Finite Group Databasebeta

← #6433940

Subgroups — #6433940

Order 512.

2048 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2C2×#2854C211yesmaximal, characteristic
3#30365C212yesmaximal, complemented
4#30364C212yesmaximal, complemented
5#30362C214yesmaximal, complemented
6#30360C214yesmaximal, complemented
7#30357C212yesmaximal, complemented
8#30356C212yesmaximal, complemented
9#23747C211yesmaximal, characteristic, complemented
10#23731C211yesmaximal, characteristic, complemented
11#23642C212yesmaximal, complemented
12#23554C211yesmaximal, characteristic, complemented
13#23480C212yesmaximal
14#23454C211yesmaximal, characteristic, complemented
15#21159C212yesmaximal, complemented
16#21095C212yesmaximal, complemented
17C4×#407C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×#123—21no—
20C22×#121C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#428C2212yes—
23C2×#428C2212yes—
24C2×#418C2212yes—
25C2×#418C2212yes—
26C2×#407C2212yes—
27C2×C4×M16C2212yes—
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2857C2211yescharacteristic, complemented
31#2857C2211yescharacteristic, complemented
32#2855—21no—
33#2855—21no—
34#2854—21no—
35#2854—21no—
36#2854—21no—
37#2854—21no—
38#2854C2212yes—
39#2854C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2851C2212yescomplemented
43#2851C2212yescomplemented
44#2848—21no—
45#2848—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50#2296C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#388—21no—
57C2×#386—21no—
58#2285C2211yescharacteristic
59#2280C2212yes—
60C2×#380C2211yescharacteristic
61#2101C2214yescomplemented
62#2100C2212yescomplemented
63#2099C2212yescomplemented
64#2094C2212yescomplemented
65#2093C2212yescomplemented
66#2092C2214yescomplemented
67#2077C2214yescomplemented
68#2077C2214yescomplemented
69#2076C2214yescomplemented
70#2075C2214yescomplemented
71#2059C2214yescomplemented
72#2058C2212yescomplemented
73#2057C2212yescomplemented
74#2034C2214yes—
75#2034C2214yes—
76#2033C2214yes—
77#2033C2214yes—
78#2025C2214yescomplemented
79#2023C2212yescomplemented
80#2023C2212yescomplemented
81#1944C2214yescomplemented
82#1943C2214yescomplemented
83#1942C2214yescomplemented
84#1941C2214yescomplemented
85#1936C2214yescomplemented
86#1936C2214yescomplemented
87#1934C2214yescomplemented
88#1934C2214yescomplemented
89#1749C2212yescomplemented
90#1749C2212yescomplemented
91C4×C22⋊C8C2212yescomplemented
92C4×C22⋊C8C2212yescomplemented
93#1736C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1736C2212yes—
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×M16C2312yes—
105C22×M16C2312yes—
106#533—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#125C2312yes—
110C2×#123—22no—
111C2×#123—22no—
112C2×#123—22no—
113C2×#123—22no—
114C2×#123—48no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—44no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×C4×Q8—21no—
127C2×C4×Q8—21no—
128C2×#117C2312yes—
129C2×#117C2312yes—
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×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C42—44no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#428—28no—
155#428—44no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160#418—28no—
161#418—44no—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166#407—28no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C4×M16—44no—
170C2×#97C2314yes—
171C2×C4×C8C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#389C2312yes—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#384C2311yescharacteristic
223#384C2311yescharacteristic
224#382C2312yes—
225#381—22no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#379—22no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262C25—21no—
263C25C2×D411yescharacteristic
264C22×Q8—21no—
265C22×Q8—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—21no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4C2412yes—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16#4118yes—
314C22×C8C2414yes—
315C22×C8C2414yes—
316C4⋊Q8—42no—
317C4⋊Q8—42no—
318#125—42no—
319#125—42no—
320#123—48no—
321#123—48no—
322#123—48no—
323#123—48no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336#117—24no—
337#117—24no—
338#117—24no—
339#117—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
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—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
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×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#107—28no—
427#107—44no—
428#106—28no—
429#106—44no—
430#102—28no—
431#102—28no—
432#102—44no—
433#102—44no—
434C22⋊C8—28no—
435C22⋊C8—28no—
436#97—44no—
437C4×C8—44no—
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—
451#95—22no—
452#95—22no—
453#95—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—41no—
461C24—41no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—816no—
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—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—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
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—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—416no—
554C22×C4—416no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4AGL(1,ℤ/8)14yes—
567C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
579C22×C4H(5,𝔽2)14yes—
580C22×C42−1+412yes—
581C22×C42−1+412yes—
582C22×C4C2511yescharacteristic
583M16—216no—
584M16—48no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8C2×#4118yes—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—44no—
657C42—44no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—28no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#53212yes—
696C23#53412yes—
697C23#53612yes—
698C23C2×AGL(1,ℤ/8)12yes—
699C23#57512yes—
700C23C23×D411yescharacteristic
701Q8—84no—
702Q8—84no—
703D4—44no—
704D4—44no—
705D4—88no—
706D4—88no—
707D4—84no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
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—21no—
732C2×C4—21no—
733C2×C4—21no—
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—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
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—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#53212yes—
778C2×C4#53412yes—
779C2×C4#53612yes—
780C2×C4#53918yes—
781C2×C4#54218yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×AGL(1,ℤ/8)12yes—
784C2×C4#57512yes—
785C2×C4#57512yes—
786C2×C4C22×#4112yes—
787C2×C4C2×H(5,𝔽2)12yes—
788C2×C4C2×2−1+411yescharacteristic
789C2×C4C2×2−1+411yescharacteristic
790C8—28no—
791C8—44no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—416no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—168no—
821C22#266314yes—
822C22C2×#53211yescharacteristic
823C22C2×#53411yescharacteristic
824C22C2×#53611yescharacteristic
825C22C22×AGL(1,ℤ/8)11yescharacteristic
826C22C2×#57511yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57511yescharacteristic
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4#266314yes—
847C4C2×#53912yes—
848C4C2×#54212yes—
849C2—24no—
850C2—42no—
851C2—42no—
852C2—162no—
853C2C2×#266311yescharacteristic
854C2#6070011yescharacteristic
855C2#6070211yescharacteristic
856C2#6075011yescharacteristic
857C2#6075211yescharacteristic
858C2#6086411yescharacteristic
859C2#6086611yescharacteristic
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. #30365C2semidirect
4. #30364C2semidirect
5. #30362C2semidirect
6. #30360C2semidirect
7. #30357C2semidirect
8. #30356C2semidirect
9. #23747C2semidirect
10. #23731C2semidirect
11. #23642C2semidirect
12. #23554C2semidirect
14. #23454C2semidirect
15. #21159C2semidirect
16. #21095C2semidirect
17. C4×#407C2semidirect
28. #2857C22semidirect
29. #2857C22semidirect
30. #2857C22semidirect
31. #2857C22semidirect
42. #2851C22semidirect
43. #2851C22semidirect
61. #2101C22semidirect
62. #2100C22semidirect
63. #2099C22semidirect
64. #2094C22semidirect
65. #2093C22semidirect
66. #2092C22semidirect
67. #2077C22semidirect
68. #2077C22semidirect
69. #2076C22semidirect
70. #2075C22semidirect
71. #2059C22semidirect
72. #2058C22semidirect
73. #2057C22semidirect
78. #2025C22semidirect
79. #2023C22semidirect
80. #2023C22semidirect
81. #1944C22semidirect
82. #1943C22semidirect
83. #1942C22semidirect
84. #1941C22semidirect
85. #1936C22semidirect
86. #1936C22semidirect
87. #1934C22semidirect
88. #1934C22semidirect
89. #1749C22semidirect
90. #1749C22semidirect
91. C4×C22⋊C8C22semidirect
92. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×#28542
#303652
#303642
#303622
#303602
#303572
#303562
#237472
#237312
#236422
#235542
#234802
#234542
#211592
#210952
C4×#4072