Finite Group Databasebeta

← #6489014

Subgroups — #6489014

Order 512.

2088 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C2×C4×#124C211yesmaximal, characteristic, complemented
3#32954C211yesmaximal, characteristic, complemented
4#32953C211yesmaximal, characteristic, complemented
5#32903C211yesmaximal, characteristic, complemented
6#32902C211yesmaximal, characteristic
7#30134C214yesmaximal, complemented
8#29131C212yesmaximal, complemented
9#28383C212yesmaximal, complemented
10#28281C212yesmaximal, complemented
11#28253C212yesmaximal, complemented
12#27684C212yesmaximal, complemented
13#24509C212yesmaximal, complemented
14#24506C212yesmaximal, complemented
15#24215C212yesmaximal, complemented
16#22155C214yesmaximal, complemented
17#20810C211yesmaximal, characteristic, complemented
18C2×#529—21no—
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C2×#475C2212yescomplemented
23C2×#474C2212yes—
24C2×#460C2212yescomplemented
25C2×#463C2214yes—
26C2×#459C2212yes—
27C2×#448C2212yes—
28C2×#447C2212yes—
29C2×#432C2212yes—
30#2861—21no—
31#2860—21no—
32#2860C2212yescomplemented
33#2859C2211yescharacteristic, complemented
34#2858C2211yescharacteristic, complemented
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2854—21no—
38#2854C2212yes—
39#2850—21no—
40C4×C4⋊Q8C2211yescharacteristic, complemented
41C4×#127C2211yescharacteristic, complemented
42C4×#124—21no—
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#124—21no—
47C4×#124C2212yes—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#124C2212yes—
51C4×#121—21no—
52C4×#121C2212yes—
53C2×#391C2211yescharacteristic
54#2293—21no—
55#2293C2212yescomplemented
56C2×#390C2211yescharacteristic
57C2×#388—21no—
58C2×#388—21no—
59C2×#382C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4—21no—
62C2×C43C2211yescharacteristic
63#2101C2214yescomplemented
64#2092C2214yescomplemented
65#2068C2214yescomplemented
66#2065C2214yes—
67#2055C2214yescomplemented
68#2054C2214yes—
69#2042C2214yes—
70#2012C2214yes—
71#1983C2214yes—
72#1973C2214yescomplemented
73#1972C2214yes—
74#1949C2214yescomplemented
75#1936C2214yes—
76#1935C2214yescomplemented
77#1880C2214yescomplemented
78#1879C2214yes—
79#1874C2212yes—
80#1874C2212yes—
81#1865C2214yescomplemented
82#1862C2214yes—
83#1853C2212yes—
84#1852C2212yes—
85#1842C2212yescomplemented
86#1831C2212yescomplemented
87#1804C2214yescomplemented
88#1803C2212yescomplemented
89#1803C2212yescomplemented
90#1802C2212yes—
91#1802C2212yes—
92#1797C2212yes—
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1787C2212yes—
96#1786C2212yes—
97#1767C2212yescomplemented
98#1767C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×SD16C2314yes—
103C22×D8C2314yes—
104C2×C4⋊Q8C2311yescharacteristic
105C2×#127C2311yescharacteristic
106#529—48no—
107C2×#126—22no—
108C2×#125—21no—
109C2×#124—28no—
110C2×#124—21no—
111C2×#124—21no—
112C2×#124—21no—
113C2×#124—21no—
114C2×#124C2312yes—
115C2×#124C2312yes—
116C2×#123—22no—
117C2×C22⋊Q8—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121C2312yes—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—21no—
124C2×C4×Q8—44no—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—44no—
133C2×C4×D4C2312yes—
134C2×C4×D4C2312yes—
135C2×C4×D4C2312yes—
136C2×#117—22no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C42—21no—
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#475—44no—
154#474—44no—
155#463—216no—
156#460—44no—
157#459—44no—
158#448—44no—
159#447—44no—
160#432—44no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×#97C2314yes—
178#391—21no—
179#391—21no—
180#391—21no—
181#391—21no—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389C2312yes—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#386—22no—
223#386—22no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#382—21no—
227#382—21no—
228#382—21no—
229#382C2312yes—
230#382C2312yes—
231#380—21no—
232#380C2312yes—
233C4×C4⋊C4—21no—
234C4×C4⋊C4C2312yes—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43D411yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256C43C2311yescharacteristic
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2314yes—
262#336C2312yes—
263#336C2312yes—
264C25—21no—
265C22×Q8—24no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—42no—
271C22×Q8C2412yes—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—42no—
280C22×D4C2412yes—
281C22×D4C2412yes—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×SD16—28no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×D8—28no—
302C2×D8—44no—
303C2×D8—44no—
304C22×C8C2414yes—
305C22×C8C2414yes—
306C4⋊Q8—24no—
307#127—24no—
308#126—48no—
309#125—44no—
310#124—28no—
311#124—28no—
312#124—24no—
313#124—24no—
314#124—24no—
315#124—44no—
316#124—44no—
317#124#4118yes—
318#123—48no—
319C22⋊Q8—44no—
320#121—24no—
321#121—24no—
322#121—44no—
323#121—44no—
324C4×Q8—24no—
325C4×Q8—24no—
326C4×Q8—42no—
327C4×Q8—42no—
328C4×Q8—44no—
329C4×Q8—44no—
330C4×Q8—44no—
331C4×D4—28no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—42no—
335C4×D4—42no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—48no—
341#117—48no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
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—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—44no—
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×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—44no—
430#106—44no—
431C4⋊C8—28no—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8—44no—
435#103—28no—
436#103—44no—
437#103—44no—
438#102—28no—
439#102—44no—
440#102—44no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445#97—44no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24C22×D411yescharacteristic
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8C2×#4114yes—
484C2×D4—24no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×#4114yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
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—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—816no—
552C22×C4AGL(1,ℤ/8)14yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4H(5,𝔽2)12yes—
567C22×C42−1+412yes—
568C22×C4C2511yescharacteristic
569SD16—88no—
570D8—88no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42C2×#4114yes—
651C42H(5,𝔽2)14yes—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—24no—
657C23—48no—
658C23—48no—
659C23—48no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23#53712yes—
678C23C2×AGL(1,ℤ/8)12yes—
679C23#57512yes—
680C23C23×D411yescharacteristic
681Q8—24no—
682Q8—24no—
683Q8—48no—
684Q8—42no—
685Q8—42no—
686Q8—84no—
687D4—24no—
688D4—24no—
689D4—48no—
690D4—42no—
691D4—44no—
692D4—42no—
693D4—44no—
694D4—84no—
695D4—88no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—24no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—88no—
755C2×C4—88no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—88no—
759C2×C4#52512yes—
760C2×C4#52512yes—
761C2×C4#53512yes—
762C2×C4#53512yes—
763C2×C4#53712yes—
764C2×C4C2×AGL(1,ℤ/8)12yes—
765C2×C4C2×AGL(1,ℤ/8)12yes—
766C2×C4#57512yes—
767C2×C4#57512yes—
768C2×C4C22×#4112yes—
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C2×C4C2×H(5,𝔽2)12yes—
771C2×C4C2×2−1+411yescharacteristic
772C8—44no—
773C8—44no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—816no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22#325114yes—
796C22C2×#52511yescharacteristic
797C22C2×#53511yescharacteristic
798C22C2×#53711yescharacteristic
799C22C22×AGL(1,ℤ/8)11yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C22C2×#57511yescharacteristic
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#321314yes—
822C4#351912yes—
823C4#352012yes—
824C2—24no—
825C2—84no—
826C2—162no—
827C2#3523611yescharacteristic
828C2#6054611yescharacteristic
829C2#6056111yescharacteristic
830C2C2×#321311yescharacteristic
831C2#6080511yescharacteristic
832C2C2×#325111yescharacteristic
833C2#6091711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32902C2
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. #36631C2semidirect
2. C2×C4×#124C2semidirect
3. #32954C2semidirect
4. #32953C2semidirect
5. #32903C2semidirect
7. #30134C2semidirect
8. #29131C2semidirect
9. #28383C2semidirect
10. #28281C2semidirect
11. #28253C2semidirect
12. #27684C2semidirect
13. #24509C2semidirect
14. #24506C2semidirect
15. #24215C2semidirect
16. #22155C2semidirect
17. #20810C2semidirect
22. C2×#475C22semidirect
24. C2×#460C22semidirect
32. #2860C22semidirect
33. #2859C22semidirect
34. #2858C22semidirect
40. C4×C4⋊Q8C22semidirect
41. C4×#127C22semidirect
55. #2293C22semidirect
63. #2101C22semidirect
64. #2092C22semidirect
65. #2068C22semidirect
67. #2055C22semidirect
72. #1973C22semidirect
74. #1949C22semidirect
76. #1935C22semidirect
77. #1880C22semidirect
81. #1865C22semidirect
85. #1842C22semidirect
86. #1831C22semidirect
87. #1804C22semidirect
88. #1803C22semidirect
89. #1803C22semidirect
97. #1767C22semidirect
98. #1767C22semidirect

Maximal subgroups

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

subgroupindex
#366312
C2×C4×#1242
#329542
#329532
#329032
#329022
#301342
#291312
#283832
#282812
#282532
#276842
#245092
#245062
#242152
#221552
#208102