Finite Group Databasebeta

← #6469296

Subgroups — #6469296

Order 512.

2022 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#35291C211yesmaximal, characteristic, complemented
2#34210C211yesmaximal, characteristic
3#29504C214yesmaximal, complemented
4#29192C211yesmaximal, characteristic, complemented
5#29190C211yesmaximal, characteristic, complemented
6#28613C211yesmaximal, characteristic, complemented
7#28613C211yesmaximal, characteristic, complemented
8#27975C211yesmaximal, characteristic, complemented
9#27949C211yesmaximal, characteristic, complemented
10#25855C211yesmaximal, characteristic
11#25717C211yesmaximal, characteristic
12#24516C214yesmaximal, complemented
13#23690C214yesmaximal, complemented
14#21692C211yesmaximal, characteristic, complemented
15C4×#492C211yesmaximal, characteristic, complemented
16#21646C211yesmaximal, characteristic, complemented
17C4×#486C211yesmaximal, characteristic, complemented
18#21459C214yesmaximal, complemented
19C4×#433C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C2×#518C2212yes—
22C2×#492C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#450C2214yes—
27C2×#440C2214yescomplemented
28C2×C4×SD16C2214yescomplemented
29C2×#433C2212yes—
30#2862C2211yescharacteristic, complemented
31#2859C2211yescharacteristic, complemented
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2645C2212yescomplemented
35#2625C2212yes—
36#2514—21no—
37#2509—21no—
38#2508—21no—
39#2495—21no—
40#2494—21no—
41#2489—21no—
42#2453—21no—
43#2421—21no—
44#2366—21no—
45#2366—21no—
46#2366—21no—
47#2366—21no—
48D4×C22⋊C4—21no—
49D4×C22⋊C4—21no—
50D4×C22⋊C4—21no—
51D4×C22⋊C4—21no—
52#2328C2212yes—
53#2328C2212yes—
54#2323C2212yes—
55#2320C2212yescomplemented
56#2309C2212yes—
57C4×C4⋊Q8C2211yescharacteristic, complemented
58C4×C4⋊Q8C2211yescharacteristic, complemented
59C4×#127C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C4×#127C2211yescharacteristic
63#2285C2211yescharacteristic
64C4×#117C2211yescharacteristic
65#2085C2214yescomplemented
66#2074C2214yescomplemented
67#2067C2214yescomplemented
68#2065C2214yescomplemented
69#2055C2214yescomplemented
70#2055C2214yescomplemented
71#2041C2214yes—
72#2014C2214yes—
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1973C2214yescomplemented
76#1968C2214yescomplemented
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic, complemented
82#1956C2211yescharacteristic, complemented
83#1936C2214yescomplemented
84#1934C2214yescomplemented
85#1877C2214yescomplemented
86#1877C2214yescomplemented
87#1873C2214yes—
88#1864C2214yescomplemented
89#1862C2214yescomplemented
90#1854C2214yes—
91#1845C2211yescharacteristic, complemented
92#1844C2211yescharacteristic, complemented
93#1834C2211yescharacteristic, complemented
94#1834C2211yescharacteristic, complemented
95#1786C2214yes—
96#1768C2212yescomplemented
97C4×C4⋊C8C2211yescharacteristic, complemented
98C4×C4⋊C8C2211yescharacteristic, complemented
99#1762C2214yescomplemented
100C4×#102C2214yescomplemented
101#1750C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1746C2212yescomplemented
105C4×#97C2211yescharacteristic, complemented
106C42×C8C2211yescharacteristic, complemented
107C23×D4—21no—
108C23×D4—21no—
109C23×D4C2312yes—
110C22×SD16C2314yes—
111C22×SD16C2314yes—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127—24no—
115C2×#127—24no—
116C2×#127—21no—
117C2×#127—21no—
118C2×#127C2312yes—
119C2×#127C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8C2312yes—
124#518—48no—
125C2×C4×Q8—21no—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×#117C2312yes—
142C2×#117C2311yescharacteristic
143C2×#117C2311yescharacteristic
144C22×C22⋊C4—22no—
145C22×C22⋊C4—22no—
146C22×C42C2311yescharacteristic
147#492—24no—
148#492—24no—
149#486—24no—
150#486—24no—
151#450—216no—
152#440—48no—
153C4×SD16—48no—
154#433—28no—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×#97C2312yes—
170C2×#97C2312yes—
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2312yes—
176C2×C4×C8C2312yes—
177#401—22no—
178#400—22no—
179#400—22no—
180#400—22no—
181#400—22no—
182#398—22no—
183#397—22no—
184#397—22no—
185#391—21no—
186#391—21no—
187#391—21no—
188#391—21no—
189#391C2312yes—
190#391C2312yes—
191#391C2312yes—
192#391C2312yes—
193#390—22no—
194#390—22no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390C2312yes—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
207#389—22no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#388—22no—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#383—22no—
238#382—21no—
239#382—21no—
240#382—21no—
241#382—22no—
242#382C2312yes—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380C2312yes—
249#379—22no—
250#379—22no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4C2312yes—
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265#376C2311yescharacteristic
266#376C2311yescharacteristic
267C43C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C25—22no—
278C22×Q8—21no—
279C22×Q8C2412yes—
280C22×D4—28no—
281C22×D4—28no—
282C22×D4—24no—
283C22×D4—24no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—28no—
292C22×D4—44no—
293C22×D4—82no—
294C22×D4—82no—
295C22×D4—82no—
296C22×D4—82no—
297C22×D4C2412yes—
298C22×D4C2412yes—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×SD16—28no—
307C2×SD16—28no—
308C2×SD16—28no—
309C2×SD16—28no—
310C2×SD16—44no—
311C2×SD16—44no—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320#127—28no—
321#127—28no—
322#127—24no—
323#127—24no—
324#127—22no—
325#127—22no—
326#127#4114yes—
327#127#4114yes—
328#125—82no—
329C22⋊Q8—28no—
330C22⋊Q8—82no—
331C4×Q8—28no—
332C4×Q8—82no—
333C4×D4—28no—
334C4×D4—28no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—48no—
338C4×D4—48no—
339C4×D4—82no—
340C4×D4—82no—
341C4×D4—82no—
342C4×D4—82no—
343C4×D4—82no—
344C4×D4—82no—
345C4×D4—82no—
346C4×D4—82no—
347#117—24no—
348#117—24no—
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—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4C2×D411yescharacteristic
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C4⋊C4C2×D411yescharacteristic
370C2×C4⋊C4C2×D411yescharacteristic
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
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—48no—
392C2×C22⋊C4—48no—
393C2×C22⋊C4C2×D411yescharacteristic
394C2×C22⋊C4C2×D411yescharacteristic
395C2×C22⋊C4C2×D411yescharacteristic
396C2×C22⋊C4C2×D411yescharacteristic
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418#107—44no—
419#106—44no—
420C4⋊C8—24no—
421C4⋊C8—24no—
422#103—44no—
423#103—44no—
424#102—28no—
425#102—28no—
426#102—28no—
427#102—28no—
428#102—44no—
429#102—44no—
430C22⋊C8—24no—
431C22⋊C8#4118yes—
432#97—24no—
433#97—24no—
434C4×C8—24no—
435C4×C8—22no—
436C4×C8—22no—
437C4×C8—22no—
438C4×C8—22no—
439C4×C8—24no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—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#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464C24—28no—
465C24—22no—
466C24—22no—
467C24—44no—
468C24—44no—
469C24—82no—
470C24—82no—
471C24—82no—
472C24—82no—
473C24C22×D411yescharacteristic
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—416no—
495C2×D4—416no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—82no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—816no—
511C2×D4—816no—
512C2×D4C2×#4114yes—
513C2×D4C2×#4114yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
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×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4114yes—
555C22×C4C2511yescharacteristic
556SD16—416no—
557SD16—416no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8C2×#4114yes—
569C2×C8C2×#4114yes—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—22no—
631C42—44no—
632C42—44no—
633C42—82no—
634C42C2×#4112yes—
635C42C2×#4112yes—
636C42H(5,𝔽2)14yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—416no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—88no—
659C23—88no—
660C23—164no—
661C23—164no—
662C23—164no—
663C23—164no—
664C23#53212yes—
665C23C23×D411yescharacteristic
666Q8—44no—
667Q8—44no—
668Q8—84no—
669D4—28no—
670D4—28no—
671D4—416no—
672D4—48no—
673D4—48no—
674D4—48no—
675D4—48no—
676D4—44no—
677D4—44no—
678D4—88no—
679D4—88no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—24no—
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—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—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
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—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—164no—
733C2×C4—164no—
734C2×C4—164no—
735C2×C4—164no—
736C2×C4#52512yes—
737C2×C4#52512yes—
738C2×C4#53212yes—
739C2×C4#53512yes—
740C2×C4#53512yes—
741C2×C4#57612yes—
742C2×C4#57712yes—
743C2×C4#57712yes—
744C2×C4#57712yes—
745C2×C4C22×#4111yescharacteristic
746C2×C4C22×#4111yescharacteristic
747C2×C4C22×#4112yes—
748C2×C4C2×H(5,𝔽2)12yes—
749C8—24no—
750C8—24no—
751C8—42no—
752C8—42no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—1616no—
775C22C2×#52511yescharacteristic
776C22C2×#53211yescharacteristic
777C22C2×#53511yescharacteristic
778C22C2×#57611yescharacteristic
779C22C2×#57711yescharacteristic
780C22C2×#57711yescharacteristic
781C22C2×#57711yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#311814yes—
800C4#312314yes—
801C4#348112yes—
802C4#348112yes—
803C2—42no—
804C2—84no—
805C2—84no—
806C2#3496511yescharacteristic
807C2C2×#311811yescharacteristic
808C2C2×#312311yescharacteristic
809C2#6071211yescharacteristic
810C2#6072211yescharacteristic
811C2#6081811yescharacteristic
812C2#6082211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35291C2semidirect
3. #29504C2semidirect
4. #29192C2semidirect
5. #29190C2semidirect
6. #28613C2semidirect
7. #28613C2semidirect
8. #27975C2semidirect
9. #27949C2semidirect
12. #24516C2semidirect
13. #23690C2semidirect
14. #21692C2semidirect
15. C4×#492C2semidirect
16. #21646C2semidirect
17. C4×#486C2semidirect
18. #21459C2semidirect
19. C4×#433C2semidirect
27. C2×#440C22semidirect
28. C2×C4×SD16C22semidirect
30. #2862C22semidirect
31. #2859C22semidirect
34. #2645C22semidirect
55. #2320C22semidirect
57. C4×C4⋊Q8C22semidirect
58. C4×C4⋊Q8C22semidirect
65. #2085C22semidirect
66. #2074C22semidirect
67. #2067C22semidirect
68. #2065C22semidirect
69. #2055C22semidirect
70. #2055C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1973C22semidirect
76. #1968C22semidirect
81. #1956C22semidirect
82. #1956C22semidirect
83. #1936C22semidirect
84. #1934C22semidirect
85. #1877C22semidirect
86. #1877C22semidirect
88. #1864C22semidirect
89. #1862C22semidirect
91. #1845C22semidirect
92. #1844C22semidirect
93. #1834C22semidirect
94. #1834C22semidirect
96. #1768C22semidirect
97. C4×C4⋊C8C22semidirect
98. C4×C4⋊C8C22semidirect
99. #1762C22semidirect
100. C4×#102C22semidirect
104. #1746C22semidirect
105. C4×#97C22semidirect
106. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#352912
#342102
#295042
#291922
#291902
#286132
#279752
#279492
#258552
#257172
#245162
#236902
#216922
C4×#4922
#216462
C4×#4862
#214592
C4×#4332