Finite Group Databasebeta

← #6345352

Subgroups — #6345352

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60561C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#60236C211yesmaximal, characteristic, complemented
4#18052C214yesmaximal, complemented
5#18050C214yesmaximal, complemented
6#18030C214yesmaximal, complemented
7#18026C214yesmaximal, complemented
8#17945C212yesmaximal, complemented
9#17940C212yesmaximal, complemented
10#17917C212yesmaximal, complemented
11#17912C212yesmaximal, complemented
12#17823C211yesmaximal, characteristic, complemented
13#17490C211yesmaximal, characteristic, complemented
14#17450C211yesmaximal, characteristic, complemented
15#17324C211yesmaximal, characteristic, complemented
16C2×#532C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18#3115C412yes—
19#3115C412yes—
20#3112C412yes—
21#3109C412yes—
22#3106C2212yes—
23#3106C2212yes—
24#3103C2212yes—
25#3100C2212yes—
26#3094C412yes—
27#3079C411yescharacteristic
28#3079C411yescharacteristic
29#3038C411yescharacteristic
30#3038C411yescharacteristic
31#3006C412yes—
32#2991C2212yes—
33#2990—22no—
34#2990C2212yes—
35#2984C2212yescomplemented
36#2981—21no—
37#2981—21no—
38#2979C2214yes—
39#2975—21no—
40#2974—22no—
41#2974C2214yescomplemented
42#2974C2212yescomplemented
43#2972—21no—
44#2965—21no—
45#2965—21no—
46#2965C2211yescharacteristic, complemented
47#2965C2211yescharacteristic, complemented
48C8×#41C2211yescharacteristic, complemented
49C8×#41C2211yescharacteristic, complemented
50C4×AGL(1,ℤ/8)C2212yes—
51C4×AGL(1,ℤ/8)C2212yes—
52#2935—22no—
53#2931C2212yescomplemented
54#2931C2212yescomplemented
55#2920—21no—
56#2920C2211yescharacteristic
57#2920C2211yescharacteristic
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60C2×#431—21no—
61C2×#431C2211yescharacteristic
62#2880—22no—
63#1594C2214yescomplemented
64#1592C2214yescomplemented
65#1590C2214yescomplemented
66#1589C2214yescomplemented
67#1588C2214yescomplemented
68#1586C2214yescomplemented
69#1586C2214yescomplemented
70#1585C2214yescomplemented
71#1583C2214yescomplemented
72#1582C2214yescomplemented
73#1581C2214yescomplemented
74#1581C2214yescomplemented
75#1580C2214yescomplemented
76SD16⋊C8C2214yescomplemented
77C8×SD16C2214yescomplemented
78C8×D8C2214yescomplemented
79#1574C2212yescomplemented
80#1574C2212yescomplemented
81#1572C2214yescomplemented
82#1569C2214yescomplemented
83#1496C2214yes—
84#1489C2212yescomplemented
85#1489C2212yescomplemented
86#1488C2212yes—
87#1488C2212yes—
88#1486C2214yescomplemented
89#1484C2212yescomplemented
90#1484C2212yescomplemented
91#1479C2212yescomplemented
92#1478C2212yescomplemented
93#1454C2214yescomplemented
94#1453C2214yescomplemented
95#1451C2212yescomplemented
96C8×M16C2212yescomplemented
97C22×#41—21no—
98C22×#41C2×C411yescharacteristic
99C2×AGL(1,ℤ/8)C2×C412yes—
100C2×AGL(1,ℤ/8)C2×C412yes—
101C2×#131—22no—
102C2×#131—22no—
103#532—21no—
104#532—21no—
105#532—21no—
106#532—21no—
107#532C2×C412yes—
108#532C2×C412yes—
109#532C2312yes—
110#532C2312yes—
111C2×C4⋊Q8C2×C411yescharacteristic
112C2×#127C2×C411yescharacteristic
113C2×#124—21no—
114C2×#121—21no—
115C2×#121C2×C412yes—
116C4×#41—21no—
117C4×#41—21no—
118C4×#41—21no—
119C4×#41—21no—
120C4×#41C2×C411yescharacteristic
121C4×#41C2×C411yescharacteristic
122C4×#41C2×C411yescharacteristic
123C4×#41C2×C411yescharacteristic
124C4×#41C2311yescharacteristic
125C4×#41C2311yescharacteristic
126C4×#41C2311yescharacteristic
127C4×#41C2311yescharacteristic
128C2×C4×Q8C2×C411yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4C2×C411yescharacteristic
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2312yes—
136C2×#117—21no—
137C2×#117C2×C411yescharacteristic
138C22×C42—21no—
139C22×C42C2311yescharacteristic
140#482C2×C414yes—
141#482C2×C414yes—
142#481C2×C414yes—
143#480C2×C414yes—
144#477C2×C412yes—
145#477C2×C412yes—
146#476C2×C412yes—
147#476C2×C412yes—
148#475C2×C412yes—
149#475C2×C412yes—
150#474C2×C412yes—
151#474C2×C412yes—
152#460C2×C412yes—
153#460C2×C412yes—
154#460C2×C412yes—
155#460C2×C412yes—
156#459C2×C412yes—
157#459C2×C412yes—
158#459C2×C412yes—
159#459C2×C412yes—
160#449C2×C414yes—
161#449C2×C414yes—
162#448C2×C414yes—
163#447C2×C414yes—
164#446—22no—
165#446—22no—
166#446C2312yes—
167#446C2312yes—
168C8×Q8C2312yes—
169C8×Q8C2312yes—
170#442C2×C414yes—
171#442C2×C414yes—
172#440C2×C414yes—
173#440C2×C414yes—
174C4×SD16C2314yes—
175C4×SD16C2314yes—
176C4×D8C2314yes—
177C4×D8C2314yes—
178#436—24no—
179#436—22no—
180#436—22no—
181#436—22no—
182#436—22no—
183#436C2312yes—
184#436C2314yes—
185#436C2312yes—
186#436C2314yes—
187#435—22no—
188#435—22no—
189#435—24no—
190#435—24no—
191#435—22no—
192#435—22no—
193#435—22no—
194#435—22no—
195C8×D4—22no—
196C8×D4—22no—
197C8×D4—24no—
198C8×D4—22no—
199C8×D4—22no—
200C8×D4C2312yes—
201C8×D4C2314yes—
202C8×D4C2314yes—
203C8×D4C2312yes—
204#432—21no—
205#432—21no—
206#432—21no—
207#432—21no—
208#432—22no—
209#432—22no—
210#432C2×C412yes—
211#432C2×C412yes—
212#432C2312yes—
213#432C2312yes—
214#431—21no—
215#431—21no—
216#431—22no—
217#431—22no—
218#431—21no—
219#431—21no—
220#431—21no—
221#431—21no—
222#431D411yescharacteristic
223#431D411yescharacteristic
224#431D411yescharacteristic
225#431D411yescharacteristic
226#431C2312yes—
227#431C2311yescharacteristic
228#431C2311yescharacteristic
229#431C2312yes—
230#431C2312yes—
231#431C2312yes—
232#431C2312yes—
233#431C2312yes—
234#431C2312yes—
235#428C2×C412yes—
236#428C2×C412yes—
237#423—21no—
238#423—22no—
239#423C2×C411yescharacteristic
240#423C2×C411yescharacteristic
241#423C2312yes—
242#423C2312yes—
243C2×C4⋊C8—22no—
244C2×C4⋊C8D412yes—
245#418C2×C412yes—
246#418C2×C412yes—
247#417C2×C412yes—
248#417C2×C412yes—
249#408—22no—
250#408—22no—
251#408—24no—
252#408—24no—
253#407—21no—
254#407—21no—
255#407—21no—
256#407—24no—
257#407—22no—
258#407C2×C412yes—
259C2×C22⋊C8—24no—
260C2×C22⋊C8—22no—
261C2×C22⋊C8D412yes—
262C4×M16—21no—
263C4×M16—21no—
264C4×M16—21no—
265C4×M16—21no—
266C4×M16C2312yes—
267C4×M16C2312yes—
268C2×C4×C8—21no—
269C2×C4×C8—21no—
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#335C2314yes—
273#335C2314yes—
274#334C2314yes—
275#334C2314yes—
276Q8⋊C8C2314yes—
277Q8⋊C8C2314yes—
278D4⋊C8C2314yes—
279D4⋊C8C2314yes—
280D4⋊C8C2314yes—
281D4⋊C8C2314yes—
282D4⋊C8C2314yes—
283D4⋊C8C2314yes—
284#322C2314yes—
285#322C2314yes—
286#322C2314yes—
287C82C2314yes—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—42no—
295C2×#41—42no—
296C2×#41—84no—
297C2×#41C22×C411yescharacteristic
298C2×#41C22×C411yescharacteristic
299C2×#41C22×C411yescharacteristic
300C2×#41C22×C411yescharacteristic
301C22×Q8—21no—
302C22×Q8C22×C411yescharacteristic
303C22×D4—21no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4C22×C411yescharacteristic
308C22×D4C22×C412yes—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—22no—
312C23×C4—21no—
313C23×C4C22×C411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4#4111yescharacteristic
316AGL(1,ℤ/8)—44no—
317AGL(1,ℤ/8)—44no—
318C2×SD16C22×C414yes—
319C2×SD16C22×C414yes—
320C2×D8C22×C414yes—
321C2×D8C22×C414yes—
322#131—84no—
323#131—84no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16C22×C412yes—
332C2×M16C22×C412yes—
333C22×C8—24no—
334C22×C8—24no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8C2×D412yes—
338C22×C8C2×D412yes—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8C22×C412yes—
342C4⋊Q8C22×C412yes—
343#127—21no—
344#127—21no—
345#127C22×C412yes—
346#127C22×C412yes—
347#124—22no—
348#124—22no—
349#124—22no—
350#124—22no—
351#121—22no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121C22×C414yes—
358#121C22×C414yes—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C22×C411yescharacteristic
364C4×Q8C22×C411yescharacteristic
365C4×Q8C22×C411yescharacteristic
366C4×Q8C22×C411yescharacteristic
367C4×Q8C22×C411yescharacteristic
368C4×Q8C22×C411yescharacteristic
369C4×Q8C2411yescharacteristic
370C4×Q8C2411yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—22no—
397C4×D4C22×C411yescharacteristic
398C4×D4C22×C411yescharacteristic
399C4×D4C22×C411yescharacteristic
400C4×D4C22×C411yescharacteristic
401C4×D4C22×C411yescharacteristic
402C4×D4C22×C411yescharacteristic
403C4×D4C22×C414yes—
404C4×D4C2411yescharacteristic
405C4×D4C2411yescharacteristic
406C4×D4C2414yes—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117C22×C411yescharacteristic
418#117C22×C411yescharacteristic
419#117C22×C411yescharacteristic
420#117C22×C411yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4C22×C411yescharacteristic
425C2×C4⋊C4C22×C411yescharacteristic
426C2×C4⋊C4C22×C412yes—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C22×C411yescharacteristic
444C2×C42C22×C411yescharacteristic
445C2×C42C22×C411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42#4111yescharacteristic
450C2×C42#4111yescharacteristic
451C2×C42#4111yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107C22×C414yes—
456#107C22×C414yes—
457#106C22×C414yes—
458#106C22×C414yes—
459C4⋊C8—22no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464C4⋊C8—22no—
465C4⋊C8—22no—
466C4⋊C8—22no—
467C4⋊C8C22×C412yes—
468C4⋊C8C22×C412yes—
469C4⋊C8C22×C412yes—
470C4⋊C8C22×C412yes—
471C4⋊C8C2×D412yes—
472C4⋊C8C2×D412yes—
473C4⋊C8C2×D412yes—
474C4⋊C8C2×D412yes—
475C4⋊C8C2412yes—
476C4⋊C8C2412yes—
477C4⋊C8C2414yes—
478#103C22×C414yes—
479#103C22×C414yes—
480#102C22×C414yes—
481#102C22×C414yes—
482#102C22×C414yes—
483#102C22×C414yes—
484#102C22×C414yes—
485#102C22×C414yes—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—21no—
490C22⋊C8—21no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—24no—
494C22⋊C8—24no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—24no—
498C22⋊C8—24no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8C22×C414yes—
502C22⋊C8C22×C414yes—
503C22⋊C8C2×D412yes—
504C22⋊C8C2×D412yes—
505C22⋊C8C2×D412yes—
506C22⋊C8C2×D412yes—
507#97—22no—
508#97—22no—
509#97—22no—
510#97—22no—
511#97—22no—
512#97C22×C414yes—
513C4×C8—22no—
514C4×C8—22no—
515C4×C8—21no—
516C4×C8—21no—
517C4×C8—22no—
518C4×C8C2×D411yescharacteristic
519C4×C8C2×D411yescharacteristic
520C4×C8C2×D411yescharacteristic
521C4×C8C2×D411yescharacteristic
522C4×C8C2414yes—
523C4×C8C2414yes—
524C4×C8C2412yes—
525C4×C8C2412yes—
526C24—21no—
527C24—22no—
528C24C4×D411yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—44no—
538#41—44no—
539#41—44no—
540#41—44no—
541#41—84no—
542#41—84no—
543#41—84no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×Q8—82no—
550C2×Q8C23×C411yescharacteristic
551C2×Q8C23×C411yescharacteristic
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C23×C411yescharacteristic
573C2×D4C23×C414yes—
574C2×D4C23×C411yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—82no—
600C22×C4—84no—
601C22×C4C4×D411yescharacteristic
602C22×C4C4×D411yescharacteristic
603C22×C4C4×D411yescharacteristic
604C22×C4C4×D411yescharacteristic
605C22×C4C4×D411yescharacteristic
606C22×C4C4×D411yescharacteristic
607C22×C4C4×D411yescharacteristic
608C22×C4C4×D411yescharacteristic
609C22×C4C4×D411yescharacteristic
610C22×C4C23×C411yescharacteristic
611C22×C4C23×C411yescharacteristic
612C22×C4C23×C411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4C2×#4111yescharacteristic
619SD16—28no—
620SD16—44no—
621D8—28no—
622D8—44no—
623M16—42no—
624M16—42no—
625M16—44no—
626M16—44no—
627M16—82no—
628M16—82no—
629M16—84no—
630M16—84no—
631M16—82no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—42no—
637C2×C8—42no—
638C2×C8—82no—
639C2×C8—82no—
640C2×C8—84no—
641C2×C8—84no—
642C2×C8C23×C414yes—
643C2×C8C23×C414yes—
644C2×C8C22×D412yes—
645C2×C8C22×D412yes—
646C2×C8C22×D412yes—
647C2×C8C22×D412yes—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C23×C411yescharacteristic
662C4⋊C4C23×C411yescharacteristic
663C4⋊C4C23×C411yescharacteristic
664C4⋊C4C23×C411yescharacteristic
665C4⋊C4C23×C414yes—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—24no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42C4×D411yescharacteristic
695C42C4×D411yescharacteristic
696C42C4×D411yescharacteristic
697C42C4×D411yescharacteristic
698C42C4×D411yescharacteristic
699C42C4×D411yescharacteristic
700C42C23×C411yescharacteristic
701C42C23×C411yescharacteristic
702C42C23×C411yescharacteristic
703C42C22×D411yescharacteristic
704C42C22×D411yescharacteristic
705C42C22×D411yescharacteristic
706C42C2×#4111yescharacteristic
707C42C2×#4111yescharacteristic
708C42C2×#4111yescharacteristic
709C42C2511yescharacteristic
710C23—21no—
711C23—21no—
712C23—24no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—81no—
720C23—82no—
721C23—82no—
722C23C2×C4×D411yescharacteristic
723C23C2×C4×D411yescharacteristic
724C23C2×C4×D411yescharacteristic
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—42no—
729Q8—44no—
730Q8—82no—
731Q8#56812yes—
732D4—24no—
733D4—21no—
734D4—24no—
735D4—21no—
736D4—24no—
737D4—21no—
738D4—42no—
739D4—42no—
740D4—44no—
741D4—44no—
742D4—42no—
743D4—42no—
744D4—48no—
745D4—44no—
746D4—82no—
747D4—82no—
748D4—84no—
749D4#56812yes—
750C2×C4—24no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—24no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—84no—
795C2×C4—81no—
796C2×C4—82no—
797C2×C4C2×C4×D411yescharacteristic
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C2×C4×D411yescharacteristic
800C2×C4C2×C4×D411yescharacteristic
801C2×C4C2×C4×D411yescharacteristic
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C2×C4×D411yescharacteristic
804C2×C4C2×C4×D411yescharacteristic
805C2×C4C2×C4×D411yescharacteristic
806C2×C4C24×C411yescharacteristic
807C2×C4C23×D411yescharacteristic
808C2×C4C22×#4111yescharacteristic
809C8—22no—
810C8—22no—
811C8—22no—
812C8—22no—
813C8—24no—
814C8—24no—
815C8—44no—
816C8—44no—
817C8—42no—
818C8—42no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—21no—
829C22—41no—
830C22—41no—
831C22—44no—
832C22—41no—
833C22—41no—
834C22—44no—
835C22—41no—
836C22—44no—
837C22—82no—
838C22—84no—
839C22—164no—
840C22C22×C4×D411yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—22no—
849C4—21no—
850C4—21no—
851C4—41no—
852C4—41no—
853C4—44no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4#295512yes—
858C4C2×#56811yescharacteristic
859C4C2×#56811yescharacteristic
860C4#358512yes—
861C2—41no—
862C2—41no—
863C2—41no—
864C2—42no—
865C2—81no—
866C2—84no—
867C2#6014111yescharacteristic
868C2#6016811yescharacteristic
869C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60561C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60278C2semidirect
3. #60236C2semidirect
4. #18052C2semidirect
5. #18050C2semidirect
6. #18030C2semidirect
7. #18026C2semidirect
8. #17945C2semidirect
9. #17940C2semidirect
10. #17917C2semidirect
11. #17912C2semidirect
12. #17823C2semidirect
13. #17490C2semidirect
14. #17450C2semidirect
15. #17324C2semidirect
35. #2984C22semidirect
41. #2974C22semidirect
42. #2974C22semidirect
46. #2965C22semidirect
47. #2965C22semidirect
48. C8×#41C22semidirect
49. C8×#41C22semidirect
53. #2931C22semidirect
54. #2931C22semidirect
63. #1594C22semidirect
64. #1592C22semidirect
65. #1590C22semidirect
66. #1589C22semidirect
67. #1588C22semidirect
68. #1586C22semidirect
69. #1586C22semidirect
70. #1585C22semidirect
71. #1583C22semidirect
72. #1582C22semidirect
73. #1581C22semidirect
74. #1581C22semidirect
75. #1580C22semidirect
76. SD16⋊C8C22semidirect
77. C8×SD16C22semidirect
78. C8×D8C22semidirect
79. #1574C22semidirect
80. #1574C22semidirect
81. #1572C22semidirect
82. #1569C22semidirect
84. #1489C22semidirect
85. #1489C22semidirect
88. #1486C22semidirect
89. #1484C22semidirect
90. #1484C22semidirect
91. #1479C22semidirect
92. #1478C22semidirect
93. #1454C22semidirect
94. #1453C22semidirect
95. #1451C22semidirect
96. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#605612
#602782
#602362
#180522
#180502
#180302
#180262
#179452
#179402
#179172
#179122
#178232
#174902
#174502
#173242