Finite Group Databasebeta

← #6469940

Subgroups — #6469940

Order 512.

4959 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#3190C212yesmaximal, complemented
3#36614C211yesmaximal, characteristic
4#32982C211yesmaximal, characteristic, complemented
5#32978C211yesmaximal, characteristic, complemented
6#32882C211yesmaximal, characteristic, complemented
7#32879C211yesmaximal, characteristic, complemented
8#29599C212yesmaximal, complemented
9#29595C212yesmaximal, complemented
10#24381C214yesmaximal, complemented
11#24380C214yesmaximal, complemented
12#24010C214yesmaximal, complemented
13#23922C214yesmaximal, complemented
14#21762C212yesmaximal, complemented
15C2×#1779C211yesmaximal, characteristic, complemented
16C24×Q8C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C2×#525C2211yescharacteristic
19C2×#525C2212yes—
20C22×C22⋊Q8—22no—
21C22×C22⋊Q8—21no—
22C22×C22⋊Q8—21no—
23C22×C22⋊Q8—22no—
24C22×C22⋊Q8—216no—
25C22×C22⋊Q8C2214yes—
26C22×C22⋊Q8C2214yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2212yes—
29C23×C4⋊C4—21no—
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4—21no—
32#3190—216no—
33C2×#485C2214yescomplemented
34C2×#483C2212yescomplemented
35C2×#480C2212yescomplemented
36C2×#467C2214yescomplemented
37C2×#465C2214yescomplemented
38C2×#452C2214yescomplemented
39C2×#451C2212yescomplemented
40C2×#451C2214yescomplemented
41C2×#448C2212yescomplemented
42C2×#448C2214yescomplemented
43C22×C22⋊C8C2212yes—
44C22×C22⋊C8C2214yes—
45#2849—22no—
46#2849—21no—
47#2848C2212yes—
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2847C2212yes—
51#2847C2211yescharacteristic
52#2847C2211yescharacteristic
53#2846—21no—
54C4×#120—21no—
55C4×#120—22no—
56C4×#120—21no—
57#2280C2211yescharacteristic
58#2280C2212yes—
59#2036C2218yescomplemented
60#2035C2218yescomplemented
61#2001C2218yescomplemented
62#2000C2218yescomplemented
63#1892C2218yescomplemented
64#1874C2214yescomplemented
65#1873C2218yescomplemented
66#1872C2214yescomplemented
67#1853C2214yescomplemented
68#1852C2214yescomplemented
69#1823C2212yescomplemented
70#1823C2212yescomplemented
71#1787C2212yescomplemented
72#1787C2212yescomplemented
73#1787C2214yescomplemented
74#1787C2214yescomplemented
75#1779C2211yescharacteristic
76#1779C2214yes—
77#1779C2211yescharacteristic
78#1779C2212yes—
79C26D411yescharacteristic
80C22×#41C2311yescharacteristic
81C23×Q8—28no—
82C23×Q8—22no—
83C23×Q8—21no—
84C23×Q8—48no—
85C23×Q8C2314yes—
86C23×Q8C2312yes—
87C24×C4—21no—
88C24×C4—21no—
89C24×C4—28no—
90C24×C4—48no—
91C24×C4D411yescharacteristic
92C24×C4D412yes—
93C24×C4D411yescharacteristic
94C24×C4D411yescharacteristic
95C24×C4D412yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C22×Q16C2314yescomplemented
102C22×SD16C2314yescomplemented
103C23×C8C2314yes—
104#525—28no—
105#525—48no—
106C2×#123—22no—
107C2×#123—21no—
108C2×C22⋊Q8—232no—
109C2×C22⋊Q8—232no—
110C2×C22⋊Q8—216no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—232no—
122C2×C22⋊Q8—232no—
123C2×C22⋊Q8—28no—
124C2×C22⋊Q8D4116yescomplemented
125C2×C22⋊Q8C2311yescharacteristic
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2311yescharacteristic
128C2×C22⋊Q8C2318yes—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2312yes—
132C2×#121C2311yescharacteristic
133C2×#121C2312yes—
134C2×#121C2311yescharacteristic
135C2×#121C2312yes—
136C2×#120—21no—
137C2×#120—21no—
138C2×#120—22no—
139C2×#120—22no—
140C2×#120—21no—
141C2×C4×D4—22no—
142C2×C4×D4—22no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×#117C2311yescharacteristic
146C2×#117C2312yes—
147C22×C4⋊C4—216no—
148C22×C4⋊C4—24no—
149C22×C4⋊C4—24no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4—22no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—22no—
154C22×C4⋊C4—28no—
155C22×C4⋊C4C2314yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4—216no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—22no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—22no—
162#485—216no—
163#483—28no—
164#480—28no—
165#467—216no—
166#465—216no—
167#452—216no—
168#451—28no—
169#451—48no—
170#448—28no—
171#448—48no—
172C2×#107C2314yescomplemented
173C2×#106C2314yescomplemented
174C2×#103C2314yescomplemented
175C2×#103C2314yescomplemented
176C2×#103C2314yescomplemented
177C2×#103C2318yescomplemented
178C2×#103C2318yescomplemented
179C2×#102C2314yescomplemented
180C2×C22⋊C8—28no—
181C2×C22⋊C8—48no—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C2×C22⋊C8C2318yes—
188#386—22no—
189#386—21no—
190#386—22no—
191#386—22no—
192#386—22no—
193#386—21no—
194#386—22no—
195#385—22no—
196#385—21no—
197#385—22no—
198#385—22no—
199#385—22no—
200#385—21no—
201#385—22no—
202#381—22no—
203#381—21no—
204#380C2311yescharacteristic
205#380C2311yescharacteristic
206#380C2312yes—
207#380C2312yes—
208#380C2312yes—
209#380C2312yes—
210#380C2312yes—
211#379—21no—
212#379—21no—
213#379—22no—
214#379—22no—
215#379—21no—
216C4×C22⋊C4—22no—
217C4×C22⋊C4—22no—
218C4×C22⋊C4—21no—
219C4×C22⋊C4—21no—
220#340C2318yescomplemented
221#340C2318yescomplemented
222C25—24no—
223C25—28no—
224C25—24no—
225C25—44no—
226C25—42no—
227C25C2×D411yescharacteristic
228C25C2×D412yes—
229C25C2×D411yescharacteristic
230C25C2×D411yescharacteristic
231C25C2×D412yes—
232C2×#41—24no—
233C2×#41—44no—
234C22×Q8—28no—
235C22×Q8—216no—
236C22×Q8—216no—
237C22×Q8—24no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—28no—
241C22×Q8—28no—
242C22×Q8—48no—
243C22×Q8—48no—
244C22×Q8—464no—
245C22×Q8—48no—
246C22×Q8—48no—
247C22×Q8—48no—
248C22×Q8C2×D418yes—
249C22×Q8C2411yescharacteristic
250C22×Q8C2414yes—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4C2411yescharacteristic
257C23×C4—24no—
258C23×C4—28no—
259C23×C4—28no—
260C23×C4—28no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—24no—
273C23×C4—28no—
274C23×C4—28no—
275C23×C4—21no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—464no—
288C23×C4—44no—
289C23×C4—48no—
290C23×C4—44no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4C2×D412yes—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D412yes—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D418yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C2×Q16—28no—
311C2×Q16—48no—
312C2×SD16—28no—
313C2×SD16—48no—
314C22×C8—28no—
315C22×C8—48no—
316C22×C8C2414yes—
317C22×C8C2414yes—
318#123—48no—
319#123—44no—
320C22⋊Q8—232no—
321C22⋊Q8—232no—
322C22⋊Q8—232no—
323C22⋊Q8—232no—
324C22⋊Q8—232no—
325C22⋊Q8—216no—
326C22⋊Q8—216no—
327C22⋊Q8—216no—
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330C22⋊Q8—216no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—28no—
334C22⋊Q8—44no—
335C22⋊Q8C2×D4116yes—
336C22⋊Q8C2×D4116yes—
337#121—24no—
338#121—24no—
339#121—28no—
340#121—44no—
341#120—44no—
342#120—48no—
343#120—44no—
344#120—44no—
345#120—48no—
346C4×D4—48no—
347C4×D4—48no—
348C4×D4—44no—
349C4×D4—44no—
350#117—24no—
351#117—44no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—216no—
354C2×C4⋊C4—232no—
355C2×C4⋊C4—232no—
356C2×C4⋊C4—216no—
357C2×C4⋊C4—216no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—216no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C2×D418yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2411yescharacteristic
373C2×C4⋊C4C2411yescharacteristic
374C2×C4⋊C4C2414yes—
375C2×C22⋊C4—216no—
376C2×C22⋊C4—232no—
377C2×C22⋊C4—232no—
378C2×C22⋊C4—216no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C42—22no—
400C2×C42—21no—
401#107—28no—
402#106—28no—
403#103—28no—
404#103—28no—
405#103—28no—
406#103—48no—
407#103—48no—
408#102—28no—
409C22⋊C8—24no—
410C22⋊C8—24no—
411C22⋊C8—28no—
412C22⋊C8—28no—
413C22⋊C8—28no—
414C22⋊C8—48no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—21no—
419#95—21no—
420#95—22no—
421#95—22no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—22no—
426C24—232no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—22no—
439C24—24no—
440C24—24no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—432no—
451C24—416no—
452C24—416no—
453C24—432no—
454C24#12014yes—
455C24#13514yes—
456C24#13718yes—
457C24C22×D411yescharacteristic
458C24C22×D412yes—
459C24C22×D411yescharacteristic
460C24C22×D411yescharacteristic
461C24C22×D412yes—
462#41—88no—
463C2×Q8—216no—
464C2×Q8—28no—
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—24no—
470C2×Q8—416no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—464no—
474C2×Q8—432no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—416no—
478C2×Q8—48no—
479C2×Q8C22×D418yes—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—42no—
495C22×C4—232no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—216no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—28no—
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—24no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—416no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—416no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—416no—
553C22×C4—416no—
554C22×C4—44no—
555C22×C4—432no—
556C22×C4—48no—
557C22×C4—416no—
558C22×C4—432no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4#12014yes—
567C22×C4#12014yes—
568C22×C4#12014yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4H(5,𝔽2)18yes—
578C22×C4C2511yescharacteristic
579Q16—88no—
580SD16—88no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—28no—
584C2×C8—28no—
585C2×C8—88no—
586C4⋊C4—216no—
587C4⋊C4—232no—
588C4⋊C4—216no—
589C4⋊C4—216no—
590C4⋊C4—28no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—44no—
600C4⋊C4C22×D418yes—
601C22⋊C4—232no—
602C22⋊C4—216no—
603C22⋊C4—216no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—42no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—44no—
621C42—44no—
622C42—42no—
623C23—28no—
624C23—28no—
625C23—216no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—216no—
631C23—28no—
632C23—21no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—28no—
638C23—216no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—216no—
644C23—28no—
645C23—28no—
646C23—216no—
647C23—22no—
648C23—21no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—21no—
653C23—44no—
654C23—48no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23—48no—
659C23—48no—
660C23—48no—
661C23—48no—
662C23—48no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—44no—
668C23—4128no—
669C23—48no—
670C23—48no—
671C23—44no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23C2×#12012yes—
678C23C2×#12012yes—
679C23C2×#12012yes—
680C23#53414yes—
681C23C2×#13514yes—
682C23C2×#13512yes—
683C23C2×#13714yes—
684C23C2×#13714yes—
685C23C2×#13714yes—
686C23#57512yes—
687C23C23×D411yescharacteristic
688Q8—28no—
689Q8—28no—
690Q8—416no—
691Q8—432no—
692Q8—48no—
693Q8—44no—
694D4—44no—
695D4—88no—
696D4—84no—
697D4—88no—
698D4—84no—
699D4—84no—
700C2×C4—216no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—216no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—432no—
727C2×C4—44no—
728C2×C4—416no—
729C2×C4—432no—
730C2×C4—48no—
731C2×C4—416no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—48no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4C2×#12012yes—
750C2×C4C2×#12012yes—
751C2×C4C2×#12012yes—
752C2×C4#53414yes—
753C2×C4C23×D412yes—
754C2×C4C2×H(5,𝔽2)14yes—
755C8—44no—
756C8—44no—
757C22—232no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—22no—
766C22—24no—
767C22—22no—
768C22—24no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—24no—
778C22—432no—
779C22—416no—
780C22—432no—
781C22—416no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—82no—
789C22—82no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22#300214yes—
794C22#300414yes—
795C22#319018yescomplemented
796C22C22×#12011yescharacteristic
797C22C2×#53412yes—
798C22C22×#13511yescharacteristic
799C22C22×#13712yes—
800C22C2×#57511yescharacteristic
801C4—22no—
802C4—24no—
803C4—22no—
804C4—22no—
805C4—42no—
806C4—48no—
807C4—48no—
808C4—82no—
809C4—82no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4#348414yes—
814C2—28no—
815C2—24no—
816C2—24no—
817C2—44no—
818C2—42no—
819C2—161no—
820C2#3498011yescharacteristic
821C2C2×#300211yescharacteristic
822C2C2×#300411yescharacteristic
823C2C2×#319012yes—
824C2#6075112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36614C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊Q8C2semidirect
2. C2×#3190C2semidirect
4. #32982C2semidirect
5. #32978C2semidirect
6. #32882C2semidirect
7. #32879C2semidirect
8. #29599C2semidirect
9. #29595C2semidirect
10. #24381C2semidirect
11. #24380C2semidirect
12. #24010C2semidirect
13. #23922C2semidirect
14. #21762C2semidirect
15. C2×#1779C2semidirect
33. C2×#485C22semidirect
34. C2×#483C22semidirect
35. C2×#480C22semidirect
36. C2×#467C22semidirect
37. C2×#465C22semidirect
38. C2×#452C22semidirect
39. C2×#451C22semidirect
40. C2×#451C22semidirect
41. C2×#448C22semidirect
42. C2×#448C22semidirect
59. #2036C22semidirect
60. #2035C22semidirect
61. #2001C22semidirect
62. #2000C22semidirect
63. #1892C22semidirect
64. #1874C22semidirect
65. #1873C22semidirect
66. #1872C22semidirect
67. #1853C22semidirect
68. #1852C22semidirect
69. #1823C22semidirect
70. #1823C22semidirect
71. #1787C22semidirect
72. #1787C22semidirect
73. #1787C22semidirect
74. #1787C22semidirect
101. C22×Q16C23semidirect
102. C22×SD16C23semidirect
124. C2×C22⋊Q8D4semidirect
172. C2×#107C23semidirect
173. C2×#106C23semidirect
174. C2×#103C23semidirect
175. C2×#103C23semidirect
176. C2×#103C23semidirect
177. C2×#103C23semidirect
178. C2×#103C23semidirect
179. C2×#102C23semidirect
220. #340C23semidirect
221. #340C23semidirect
795. C22#3190semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C2×#31902
#366142
#329822
#329782
#328822
#328792
#295992
#295952
#243812
#243802
#240102
#239222
#217622
C2×#17792