Finite Group Databasebeta

← #72265321

Subgroups — #72265321

Order 1024.

3177 conjugacy classes of subgroups.

The subgroup lattice has 1508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623305C211yesmaximal, characteristic
2#6389191C211yesmaximal, characteristic, complemented
3C2×#23031C211yesmaximal, characteristic, complemented
4#498510C214yesmaximal, complemented
5#498377C214yesmaximal, complemented
6#498233C214yesmaximal, complemented
7#498122C214yesmaximal, complemented
8#496884C212yesmaximal, complemented
9#496836C212yesmaximal, complemented
10#496279C211yesmaximal, characteristic, complemented
11#495949C212yesmaximal, complemented
12#495725C212yesmaximal, complemented
13#494468C211yesmaximal, characteristic, complemented
14#494266C211yesmaximal, characteristic, complemented
15#493273C211yesmaximal, characteristic, complemented
16C2×#3050C2211yescharacteristic
17C22×#466C2211yescharacteristic
18#60233—21no—
19C22×#442C2211yescharacteristic, complemented
20C22×#427C2211yescharacteristic
21C2×#2363—21no—
22#33760C414yescomplemented
23#33759C412yescomplemented
24#33758C412yescomplemented
25#33754C414yescomplemented
26#33753C412yescomplemented
27#33752C412yescomplemented
28#33648C2212yes—
29#33646C2212yes—
30#33605C2214yes—
31#33520C2212yes—
32#33517C2212yes—
33C2×AGL(1,ℤ/16)C2214yescomplemented
34C2×#2155C2212yescomplemented
35C2×#2145C2212yescomplemented
36C2×#2112C2211yescharacteristic
37C2×#2112C2211yescharacteristic
38#23147—22no—
39#23031—22no—
40#23031—22no—
41#23031C2214yes—
42#23031C2214yescomplemented
43#23019C2212yescomplemented
44#23019C2212yescomplemented
45#22607C2212yescomplemented
46#22586—22no—
47#22452C2212yescomplemented
48#22204—21no—
49#22204—21no—
50#21773—21no—
51#21546C2212yes—
52#21546C2212yes—
53C2×#1972C2211yescharacteristic, complemented
54C2×#1943C2211yescharacteristic, complemented
55C2×#1925—21no—
56C2×#1875—21no—
57C2×#1862—21no—
58C2×#1810C2211yescharacteristic
59C2×#1776C2211yescharacteristic, complemented
60C2×#1752C2211yescharacteristic
61#13249C2214yescomplemented
62#13174C2214yescomplemented
63#13155C2214yescomplemented
64#13153C2214yescomplemented
65#13143C2214yescomplemented
66#13142C2214yescomplemented
67#13119C2214yescomplemented
68#13118C2214yescomplemented
69#13067C2214yes—
70#13040C2214yescomplemented
71#13037C2214yescomplemented
72#13004C2212yescomplemented
73#13004C2212yescomplemented
74#13002C2214yescomplemented
75#13001C2212yes—
76#13001C2212yes—
77#12956C2214yescomplemented
78#12955C2214yescomplemented
79#12930C2214yescomplemented
80#12929C2212yescomplemented
81#12929C2212yescomplemented
82#12871C2212yescomplemented
83#12736C2212yescomplemented
84#12677C2214yescomplemented
85#12650C2214yescomplemented
86#12647C2214yescomplemented
87#12616C2214yescomplemented
88#12616C2214yescomplemented
89#12605C2212yescomplemented
90#12605C2212yescomplemented
91#12567C2212yescomplemented
92#12563C2212yescomplemented
93C22×#135C2311yescharacteristic
94C23×D8C2311yescharacteristic
95C24×C8C2311yescharacteristic
96C2×#525—21no—
97C22×#121—21no—
98C22×C4×D4—21no—
99C22×#117—21no—
100C2×#509C2314yes—
101C22×M32C2312yes—
102C22×M32C2312yes—
103#3050—21no—
104#3050—21no—
105#3050—21no—
106#3050—21no—
107#3050C2×C412yescomplemented
108#3050C2×C412yescomplemented
109#3050C2312yes—
110#3050C2312yes—
111C2×#467C2×C411yescharacteristic, complemented
112C2×#467C2×C411yescharacteristic, complemented
113C2×#466—21no—
114C2×#466—21no—
115C2×#466—21no—
116C2×#466—21no—
117C2×#466—21no—
118C2×#466—21no—
119C2×#466C2×C412yes—
120C2×#466C2×C412yes—
121C2×#466C2×C412yes—
122C2×#466C2×C412yes—
123C2×#466C2×C411yescharacteristic, complemented
124C2×#466C2×C411yescharacteristic, complemented
125C2×#466C2312yes—
126C2×#466C2312yes—
127C2×#465—21no—
128C2×#465—21no—
129#2977—42no—
130#2976—41no—
131#2976—41no—
132#2974—42no—
133#2973—41no—
134#2972—41no—
135C2×#444C2312yes—
136C2×#444C2312yes—
137C2×#442—22no—
138C2×#442—44no—
139C2×#442C2314yes—
140#2933—22no—
141#2933—22no—
142#2929—22no—
143#2929—22no—
144#2924—22no—
145C22×#108C2311yescharacteristic
146C22×#108C2311yescharacteristic
147C2×#427—21no—
148C2×#427—21no—
149C2×#427—44no—
150C2×#427C2311yescharacteristic
151C2×#427C2312yes—
152C2×#427C2312yes—
153C22×#107—21no—
154C22×#107C2311yescharacteristic
155C22×#106C2311yescharacteristic
156C22×#106C2311yescharacteristic
157C2×#416—21no—
158C22×#102—21no—
159C22×#102—21no—
160C22×#102—21no—
161#2880—22no—
162C2×#407—21no—
163C22×C22⋊C8D411yescharacteristic
164C22×#97C2311yescharacteristic
165C22×#97C2311yescharacteristic
166#2363—24no—
167#2363—24no—
168#2363—42no—
169#2363—42no—
170C2×#390—21no—
171C2×#390—41no—
172C2×#389—21no—
173C2×#388—41no—
174C2×#386—41no—
175C2×C4×C4⋊C4—21no—
176C2×C4×C22⋊C4—41no—
177C2×C4×C22⋊C4D411yescharacteristic
178#2236C2×C414yescomplemented
179#2235C2×C414yescomplemented
180#2234C2×C418yescomplemented
181#2233C2×C414yescomplemented
182#2233C2×C414yescomplemented
183#2232C2×C414yescomplemented
184#2232C2×C414yescomplemented
185#2220C2×C418yescomplemented
186#2218C2×C418yescomplemented
187#2217C2×C418yescomplemented
188#2215C2×C418yescomplemented
189#2187C2×C414yes—
190#2187C2×C414yes—
191#2186C2×C418yescomplemented
192#2185C2×C414yescomplemented
193#2184C2×C414yes—
194#2184C2×C414yes—
195#2184C2×C414yescomplemented
196AGL(1,ℤ/16)—48no—
197#2159C2314yes—
198#2155—44no—
199C2×#365C2314yes—
200C2×#365C2314yes—
201C2×#361C2314yes—
202C2×#361C2314yes—
203#2145—44no—
204C2×#360C2314yes—
205C2×#360C2314yes—
206#2140C2314yes—
207#2139C2314yes—
208#2112—21no—
209#2112—21no—
210#2112C2×C412yescomplemented
211#2112C2×C412yescomplemented
212#2112C2312yes—
213#2112C2312yes—
214#2112C2312yes—
215#2112C2312yes—
216C2×C22⋊C16—21no—
217C2×C22⋊C16—21no—
218C2×C22⋊C16C2×C412yescomplemented
219C2×C22⋊C16C2×C412yescomplemented
220C2×#347C2314yes—
221C2×#347C2314yes—
222#1975C2312yes—
223#1975C2312yes—
224#1972—22no—
225#1972C2314yes—
226#1946C2312yes—
227#1946C2312yes—
228#1943—22no—
229#1943C2314yes—
230#1938—22no—
231#1938—22no—
232#1929—22no—
233#1929—22no—
234#1925—24no—
235#1925—24no—
236#1922—22no—
237#1922—22no—
238#1896—22no—
239#1896—22no—
240#1876—22no—
241#1876—22no—
242#1875—24no—
243#1875—24no—
244#1871—22no—
245#1871—22no—
246#1866—22no—
247#1866—22no—
248#1862—24no—
249#1862—24no—
250#1826—22no—
251#1810—21no—
252#1810—21no—
253#1810C2312yes—
254#1810C2312yes—
255#1789—22no—
256#1776—22no—
257#1776C2314yes—
258#1773C2312yes—
259#1773C2312yes—
260#1765—22no—
261#1765—22no—
262#1752D412yes—
263#1752D412yes—
264#1752C2312yes—
265#1752C2312yes—
266C2×#341—21no—
267C2×#340—21no—
268C2×#340—21no—
269C2×#336D411yescharacteristic
270C2×#336D411yescharacteristic
271#1387C2314yes—
272#1387C2314yes—
273#1386C2314yes—
274#1386C2314yes—
275#1383C2314yes—
276#1383C2314yes—
277#1375C2314yes—
278#1375C2314yes—
279C22×#41—21no—
280C23×D4—21no—
281C23×D4—41no—
282C24×C4—41no—
283C24×C4C2×D411yescharacteristic
284C2×#135—21no—
285C2×#135—21no—
286C2×#135—42no—
287C2×#135—42no—
288C2×#135C22×C412yescomplemented
289C2×#135C2412yes—
290C22×Q16C22×C411yescharacteristic, complemented
291C22×SD16—21no—
292C22×D8—21no—
293C22×D8—21no—
294C22×D8—21no—
295C22×D8—42no—
296C22×D8—42no—
297C22×D8C22×C412yes—
298C22×D8C22×C412yes—
299C22×D8C22×C411yescharacteristic, complemented
300C22×D8C2412yes—
301C2×#131—22no—
302C2×#131—22no—
303C22×M16—21no—
304C22×M16—21no—
305C23×C8—42no—
306C23×C8—42no—
307C23×C8C22×C411yescharacteristic
308C23×C8C22×C411yescharacteristic
309C23×C8C22×C411yescharacteristic
310C23×C8C22×C411yescharacteristic
311C23×C8C2×D411yescharacteristic
312C23×C8C2×D411yescharacteristic
313C23×C8C2×D411yescharacteristic
314C23×C8C2×D411yescharacteristic
315C23×C8C2×D411yescharacteristic
316C23×C8#4111yescharacteristic
317C23×C8#4111yescharacteristic
318C23×C8#4111yescharacteristic
319C23×C8#4111yescharacteristic
320C23×C8C2411yescharacteristic
321C23×C8C2411yescharacteristic
322C23×C8C2411yescharacteristic
323#525—22no—
324#525—22no—
325#525—22no—
326#525—22no—
327#525—41no—
328#525—41no—
329#525—41no—
330#525—41no—
331C2×#123—41no—
332C2×C22⋊Q8—21no—
333C2×C22⋊Q8—21no—
334C2×#121—22no—
335C2×#121—22no—
336C2×#121—22no—
337C2×#121—22no—
338C2×#121—21no—
339C2×#121—21no—
340C2×#121—22no—
341C2×#121—22no—
342C2×#121—41no—
343C2×#121—41no—
344C2×#121—41no—
345C2×#121—41no—
346C2×#121—41no—
347C2×#121—41no—
348C2×#120—41no—
349C2×C4×D4—24no—
350C2×C4×D4—42no—
351C2×C4×D4—41no—
352C2×C4×D4—41no—
353C2×C4×D4—44no—
354C2×C4×D4—82no—
355C2×#117—21no—
356C2×#117—22no—
357C2×#117—22no—
358C2×#117—41no—
359C2×#117—41no—
360C2×#117—44no—
361C2×#117—82no—
362C22×C4⋊C4—21no—
363C22×C4⋊C4—21no—
364C22×C4⋊C4—21no—
365C22×C4⋊C4—41no—
366C22×C22⋊C4—21no—
367C22×C22⋊C4—41no—
368C22×C22⋊C4—41no—
369C22×C22⋊C4—41no—
370C22×C22⋊C4—41no—
371C22×C22⋊C4—41no—
372C22×C42—41no—
373C22×C42—41no—
374C22×C42C2×D411yescharacteristic
375C22×C42C2×D411yescharacteristic
376#509—44no—
377#509—44no—
378C2×SD32C22×C418yes—
379C2×D16C22×C418yes—
380C2×M32—22no—
381C2×M32—42no—
382C2×M32—42no—
383C2×M32—42no—
384C2×M32—42no—
385C2×M32C22×C414yescomplemented
386C2×M32C2414yes—
387C2×M32C2414yes—
388C22×C16—22no—
389C22×C16C22×C414yescomplemented
390#467—21no—
391#467—21no—
392#467—21no—
393#467—21no—
394#467C22×C412yes—
395#467C22×C412yes—
396#467C22×C412yescomplemented
397#467C22×C412yescomplemented
398#466—22no—
399#466—22no—
400#466—22no—
401#466—22no—
402#466—22no—
403#466—22no—
404#466—22no—
405#466—22no—
406#466—21no—
407#466—21no—
408#466—21no—
409#466—21no—
410#466—22no—
411#466—22no—
412#466—22no—
413#466—22no—
414#466C22×C412yes—
415#466C22×C412yes—
416#466C22×C414yes—
417#466C22×C414yes—
418#466C22×C414yes—
419#466C22×C414yes—
420#466C22×C412yescomplemented
421#466C22×C412yescomplemented
422#465—22no—
423#465—22no—
424#465—22no—
425#465—22no—
426#465—22no—
427#465—22no—
428#465—22no—
429#465—22no—
430#444—44no—
431#444—44no—
432#442—28no—
433#442—44no—
434#442—48no—
435#436—42no—
436#436—42no—
437#435—42no—
438#435—42no—
439#435—42no—
440#435—42no—
441#435—42no—
442#435—42no—
443#435—42no—
444#435—42no—
445C8×D4—42no—
446C8×D4—42no—
447C8×D4—42no—
448C8×D4—42no—
449C8×D4—42no—
450C8×D4—42no—
451#433—42no—
452#433—42no—
453#432—42no—
454#431—42no—
455C2×#108—21no—
456C2×#108—21no—
457C2×#108—42no—
458C2×#108—42no—
459C2×#108C2412yes—
460C2×#108C2412yes—
461#427—21no—
462#427—21no—
463#427—24no—
464#427—24no—
465#427—42no—
466#427—42no—
467#427—44no—
468#427—44no—
469#427C22×C412yescomplemented
470#427C2412yes—
471C2×#107—21no—
472C2×#107—21no—
473C2×#107—21no—
474C2×#107—22no—
475C2×#107—22no—
476C2×#107—44no—
477C2×#107C22×C412yes—
478C2×#107C22×C412yes—
479C2×#107C22×C411yescharacteristic, complemented
480C2×#107C22×C411yescharacteristic, complemented
481C2×#107C2412yes—
482C2×#106—21no—
483C2×#106—21no—
484C2×#106—24no—
485C2×#106—21no—
486C2×#106—42no—
487C2×#106C2412yes—
488C2×#106C2412yes—
489#424—22no—
490#424—22no—
491C2×#104—22no—
492C2×#104—22no—
493C2×#104—22no—
494C2×#104—22no—
495#416—22no—
496#416—22no—
497#416—22no—
498#416—22no—
499C2×#103—21no—
500C2×#103—21no—
501C2×#102—22no—
502C2×#102—22no—
503C2×#102—22no—
504C2×#102—22no—
505C2×#102—21no—
506C2×#102—21no—
507C2×#102—22no—
508C2×#102—22no—
509C2×#102—24no—
510C2×#102—24no—
511C2×#102—44no—
512C2×#102—82no—
513#408—22no—
514#408—22no—
515#408—42no—
516#408—42no—
517#407—22no—
518#407—22no—
519#407—42no—
520#407—41no—
521#407—41no—
522C2×C22⋊C8—21no—
523C2×C22⋊C8—21no—
524C2×C22⋊C8—21no—
525C2×C22⋊C8—21no—
526C2×C22⋊C8—42no—
527C2×C22⋊C8—41no—
528C2×C22⋊C8—41no—
529C2×C22⋊C8C2×D412yes—
530C2×C22⋊C8C2×D412yes—
531#405—22no—
532#405—22no—
533C2×#97—42no—
534C2×#97—42no—
535C2×#97C2×D412yes—
536C2×#97C2×D412yes—
537C2×#97C2412yes—
538C2×#97C2412yes—
539#390—24no—
540#390—42no—
541#390—44no—
542#390—44no—
543#389—24no—
544#389—42no—
545#388—44no—
546#388—44no—
547#386—44no—
548#386—44no—
549C4×C4⋊C4—24no—
550C4×C4⋊C4—42no—
551C4×C22⋊C4—21no—
552C4×C22⋊C4—21no—
553C4×C22⋊C4—44no—
554C4×C22⋊C4—44no—
555C4×C22⋊C4C2×D412yes—
556C4×C22⋊C4C2×D412yes—
557C2×#95—21no—
558C2×#95—41no—
559C2×#95—41no—
560#367C22×C418yescomplemented
561#366C22×C418yescomplemented
562#365—28no—
563#365—44no—
564#361—44no—
565#361—44no—
566#360—28no—
567#360—44no—
568#358C22×C418yescomplemented
569#357C22×C418yes—
570#357C22×C418yes—
571#357C22×C418yescomplemented
572C22⋊C16—22no—
573C22⋊C16—22no—
574C22⋊C16—22no—
575C22⋊C16—22no—
576C22⋊C16C22×C414yes—
577C22⋊C16C22×C414yes—
578C22⋊C16C22×C414yescomplemented
579C22⋊C16C22×C414yescomplemented
580#347—44no—
581#347—44no—
582#341—22no—
583#341—22no—
584#340—24no—
585#340—24no—
586#339—22no—
587#339—22no—
588#339—22no—
589#339—22no—
590#336C2×D412yes—
591#336C2×D412yes—
592#336C2×D412yes—
593#336C2×D412yes—
594C25—41no—
595C25AGL(1,ℤ/8)11yescharacteristic
596C2×#41—22no—
597C2×#41—22no—
598C2×#41—41no—
599C2×#41—41no—
600C2×#41—81no—
601C2×#41—81no—
602C2×#41—81no—
603C2×#41—81no—
604C22×Q8—21no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—21no—
608C22×D4—22no—
609C22×D4—42no—
610C22×D4—42no—
611C22×D4—42no—
612C22×D4—42no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—41no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4—42no—
622C22×D4—41no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4—162no—
626C22×D4—162no—
627C23×C4—21no—
628C23×C4—21no—
629C23×C4—41no—
630C23×C4—41no—
631C23×C4—41no—
632C23×C4—41no—
633C23×C4—44no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—84no—
639C23×C4—84no—
640C23×C4—162no—
641C23×C4C4×D411yescharacteristic
642C23×C4C4×D411yescharacteristic
643C23×C4C4×D411yescharacteristic
644C23×C4C4×D411yescharacteristic
645C23×C4AGL(1,ℤ/8)11yescharacteristic
646C23×C4AGL(1,ℤ/8)11yescharacteristic
647C23×C4AGL(1,ℤ/8)11yescharacteristic
648C23×C4AGL(1,ℤ/8)11yescharacteristic
649C23×C4AGL(1,ℤ/8)11yescharacteristic
650C23×C4AGL(1,ℤ/8)11yescharacteristic
651C23×C4AGL(1,ℤ/8)11yescharacteristic
652C23×C4C22×D411yescharacteristic
653C23×C4C22×D411yescharacteristic
654C23×C4C22×D411yescharacteristic
655#135—24no—
656#135—24no—
657#135—44no—
658#135—82no—
659#135—81no—
660#135—81no—
661C2×Q16—21no—
662C2×Q16—42no—
663C2×Q16C23×C412yes—
664C2×SD16—22no—
665C2×SD16—22no—
666C2×SD16—82no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—21no—
670C2×D8—22no—
671C2×D8—24no—
672C2×D8—24no—
673C2×D8—44no—
674C2×D8—44no—
675C2×D8—42no—
676C2×D8—42no—
677C2×D8—44no—
678C2×D8—44no—
679C2×D8—42no—
680C2×D8C23×C414yes—
681C2×D8C23×C412yes—
682#131—82no—
683#131—82no—
684#131—82no—
685#131—82no—
686C2×M16—22no—
687C2×M16—22no—
688C2×M16—42no—
689C2×M16—42no—
690C2×M16—41no—
691C2×M16—41no—
692C2×M16—81no—
693C2×M16—81no—
694C2×M16—81no—
695C2×M16—81no—
696C22×C8—22no—
697C22×C8—22no—
698C22×C8—22no—
699C22×C8—22no—
700C22×C8—22no—
701C22×C8—22no—
702C22×C8—21no—
703C22×C8—21no—
704C22×C8—21no—
705C22×C8—21no—
706C22×C8—42no—
707C22×C8—42no—
708C22×C8—42no—
709C22×C8—42no—
710C22×C8—42no—
711C22×C8—42no—
712C22×C8—42no—
713C22×C8—42no—
714C22×C8—41no—
715C22×C8—41no—
716C22×C8—41no—
717C22×C8—41no—
718C22×C8—41no—
719C22×C8—41no—
720C22×C8—41no—
721C22×C8—41no—
722C22×C8—41no—
723C22×C8—41no—
724C22×C8—42no—
725C22×C8—42no—
726C22×C8—41no—
727C22×C8—41no—
728C22×C8C4×D411yescharacteristic
729C22×C8C4×D411yescharacteristic
730C22×C8C4×D411yescharacteristic
731C22×C8C4×D411yescharacteristic
732C22×C8C4×D411yescharacteristic
733C22×C8C4×D411yescharacteristic
734C22×C8C4×D411yescharacteristic
735C22×C8C4×D411yescharacteristic
736C22×C8C4×D411yescharacteristic
737C22×C8C4×D411yescharacteristic
738C22×C8C4×D411yescharacteristic
739C22×C8C4×D411yescharacteristic
740C22×C8C23×C411yescharacteristic
741C22×C8C23×C411yescharacteristic
742C22×C8C23×C411yescharacteristic
743C22×C8C23×C411yescharacteristic
744C22×C8C23×C411yescharacteristic
745C22×C8C23×C411yescharacteristic
746C22×C8C22×D412yes—
747C22×C8C22×D412yes—
748C22×C8C22×D411yescharacteristic
749C22×C8C22×D411yescharacteristic
750C22×C8C22×D411yescharacteristic
751C22×C8C2×#4111yescharacteristic
752C22×C8C2×#4111yescharacteristic
753C22×C8C2×#4111yescharacteristic
754C22×C8C2×#4111yescharacteristic
755C22×C8C2×#4111yescharacteristic
756C22×C8C2×#4111yescharacteristic
757C22×C8C2511yescharacteristic
758#123—42no—
759#123—42no—
760#123—42no—
761#123—42no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8—41no—
767C22⋊Q8—41no—
768C22⋊Q8—41no—
769C22⋊Q8—41no—
770#121—24no—
771#121—24no—
772#121—24no—
773#121—24no—
774#121—22no—
775#121—22no—
776#121—22no—
777#121—22no—
778#121—42no—
779#121—42no—
780#121—42no—
781#121—42no—
782#121—42no—
783#121—42no—
784#121—42no—
785#121—42no—
786#121—42no—
787#121—42no—
788#121—42no—
789#121—42no—
790#121—41no—
791#121—41no—
792#121—41no—
793#121—41no—
794#120—42no—
795#120—42no—
796#120—42no—
797#120—42no—
798C4×D4—48no—
799C4×D4—42no—
800C4×D4—42no—
801C4×D4—42no—
802C4×D4—42no—
803C4×D4—42no—
804C4×D4—42no—
805C4×D4—42no—
806C4×D4—42no—
807C4×D4—84no—
808C4×D4—88no—
809#117—22no—
810#117—22no—
811#117—41no—
812#117—41no—
813#117—44no—
814#117—44no—
815#117—82no—
816#117—82no—
817#117—84no—
818#117—84no—
819C2×C4⋊C4—24no—
820C2×C4⋊C4—22no—
821C2×C4⋊C4—22no—
822C2×C4⋊C4—21no—
823C2×C4⋊C4—21no—
824C2×C4⋊C4—22no—
825C2×C4⋊C4—22no—
826C2×C4⋊C4—22no—
827C2×C4⋊C4—42no—
828C2×C4⋊C4—41no—
829C2×C4⋊C4—41no—
830C2×C4⋊C4—41no—
831C2×C4⋊C4—41no—
832C2×C4⋊C4—41no—
833C2×C4⋊C4—41no—
834C2×C4⋊C4—42no—
835C2×C4⋊C4—42no—
836C2×C4⋊C4—41no—
837C2×C4⋊C4—44no—
838C2×C4⋊C4—162no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—22no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4—41no—
844C2×C22⋊C4—42no—
845C2×C22⋊C4—42no—
846C2×C22⋊C4—42no—
847C2×C22⋊C4—42no—
848C2×C22⋊C4—42no—
849C2×C22⋊C4—42no—
850C2×C22⋊C4—41no—
851C2×C22⋊C4—41no—
852C2×C22⋊C4—44no—
853C2×C22⋊C4—44no—
854C2×C22⋊C4—42no—
855C2×C22⋊C4—42no—
856C2×C22⋊C4—44no—
857C2×C22⋊C4—82no—
858C2×C22⋊C4—84no—
859C2×C22⋊C4—84no—
860C2×C22⋊C4—84no—
861C2×C22⋊C4—162no—
862C2×C42—21no—
863C2×C42—21no—
864C2×C42—41no—
865C2×C42—41no—
866C2×C42—41no—
867C2×C42—41no—
868C2×C42—41no—
869C2×C42—42no—
870C2×C42—42no—
871C2×C42—44no—
872C2×C42—84no—
873C2×C42—162no—
874C2×C42C22×D412yes—
875C2×C42C22×D412yes—
876SD32—48no—
877D16—48no—
878M32—24no—
879M32—24no—
880M32—24no—
881M32—24no—
882M32—44no—
883M32—82no—
884C2×C16—24no—
885C2×C16—44no—
886C2×C16—82no—
887C2×C16C23×C418yes—
888#108—24no—
889#108—24no—
890#108—81no—
891#108—81no—
892#107—22no—
893#107—22no—
894#107—21no—
895#107—21no—
896#107—22no—
897#107—44no—
898#107—44no—
899#107C23×C412yes—
900#107C23×C412yes—
901#107C23×C414yes—
902#106—24no—
903#106—22no—
904#106—22no—
905#106—22no—
906#106—22no—
907#106—22no—
908#106—42no—
909#106H(5,𝔽2)14yes—
910C4⋊C8—42no—
911C4⋊C8—42no—
912C4⋊C8—42no—
913C4⋊C8—42no—
914#104—82no—
915#104—82no—
916#104—82no—
917#104—82no—
918#103—22no—
919#103—22no—
920#103—22no—
921#103—22no—
922#102—24no—
923#102—24no—
924#102—24no—
925#102—24no—
926#102—22no—
927#102—22no—
928#102—22no—
929#102—22no—
930#102—48no—
931#102—84no—
932C22⋊C8—22no—
933C22⋊C8—22no—
934C22⋊C8—22no—
935C22⋊C8—22no—
936C22⋊C8—42no—
937C22⋊C8—42no—
938C22⋊C8—42no—
939C22⋊C8—42no—
940C22⋊C8—42no—
941C22⋊C8—42no—
942C22⋊C8—42no—
943C22⋊C8—42no—
944#97—24no—
945#97—24no—
946#97—42no—
947#97—42no—
948#97—42no—
949#97—42no—
950C4×C8—42no—
951C4×C8—42no—
952#95—22no—
953#95—22no—
954#95—44no—
955#95—44no—
956C24—41no—
957C24—42no—
958C24—41no—
959C24—42no—
960C24—42no—
961C24—42no—
962C24—42no—
963C24—41no—
964C24—82no—
965C24—82no—
966C24—82no—
967C24—82no—
968C24—82no—
969C24—82no—
970C24#44211yescharacteristic
971C24#44211yescharacteristic
972C24#44211yescharacteristic
973C24#44211yescharacteristic
974C24C2×AGL(1,ℤ/8)11yescharacteristic
975C24C2×AGL(1,ℤ/8)11yescharacteristic
976C24C2×AGL(1,ℤ/8)11yescharacteristic
977#41—42no—
978#41—42no—
979#41—42no—
980#41—42no—
981#41—82no—
982#41—82no—
983#41—161no—
984#41—161no—
985#41—161no—
986#41—161no—
987C2×Q8—22no—
988C2×Q8—41no—
989C2×Q8—81no—
990C2×Q8—81no—
991C2×D4—24no—
992C2×D4—22no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—41no—
1012C2×D4—42no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—81no—
1016C2×D4—81no—
1017C2×D4—82no—
1018C2×D4—82no—
1019C2×D4—82no—
1020C2×D4—82no—
1021C2×D4—82no—
1022C2×D4—82no—
1023C2×D4—84no—
1024C2×D4—164no—
1025C2×D4—164no—
1026C2×D4—162no—
1027C2×D4—162no—
1028C2×D4—162no—
1029C2×D4—162no—
1030C2×D4—164no—
1031C2×D4—164no—
1032C2×D4—162no—
1033C2×D4—161no—
1034C2×D4—161no—
1035C22×C4—21no—
1036C22×C4—21no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—21no—
1042C22×C4—21no—
1043C22×C4—21no—
1044C22×C4—21no—
1045C22×C4—21no—
1046C22×C4—21no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—41no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—88no—
1089C22×C4—88no—
1090C22×C4—82no—
1091C22×C4—82no—
1092C22×C4—82no—
1093C22×C4—82no—
1094C22×C4—82no—
1095C22×C4—82no—
1096C22×C4—82no—
1097C22×C4—161no—
1098C22×C4—161no—
1099C22×C4—164no—
1100C22×C4—1616no—
1101C22×C4#44211yescharacteristic
1102C22×C4#44211yescharacteristic
1103C22×C4#44211yescharacteristic
1104C22×C4#44211yescharacteristic
1105C22×C4#44211yescharacteristic
1106C22×C4#44211yescharacteristic
1107C22×C4#44211yescharacteristic
1108C22×C4#44211yescharacteristic
1109C22×C4#44211yescharacteristic
1110C22×C4#44211yescharacteristic
1111C22×C4#44211yescharacteristic
1112C22×C4#44211yescharacteristic
1113C22×C4C2×C4×D411yescharacteristic
1114C22×C4C2×C4×D411yescharacteristic
1115C22×C4C2×C4×D411yescharacteristic
1116C22×C4C2×C4×D411yescharacteristic
1117C22×C4C2×C4×D411yescharacteristic
1118C22×C4C2×C4×D411yescharacteristic
1119C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1120C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1121C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1122C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1123C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1124C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1125C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1126C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1127C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1128C22×C4C23×D411yescharacteristic
1129Q16—24no—
1130Q16—81no—
1131SD16—44no—
1132SD16—82no—
1133D8—24no—
1134D8—28no—
1135D8—44no—
1136D8—44no—
1137D8—44no—
1138D8—81no—
1139M16—42no—
1140M16—42no—
1141M16—42no—
1142M16—42no—
1143M16—162no—
1144M16—162no—
1145M16—161no—
1146M16—161no—
1147C2×C8—21no—
1148C2×C8—21no—
1149C2×C8—21no—
1150C2×C8—21no—
1151C2×C8—21no—
1152C2×C8—21no—
1153C2×C8—22no—
1154C2×C8—22no—
1155C2×C8—22no—
1156C2×C8—22no—
1157C2×C8—22no—
1158C2×C8—22no—
1159C2×C8—22no—
1160C2×C8—22no—
1161C2×C8—22no—
1162C2×C8—22no—
1163C2×C8—22no—
1164C2×C8—22no—
1165C2×C8—22no—
1166C2×C8—22no—
1167C2×C8—22no—
1168C2×C8—22no—
1169C2×C8—22no—
1170C2×C8—22no—
1171C2×C8—41no—
1172C2×C8—41no—
1173C2×C8—41no—
1174C2×C8—41no—
1175C2×C8—41no—
1176C2×C8—41no—
1177C2×C8—41no—
1178C2×C8—41no—
1179C2×C8—41no—
1180C2×C8—41no—
1181C2×C8—41no—
1182C2×C8—41no—
1183C2×C8—42no—
1184C2×C8—42no—
1185C2×C8—81no—
1186C2×C8—81no—
1187C2×C8—81no—
1188C2×C8—81no—
1189C2×C8—162no—
1190C2×C8—162no—
1191C2×C8—161no—
1192C2×C8—161no—
1193C2×C8C2×C4×D411yescharacteristic
1194C2×C8C2×C4×D411yescharacteristic
1195C2×C8C2×C4×D411yescharacteristic
1196C2×C8C2×C4×D411yescharacteristic
1197C2×C8C2×C4×D411yescharacteristic
1198C2×C8C2×C4×D411yescharacteristic
1199C2×C8C24×C411yescharacteristic
1200C2×C8C22×#4111yescharacteristic
1201C2×C8C2×H(5,𝔽2)12yes—
1202C2×C8#58512yes—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—82no—
1221C4⋊C4—164no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—82no—
1237C22⋊C4—82no—
1238C22⋊C4—88no—
1239C22⋊C4—84no—
1240C22⋊C4—84no—
1241C22⋊C4—88no—
1242C22⋊C4—164no—
1243C42—22no—
1244C42—22no—
1245C42—22no—
1246C42—22no—
1247C42—42no—
1248C42—42no—
1249C42—42no—
1250C42—42no—
1251C42—84no—
1252C42—84no—
1253C42—164no—
1254C16—28no—
1255C16—44no—
1256C23—21no—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—21no—
1261C23—21no—
1262C23—21no—
1263C23—21no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—42no—
1281C23—44no—
1282C23—84no—
1283C23—84no—
1284C23—82no—
1285C23—82no—
1286C23—82no—
1287C23—82no—
1288C23—84no—
1289C23—84no—
1290C23—84no—
1291C23—84no—
1292C23—82no—
1293C23—82no—
1294C23—82no—
1295C23—84no—
1296C23—84no—
1297C23—161no—
1298C23—161no—
1299C23—164no—
1300C23—164no—
1301C23—164no—
1302C23—164no—
1303C23C2×#44211yescharacteristic
1304C23C2×#44211yescharacteristic
1305C23C2×#44211yescharacteristic
1306C23C2×#44211yescharacteristic
1307C23C2×#44211yescharacteristic
1308C23C2×#44211yescharacteristic
1309C23C22×AGL(1,ℤ/8)11yescharacteristic
1310Q8—42no—
1311Q8—42no—
1312Q8—161no—
1313D4—44no—
1314D4—42no—
1315D4—44no—
1316D4—42no—
1317D4—84no—
1318D4—84no—
1319D4—84no—
1320D4—82no—
1321D4—82no—
1322D4—84no—
1323D4—84no—
1324D4—82no—
1325D4—82no—
1326D4—161no—
1327D4—162no—
1328D4—164no—
1329D4—164no—
1330D4—164no—
1331D4—164no—
1332D4—162no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—42no—
1376C2×C4—42no—
1377C2×C4—42no—
1378C2×C4—42no—
1379C2×C4—42no—
1380C2×C4—42no—
1381C2×C4—44no—
1382C2×C4—42no—
1383C2×C4—42no—
1384C2×C4—44no—
1385C2×C4—42no—
1386C2×C4—82no—
1387C2×C4—82no—
1388C2×C4—82no—
1389C2×C4—84no—
1390C2×C4—84no—
1391C2×C4—82no—
1392C2×C4—88no—
1393C2×C4—84no—
1394C2×C4—82no—
1395C2×C4—84no—
1396C2×C4—82no—
1397C2×C4—82no—
1398C2×C4—82no—
1399C2×C4—82no—
1400C2×C4—82no—
1401C2×C4—162no—
1402C2×C4—161no—
1403C2×C4—161no—
1404C2×C4—1616no—
1405C2×C4—164no—
1406C2×C4C2×#44211yescharacteristic
1407C2×C4C2×#44211yescharacteristic
1408C2×C4C2×#44211yescharacteristic
1409C2×C4C2×#44211yescharacteristic
1410C2×C4C2×#44211yescharacteristic
1411C2×C4C2×#44211yescharacteristic
1412C2×C4C22×C4×D411yescharacteristic
1413C2×C4#348411yescharacteristic
1414C2×C4#348511yescharacteristic
1415C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1416C2×C4#358511yescharacteristic
1417C2×C4#358611yescharacteristic
1418C8—21no—
1419C8—21no—
1420C8—21no—
1421C8—21no—
1422C8—21no—
1423C8—21no—
1424C8—42no—
1425C8—42no—
1426C8—82no—
1427C8—82no—
1428C8C4×H(5,𝔽2)12yes—
1429C8#350512yes—
1430C22—24no—
1431C22—24no—
1432C22—21no—
1433C22—21no—
1434C22—21no—
1435C22—21no—
1436C22—21no—
1437C22—21no—
1438C22—21no—
1439C22—21no—
1440C22—21no—
1441C22—21no—
1442C22—21no—
1443C22—21no—
1444C22—21no—
1445C22—21no—
1446C22—21no—
1447C22—21no—
1448C22—21no—
1449C22—21no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—82no—
1455C22—82no—
1456C22—82no—
1457C22—82no—
1458C22—82no—
1459C22—84no—
1460C22—82no—
1461C22—84no—
1462C22—82no—
1463C22—84no—
1464C22—162no—
1465C22—162no—
1466C22—162no—
1467C22—162no—
1468C22—168no—
1469C22—168no—
1470C22—322no—
1471C22#3346812yes—
1472C22#3347112yes—
1473C22C22×#44211yescharacteristic
1474C22#6157111yescharacteristic
1475C22#6170611yescharacteristic
1476C4—21no—
1477C4—21no—
1478C4—21no—
1479C4—21no—
1480C4—21no—
1481C4—21no—
1482C4—82no—
1483C4—82no—
1484C4—84no—
1485C4—82no—
1486C4—82no—
1487C4—84no—
1488C4—82no—
1489C4—162no—
1490C4#3426411yescharacteristic
1491C4#6017011yescharacteristic
1492C4#6157211yescharacteristic
1493C4#6170711yescharacteristic
1494C2—21no—
1495C2—21no—
1496C2—22no—
1497C2—22no—
1498C2—41no—
1499C2—41no—
1500C2—41no—
1501C2—41no—
1502C2—164no—
1503C2—162no—
1504C2#639456111yescharacteristic
1505C2C2×#3346811yescharacteristic
1506C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radical#7623305C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#1752 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6389191C2semidirect
3. C2×#23031C2semidirect
4. #498510C2semidirect
5. #498377C2semidirect
6. #498233C2semidirect
7. #498122C2semidirect
8. #496884C2semidirect
9. #496836C2semidirect
10. #496279C2semidirect
11. #495949C2semidirect
12. #495725C2semidirect
13. #494468C2semidirect
14. #494266C2semidirect
15. #493273C2semidirect
19. C22×#442C22semidirect
22. #33760C4semidirect
23. #33759C4semidirect
24. #33758C4semidirect
25. #33754C4semidirect
26. #33753C4semidirect
27. #33752C4semidirect
33. C2×AGL(1,ℤ/16)C22semidirect
34. C2×#2155C22semidirect
35. C2×#2145C22semidirect
42. #23031C22semidirect
43. #23019C22semidirect
44. #23019C22semidirect
45. #22607C22semidirect
47. #22452C22semidirect
53. C2×#1972C22semidirect
54. C2×#1943C22semidirect
59. C2×#1776C22semidirect
61. #13249C22semidirect
62. #13174C22semidirect
63. #13155C22semidirect
64. #13153C22semidirect
65. #13143C22semidirect
66. #13142C22semidirect
67. #13119C22semidirect
68. #13118C22semidirect
70. #13040C22semidirect
71. #13037C22semidirect
72. #13004C22semidirect
73. #13004C22semidirect
74. #13002C22semidirect
77. #12956C22semidirect
78. #12955C22semidirect
79. #12930C22semidirect
80. #12929C22semidirect
81. #12929C22semidirect
82. #12871C22semidirect
83. #12736C22semidirect
84. #12677C22semidirect
85. #12650C22semidirect
86. #12647C22semidirect
87. #12616C22semidirect
88. #12616C22semidirect
89. #12605C22semidirect
90. #12605C22semidirect
91. #12567C22semidirect
92. #12563C22semidirect
107. #3050C2×C4semidirect
108. #3050C2×C4semidirect
111. C2×#467C2×C4semidirect
112. C2×#467C2×C4semidirect
123. C2×#466C2×C4semidirect
124. C2×#466C2×C4semidirect
178. #2236C2×C4semidirect
179. #2235C2×C4semidirect
180. #2234C2×C4semidirect
181. #2233C2×C4semidirect
182. #2233C2×C4semidirect
183. #2232C2×C4semidirect
184. #2232C2×C4semidirect
185. #2220C2×C4semidirect
186. #2218C2×C4semidirect
187. #2217C2×C4semidirect
188. #2215C2×C4semidirect
191. #2186C2×C4semidirect
192. #2185C2×C4semidirect
195. #2184C2×C4semidirect
210. #2112C2×C4semidirect
211. #2112C2×C4semidirect
218. C2×C22⋊C16C2×C4semidirect
219. C2×C22⋊C16C2×C4semidirect
288. C2×#135C22×C4semidirect
290. C22×Q16C22×C4semidirect
299. C22×D8C22×C4semidirect
385. C2×M32C22×C4semidirect
389. C22×C16C22×C4semidirect
396. #467C22×C4semidirect
397. #467C22×C4semidirect
420. #466C22×C4semidirect
421. #466C22×C4semidirect
469. #427C22×C4semidirect
479. C2×#107C22×C4semidirect
480. C2×#107C22×C4semidirect
560. #367C22×C4semidirect
561. #366C22×C4semidirect
568. #358C22×C4semidirect
571. #357C22×C4semidirect
578. C22⋊C16C22×C4semidirect
579. C22⋊C16C22×C4semidirect

Maximal subgroups

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

subgroupindex
#76233052
#63891912
C2×#230312
#4985102
#4983772
#4982332
#4981222
#4968842
#4968362
#4962792
#4959492
#4957252
#4944682
#4942662
#4932732