Finite Group Databasebeta

← #6477090

Subgroups — #6477090

Order 512.

2202 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33150C212yesmaximal, complemented
4#32959C212yesmaximal, complemented
5#30166C212yesmaximal, complemented
6#30165C212yesmaximal, complemented
7#29302C211yesmaximal, characteristic, complemented
8#29301C211yesmaximal, characteristic, complemented
9#29109C211yesmaximal, characteristic, complemented
10#29109C211yesmaximal, characteristic, complemented
11#27650C212yesmaximal, complemented
12#27604C212yesmaximal, complemented
13#24706C214yesmaximal, complemented
14#24304C212yesmaximal, complemented
15#24009C212yesmaximal
16#22086C214yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#482C2214yes—
24C2×#478C2214yescomplemented
25C2×#432C2212yescomplemented
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2855—21no—
31#2855—21no—
32#2851C2212yes—
33#2851C2212yescomplemented
34#2848—21no—
35#2848—21no—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48#2296C2212yescomplemented
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#388—21no—
52C2×#386—21no—
53#2285C2211yescharacteristic, complemented
54#2280C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4—21no—
58#2084C2212yescomplemented
59#2083C2212yescomplemented
60#2077C2214yescomplemented
61#2075C2214yescomplemented
62#2071C2212yescomplemented
63#2071C2212yescomplemented
64#2058C2212yescomplemented
65#2057C2212yescomplemented
66#2034C2214yes—
67#2033C2214yes—
68#2023C2212yescomplemented
69#2023C2212yescomplemented
70#1989C2214yescomplemented
71#1949C2214yescomplemented
72#1944C2214yescomplemented
73#1943C2214yescomplemented
74#1936C2214yescomplemented
75#1936C2214yescomplemented
76#1920C2214yescomplemented
77#1918C2214yescomplemented
78#1875C2214yes—
79#1864C2214yescomplemented
80#1862C2214yescomplemented
81#1854C2214yescomplemented
82#1853C2212yes—
83#1853C2212yes—
84#1852C2212yes—
85#1852C2212yes—
86#1825C2214yescomplemented
87#1824C2212yes—
88#1824C2212yes—
89#1817C2212yescomplemented
90#1804C2214yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1786C2212yes—
94#1786C2212yes—
95#1779C2212yes—
96#1749C2211yescharacteristic
97#1749C2211yescharacteristic
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105#533—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#125C2312yes—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—28no—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—44no—
129C2×C4×D4—48no—
130C2×C4×D4C2312yes—
131C2×C4×D4C2312yes—
132C2×#117C2312yes—
133C2×#117C2312yes—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C42—21no—
144C22×C42—44no—
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#482—216no—
158#478—48no—
159#432—44no—
160C2×#107C2314yes—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×C4⋊C8C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C2×#97C2312yes—
174C2×#97C2312yes—
175#391—21no—
176#391—21no—
177#391—21no—
178#391—21no—
179#390—21no—
180#390—21no—
181#390C2312yes—
182#390C2312yes—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#388—22no—
196#388—22no—
197#388—22no—
198#388—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#384C2311yescharacteristic
214#384C2311yescharacteristic
215#382C2312yes—
216#381—22no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#379—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#336C2314yes—
258#336C2312yes—
259#336C2312yes—
260C25—21no—
261C25C2×D411yescharacteristic
262C22×Q8—21no—
263C22×Q8—21no—
264C22×D4—28no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—24no—
268C22×D4—21no—
269C22×D4—24no—
270C22×D4—42no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4C2412yes—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
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×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C22×C8C2414yes—
310C22×C8C2414yes—
311C4⋊Q8—42no—
312C4⋊Q8—42no—
313#125—28no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320#121—28no—
321#121—28no—
322#121—24no—
323#121—24no—
324#121—24no—
325#121#4118yes—
326C4×Q8—44no—
327C4×Q8—44no—
328C4×D4—28no—
329C4×D4—44no—
330C4×D4—44no—
331C4×D4—44no—
332C4×D4—48no—
333C4×D4—48no—
334C4×D4—48no—
335C4×D4—48no—
336#117—28no—
337#117—44no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
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⋊C4C2412yes—
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—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—44no—
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×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420#107—28no—
421#107—44no—
422#106—28no—
423#106—44no—
424C4⋊C8—28no—
425#102—28no—
426#102—28no—
427#102—44no—
428#102—44no—
429C22⋊C8—28no—
430C22⋊C8—24no—
431C22⋊C8—24no—
432C22⋊C8—44no—
433#97—42no—
434#97—42no—
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—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—41no—
459C24—41no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468C24C22×D411yescharacteristic
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×D4—24no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—416no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—432no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4C2×#4114yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
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—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—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—42no—
556C22×C4—416no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—816no—
567C22×C4AGL(1,ℤ/8)14yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C2×#4114yes—
580C22×C42−1+414yes—
581C22×C4C2511yescharacteristic
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4C2×#4114yes—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—44no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42H(5,𝔽2)14yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—28no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—24no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—48no—
673C23—48no—
674C23—48no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#52512yes—
687C23#53612yes—
688C23C2×AGL(1,ℤ/8)12yes—
689C23#57512yes—
690C23#57512yes—
691C23C23×D411yescharacteristic
692Q8—84no—
693Q8—84no—
694D4—28no—
695D4—48no—
696D4—416no—
697D4—416no—
698D4—44no—
699C2×C4—28no—
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—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—21no—
717C2×C4—24no—
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—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—48no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—88no—
766C2×C4—88no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4#52512yes—
770C2×C4#53412yes—
771C2×C4#53412yes—
772C2×C4#53612yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4C2×AGL(1,ℤ/8)12yes—
775C2×C4#57512yes—
776C2×C4C22×#4112yes—
777C2×C4C2×H(5,𝔽2)12yes—
778C2×C4C2×2−1+412yes—
779C8—44no—
780C8—44no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—416no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—816no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22#324014yes—
811C22C2×#52511yescharacteristic
812C22C2×#53411yescharacteristic
813C22C2×#53611yescharacteristic
814C22C22×AGL(1,ℤ/8)11yescharacteristic
815C22C2×#57511yescharacteristic
816C22C2×#57511yescharacteristic
817C22C2×#57511yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—44no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4#352014yes—
837C2—24no—
838C2—42no—
839C2—42no—
840C2—84no—
841C2#3508411yescharacteristic
842C2#6054611yescharacteristic
843C2#6055811yescharacteristic
844C2#6074111yescharacteristic
845C2#6075011yescharacteristic
846C2C2×#324011yescharacteristic
847C2#6086411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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
1. #36625C2semidirect
3. #33150C2semidirect
4. #32959C2semidirect
5. #30166C2semidirect
6. #30165C2semidirect
7. #29302C2semidirect
8. #29301C2semidirect
9. #29109C2semidirect
10. #29109C2semidirect
11. #27650C2semidirect
12. #27604C2semidirect
13. #24706C2semidirect
14. #24304C2semidirect
16. #22086C2semidirect
17. #20715C2semidirect
18. C2×#533C22semidirect
24. C2×#478C22semidirect
25. C2×#432C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
33. #2851C22semidirect
48. #2296C22semidirect
53. #2285C22semidirect
58. #2084C22semidirect
59. #2083C22semidirect
60. #2077C22semidirect
61. #2075C22semidirect
62. #2071C22semidirect
63. #2071C22semidirect
64. #2058C22semidirect
65. #2057C22semidirect
68. #2023C22semidirect
69. #2023C22semidirect
70. #1989C22semidirect
71. #1949C22semidirect
72. #1944C22semidirect
73. #1943C22semidirect
74. #1936C22semidirect
75. #1936C22semidirect
76. #1920C22semidirect
77. #1918C22semidirect
79. #1864C22semidirect
80. #1862C22semidirect
81. #1854C22semidirect
86. #1825C22semidirect
89. #1817C22semidirect
90. #1804C22semidirect
92. #1797C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#331502
#329592
#301662
#301652
#293022
#293012
#291092
#276502
#276042
#247062
#243042
#240092
#220862
#207152