Finite Group Databasebeta

← #72343005

Subgroups — #72343005

Order 1024.

2399 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623513C211yesmaximal, characteristic
2#6345725C211yesmaximal, characteristic, complemented
3C2×#18073C211yesmaximal, characteristic, complemented
4#484140C218yesmaximal, complemented
5#484043C214yesmaximal, complemented
6#484040C214yesmaximal, complemented
7#483924C214yesmaximal, complemented
8#483878C214yesmaximal, complemented
9C2×#12028C211yesmaximal, characteristic, complemented
10#481389C211yesmaximal, characteristic, complemented
11C2×#11651C211yesmaximal, characteristic, complemented
12#479970C211yesmaximal, characteristic, complemented
13C2×#3169C2211yescharacteristic
14C2×#3168C2211yescharacteristic
15#60288—21no—
16C2×#2935—21no—
17#33813C414yes—
18#33804C412yes—
19#33800C412yes—
20#33783C412yes—
21#33779C412yes—
22#33753C412yes—
23#33752C412yes—
24#33746C2214yes—
25#33674C2214yes—
26#33672C2212yes—
27#33669C2212yes—
28C2×#2163C2211yescharacteristic
29C2×#2163C2211yescharacteristic
30#18093C2214yescomplemented
31#18092—22no—
32#18073—22no—
33#18073—22no—
34#18073C2214yes—
35#18073C2214yescomplemented
36#18064C2212yescomplemented
37#18062C2212yescomplemented
38#18060—22no—
39#17978—22no—
40#17963C2214yes—
41C2×#1594C2212yescomplemented
42C2×#1586—22no—
43C2×#1580C2212yescomplemented
44C2×#1568C2211yescharacteristic
45C22×#334C2211yescharacteristic
46#17502—21no—
47C2×#1480—21no—
48C2×#1451C2211yescharacteristic
49#12089C2218yescomplemented
50#12087C2218yescomplemented
51#12080C2218yescomplemented
52#12078C2218yescomplemented
53#12078C2218yescomplemented
54#12077C2218yescomplemented
55#12067C2218yescomplemented
56#12065C2218yescomplemented
57#12028C2212yescomplemented
58#12028C2212yescomplemented
59#12028C2214yescomplemented
60C2×#1368C2214yescomplemented
61#11678C2214yes—
62#11667C2214yescomplemented
63#11654C2214yescomplemented
64#11651C2212yes—
65#11651C2212yes—
66#11651C2214yescomplemented
67C2×#1334C2212yescomplemented
68C2×#1333C2212yescomplemented
69#11415C2214yescomplemented
70#11413C2214yescomplemented
71#11413C2214yescomplemented
72C22×#131—41no—
73C2×#532—21no—
74C2×#529—21no—
75#3169—21no—
76#3169—21no—
77#3169—21no—
78#3169—21no—
79#3169C2×C412yes—
80#3169C2×C412yes—
81#3169C2312yes—
82#3169C2312yes—
83#3168—21no—
84#3168—21no—
85#3168—21no—
86#3168—21no—
87#3168C2×C412yes—
88#3168C2×C412yes—
89#3168C2312yes—
90#3168C2312yes—
91C2×#500C2×C411yescharacteristic
92C2×#499C2×C411yescharacteristic
93C2×#495C2×C411yescharacteristic
94C2×#493C2×C411yescharacteristic
95C2×#488—21no—
96C2×#486—21no—
97C2×#467C2×C411yescharacteristic
98C2×#466—21no—
99C2×#466C2×C411yescharacteristic
100C2×#466C2×C412yes—
101C2×#465—21no—
102#2994—24no—
103#2992—42no—
104#2984—22no—
105#2974—22no—
106#2973—41no—
107#2972—41no—
108#2968—42no—
109#2966—24no—
110C2×C4×Q16C2311yescharacteristic
111C2×C4×SD16—21no—
112C2×C4×D8—21no—
113C2×C4×D8C2311yescharacteristic
114C2×C4×D8C2312yes—
115#2935—24no—
116#2935—24no—
117#2935—42no—
118#2935—42no—
119C2×#436—22no—
120C2×#435—42no—
121C2×C8×D4—22no—
122#2924—42no—
123C2×#432—21no—
124C2×#431D411yescharacteristic
125C22×C4⋊C8—21no—
126C2×#408—41no—
127C2×C4×M16D411yescharacteristic
128C22×C4×C8C2311yescharacteristic
129#2255C2×C414yes—
130#2250C2×C414yes—
131#2244C2×C414yes—
132#2243C2×C414yes—
133#2235C2×C414yes—
134#2233C2×C414yes—
135#2232C2×C414yes—
136#2232C2×C414yes—
137#2228C2×C418yes—
138#2227C2×C414yes—
139#2226C2×C414yes—
140#2217C2×C418yes—
141#2215C2×C418yes—
142#2210C2×C418yes—
143#2207C2×C414yes—
144#2206C2×C414yes—
145#2187C2×C414yes—
146#2185C2×C414yes—
147#2184C2×C414yes—
148#2184C2×C414yes—
149#2177C2318yes—
150#2175C2318yes—
151#2163—21no—
152#2163—21no—
153#2163C2×C412yes—
154#2163C2×C412yes—
155#2163C2312yes—
156#2163C2312yes—
157#2163C2312yes—
158#2163C2312yes—
159C2×C4⋊C16—21no—
160C2×C4⋊C16C2×C412yes—
161C2×C22⋊C16—21no—
162C2×C22⋊C16C2×C412yes—
163C2×#346C2312yes—
164C2×#346C2312yes—
165#1594—24no—
166#1594C2314yes—
167#1594C2318yes—
168#1593C2314yes—
169#1592—24no—
170#1586—28no—
171#1586—28no—
172#1584—24no—
173#1583—24no—
174#1582—24no—
175#1581—24no—
176#1580—24no—
177#1580C2318yes—
178#1580C2314yes—
179#1579C2314yes—
180SD16⋊C8—24no—
181#1568—21no—
182#1568—21no—
183#1568C2312yes—
184#1568C2312yes—
185C2×#335—21no—
186C2×#334—21no—
187C2×#334—21no—
188C2×#334—21no—
189C2×#334C2312yes—
190C2×#334C2311yescharacteristic
191C2×#334C2311yescharacteristic
192C2×#334C2312yes—
193C2×#334C2312yes—
194#1494—24no—
195#1491—22no—
196#1490—22no—
197#1483—24no—
198#1480—24no—
199#1480—24no—
200C2×D4⋊C8—22no—
201C2×D4⋊C8—22no—
202#1451D412yes—
203#1451D412yes—
204#1451C2312yes—
205#1451C2312yes—
206C2×#322D412yes—
207C2×#322C2312yes—
208#1368C2318yes—
209#1368C2318yes—
210#1334C2314yes—
211#1334C2314yes—
212#1333C2318yes—
213#1333C2314yes—
214#1333C2318yes—
215#1333C2314yes—
216#1313C2318yes—
217#1313C2318yes—
218C22×#41—41no—
219C22×Q16C22×C411yescharacteristic
220C22×SD16—21no—
221C22×D8—21no—
222C22×D8C22×C412yes—
223C22×D8C22×C411yescharacteristic
224C2×#131—44no—
225C2×#131—44no—
226C2×#131—88no—
227C22×M16—21no—
228C22×M16—42no—
229C23×C8—42no—
230C23×C8—41no—
231C23×C8C22×C411yescharacteristic
232C23×C8#4111yescharacteristic
233#532—22no—
234#532—22no—
235#532—22no—
236#532—22no—
237#532—41no—
238#532—41no—
239#532—41no—
240#532—41no—
241C2×C4⋊Q8—21no—
242C2×#127—21no—
243#529—22no—
244#529—22no—
245#529—22no—
246#529—22no—
247#529—41no—
248#529—41no—
249#529—41no—
250#529—41no—
251C2×#126—41no—
252C2×#125—21no—
253C2×#124—21no—
254C2×#124—41no—
255C2×#123—41no—
256C2×C22⋊Q8—21no—
257C2×#121—21no—
258C2×#121—22no—
259C2×#121—41no—
260C2×C4×Q8—21no—
261C2×C4×D4—22no—
262C2×C4×D4—21no—
263C2×C4×D4—41no—
264C2×C4×D4—41no—
265C2×#117—41no—
266C22×C42C2×D411yescharacteristic
267C2×SD32C22×C418yes—
268C2×D16C22×C418yes—
269C22×C16—22no—
270C22×C16C22×C414yes—
271#500—21no—
272#500—21no—
273#500C22×C412yes—
274#500C22×C412yes—
275#499—21no—
276#499—21no—
277#499C22×C412yes—
278#499C22×C412yes—
279#495—21no—
280#495—21no—
281#495C22×C412yes—
282#495C22×C412yes—
283#493—21no—
284#493—21no—
285#493C22×C412yes—
286#493C22×C412yes—
287#488—22no—
288#488—22no—
289#488—22no—
290#488—22no—
291#486—22no—
292#486—22no—
293#486—22no—
294#486—22no—
295#467—21no—
296#467—21no—
297#467C22×C412yes—
298#467C22×C412yes—
299#466—21no—
300#466—21no—
301#466—22no—
302#466—22no—
303#466—22no—
304#466—22no—
305#466—22no—
306#466—22no—
307#466C22×C412yes—
308#466C22×C412yes—
309#466C22×C414yes—
310#466C22×C414yes—
311#465—22no—
312#465—22no—
313#465—22no—
314#465—22no—
315#446—24no—
316#446—44no—
317C8×Q8—24no—
318C4×Q16—21no—
319C4×Q16—21no—
320C4×Q16C22×C412yes—
321C4×Q16C2412yes—
322C4×SD16—22no—
323C4×SD16—22no—
324C4×SD16—22no—
325C4×SD16—22no—
326C4×D8—22no—
327C4×D8—22no—
328C4×D8—22no—
329C4×D8—21no—
330C4×D8—22no—
331C4×D8—22no—
332C4×D8—21no—
333C4×D8—22no—
334C4×D8C22×C412yes—
335C4×D8C22×C414yes—
336C4×D8C2412yes—
337C4×D8C2414yes—
338#436—24no—
339#436—28no—
340#436—44no—
341#435—48no—
342#435—48no—
343#435—44no—
344#435—44no—
345#435—44no—
346C8×D4—24no—
347C8×D4—28no—
348C8×D4—44no—
349C8×D4—44no—
350C8×D4—44no—
351#433—44no—
352#433—44no—
353#432—22no—
354#432—22no—
355#432—42no—
356#432—41no—
357#432—41no—
358#431—21no—
359#431—21no—
360#431—42no—
361#431C2×D412yes—
362#431C2×D412yes—
363C2×#107—21no—
364C2×#107C22×C411yescharacteristic
365C2×#107C22×C411yescharacteristic
366C2×#107C22×C412yes—
367C2×#106—21no—
368#424—44no—
369C2×C4⋊C8—21no—
370C2×C4⋊C8—21no—
371C2×C4⋊C8—21no—
372C2×C4⋊C8—22no—
373C2×C4⋊C8—22no—
374C2×C4⋊C8—22no—
375C2×C4⋊C8—41no—
376C2×C4⋊C8—41no—
377C2×C4⋊C8—41no—
378C2×#103—21no—
379C2×#103—21no—
380C2×#102—22no—
381C2×#102—21no—
382C2×#102—22no—
383C2×#102—21no—
384#408—44no—
385#408—44no—
386#407—42no—
387C2×C22⋊C8—21no—
388C2×C22⋊C8—42no—
389C2×C22⋊C8—42no—
390C2×C22⋊C8—42no—
391C2×C22⋊C8—41no—
392#405—44no—
393C4×M16—21no—
394C4×M16—21no—
395C4×M16C2×D412yes—
396C4×M16C2×D412yes—
397C2×#97—21no—
398C2×#97—41no—
399C2×C4×C8C22×C411yescharacteristic
400C2×C4×C8C22×C411yescharacteristic
401C2×C4×C8C22×C411yescharacteristic
402C2×C4×C8C2×D412yes—
403C2×C4×C8C2×D412yes—
404C2×C4×C8C2×D411yescharacteristic
405C2×C4×C8C2×D411yescharacteristic
406C2×C4×C8C2×D411yescharacteristic
407C2×C4×C8#4111yescharacteristic
408C2×C4×C8#4111yescharacteristic
409C2×C4×C8#4111yescharacteristic
410C2×C4×C8C2411yescharacteristic
411C2×C4×C8C2411yescharacteristic
412C2×C4×C8C2411yescharacteristic
413#367C22×C418yes—
414#366C22×C418yes—
415C4⋊C16—22no—
416C4⋊C16—22no—
417C4⋊C16C22×C414yes—
418C4⋊C16C22×C414yes—
419#358C22×C418yes—
420#357C22×C418yes—
421#357C22×C418yes—
422#357C22×C418yes—
423C22⋊C16—22no—
424C22⋊C16—22no—
425C22⋊C16C22×C414yes—
426C22⋊C16C22×C414yes—
427#346—22no—
428#346C22×C414yes—
429#346C2414yes—
430#346C2414yes—
431#335—22no—
432#335—22no—
433#334—21no—
434#334—22no—
435#334—22no—
436#334—21no—
437#334—22no—
438#334C2412yes—
439#334C2412yes—
440#334C2414yes—
441Q8⋊C8—24no—
442Q8⋊C8—24no—
443D4⋊C8—24no—
444D4⋊C8—28no—
445D4⋊C8—24no—
446D4⋊C8—28no—
447#322C2×D414yes—
448#322C2×D414yes—
449#322C2×D414yes—
450#322C2414yes—
451C2×#41—42no—
452C2×#41—42no—
453C2×#41—42no—
454C2×#41—42no—
455C2×#41—84no—
456C2×#41—84no—
457C22×Q8—21no—
458C22×Q8—41no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—41no—
462C22×D4—42no—
463C22×D4—41no—
464C22×D4—41no—
465C23×C4—42no—
466C23×C4—41no—
467C23×C4C4×D411yescharacteristic
468C23×C4AGL(1,ℤ/8)11yescharacteristic
469C23×C4AGL(1,ℤ/8)11yescharacteristic
470C2×Q16—21no—
471C2×Q16—42no—
472C2×Q16C23×C412yes—
473C2×SD16—22no—
474C2×SD16—22no—
475C2×SD16—82no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—22no—
479C2×D8—21no—
480C2×D8—44no—
481C2×D8—42no—
482C2×D8—82no—
483C2×D8C23×C414yes—
484C2×D8C23×C412yes—
485#131—816no—
486#131—816no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—48no—
490C2×M16—44no—
491C2×M16—44no—
492C2×M16—88no—
493C22×C8—22no—
494C22×C8—22no—
495C22×C8—42no—
496C22×C8—48no—
497C22×C8—44no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—42no—
501C22×C8—42no—
502C22×C8—42no—
503C22×C8—81no—
504C22×C8—88no—
505C22×C8—84no—
506C22×C8C4×D411yescharacteristic
507C22×C8C4×D411yescharacteristic
508C22×C8C4×D411yescharacteristic
509C22×C8C4×D411yescharacteristic
510C22×C8C4×D411yescharacteristic
511C22×C8C4×D411yescharacteristic
512C22×C8C23×C411yescharacteristic
513C22×C8C23×C411yescharacteristic
514C22×C8C23×C411yescharacteristic
515C22×C8C2×#4111yescharacteristic
516C22×C8C2×#4111yescharacteristic
517C22×C8C2×#4111yescharacteristic
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522#127—22no—
523#127—22no—
524#127—41no—
525#127—41no—
526#126—42no—
527#126—42no—
528#126—42no—
529#126—42no—
530#125—22no—
531#125—22no—
532#125—41no—
533#125—41no—
534#124—22no—
535#124—22no—
536#124—42no—
537#124—42no—
538#124—41no—
539#124—41no—
540#124—42no—
541#124—42no—
542#123—42no—
543#123—42no—
544#123—42no—
545#123—42no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550#121—22no—
551#121—22no—
552#121—24no—
553#121—24no—
554#121—42no—
555#121—42no—
556#121—41no—
557#121—41no—
558#121—42no—
559#121—42no—
560#121—42no—
561#121—42no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—22no—
567C4×D4—24no—
568C4×D4—22no—
569C4×D4—24no—
570C4×D4—42no—
571C4×D4—42no—
572C4×D4—42no—
573C4×D4—42no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—42no—
577C4×D4—42no—
578C4×D4—42no—
579C4×D4—42no—
580C4×D4—42no—
581C4×D4—42no—
582#117—42no—
583#117—42no—
584#117—42no—
585#117—42no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—41no—
601C2×C42—41no—
602C2×C42C4×D411yescharacteristic
603C2×C42C4×D411yescharacteristic
604C2×C42C4×D411yescharacteristic
605C2×C42AGL(1,ℤ/8)11yescharacteristic
606C2×C42AGL(1,ℤ/8)11yescharacteristic
607C2×C42AGL(1,ℤ/8)11yescharacteristic
608C2×C42AGL(1,ℤ/8)11yescharacteristic
609C2×C42AGL(1,ℤ/8)11yescharacteristic
610C2×C42AGL(1,ℤ/8)11yescharacteristic
611C2×C42C22×D411yescharacteristic
612C2×C42C22×D411yescharacteristic
613C2×C42C22×D411yescharacteristic
614SD32—48no—
615D16—48no—
616C2×C16—24no—
617C2×C16—44no—
618C2×C16—82no—
619C2×C16C23×C418yes—
620#107—22no—
621#107—22no—
622#107—22no—
623#107—21no—
624#107—21no—
625#107C23×C412yes—
626#107C23×C412yes—
627#107C23×C414yes—
628#106—22no—
629#106—22no—
630C4⋊C8—22no—
631C4⋊C8—22no—
632C4⋊C8—22no—
633C4⋊C8—22no—
634C4⋊C8—24no—
635C4⋊C8—44no—
636C4⋊C8—44no—
637C4⋊C8—41no—
638C4⋊C8—42no—
639C4⋊C8—42no—
640C4⋊C8—41no—
641C4⋊C8—42no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—22no—
646#102—24no—
647#102—24no—
648#102—22no—
649#102—24no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—24no—
654C22⋊C8—22no—
655C22⋊C8—22no—
656C22⋊C8—48no—
657C22⋊C8—48no—
658C22⋊C8—44no—
659C22⋊C8—44no—
660C22⋊C8—42no—
661C22⋊C8—42no—
662#97—22no—
663#97—22no—
664#97—44no—
665#97—42no—
666#97—42no—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—44no—
670C4×C8C4×D411yescharacteristic
671C4×C8C4×D411yescharacteristic
672C4×C8C4×D411yescharacteristic
673C4×C8C4×D411yescharacteristic
674C4×C8C4×D411yescharacteristic
675C4×C8C4×D411yescharacteristic
676C4×C8C23×C411yescharacteristic
677C4×C8C23×C411yescharacteristic
678C4×C8C23×C411yescharacteristic
679C4×C8C22×D414yes—
680C4×C8C22×D414yes—
681C4×C8C22×D411yescharacteristic
682C4×C8C22×D411yescharacteristic
683C4×C8C22×D411yescharacteristic
684C4×C8C2×#4111yescharacteristic
685C4×C8C2×#4111yescharacteristic
686C4×C8C2×#4111yescharacteristic
687C4×C8C2511yescharacteristic
688C24—42no—
689C24—41no—
690C24#44211yescharacteristic
691#41—84no—
692#41—84no—
693#41—84no—
694#41—84no—
695#41—88no—
696#41—88no—
697C2×Q8—22no—
698C2×Q8—42no—
699C2×Q8—42no—
700C2×Q8—41no—
701C2×Q8—84no—
702C2×Q8—81no—
703C2×Q8—81no—
704C2×D4—22no—
705C2×D4—24no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—88no—
723C2×D4—162no—
724C22×C4—24no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—42no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—44no—
732C22×C4—42no—
733C22×C4—44no—
734C22×C4—42no—
735C22×C4—84no—
736C22×C4—84no—
737C22×C4—81no—
738C22×C4—162no—
739C22×C4#44211yescharacteristic
740C22×C4#44211yescharacteristic
741C22×C4#44211yescharacteristic
742C22×C4#44211yescharacteristic
743C22×C4#44211yescharacteristic
744C22×C4#44211yescharacteristic
745C22×C4#44211yescharacteristic
746C22×C4#44211yescharacteristic
747C22×C4#44211yescharacteristic
748C22×C4C2×C4×D411yescharacteristic
749C22×C4C2×C4×D411yescharacteristic
750C22×C4C2×C4×D411yescharacteristic
751C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
752C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
753C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
754C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
755C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
756C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
757Q16—24no—
758Q16—81no—
759SD16—44no—
760SD16—82no—
761D8—24no—
762D8—28no—
763D8—44no—
764D8—81no—
765D8—82no—
766D8—82no—
767M16—44no—
768M16—44no—
769M16—816no—
770M16—164no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—24no—
775C2×C8—24no—
776C2×C8—41no—
777C2×C8—41no—
778C2×C8—41no—
779C2×C8—41no—
780C2×C8—41no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8—41no—
784C2×C8—41no—
785C2×C8—44no—
786C2×C8—44no—
787C2×C8—42no—
788C2×C8—42no—
789C2×C8—82no—
790C2×C8—816no—
791C2×C8—82no—
792C2×C8—82no—
793C2×C8—84no—
794C2×C8—84no—
795C2×C8—164no—
796C2×C8—162no—
797C2×C8C2×C4×D411yescharacteristic
798C2×C8C2×C4×D411yescharacteristic
799C2×C8C2×C4×D411yescharacteristic
800C2×C8C2×C4×D411yescharacteristic
801C2×C8C2×C4×D411yescharacteristic
802C2×C8C2×C4×D411yescharacteristic
803C2×C8C24×C411yescharacteristic
804C2×C8C22×#4111yescharacteristic
805C4⋊C4—24no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—42no—
809C4⋊C4—41no—
810C4⋊C4—41no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—42no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—44no—
828C22⋊C4—42no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—42no—
835C42—42no—
836C42—42no—
837C42#44211yescharacteristic
838C42#44211yescharacteristic
839C42#44211yescharacteristic
840C42#44211yescharacteristic
841C42#44211yescharacteristic
842C42#44211yescharacteristic
843C42C2×C4×D411yescharacteristic
844C42C2×C4×D411yescharacteristic
845C42C2×C4×D411yescharacteristic
846C42C2×AGL(1,ℤ/8)11yescharacteristic
847C42C2×AGL(1,ℤ/8)11yescharacteristic
848C42C2×AGL(1,ℤ/8)11yescharacteristic
849C42C2×AGL(1,ℤ/8)11yescharacteristic
850C42C2×AGL(1,ℤ/8)11yescharacteristic
851C42C2×AGL(1,ℤ/8)11yescharacteristic
852C42C23×D411yescharacteristic
853C16—28no—
854C16—44no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—44no—
859C23—84no—
860C23—84no—
861C23—84no—
862C23—82no—
863C23—161no—
864C23—161no—
865C23AGL(1,ℤ/16)14yes—
866C23C2×#44211yescharacteristic
867C23C2×#44211yescharacteristic
868C23C2×#44211yescharacteristic
869Q8—42no—
870Q8—42no—
871Q8—84no—
872Q8—84no—
873Q8—161no—
874D4—44no—
875D4—42no—
876D4—44no—
877D4—42no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882D4—84no—
883D4—88no—
884D4—88no—
885D4—161no—
886D4—162no—
887D4—162no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—44no—
913C2×C4—84no—
914C2×C4—84no—
915C2×C4—84no—
916C2×C4—88no—
917C2×C4—84no—
918C2×C4—82no—
919C2×C4—162no—
920C2×C4—161no—
921C2×C4—161no—
922C2×C4C2×#44211yescharacteristic
923C2×C4C2×#44211yescharacteristic
924C2×C4C2×#44211yescharacteristic
925C2×C4C2×#44211yescharacteristic
926C2×C4C2×#44211yescharacteristic
927C2×C4C2×#44211yescharacteristic
928C2×C4C2×#44211yescharacteristic
929C2×C4C2×#44211yescharacteristic
930C2×C4C2×#44211yescharacteristic
931C2×C4C22×C4×D411yescharacteristic
932C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
933C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
934C8—21no—
935C8—21no—
936C8—21no—
937C8—21no—
938C8—21no—
939C8—21no—
940C8—21no—
941C8—44no—
942C8—44no—
943C8—82no—
944C8—82no—
945C8—84no—
946C8#357312yes—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—44no—
954C22—84no—
955C22—82no—
956C22—82no—
957C22—84no—
958C22—84no—
959C22—82no—
960C22—168no—
961C22—322no—
962C22C2×AGL(1,ℤ/16)12yes—
963C22C2×AGL(1,ℤ/16)12yes—
964C22C2×AGL(1,ℤ/16)12yes—
965C22C22×#44211yescharacteristic
966C4—21no—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—21no—
972C4—21no—
973C4—21no—
974C4—21no—
975C4—21no—
976C4—21no—
977C4—84no—
978C4—82no—
979C4—82no—
980C4—82no—
981C4#6014211yescharacteristic
982C4#6018211yescharacteristic
983C2—22no—
984C2—22no—
985C2—22no—
986C2—164no—
987C2—162no—
988C2#634545811yescharacteristic
989C2C22×AGL(1,ℤ/16)11yescharacteristic
990C2#762263511yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623513C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1451 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6345725C2semidirect
3. C2×#18073C2semidirect
4. #484140C2semidirect
5. #484043C2semidirect
6. #484040C2semidirect
7. #483924C2semidirect
8. #483878C2semidirect
9. C2×#12028C2semidirect
10. #481389C2semidirect
11. C2×#11651C2semidirect
12. #479970C2semidirect
30. #18093C22semidirect
35. #18073C22semidirect
36. #18064C22semidirect
37. #18062C22semidirect
41. C2×#1594C22semidirect
43. C2×#1580C22semidirect
49. #12089C22semidirect
50. #12087C22semidirect
51. #12080C22semidirect
52. #12078C22semidirect
53. #12078C22semidirect
54. #12077C22semidirect
55. #12067C22semidirect
56. #12065C22semidirect
57. #12028C22semidirect
58. #12028C22semidirect
59. #12028C22semidirect
60. C2×#1368C22semidirect
62. #11667C22semidirect
63. #11654C22semidirect
66. #11651C22semidirect
67. C2×#1334C22semidirect
68. C2×#1333C22semidirect
69. #11415C22semidirect
70. #11413C22semidirect
71. #11413C22semidirect

Maximal subgroups

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

subgroupindex
#76235132
#63457252
C2×#180732
#4841402
#4840432
#4840402
#4839242
#4838782
C2×#120282
#4813892
C2×#116512
#4799702