Finite Group Databasebeta

← #6499265

Subgroups — #6499265

Order 512.

1672 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#33073C212yesmaximal, complemented
4#33072C212yesmaximal, complemented
5#29984C211yesmaximal, characteristic, complemented
6#29983C211yesmaximal, characteristic, complemented
7#29981C211yesmaximal, characteristic, complemented
8#29980C211yesmaximal, characteristic, complemented
9#29280C212yesmaximal, complemented
10#29278C212yesmaximal, complemented
11#29262C212yesmaximal, complemented
12#29260C212yesmaximal, complemented
13#29160C212yesmaximal, complemented
14#29159C212yesmaximal, complemented
15#29157C212yesmaximal
16#29156C212yesmaximal
17#21962C212yesmaximal, complemented
18#21887C212yesmaximal
19C2×#1831C211yesmaximal, characteristic, complemented
20C2×#533—21no—
21C2×#529C2211yescharacteristic
22C22×C4⋊C8C2212yes—
23#2868C2211yescharacteristic
24#2868C2211yescharacteristic
25#2862—21no—
26#2859—21no—
27#2859C2212yes—
28#2857—21no—
29#2857—21no—
30#2857C2212yes—
31#2857C2212yes—
32C4×C4⋊Q8—21no—
33C4×C4⋊Q8—21no—
34C4×C4⋊Q8C2212yes—
35C4×C4⋊Q8C2212yes—
36C4×#125C2211yescharacteristic
37C4×#125C2211yescharacteristic
38C4×#126—21no—
39C4×#126—21no—
40C4×#124C2211yescharacteristic
41C4×#124C2211yescharacteristic
42C4×C22⋊Q8C2211yescharacteristic
43C4×C22⋊Q8C2211yescharacteristic
44C4×#123—21no—
45C4×#123—21no—
46C4×#121C2211yescharacteristic
47C4×#121C2211yescharacteristic
48#2298—21no—
49#2295C2211yescharacteristic
50#2293C2211yescharacteristic
51#2290—21no—
52#2285—21no—
53#2285C2212yes—
54#2283C2211yescharacteristic
55C42×Q8C2211yescharacteristic
56C42×D4—21no—
57C42×D4C2211yescharacteristic
58C4×#117—21no—
59C2×C43C2211yescharacteristic
60#2100C2212yes—
61#2100C2212yes—
62#2099C2212yes—
63#2099C2212yes—
64#2096C2212yes—
65#2095C2212yes—
66#2094C2212yes—
67#2093C2212yes—
68#2058C2212yes—
69#2058C2212yes—
70#2057C2212yes—
71#2057C2212yes—
72#2024C2212yes—
73#2024C2212yes—
74#2023C2212yes—
75#2023C2212yes—
76#1989C2214yes—
77#1983C2214yes—
78#1949C2214yes—
79#1949C2214yes—
80#1948C2212yes—
81#1948C2212yes—
82#1947C2212yes—
83#1947C2212yes—
84#1921C2214yes—
85#1920C2214yes—
86#1919C2214yes—
87#1918C2214yes—
88#1893C2214yes—
89#1892C2214yes—
90#1865C2214yes—
91#1864C2214yes—
92#1863C2214yes—
93#1862C2214yes—
94#1831C2211yescharacteristic
95#1831C2211yescharacteristic
96#1831C2212yes—
97#1831C2212yes—
98#1831C2212yes—
99#1808C2214yes—
100#1807C2214yes—
101#1803C2212yes—
102#1803C2212yes—
103#1802C2212yes—
104#1802C2212yes—
105C2×#336C2212yes—
106C2×#336C2212yes—
107C23×C8C2314yes—
108#533—48no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115#529—24no—
116#529Q818yescomplemented
117C2×#126—21no—
118C2×#125—22no—
119C2×#125C2311yescharacteristic
120C2×#124C2311yescharacteristic
121C2×#123—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8C2311yescharacteristic
125C2×#121C2311yescharacteristic
126C2×C4×Q8—22no—
127C2×C4×Q8—22no—
128C2×C4×Q8C2311yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×#117—22no—
138C2×#117—21no—
139C2×#117—21no—
140C22×C42—21no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C2×#107C2314yes—
149C2×#107C2314yes—
150C2×#106C2314yes—
151C2×#106C2314yes—
152C2×C4⋊C8—28no—
153C2×C4⋊C8C2312yes—
154C2×C4⋊C8C2312yes—
155C2×C4⋊C8C2314yes—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160#391—22no—
161#391—22no—
162#391—22no—
163#391—22no—
164#391C2311yescharacteristic
165#391C2311yescharacteristic
166#390C2311yescharacteristic
167#390C2311yescharacteristic
168#389—22no—
169#389—22no—
170#389—22no—
171#389—22no—
172#389—22no—
173#389—22no—
174#389C2311yescharacteristic
175#389C2311yescharacteristic
176#389C2311yescharacteristic
177#389C2311yescharacteristic
178#389C2314yes—
179#389C2314yes—
180#388—21no—
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187#388—21no—
188#387—21no—
189#387—21no—
190#387—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#387—21no—
195#387—21no—
196#386—21no—
197#386—21no—
198#385—21no—
199#385—21no—
200#384—21no—
201#384—21no—
202#384—21no—
203#384—21no—
204#384C2312yes—
205#384C2312yes—
206#384C2312yes—
207#384C2312yes—
208#383—21no—
209#382—22no—
210#382—22no—
211#382C2311yescharacteristic
212#382C2311yescharacteristic
213#381—21no—
214#380—22no—
215#380—22no—
216#380—22no—
217#380C2311yescharacteristic
218#380C2314yes—
219#380C2311yescharacteristic
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4C2311yescharacteristic
234C4×C4⋊C4C2311yescharacteristic
235C4×C4⋊C4C2311yescharacteristic
236C4×C4⋊C4C2311yescharacteristic
237C4×C4⋊C4C2314yes—
238C4×C4⋊C4C2311yescharacteristic
239C4×C4⋊C4C2311yescharacteristic
240C4×C22⋊C4—21no—
241C4×C22⋊C4—21no—
242C4×C22⋊C4—21no—
243C4×C22⋊C4—21no—
244C4×C22⋊C4—21no—
245C4×C22⋊C4—21no—
246C4×C22⋊C4—21no—
247C4×C22⋊C4—21no—
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C4×C22⋊C4—21no—
253#376—21no—
254#376—21no—
255C43—21no—
256C43D411yescharacteristic
257C43D411yescharacteristic
258C43D411yescharacteristic
259C43D411yescharacteristic
260C43C2311yescharacteristic
261C43C2311yescharacteristic
262C43C2311yescharacteristic
263C43C2311yescharacteristic
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2314yes—
277#336C2314yes—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8C2411yescharacteristic
281C22×D4—21no—
282C22×D4C2411yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C22×C8—28no—
294C22×C8—44no—
295C22×C8—44no—
296C22×C8C2414yes—
297C22×C8C2414yes—
298C4⋊Q8—44no—
299C4⋊Q8—44no—
300C4⋊Q8—44no—
301C4⋊Q8—44no—
302C4⋊Q8—44no—
303C4⋊Q8—44no—
304#126—28no—
305#125—22no—
306#125—48no—
307#125C2×Q814yes—
308#124—22no—
309#124C2×Q814yes—
310#123—28no—
311C22⋊Q8—22no—
312C22⋊Q8—48no—
313C22⋊Q8—48no—
314C22⋊Q8C2×Q814yes—
315#121—22no—
316#121C2×Q814yes—
317C4×Q8—22no—
318C4×Q8—42no—
319C4×Q8—42no—
320C4×Q8—48no—
321C4×Q8—48no—
322C4×Q8C2×Q814yes—
323C4×D4—28no—
324C4×D4—22no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—44no—
328C4×D4—44no—
329C4×D4C2×Q814yes—
330#117—28no—
331#117—48no—
332#117—44no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4C2411yescharacteristic
356C2×C4⋊C4C2411yescharacteristic
357C2×C4⋊C4C2411yescharacteristic
358C2×C4⋊C4C2411yescharacteristic
359C2×C4⋊C4C2414yes—
360C2×C4⋊C4C2414yes—
361C2×C4⋊C4C2411yescharacteristic
362C2×C4⋊C4C2411yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—21no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—44no—
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×Q814yes—
417C2×C42#4114yes—
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107—44no—
425#107—44no—
426#106—44no—
427#106—44no—
428C4⋊C8—24no—
429C4⋊C8—24no—
430C4⋊C8—28no—
431#103—44no—
432#103—44no—
433#102—44no—
434#102—44no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459C24—21no—
460C24C22×D411yescharacteristic
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8C22×Q812yes—
471C2×D4—24no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4C22×Q812yes—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4C22⋊Q814yes—
513C22×C4C22⋊Q814yes—
514C22×C4AGL(1,ℤ/8)14yes—
515C22×C4#13714yes—
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×Q812yes—
530C22×C4C2×#4112yes—
531C22×C4C2511yescharacteristic
532C2×C8—24no—
533C2×C8—24no—
534C2×C8—24no—
535C2×C8—24no—
536C2×C8—24no—
537C2×C8—24no—
538C2×C8—88no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—48no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—42no—
567C4⋊C4—48no—
568C4⋊C4—44no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4C22×Q812yes—
572C4⋊C4C22×Q812yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—48no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C42—24no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—42no—
612C42—42no—
613C42—48no—
614C42—42no—
615C42—42no—
616C42—42no—
617C42—42no—
618C42—42no—
619C42—42no—
620C42C22⋊Q814yes—
621C42C22⋊Q814yes—
622C42#13514yes—
623C42C22×Q812yes—
624C42C22×Q812yes—
625C42C2×#4112yes—
626C42C2×#4112yes—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C2×C22⋊Q812yes—
639C23C2×AGL(1,ℤ/8)12yes—
640C23C2×#13712yes—
641C23C23×D411yescharacteristic
642Q8—24no—
643Q8—42no—
644Q8—88no—
645Q8—88no—
646D4—24no—
647D4—48no—
648D4—42no—
649C2×C4—28no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—48no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—44no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—44no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4C2×C22⋊Q812yes—
714C2×C4C2×C22⋊Q812yes—
715C2×C4C2×C22⋊Q812yes—
716C2×C4C2×C22⋊Q812yes—
717C2×C4C2×C22⋊Q812yes—
718C2×C4C2×#13512yes—
719C2×C4C2×#13512yes—
720C2×C4C2×#13512yes—
721C2×C4C2×AGL(1,ℤ/8)12yes—
722C2×C4C2×AGL(1,ℤ/8)12yes—
723C2×C4C2×#13712yes—
724C2×C4C2×#13712yes—
725C2×C4#57512yes—
726C2×C4C23×Q811yescharacteristic
727C2×C4C22×#4111yescharacteristic
728C2×C4#58512yes—
729C2×C4#58512yes—
730C8—44no—
731C8—44no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#307914yes—
746C22C22×C22⋊Q811yescharacteristic
747C22#344911yescharacteristic
748C22#344911yescharacteristic
749C22C22×#13511yescharacteristic
750C22C22×AGL(1,ℤ/8)11yescharacteristic
751C22C22×#13711yescharacteristic
752C22C2×#57511yescharacteristic
753C4—22no—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—42no—
768C4—81no—
769C4—84no—
770C4—81no—
771C4—81no—
772C4—84no—
773C4—81no—
774C4#307614yes—
775C4#350412yes—
776C4#351012yes—
777C2—24no—
778C2—82no—
779C2#3533411yescharacteristic
780C2C2×#307611yescharacteristic
781C2C2×#307911yescharacteristic
782C2#6094611yescharacteristic
783C2#6094711yescharacteristic
784C2#6095811yescharacteristic
785C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36645C2semidirect
3. #33073C2semidirect
4. #33072C2semidirect
5. #29984C2semidirect
6. #29983C2semidirect
7. #29981C2semidirect
8. #29980C2semidirect
9. #29280C2semidirect
10. #29278C2semidirect
11. #29262C2semidirect
12. #29260C2semidirect
13. #29160C2semidirect
14. #29159C2semidirect
17. #21962C2semidirect
19. C2×#1831C2semidirect
116. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#330732
#330722
#299842
#299832
#299812
#299802
#292802
#292782
#292622
#292602
#291602
#291592
#291572
#291562
#219622
#218872
C2×#18312