Finite Group Databasebeta

← #6476343

Subgroups — #6476343

Order 512.

1946 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3#33100C212yesmaximal, complemented
4#33008C212yesmaximal, complemented
5#30168C212yesmaximal, complemented
6#30109C212yesmaximal, complemented
7#29417C214yesmaximal, complemented
8#29166C212yesmaximal, complemented
9#28581C212yesmaximal, complemented
10#27613C211yesmaximal, characteristic, complemented
11#27586C211yesmaximal, characteristic, complemented
12#24559C212yesmaximal
13#24386C212yesmaximal
14#24063C211yesmaximal, characteristic, complemented
15#23934C211yesmaximal, characteristic, complemented
16#22189C214yesmaximal, complemented
17#20682C211yesmaximal, characteristic
18C2×#533C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#483C2212yes—
23C2×#470C2214yes—
24C2×#451C2212yes—
25C2×#407C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2855—21no—
31#2855C2212yes—
32#2851—21no—
33#2851—21no—
34#2848—21no—
35#2848C2212yes—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yes—
44C4×C22⋊Q8C2212yes—
45C4×C22⋊Q8C2212yes—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48#2296—21no—
49C2×#391C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#387—21no—
52C2×#385—21no—
53#2285C2211yescharacteristic
54#2280—21no—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2100C2212yescomplemented
60#2095C2212yescomplemented
61#2084C2212yescomplemented
62#2077C2214yes—
63#2072C2212yescomplemented
64#2058C2212yescomplemented
65#2043C2212yescomplemented
66#2036C2214yes—
67#2035C2214yes—
68#2024C2212yescomplemented
69#2016C2212yescomplemented
70#2001C2214yes—
71#1928C2214yescomplemented
72#1928C2214yescomplemented
73#1927C2214yescomplemented
74#1919C2214yescomplemented
75#1919C2214yescomplemented
76#1918C2214yescomplemented
77#1894C2214yes—
78#1894C2214yes—
79#1878C2214yescomplemented
80#1878C2214yescomplemented
81#1878C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1865C2214yescomplemented
85#1865C2214yescomplemented
86#1865C2214yescomplemented
87#1853C2212yes—
88#1852C2212yes—
89#1823C2212yes—
90#1817C2212yes—
91#1817C2211yescharacteristic
92#1817C2212yes—
93#1817C2211yescharacteristic
94#1817C2212yes—
95#1809C2214yes—
96#1787C2212yes—
97#1728C2212yes—
98#1728C2212yes—
99C23×Q8C2311yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×Q16C2314yes—
104C22×M16C2314yes—
105#533—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#125—21no—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8C2312yes—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—44no—
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×#117—21no—
128C2×#117—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—44no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#483—44no—
153#470—216no—
154#451—44no—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164#407—44no—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2314yes—
168#391—21no—
169#391—21no—
170#391—21no—
171#391—21no—
172#391C2312yes—
173#391C2312yes—
174#391C2312yes—
175#391C2312yes—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183#389—21no—
184#389C2312yes—
185#389C2312yes—
186#389C2312yes—
187#389C2312yes—
188#387—22no—
189#387—22no—
190#387—22no—
191#387—22no—
192#387—22no—
193#387—22no—
194#387—22no—
195#387—22no—
196#385—22no—
197#385—22no—
198#385—22no—
199#385—22no—
200#385—22no—
201#385—22no—
202#385—22no—
203#385—22no—
204#385—22no—
205#385—22no—
206#384C2311yescharacteristic
207#384C2311yescharacteristic
208#382—21no—
209#381—22no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380C2312yes—
220#380C2312yes—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#379—22no—
225C4×C4⋊C4—22no—
226C4×C4⋊C4—22no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4—22no—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#336C2312yes—
255#336C2312yes—
256#336C2312yes—
257#336C2314yes—
258#336C2314yes—
259#336C2312yes—
260C25C2×D411yescharacteristic
261C22×Q8—24no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8—24no—
265C22×Q8—42no—
266C22×Q8C2412yes—
267C22×Q8C2412yes—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C2×Q16—28no—
300C2×Q16—44no—
301C2×Q16—44no—
302C2×M16—28no—
303C2×M16—44no—
304C2×M16—44no—
305C22×C8C2414yes—
306C22×C8C2414yes—
307C4⋊Q8—42no—
308C4⋊Q8—42no—
309#125—44no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—28no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8#4118yes—
323C4×Q8—44no—
324C4×Q8—44no—
325C4×Q8—42no—
326C4×Q8—42no—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×Q8—44no—
330#117—44no—
331#117—44no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—44no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—44no—
397C2×C42—44no—
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×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414#107—44no—
415#106—28no—
416#106—44no—
417#103—28no—
418#103—28no—
419#103—44no—
420#103—44no—
421#103—44no—
422#103—44no—
423C22⋊C8—24no—
424C22⋊C8—24no—
425C22⋊C8—44no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—41no—
452C24—41no—
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455C24C22×D411yescharacteristic
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—24no—
463C2×Q8—24no—
464C2×Q8—416no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8C2×#4114yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—416no—
532C22×C4—416no—
533C22×C4—416no—
534C22×C4—42no—
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#13714yes—
545C22×C4#13714yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C2×#4114yes—
558C22×C4H(5,𝔽2)14yes—
559C22×C4C2511yescharacteristic
560Q16—88no—
561M16—88no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C4⋊C4—24no—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4C2×#4114yes—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—44no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—28no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#52512yes—
654C23#53412yes—
655C23C2×#13712yes—
656C23C2×#13712yes—
657C23#57512yes—
658C23C23×D411yescharacteristic
659Q8—28no—
660Q8—48no—
661Q8—44no—
662Q8—44no—
663Q8—44no—
664Q8—84no—
665C2×C4—28no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—28no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
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—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4#52512yes—
738C2×C4#53412yes—
739C2×C4C2×#13712yes—
740C2×C4C2×#13712yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4#57512yes—
744C2×C4C22×#4112yes—
745C2×C4C2×H(5,𝔽2)12yes—
746C2×C4#58512yes—
747C8—44no—
748C8—44no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—416no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22#319614yes—
771C22C2×#52511yescharacteristic
772C22C2×#53411yescharacteristic
773C22#344911yescharacteristic
774C22C22×#13711yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57511yescharacteristic
777C22C2×#57511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—44no—
789C4—41no—
790C4—44no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#351314yes—
798C2—24no—
799C2—42no—
800C2—42no—
801C2#3506311yescharacteristic
802C2#6056011yescharacteristic
803C2#6056211yescharacteristic
804C2C2×#319611yescharacteristic
805C2#6075111yescharacteristic
806C2#6095411yescharacteristic
807C2#6097111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33100C2semidirect
4. #33008C2semidirect
5. #30168C2semidirect
6. #30109C2semidirect
7. #29417C2semidirect
8. #29166C2semidirect
9. #28581C2semidirect
10. #27613C2semidirect
11. #27586C2semidirect
14. #24063C2semidirect
15. #23934C2semidirect
16. #22189C2semidirect
59. #2100C22semidirect
60. #2095C22semidirect
61. #2084C22semidirect
63. #2072C22semidirect
64. #2058C22semidirect
65. #2043C22semidirect
68. #2024C22semidirect
69. #2016C22semidirect
71. #1928C22semidirect
72. #1928C22semidirect
73. #1927C22semidirect
74. #1919C22semidirect
75. #1919C22semidirect
76. #1918C22semidirect
79. #1878C22semidirect
80. #1878C22semidirect
81. #1878C22semidirect
84. #1865C22semidirect
85. #1865C22semidirect
86. #1865C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×C22⋊Q82
#331002
#330082
#301682
#301092
#294172
#291662
#285812
#276132
#275862
#245592
#243862
#240632
#239342
#221892
#206822