Finite Group Databasebeta

← #6765294

Subgroups — #6765294

Order 512.

1772 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic, complemented
3#33170C211yesmaximal, characteristic, complemented
4#30705C214yesmaximal, complemented
5#30597C214yesmaximal, complemented
6#30220C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29177C211yesmaximal, characteristic, complemented
9#28438C211yesmaximal, characteristic, complemented
10#27905C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#27066C214yesmaximal, complemented
13#26928C214yesmaximal, complemented
14#25598C211yesmaximal, characteristic, complemented
15#25598C211yesmaximal, characteristic, complemented
16#22219C211yesmaximal, characteristic, complemented
17#21860C211yesmaximal, characteristic, complemented
18#21400C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#483C2214yes—
27C2×#465C2214yes—
28C2×#461C2214yes—
29C2×#431C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2868C2211yescharacteristic
32#2859C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2856C2211yescharacteristic
37#2566—21no—
38#2552—21no—
39#2542C2212yes—
40#2538—21no—
41#2512—21no—
42#2512C2212yes—
43#2504—21no—
44#2500—21no—
45#2441—21no—
46#2441—21no—
47#2429C2212yes—
48#2429C2212yes—
49#2423—21no—
50#2423—21no—
51#2422—21no—
52#2422C2212yes—
53#2416—21no—
54#2416C2212yes—
55#2365C2212yes—
56#2361—21no—
57#2361C2212yes—
58#2354—21no—
59Q8×C4⋊C4—21no—
60C4×C4⋊Q8C2211yescharacteristic
61C4×#127C2211yescharacteristic
62#2285C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C42×D4C2211yescharacteristic
65#2096C2214yes—
66#2088C2214yes—
67#2055C2214yes—
68#2043C2214yes—
69#2043C2214yes—
70#2035C2214yes—
71#2013C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#2000C2214yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1968C2214yes—
79#1957C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1927C2214yes—
87#1926C2214yes—
88#1923C2212yes—
89#1919C2214yes—
90#1916C2212yes—
91#1892C2214yes—
92#1880C2214yes—
93#1880C2214yes—
94#1872C2214yes—
95#1869C2212yes—
96#1864C2214yes—
97#1850C2212yes—
98#1844C2211yescharacteristic
99#1844C2211yescharacteristic
100#1834C2211yescharacteristic
101#1803C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#103C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C23×C8C2312yes—
110#553—48no—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#126—22no—
122C2×#125—21no—
123C2×#125—21no—
124C2×#125—21no—
125C2×#123—22no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×#121—22no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2312yes—
144C2×C4×D4—22no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4D411yescharacteristic
148C2×C4×D4D411yescharacteristic
149C2×C4×D4C2312yes—
150C2×C4×D4C2311yescharacteristic
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#492—42no—
160#492—42no—
161#486—24no—
162#483—48no—
163#465—48no—
164#461—48no—
165#431—42no—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C4×C8—42no—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187#399—22no—
188#399—22no—
189#398—22no—
190#398—22no—
191#397—22no—
192#397—22no—
193#396—22no—
194#396—22no—
195#396—22no—
196#396—22no—
197#394—22no—
198#394—22no—
199#391—21no—
200#391C2312yes—
201#391C2312yes—
202#390—22no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#389—22no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—22no—
221#389—22no—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#387—22no—
230#387—22no—
231#386—22no—
232#386—22no—
233#385—22no—
234#385—22no—
235#384—22no—
236#384—21no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384—21no—
241#384—21no—
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#384C2312yes—
245#384C2311yescharacteristic
246#384C2311yescharacteristic
247#382—21no—
248#382—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380C2312yes—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2311yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269C43C2311yescharacteristic
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C22×Q8—21no—
280C22×Q8C2412yes—
281C22×Q8C2412yes—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2×D411yescharacteristic
287C22×D4C2412yes—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×SD16—28no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—44no—
302C22×C8—24no—
303C22×C8—42no—
304C22×C8—42no—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—44no—
315C4⋊Q8—44no—
316C4⋊Q8#4114yes—
317#127—22no—
318#127—22no—
319#126—48no—
320#125—44no—
321#125—44no—
322#125—44no—
323#123—48no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—42no—
327C22⋊Q8—42no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332#121—44no—
333#121—44no—
334#121—48no—
335#121—44no—
336#121—44no—
337#121—44no—
338#121—82no—
339C4×Q8—24no—
340C4×Q8—24no—
341C4×Q8—42no—
342C4×Q8—42no—
343C4×Q8—44no—
344C4×Q8—44no—
345C4×Q8—44no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—44no—
349C4×D4—48no—
350C4×D4—44no—
351C4×D4—82no—
352C4×D4SD1618yescomplemented
353#117—44no—
354#117—44no—
355#117—44no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#106—28no—
438#106—44no—
439C4⋊C8—24no—
440C4⋊C8—42no—
441#103—28no—
442#103—44no—
443#103—44no—
444#103—44no—
445#103—44no—
446#103—44no—
447#102—28no—
448#102—44no—
449C22⋊C8—24no—
450C22⋊C8—42no—
451C22⋊C8—42no—
452C4×C8—22no—
453C4×C8—22no—
454C4×C8—22no—
455C4×C8—22no—
456C4×C8—42no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473C24—22no—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—82no—
504C2×D4—82no—
505C2×D4C2×SD1614yes—
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—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
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—22no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4C2×SD1614yes—
538C22×C4C2×SD1614yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C2511yescharacteristic
552SD16—88no—
553SD16—88no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—48no—
566C2×C8H(5,𝔽2)14yes—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C2×SD1614yes—
604C4⋊C4C2×#4114yes—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
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—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4C2×SD1614yes—
624C22⋊C4C2×SD1614yes—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—22no—
636C42—21no—
637C42—22no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42C2×SD1614yes—
643C42C2×#4112yes—
644C42H(5,𝔽2)12yes—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C22×SD1612yes—
665C23C22×SD1612yes—
666C23C23×D411yescharacteristic
667Q8—48no—
668Q8—44no—
669Q8—44no—
670Q8—44no—
671Q8—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—88no—
676D4—84no—
677D4—84no—
678D4—164no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—24no—
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—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—164no—
735C2×C4—164no—
736C2×C4#54612yes—
737C2×C4#54612yes—
738C2×C4C22×SD1612yes—
739C2×C4C22×SD1612yes—
740C2×C4C22×SD1612yes—
741C2×C4C22×SD1612yes—
742C2×C4C22×SD1612yes—
743C2×C4#57512yes—
744C2×C4#57712yes—
745C2×C4#57812yes—
746C2×C4C22×#4111yescharacteristic
747C2×C4C2×H(5,𝔽2)12yes—
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4#58512yes—
750C8—24no—
751C8—42no—
752C8—42no—
753C8—42no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22#344911yescharacteristic
776C22C2×#54611yescharacteristic
777C22#349811yescharacteristic
778C22C23×SD1611yescharacteristic
779C22C2×#57511yescharacteristic
780C22C2×#57711yescharacteristic
781C22C2×#57811yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—44no—
792C4—41no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#329814yes—
800C4#330714yes—
801C4#351712yes—
802C4#354212yes—
803C2—42no—
804C2—42no—
805C2—162no—
806C2#3808911yescharacteristic
807C2#6094111yescharacteristic
808C2#6100811yescharacteristic
809C2C2×#329811yescharacteristic
810C2C2×#330711yescharacteristic
811C2#6241311yescharacteristic
812C2#6242511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36182C2
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. #36134C2semidirect
3. #33170C2semidirect
4. #30705C2semidirect
5. #30597C2semidirect
6. #30220C2semidirect
7. #29807C2semidirect
8. #29177C2semidirect
9. #28438C2semidirect
10. #27905C2semidirect
11. #27889C2semidirect
12. #27066C2semidirect
13. #26928C2semidirect
14. #25598C2semidirect
15. #25598C2semidirect
16. #22219C2semidirect
17. #21860C2semidirect
18. #21400C2semidirect
19. #21101C2semidirect
352. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
#361822
#361342
#331702
#307052
#305972
#302202
#298072
#291772
#284382
#279052
#278892
#270662
#269282
#255982
#222192
#218602
#214002
#211012