2×Q8—82no—
482C2×Q8—82no—
483C2×Q8—82no—
484C2×Q8—816no—
485C2×Q8#12014yes—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—216no—
489C2×D4—216no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C22×D414yes—
502C2×D4C2×#4114yes—
503C2×D42−1+414yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—216no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—28no—
521C22×C4—216no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—44no—
531C22×C4—432no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—42no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4—832no—
547C22×C4#13514yes—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C2×#4112yes—
558C22×C42−1+412yes—
559C22×C4C2511yescharacteristic
560SD16—416no—
561D8—48no—
562C2×C8—22no—
563C2×C8—24no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—24no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—24no—
571C4⋊C4—216no—
572C4⋊C4—28no—
573C4⋊C4—24no—
574C4⋊C4—28no—
575C4⋊C4—216no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—216no—
579C4⋊C4—28no—
580C4⋊C4—216no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4#12014yes—
601C4⋊C4#12018yes—
602C4⋊C4C22×D418yes—
603C4⋊C4C22×D414yes—
604C22⋊C4—216no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—216no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—42no—
611C22⋊C4—44no—
612C22⋊C4—42no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—82no—
617C22⋊C4—81no—
618C42—24no—
619C42—24no—
620C42—22no—
621C42—22no—
622C42—24no—
623C42—22no—
624C42—44no—
625C42—42no—
626C42—82no—
627C42C22×D414yes—
628C42C22×D418yes—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—216no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—48no—
638C23—48no—
639C23—48no—
640C23—48no—
641C23—48no—
642C23—42no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23#54812yes—
655C23C2×#13512yes—
656C23#57712yes—
657C23C23×D411yescharacteristic
658Q8—28no—
659Q8—48no—
660Q8—44no—
661Q8—44no—
662Q8—44no—
663Q8—88no—
664Q8—88no—
665D4—216no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4#54818yes—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—44no—
700C2×C4—416no—
701C2×C4—48no—
702C2×C4—416no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—416no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—816no—
724C2×C4—816no—
725C2×C4—84no—
726C2×C4C2×#12014yes—
727C2×C4C2×#12014yes—
728C2×C4C2×#12012yes—
729C2×C4C2×#12012yes—
730C2×C4#54812yes—
731C2×C4C2×#13512yes—
732C2×C4C2×#13512yes—
733C2×C4#57512yes—
734C2×C4C23×D412yes—
735C2×C4C22×#4111yescharacteristic
736C2×C4C2×2−1+412yes—
737C2×C4C2×2−1+411yescharacteristic
738C8—42no—
739C8—44no—
740C8—42no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—28no—
748C22—432no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#336014yescomplemented
763C22C22×#12011yescharacteristic
764C22C2×#54811yescharacteristic
765C22#348611yescharacteristic
766C22C22×#13511yescharacteristic
767C22C2×#57511yescharacteristic
768C22C2×#57711yescharacteristic
769C22#358511yescharacteristic
770C4—22no—
771C4—24no—
772C4—24no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—44no—
777C4—42no—
778C4—41no—
779C4—48no—
780C4—81no—
781C4—81no—
782C4—82no—
783C4—81no—
784C4—82no—
785C4#300214yes—
786C4C2×#54812yes—
787C4#348612yes—
788C2—24no—
789C2—48no—
790C2—161no—
791C2#3657511yescharacteristic
792C2C2×#300211yescharacteristic
793C2#6037311yescharacteristic
794C2C2×#336011yescharacteristic
795C2#6131811yescharacteristic
796C2#6181911yescharacteristic
797C2#6184111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#554C2semidirect
2. C2×#3360C2semidirect
3. #36579C2semidirect
5. #32905C2semidirect
6. #25938C2semidirect
7. #25934C2semidirect
8. #25907C2semidirect
9. #25902C2semidirect
10. #24337C2semidirect
11. #24327C2semidirect
12. #24307C2semidirect
13. #24299C2semidirect
14. #22519C2semidirect
15. Q8×C22⋊C8C2semidirect
16. C4×#450C2semidirect
18. C2×#556C22semidirect
35. C2×#488C22semidirect
36. C2×#487C22semidirect
37. C2×#479C22semidirect
38. C2×#476C22semidirect
43. C2×C8×Q8C22semidirect
48. #2592C22semidirect
49. #2581C22semidirect
50. #2568C22semidirect
51. #2538C22semidirect
57. #2355C22semidirect
61. #2059C22semidirect
62. #2058C22semidirect
63. #2026C22semidirect
64. #2026C22semidirect
65. #2025C22semidirect
66. #2024C22semidirect
67. #2023C22semidirect
68. #1991C22semidirect
69. #1990C22semidirect
70. #1989C22semidirect
71. #1987C22semidirect
72. #1984C22semidirect
73. #1984C22semidirect
113. #554D4semidirect
762. C22#3360semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#33602
#365792
#329082
#329052
#259382
#259342
#259072
#259022
#243372
#243272
#243072
#242992
#225192
Q8×C22⋊C82
C4×#4502
C4×#4472