Finite Group Databasebeta

← #6432484

Subgroups — #6432484

Order 512.

2346 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#23764C214yesmaximal, complemented
4#23761C212yesmaximal, complemented
5#23760C212yesmaximal, complemented
6#23758C214yesmaximal, complemented
7#23755C212yesmaximal, complemented
8#23754C212yesmaximal, complemented
9#23747C211yesmaximal, characteristic, complemented
10#23731C211yesmaximal, characteristic, complemented
11#23657C211yesmaximal, characteristic, complemented
12#23642C212yesmaximal, complemented
13#23628C211yesmaximal, characteristic, complemented
14#23480C212yesmaximal
15C4×#428C212yesmaximal, complemented
16C4×#418C212yesmaximal, complemented
17C4×#407C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#428C2212yes—
23C2×#428C2212yes—
24C2×#418C2212yes—
25C2×#418C2212yes—
26C2×#407C2212yes—
27C2×C4×M16C2212yes—
28C4×#121—21no—
29C4×#121—21no—
30C4×#121—21no—
31C4×#121—21no—
32C4×#121C2212yes—
33C4×#121C2212yes—
34C4×#121C2212yes—
35C4×#121C2212yes—
36C2×#390C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#388—21no—
39C2×#386—21no—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic, complemented
43#2285C2211yescharacteristic, complemented
44#2285C2211yescharacteristic, complemented
45#2285C2211yescharacteristic, complemented
46#2283—21no—
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283C2212yescomplemented
51#2283C2212yescomplemented
52#2280—21no—
53#2280—21no—
54#2280C2212yes—
55C2×#380C2211yescharacteristic
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61#2101C2214yescomplemented
62#2100C2212yescomplemented
63#2099C2212yescomplemented
64#2094C2212yescomplemented
65#2093C2212yescomplemented
66#2092C2214yescomplemented
67#2085C2214yescomplemented
68#2084C2212yescomplemented
69#2083C2212yescomplemented
70#2077C2214yescomplemented
71#2077C2214yescomplemented
72#2076C2214yescomplemented
73#2075C2214yescomplemented
74#2073C2214yescomplemented
75#2071C2212yescomplemented
76#2071C2212yescomplemented
77#2034C2214yes—
78#2034C2214yes—
79#2033C2214yes—
80#2033C2214yes—
81#1776C2214yescomplemented
82#1776C2214yescomplemented
83C4×#107C2214yescomplemented
84C4×#106C2214yescomplemented
85#1762C2214yescomplemented
86#1762C2214yescomplemented
87C4×#102C2214yescomplemented
88C4×#102C2214yescomplemented
89#1749C2212yescomplemented
90#1749C2212yescomplemented
91C4×C22⋊C8C2212yescomplemented
92C4×C22⋊C8C2212yescomplemented
93#1736C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1736C2212yes—
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×M16C2312yes—
106C22×M16C2312yes—
107C2×#121—24no—
108C2×#121—21no—
109C2×#121—21no—
110C2×#121—24no—
111C2×#121C2312yes—
112C2×#121C2312yes—
113C2×C4×D4—22no—
114C2×C4×D4—22no—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—28no—
120C2×C4×D4—48no—
121C2×C4×D4C2312yes—
122C2×C4×D4C2312yes—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117C2312yes—
128C2×#117C2312yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C42—28no—
139C22×C42—21no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#428—28no—
153#428—28no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158#418—28no—
159#418—28no—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164#407—28no—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C4×M16—28no—
168C2×#97C2314yes—
169C2×C4×C8C2314yes—
170#390—21no—
171#390—21no—
172#390C2312yes—
173#390C2312yes—
174#389—21no—
175#389—21no—
176#389C2312yes—
177#389C2312yes—
178#388—22no—
179#388—22no—
180#388—22no—
181#388—22no—
182#386—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#384C2311yescharacteristic
187#384C2311yescharacteristic
188#384C2311yescharacteristic
189#384C2311yescharacteristic
190#383—22no—
191#383—22no—
192#382—21no—
193#382—21no—
194#382—21no—
195#382—21no—
196#382C2312yes—
197#382C2312yes—
198#381—22no—
199#381—22no—
200#381—22no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380C2312yes—
212#380C2312yes—
213#380C2312yes—
214#380C2312yes—
215#380C2312yes—
216#380C2312yes—
217#379—22no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244#376—22no—
245#376—22no—
246#376—22no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C43—22no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262#336C2312yes—
263C25—21no—
264C25C2×D411yescharacteristic
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—21no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4#4114yes—
275C22×D4C2412yes—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16#4118yes—
318C22×C8C2414yes—
319C22×C8C2414yes—
320#121—28no—
321#121—28no—
322#121—24no—
323#121—24no—
324#121—24no—
325#121—24no—
326C4×D4—28no—
327C4×D4—28no—
328C4×D4—48no—
329C4×D4—48no—
330C4×D4—48no—
331C4×D4—48no—
332C4×D4—44no—
333C4×D4—44no—
334#117—24no—
335#117—24no—
336#117—24no—
337#117—24no—
338#117—44no—
339#117—44no—
340#117—44no—
341#117—44no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
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—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4#4114yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
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—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—44no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42#4118yes—
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425#107—28no—
426#107—28no—
427#106—28no—
428#106—28no—
429#102—28no—
430#102—28no—
431#102—28no—
432#102—28no—
433C22⋊C8—28no—
434C22⋊C8—28no—
435#97—28no—
436C4×C8—28no—
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—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—24no—
476C2×D4—216no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—44no—
481C2×D4—432no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4C2×#4114yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
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—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—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
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—416no—
548C22×C4—416no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—816no—
566C22×C4#12314yes—
567C22×C4#12314yes—
568C22×C4AGL(1,ℤ/8)14yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C2×#4114yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4114yes—
584C22×C4C2511yescharacteristic
585M16—216no—
586M16—48no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8C2×#4118yes—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4C2×#4114yes—
618C22⋊C4—28no—
619C22⋊C4—28no—
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—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42#12314yes—
655C42#12314yes—
656C42C2×#4114yes—
657C42C2×#4114yes—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—28no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—24no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—48no—
682C23—48no—
683C23—44no—
684C23—48no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23C2×#12312yes—
696C23#52512yes—
697C23#53212yes—
698C23C2×AGL(1,ℤ/8)12yes—
699C23#57512yes—
700C23C23×D411yescharacteristic
701D4—28no—
702D4—416no—
703D4—416no—
704D4—48no—
705D4—44no—
706C2×C4—28no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—48no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
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—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—88no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—88no—
773C2×C4C2×#12312yes—
774C2×C4C2×#12312yes—
775C2×C4C2×#12312yes—
776C2×C4C2×#12312yes—
777C2×C4C2×#12312yes—
778C2×C4#52512yes—
779C2×C4#52918yes—
780C2×C4#52918yes—
781C2×C4#53212yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×AGL(1,ℤ/8)12yes—
784C2×C4#57512yes—
785C2×C4#57512yes—
786C2×C4C22×#4112yes—
787C2×C4C22×#4111yescharacteristic
788C2×C4C22×#4111yescharacteristic
789C2×C4C22×#4112yes—
790C8—28no—
791C8—44no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—416no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—816no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22#239514yes—
822C22C22×#12311yescharacteristic
823C22C2×#52511yescharacteristic
824C22C2×#53211yescharacteristic
825C22C22×AGL(1,ℤ/8)11yescharacteristic
826C22C2×#57511yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57511yescharacteristic
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—41no—
835C4—41no—
836C4—44no—
837C4—41no—
838C4—41no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4#239514yes—
846C4#309414yes—
847C4C2×#52912yes—
848C4C2×#52912yes—
849C2—24no—
850C2—42no—
851C2—42no—
852C2—84no—
853C2C2×#239511yescharacteristic
854C2C2×#309411yescharacteristic
855C2#6051111yescharacteristic
856C2#6055811yescharacteristic
857C2#6055911yescharacteristic
858C2#6070011yescharacteristic
859C2#6070211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34012C2semidirect
3. #23764C2semidirect
4. #23761C2semidirect
5. #23760C2semidirect
6. #23758C2semidirect
7. #23755C2semidirect
8. #23754C2semidirect
9. #23747C2semidirect
10. #23731C2semidirect
11. #23657C2semidirect
12. #23642C2semidirect
13. #23628C2semidirect
15. C4×#428C2semidirect
16. C4×#418C2semidirect
17. C4×#407C2semidirect
42. #2285C22semidirect
43. #2285C22semidirect
44. #2285C22semidirect
45. #2285C22semidirect
50. #2283C22semidirect
51. #2283C22semidirect
61. #2101C22semidirect
62. #2100C22semidirect
63. #2099C22semidirect
64. #2094C22semidirect
65. #2093C22semidirect
66. #2092C22semidirect
67. #2085C22semidirect
68. #2084C22semidirect
69. #2083C22semidirect
70. #2077C22semidirect
71. #2077C22semidirect
72. #2076C22semidirect
73. #2075C22semidirect
74. #2073C22semidirect
75. #2071C22semidirect
76. #2071C22semidirect
81. #1776C22semidirect
82. #1776C22semidirect
83. C4×#107C22semidirect
84. C4×#106C22semidirect
85. #1762C22semidirect
86. #1762C22semidirect
87. C4×#102C22semidirect
88. C4×#102C22semidirect
89. #1749C22semidirect
90. #1749C22semidirect
91. C4×C22⋊C8C22semidirect
92. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
#340122
#237642
#237612
#237602
#237582
#237552
#237542
#237472
#237312
#236572
#236422
#236282
#234802
C4×#4282
C4×#4182
C4×#4072