Finite Group Databasebeta

← #6765818

Subgroups — #6765818

Order 512.

1661 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic, complemented
3#33048C211yesmaximal, characteristic, complemented
4#31566C214yesmaximal, complemented
5#31400C214yesmaximal, complemented
6#30228C211yesmaximal, characteristic, complemented
7#29843C211yesmaximal, characteristic, complemented
8#29191C211yesmaximal, characteristic, complemented
9#28716C211yesmaximal, characteristic, complemented
10#27961C211yesmaximal, characteristic, complemented
11#27876C211yesmaximal, characteristic, complemented
12#27567C214yesmaximal, complemented
13#26675C214yesmaximal, complemented
14#25598C211yesmaximal, characteristic, complemented
15#25598C211yesmaximal, characteristic, complemented
16#22268C211yesmaximal, characteristic, complemented
17#21860C211yesmaximal, characteristic, complemented
18#21409C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28#2868C2211yescharacteristic
29#2859C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2566—21no—
35#2552—21no—
36#2542—21no—
37#2538C2212yes—
38#2512—21no—
39#2512C2212yes—
40#2504—21no—
41#2500—21no—
42#2441—21no—
43#2441—21no—
44#2429—21no—
45#2429—21no—
46#2423C2212yes—
47#2423C2212yes—
48#2422—21no—
49#2422C2212yes—
50#2416—21no—
51#2416C2212yes—
52#2365—21no—
53#2361—21no—
54#2361C2212yes—
55#2354—21no—
56Q8×C4⋊C4C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2099C2214yes—
64#2099C2214yes—
65#2077C2214yes—
66#2071C2214yes—
67#2066C2214yes—
68#2065C2214yes—
69#2034C2214yes—
70#2000C2214yes—
71#2000C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1957C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1936C2214yes—
83#1924C2212yes—
84#1919C2214yes—
85#1917C2212yes—
86#1895C2214yes—
87#1894C2214yes—
88#1880C2214yes—
89#1880C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1872C2214yes—
93#1870C2212yes—
94#1865C2214yes—
95#1851C2212yes—
96#1844C2211yescharacteristic
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1824C2214yes—
100#1803C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×SD16C2314yes—
108C22×M16C2312yes—
109#553—48no—
110#533—24no—
111#533—24no—
112#533—42no—
113#533—42no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#126—22no—
121C2×#125—21no—
122C2×#125—21no—
123C2×#125—21no—
124C2×#123—22no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8C2312yes—
141C2×C4×Q8C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×D4—22no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4C2312yes—
149C2×C4×D4C2311yescharacteristic
150C2×#117—21no—
151C2×#117—21no—
152C2×#117—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#492—24no—
159#486—42no—
160#486—42no—
161#431—42no—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C4×M16—42no—
175C2×#97C2312yes—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180#399—22no—
181#399—22no—
182#398—22no—
183#398—22no—
184#397—22no—
185#397—22no—
186#396—22no—
187#396—22no—
188#396—22no—
189#396—22no—
190#394—22no—
191#394—22no—
192#391—21no—
193#391—21no—
194#391C2312yes—
195#390—22no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#390C2312yes—
205#389—22no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—22no—
213#389—22no—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#387—22no—
223#387—22no—
224#386—22no—
225#386—22no—
226#385—22no—
227#385—22no—
228#384—22no—
229#384—21no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#384C2312yes—
236#384C2312yes—
237#384C2312yes—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#382—21no—
241#382—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380C2312yes—
246#380C2312yes—
247#380C2312yes—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2311yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C4×C22⋊C4C2311yescharacteristic
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8C2412yes—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2×D411yescharacteristic
284C22×D4C2412yes—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×SD16—28no—
294C2×SD16—44no—
295C2×SD16—44no—
296C2×M16—42no—
297C2×M16—42no—
298C2×M16—42no—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—44no—
309C4⋊Q8—82no—
310C4⋊Q8#4114yes—
311#127—22no—
312#127—22no—
313#126—48no—
314#125—44no—
315#125—44no—
316#125—44no—
317#123—48no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—42no—
321C22⋊Q8—42no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—82no—
325C22⋊Q8—82no—
326#121—44no—
327#121—44no—
328#121—44no—
329#121—48no—
330#121—44no—
331#121—44no—
332#121—82no—
333C4×Q8—24no—
334C4×Q8—24no—
335C4×Q8—44no—
336C4×Q8—42no—
337C4×Q8—42no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—42no—
343C4×D4—44no—
344C4×D4—48no—
345C4×D4—44no—
346C4×D4—82no—
347#117—44no—
348#117—44no—
349#117—44no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—82no—
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431#106—44no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434#103—44no—
435#103—44no—
436#103—44no—
437#102—44no—
438#102—44no—
439#102—44no—
440C22⋊C8—42no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443#97—42no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464C24—22no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C2×Q8—22no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8C2×#4114yes—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—41no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—82no—
495C2×D4—82no—
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—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
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—44no—
523C22×C4—44no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4#13714yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C2511yescharacteristic
542SD16—88no—
543M16—48no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—41no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—22no—
627C42—22no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42AGL(1,ℤ/8)14yes—
633C42C2×#4112yes—
634C42H(5,𝔽2)12yes—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×#13712yes—
656C23C23×D411yescharacteristic
657Q8—28no—
658Q8—44no—
659Q8—84no—
660Q8—84no—
661D4—44no—
662D4—44no—
663D4—44no—
664D4—88no—
665D4—84no—
666D4—84no—
667D4—164no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—28no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
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—164no—
725C2×C4—164no—
726C2×C4#54612yes—
727C2×C4#54612yes—
728C2×C4C2×AGL(1,ℤ/8)12yes—
729C2×C4C2×AGL(1,ℤ/8)12yes—
730C2×C4C2×AGL(1,ℤ/8)12yes—
731C2×C4C2×#13712yes—
732C2×C4C2×#13712yes—
733C2×C4#57712yes—
734C2×C4#57712yes—
735C2×C4C22×#4111yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4#58512yes—
738C2×C4#58512yes—
739C8—42no—
740C8—42no—
741C8—42no—
742C8—42no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22#344911yescharacteristic
765C22C2×#54611yescharacteristic
766C22#350011yescharacteristic
767C22C22×AGL(1,ℤ/8)11yescharacteristic
768C22C22×#13711yescharacteristic
769C22C2×#57711yescharacteristic
770C22C2×#57711yescharacteristic
771C4—22no—
772C4—22no—
773C4—22no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—44no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#332014yes—
789C4#333214yes—
790C4#352112yes—
791C4#353912yes—
792C2—42no—
793C2—81no—
794C2—162no—
795C2#3809211yescharacteristic
796C2#6096911yescharacteristic
797C2#6101511yescharacteristic
798C2C2×#332011yescharacteristic
799C2C2×#333211yescharacteristic
800C2#6253911yescharacteristic
801C2#6254211yescharacteristic
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. #33048C2semidirect
4. #31566C2semidirect
5. #31400C2semidirect
6. #30228C2semidirect
7. #29843C2semidirect
8. #29191C2semidirect
9. #28716C2semidirect
10. #27961C2semidirect
11. #27876C2semidirect
12. #27567C2semidirect
13. #26675C2semidirect
14. #25598C2semidirect
15. #25598C2semidirect
16. #22268C2semidirect
17. #21860C2semidirect
18. #21409C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361822
#361342
#330482
#315662
#314002
#302282
#298432
#291912
#287162
#279612
#278762
#275672
#266752
#255982
#222682
#218602
#214092
#211022