Finite Group Databasebeta

← #6766141

Subgroups — #6766141

Order 512.

1894 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36210C211yesmaximal, characteristic, complemented
2#36121C211yesmaximal, characteristic
3#33042C211yesmaximal, characteristic, complemented
4#31499C214yesmaximal, complemented
5#31266C214yesmaximal, complemented
6#30204C211yesmaximal, characteristic, complemented
7#29877C211yesmaximal, characteristic, complemented
8#29143C211yesmaximal, characteristic, complemented
9#28654C211yesmaximal, characteristic, complemented
10#27891C211yesmaximal, characteristic, complemented
11#27878C211yesmaximal, characteristic, complemented
12#27523C214yesmaximal, complemented
13#26697C214yesmaximal, complemented
14#25855C211yesmaximal, characteristic, complemented
15#25671C211yesmaximal, characteristic, complemented
16#22220C211yesmaximal, characteristic, complemented
17#21803C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#546—21no—
21C2×#532C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C2×#498C2211yescharacteristic, complemented
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic, complemented
28#2859C2211yescharacteristic, complemented
29#2858C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic, complemented
33#2856C2211yescharacteristic
34#2562C2212yes—
35#2544—21no—
36#2514—21no—
37#2509—21no—
38#2495C2212yes—
39#2494—21no—
40#2494C2212yescomplemented
41#2485—21no—
42#2445—21no—
43#2445C2212yes—
44#2435—21no—
45#2431—21no—
46#2428—21no—
47#2428C2212yes—
48#2421—21no—
49#2415—21no—
50#2408—21no—
51#2408C2212yes—
52#2370C2212yescomplemented
53#2362—21no—
54#2347—21no—
55D4×C22⋊C4—21no—
56D4×C22⋊C4C2212yes—
57C4×C4⋊Q8C2211yescharacteristic, complemented
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic, complemented
61C42×D4C2211yescharacteristic
62#2088C2214yescomplemented
63#2077C2214yes—
64#2076C2214yes—
65#2073C2214yescomplemented
66#2065C2214yescomplemented
67#2041C2214yes—
68#2034C2214yescomplemented
69#2033C2214yescomplemented
70#2025C2214yescomplemented
71#2025C2214yescomplemented
72#1990C2211yescharacteristic, complemented
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1990C2211yescharacteristic, complemented
76#1982C2214yes—
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1934C2214yescomplemented
84#1926C2214yescomplemented
85#1925C2214yescomplemented
86#1925C2214yescomplemented
87#1923C2212yes—
88#1921C2214yescomplemented
89#1916C2212yescomplemented
90#1893C2214yescomplemented
91#1893C2214yescomplemented
92#1869C2212yes—
93#1864C2214yescomplemented
94#1862C2214yescomplemented
95#1850C2212yescomplemented
96#1845C2211yescharacteristic, complemented
97#1834C2211yescharacteristic, complemented
98#1834C2211yescharacteristic, complemented
99#1804C2214yescomplemented
100#1786C2214yes—
101#1786C2214yes—
102C4×C4⋊C8C2211yescharacteristic, complemented
103C4×#102C2214yescomplemented
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic, complemented
106#1744C2211yescharacteristic, complemented
107C22×#41—21no—
108C23×D4—21no—
109C23×D4—21no—
110C23×D4C2312yes—
111C23×C8C2312yes—
112#546—48no—
113#532—24no—
114#532—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×#127—24no—
118C2×#127—21no—
119C2×#127—21no—
120C2×#127—42no—
121C2×#127C2311yescharacteristic
122C2×#127C2312yes—
123C2×#127C2311yescharacteristic
124C2×#125C2312yes—
125C2×#124—21no—
126C2×#124—21no—
127C2×#124—21no—
128C2×#123—22no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—22no—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×#120—22no—
139C2×C4×Q8—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2312yes—
147C2×C4×D4C2311yescharacteristic
148C2×#117—21no—
149C2×#117—21no—
150C22×C22⋊C4—22no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#498—42no—
154#486—24no—
155#486—42no—
156#431—42no—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C4×C8—42no—
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2312yes—
178#401—22no—
179#400—22no—
180#400—22no—
181#397—22no—
182#397—22no—
183#394—22no—
184#394—22no—
185#394—22no—
186#394—22no—
187#394—22no—
188#392—22no—
189#392—22no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390C2312yes—
201#390C2312yes—
202#390C2312yes—
203#390C2312yes—
204#389—22no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#383—22no—
233#382—21no—
234#382—21no—
235#382C2312yes—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380C2312yes—
242#380C2312yes—
243#380C2312yes—
244#380C2312yes—
245#380C2312yes—
246#379—22no—
247#379—22no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2311yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4C2311yescharacteristic
263C4×C22⋊C4C2311yescharacteristic
264C43C2311yescharacteristic
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C25—22no—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—82no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×D4—24no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—42no—
293C22×D4—44no—
294C22×D4—44no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4—44no—
298C22×D4—44no—
299C22×D4—82no—
300C22×D4—82no—
301C22×D4C2×D411yescharacteristic
302C22×D4C2412yes—
303C22×D4C2412yes—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C22×C8—42no—
313C22×C8—42no—
314C22×C8—42no—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323#127—24no—
324#127—22no—
325#127—22no—
326#127—22no—
327#127—42no—
328#127—44no—
329#127—44no—
330#127#4114yes—
331#125—44no—
332#124—44no—
333#124—44no—
334#124—82no—
335#123—48no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—82no—
339#121—24no—
340#121—48no—
341#121—42no—
342#121—44no—
343#121—44no—
344#121—44no—
345#121—82no—
346#120—48no—
347C4×Q8—82no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—42no—
352C4×D4—42no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—82no—
357#117—44no—
358#117—82no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
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—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—48no—
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—44no—
429#106—44no—
430C4⋊C8—42no—
431C4⋊C8—42no—
432#102—28no—
433#102—44no—
434#102—44no—
435#102—44no—
436#102—44no—
437#102—44no—
438#102—44no—
439#102—44no—
440C22⋊C8—42no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—42no—
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#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468C24—22no—
469C24—22no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—82no—
475C24—82no—
476C24—82no—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479#41—816no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—41no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—816no—
518C2×D4—82no—
519C2×D4—82no—
520C2×D4—82no—
521C2×D4—88no—
522C2×D4—88no—
523C2×D4—816no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4—82no—
527C2×D4C2×#4114yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4#13514yes—
559C22×C4AGL(1,ℤ/8)14yes—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C2511yescharacteristic
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—48no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—41no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C22⋊C4—82no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—22no—
649C42—22no—
650C42—44no—
651C42—82no—
652C42—82no—
653C42C2×#4112yes—
654C42H(5,𝔽2)12yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—24no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—88no—
682C23—88no—
683C23—88no—
684C23—88no—
685C23—164no—
686C23—164no—
687C23—164no—
688C23C2×#13512yes—
689C23C2×AGL(1,ℤ/8)12yes—
690C23C23×D411yescharacteristic
691Q8—84no—
692Q8—84no—
693D4—28no—
694D4—44no—
695D4—44no—
696D4—44no—
697D4—44no—
698D4—48no—
699D4—48no—
700D4—88no—
701D4—88no—
702D4—88no—
703D4—88no—
704D4—84no—
705D4—84no—
706D4—164no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—28no—
712C2×C4—28no—
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—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
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—88no—
762C2×C4—164no—
763C2×C4#54612yes—
764C2×C4#54612yes—
765C2×C4C2×#13512yes—
766C2×C4C2×#13512yes—
767C2×C4C2×AGL(1,ℤ/8)12yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4#57612yes—
770C2×C4#57712yes—
771C2×C4C22×#4111yescharacteristic
772C2×C4C2×H(5,𝔽2)11yescharacteristic
773C2×C4#58512yes—
774C2×C4#58512yes—
775C8—42no—
776C8—42no—
777C8—42no—
778C8—42no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—1616no—
808C22#344911yescharacteristic
809C22C2×#54611yescharacteristic
810C22#350011yescharacteristic
811C22C22×#13511yescharacteristic
812C22C22×AGL(1,ℤ/8)11yescharacteristic
813C22C2×#57611yescharacteristic
814C22C2×#57711yescharacteristic
815C4—22no—
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#329714yes—
832C4#331014yes—
833C4#352112yes—
834C4#354012yes—
835C2—42no—
836C2—42no—
837C2—84no—
838C2—162no—
839C2#3809411yescharacteristic
840C2#6094611yescharacteristic
841C2#6100611yescharacteristic
842C2C2×#329711yescharacteristic
843C2C2×#331011yescharacteristic
844C2#6253111yescharacteristic
845C2#6253511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36121C2
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
1. #36210C2semidirect
3. #33042C2semidirect
4. #31499C2semidirect
5. #31266C2semidirect
6. #30204C2semidirect
7. #29877C2semidirect
8. #29143C2semidirect
9. #28654C2semidirect
10. #27891C2semidirect
11. #27878C2semidirect
12. #27523C2semidirect
13. #26697C2semidirect
14. #25855C2semidirect
15. #25671C2semidirect
16. #22220C2semidirect
17. #21803C2semidirect
18. #21401C2semidirect
19. #21101C2semidirect
23. C2×#498C22semidirect
27. C22×C4×C8C22semidirect
28. #2859C22semidirect
32. #2857C22semidirect
40. #2494C22semidirect
52. #2370C22semidirect
57. C4×C4⋊Q8C22semidirect
60. #2285C22semidirect
62. #2088C22semidirect
65. #2073C22semidirect
66. #2065C22semidirect
68. #2034C22semidirect
69. #2033C22semidirect
70. #2025C22semidirect
71. #2025C22semidirect
72. #1990C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1990C22semidirect
83. #1934C22semidirect
84. #1926C22semidirect
85. #1925C22semidirect
86. #1925C22semidirect
88. #1921C22semidirect
89. #1916C22semidirect
90. #1893C22semidirect
91. #1893C22semidirect
93. #1864C22semidirect
94. #1862C22semidirect
95. #1850C22semidirect
96. #1845C22semidirect
97. #1834C22semidirect
98. #1834C22semidirect
99. #1804C22semidirect
102. C4×C4⋊C8C22semidirect
103. C4×#102C22semidirect
105. C4×C22⋊C8C22semidirect
106. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#362102
#361212
#330422
#314992
#312662
#302042
#298772
#291432
#286542
#278912
#278782
#275232
#266972
#258552
#256712
#222202
#218032
#214012
#211012