Finite Group Databasebeta

← #7341160

Subgroups — #7341160

Order 512.

1925 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59219C211yesmaximal, characteristic, complemented
2#39358C211yesmaximal, characteristic
3#31800C212yesmaximal, complemented
4#31617C212yesmaximal, complemented
5#31597C212yesmaximal, complemented
6#31310C212yesmaximal, complemented
7#30571C212yesmaximal, complemented
8#30404C212yesmaximal, complemented
9#30115C211yesmaximal, characteristic, complemented
10#29920C211yesmaximal, characteristic, complemented
11#28123C211yesmaximal, characteristic, complemented
12#27585C211yesmaximal, characteristic, complemented
13#26566C212yesmaximal, complemented
14#26179C212yesmaximal, complemented
15#25080C212yesmaximal, complemented
16#24861C212yesmaximal, complemented
17#24252C212yesmaximal, complemented
18#24032C212yesmaximal, complemented
19#23333C211yesmaximal, characteristic, complemented
20C2×D42C2212yes—
21C2×#534—21no—
22C2×#484C2211yescharacteristic, complemented
23C2×#480C2212yes—
24C2×#465C2212yescomplemented
25C2×#460C2212yes—
26C2×#450C2211yescharacteristic
27C2×#450C2212yescomplemented
28C2×#440C2212yescomplemented
29C22×#102C2212yescomplemented
30#2856C2211yescharacteristic
31#2765—22no—
32#2682—21no—
33#2679—21no—
34#2678—22no—
35#2617—21no—
36#2571C2211yescharacteristic, complemented
37#2538C2211yescharacteristic, complemented
38#2536C2212yescomplemented
39#2507—21no—
40#2494—21no—
41#2494C2212yescomplemented
42#2486C2212yescomplemented
43#2470—22no—
44#2445C2212yes—
45#2433C2212yes—
46#2422—21no—
47#2422C2212yes—
48#2416C2212yes—
49#2410—22no—
50#2408C2212yes—
51#2360C2212yescomplemented
52#2357—21no—
53Q8×C4⋊C4C2211yescharacteristic, complemented
54D4×C4⋊C4C2211yescharacteristic, complemented
55C4×C22⋊Q8C2211yescharacteristic, complemented
56C4×#121C2211yescharacteristic
57C2×#390C2211yescharacteristic
58#2285C2211yescharacteristic, complemented
59#2100C2211yescharacteristic, complemented
60#2095C2211yescharacteristic, complemented
61#2094C2212yescomplemented
62#2093C2212yescomplemented
63#2092C2212yescomplemented
64#2087C2212yescomplemented
65#2085C2212yescomplemented
66#2077C2212yescomplemented
67#2071C2212yescomplemented
68#2071C2212yescomplemented
69#2067C2212yescomplemented
70#2065C2212yescomplemented
71#2055C2212yescomplemented
72#2041C2212yes—
73#2041C2212yes—
74#2041C2211yescharacteristic, complemented
75#2035C2212yescomplemented
76#2034C2212yescomplemented
77#2033C2212yes—
78#2033C2212yescomplemented
79#2033C2212yescomplemented
80#2033C2212yescomplemented
81#2033C2212yescomplemented
82#2014C2211yescharacteristic, complemented
83#2000C2212yes—
84#2000C2212yescomplemented
85#1982C2212yescomplemented
86#1961C2212yes—
87#1955C2212yescomplemented
88#1947C2212yescomplemented
89#1944C2212yescomplemented
90#1936C2212yescomplemented
91#1926C2212yescomplemented
92#1926C2212yescomplemented
93#1925C2212yescomplemented
94#1925C2212yescomplemented
95#1924C2212yescomplemented
96#1917C2212yescomplemented
97#1893C2212yes—
98#1880C2212yescomplemented
99#1880C2212yescomplemented
100#1880C2212yescomplemented
101#1874C2212yescomplemented
102#1869C2212yescomplemented
103#1869C2212yescomplemented
104#1863C2212yescomplemented
105#1862C2212yescomplemented
106#1862C2212yescomplemented
107#1853C2212yescomplemented
108#1852C2212yescomplemented
109#1850C2212yescomplemented
110#1824C2211yescharacteristic, complemented
111#1817C2211yescharacteristic, complemented
112#1808C2212yescomplemented
113#1804C2212yescomplemented
114#1797C2211yescharacteristic, complemented
115#1786C2212yes—
116#1786C2211yescharacteristic
117#1786C2212yescomplemented
118#1786C2212yescomplemented
119C23×D4—22no—
120C23×D4C2311yescharacteristic
121C23×D4C2312yes—
122C22×SD16C2312yes—
123C22×SD16C2312yes—
124C23×C8C2312yes—
125D42—44no—
126D42—44no—
127#534—48no—
128C2×#127C2312yes—
129C2×#127C2311yescharacteristic
130C2×#123—22no—
131C2×#123—22no—
132C2×#123—22no—
133C2×C22⋊Q8C2311yescharacteristic
134C2×C22⋊Q8C2312yes—
135C2×#121—22no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—22no—
139C2×#121D411yescharacteristic
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#120—22no—
144C2×#120—22no—
145C2×#120—22no—
146C2×#120—22no—
147C2×#120—22no—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2311yescharacteristic
150C2×C4×D4—21no—
151C2×C4×D4C2312yes—
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2312yes—
154C2×#117—21no—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C42C2311yescharacteristic
160#484—42no—
161#480—44no—
162#465—44no—
163#460—44no—
164#450—42no—
165#450—44no—
166#440—44no—
167C2×#107C2312yes—
168C2×#107C2312yes—
169C2×#107C2312yes—
170C2×#107C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#102—44no—
178C2×#102C2312yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×#97C2312yes—
199#401—22no—
200#400—22no—
201#398—22no—
202#398—22no—
203#397—22no—
204#397—22no—
205#397—22no—
206#396—22no—
207#396—22no—
208#394—22no—
209#394—22no—
210#394—22no—
211#394—22no—
212#394—22no—
213#394—22no—
214#392—22no—
215#392—22no—
216#392—22no—
217#391C2311yescharacteristic
218#390—21no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390—21no—
223#390D411yescharacteristic
224#390C2312yes—
225#390C2312yes—
226#390C2312yes—
227#390C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389D411yescharacteristic
234#389C2312yes—
235#389C2311yescharacteristic
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#388—22no—
241#388D412yes—
242#387—21no—
243#387—22no—
244#387—22no—
245#386—22no—
246#386—22no—
247#386D412yes—
248#385—21no—
249#385—22no—
250#385—22no—
251#385—22no—
252#384—21no—
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#382—21no—
257#382—21no—
258#382C2312yes—
259#381—22no—
260#380—21no—
261#380D411yescharacteristic
262#380C2312yes—
263#380C2312yes—
264#380C2312yes—
265#380C2311yescharacteristic
266#380C2312yes—
267#379—22no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4C2311yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C22⋊C4—21no—
275C4×C22⋊C4—22no—
276C4×C22⋊C4C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2311yescharacteristic
288#336C2311yescharacteristic
289#336C2312yes—
290#336C2312yes—
291C25—21no—
292C25—22no—
293C22×Q8C2411yescharacteristic
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—21no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—22no—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—42no—
308C22×D4—42no—
309C22×D4—41no—
310C22×D4—42no—
311C22×D4—41no—
312C22×D4—42no—
313C22×D4—48no—
314C22×D4—48no—
315C22×D4—84no—
316C22×D4C2×D412yes—
317C22×D4C2×D411yescharacteristic
318C22×D4C2412yes—
319C22×D4C2412yes—
320C23×C4—21no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—42no—
331C2×SD16—42no—
332C2×SD16—42no—
333C22×C8—42no—
334C22×C8—42no—
335C22×C8—42no—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340#127—24no—
341#127—42no—
342#127—42no—
343#123—48no—
344#123—48no—
345#123—84no—
346C22⋊Q8—24no—
347C22⋊Q8—22no—
348C22⋊Q8—41no—
349C22⋊Q8—42no—
350#121—24no—
351#121—24no—
352#121—42no—
353#121—42no—
354#121—42no—
355#121—44no—
356#121—48no—
357#121—48no—
358#121—42no—
359#121—42no—
360#121—82no—
361#120—48no—
362#120—48no—
363#120—48no—
364#120—48no—
365#120—84no—
366C4×Q8—42no—
367C4×Q8—42no—
368C4×Q8—42no—
369C4×D4—24no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—42no—
373C4×D4—42no—
374C4×D4—44no—
375#117—82no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D412yes—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2411yescharacteristic
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—82no—
428C2×C22⋊C4C2×D412yes—
429C2×C22⋊C4C2×D412yes—
430C2×C22⋊C4C2×D412yes—
431C2×C22⋊C4C2×D412yes—
432C2×C22⋊C4C2×D412yes—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—42no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2412yes—
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107—42no—
444#107—42no—
445#107—42no—
446#107—42no—
447#106—42no—
448#106—42no—
449C4⋊C8—42no—
450C4⋊C8—42no—
451#103—24no—
452#103—42no—
453#102—24no—
454#102—24no—
455#102—24no—
456#102—42no—
457#102—42no—
458#102—42no—
459#102—42no—
460#102—42no—
461#102—42no—
462#102—42no—
463#102—42no—
464#102—42no—
465#102—42no—
466#102—42no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469C22⋊C8—41no—
470C22⋊C8—42no—
471C22⋊C8—42no—
472C22⋊C8—41no—
473#97—42no—
474#95—21no—
475#95—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—21no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95C2×D412yes—
490#95C2×D412yes—
491#95C2×D412yes—
492C24—24no—
493C24—22no—
494C24—22no—
495C24—44no—
496C24—42no—
497C24—42no—
498C24—44no—
499C24—81no—
500C24—82no—
501C24—81no—
502C24—81no—
503C24—82no—
504C24—82no—
505C24—81no—
506C24—82no—
507C24—82no—
508C24C22×D412yes—
509C24C22×D411yescharacteristic
510C2×Q8—21no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8H(5,𝔽2)12yes—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—42no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—48no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—42no—
544C2×D4—81no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—82no—
554C2×D4—81no—
555C2×D4—84no—
556C2×D4—84no—
557C2×D4—84no—
558C2×D4—84no—
559C2×D4—84no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—832no—
564C2×D4AGL(1,ℤ/8)14yes—
565C2×D4H(5,𝔽2)14yes—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—82no—
595C22×C4—81no—
596C22×C4—82no—
597C22×C4—81no—
598C22×C4—82no—
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C2511yescharacteristic
608SD16—48no—
609SD16—84no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—84no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—42no—
639C4⋊C4—44no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—82no—
648C4⋊C4—81no—
649C4⋊C4—81no—
650C4⋊C4—81no—
651C4⋊C4—82no—
652C4⋊C4—81no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—42no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—42no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—41no—
684C42—41no—
685C42—42no—
686C42—42no—
687C42—82no—
688C42—82no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—24no—
702C23—48no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—88no—
717C23—84no—
718C23—84no—
719C23—88no—
720C23—164no—
721C23—164no—
722C23—162no—
723C23—162no—
724C23—164no—
725C23—162no—
726C23—162no—
727C23—164no—
728C23—164no—
729C23C2×AGL(1,ℤ/8)14yes—
730C23#57612yes—
731C23C23×D411yescharacteristic
732Q8—24no—
733Q8—42no—
734D4—24no—
735D4—24no—
736D4—44no—
737D4—48no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—84no—
745D4—88no—
746D4—88no—
747D4—88no—
748D4—88no—
749D4—162no—
750D4—164no—
751D4—162no—
752D4—164no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—82no—
807C2×C4—88no—
808C2×C4—164no—
809C2×C4—162no—
810C2×C4C2×AGL(1,ℤ/8)12yes—
811C2×C4#57712yes—
812C2×C4C2×H(5,𝔽2)12yes—
813C2×C4C2×H(5,𝔽2)11yescharacteristic
814C2×C4#58511yescharacteristic
815C2×C4#58512yes—
816C8—42no—
817C8—42no—
818C8—42no—
819C8—42no—
820C22—24no—
821C22—24no—
822C22—22no—
823C22—22no—
824C22—24no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—168no—
849C22—1616no—
850C22#348411yescharacteristic
851C22#348511yescharacteristic
852C22#348811yescharacteristic
853C22C22×AGL(1,ℤ/8)11yescharacteristic
854C22C2×#57611yescharacteristic
855C22C2×#57711yescharacteristic
856C22#358611yescharacteristic
857C4—22no—
858C4—22no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—82no—
868C4—81no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4#353312yes—
874C4#353412yes—
875C2—44no—
876C2—42no—
877C2—84no—
878C2—162no—
879C2#4877611yescharacteristic
880C2#6159111yescharacteristic
881C2#6168011yescharacteristic
882C2#6170411yescharacteristic
883C2#6176611yescharacteristic
884C2#6198311yescharacteristic
885C2#6202211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39358C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59219C2semidirect
3. #31800C2semidirect
4. #31617C2semidirect
5. #31597C2semidirect
6. #31310C2semidirect
7. #30571C2semidirect
8. #30404C2semidirect
9. #30115C2semidirect
10. #29920C2semidirect
11. #28123C2semidirect
12. #27585C2semidirect
13. #26566C2semidirect
14. #26179C2semidirect
15. #25080C2semidirect
16. #24861C2semidirect
17. #24252C2semidirect
18. #24032C2semidirect
19. #23333C2semidirect
22. C2×#484C22semidirect
24. C2×#465C22semidirect
27. C2×#450C22semidirect
28. C2×#440C22semidirect
29. C22×#102C22semidirect
36. #2571C22semidirect
37. #2538C22semidirect
38. #2536C22semidirect
41. #2494C22semidirect
42. #2486C22semidirect
51. #2360C22semidirect
53. Q8×C4⋊C4C22semidirect
54. D4×C4⋊C4C22semidirect
55. C4×C22⋊Q8C22semidirect
58. #2285C22semidirect
59. #2100C22semidirect
60. #2095C22semidirect
61. #2094C22semidirect
62. #2093C22semidirect
63. #2092C22semidirect
64. #2087C22semidirect
65. #2085C22semidirect
66. #2077C22semidirect
67. #2071C22semidirect
68. #2071C22semidirect
69. #2067C22semidirect
70. #2065C22semidirect
71. #2055C22semidirect
74. #2041C22semidirect
75. #2035C22semidirect
76. #2034C22semidirect
78. #2033C22semidirect
79. #2033C22semidirect
80. #2033C22semidirect
81. #2033C22semidirect
82. #2014C22semidirect
84. #2000C22semidirect
85. #1982C22semidirect
87. #1955C22semidirect
88. #1947C22semidirect
89. #1944C22semidirect
90. #1936C22semidirect
91. #1926C22semidirect
92. #1926C22semidirect
93. #1925C22semidirect
94. #1925C22semidirect
95. #1924C22semidirect
96. #1917C22semidirect
98. #1880C22semidirect
99. #1880C22semidirect
100. #1880C22semidirect
101. #1874C22semidirect
102. #1869C22semidirect
103. #1869C22semidirect
104. #1863C22semidirect
105. #1862C22semidirect
106. #1862C22semidirect
107. #1853C22semidirect
108. #1852C22semidirect
109. #1850C22semidirect
110. #1824C22semidirect
111. #1817C22semidirect
112. #1808C22semidirect
113. #1804C22semidirect
114. #1797C22semidirect
117. #1786C22semidirect
118. #1786C22semidirect

Maximal subgroups

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

subgroupindex
#592192
#393582
#318002
#316172
#315972
#313102
#305712
#304042
#301152
#299202
#281232
#275852
#265662
#261792
#250802
#248612
#242522
#240322
#233332