Finite Group Databasebeta

← #72314113

Subgroups — #72314113

Order 1024.

4299 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33520C211yesmaximal, characteristic
2#6389124C211yesmaximal, characteristic, complemented
3C2×#22452C211yesmaximal, characteristic, complemented
4#498122C218yesmaximal, complemented
5#497707C214yesmaximal, complemented
6#497422C214yesmaximal, complemented
7#496832C214yesmaximal, complemented
8#496668C211yesmaximal, characteristic, complemented
9#496279C211yesmaximal, characteristic, complemented
10#495721C214yesmaximal, complemented
11#493522C211yesmaximal, characteristic, complemented
12#493273C211yesmaximal, characteristic, complemented
13C23×#135C2211yescharacteristic
14C22×#509C2212yes—
15C22×#466C2211yescharacteristic
16C22×#444C2212yescomplemented
17C2×#2880—21no—
18#34246—21no—
19#33520C412yescomplemented
20#33520C414yescomplemented
21#33520C412yescomplemented
22#33520C2212yes—
23#33520C2212yes—
24#33520C2214yes—
25C2×#2186C414yescomplemented
26C2×#2185C412yescomplemented
27C2×#2184C412yescomplemented
28C2×AGL(1,ℤ/16)C2218yescomplemented
29C2×#2145C2214yescomplemented
30C2×#2139C2212yes—
31C2×#2112C2211yescharacteristic
32C2×#2112C2211yescharacteristic
33#23137—22no—
34#23031C2214yescomplemented
35#22618C2212yescomplemented
36#22566—22no—
37#22452—22no—
38#22452—22no—
39#22452C2214yes—
40#22452C2214yescomplemented
41#22436C2212yescomplemented
42#22181—22no—
43#21761—21no—
44#21526C2214yescomplemented
45C2×#1975C2212yescomplemented
46C2×#1876—22no—
47C2×#1810C2211yescharacteristic
48#20658C2211yescharacteristic
49C2×#1789—21no—
50C2×#1752C2211yescharacteristic
51#13249C2218yescomplemented
52#13153C2218yescomplemented
53#13143C2218yescomplemented
54#13067C2214yescomplemented
55#13040C2218yescomplemented
56#13037C2218yescomplemented
57#13004C2214yescomplemented
58#12955C2218yescomplemented
59#12930C2214yescomplemented
60#12928C2214yescomplemented
61#12871C2212yescomplemented
62#12831C2214yescomplemented
63#12736C2212yescomplemented
64#12735C2214yes—
65#12735C2212yescomplemented
66#12735C2212yescomplemented
67#12650C2218yescomplemented
68#12616C2214yescomplemented
69#12616C2214yescomplemented
70#12605C2214yescomplemented
71C23×#41—21no—
72C22×#135—21no—
73C22×#135—21no—
74C22×#135—21no—
75C22×#135—21no—
76C22×#135—21no—
77C22×#135—21no—
78C22×#135—48no—
79C22×#135C2×C412yescomplemented
80C22×#135C2×C411yescharacteristic, complemented
81C22×#135C2×C412yescomplemented
82C22×#135C2×C411yescharacteristic, complemented
83C22×#135C2311yescharacteristic
84C22×#135C2312yes—
85C22×#135C2312yes—
86C22×#135C2311yescharacteristic
87C23×Q16C2×C411yescharacteristic, complemented
88C23×SD16—21no—
89C23×D8C2×C411yescharacteristic, complemented
90C23×D8C2311yescharacteristic
91C22×#131—22no—
92C24×C8C2311yescharacteristic
93C22×#121—21no—
94C2×#509—48no—
95C2×#509C2×C414yescomplemented
96C2×#509C2×C414yescomplemented
97C2×#509C2314yes—
98C2×#509C2314yes—
99C22×SD32C2×C414yescomplemented
100C22×D16C2×C414yescomplemented
101C22×M32C2312yes—
102C22×M32C2312yes—
103C2×#466—21no—
104C2×#466—21no—
105C2×#466—21no—
106C2×#466—21no—
107C2×#466—21no—
108C2×#466—21no—
109C2×#466C2×C412yes—
110C2×#466C2×C412yes—
111C2×#466C2×C412yes—
112C2×#466C2×C412yes—
113C2×#466C2312yes—
114C2×#466C2312yes—
115C2×#444—24no—
116C2×#444—48no—
117C2×#444C2318yes—
118C2×#442C2314yescomplemented
119C22×#108C2312yes—
120C2×#427C2312yes—
121C22×#107C2311yescharacteristic
122C22×#104—22no—
123C22×#104—22no—
124C22×#102—21no—
125#2880—24no—
126#2880—24no—
127#2880—42no—
128#2880—42no—
129C2×#408—22no—
130C2×#408—42no—
131C2×#407—21no—
132C2×#407—41no—
133C22×C22⋊C8—41no—
134C22×C22⋊C8D411yescharacteristic
135C22×#97C2312yes—
136#2364—42no—
137#2363—24no—
138#2345—22no—
139D4×C22⋊C4—22no—
140D4×C22⋊C4—42no—
141#2333—42no—
142#2312—41no—
143C4×#121—24no—
144#2280—21no—
145#2273—41no—
146C2×C4×C22⋊C4D411yescharacteristic
147#2186C2×C418yescomplemented
148#2186C2×C418yescomplemented
149#2186C2×C418yescomplemented
150#2186C2×C418yescomplemented
151#2185C2×C414yescomplemented
152#2185C2×C418yescomplemented
153#2185C2×C414yescomplemented
154#2184C2×C414yescomplemented
155#2184C2×C418yescomplemented
156#2184C2×C414yescomplemented
157AGL(1,ℤ/16)—416no—
158C2×#365C2318yescomplemented
159C2×#361C2318yescomplemented
160#2145—48no—
161C2×#360C2318yes—
162C2×#360C2318yes—
163#2139C2×C414yescomplemented
164#2139C2×C414yescomplemented
165#2139C2314yes—
166#2139C2314yes—
167C2×#358C2×C414yescomplemented
168C2×#357C2×C414yescomplemented
169#2112—21no—
170#2112—21no—
171#2112C2×C412yescomplemented
172#2112C2×C412yescomplemented
173#2112C2312yes—
174#2112C2312yes—
175#2112C2312yes—
176#2112C2312yes—
177C2×C22⋊C16—21no—
178C2×C22⋊C16—21no—
179C2×C22⋊C16C2×C412yescomplemented
180C2×C22⋊C16C2×C412yescomplemented
181C2×#347C2318yescomplemented
182#1975—24no—
183#1975C2318yes—
184#1972C2314yescomplemented
185#1943C2314yescomplemented
186#1936—24no—
187#1925—24no—
188#1918—24no—
189#1893—24no—
190#1879—24no—
191#1876—28no—
192#1876—28no—
193#1875—24no—
194#1862—24no—
195#1824—22no—
196#1810—21no—
197#1810—21no—
198#1810C2312yes—
199#1810C2312yes—
200#1808—21no—
201#1808—21no—
202#1807C2312yes—
203#1807C2312yes—
204#1789—24no—
205#1789—24no—
206#1786—22no—
207#1776C2314yescomplemented
208#1762—24no—
209#1752D412yes—
210#1752D412yes—
211#1752C2312yes—
212#1752C2312yes—
213C2×#341—21no—
214#1735—21no—
215C2×#336D412yes—
216#1387C2318yescomplemented
217#1383C2318yescomplemented
218#1375C2318yescomplemented
219C22×#41—21no—
220C22×#41—21no—
221C22×#41—22no—
222C22×#41—22no—
223C22×#41—21no—
224C22×#41—21no—
225C22×#41—22no—
226C22×#41—22no—
227C22×#41—41no—
228C22×#41—41no—
229C22×#41—41no—
230C22×#41—41no—
231C22×#41—41no—
232C22×#41—41no—
233C22×#41—48no—
234C22×#41—84no—
235C23×Q8—21no—
236C23×D4—21no—
237C23×D4—21no—
238C23×D4—41no—
239C23×D4—41no—
240C24×C4—41no—
241C24×C4C2×D411yescharacteristic
242C2×#135—28no—
243C2×#135—28no—
244C2×#135—28no—
245C2×#135—21no—
246C2×#135—22no—
247C2×#135—21no—
248C2×#135—21no—
249C2×#135—22no—
250C2×#135—21no—
251C2×#135—22no—
252C2×#135—22no—
253C2×#135—21no—
254C2×#135—22no—
255C2×#135—22no—
256C2×#135—21no—
257C2×#135—21no—
258C2×#135—22no—
259C2×#135—21no—
260C2×#135—22no—
261C2×#135—44no—
262C2×#135—44no—
263C2×#135—44no—
264C2×#135—44no—
265C2×#135—44no—
266C2×#135—44no—
267C2×#135—48no—
268C2×#135—44no—
269C2×#135—44no—
270C2×#135—44no—
271C2×#135—48no—
272C2×#135—48no—
273C2×#135—48no—
274C2×#135—48no—
275C2×#135—48no—
276C2×#135C22×C412yes—
277C2×#135C22×C412yes—
278C2×#135C22×C412yes—
279C2×#135C22×C412yes—
280C2×#135C22×C412yes—
281C2×#135C22×C412yes—
282C2×#135C2412yes—
283C2×#135C2412yes—
284C22×Q16—21no—
285C22×Q16—21no—
286C22×Q16—21no—
287C22×Q16—44no—
288C22×Q16C22×C411yescharacteristic
289C22×Q16C22×C412yes—
290C22×Q16C22×C412yes—
291C22×Q16C22×C411yescharacteristic
292C22×SD16—22no—
293C22×SD16—22no—
294C22×SD16—21no—
295C22×SD16—21no—
296C22×SD16—21no—
297C22×SD16—22no—
298C22×SD16—21no—
299C22×SD16—22no—
300C22×SD16—48no—
301C22×D8—21no—
302C22×D8—21no—
303C22×D8—21no—
304C22×D8—21no—
305C22×D8—21no—
306C22×D8—21no—
307C22×D8—44no—
308C22×D8—44no—
309C22×D8C22×C411yescharacteristic
310C22×D8C22×C412yes—
311C22×D8C22×C412yes—
312C22×D8C22×C412yes—
313C22×D8C22×C412yes—
314C22×D8C22×C411yescharacteristic
315C22×D8C2412yes—
316C2×#131—28no—
317C2×#131—44no—
318C2×#131—48no—
319C2×#131—84no—
320C22×M16—22no—
321C22×M16—42no—
322C23×C8—44no—
323C23×C8—42no—
324C23×C8C22×C411yescharacteristic
325C23×C8C22×C411yescharacteristic
326C23×C8C22×C411yescharacteristic
327C23×C8C22×C411yescharacteristic
328C23×C8C2×D412yes—
329C23×C8C2×D411yescharacteristic
330C23×C8C2×D411yescharacteristic
331C23×C8C2×D411yescharacteristic
332C23×C8#4111yescharacteristic
333C23×C8#4111yescharacteristic
334C23×C8#4111yescharacteristic
335C23×C8#4111yescharacteristic
336C23×C8C2411yescharacteristic
337C23×C8C2411yescharacteristic
338C23×C8C2411yescharacteristic
339C2×#121—22no—
340C2×#121—22no—
341C2×#121—22no—
342C2×#121—22no—
343C2×#121—22no—
344C2×#121—22no—
345C2×#121—41no—
346C2×#121—41no—
347C2×#121—41no—
348C2×#121—41no—
349C2×#121—41no—
350C2×#121—41no—
351C2×C4×D4—24no—
352C2×C4×D4—44no—
353C2×#117—22no—
354C22×C4⋊C4—21no—
355C22×C22⋊C4—21no—
356C22×C22⋊C4—42no—
357C22×C22⋊C4—41no—
358C22×C42C2×D412yes—
359#509—216no—
360#509—48no—
361#509—48no—
362#509—48no—
363C2×SD32—48no—
364C2×SD32C22×C418yes—
365C2×SD32C22×C418yes—
366C2×D16—48no—
367C2×D16C22×C418yes—
368C2×D16C22×C418yes—
369C2×M32—22no—
370C2×M32—44no—
371C2×M32—44no—
372C2×M32C22×C414yes—
373C2×M32C2414yes—
374C2×M32C2414yes—
375C22×C16—22no—
376C22×C16C22×C414yes—
377#466—22no—
378#466—22no—
379#466—22no—
380#466—22no—
381#466—22no—
382#466—22no—
383#466—22no—
384#466—22no—
385#466—22no—
386#466—22no—
387#466—22no—
388#466—22no—
389#466C22×C414yes—
390#466C22×C414yes—
391#466C22×C414yes—
392#466C22×C414yes—
393#444—216no—
394#444—48no—
395#444—416no—
396#442—48no—
397C2×#108—22no—
398C2×#108—44no—
399C2×#108C2414yes—
400#427—44no—
401C2×#107—21no—
402C2×#107—21no—
403C2×#107—21no—
404C2×#107—22no—
405C2×#107C22×C412yes—
406C2×#107C22×C412yes—
407C2×#107C2412yes—
408C2×#106C2414yes—
409C2×#104—28no—
410C2×#104—28no—
411C2×#104—48no—
412C2×#104—84no—
413C2×#102—22no—
414C2×#102—22no—
415C2×#102—22no—
416C2×#102—22no—
417C2×#102—22no—
418C2×#102—22no—
419C2×#102—24no—
420C2×#102—24no—
421#408—28no—
422#408—48no—
423#408—48no—
424#408—44no—
425#407—22no—
426#407—22no—
427#407—44no—
428#407—44no—
429#407—41no—
430#407—41no—
431C2×C22⋊C8—21no—
432C2×C22⋊C8—21no—
433C2×C22⋊C8—21no—
434C2×C22⋊C8—21no—
435C2×C22⋊C8—44no—
436C2×C22⋊C8—44no—
437C2×C22⋊C8—42no—
438C2×C22⋊C8—42no—
439C2×C22⋊C8—41no—
440C2×C22⋊C8—41no—
441C2×C22⋊C8C2×D412yes—
442C2×C22⋊C8C2×D412yes—
443C2×#97—44no—
444C2×#97C2×D414yes—
445C2×#97C2414yes—
446#390—24no—
447#390—44no—
448#389—24no—
449#388—44no—
450#388—44no—
451#387—44no—
452#386—44no—
453#386—44no—
454#386—44no—
455#381—41no—
456#380—22no—
457#380—22no—
458#380—42no—
459#379—42no—
460#379—41no—
461C4×C4⋊C4—24no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—44no—
465C4×C22⋊C4—44no—
466C4×C22⋊C4—42no—
467C4×C22⋊C4—41no—
468C4×C22⋊C4—41no—
469C4×C22⋊C4C2×D412yes—
470C4×C22⋊C4C2×D412yes—
471C2×#95—21no—
472#365—48no—
473#361—48no—
474#360—216no—
475#360—48no—
476#358C22×C418yes—
477#358C22×C418yes—
478#357C22×C418yes—
479#357C22×C418yes—
480C22⋊C16—22no—
481C22⋊C16—22no—
482C22⋊C16—22no—
483C22⋊C16—22no—
484C22⋊C16C22×C414yes—
485C22⋊C16C22×C414yes—
486C22⋊C16C22×C414yes—
487C22⋊C16C22×C414yes—
488#347—48no—
489#341—22no—
490#341—22no—
491#340—22no—
492#340—22no—
493#340—24no—
494#340—24no—
495#336C2×D414yes—
496#336C2×D414yes—
497C25—41no—
498C25—41no—
499C25AGL(1,ℤ/8)11yescharacteristic
500C2×#41—28no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—44no—
510C2×#41—48no—
511C2×#41—48no—
512C2×#41—44no—
513C2×#41—44no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—42no—
517C2×#41—42no—
518C2×#41—41no—
519C2×#41—42no—
520C2×#41—42no—
521C2×#41—41no—
522C2×#41—42no—
523C2×#41—42no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—44no—
531C2×#41—44no—
532C2×#41—48no—
533C2×#41—48no—
534C2×#41—84no—
535C2×#41—84no—
536C2×#41—88no—
537C2×#41—82no—
538C2×#41—82no—
539C2×#41—88no—
540C2×#41—84no—
541C2×#41—84no—
542C2×#41—88no—
543C2×#41—88no—
544C2×#41—88no—
545C2×#41—88no—
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—41no—
551C22×Q8—41no—
552C22×Q8—41no—
553C22×Q8—44no—
554C22×Q8—82no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—44no—
563C22×D4—41no—
564C22×D4—42no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4—41no—
568C22×D4—41no—
569C22×D4—42no—
570C22×D4—42no—
571C22×D4—41no—
572C22×D4—42no—
573C22×D4—42no—
574C22×D4—42no—
575C22×D4—42no—
576C22×D4—42no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—82no—
584C22×D4—82no—
585C22×D4—82no—
586C22×D4—88no—
587C22×D4—164no—
588C23×C4—22no—
589C23×C4—42no—
590C23×C4—42no—
591C23×C4—44no—
592C23×C4—41no—
593C23×C4—41no—
594C23×C4—41no—
595C23×C4—41no—
596C23×C4—42no—
597C23×C4—42no—
598C23×C4—41no—
599C23×C4—42no—
600C23×C4—42no—
601C23×C4—41no—
602C23×C4—88no—
603C23×C4C4×D411yescharacteristic
604C23×C4C4×D411yescharacteristic
605C23×C4C4×D411yescharacteristic
606C23×C4C4×D411yescharacteristic
607C23×C4AGL(1,ℤ/8)11yescharacteristic
608C23×C4AGL(1,ℤ/8)11yescharacteristic
609C23×C4AGL(1,ℤ/8)11yescharacteristic
610C23×C4AGL(1,ℤ/8)11yescharacteristic
611C23×C4AGL(1,ℤ/8)11yescharacteristic
612C23×C4AGL(1,ℤ/8)11yescharacteristic
613C23×C4AGL(1,ℤ/8)11yescharacteristic
614C23×C4C22×D411yescharacteristic
615C23×C4C22×D411yescharacteristic
616C23×C4C22×D411yescharacteristic
617#135—28no—
618#135—28no—
619#135—24no—
620#135—24no—
621#135—24no—
622#135—24no—
623#135—24no—
624#135—24no—
625#135—24no—
626#135—24no—
627#135—24no—
628#135—42no—
629#135—42no—
630#135—42no—
631#135—42no—
632#135—42no—
633#135—42no—
634#135—48no—
635#135—48no—
636#135—48no—
637#135—48no—
638#135—44no—
639#135—44no—
640#135—44no—
641#135—44no—
642#135—48no—
643#135—48no—
644#135—44no—
645#135—44no—
646#135—48no—
647#135—48no—
648#135H(5,𝔽2)18yes—
649C2×Q16—24no—
650C2×Q16—24no—
651C2×Q16—24no—
652C2×Q16—21no—
653C2×Q16—22no—
654C2×Q16—21no—
655C2×Q16—22no—
656C2×Q16—42no—
657C2×Q16—42no—
658C2×Q16—42no—
659C2×Q16—44no—
660C2×Q16—44no—
661C2×Q16—44no—
662C2×Q16C23×C412yes—
663C2×Q16C23×C412yes—
664C2×SD16—28no—
665C2×SD16—22no—
666C2×SD16—22no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—22no—
670C2×SD16—22no—
671C2×SD16—22no—
672C2×SD16—22no—
673C2×SD16—48no—
674C2×SD16—48no—
675C2×SD16—44no—
676C2×SD16—48no—
677C2×SD16—48no—
678C2×SD16—44no—
679C2×SD16—44no—
680C2×D8—24no—
681C2×D8—24no—
682C2×D8—24no—
683C2×D8—21no—
684C2×D8—22no—
685C2×D8—21no—
686C2×D8—22no—
687C2×D8—22no—
688C2×D8—22no—
689C2×D8—22no—
690C2×D8—28no—
691C2×D8—42no—
692C2×D8—42no—
693C2×D8—42no—
694C2×D8—44no—
695C2×D8—44no—
696C2×D8—44no—
697C2×D8—44no—
698C2×D8—44no—
699C2×D8—82no—
700C2×D8—82no—
701C2×D8—82no—
702C2×D8C23×C412yes—
703C2×D8C23×C414yes—
704C2×D8C23×C412yes—
705#131—416no—
706#131—88no—
707#131—816no—
708C2×M16—24no—
709C2×M16—48no—
710C2×M16—42no—
711C2×M16—44no—
712C2×M16—44no—
713C2×M16—88no—
714C22×C8—24no—
715C22×C8—24no—
716C22×C8—24no—
717C22×C8—22no—
718C22×C8—22no—
719C22×C8—42no—
720C22×C8—42no—
721C22×C8—42no—
722C22×C8—42no—
723C22×C8—42no—
724C22×C8—42no—
725C22×C8—42no—
726C22×C8—42no—
727C22×C8—42no—
728C22×C8—42no—
729C22×C8—42no—
730C22×C8—42no—
731C22×C8—42no—
732C22×C8—48no—
733C22×C8—42no—
734C22×C8—88no—
735C22×C8C4×D411yescharacteristic
736C22×C8C4×D411yescharacteristic
737C22×C8C4×D411yescharacteristic
738C22×C8C4×D411yescharacteristic
739C22×C8C4×D411yescharacteristic
740C22×C8C4×D411yescharacteristic
741C22×C8C4×D411yescharacteristic
742C22×C8C4×D411yescharacteristic
743C22×C8C4×D411yescharacteristic
744C22×C8C4×D411yescharacteristic
745C22×C8C4×D411yescharacteristic
746C22×C8C4×D411yescharacteristic
747C22×C8C23×C411yescharacteristic
748C22×C8C23×C411yescharacteristic
749C22×C8C23×C411yescharacteristic
750C22×C8C23×C411yescharacteristic
751C22×C8C23×C411yescharacteristic
752C22×C8C23×C411yescharacteristic
753C22×C8C22×D414yes—
754C22×C8C22×D411yescharacteristic
755C22×C8C22×D411yescharacteristic
756C22×C8C22×D411yescharacteristic
757C22×C8C2×#4111yescharacteristic
758C22×C8C2×#4111yescharacteristic
759C22×C8C2×#4111yescharacteristic
760C22×C8C2×#4111yescharacteristic
761C22×C8C2×#4111yescharacteristic
762C22×C8C2×#4111yescharacteristic
763C22×C8C2511yescharacteristic
764#121—24no—
765#121—24no—
766#121—24no—
767#121—24no—
768#121—42no—
769#121—42no—
770#121—42no—
771#121—42no—
772#121—42no—
773#121—42no—
774#121—42no—
775#121—42no—
776#121—42no—
777#121—42no—
778#121—42no—
779#121—42no—
780C4×D4—84no—
781C4×D4—84no—
782C4×D4—168no—
783#117—82no—
784#117—82no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—41no—
790C2×C4⋊C4—41no—
791C2×C4⋊C4—41no—
792C2×C4⋊C4—44no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—42no—
796C2×C22⋊C4—42no—
797C2×C22⋊C4—42no—
798C2×C22⋊C4—42no—
799C2×C22⋊C4—42no—
800C2×C22⋊C4—42no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—42no—
803C2×C22⋊C4—42no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—44no—
806C2×C22⋊C4—42no—
807C2×C22⋊C4—82no—
808C2×C22⋊C4—88no—
809C2×C42—22no—
810C2×C42—42no—
811C2×C42—42no—
812C2×C42—44no—
813C2×C42—42no—
814C2×C42C22×D414yes—
815SD32—216no—
816SD32—48no—
817D16—216no—
818D16—48no—
819M32—28no—
820M32—28no—
821M32—44no—
822M32—82no—
823C2×C16—24no—
824C2×C16—44no—
825C2×C16—82no—
826C2×C16C23×C418yes—
827#108—28no—
828#108—44no—
829#107—22no—
830#107—22no—
831#107—22no—
832#107—82no—
833#107C23×C414yes—
834#106—28no—
835#104—416no—
836#104—88no—
837#102—24no—
838#102—24no—
839#102—24no—
840#102—24no—
841#102—84no—
842#102—84no—
843C22⋊C8—22no—
844C22⋊C8—22no—
845C22⋊C8—22no—
846C22⋊C8—22no—
847C22⋊C8—48no—
848C22⋊C8—48no—
849C22⋊C8—42no—
850C22⋊C8—42no—
851C22⋊C8—42no—
852C22⋊C8—42no—
853#97—28no—
854#97—44no—
855#95—22no—
856#95—22no—
857#95—44no—
858#95—44no—
859#95—42no—
860#95—42no—
861C24—42no—
862C24—42no—
863C24—42no—
864C24—41no—
865C24—41no—
866C24—42no—
867C24—42no—
868C24—42no—
869C24—42no—
870C24—42no—
871C24—84no—
872C24—84no—
873C24—84no—
874C24—162no—
875C24—162no—
876C24—162no—
877C24#44211yescharacteristic
878C24#44211yescharacteristic
879C24#44211yescharacteristic
880C24#44211yescharacteristic
881C24C2×AGL(1,ℤ/8)11yescharacteristic
882C24C2×AGL(1,ℤ/8)11yescharacteristic
883C24C2×AGL(1,ℤ/8)11yescharacteristic
884#41—28no—
885#41—28no—
886#41—48no—
887#41—48no—
888#41—44no—
889#41—44no—
890#41—44no—
891#41—44no—
892#41—44no—
893#41—44no—
894#41—44no—
895#41—44no—
896#41—44no—
897#41—44no—
898#41—88no—
899#41—88no—
900#41—82no—
901#41—82no—
902#41—82no—
903#41—82no—
904#41—88no—
905#41—88no—
906#41—84no—
907#41—84no—
908#41—88no—
909#41—88no—
910#41—88no—
911#41—88no—
912#41—84no—
913#41—84no—
914#41—84no—
915#41—84no—
916C2×Q8—24no—
917C2×Q8—22no—
918C2×Q8—22no—
919C2×Q8—42no—
920C2×Q8—44no—
921C2×Q8—44no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—41no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—41no—
928C2×Q8—82no—
929C2×Q8—82no—
930C2×Q8—84no—
931C2×Q8—84no—
932C2×Q8—84no—
933C2×D4—24no—
934C2×D4—22no—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—48no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—41no—
957C2×D4—42no—
958C2×D4—41no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—42no—
964C2×D4—82no—
965C2×D4—82no—
966C2×D4—82no—
967C2×D4—82no—
968C2×D4—82no—
969C2×D4—82no—
970C2×D4—84no—
971C2×D4—84no—
972C2×D4—84no—
973C2×D4—84no—
974C2×D4—88no—
975C2×D4—88no—
976C2×D4—88no—
977C2×D4—88no—
978C2×D4—88no—
979C2×D4—84no—
980C2×D4—84no—
981C2×D4—162no—
982C2×D4—162no—
983C2×D4—162no—
984C2×D4—164no—
985C2×D4—164no—
986C2×D4—164no—
987C2×D4—164no—
988C2×D4—164no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—42no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—48no—
1012C22×C4—41no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—41no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—88no—
1030C22×C4—88no—
1031C22×C4—84no—
1032C22×C4—88no—
1033C22×C4—88no—
1034C22×C4—84no—
1035C22×C4—82no—
1036C22×C4—82no—
1037C22×C4—84no—
1038C22×C4—84no—
1039C22×C4—88no—
1040C22×C4—164no—
1041C22×C4—164no—
1042C22×C4—162no—
1043C22×C4#44211yescharacteristic
1044C22×C4#44211yescharacteristic
1045C22×C4#44211yescharacteristic
1046C22×C4#44211yescharacteristic
1047C22×C4#44211yescharacteristic
1048C22×C4#44211yescharacteristic
1049C22×C4#44211yescharacteristic
1050C22×C4#44211yescharacteristic
1051C22×C4#44211yescharacteristic
1052C22×C4#44211yescharacteristic
1053C22×C4#44211yescharacteristic
1054C22×C4#44211yescharacteristic
1055C22×C4C2×C4×D411yescharacteristic
1056C22×C4C2×C4×D411yescharacteristic
1057C22×C4C2×C4×D411yescharacteristic
1058C22×C4C2×C4×D411yescharacteristic
1059C22×C4C2×C4×D411yescharacteristic
1060C22×C4C2×C4×D411yescharacteristic
1061C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1062C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1063C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1064C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1065C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1066C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1067C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1068C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1069C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1070C22×C4C23×D411yescharacteristic
1071Q16—24no—
1072Q16—22no—
1073Q16—22no—
1074Q16—22no—
1075Q16—44no—
1076Q16—44no—
1077Q16—42no—
1078Q16#51814yes—
1079SD16—28no—
1080SD16—28no—
1081SD16—44no—
1082SD16—44no—
1083SD16—44no—
1084SD16—44no—
1085SD16—44no—
1086SD16—44no—
1087D8—24no—
1088D8—22no—
1089D8—28no—
1090D8—22no—
1091D8—22no—
1092D8—44no—
1093D8—44no—
1094D8—42no—
1095D8—44no—
1096D8—82no—
1097D8—82no—
1098D8#51814yes—
1099M16—44no—
1100M16—44no—
1101M16—816no—
1102M16—84no—
1103C2×C8—22no—
1104C2×C8—22no—
1105C2×C8—22no—
1106C2×C8—22no—
1107C2×C8—22no—
1108C2×C8—22no—
1109C2×C8—22no—
1110C2×C8—22no—
1111C2×C8—22no—
1112C2×C8—22no—
1113C2×C8—22no—
1114C2×C8—22no—
1115C2×C8—22no—
1116C2×C8—22no—
1117C2×C8—22no—
1118C2×C8—24no—
1119C2×C8—24no—
1120C2×C8—24no—
1121C2×C8—41no—
1122C2×C8—41no—
1123C2×C8—41no—
1124C2×C8—41no—
1125C2×C8—41no—
1126C2×C8—41no—
1127C2×C8—41no—
1128C2×C8—41no—
1129C2×C8—41no—
1130C2×C8—41no—
1131C2×C8—41no—
1132C2×C8—41no—
1133C2×C8—44no—
1134C2×C8—44no—
1135C2×C8—44no—
1136C2×C8—816no—
1137C2×C8—84no—
1138C2×C8C2×C4×D411yescharacteristic
1139C2×C8C2×C4×D411yescharacteristic
1140C2×C8C2×C4×D411yescharacteristic
1141C2×C8C2×C4×D411yescharacteristic
1142C2×C8C2×C4×D411yescharacteristic
1143C2×C8C2×C4×D411yescharacteristic
1144C2×C8C24×C411yescharacteristic
1145C2×C8C22×#4111yescharacteristic
1146C2×C8C2×H(5,𝔽2)14yes—
1147C4⋊C4—24no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—164no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—82no—
1160C22⋊C4—88no—
1161C22⋊C4—84no—
1162C22⋊C4—84no—
1163C22⋊C4—164no—
1164C22⋊C4—164no—
1165C22⋊C4—162no—
1166C42—24no—
1167C42—24no—
1168C42—82no—
1169C42—162no—
1170C42—164no—
1171C16—28no—
1172C16—44no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—44no—
1195C23—42no—
1196C23—44no—
1197C23—42no—
1198C23—84no—
1199C23—84no—
1200C23—82no—
1201C23—82no—
1202C23—84no—
1203C23—82no—
1204C23—82no—
1205C23—82no—
1206C23—84no—
1207C23—84no—
1208C23—88no—
1209C23—82no—
1210C23—84no—
1211C23—84no—
1212C23—82no—
1213C23—84no—
1214C23—162no—
1215C23—162no—
1216C23—162no—
1217C23—162no—
1218C23—162no—
1219C23—162no—
1220C23—1616no—
1221C23—328no—
1222C23C2×#44211yescharacteristic
1223C23C2×#44211yescharacteristic
1224C23C2×#44211yescharacteristic
1225C23C2×#44211yescharacteristic
1226C23C2×#44211yescharacteristic
1227C23C2×#44211yescharacteristic
1228C23C22×AGL(1,ℤ/8)11yescharacteristic
1229Q8—24no—
1230Q8—44no—
1231Q8—42no—
1232Q8—42no—
1233Q8—42no—
1234Q8—84no—
1235Q8—84no—
1236Q8—82no—
1237D4—24no—
1238D4—44no—
1239D4—48no—
1240D4—48no—
1241D4—42no—
1242D4—44no—
1243D4—42no—
1244D4—42no—
1245D4—44no—
1246D4—84no—
1247D4—84no—
1248D4—82no—
1249D4—84no—
1250D4—84no—
1251D4—84no—
1252D4—84no—
1253D4—84no—
1254D4—88no—
1255D4—84no—
1256D4—88no—
1257D4—84no—
1258D4—162no—
1259D4—162no—
1260D4—164no—
1261D4—164no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—48no—
1296C2×C4—44no—
1297C2×C4—42no—
1298C2×C4—48no—
1299C2×C4—44no—
1300C2×C4—44no—
1301C2×C4—44no—
1302C2×C4—44no—
1303C2×C4—42no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4—82no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—164no—
1320C2×C4—328no—
1321C2×C4C2×#44211yescharacteristic
1322C2×C4C2×#44211yescharacteristic
1323C2×C4C2×#44211yescharacteristic
1324C2×C4C2×#44211yescharacteristic
1325C2×C4C2×#44211yescharacteristic
1326C2×C4C2×#44211yescharacteristic
1327C2×C4C22×C4×D411yescharacteristic
1328C2×C4#348412yes—
1329C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1330C2×C4#358512yes—
1331C8—21no—
1332C8—21no—
1333C8—21no—
1334C8—21no—
1335C8—21no—
1336C8—21no—
1337C8—44no—
1338C8—84no—
1339C8C2×#51812yes—
1340C8#349012yes—
1341C22—21no—
1342C22—21no—
1343C22—21no—
1344C22—21no—
1345C22—21no—
1346C22—21no—
1347C22—21no—
1348C22—21no—
1349C22—21no—
1350C22—21no—
1351C22—21no—
1352C22—21no—
1353C22—21no—
1354C22—21no—
1355C22—21no—
1356C22—21no—
1357C22—21no—
1358C22—21no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—82no—
1364C22—82no—
1365C22—82no—
1366C22—88no—
1367C22—82no—
1368C22—82no—
1369C22—82no—
1370C22—82no—
1371C22—84no—
1372C22—82no—
1373C22—84no—
1374C22—84no—
1375C22—82no—
1376C22—168no—
1377C22—164no—
1378C22—164no—
1379C22—164no—
1380C22—168no—
1381C22—324no—
1382C22—324no—
1383C22#3346812yes—
1384C22#3347112yes—
1385C22C22×#44211yescharacteristic
1386C22#6156912yes—
1387C4—21no—
1388C4—21no—
1389C4—21no—
1390C4—21no—
1391C4—21no—
1392C4—21no—
1393C4—44no—
1394C4—84no—
1395C4—82no—
1396C4—84no—
1397C4—164no—
1398C4#3419811yescharacteristic
1399C4#6016811yescharacteristic
1400C4#6157112yes—
1401C2—22no—
1402C2—22no—
1403C2—22no—
1404C2—41no—
1405C2—41no—
1406C2—41no—
1407C2—41no—
1408C2—84no—
1409C2—162no—
1410C2—164no—
1411C2#638759311yescharacteristic
1412C2C2×#3346811yescharacteristic
1413C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radicalC2×#33520C2
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. #6389124C2semidirect
3. C2×#22452C2semidirect
4. #498122C2semidirect
5. #497707C2semidirect
6. #497422C2semidirect
7. #496832C2semidirect
8. #496668C2semidirect
9. #496279C2semidirect
10. #495721C2semidirect
11. #493522C2semidirect
12. #493273C2semidirect
16. C22×#444C22semidirect
19. #33520C4semidirect
20. #33520C4semidirect
21. #33520C4semidirect
25. C2×#2186C4semidirect
26. C2×#2185C4semidirect
27. C2×#2184C4semidirect
28. C2×AGL(1,ℤ/16)C22semidirect
29. C2×#2145C22semidirect
34. #23031C22semidirect
35. #22618C22semidirect
40. #22452C22semidirect
41. #22436C22semidirect
44. #21526C22semidirect
45. C2×#1975C22semidirect
51. #13249C22semidirect
52. #13153C22semidirect
53. #13143C22semidirect
54. #13067C22semidirect
55. #13040C22semidirect
56. #13037C22semidirect
57. #13004C22semidirect
58. #12955C22semidirect
59. #12930C22semidirect
60. #12928C22semidirect
61. #12871C22semidirect
62. #12831C22semidirect
63. #12736C22semidirect
65. #12735C22semidirect
66. #12735C22semidirect
67. #12650C22semidirect
68. #12616C22semidirect
69. #12616C22semidirect
70. #12605C22semidirect
79. C22×#135C2×C4semidirect
80. C22×#135C2×C4semidirect
81. C22×#135C2×C4semidirect
82. C22×#135C2×C4semidirect
87. C23×Q16C2×C4semidirect
89. C23×D8C2×C4semidirect
95. C2×#509C2×C4semidirect
96. C2×#509C2×C4semidirect
99. C22×SD32C2×C4semidirect
100. C22×D16C2×C4semidirect
118. C2×#442C23semidirect
147. #2186C2×C4semidirect
148. #2186C2×C4semidirect
149. #2186C2×C4semidirect
150. #2186C2×C4semidirect
151. #2185C2×C4semidirect
152. #2185C2×C4semidirect
153. #2185C2×C4semidirect
154. #2184C2×C4semidirect
155. #2184C2×C4semidirect
156. #2184C2×C4semidirect
158. C2×#365C23semidirect
159. C2×#361C23semidirect
163. #2139C2×C4semidirect
164. #2139C2×C4semidirect
167. C2×#358C2×C4semidirect
168. C2×#357C2×C4semidirect
171. #2112C2×C4semidirect
172. #2112C2×C4semidirect
179. C2×C22⋊C16C2×C4semidirect
180. C2×C22⋊C16C2×C4semidirect
181. C2×#347C23semidirect
184. #1972C23semidirect
185. #1943C23semidirect
207. #1776C23semidirect
216. #1387C23semidirect
217. #1383C23semidirect
218. #1375C23semidirect

Maximal subgroups

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

subgroupindex
C2×#335202
#63891242
C2×#224522
#4981222
#4977072
#4974222
#4968322
#4966682
#4962792
#4957212
#4935222
#4932732