Finite Group Databasebeta

← C2×#494893 #72320767

Subgroups — C2×#494893 #72320767

Order 1024.

5165 conjugacy classes of subgroups.

The subgroup lattice has 977 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#365C211yesmaximal, characteristic, complemented
2C23×#360C211yesmaximal, characteristic
3C2×#33380C211yesmaximal, characteristic
4C2×#21240C211yesmaximal, characteristic
5C2×#20454C211yesmaximal, characteristic, complemented
6#494893C2116yesmaximal, direct product factor
7C2×#13143C218yesmaximal, complemented
8C2×#12569C211yesmaximal, characteristic, complemented
9C2×#12547C211yesmaximal, characteristic, complemented
10C23×#135C2211yescharacteristic
11C23×M32C2211yescharacteristic
12C23×M32C2211yescharacteristic
13C23×#108C2211yescharacteristic
14C22×#427C2211yescharacteristic
15C23×#106C2211yescharacteristic
16C22×#421—21no—
17C2×#2879—21no—
18C22×#405C2211yescharacteristic
19C2×#2274—21no—
20C22×#365—28no—
21C22×#365C2214yescomplemented
22C22×#365C2218yescomplemented
23C22×#360—28no—
24C22×#360C2214yes—
25C22×#360C2218yes—
26#33380C418yescomplemented
27#33380C2218yes—
28C2×#2139C2214yes—
29C2×#2141C412yescomplemented
30C2×#2140C412yescomplemented
31C2×#2138C414yescomplemented
32#21240—24no—
33#21240C2218yes—
34C2×#1975C2214yes—
35C2×#1974—22no—
36#20454—24no—
37#20454C2218yescomplemented
38C2×#1776C2214yescomplemented
39C2×C4×#106—22no—
40C2×#1736—21no—
41#13143C22164yescomplemented
42#12569C2218yescomplemented
43C2×#1387C2214yescomplemented
44#12547C2218yescomplemented
45C2×#1375C2214yescomplemented
46C23×#41—21no—
47C22×#135—21no—
48C22×#135—22no—
49C22×#135—24no—
50C22×#135—21no—
51C22×#135—22no—
52C22×#135—24no—
53C22×#135—24no—
54C22×#135—24no—
55C22×#135C2×C412yes—
56C22×#135C2×C414yes—
57C22×#135C2312yes—
58C22×#135C2314yes—
59C23×Q16C2×C411yescharacteristic
60C23×SD16—21no—
61C23×D8C2×C411yescharacteristic
62C23×M16—21no—
63C23×M16D411yescharacteristic
64C24×C8C2311yescharacteristic
65C22×#117—21no—
66C22×#117D411yescharacteristic
67C23×C4⋊C4—21no—
68C22×M32—24no—
69C22×M32—24no—
70C22×M32—24no—
71C22×M32—21no—
72C22×M32—22no—
73C22×M32—24no—
74C22×M32C2×C412yes—
75C22×M32C2×C414yes—
76C22×M32C2312yes—
77C22×M32C2314yes—
78C22×M32C2312yes—
79C22×M32C2314yes—
80C23×C16—21no—
81C23×C16C2×C412yes—
82C22×#108—21no—
83C22×#108—22no—
84C22×#108—24no—
85C22×#108—24no—
86C22×#108C2312yes—
87C22×#108C2314yes—
88C2×#427—22no—
89C2×#427—21no—
90C2×#427—21no—
91C2×#427—22no—
92C2×#427C2×C412yes—
93C2×#427C2×C412yes—
94C2×#427C2×C414yes—
95C2×#427C2314yes—
96C22×#107C2312yes—
97C22×#106—21no—
98C22×#106—22no—
99C22×#106—21no—
100C22×#106—24no—
101C22×#106D418yes—
102C22×#106C2312yes—
103C22×#106C2314yes—
104C2×#421—28no—
105C2×#421—48no—
106C22×#104—24no—
107#2879—28no—
108#2879—44no—
109C2×#408—24no—
110C2×#408—42no—
111C2×#407—42no—
112C2×#405—24no—
113C2×#405—24no—
114C2×#405D414yes—
115C2×#405C2314yes—
116C22×#97C2312yes—
117C22×C4×C8D412yes—
118#2274—28no—
119#2274—44no—
120C2×C4×C4⋊C4—24no—
121C2×C4×C4⋊C4—42no—
122C2×C4×C22⋊C4—42no—
123C2×#365—216no—
124C2×#365—232no—
125C2×#365C23116yescomplemented
126C2×#360—216no—
127C2×#360—232no—
128C2×#360C23116yes—
129#2141C2×C4116yescomplemented
130#2140C2×C4116yescomplemented
131#2139C2×C4116yescomplemented
132#2139C23116yes—
133#2138C2×C4132yescomplemented
134C2×#358C2×C418yescomplemented
135C2×#357C2×C418yescomplemented
136#1975—28no—
137#1975C23116yes—
138#1974—216no—
139#1776—28no—
140#1776C23116yescomplemented
141C4×#106—216no—
142#1736—28no—
143C2×#340—24no—
144#1387C23116yescomplemented
145#1375C23116yescomplemented
146C22×#41—22no—
147C22×#41—24no—
148C22×#41—22no—
149C22×#41—24no—
150C22×#41—41no—
151C22×#41—42no—
152C22×#41—41no—
153C22×#41—42no—
154C22×#41—44no—
155C22×#41—44no—
156C22×#41—44no—
157C22×#41—44no—
158C23×Q8—21no—
159C23×D4—21no—
160C23×D4—41no—
161C24×C4—41no—
162C24×C4—41no—
163C24×C4C2×D411yescharacteristic
164C2×#135—28no—
165C2×#135—216no—
166C2×#135—24no—
167C2×#135—24no—
168C2×#135—24no—
169C2×#135—28no—
170C2×#135—216no—
171C2×#135—24no—
172C2×#135—22no—
173C2×#135—24no—
174C2×#135—28no—
175C2×#135—22no—
176C2×#135—24no—
177C2×#135—24no—
178C2×#135—28no—
179C2×#135—24no—
180C2×#135—28no—
181C2×#135—24no—
182C2×#135—28no—
183C2×#135—44no—
184C2×#135—48no—
185C2×#135—44no—
186C2×#135—48no—
187C2×#135—44no—
188C2×#135—48no—
189C2×#135—44no—
190C2×#135—48no—
191C2×#135C22×C418yes—
192C2×#135C22×C414yes—
193C2×#135C2414yes—
194C22×Q16—24no—
195C22×Q16—24no—
196C22×Q16—21no—
197C22×Q16—22no—
198C22×Q16C22×C412yes—
199C22×Q16C22×C414yes—
200C22×SD16—22no—
201C22×SD16—24no—
202C22×SD16—22no—
203C22×SD16—24no—
204C22×SD16—44no—
205C22×SD16—44no—
206C22×D8—24no—
207C22×D8—24no—
208C22×D8—21no—
209C22×D8—22no—
210C22×D8C22×C412yes—
211C22×D8C22×C414yes—
212C22×M16—24no—
213C22×M16—24no—
214C22×M16—21no—
215C22×M16—21no—
216C22×M16—22no—
217C22×M16—22no—
218C22×M16—24no—
219C22×M16—41no—
220C22×M16—42no—
221C22×M16—44no—
222C22×M16—44no—
223C22×M16C2×D414yes—
224C23×C8—41no—
225C23×C8C22×C411yescharacteristic
226C23×C8C22×C411yescharacteristic
227C23×C8C22×C412yes—
228C23×C8C2×D412yes—
229C23×C8C2×D411yescharacteristic
230C23×C8C2×D412yes—
231C23×C8C2×D414yes—
232C23×C8#4114yes—
233C23×C8#4114yes—
234C23×C8#4114yes—
235C23×C8#4111yescharacteristic
236C23×C8#4111yescharacteristic
237C23×C8#4112yes—
238C23×C8C2411yescharacteristic
239C23×C8C2412yes—
240C2×#117—24no—
241C2×#117—22no—
242C2×#117—22no—
243C2×#117—22no—
244C2×#117—24no—
245C2×#117—24no—
246C2×#117—41no—
247C2×#117—41no—
248C2×#117—42no—
249C2×#117—42no—
250C2×#117SD1618yes—
251C2×#117C2×D414yes—
252C22×C4⋊C4—21no—
253C22×C4⋊C4—28no—
254C22×C4⋊C4—22no—
255C22×C4⋊C4—24no—
256C22×C4⋊C4—22no—
257C22×C4⋊C4—44no—
258C22×C4⋊C4—41no—
259C22×C4⋊C4—42no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—41no—
262C22×C42—41no—
263C22×C42—44no—
264C22×C42C2×D412yes—
265C2×M32—28no—
266C2×M32—216no—
267C2×M32—24no—
268C2×M32—28no—
269C2×M32—24no—
270C2×M32—28no—
271C2×M32—22no—
272C2×M32—24no—
273C2×M32—24no—
274C2×M32—28no—
275C2×M32—24no—
276C2×M32—28no—
277C2×M32—44no—
278C2×M32—48no—
279C2×M32C22×C414yes—
280C2×M32C22×C418yes—
281C2×M32C2414yes—
282C2×M32C2414yes—
283C22×C16—28no—
284C22×C16—22no—
285C22×C16—24no—
286C22×C16—44no—
287C22×C16C22×C414yes—
288C22×C16C22×C418yes—
289C2×#108—24no—
290C2×#108—28no—
291C2×#108—24no—
292C2×#108—28no—
293C2×#108—24no—
294C2×#108—22no—
295C2×#108—44no—
296C2×#108—48no—
297C2×#108C2414yes—
298#427—24no—
299#427—24no—
300#427—24no—
301#427—24no—
302#427—24no—
303#427—24no—
304#427C22×C418yes—
305#427C22×C418yes—
306C2×#107—22no—
307C2×#107—22no—
308C2×#107—22no—
309C2×#107C22×C414yes—
310C2×#107C22×C414yes—
311C2×#107C2414yes—
312C2×#106—22no—
313C2×#106—22no—
314C2×#106—24no—
315C2×#106—28no—
316C2×#106—216no—
317C2×#106—24no—
318C2×#106—22no—
319C2×#106—24no—
320C2×#106—24no—
321C2×#106—28no—
322C2×#106C2×D418yes—
323C2×#106C2×D4116yes—
324C2×#106C2414yes—
325#421—432no—
326C2×#104—216no—
327C2×#104—416no—
328#408—216no—
329#408—48no—
330#408—416no—
331#407—416no—
332C2×C22⋊C8—48no—
333#405—216no—
334#405—28no—
335#405—28no—
336C2×#97—24no—
337C2×#97—24no—
338C2×#97C2×D414yes—
339C2×#97C2414yes—
340C2×C4×C8—28no—
341C2×C4×C8C2×D418yes—
342C4×C4⋊C4—216no—
343C4×C4⋊C4—48no—
344C4×C4⋊C4—416no—
345C4×C22⋊C4—416no—
346C2×#95—44no—
347#365—232no—
348#360—232no—
349#358C22×C4132yescomplemented
350#357C22×C4132yescomplemented
351#340—216no—
352C25—41no—
353C25AGL(1,ℤ/8)11yescharacteristic
354C2×#41—24no—
355C2×#41—28no—
356C2×#41—24no—
357C2×#41—42no—
358C2×#41—44no—
359C2×#41—42no—
360C2×#41—44no—
361C2×#41—44no—
362C2×#41—44no—
363C2×#41—44no—
364C2×#41—44no—
365C2×#41—48no—
366C2×#41—44no—
367C2×#41—48no—
368C2×#41—44no—
369C2×#41—48no—
370C2×#41—44no—
371C2×#41—48no—
372C2×#41—48no—
373C2×#41—416no—
374C2×#41—48no—
375C2×#41—416no—
376C2×#41—84no—
377C2×#41—88no—
378C2×#41—84no—
379C2×#41—88no—
380C2×#41—84no—
381C2×#41—88no—
382C2×#41—84no—
383C2×#41—88no—
384C22×Q8—24no—
385C22×Q8—22no—
386C22×Q8—42no—
387C22×Q8—41no—
388C22×Q8—44no—
389C22×Q8—44no—
390C22×D4—24no—
391C22×D4—22no—
392C22×D4—44no—
393C22×D4—42no—
394C22×D4—44no—
395C22×D4—42no—
396C22×D4—44no—
397C22×D4—44no—
398C22×D4—42no—
399C22×D4—41no—
400C22×D4—84no—
401C22×D4—84no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—41no—
406C23×C4—44no—
407C23×C4—48no—
408C23×C4—42no—
409C23×C4—44no—
410C23×C4—44no—
411C23×C4—42no—
412C23×C4—84no—
413C23×C4—84no—
414C23×C4—164no—
415C23×C4C4×D411yescharacteristic
416C23×C4C4×D412yes—
417C23×C4C4×D411yescharacteristic
418C23×C4#12114yes—
419C23×C4#12314yes—
420C23×C4C2×SD1614yes—
421C23×C4#13514yes—
422C23×C4AGL(1,ℤ/8)11yescharacteristic
423C23×C4AGL(1,ℤ/8)11yescharacteristic
424C23×C4AGL(1,ℤ/8)12yes—
425C23×C4AGL(1,ℤ/8)11yescharacteristic
426C23×C4AGL(1,ℤ/8)12yes—
427C23×C4C22×D411yescharacteristic
428C23×C4C22×D412yes—
429#135—216no—
430#135—28no—
431#135—216no—
432#135—28no—
433#135—24no—
434#135—24no—
435#135—24no—
436#135—24no—
437#135—48no—
438#135—44no—
439#135—48no—
440#135—44no—
441#135—44no—
442#135—48no—
443#135—44no—
444#135—48no—
445#135—416no—
446#135—416no—
447#135—416no—
448C2×Q16—24no—
449C2×Q16—28no—
450C2×Q16—24no—
451C2×Q16—28no—
452C2×Q16—24no—
453C2×Q16—22no—
454C2×Q16—44no—
455C2×Q16—48no—
456C2×Q16C23×C414yes—
457C2×SD16—28no—
458C2×SD16—24no—
459C2×SD16—24no—
460C2×SD16—44no—
461C2×SD16—48no—
462C2×SD16—44no—
463C2×SD16—48no—
464C2×SD16—48no—
465C2×SD16—416no—
466C2×D8—24no—
467C2×D8—28no—
468C2×D8—24no—
469C2×D8—28no—
470C2×D8—24no—
471C2×D8—22no—
472C2×D8—44no—
473C2×D8—48no—
474C2×D8C23×C414yes—
475C2×M16—28no—
476C2×M16—28no—
477C2×M16—24no—
478C2×M16—24no—
479C2×M16—24no—
480C2×M16—44no—
481C2×M16—44no—
482C2×M16—48no—
483C2×M16—44no—
484C2×M16—42no—
485C2×M16—44no—
486C2×M16—48no—
487C2×M16—44no—
488C2×M16—48no—
489C2×M16—84no—
490C2×M16—88no—
491C22×C8—24no—
492C22×C8—24no—
493C22×C8—22no—
494C22×C8—22no—
495C22×C8—42no—
496C22×C8—44no—
497C22×C8—84no—
498C22×C8#11714yes—
499C22×C8#11714yes—
500C22×C8#11718yes—
501C22×C8C4×D414yes—
502C22×C8C4×D414yes—
503C22×C8C4×D418yes—
504C22×C8C4×D411yescharacteristic
505C22×C8C4×D412yes—
506C22×C8C4×D411yescharacteristic
507C22×C8C4×D412yes—
508C22×C8C4×D412yes—
509C22×C8C4×D412yes—
510C22×C8C4×D412yes—
511C22×C8#12114yes—
512C22×C8#12118yes—
513C22×C8#12314yes—
514C22×C8#12318yes—
515C22×C8#12414yes—
516C22×C8#12414yes—
517C22×C8#12418yes—
518C22×C8#12614yes—
519C22×C8#12614yes—
520C22×C8#12618yes—
521C22×C8C23×C411yescharacteristic
522C22×C8C23×C412yes—
523C22×C8C23×C411yescharacteristic
524C22×C8C23×C412yes—
525C22×C8C22×D414yes—
526C22×C8C22×D412yes—
527C22×C8C22×D411yescharacteristic
528C22×C8C22×D412yes—
529C22×C8C22×D414yes—
530C22×C8C2×#4112yes—
531C22×C8C2×#4114yes—
532C22×C8C2×#4112yes—
533C22×C8C2×#4114yes—
534C22×C8C2×#4112yes—
535C22×C8C2×#4114yes—
536C22×C8C2×#4111yescharacteristic
537C22×C8C2×#4112yes—
538C22×C8C2×#4111yescharacteristic
539C22×C8C2×#4112yes—
540C22×C8C2511yescharacteristic
541#117—28no—
542#117—216no—
543#117—28no—
544#117—28no—
545#117—44no—
546#117—44no—
547#117—44no—
548#117—44no—
549#117—44no—
550#117—44no—
551#117C2×SD16116yes—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4—48no—
562C2×C4⋊C4—42no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—42no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4—42no—
567C2×C4⋊C4—48no—
568C2×C4⋊C4—416no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—28no—
571C2×C22⋊C4—44no—
572C2×C22⋊C4—44no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C42—24no—
576C2×C42—22no—
577C2×C42—44no—
578C2×C42—44no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—416no—
582C2×C42—168no—
583C2×C42C2×SD1618yes—
584C2×C42C22×D414yes—
585M32—216no—
586M32—28no—
587M32—24no—
588M32—24no—
589M32—24no—
590M32—24no—
591M32—44no—
592M32—48no—
593C2×C16—28no—
594C2×C16—216no—
595C2×C16—24no—
596C2×C16—44no—
597C2×C16—48no—
598C2×C16C23×C418yes—
599#108—24no—
600#108—24no—
601#108—48no—
602#108—44no—
603#107—24no—
604#107—24no—
605#107—24no—
606#107C23×C418yes—
607#106—28no—
608#106—28no—
609#106—216no—
610#106—28no—
611#106—24no—
612#106C22×D418yes—
613#104—432no—
614C22⋊C8—432no—
615#97—28no—
616#97—24no—
617#97—24no—
618C4×C8—216no—
619#95—416no—
620C24—44no—
621C24—42no—
622C24—44no—
623C24—84no—
624C24—164no—
625C24#44211yescharacteristic
626C24#44211yescharacteristic
627C24#44212yes—
628C24#46314yes—
629C24#48114yes—
630C24C2×AGL(1,ℤ/8)11yescharacteristic
631C24C2×AGL(1,ℤ/8)12yes—
632#41—44no—
633#41—44no—
634#41—48no—
635#41—416no—
636#41—416no—
637#41—48no—
638#41—44no—
639#41—44no—
640#41—84no—
641#41—88no—
642#41—84no—
643#41—88no—
644#41—816no—
645#41—816no—
646#41—816no—
647#41—84no—
648#41—88no—
649#41—88no—
650#41—84no—
651C2×Q8—24no—
652C2×Q8—44no—
653C2×Q8—42no—
654C2×Q8—44no—
655C2×Q8—48no—
656C2×Q8—48no—
657C2×Q8—44no—
658C2×Q8—88no—
659C2×Q8—84no—
660C2×D4—24no—
661C2×D4—48no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—48no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—48no—
669C2×D4—44no—
670C2×D4—84no—
671C2×D4—88no—
672C2×D4—88no—
673C2×D4—816no—
674C2×D4—84no—
675C2×D4—88no—
676C2×D4—88no—
677C2×D4—84no—
678C22×C4—28no—
679C22×C4—24no—
680C22×C4—48no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—42no—
685C22×C4—48no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—416no—
689C22×C4—48no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—84no—
693C22×C4—88no—
694C22×C4—84no—
695C22×C4—84no—
696C22×C4—84no—
697C22×C4—88no—
698C22×C4—816no—
699C22×C4—88no—
700C22×C4—84no—
701C22×C4—88no—
702C22×C4—168no—
703C22×C4—1616no—
704C22×C4#38814yes—
705C22×C4#38814yes—
706C22×C4#38818yes—
707C22×C4C4×SD1614yes—
708C22×C4C4×SD1614yes—
709C22×C4C4×SD1618yes—
710C22×C4#44212yes—
711C22×C4#44212yes—
712C22×C4#44212yes—
713C22×C4#44212yes—
714C22×C4#44212yes—
715C22×C4#44211yescharacteristic
716C22×C4#44211yescharacteristic
717C22×C4#46014yes—
718C22×C4#46014yes—
719C22×C4#46018yes—
720C22×C4#46314yes—
721C22×C4#46318yes—
722C22×C4#48114yes—
723C22×C4#48118yes—
724C22×C4#48214yes—
725C22×C4#48214yes—
726C22×C4#48218yes—
727C22×C4C2×C4×D411yescharacteristic
728C22×C4C2×C4×D412yes—
729C22×C4C2×C4×D412yes—
730C22×C4C2×C4×D411yescharacteristic
731C22×C4C2×#12112yes—
732C22×C4C2×#12114yes—
733C22×C4C2×#12312yes—
734C22×C4C2×#12314yes—
735C22×C4C22×SD1612yes—
736C22×C4C22×SD1614yes—
737C22×C4C2×#13512yes—
738C22×C4C2×#13514yes—
739C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
740C22×C4C2×AGL(1,ℤ/8)12yes—
741C22×C4C2×AGL(1,ℤ/8)12yes—
742C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
743C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
744C22×C4C2×AGL(1,ℤ/8)12yes—
745C22×C4C23×D411yescharacteristic
746Q16—24no—
747Q16—24no—
748Q16—44no—
749Q16—48no—
750SD16—44no—
751SD16—44no—
752SD16—416no—
753SD16—48no—
754D8—24no—
755D8—24no—
756D8—44no—
757D8—48no—
758M16—48no—
759M16—48no—
760M16—44no—
761M16—44no—
762M16—88no—
763M16—84no—
764C2×C8—24no—
765C2×C8—24no—
766C2×C8—24no—
767C2×C8—44no—
768C2×C8—44no—
769C2×C8—44no—
770C2×C8—84no—
771C2×C8—88no—
772C2×C8#38814yes—
773C2×C8#38818yes—
774C2×C8#38814yes—
775C2×C8#38818yes—
776C2×C8#38818yes—
777C2×C8#38818yes—
778C2×C8#38818yes—
779C2×C8C2×#11712yes—
780C2×C8C2×#11714yes—
781C2×C8C2×#11712yes—
782C2×C8C2×#11714yes—
783C2×C8C2×C4×D412yes—
784C2×C8C2×C4×D414yes—
785C2×C8C2×C4×D414yes—
786C2×C8C2×C4×D412yes—
787C2×C8C2×C4×D412yes—
788C2×C8C2×C4×D412yes—
789C2×C8C2×C4×D411yescharacteristic
790C2×C8C2×C4×D411yescharacteristic
791C2×C8C2×#12114yes—
792C2×C8C2×#12112yes—
793C2×C8C2×#12314yes—
794C2×C8C2×#12312yes—
795C2×C8C2×#12412yes—
796C2×C8C2×#12414yes—
797C2×C8C2×#12412yes—
798C2×C8C2×#12414yes—
799C2×C8C2×#12612yes—
800C2×C8C2×#12614yes—
801C2×C8C2×#12612yes—
802C2×C8C2×#12614yes—
803C2×C8C24×C411yescharacteristic
804C2×C8C23×D411yescharacteristic
805C2×C8C22×#4111yescharacteristic
806C2×C8C22×#4111yescharacteristic
807C2×C8C22×#4111yescharacteristic
808C2×C8C22×#4111yescharacteristic
809C4⋊C4—216no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—416no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C22⋊C4—216no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C42—28no—
822C42—24no—
823C42—48no—
824C42—48no—
825C42—1616no—
826C42C22×SD1618yes—
827C16—28no—
828C16—44no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—44no—
833C23—48no—
834C23—44no—
835C23—48no—
836C23—44no—
837C23—88no—
838C23—84no—
839C23—88no—
840C23—168no—
841C23—1616no—
842C23#192614yes—
843C23#192614yes—
844C23#192618yes—
845C23C2×#44212yes—
846C23C2×#44212yes—
847C23C2×#44211yescharacteristic
848C23C2×#44211yescharacteristic
849C23C2×#46312yes—
850C23C2×#46314yes—
851C23C2×#48112yes—
852C23C2×#48114yes—
853C23C22×AGL(1,ℤ/8)11yescharacteristic
854Q8—44no—
855Q8—44no—
856Q8—84no—
857Q8—88no—
858D4—44no—
859D4—44no—
860D4—88no—
861D4—816no—
862D4—84no—
863D4—84no—
864D4—84no—
865D4—88no—
866C2×C4—28no—
867C2×C4—48no—
868C2×C4—416no—
869C2×C4—48no—
870C2×C4—48no—
871C2×C4—44no—
872C2×C4—84no—
873C2×C4—88no—
874C2×C4—84no—
875C2×C4—88no—
876C2×C4—816no—
877C2×C4—88no—
878C2×C4—84no—
879C2×C4—88no—
880C2×C4—88no—
881C2×C4—816no—
882C2×C4—84no—
883C2×C4—84no—
884C2×C4—1616no—
885C2×C4#192618yes—
886C2×C4#192614yes—
887C2×C4#192618yes—
888C2×C4#192614yes—
889C2×C4#192618yes—
890C2×C4#192618yes—
891C2×C4#192618yes—
892C2×C4C2×#38814yes—
893C2×C4C2×#38812yes—
894C2×C4C2×#38814yes—
895C2×C4C2×#38812yes—
896C2×C4C2×C4×SD1614yes—
897C2×C4C2×C4×SD1612yes—
898C2×C4C2×C4×SD1612yes—
899C2×C4C2×C4×SD1614yes—
900C2×C4C2×#44212yes—
901C2×C4C2×#44212yes—
902C2×C4C2×#44211yescharacteristic
903C2×C4C2×#44211yescharacteristic
904C2×C4C2×#46312yes—
905C2×C4C2×#46314yes—
906C2×C4C2×#46012yes—
907C2×C4C2×#46014yes—
908C2×C4C2×#46014yes—
909C2×C4C2×#46012yes—
910C2×C4C2×#48212yes—
911C2×C4C2×#48212yes—
912C2×C4C2×#48214yes—
913C2×C4C2×#48214yes—
914C2×C4C2×#48112yes—
915C2×C4C2×#48114yes—
916C2×C4C22×C4×D411yescharacteristic
917C2×C4C22×#12111yescharacteristic
918C2×C4C22×#12311yescharacteristic
919C2×C4C23×SD1611yescharacteristic
920C2×C4C22×#13511yescharacteristic
921C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
922C8—44no—
923C8—84no—
924C8C2×#38812yes—
925C8C2×#38814yes—
926C8C2×#38814yes—
927C8C2×#38812yes—
928C8C22×#11711yescharacteristic
929C8C22×C4×D411yescharacteristic
930C8C22×#12411yescharacteristic
931C8C22×#12611yescharacteristic
932C22—24no—
933C22—24no—
934C22—28no—
935C22—28no—
936C22—22no—
937C22—22no—
938C22—24no—
939C22—24no—
940C22—44no—
941C22—44no—
942C22—48no—
943C22—84no—
944C22—88no—
945C22—1616no—
946C22—168no—
947C22C2×#192614yes—
948C22C2×#192612yes—
949C22C2×#192614yes—
950C22C2×#192612yes—
951C22#3346914yes—
952C22C22×#44211yescharacteristic
953C22C22×#46311yescharacteristic
954C22C22×#48111yescharacteristic
955C4—48no—
956C4—88no—
957C4—84no—
958C4—88no—
959C4C2×#192612yes—
960C4C2×#192614yes—
961C4C2×#192612yes—
962C4C2×#192614yes—
963C4C22×#38811yescharacteristic
964C4C22×C4×SD1611yescharacteristic
965C4C22×#46011yescharacteristic
966C4C22×#48211yescharacteristic
967C2—21no—
968C2—21no—
969C2—24no—
970C2—22no—
971C2—24no—
972C2—164no—
973C2#49489314yesdirect product factor
974C2C22×#192611yescharacteristic
975C2C2×#3346912yes—
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radicalC23×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#405 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#365C2semidirect
5. C2×#20454C2semidirect
6. #494893C2direct (N × H)
7. C2×#13143C2semidirect
8. C2×#12569C2semidirect
9. C2×#12547C2semidirect
21. C22×#365C22semidirect
22. C22×#365C22semidirect
26. #33380C4semidirect
29. C2×#2141C4semidirect
30. C2×#2140C4semidirect
31. C2×#2138C4semidirect
37. #20454C22semidirect
38. C2×#1776C22semidirect
41. #13143C22semidirect
42. #12569C22semidirect
43. C2×#1387C22semidirect
44. #12547C22semidirect
45. C2×#1375C22semidirect
125. C2×#365C23semidirect
129. #2141C2×C4semidirect
130. #2140C2×C4semidirect
131. #2139C2×C4semidirect
133. #2138C2×C4semidirect
134. C2×#358C2×C4semidirect
135. C2×#357C2×C4semidirect
140. #1776C23semidirect
144. #1387C23semidirect
145. #1375C23semidirect
349. #358C22×C4semidirect
350. #357C22×C4semidirect
973. C2#494893direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#3652
C23×#3602
C2×#333802
C2×#212402
C2×#204542
#4948932
C2×#131432
C2×#125692
C2×#125472