Finite Group Databasebeta

← #6445566

Subgroups — #6445566

Order 512.

2594 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3077C211yesmaximal, characteristic, complemented
2C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
3#34947C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5#24825C214yesmaximal, complemented
6#24823C214yesmaximal, complemented
7#24816C212yesmaximal, complemented
8#24815C212yesmaximal, complemented
9#24812C212yesmaximal, complemented
10#24811C212yesmaximal, complemented
11#23657C212yesmaximal, complemented
12#23617C212yesmaximal, complemented
13#21322C211yesmaximal, characteristic, complemented
14#21146C211yesmaximal, characteristic, complemented
15#20925C212yesmaximal
16#20648C211yesmaximal, characteristic, complemented
17#20646C212yesmaximal, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×#533C2211yescharacteristic
20C2×C4×#41C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4—21no—
24#3077—28no—
25C2×#478C2214yes—
26C2×#476C2212yes—
27C2×#474C2212yes—
28C4×AGL(1,ℤ/8)—28no—
29C2×#442C2212yes—
30C2×#440C2212yes—
31C2×C4×SD16C2212yes—
32C2×C4×D8C2212yes—
33C2×#428C2212yes—
34C2×#428C2211yescharacteristic
35C2×#423C2211yescharacteristic
36C2×#423C2212yes—
37C2×#417C2211yescharacteristic
38C2×#417C2212yes—
39C2×#418C2212yes—
40C2×#418C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2568C2211yescharacteristic, complemented
43#2567C2211yescharacteristic, complemented
44#2566C2212yescomplemented
45#2565C2212yescomplemented
46#2564—22no—
47#2563C2211yescharacteristic, complemented
48#2542C2211yescharacteristic, complemented
49#2417—21no—
50#2417—21no—
51#2396—22no—
52D4×C4⋊C4—22no—
53D4×C4⋊C4—21no—
54D4×C4⋊C4—21no—
55D4×C4⋊C4C2212yes—
56D4×C4⋊C4C2212yes—
57D4×C4⋊C4C2214yes—
58C4×C22⋊Q8—21no—
59C4×C22⋊Q8—21no—
60#2297C2212yes—
61C2×#389C2212yes—
62C2×#385—22no—
63#2285C2212yes—
64C2×#384C2211yescharacteristic
65C2×#380—21no—
66C2×C4×C4⋊C4C2211yescharacteristic
67#2085C2214yescomplemented
68#2085C2214yescomplemented
69#2084C2214yescomplemented
70#2083C2214yescomplemented
71#2068C2214yescomplemented
72#2067C2214yescomplemented
73#2066C2214yescomplemented
74#2065C2214yescomplemented
75#1992C2214yescomplemented
76#1990C2212yescomplemented
77#1990C2212yescomplemented
78#1940C2214yescomplemented
79#1939C2212yescomplemented
80#1939C2212yescomplemented
81#1879C2214yes—
82#1879C2214yes—
83#1877C2214yes—
84#1877C2214yes—
85#1804C2214yes—
86#1804C2214yes—
87#1803C2212yescomplemented
88#1803C2212yescomplemented
89#1802C2214yes—
90#1802C2214yes—
91#1802C2212yescomplemented
92#1802C2212yescomplemented
93#1736C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1728C2212yes—
97C22×#41C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4—21no—
100C24×C4—22no—
101C2×AGL(1,ℤ/8)—24no—
102C2×AGL(1,ℤ/8)—24no—
103C2×AGL(1,ℤ/8)Q818yescomplemented
104C22×SD16C2312yes—
105C22×D8C2312yes—
106C22×M16C2311yescharacteristic
107C22×M16C2312yes—
108C22×M16C2311yescharacteristic
109#533—24no—
110#533—24no—
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×#125C2312yes—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C4×#41—24no—
119C4×#41—24no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8C2311yescharacteristic
123C2×C4×Q8C2311yescharacteristic
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—28no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—24no—
132C2×C4×D4—44no—
133C2×C4×D4D418yes—
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2314yes—
137C2×C4×D4C2314yes—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×#117—21no—
141C2×#117C2311yescharacteristic
142C2×#117C2312yes—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—22no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—22no—
147C22×C4⋊C4—24no—
148C22×C4⋊C4—22no—
149C22×C4⋊C4—48no—
150C22×C4⋊C4D411yescharacteristic
151C22×C4⋊C4D411yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4—21no—
155C22×C22⋊C4—22no—
156C22×C42—21no—
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159#478—216no—
160#476—28no—
161#474—28no—
162#442—28no—
163#440—28no—
164C4×SD16—28no—
165C4×D8—28no—
166#428—28no—
167#428—24no—
168C2×#107C2314yes—
169C2×#107C2312yes—
170C2×#106C2314yes—
171C2×#106C2312yes—
172#423—24no—
173#423—44no—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2314yes—
177C2×C4⋊C8C2314yes—
178#418—28no—
179#418—24no—
180#417—24no—
181#417—44no—
182C2×#103C2312yes—
183C2×#103C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2314yes—
190C4×M16—24no—
191C2×#97C2312yes—
192C2×C4×C8C2312yes—
193#400—22no—
194#399—22no—
195#398—22no—
196#398—22no—
197#396—22no—
198#396—22no—
199#395—22no—
200#393—22no—
201#391—21no—
202#391—21no—
203#391C2312yes—
204#391C2312yes—
205#390C2312yes—
206#390C2312yes—
207#389—21no—
208#389—21no—
209#389—22no—
210#389—22no—
211#389C2314yes—
212#389C2314yes—
213#387—22no—
214#387—22no—
215#386—22no—
216#386—22no—
217#385—22no—
218#385—22no—
219#385—24no—
220#385—24no—
221#385—24no—
222#385—24no—
223#384—21no—
224#384—21no—
225#384C2312yes—
226#384C2312yes—
227#384C2312yes—
228#384C2312yes—
229#382C2312yes—
230#382C2312yes—
231#380—22no—
232#380—22no—
233#380—21no—
234#380—21no—
235#380—22no—
236#380—22no—
237#380—24no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4D412yes—
241C4×C4⋊C4D411yescharacteristic
242C4×C4⋊C4D411yescharacteristic
243C4×C4⋊C4C2311yescharacteristic
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2311yescharacteristic
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C2×#95—22no—
249C2×#95D412yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2314yes—
257#336C2314yes—
258C25—21no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41C2×Q814yes—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8C2411yescharacteristic
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4C2×D414yes—
274C22×D4C2×Q814yes—
275C22×D4#4114yes—
276C22×D4C2411yescharacteristic
277C22×D4C2412yes—
278C23×C4—21no—
279C23×C4—28no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—21no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—48no—
291C23×C4—48no—
292C23×C4—84no—
293C23×C4C2×D412yes—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D412yes—
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298AGL(1,ℤ/8)—232no—
299C2×SD16—24no—
300C2×SD16—24no—
301C2×SD16C2×Q818yes—
302C2×D8—24no—
303C2×D8—24no—
304C2×D8C2×Q818yes—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—24no—
313C2×M16C2×Q814yes—
314C22×C8C2414yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321#125—24no—
322#125—24no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×D4—28no—
334C4×D4—28no—
335C4×D4—28no—
336C4×D4—28no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—48no—
346C4×D4—48no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4C2×D418yes—
350C4×D4C2×D418yes—
351#117—22no—
352#117—24no—
353#117—22no—
354#117—24no—
355#117—44no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
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—42no—
379C2×C4⋊C4—416no—
380C2×C4⋊C4—48no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—48no—
383C2×C4⋊C4—48no—
384C2×C4⋊C4—82no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D412yes—
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2414yes—
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—48no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—21no—
415C2×C42—22no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—44no—
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D414yes—
424C2×C42#4114yes—
425C2×C42C2412yes—
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—24no—
430#107—28no—
431#106—24no—
432#106—28no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8—44no—
436C4⋊C8—44no—
437#103—24no—
438#103—44no—
439#102—24no—
440#102—24no—
441#102—28no—
442#102—28no—
443#102—24no—
444#102—44no—
445#97—24no—
446C4×C8—24no—
447#95—24no—
448#95—24no—
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#95C2×D412yes—
458#95C2×D412yes—
459#95C2×D412yes—
460#95C2×D412yes—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—22no—
465C24—21no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24C22×D411yescharacteristic
471#41—28no—
472#41—28no—
473#41—44no—
474#41—44no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8C22×Q812yes—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4C22⋊Q8116yescomplemented
505C2×D4C22×D414yes—
506C2×D4C22×Q812yes—
507C2×D4C22×Q814yes—
508C2×D4C2×#4114yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—432no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—48no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—832no—
555C22×C4#12114yes—
556C22×C4#12114yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D412yes—
567C22×C4C22×Q812yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C42−1+412yes—
572C22×C4C2511yescharacteristic
573SD16—216no—
574D8—216no—
575M16—28no—
576M16—44no—
577M16—48no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—22no—
584C2×C8—24no—
585C2×C8—22no—
586C2×C8C22×Q814yes—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4AGL(1,ℤ/8)14yescomplemented
622C4⋊C4C22×D414yes—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—44no—
628C22⋊C4—42no—
629C22⋊C4—44no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C42—24no—
636C42—24no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—42no—
642C42—42no—
643C42—42no—
644C42—44no—
645C42#12114yes—
646C42#12114yes—
647C42C22×D412yes—
648C42C22×D412yes—
649C42C2×#4112yes—
650C42C2×#4112yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—24no—
656C23—216no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—48no—
661C23—48no—
662C23—48no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23C2×#12112yes—
677C23#54612yes—
678C23D4×Q812yes—
679C23C23×D411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—84no—
685Q8—84no—
686D4—22no—
687D4—216no—
688D4—24no—
689D4—24no—
690D4—24no—
691D4—22no—
692D4—48no—
693D4—41no—
694D4—41no—
695D4C2×C22⋊Q818yes—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—416no—
719C2×C4—48no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—48no—
725C2×C4—416no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—816no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—816no—
745C2×C4—88no—
746C2×C4—84no—
747C2×C4C2×#12112yes—
748C2×C4C2×#12112yes—
749C2×C4C2×#12112yes—
750C2×C4C2×#12112yes—
751C2×C4C2×#12112yes—
752C2×C4C2×C22⋊Q814yes—
753C2×C4#53714yes—
754C2×C4#54612yes—
755C2×C4D4×Q812yes—
756C2×C4#55214yes—
757C2×C4#55414yes—
758C2×C4C2×AGL(1,ℤ/8)14yes—
759C2×C4C2×AGL(1,ℤ/8)12yes—
760C2×C4#57512yes—
761C2×C4C23×D411yescharacteristic
762C2×C4C23×Q811yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C22×#4111yescharacteristic
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C2×C4C2×2−1+411yescharacteristic
767C8—24no—
768C8—42no—
769C8—44no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—28no—
777C22—432no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#241714yes—
792C22C22×#12111yescharacteristic
793C22C2×#54611yescharacteristic
794C22C2×D4×Q811yescharacteristic
795C22C22×AGL(1,ℤ/8)11yescharacteristic
796C22C2×#57511yescharacteristic
797C22#358511yescharacteristic
798C22#358611yescharacteristic
799C4—22no—
800C4—22no—
801C4—24no—
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—44no—
808C4—81no—
809C4—82no—
810C4—84no—
811C4—81no—
812C4—82no—
813C4#241714yes—
814C4#303614yes—
815C4C22×C22⋊Q811yescharacteristic
816C4C2×#53711yescharacteristic
817C4C2×#55211yescharacteristic
818C4C2×#55411yescharacteristic
819C2—24no—
820C2—48no—
821C2—82no—
822C2C2×#241711yescharacteristic
823C2C2×#303611yescharacteristic
824C2#6042511yescharacteristic
825C2#6115511yescharacteristic
826C2#6115911yescharacteristic
827C2Q8×AGL(1,ℤ/8)11yescharacteristic
828C2#6136711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3077C2semidirect
3. #34947C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. #24825C2semidirect
6. #24823C2semidirect
7. #24816C2semidirect
8. #24815C2semidirect
9. #24812C2semidirect
10. #24811C2semidirect
11. #23657C2semidirect
12. #23617C2semidirect
13. #21322C2semidirect
14. #21146C2semidirect
16. #20648C2semidirect
17. #20646C2semidirect
42. #2568C22semidirect
43. #2567C22semidirect
44. #2566C22semidirect
45. #2565C22semidirect
47. #2563C22semidirect
48. #2542C22semidirect
67. #2085C22semidirect
68. #2085C22semidirect
69. #2084C22semidirect
70. #2083C22semidirect
71. #2068C22semidirect
72. #2067C22semidirect
73. #2066C22semidirect
74. #2065C22semidirect
75. #1992C22semidirect
76. #1990C22semidirect
77. #1990C22semidirect
78. #1940C22semidirect
79. #1939C22semidirect
80. #1939C22semidirect
87. #1803C22semidirect
88. #1803C22semidirect
91. #1802C22semidirect
92. #1802C22semidirect
103. C2×AGL(1,ℤ/8)Q8semidirect
504. C2×D4C22⋊Q8semidirect
621. C4⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#30772
C2×C4×AGL(1,ℤ/8)2
#349472
C2×D4×C4⋊C42
#248252
#248232
#248162
#248152
#248122
#248112
#236572
#236172
#213222
#211462
#209252
#206482
#206462