Finite Group Databasebeta

← #72287082

Subgroups — #72287082

Order 1024.

6862 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#576C211yesmaximal, characteristic
2#7622556C211yesmaximal, characteristic, complemented
3#6344475C211yesmaximal, characteristic, complemented
4#481284C2112yesmaximal, complemented
5#481282C213yesmaximal, complemented
6#481279C213yesmaximal, complemented
7#481274C213yesmaximal, complemented
8C2×#11663C213yesmaximal, complemented
9#481066C214yesmaximal, complemented
10C22×#576C411yescharacteristic
11C2×C4×H(5,𝔽2)—21no—
12#60263—21no—
13C4×#576—21no—
14C4×#576—23no—
15C4×#576—21no—
16C4×#576—23no—
17C4×#576C416yes—
18C4×#576C412yes—
19C4×#576C2216yes—
20C4×#576C2212yes—
21C2×#2951C413yes—
22C2×#2948C413yes—
23C2×#2946—23no—
24C2×C4×AGL(1,ℤ/8)—23no—
25C2×C4×#135C2213yes—
26C22×C4×D8C2213yes—
27C2×#2913C411yescharacteristic
28C2×#2897—21no—
29C2×C4×#131C2211yescharacteristic
30#33423—23no—
31#33422—23no—
32#33421C2216yescomplemented
33#33418C2213yescomplemented
34C2×#2163C2213yescomplemented
35#33398—21no—
36#33334—21no—
37#33326C2212yescomplemented
38#17798—23no—
39#17798C2216yescomplemented
40#17796—23no—
41#17793C2213yescomplemented
42C2×#1566C2213yescomplemented
43#17788—21no—
44#17788C2212yescomplemented
45#11667C22112yescomplemented
46#11666C22112yescomplemented
47#11665C22112yescomplemented
48#11664C2213yescomplemented
49#11664C2211yescharacteristic, complemented
50#11663C2216yescomplemented
51#11663C2213yescomplemented
52#11663C2213yescomplemented
53#11663C22112yescomplemented
54#11599C22112yescomplemented
55#11598C22112yescomplemented
56#11597C22112yescomplemented
57C2×#1333C22112yescomplemented
58C22×H(5,𝔽2)—21no—
59C2×#576—216no—
60C2×#576—21no—
61C2×#576—23no—
62C2×#576C2×C416yes—
63C2×#576C2×C412yes—
64C22×AGL(1,ℤ/8)—23no—
65C22×#135C2×C413yes—
66C23×D8C2×C413yes—
67C22×#131C2×C411yescharacteristic
68C22×#131D411yescharacteristic
69C4×H(5,𝔽2)—26no—
70C4×H(5,𝔽2)—22no—
71C4×H(5,𝔽2)—22no—
72C4×H(5,𝔽2)—26no—
73C4×H(5,𝔽2)—43no—
74C4×H(5,𝔽2)—41no—
75C4×H(5,𝔽2)—41no—
76C4×H(5,𝔽2)—43no—
77C2×#520—21no—
78C2×#520—23no—
79C2×#520—41no—
80C2×#518—23no—
81C2×#518—43no—
82C2×C4×#41—23no—
83C2×C4×#41—41no—
84C2×C4×#41D411yescharacteristic
85C22×C4×D4—23no—
86C22×C4×D4—43no—
87C2×#504—22no—
88#2991—41no—
89#2990—43no—
90#2989—26no—
91#2988—22no—
92Q8×M16—41no—
93#2951—23no—
94#2951—23no—
95#2951—26no—
96#2951C2×C4112yes—
97#2951C2×C416yes—
98#2951C2×C416yes—
99#2948—23no—
100#2948—23no—
101#2948—26no—
102#2948C2×C4112yes—
103#2948C2×C416yes—
104#2948C2×C416yes—
105#2946—26no—
106#2946—212no—
107#2946—26no—
108#2946—26no—
109#2946—26no—
110#2946—212no—
111C4×AGL(1,ℤ/8)—26no—
112C4×AGL(1,ℤ/8)—212no—
113C4×AGL(1,ℤ/8)—26no—
114C4×AGL(1,ℤ/8)—26no—
115C4×AGL(1,ℤ/8)—26no—
116C4×AGL(1,ℤ/8)—212no—
117C2×#442—26no—
118C2×#440—26no—
119C4×#135—23no—
120C4×#135—23no—
121C4×#135—23no—
122C4×#135—23no—
123C4×#135C2×C416yes—
124C4×#135C2×C416yes—
125C4×#135C2316yes—
126C4×#135C2316yes—
127C2×C4×Q16C2×C413yes—
128C2×C4×Q16C2311yescharacteristic
129C2×C4×SD16—23no—
130C2×C4×SD16—23no—
131C2×C4×D8—23no—
132C2×C4×D8—23no—
133C2×C4×D8—23no—
134C2×C4×D8—23no—
135C2×C4×D8—23no—
136C2×C4×D8—23no—
137C2×C4×D8C2×C413yes—
138C2×C4×D8C2×C416yes—
139C2×C4×D8C2×C416yes—
140C2×C4×D8C2×C416yes—
141C2×C4×D8C2316yes—
142C2×C4×D8C2316yes—
143C2×C4×D8C2313yes—
144D4×M16—43no—
145#2920—23no—
146#2913—23no—
147#2913—21no—
148#2913C2×C416yes—
149#2913C2×C412yes—
150C2×#428—23no—
151C2×#427C2×C413yes—
152C22×#107C2×C413yes—
153C2×#423—23no—
154#2897—22no—
155#2897—26no—
156#2897—22no—
157#2897—26no—
158C2×#417—23no—
159C2×#418—23no—
160C2×#416—23no—
161C22×#102—23no—
162C4×#131C2×C411yescharacteristic
163C4×#131C2×C413yes—
164C4×#131D411yescharacteristic
165C4×#131D413yes—
166C4×#131D411yescharacteristic
167C4×#131D413yes—
168C4×#131C2311yescharacteristic
169C4×#131C2313yes—
170C2×#405C2×C413yes—
171C2×#405D413yes—
172C2×C4×M16D413yes—
173C22×C4×C8C2313yes—
174#2164—212no—
175#2163—23no—
176#2163—23no—
177#2163C2311yescharacteristic
178#2163C2313yes—
179#2163C2316yescomplemented
180#2163C2316yescomplemented
181#2162—23no—
182#2162—23no—
183#2151—26no—
184#2150—23no—
185C2×C4⋊C16—23no—
186#2113—26no—
187#2112—23no—
188C2×C22⋊C16—23no—
189#2108—26no—
190C4×M32C2316yescomplemented
191C2×#346C2316yescomplemented
192#1569—212no—
193#1568—23no—
194#1568C2316yescomplemented
195#1567—23no—
196#1566—23no—
197#1566—23no—
198#1566C2313yes—
199#1566C2311yescharacteristic
200#1566C2316yescomplemented
201#1565—26no—
202#1565—26no—
203#1564—23no—
204#1564C2316yescomplemented
205C2×#334—23no—
206C2×#334C2316yescomplemented
207#1334C2314yescomplemented
208#1334C23112yescomplemented
209#1333C23112yescomplemented
210#1333C23124yescomplemented
211#1333C23112yescomplemented
212C2×H(5,𝔽2)—216no—
213C2×H(5,𝔽2)—26no—
214C2×H(5,𝔽2)—22no—
215C2×H(5,𝔽2)—48no—
216C2×H(5,𝔽2)—41no—
217C2×H(5,𝔽2)—43no—
218C22×#41—23no—
219C22×#41—41no—
220C22×#41C22⋊C411yescharacteristic
221C23×D4—23no—
222C23×D4—43no—
223C24×C4—43no—
224#576—216no—
225#576—248no—
226#576—224no—
227#576—224no—
228#576—28no—
229#576M16116yescomplemented
230C2×AGL(1,ℤ/8)—248no—
231C2×AGL(1,ℤ/8)—26no—
232C2×AGL(1,ℤ/8)—212no—
233C2×AGL(1,ℤ/8)—26no—
234C2×#135—224no—
235C2×#135—23no—
236C2×#135—23no—
237C2×#135C22×C416yes—
238C2×#135C22×C416yes—
239C22×Q16C22×C411yescharacteristic
240C22×SD16—23no—
241C22×D8—224no—
242C22×D8—23no—
243C22×D8—23no—
244C22×D8—23no—
245C22×D8C22×C413yes—
246C22×D8C22×C416yes—
247C22×D8C22×C416yes—
248C2×#131—28no—
249C2×#131—44no—
250C2×#131C22⋊C411yescharacteristic
251C2×#131C22⋊C411yescharacteristic
252C2×#131C22⋊C413yes—
253C2×#131C22⋊C413yes—
254C2×#131C22×C413yes—
255C2×#131C22×C411yescharacteristic
256C2×#131C2×D411yescharacteristic
257C2×#131C2×D413yes—
258C22×M16—43no—
259C22×M16C22⋊C413yes—
260C22×M16C22⋊C413yes—
261C23×C8C22×C413yes—
262C23×C8C2×D413yes—
263#520—26no—
264#520—22no—
265#520—212no—
266#520—26no—
267#520—26no—
268#520—41no—
269#520—43no—
270#520—46no—
271#520—42no—
272#520—42no—
273#520—46no—
274#520—46no—
275#520—43no—
276#520—43no—
277#518—212no—
278#518—26no—
279#518—26no—
280#518—46no—
281#518—412no—
282#518—46no—
283#518—46no—
284#518—412no—
285#518—46no—
286#518—43no—
287#518—46no—
288#518—43no—
289C4×#41—26no—
290C4×#41—26no—
291C4×#41—26no—
292C4×#41—26no—
293C4×#41—46no—
294C4×#41—42no—
295C4×#41—46no—
296C4×#41—42no—
297C4×#41—43no—
298C4×#41—43no—
299C4×#41—43no—
300C4×#41—43no—
301C4×#41C22⋊C413yes—
302C4×#41C22⋊C411yescharacteristic
303C4×#41D813yes—
304C4×#41D811yescharacteristic
305C4×#41SD1611yescharacteristic
306C4×#41SD1613yes—
307C4×#41C2×D411yescharacteristic
308C4×#41C2×D413yes—
309C2×C4×Q8—23no—
310C2×C4×Q8—21no—
311C2×C4×Q8—41no—
312C2×C4×Q8D811yescharacteristic
313C2×C4×Q8SD1611yescharacteristic
314C2×C4×D4—26no—
315C2×C4×D4—26no—
316C2×C4×D4—26no—
317C2×C4×D4—23no—
318C2×C4×D4—23no—
319C2×C4×D4—26no—
320C2×C4×D4—26no—
321C2×C4×D4—43no—
322C2×C4×D4—43no—
323C2×C4×D4—43no—
324C2×C4×D4—412no—
325C2×C4×D4—46no—
326C2×C4×D4—46no—
327C2×C4×D4—412no—
328C2×C4×D4—46no—
329C2×C4×D4—46no—
330C2×C4×D4—43no—
331C2×C4×D4—43no—
332C2×C4×D4—46no—
333C2×C4×D4—43no—
334C2×C4×D4—43no—
335C2×C4×D4—43no—
336C2×C4×D4—43no—
337C2×C4×D4—43no—
338C2×C4×D4—43no—
339C2×C4×D4D813yes—
340C2×C4×D4SD1613yes—
341C2×#117—23no—
342C2×#117—43no—
343C2×#117—43no—
344C2×#117C22⋊C413yes—
345C22×C4⋊C4—23no—
346C22×C4⋊C4—43no—
347C22×C22⋊C4—43no—
348C22×C22⋊C4—46no—
349C22×C42—43no—
350C22×C42C2×D413yes—
351#504—48no—
352C2×M32—26no—
353C22×C16—26no—
354#446—46no—
355C8×Q8—42no—
356#442—212no—
357#442—212no—
358#442—212no—
359#442—212no—
360#440—212no—
361#440—212no—
362#440—212no—
363#440—212no—
364C4×Q16—23no—
365C4×Q16—23no—
366C4×Q16—21no—
367C4×Q16—21no—
368C4×Q16C22×C416yes—
369C4×Q16C22×C416yes—
370C4×Q16C22×C412yes—
371C4×Q16C2412yes—
372C4×SD16—26no—
373C4×SD16—26no—
374C4×SD16—26no—
375C4×SD16—26no—
376C4×SD16—26no—
377C4×SD16—26no—
378C4×SD16—26no—
379C4×SD16—26no—
380C4×D8—26no—
381C4×D8—26no—
382C4×D8—26no—
383C4×D8—26no—
384C4×D8—26no—
385C4×D8—26no—
386C4×D8—23no—
387C4×D8—23no—
388C4×D8—23no—
389C4×D8—23no—
390C4×D8—26no—
391C4×D8—26no—
392C4×D8—26no—
393C4×D8—26no—
394C4×D8C22×C416yes—
395C4×D8C22×C4112yes—
396C4×D8C22×C4112yes—
397C4×D8C22×C416yes—
398C4×D8C22×C416yes—
399C4×D8C2416yes—
400#436—46no—
401#435—412no—
402C8×D4—46no—
403#432—26no—
404#432—43no—
405#431—26no—
406#431—43no—
407#428—26no—
408#428—212no—
409#428—26no—
410#427—23no—
411#427—23no—
412#427C22×C416yes—
413#427C22×C416yes—
414C2×#107—23no—
415C2×#107—23no—
416C2×#107—23no—
417C2×#107C22×C413yes—
418C2×#107C22×C416yes—
419C2×#107C22×C416yes—
420C2×#107C22×C411yescharacteristic
421C2×#106—23no—
422#423—23no—
423#423—26no—
424#423—21no—
425#423—43no—
426#423—43no—
427C2×C4⋊C8—26no—
428C2×C4⋊C8—43no—
429#418—26no—
430#418—26no—
431#418—212no—
432#417—26no—
433#417—26no—
434#417—212no—
435#416—26no—
436#416—26no—
437#416—26no—
438#416—26no—
439C2×#103—23no—
440C2×#103—21no—
441C2×#102—26no—
442C2×#102—26no—
443C2×#102—26no—
444C2×#102—23no—
445C2×#102—23no—
446C2×#102—26no—
447C2×#102—26no—
448#407—43no—
449#405C22⋊C413yes—
450#405C22⋊C413yes—
451#405C22⋊C416yes—
452#405C22⋊C413yes—
453#405C22⋊C413yes—
454#405C22⋊C416yes—
455#405C22×C416yes—
456#405C22×C413yes—
457#405C22×C413yes—
458#405C2×D413yes—
459#405C2×D413yes—
460#405C2×D416yes—
461C4×M16—43no—
462C4×M16C22⋊C413yes—
463C4×M16C22⋊C416yes—
464C4×M16C22⋊C413yes—
465C4×M16C2×D413yes—
466C4×M16C2×D413yes—
467C4×M16C2×D416yes—
468C2×#97C22⋊C416yes—
469C2×C4×C8C22×C413yes—
470C2×C4×C8C22×C413yes—
471C2×C4×C8C22×C413yes—
472C2×C4×C8C2×D413yes—
473C2×C4×C8C2×D413yes—
474C2×C4×C8C2×D413yes—
475C2×C4×C8C2×D413yes—
476C2×C4×C8C2×D413yes—
477C2×C4×C8C2×D413yes—
478C2×C4×C8C2413yes—
479C2×C4×C8C2411yescharacteristic
480C2×C4×C8C2413yes—
481C4⋊C16—21no—
482C4⋊C16—23no—
483C4⋊C16—26no—
484C4⋊C16—26no—
485C22⋊C16—21no—
486C22⋊C16—23no—
487C22⋊C16—26no—
488C22⋊C16—26no—
489#346—26no—
490#346C2412yes—
491#346C2416yes—
492C4×C16—26no—
493#335—26no—
494#335—26no—
495#334—23no—
496#334—26no—
497#334—26no—
498#334—21no—
499#334C2416yes—
500#334C2412yes—
501C25—43no—
502H(5,𝔽2)—248no—
503H(5,𝔽2)—216no—
504H(5,𝔽2)—416no—
505H(5,𝔽2)—448no—
506H(5,𝔽2)—424no—
507H(5,𝔽2)—48no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—224no—
511C2×#41—26no—
512C2×#41—26no—
513C2×#41—412no—
514C2×#41—416no—
515C2×#41—46no—
516C2×#41—42no—
517C2×#41—43no—
518C2×#41—43no—
519C2×#41#10211yescharacteristic
520C2×#41#10213yes—
521C2×#41C2×C22⋊C413yes—
522C2×#41C2×C22⋊C411yescharacteristic
523C22×Q8—21no—
524C22×Q8#10211yescharacteristic
525C22×D4—224no—
526C22×D4—23no—
527C22×D4—26no—
528C22×D4—26no—
529C22×D4—412no—
530C22×D4—448no—
531C22×D4—43no—
532C22×D4—412no—
533C22×D4—46no—
534C22×D4—46no—
535C22×D4—43no—
536C22×D4—43no—
537C22×D4—43no—
538C22×D4#10213yes—
539C23×C4—43no—
540C23×C4—43no—
541C23×C4—43no—
542C23×C4—46no—
543C23×C4—46no—
544C23×C4—43no—
545C23×C4—46no—
546C23×C4—46no—
547C23×C4—46no—
548C23×C4—1612no—
549C23×C4C2×C22⋊C413yes—
550C23×C4C2×D813yes—
551C23×C4C2×SD1613yes—
552AGL(1,ℤ/8)—248no—
553AGL(1,ℤ/8)—296no—
554AGL(1,ℤ/8)—248no—
555#135—224no—
556#135—224no—
557#135—212no—
558#135—212no—
559#135—212no—
560#135C2×M16124yescomplemented
561C2×Q16—24no—
562C2×Q16—21no—
563C2×Q16C23×C412yes—
564C2×SD16—224no—
565C2×SD16—26no—
566C2×SD16—26no—
567C2×D8—224no—
568C2×D8—224no—
569C2×D8—224no—
570C2×D8—212no—
571C2×D8—224no—
572C2×D8—23no—
573C2×D8—26no—
574C2×D8—26no—
575C2×D8—212no—
576C2×D8C2×M16124yescomplemented
577C2×D8C23×C416yes—
578#131—24no—
579#131—24no—
580#131—24no—
581#131—212no—
582#131—212no—
583#131—46no—
584#131—46no—
585#131C2×M1618yes—
586C2×M16—212no—
587C2×M16—46no—
588C2×M16—43no—
589C2×M16—41no—
590C2×M16—46no—
591C2×M16—166no—
592C2×M16C2×C22⋊C413yes—
593C2×M16C2×C22⋊C416yes—
594C2×M16C2×C22⋊C413yes—
595C2×M16C2×C22⋊C413yes—
596C2×M16C2×C22⋊C416yes—
597C2×M16C2×C22⋊C413yes—
598C22×C8—212no—
599C22×C8—46no—
600C22×C8—46no—
601C22×C8C2×C22⋊C413yes—
602C22×C8C2×C22⋊C413yes—
603C22×C8C2×C22⋊C413yes—
604C22×C8C2×C22⋊C413yes—
605C22×C8C2×C22⋊C413yes—
606C22×C8C2×C22⋊C413yes—
607C22×C8C23×C411yescharacteristic
608C22×C8C23×C413yes—
609C22×C8C23×C413yes—
610C22×C8C22×D413yes—
611C22×C8C22×D411yescharacteristic
612C22×C8C22×D413yes—
613C4×Q8—22no—
614C4×Q8—26no—
615C4×Q8—26no—
616C4×Q8—22no—
617C4×Q8—46no—
618C4×Q8—42no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—43no—
622C4×Q8—43no—
623C4×Q8#10213yes—
624C4×Q8#10211yescharacteristic
625C4×Q8#10213yes—
626C4×Q8#10211yescharacteristic
627C4×Q8C2×D811yescharacteristic
628C4×Q8C2×D813yes—
629C4×Q8C2×SD1613yes—
630C4×Q8C2×SD1611yescharacteristic
631C4×D4—26no—
632C4×D4—212no—
633C4×D4—212no—
634C4×D4—26no—
635C4×D4—26no—
636C4×D4—26no—
637C4×D4—412no—
638C4×D4—46no—
639C4×D4—46no—
640C4×D4—46no—
641C4×D4—46no—
642C4×D4—46no—
643C4×D4—46no—
644C4×D4—46no—
645C4×D4—46no—
646C4×D4—46no—
647C4×D4—46no—
648C4×D4—412no—
649C4×D4—46no—
650C4×D4—46no—
651C4×D4—412no—
652C4×D4—46no—
653C4×D4—46no—
654C4×D4—412no—
655C4×D4—412no—
656C4×D4—412no—
657C4×D4—412no—
658C4×D4—43no—
659C4×D4—46no—
660C4×D4—46no—
661C4×D4—46no—
662C4×D4—46no—
663C4×D4—43no—
664C4×D4—46no—
665C4×D4—46no—
666C4×D4—46no—
667C4×D4—46no—
668C4×D4—46no—
669C4×D4—46no—
670C4×D4—43no—
671C4×D4—43no—
672C4×D4#10216yes—
673C4×D4#10213yes—
674C4×D4#10213yes—
675C4×D4#10216yes—
676C4×D4#10213yes—
677C4×D4#10213yes—
678C4×D4C2×D813yes—
679C4×D4C2×D816yes—
680C4×D4C2×D813yes—
681C4×D4C2×SD1616yes—
682C4×D4C2×SD1613yes—
683C4×D4C2×SD1613yes—
684#117—26no—
685#117—26no—
686#117—43no—
687#117—43no—
688#117—412no—
689#117—46no—
690#117—46no—
691#117—46no—
692#117—46no—
693#117—46no—
694#117—46no—
695#117#10213yes—
696#117#10216yes—
697#117#10213yes—
698#117C2×C22⋊C416yes—
699#117C2×C22⋊C413yes—
700#117C2×C22⋊C413yes—
701C2×C4⋊C4—23no—
702C2×C4⋊C4—26no—
703C2×C4⋊C4—26no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—43no—
707C2×C4⋊C4—43no—
708C2×C4⋊C4—43no—
709C2×C4⋊C4—43no—
710C2×C4⋊C4—412no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4—46no—
713C2×C4⋊C4#10213yes—
714C2×C4⋊C4#10213yes—
715C2×C22⋊C4—43no—
716C2×C22⋊C4—43no—
717C2×C22⋊C4—46no—
718C2×C22⋊C4—46no—
719C2×C22⋊C4—43no—
720C2×C22⋊C4—46no—
721C2×C22⋊C4—46no—
722C2×C22⋊C4—46no—
723C2×C22⋊C4—412no—
724C2×C22⋊C4—412no—
725C2×C22⋊C4—412no—
726C2×C22⋊C4—412no—
727C2×C22⋊C4#10216yes—
728C2×C42—41no—
729C2×C42—43no—
730C2×C42—43no—
731C2×C42—46no—
732C2×C42—46no—
733C2×C42—46no—
734C2×C42—46no—
735C2×C42C2×C22⋊C413yes—
736C2×C42C2×C22⋊C413yes—
737C2×C42C2×C22⋊C413yes—
738C2×C42C2×D813yes—
739C2×C42C2×D813yes—
740C2×C42C2×D813yes—
741C2×C42C2×SD1613yes—
742C2×C42C2×SD1613yes—
743C2×C42C2×SD1613yes—
744C2×C42C22×D411yescharacteristic
745C2×C42C22×D413yes—
746C2×C42C22×D413yes—
747M32—412no—
748C2×C16—26no—
749C2×C16—22no—
750C2×C16—412no—
751#107—23no—
752#107—26no—
753#107—26no—
754#107—21no—
755#107C23×C416yes—
756#107C23×C412yes—
757#106—26no—
758#106—26no—
759C4⋊C8—26no—
760C4⋊C8—22no—
761C4⋊C8—46no—
762C4⋊C8—43no—
763C4⋊C8—46no—
764C4⋊C8—41no—
765#103—22no—
766#103—26no—
767#103—26no—
768#103—22no—
769#102—26no—
770#102—212no—
771#102—212no—
772#102—26no—
773#102—26no—
774#102—26no—
775C22⋊C8—46no—
776C22⋊C8—46no—
777#97—46no—
778#97C2×C22⋊C416yes—
779#97C2×C22⋊C416yes—
780#97C2×C22⋊C416yes—
781#97C2×C22⋊C416yes—
782C4×C8—46no—
783C4×C8C2×C22⋊C413yes—
784C4×C8C2×C22⋊C413yes—
785C4×C8C2×C22⋊C413yes—
786C4×C8C2×C22⋊C413yes—
787C4×C8C2×C22⋊C413yes—
788C4×C8C2×C22⋊C413yes—
789C4×C8C23×C411yescharacteristic
790C4×C8C23×C413yes—
791C4×C8C23×C413yes—
792C4×C8C22×D413yes—
793C4×C8C22×D411yescharacteristic
794C4×C8C22×D413yes—
795C4×C8C22×D411yescharacteristic
796C4×C8C22×D413yes—
797C4×C8C22×D413yes—
798C4×C8C2511yescharacteristic
799C24—424no—
800C24—43no—
801C24—46no—
802C24—46no—
803C24—166no—
804C24—166no—
805C24C2×#10213yes—
806#41—24no—
807#41—212no—
808#41—26no—
809#41—26no—
810#41—224no—
811#41—224no—
812#41—424no—
813#41—424no—
814#41—412no—
815#41—448no—
816#41—416no—
817#41—412no—
818#41#40714yes—
819#41#42114yes—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—22no—
823C2×Q8—42no—
824C2×Q8—41no—
825C2×Q8C2×#10213yes—
826C2×Q8C2×#10211yescharacteristic
827C2×D4—212no—
828C2×D4—212no—
829C2×D4—224no—
830C2×D4—224no—
831C2×D4—26no—
832C2×D4—424no—
833C2×D4—46no—
834C2×D4—424no—
835C2×D4—424no—
836C2×D4—412no—
837C2×D4—496no—
838C2×D4—448no—
839C2×D4—424no—
840C2×D4—46no—
841C2×D4—46no—
842C2×D4—448no—
843C2×D4—46no—
844C2×D4—43no—
845C2×D4—46no—
846C2×D4—412no—
847C2×D4C2×#10216yes—
848C2×D4C2×#10213yes—
849C2×D4C2×#10213yes—
850C22×C4—26no—
851C22×C4—26no—
852C22×C4—46no—
853C22×C4—46no—
854C22×C4—424no—
855C22×C4—41no—
856C22×C4—46no—
857C22×C4—46no—
858C22×C4—41no—
859C22×C4—43no—
860C22×C4—46no—
861C22×C4—46no—
862C22×C4—46no—
863C22×C4—46no—
864C22×C4—46no—
865C22×C4—46no—
866C22×C4—412no—
867C22×C4—412no—
868C22×C4—812no—
869C22×C4—1612no—
870C22×C4—1612no—
871C22×C4—166no—
872C22×C4—1612no—
873C22×C4—1612no—
874C22×C4—1612no—
875C22×C4—166no—
876C22×C4C2×#10213yes—
877C22×C4C2×#10213yes—
878C22×C4C2×#10213yes—
879C22×C4C2×#10213yes—
880C22×C4C2×#10213yes—
881C22×C4C2×#10213yes—
882C22×C4C2×#10213yes—
883C22×C4C2×#10213yes—
884C22×C4C2×#10213yes—
885C22×C4C22×C22⋊C411yescharacteristic
886C22×C4C22×C22⋊C413yes—
887C22×C4C22×C22⋊C413yes—
888C22×C4C22×D811yescharacteristic
889C22×C4C22×D813yes—
890C22×C4C22×D813yes—
891C22×C4C22×SD1611yescharacteristic
892C22×C4C22×SD1613yes—
893C22×C4C22×SD1613yes—
894Q16—24no—
895Q16—22no—
896Q16C22×M1614yes—
897SD16—224no—
898SD16—224no—
899D8—212no—
900D8—224no—
901D8—224no—
902D8—26no—
903D8C22×M16112yes—
904M16—26no—
905M16—26no—
906M16—26no—
907M16—212no—
908M16—46no—
909M16—82no—
910M16—86no—
911M16—166no—
912M16#407112yes—
913C2×C8—26no—
914C2×C8—26no—
915C2×C8—26no—
916C2×C8—26no—
917C2×C8—26no—
918C2×C8—22no—
919C2×C8—26no—
920C2×C8—41no—
921C2×C8—43no—
922C2×C8—43no—
923C2×C8—43no—
924C2×C8—42no—
925C2×C8—46no—
926C2×C8—166no—
927C2×C8C22×C22⋊C411yescharacteristic
928C2×C8C22×C22⋊C411yescharacteristic
929C2×C8C22×C22⋊C413yes—
930C2×C8C22×C22⋊C413yes—
931C2×C8C22×C22⋊C413yes—
932C2×C8C22×C22⋊C413yes—
933C2×C8C22×M16112yes—
934C2×C8C24×C411yescharacteristic
935C2×C8C23×D411yescharacteristic
936C4⋊C4—22no—
937C4⋊C4—26no—
938C4⋊C4—46no—
939C4⋊C4—43no—
940C4⋊C4—46no—
941C4⋊C4—41no—
942C4⋊C4—46no—
943C4⋊C4—46no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4C2×#10216yes—
947C4⋊C4C2×#10213yes—
948C4⋊C4C2×#10213yes—
949C4⋊C4C2×#10216yes—
950C4⋊C4C2×#10213yes—
951C4⋊C4C2×#10213yes—
952C22⋊C4—46no—
953C22⋊C4—46no—
954C22⋊C4—46no—
955C22⋊C4—46no—
956C22⋊C4—412no—
957C22⋊C4—412no—
958C22⋊C4—46no—
959C22⋊C4—46no—
960C22⋊C4C2×#10216yes—
961C22⋊C4C2×#10216yes—
962C22⋊C4C2×#10216yes—
963C22⋊C4C2×#10216yes—
964C42—42no—
965C42—46no—
966C42—46no—
967C42—46no—
968C42—46no—
969C42—42no—
970C42C2×#10213yes—
971C42C2×#10213yes—
972C42C2×#10213yes—
973C42C2×#10213yes—
974C42C2×#10213yes—
975C42C2×#10213yes—
976C42C22×C22⋊C411yescharacteristic
977C42C22×C22⋊C413yes—
978C42C22×C22⋊C413yes—
979C42C22×D813yes—
980C42C22×D813yes—
981C42C22×D811yescharacteristic
982C42C22×SD1613yes—
983C42C22×SD1613yes—
984C42C22×SD1611yescharacteristic
985C42C23×D411yescharacteristic
986C16—42no—
987C16—46no—
988C23—26no—
989C23—26no—
990C23—43no—
991C23—412no—
992C23—424no—
993C23—46no—
994C23—424no—
995C23—86no—
996C23—86no—
997C23—166no—
998C23—166no—
999C23—166no—
1000C23—166no—
1001C23—1648no—
1002C23C22×#10213yes—
1003C23C22×#10213yes—
1004C23C22×#10211yescharacteristic
1005Q8—26no—
1006Q8—24no—
1007Q8—44no—
1008Q8—42no—
1009Q8#148614yes—
1010D4—212no—
1011D4—26no—
1012D4—212no—
1013D4—412no—
1014D4—424no—
1015D4—424no—
1016D4—424no—
1017D4—424no—
1018D4—46no—
1019D4#1486112yes—
1020C2×C4—26no—
1021C2×C4—22no—
1022C2×C4—26no—
1023C2×C4—26no—
1024C2×C4—26no—
1025C2×C4—22no—
1026C2×C4—26no—
1027C2×C4—26no—
1028C2×C4—21no—
1029C2×C4—23no—
1030C2×C4—21no—
1031C2×C4—23no—
1032C2×C4—43no—
1033C2×C4—43no—
1034C2×C4—43no—
1035C2×C4—43no—
1036C2×C4—43no—
1037C2×C4—43no—
1038C2×C4—43no—
1039C2×C4—424no—
1040C2×C4—44no—
1041C2×C4—42no—
1042C2×C4—424no—
1043C2×C4—42no—
1044C2×C4—46no—
1045C2×C4—812no—
1046C2×C4—86no—
1047C2×C4—82no—
1048C2×C4—812no—
1049C2×C4—166no—
1050C2×C4—166no—
1051C2×C4—1612no—
1052C2×C4—1612no—
1053C2×C4—166no—
1054C2×C4—166no—
1055C2×C4C2×#40716yes—
1056C2×C4C22×#10213yes—
1057C2×C4C22×#10213yes—
1058C2×C4C22×#10213yes—
1059C2×C4C22×#10213yes—
1060C2×C4C22×#10213yes—
1061C2×C4C22×#10211yescharacteristic
1062C2×C4C22×#10211yescharacteristic
1063C2×C4C22×#10213yes—
1064C2×C4C22×#10211yescharacteristic
1065C2×C4C2×#42116yes—
1066C2×C4C23×C22⋊C411yescharacteristic
1067C2×C4C23×D811yescharacteristic
1068C2×C4C23×SD1611yescharacteristic
1069C8—21no—
1070C8—23no—
1071C8—21no—
1072C8—21no—
1073C8—23no—
1074C8—23no—
1075C8—86no—
1076C8—82no—
1077C8C2×#40716yes—
1078C8C23×M1612yes—
1079C22—23no—
1080C22—21no—
1081C22—23no—
1082C22—21no—
1083C22—23no—
1084C22—23no—
1085C22—23no—
1086C22—412no—
1087C22—412no—
1088C22—824no—
1089C22—86no—
1090C22—86no—
1091C22—1624no—
1092C22—1624no—
1093C22C2×#148616yes—
1094C22#3338812yes—
1095C22C23×#10211yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—23no—
1099C4—23no—
1100C4—21no—
1101C4—23no—
1102C4—23no—
1103C4—21no—
1104C4—23no—
1105C4—44no—
1106C4—82no—
1107C4—86no—
1108C4C2×#148616yes—
1109C4#3339212yes—
1110C4C22×#40711yescharacteristic
1111C4C22×#42111yescharacteristic
1112C2—22no—
1113C2—26no—
1114C2—43no—
1115C2—812no—
1116C2C22×#148611yescharacteristic
1117C2C2×#3338811yescharacteristic
1118C2C2×#3339211yescharacteristic
subgroupG/H
center, socleC22C23×#102
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radicalC22×#576C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ C2×C4×#131 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #7622556C2semidirect
3. #6344475C2semidirect
4. #481284C2semidirect
5. #481282C2semidirect
6. #481279C2semidirect
7. #481274C2semidirect
8. C2×#11663C2semidirect
9. #481066C2semidirect
32. #33421C22semidirect
33. #33418C22semidirect
34. C2×#2163C22semidirect
37. #33326C22semidirect
39. #17798C22semidirect
41. #17793C22semidirect
42. C2×#1566C22semidirect
44. #17788C22semidirect
45. #11667C22semidirect
46. #11666C22semidirect
47. #11665C22semidirect
48. #11664C22semidirect
49. #11664C22semidirect
50. #11663C22semidirect
51. #11663C22semidirect
52. #11663C22semidirect
53. #11663C22semidirect
54. #11599C22semidirect
55. #11598C22semidirect
56. #11597C22semidirect
57. C2×#1333C22semidirect
179. #2163C23semidirect
180. #2163C23semidirect
190. C4×M32C23semidirect
191. C2×#346C23semidirect
194. #1568C23semidirect
200. #1566C23semidirect
204. #1564C23semidirect
206. C2×#334C23semidirect
207. #1334C23semidirect
208. #1334C23semidirect
209. #1333C23semidirect
210. #1333C23semidirect
211. #1333C23semidirect
229. #576M16semidirect
560. #135C2×M16semidirect
576. C2×D8C2×M16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#5762
#76225562
#63444752
#4812842
#4812822
#4812792
#4812742
C2×#116632
#4810662