Finite Group Databasebeta

← #6561703

Subgroups — #6561703

Order 512.

1506 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36499C211yesmaximal, characteristic
2#36188C211yesmaximal, characteristic, complemented
3#30367C211yesmaximal, characteristic, complemented
4#30357C211yesmaximal, characteristic, complemented
5#30285C211yesmaximal, characteristic, complemented
6#29350C211yesmaximal, characteristic, complemented
7#29218C211yesmaximal, characteristic, complemented
8#29166C211yesmaximal, characteristic, complemented
9#29156C211yesmaximal, characteristic, complemented
10#28869C212yesmaximal, complemented
11#28847C212yesmaximal, complemented
12#28714C212yesmaximal, complemented
13#28610C212yesmaximal
14#28087C212yesmaximal, complemented
15#28065C212yesmaximal, complemented
16#27863C211yesmaximal, characteristic, complemented
17#27858C211yesmaximal, characteristic, complemented
18#23839C211yesmaximal, characteristic, complemented
19#23760C211yesmaximal, characteristic, complemented
20#23757C211yesmaximal, characteristic, complemented
21#23228C212yesmaximal, complemented
22#23166C212yesmaximal, complemented
23#20559C211yesmaximal, characteristic, complemented
24C2×#556—21no—
25C2×#501C2212yes—
26C2×#489C2212yes—
27C2×#435C2212yes—
28#2868C2211yescharacteristic
29#2861C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2855C2211yescharacteristic
33#2854C2211yescharacteristic
34#2596—21no—
35#2589—21no—
36#2568—21no—
37#2562C2211yescharacteristic
38#2547—21no—
39#2547C2212yes—
40#2540C2211yescharacteristic
41#2516—21no—
42#2499—21no—
43#2499—21no—
44#2496—21no—
45#2496—21no—
46#2496C2212yes—
47#2496C2212yes—
48#2492C2211yescharacteristic
49#2491C2211yescharacteristic
50#2459—21no—
51#2458—21no—
52#2455—21no—
53#2423C2211yescharacteristic
54#2422C2211yescharacteristic
55#2374—21no—
56#2370C2211yescharacteristic
57#2367—21no—
58#2367C2211yescharacteristic
59#2365—21no—
60#2365C2212yes—
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C4×#121C2211yescharacteristic
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67C42×D4C2211yescharacteristic
68#2100C2211yescharacteristic
69#2100C2211yescharacteristic
70#2100C2211yescharacteristic
71#2100C2211yescharacteristic
72#2096C2212yes—
73#2095C2211yescharacteristic
74#2095C2211yescharacteristic
75#2094C2211yescharacteristic
76#2094C2211yescharacteristic
77#2093C2212yes—
78#2084C2212yes—
79#2083C2211yescharacteristic
80#2083C2211yescharacteristic
81#2077C2212yes—
82#2077C2212yes—
83#2076C2212yes—
84#2075C2212yes—
85#2072C2211yescharacteristic
86#2071C2211yescharacteristic
87#2058C2211yescharacteristic
88#2058C2211yescharacteristic
89#2057C2212yes—
90#2036C2212yes—
91#2035C2212yes—
92#2034C2212yes—
93#2033C2212yes—
94#2024C2211yescharacteristic
95#2023C2211yescharacteristic
96#1990C2212yes—
97#1989C2212yes—
98#1987C2212yes—
99#1987C2212yes—
100#1983C2212yes—
101#1943C2212yes—
102#1941C2212yes—
103#1935C2212yes—
104#1934C2212yes—
105#1934C2212yes—
106#1933C2212yes—
107#1928C2212yes—
108#1925C2212yes—
109#1921C2212yes—
110#1920C2212yes—
111#1920C2212yes—
112#1918C2212yes—
113#1895C2212yes—
114#1894C2212yes—
115#1893C2212yes—
116#1892C2212yes—
117#1865C2212yes—
118#1864C2212yes—
119#1834C2212yes—
120#1809C2212yes—
121#1809C2212yes—
122#1808C2212yes—
123#1807C2212yes—
124#1776C2212yes—
125#1776C2212yes—
126#1776C2212yes—
127C4×#107C2212yes—
128#1771C2212yes—
129C4×C4⋊C8C2211yescharacteristic
130#1762C2212yes—
131C4×#103C2212yes—
132#1753C2212yes—
133C8×C22⋊C4C2212yes—
134#1749C2211yescharacteristic
135C4×C22⋊C8C2211yescharacteristic
136#1745C2211yescharacteristic
137#1728C2211yescharacteristic
138C2×#336C2211yescharacteristic
139C22×M16C2312yes—
140C23×C8C2312yes—
141#556—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#126—22no—
148C2×#126—22no—
149C2×#125C2311yescharacteristic
150C2×#124—22no—
151C2×#124—21no—
152C2×#124C2311yescharacteristic
153C2×#123—21no—
154C2×#123—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8C2311yescharacteristic
158C2×C22⋊Q8C2311yescharacteristic
159C2×#121C2311yescharacteristic
160C2×#121C2311yescharacteristic
161C2×C4×Q8—22no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8C2311yescharacteristic
165C2×C4×D4—21no—
166C2×C4×D4D411yescharacteristic
167C2×C4×D4D411yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×#117—21no—
171C2×#117—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#501—28no—
175#489—28no—
176#435—28no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×C4⋊C8C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×C4×C8C2312yes—
199C2×C4×C8C2312yes—
200#400—21no—
201#400—22no—
202#400—22no—
203#400—21no—
204#399—21no—
205#399—21no—
206#398—21no—
207#397—22no—
208#397—22no—
209#397—22no—
210#397—22no—
211#397—21no—
212#394—21no—
213#394—21no—
214#394—21no—
215#393—21no—
216#393—21no—
217#392—21no—
218#391—22no—
219#391—22no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391C2311yescharacteristic
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#390—21no—
229#390—21no—
230#390C2311yescharacteristic
231#390C2311yescharacteristic
232#390C2311yescharacteristic
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389C2312yes—
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2312yes—
244#389C2312yes—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—21no—
256#388—21no—
257#388—21no—
258#388—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#387—21no—
269#386—21no—
270#386—21no—
271#385—21no—
272#385—21no—
273#385—21no—
274#385—21no—
275#384—21no—
276#384—21no—
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2312yes—
282#382—21no—
283#382—21no—
284#381—21no—
285#380—21no—
286#380—21no—
287#380—21no—
288#380—21no—
289#380C2311yescharacteristic
290#380C2311yescharacteristic
291#380C2311yescharacteristic
292#380C2311yescharacteristic
293#380C2312yes—
294#380C2312yes—
295#380C2312yes—
296#380C2312yes—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4C2311yescharacteristic
321C4×C22⋊C4C2311yescharacteristic
322C43C2311yescharacteristic
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#336C2312yes—
340#336C2311yescharacteristic
341#336C2311yescharacteristic
342#336C2311yescharacteristic
343#336C2311yescharacteristic
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—22no—
348C22×Q8—21no—
349C22×Q8C2411yescharacteristic
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C2×D411yescharacteristic
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C2×M16—24no—
362C2×M16—42no—
363C2×M16—42no—
364C22×C8—24no—
365C22×C8—42no—
366C22×C8—42no—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C4⋊Q8—22no—
372C4⋊Q8—24no—
373C4⋊Q8—24no—
374C4⋊Q8—41no—
375C4⋊Q8—42no—
376C4⋊Q8—44no—
377C4⋊Q8—44no—
378#126—48no—
379#126—48no—
380#125—24no—
381#124—24no—
382#124—48no—
383#124—44no—
384#123—44no—
385#123—82no—
386C22⋊Q8—22no—
387C22⋊Q8—41no—
388C22⋊Q8—44no—
389C22⋊Q8—44no—
390C22⋊Q8—42no—
391#121—22no—
392#121—41no—
393#121—42no—
394C4×Q8—44no—
395C4×Q8—42no—
396C4×Q8—48no—
397C4×Q8—82no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—42no—
401C4×D4—42no—
402C4×D4—82no—
403#117—44no—
404#117—44no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—42no—
479C2×C42—42no—
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#107—24no—
494#107—24no—
495#107—24no—
496#107—42no—
497#106—24no—
498#106—24no—
499#106—42no—
500#106—42no—
501C4⋊C8—24no—
502#103—24no—
503#103—24no—
504#103—42no—
505#103—42no—
506#102—24no—
507#102—24no—
508#102—42no—
509#102—42no—
510C22⋊C8—24no—
511C22⋊C8—24no—
512#97—42no—
513#97#4118yes—
514C4×C8—42no—
515C4×C8—42no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—22no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550C24—21no—
551C24C22×D411yescharacteristic
552C24C22×D411yescharacteristic
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—44no—
560C2×Q8—42no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—81no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—41no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2511yescharacteristic
626M16—84no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—84no—
638C2×C8C2×#4114yes—
639C2×C8C2×#4114yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C42−1+412yes—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4AGL(1,ℤ/8)14yes—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—41no—
724C42—44no—
725C42—44no—
726C42—44no—
727C42—42no—
728C42—81no—
729C42—81no—
730C42—81no—
731C42—81no—
732C42C2×#4114yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23C2×AGL(1,ℤ/8)12yes—
754C23C23×D411yescharacteristic
755Q8—42no—
756Q8—42no—
757Q8—84no—
758Q8—88no—
759Q8—84no—
760D4—44no—
761D4—42no—
762D4—42no—
763D4—84no—
764D4—162no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—162no—
836C2×C4#53212yes—
837C2×C4#53212yes—
838C2×C4C2×AGL(1,ℤ/8)12yes—
839C2×C4C2×AGL(1,ℤ/8)12yes—
840C2×C4#57512yes—
841C2×C4#57712yes—
842C2×C4#57812yes—
843C2×C4C22×#4112yes—
844C2×C4C2×2−1+411yescharacteristic
845C2×C4#58512yes—
846C2×C4#58511yescharacteristic
847C8—24no—
848C8—24no—
849C8—42no—
850C8—42no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22C2×#53211yescharacteristic
873C22#348511yescharacteristic
874C22#348911yescharacteristic
875C22C22×AGL(1,ℤ/8)11yescharacteristic
876C22C2×#57511yescharacteristic
877C22C2×#57711yescharacteristic
878C22C2×#57811yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4—82no—
901C4—81no—
902C4#350712yes—
903C4#351012yes—
904C2—42no—
905C2—81no—
906C2—161no—
907C2#3595911yescharacteristic
908C2#6070011yescharacteristic
909C2#6072311yescharacteristic
910C2#6173711yescharacteristic
911C2#6173911yescharacteristic
912C2#6212811yescharacteristic
913C2#6213011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36188C2semidirect
3. #30367C2semidirect
4. #30357C2semidirect
5. #30285C2semidirect
6. #29350C2semidirect
7. #29218C2semidirect
8. #29166C2semidirect
9. #29156C2semidirect
10. #28869C2semidirect
11. #28847C2semidirect
12. #28714C2semidirect
14. #28087C2semidirect
15. #28065C2semidirect
16. #27863C2semidirect
17. #27858C2semidirect
18. #23839C2semidirect
19. #23760C2semidirect
20. #23757C2semidirect
21. #23228C2semidirect
22. #23166C2semidirect
23. #20559C2semidirect

Maximal subgroups

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

subgroupindex
#364992
#361882
#303672
#303572
#302852
#293502
#292182
#291662
#291562
#288692
#288472
#287142
#286102
#280872
#280652
#278632
#278582
#238392
#237602
#237572
#232282
#231662
#205592