Finite Group Databasebeta

← #6502778

Subgroups — #6502778

Order 512.

2272 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3189C211yesmaximal, characteristic, complemented
2C2×#2973C211yesmaximal, characteristic
3#35010C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic
5#28563C214yesmaximal, complemented
6#25248C214yesmaximal, complemented
7#25126C214yesmaximal, complemented
8#24783C214yesmaximal, complemented
9#24606C212yesmaximal, complemented
10#24556C212yesmaximal, complemented
11#24508C212yesmaximal, complemented
12#24386C212yesmaximal, complemented
13#21759C211yesmaximal, characteristic, complemented
14C2×#1872C211yesmaximal, characteristic, complemented
15C2×#1853C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21#3189—28no—
22C2×#484C2212yes—
23C2×#484C2212yescomplemented
24C2×#470C2214yescomplemented
25C2×#467C2214yescomplemented
26C2×#451C2212yes—
27C2×#451C2212yescomplemented
28#2973—28no—
29C2×#435C2214yes—
30C2×#435C2214yes—
31C2×#432C2212yes—
32C22×#106C2212yescomplemented
33C22×#103C2212yescomplemented
34C2×#407C2212yes—
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37#2855C2212yes—
38#2848C2212yes—
39#2627—21no—
40#2626—21no—
41#2579—22no—
42#2564—22no—
43#2487C2212yes—
44#2417—22no—
45#2417—22no—
46#2417C2214yes—
47#2417C2214yes—
48#2417C2212yes—
49#2417C2212yes—
50#2409C2212yes—
51C2×#398—21no—
52C2×#396—21no—
53#2315—21no—
54#2308—21no—
55C2×#391C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#386—21no—
58C2×#380—21no—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61#2086C2214yescomplemented
62#2075C2214yescomplemented
63#2066C2214yescomplemented
64#2066C2214yescomplemented
65#2056C2214yescomplemented
66#2035C2214yescomplemented
67#2035C2214yescomplemented
68#2001C2214yescomplemented
69#1971C2214yescomplemented
70#1944C2214yescomplemented
71#1935C2214yescomplemented
72#1935C2214yescomplemented
73#1894C2214yescomplemented
74#1894C2214yescomplemented
75#1892C2214yescomplemented
76#1872C2212yes—
77#1872C2212yes—
78#1872C2212yescomplemented
79#1872C2214yescomplemented
80#1872C2212yescomplemented
81#1853C2212yes—
82#1853C2212yes—
83#1853C2214yescomplemented
84#1824C2212yes—
85#1809C2214yescomplemented
86#1787C2212yes—
87C2×#340C2212yescomplemented
88C2×#340C2212yescomplemented
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×D4D411yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C22×Q16C2314yes—
96C22×M16C2314yes—
97C23×C8C2312yes—
98C23×C8C2312yes—
99C2×C22⋊Q8—21no—
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—21no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—44no—
109C2×C22⋊Q8C2312yes—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×C22⋊Q8C2312yes—
113C2×C22⋊Q8C2314yes—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4D412yes—
119C2×C4×D4D412yes—
120C2×C4×D4C2312yes—
121C2×C4×D4C2312yes—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—44no—
130C22×C4⋊C4D411yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4D411yescharacteristic
145C22×C22⋊C4D411yescharacteristic
146C22×C42C2311yescharacteristic
147#484—28no—
148#484—28no—
149#470—48no—
150#467—216no—
151#451—28no—
152#451—28no—
153#435—216no—
154#435—216no—
155#432—28no—
156C2×#107C2314yes—
157C2×#106—44no—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2314yes—
161C2×#103—44no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168#407—28no—
169C2×C22⋊C8—24no—
170C2×C22⋊C8D418yes—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×#97C2314yes—
177#400—22no—
178#399—22no—
179#398—22no—
180#398—22no—
181#398—24no—
182#398—24no—
183#396—22no—
184#396—22no—
185#396—24no—
186#396—24no—
187#395—22no—
188#393—22no—
189#391—22no—
190#391C2312yes—
191#391C2314yes—
192#391C2312yes—
193#389—22no—
194#389C2312yes—
195#389C2314yes—
196#389C2312yes—
197#387—22no—
198#387—22no—
199#386—22no—
200#386—22no—
201#386—22no—
202#386—22no—
203#386—24no—
204#386—24no—
205#385—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#381—22no—
212#380—21no—
213#380—21no—
214#380—22no—
215#380—22no—
216#380—22no—
217#380—24no—
218#380—24no—
219#380C2312yes—
220#380C2314yes—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#379—22no—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95—21no—
228C2×#95—21no—
229C2×#95—21no—
230#340C2314yes—
231#340C2314yes—
232#340C2314yes—
233#340C2314yes—
234#340C2314yes—
235#340C2314yes—
236C25C2×D411yescharacteristic
237C25C2×D411yescharacteristic
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—42no—
247C22×Q8—42no—
248C22×Q8C2412yes—
249C22×Q8C2412yes—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4C2×D412yes—
254C22×D4C2×D412yes—
255C23×C4—21no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—82no—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D412yes—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D414yes—
282C23×C4#4114yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C2×Q16—28no—
288C2×Q16—44no—
289C2×Q16—44no—
290C2×M16—28no—
291C2×M16—44no—
292C2×M16—44no—
293C22×C8—24no—
294C22×C8—42no—
295C22×C8—42no—
296C22×C8—42no—
297C22×C8—42no—
298C22×C8C2×D418yes—
299C22×C8C2414yes—
300C22×C8C2414yes—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—24no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—28no—
310C22⋊Q8—44no—
311C22⋊Q8—48no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4C2×D412yes—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—82no—
389C2×C22⋊C4C2×D412yes—
390C2×C22⋊C4C2×D412yes—
391C2×C22⋊C4C2×D412yes—
392C2×C22⋊C4C2×D412yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42C2×D412yes—
396C2×C42C2412yes—
397#107—28no—
398#106—28no—
399#106—44no—
400C4⋊C8—28no—
401#103—28no—
402#103—28no—
403#103—28no—
404#103—44no—
405#103—44no—
406#103—44no—
407C22⋊C8—24no—
408C22⋊C8—24no—
409C22⋊C8—28no—
410C22⋊C8C2×D418yes—
411C22⋊C8C2×D418yes—
412#97—28no—
413#95—24no—
414#95—24no—
415#95—22no—
416#95—22no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24#12114yes—
439C24#13714yes—
440C24#13714yes—
441C24C22×D412yes—
442C24C22×D411yescharacteristic
443C24C22×D411yescharacteristic
444C24C22×D411yescharacteristic
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—48no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—81no—
459C2×Q8—81no—
460C2×Q8—84no—
461C2×Q8—84no—
462C2×Q8—84no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—416no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—816no—
541C22×C4#12114yes—
542C22×C4#12114yes—
543C22×C4#12114yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2511yescharacteristic
557Q16—88no—
558M16—88no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—48no—
565C2×C8—84no—
566C2×C8C22×D418yes—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—81no—
592C4⋊C4—81no—
593C4⋊C4—84no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4H(5,𝔽2)14yes—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—48no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—84no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C42—24no—
614C42—22no—
615C42—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—82no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23#470116yescomplemented
649C23C2×#12112yes—
650C23C2×#12112yes—
651C23C2×#12112yes—
652C23C2×#13712yes—
653C23C2×#13712yes—
654C23C2×#13712yes—
655C23C2×#13712yes—
656C23C2×#13712yes—
657C23C2×#13712yes—
658C23C23×D411yescharacteristic
659Q8—44no—
660Q8—44no—
661Q8—44no—
662Q8—44no—
663Q8—84no—
664Q8—84no—
665D4—48no—
666D4—48no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—48no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—88no—
723C2×C4—88no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—162no—
730C2×C4—162no—
731C2×C4C2×#12112yes—
732C2×C4C2×#12112yes—
733C2×C4C2×#12112yes—
734C2×C4C23×D411yescharacteristic
735C2×C4C22×#4111yescharacteristic
736C2×C4C2×H(5,𝔽2)12yes—
737C2×C4#58512yes—
738C8—28no—
739C8—44no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—416no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—88no—
767C22C2×#47014yes—
768C22C2×#47014yes—
769C22C2×#47014yes—
770C22C22×#12111yescharacteristic
771C22#348411yescharacteristic
772C22#348511yescharacteristic
773C22C22×#13711yescharacteristic
774C22C22×#13711yescharacteristic
775C22#358511yescharacteristic
776C22#358611yescharacteristic
777C4—22no—
778C4—22no—
779C4—22no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—44no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4#349612yes—
792C4#350512yes—
793C2—24no—
794C2—24no—
795C2—24no—
796C2—82no—
797C2#3535811yescharacteristic
798C2C22×#47011yescharacteristic
799C2#6045611yescharacteristic
800C2#6157011yescharacteristic
801C2#6157411yescharacteristic
802C2#6170511yescharacteristic
803C2#6170911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3189C2semidirect
5. #28563C2semidirect
6. #25248C2semidirect
7. #25126C2semidirect
8. #24783C2semidirect
9. #24606C2semidirect
10. #24556C2semidirect
11. #24508C2semidirect
12. #24386C2semidirect
13. #21759C2semidirect
14. C2×#1872C2semidirect
15. C2×#1853C2semidirect
23. C2×#484C22semidirect
24. C2×#470C22semidirect
25. C2×#467C22semidirect
27. C2×#451C22semidirect
32. C22×#106C22semidirect
33. C22×#103C22semidirect
61. #2086C22semidirect
62. #2075C22semidirect
63. #2066C22semidirect
64. #2066C22semidirect
65. #2056C22semidirect
66. #2035C22semidirect
67. #2035C22semidirect
68. #2001C22semidirect
69. #1971C22semidirect
70. #1944C22semidirect
71. #1935C22semidirect
72. #1935C22semidirect
73. #1894C22semidirect
74. #1894C22semidirect
75. #1892C22semidirect
78. #1872C22semidirect
79. #1872C22semidirect
80. #1872C22semidirect
83. #1853C22semidirect
85. #1809C22semidirect
87. C2×#340C22semidirect
88. C2×#340C22semidirect
648. C23#470semidirect

Maximal subgroups

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

subgroupindex
C2×#31892
C2×#29732
#350102
C2×#24172
#285632
#252482
#251262
#247832
#246062
#245562
#245082
#243862
#217592
C2×#18722
C2×#18532