Finite Group Databasebeta

← #6661068

Subgroups — #6661068

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32742C212yesmaximal, complemented
4#32738C212yesmaximal, complemented
5#30298C211yesmaximal, characteristic, complemented
6#30296C211yesmaximal, characteristic, complemented
7#30197C211yesmaximal, characteristic, complemented
8#30197C211yesmaximal, characteristic, complemented
9#29970C212yesmaximal, complemented
10#29944C212yesmaximal, complemented
11#29758C212yesmaximal, complemented
12#29694C212yesmaximal, complemented
13#27650C212yesmaximal, complemented
14#24841C214yesmaximal, complemented
15#24560C214yesmaximal, complemented
16#24304C212yesmaximal, complemented
17#20626C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#482C2214yes—
23C2×#478C2214yescomplemented
24C2×#423C2212yes—
25C2×#407C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2855—21no—
35#2855—21no—
36#2854—21no—
37#2854C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2850—21no—
41#2850—21no—
42#2848—21no—
43#2848—21no—
44#2847—21no—
45#2847C2212yes—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55#2296C2212yes—
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58#2280C2212yes—
59#2100C2212yescomplemented
60#2100C2212yescomplemented
61#2088C2214yescomplemented
62#2086C2214yescomplemented
63#2084C2212yescomplemented
64#2084C2212yescomplemented
65#2083C2212yescomplemented
66#2083C2212yescomplemented
67#2077C2214yes—
68#2075C2214yes—
69#2071C2212yescomplemented
70#2071C2212yescomplemented
71#2067C2214yescomplemented
72#2065C2214yescomplemented
73#2058C2212yescomplemented
74#2058C2212yescomplemented
75#2057C2212yescomplemented
76#2057C2212yescomplemented
77#2041C2212yescomplemented
78#2041C2212yescomplemented
79#2034C2214yes—
80#2033C2214yes—
81#2023C2212yescomplemented
82#2023C2212yescomplemented
83#1989C2214yescomplemented
84#1949C2214yescomplemented
85#1895C2214yes—
86#1895C2214yes—
87#1875C2214yes—
88#1854C2214yes—
89#1825C2214yes—
90#1809C2214yes—
91#1809C2214yes—
92#1804C2214yescomplemented
93#1797C2212yes—
94#1797C2212yes—
95#1797C2212yes—
96#1797C2212yes—
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×M16C2312yes—
104C22×M16C2312yes—
105#533—44no—
106#532—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#125C2312yes—
112C2×#124—21no—
113#525—48no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#120—22no—
132C2×C4×Q8—21no—
133C2×C4×Q8—21no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4C2312yes—
138C2×#117—21no—
139C2×#117C2312yes—
140C2×#117C2312yes—
141C22×C42—44no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#482—48no—
155#478—48no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160#423—44no—
161C2×C4⋊C8C2314yes—
162C2×C4⋊C8C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167#407—44no—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170#391—21no—
171#391—21no—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#386—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—21no—
219#382C2312yes—
220#381—22no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#379—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2312yes—
259#336C2312yes—
260C25C2×D411yescharacteristic
261C2×#41—44no—
262C2×#41—44no—
263C2×#41—44no—
264C22×Q8—21no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C2412yes—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—42no—
305C2×M16—42no—
306C2×M16—42no—
307C2×M16—42no—
308C22×C8C2414yes—
309C22×C8C2414yes—
310C4⋊Q8—42no—
311C4⋊Q8—42no—
312C4⋊Q8—42no—
313#127—42no—
314#125—28no—
315#124—44no—
316#123—48no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325#121—24no—
326#121—28no—
327#121—24no—
328#121—44no—
329#121—44no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334#120—48no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—28no—
338C4×D4—44no—
339C4×D4—48no—
340C4×D4—48no—
341#117—24no—
342#117—24no—
343#117—44no—
344#117—44no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
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⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
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×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
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×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419#107—44no—
420#107—44no—
421#106—44no—
422#106—44no—
423C4⋊C8—28no—
424C4⋊C8—44no—
425#102—44no—
426#102—44no—
427#102—44no—
428#102—44no—
429C22⋊C8—28no—
430C22⋊C8—44no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24C22×D411yescharacteristic
456C24C22×D411yescharacteristic
457C24C22×D411yescharacteristic
458#41—816no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×D4—22no—
469C2×D4—24no—
470C2×D4—24no—
471C2×D4—22no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—42no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
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—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—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
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—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—416no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—416no—
553C22×C4—44no—
554C22×C4AGL(1,ℤ/8)14yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4H(5,𝔽2)12yes—
567C22×C42−1+414yes—
568C22×C42−1+412yes—
569C22×C4C2511yescharacteristic
570M16—84no—
571M16—84no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
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—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42H(5,𝔽2)14yes—
643C23—21no—
644C23—21no—
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—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23#53612yes—
676C23#53712yes—
677C23C2×AGL(1,ℤ/8)12yes—
678C23C23×D411yescharacteristic
679Q8—84no—
680Q8—84no—
681Q8—84no—
682D4—44no—
683D4—44no—
684D4—84no—
685D4—84no—
686D4—88no—
687D4—88no—
688D4—88no—
689C2×C4—28no—
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—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
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—88no—
756C2×C4#53412yes—
757C2×C4#53412yes—
758C2×C4#53612yes—
759C2×C4#53712yes—
760C2×C4C2×AGL(1,ℤ/8)12yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4#57512yes—
763C2×C4#57512yes—
764C2×C4#57512yes—
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C2×C4C2×H(5,𝔽2)12yes—
767C2×C4C2×2−1+412yes—
768C2×C4C2×2−1+411yescharacteristic
769C8—44no—
770C8—44no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—416no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22C2×#53411yescharacteristic
801C22C2×#53611yescharacteristic
802C22C2×#53711yescharacteristic
803C22C22×AGL(1,ℤ/8)11yescharacteristic
804C22C2×#57511yescharacteristic
805C22C2×#57511yescharacteristic
806C22C2×#57511yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4#353612yes—
826C4#353812yes—
827C2—42no—
828C2—42no—
829C2—42no—
830C2—162no—
831C2#3744211yescharacteristic
832C2#6074111yescharacteristic
833C2#6075011yescharacteristic
834C2#6086211yescharacteristic
835C2#6086411yescharacteristic
836C2#6090711yescharacteristic
837C2#6091611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36625C2semidirect
3. #32742C2semidirect
4. #32738C2semidirect
5. #30298C2semidirect
6. #30296C2semidirect
7. #30197C2semidirect
8. #30197C2semidirect
9. #29970C2semidirect
10. #29944C2semidirect
11. #29758C2semidirect
12. #29694C2semidirect
13. #27650C2semidirect
14. #24841C2semidirect
15. #24560C2semidirect
16. #24304C2semidirect
17. #20626C2semidirect
23. C2×#478C22semidirect
59. #2100C22semidirect
60. #2100C22semidirect
61. #2088C22semidirect
62. #2086C22semidirect
63. #2084C22semidirect
64. #2084C22semidirect
65. #2083C22semidirect
66. #2083C22semidirect
69. #2071C22semidirect
70. #2071C22semidirect
71. #2067C22semidirect
72. #2065C22semidirect
73. #2058C22semidirect
74. #2058C22semidirect
75. #2057C22semidirect
76. #2057C22semidirect
77. #2041C22semidirect
78. #2041C22semidirect
81. #2023C22semidirect
82. #2023C22semidirect
83. #1989C22semidirect
84. #1949C22semidirect
92. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327422
#327382
#302982
#302962
#301972
#299702
#299442
#297582
#296942
#276502
#248412
#245602
#243042
#206262