Finite Group Databasebeta

← C2×#83943 #11662588

Subgroups — C2×#83943 #11662588

Order 768.

2746 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic, complemented
3C2×#5819C211yesmaximal, characteristic, complemented
4C22×#932C211yesmaximal, characteristic, complemented
5C22×#833C211yesmaximal, characteristic, complemented
6#83943C2116yesmaximal, direct product factor
7C2×#5199C214yesmaximal, complemented
8C2×#5200C214yesmaximal, complemented
9C2×#5132C211yesmaximal, characteristic, complemented
10C2×#5124C211yesmaximal, characteristic, complemented
11C2×#3068—31nomaximal, Sylow
12C22×C3×#41C2211yescharacteristic
13C23×C3×D4C2211yescharacteristic
14C22×#235C2211yescharacteristic
15C2×C3×AGL(1,ℤ/8)—22no—
16C2×C3×AGL(1,ℤ/8)—24no—
17C2×C3×AGL(1,ℤ/8)C2214yes—
18C2×C3×AGL(1,ℤ/8)C2218yescomplemented
19C22×C3×SD16—21no—
20C22×C3×D8—21no—
21C22×C3×M16C2211yescharacteristic
22C2×#951C2212yescomplemented
23#5822—24no—
24#5822C2218yescomplemented
25C2×#950—22no—
26C2×#949C2212yescomplemented
27#5819—24no—
28#5819C2218yescomplemented
29C2×#948—22no—
30C2×#948C2214yescomplemented
31C2×#942—21no—
32C22×#214C2212yescomplemented
33C2×#932—21no—
34C2×#932—22no—
35C2×#932—22no—
36C2×#932—24no—
37C2×#932C2218yescomplemented
38C22×#213C2212yescomplemented
39C22×#208—22no—
40C22×#208C2211yescharacteristic
41C22×#208C2211yescharacteristic
42C22×#208C2211yescharacteristic
43C2×#833C2214yescomplemented
44C2×#833C2218yescomplemented
45#5200C22132yescomplemented
46#5199C22132yescomplemented
47C2×#824C2212yescomplemented
48#5132C2218yescomplemented
49C2×#823C2212yescomplemented
50#5124C2218yescomplemented
51C2×#822C2214yescomplemented
52C2×#575—31no—
53C22×AGL(1,ℤ/8)—31no—
54C22×AGL(1,ℤ/8)D311yescharacteristic, complemented
55C2×#568—31no—
56#3068—316no—
57C2×#472—34no—
58C2×#471—34no—
59C2×#430—31no—
60C2×#413—31no—
61C22×#100—31no—
62C25×C3—21no—
63C2×C3×#41—21no—
64C2×C3×#41—22no—
65C2×C3×#41—21no—
66C2×C3×#41—22no—
67C2×C3×#41D412yes—
68C2×C3×#41D414yes—
69C2×C3×#41C2312yes—
70C2×C3×#41C2314yes—
71C22×C3×Q8D411yescharacteristic
72C22×C3×D4—21no—
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—22no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4—22no—
79C22×C3×D4—21no—
80C22×C3×D4—22no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2312yes—
83C22×C3×D4C2314yes—
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C2×#235—22no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—22no—
91C2×#235—21no—
92C2×#235—21no—
93C2×#235—22no—
94C2×#235C2314yes—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×Dic6C2311yescharacteristic
98C3×AGL(1,ℤ/8)—28no—
99C3×AGL(1,ℤ/8)—216no—
100C3×AGL(1,ℤ/8)C23116yes—
101C2×C3×SD16—24no—
102C2×C3×SD16—28no—
103C2×C3×D8—24no—
104C2×C3×D8—28no—
105C2×C3×M16—21no—
106C2×C3×M16—22no—
107C2×C3×M16C2312yes—
108C2×C3×M16C2314yes—
109C22×C3×C8—21no—
110#951—24no—
111#951C2318yescomplemented
112#950—216no—
113#949—24no—
114#949C2318yescomplemented
115#948—216no—
116#948—28no—
117#948C23116yescomplemented
118C2×#216—22no—
119#942—28no—
120C2×#215—22no—
121C2×#214—22no—
122C2×#214—24no—
123C2×#214—24no—
124C2×#214C2318yescomplemented
125#932—28no—
126#932—216no—
127#932—216no—
128C2×#213—22no—
129C2×#213—24no—
130C2×#213—24no—
131C2×#213C2318yescomplemented
132C2×#208—21no—
133C2×#208—21no—
134C2×#208—22no—
135C2×#208—22no—
136C2×#208—216no—
137C2×#208—24no—
138C2×#208D412yes—
139C2×#208D412yes—
140C2×#208D414yes—
141C2×#208C2312yes—
142C2×#208C2314yes—
143C2×#208C2312yes—
144C2×#208C2314yes—
145C2×#208C2314yes—
146C22×C3⋊C8—21no—
147C22×C3⋊C8—21no—
148C22×C3⋊C8—24no—
149C22×C3⋊C8C2312yes—
150#833C23116yescomplemented
151#824C2318yescomplemented
152#823C2318yescomplemented
153#822C23116yescomplemented
154C22×#41—31no—
155C22×#41C2×D311yescharacteristic
156C23×D4C2×D311yescharacteristic
157#575—38no—
158#575—64no—
159C2×#137—32no—
160C2×#137—61no—
161C2×AGL(1,ℤ/8)—22no—
162C2×AGL(1,ℤ/8)—24no—
163C2×AGL(1,ℤ/8)—38no—
164C2×AGL(1,ℤ/8)—32no—
165C2×AGL(1,ℤ/8)—62no—
166C2×AGL(1,ℤ/8)—62no—
167C2×AGL(1,ℤ/8)—64no—
168C2×AGL(1,ℤ/8)—61no—
169C2×AGL(1,ℤ/8)C2×D314yes—
170C2×AGL(1,ℤ/8)C2×D318yescomplemented
171C2×#135—62no—
172C22×SD16—21no—
173C22×SD16—32no—
174C22×D8—21no—
175C22×D8—32no—
176#568—38no—
177#568—64no—
178C2×#131—34no—
179C2×#131—62no—
180C22×M16—31no—
181C22×M16—31no—
182C22×M16—31no—
183C22×M16—62no—
184C22×M16C2×D311yescharacteristic
185#472—332no—
186#471—332no—
187#430—38no—
188C2×#108—34no—
189#413—38no—
190C2×#101—32no—
191C2×#100—34no—
192C2×#100—38no—
193C2×#100—32no—
194C24×C3—21no—
195C24×C3—22no—
196C24×C3—24no—
197C24×C3—41no—
198C24×C3—41no—
199C24×C3—42no—
200C24×C3—84no—
201C24×C3#4111yescharacteristic
202C23×D3—21no—
203C3×#41—24no—
204C3×#41—24no—
205C3×#41—24no—
206C3×#41—24no—
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—24no—
210C3×#41C2×D414yes—
211C3×#41C2×D418yes—
212C3×#41C2414yes—
213C2×C3×Q8—21no—
214C2×C3×Q8—22no—
215C2×C3×Q8C2×D412yes—
216C2×C3×Q8C2×D414yes—
217C2×C3×D4—22no—
218C2×C3×D4—24no—
219C2×C3×D4—22no—
220C2×C3×D4—24no—
221C2×C3×D4—21no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—24no—
226C2×C3×D4—24no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—24no—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—24no—
233C2×C3×D4—41no—
234C2×C3×D4—41no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4C2×D412yes—
241C2×C3×D4C2×D414yes—
242C2×C3×D4C2414yes—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4—24no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4#4111yescharacteristic
255C22×C3×C4#4112yes—
256C22×C3×C4C2411yescharacteristic
257C22×C3×C4C2412yes—
258C2×#67—24no—
259C2×#67—41no—
260C2×#67—41no—
261C2×#67—42no—
262C22×Dic3—21no—
263#235—24no—
264#235—24no—
265#235—24no—
266#235—24no—
267#235—42no—
268#235—42no—
269#235—42no—
270#235—42no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12C2412yes—
277C2×C4×D3—24no—
278C2×C4×D3—41no—
279C2×C4×D3—41no—
280C2×C4×D3—42no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6C2412yes—
287C3×SD16—216no—
288C3×D8—216no—
289C3×M16—24no—
290C3×M16—22no—
291C3×M16C2414yes—
292C2×C3×C8—22no—
293C2×C3×C8—24no—
294#216—28no—
295#215—28no—
296#214—28no—
297#214—216no—
298#213—28no—
299#213—216no—
300#208—24no—
301#208—24no—
302#208—22no—
303#208—22no—
304#208—216no—
305#208C2×D418yes—
306#208C2×D418yes—
307#208C2414yes—
308#208C2414yes—
309C2×C3⋊C8—22no—
310C2×C3⋊C8—22no—
311C2×C3⋊C8—24no—
312C2×C3⋊C8—24no—
313C2×C3⋊C8—216no—
314C2×C3⋊C8C2×D414yes—
315C2×C3⋊C8C2×D414yes—
316C2×C3⋊C8C2414yes—
317C25—21no—
318C2×#41—21no—
319C2×#41—22no—
320C2×#41—21no—
321C2×#41—22no—
322C2×#41—34no—
323C2×#41—62no—
324C2×#41—61no—
325C2×#41—61no—
326C2×#41—62no—
327C2×#41—61no—
328C2×#41—61no—
329C2×#41—62no—
330C2×#41#6712yes—
331C2×#41#6714yes—
332C2×#41C22×D312yes—
333C2×#41C22×D314yes—
334C22×Q8—31no—
335C22×Q8#6711yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—31no—
346C22×D4—61no—
347C22×D4#6711yescharacteristic
348C22×D4C22×D312yes—
349C22×D4C22×D314yes—
350C23×C4—21no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353#137—38no—
354#137—64no—
355#137—68no—
356AGL(1,ℤ/8)—28no—
357AGL(1,ℤ/8)—216no—
358AGL(1,ℤ/8)—38no—
359AGL(1,ℤ/8)—616no—
360AGL(1,ℤ/8)—616no—
361AGL(1,ℤ/8)—64no—
362AGL(1,ℤ/8)—68no—
363AGL(1,ℤ/8)C22×D3116yes—
364#135—616no—
365C2×Q16—62no—
366C2×SD16—24no—
367C2×SD16—28no—
368C2×SD16—38no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×SD16—62no—
372C2×SD16—62no—
373C2×D8—24no—
374C2×D8—28no—
375C2×D8—38no—
376C2×D8—64no—
377C2×D8—64no—
378C2×D8—62no—
379#131—316no—
380#131—68no—
381#131—616no—
382C2×M16—21no—
383C2×M16—22no—
384C2×M16—32no—
385C2×M16—32no—
386C2×M16—34no—
387C2×M16—34no—
388C2×M16—32no—
389C2×M16—34no—
390C2×M16—32no—
391C2×M16—34no—
392C2×M16—64no—
393C2×M16—616no—
394C2×M16—61no—
395C2×M16—62no—
396C2×M16—61no—
397C2×M16—62no—
398C2×M16C22×D312yes—
399C2×M16C22×D314yes—
400C22×C8—21no—
401C22×C8—32no—
402C22×C8—64no—
403C22×C8—61no—
404C22×C8—61no—
405#108—316no—
406#101—38no—
407#100—316no—
408#100—38no—
409C23×C3—22no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—42no—
413C23×C3—44no—
414C23×C3—42no—
415C23×C3—44no—
416C23×C3—42no—
417C23×C3—82no—
418C23×C3—84no—
419C23×C3—84no—
420C23×C3—84no—
421C23×C3—88no—
422C23×C3—88no—
423C23×C3#12111yescharacteristic
424C23×C3#12111yescharacteristic
425C23×C3#12112yes—
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4112yes—
428C22×D3—22no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—82no—
432C3×Q8—22no—
433C3×Q8—24no—
434C3×Q8C22×D414yes—
435C3×D4—24no—
436C3×D4—28no—
437C3×D4—24no—
438C3×D4—22no—
439C3×D4—24no—
440C3×D4—24no—
441C3×D4—24no—
442C3×D4—42no—
443C3×D4—42no—
444C3×D4—44no—
445C3×D4—44no—
446C3×D4C22×D414yes—
447C2×C3×C4—24no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—28no—
451C2×C3×C4—24no—
452C2×C3×C4#12111yescharacteristic
453C2×C3×C4#12111yescharacteristic
454C2×C3×C4#12112yes—
455C2×C3×C4#12112yes—
456C2×C3×C4#12112yes—
457C2×C3×C4#12112yes—
458C2×C3×C4#12112yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D412yes—
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D412yes—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D412yes—
465C2×C3×C4C22×D412yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4112yes—
469C2×C3×C4C2511yescharacteristic
470#67—44no—
471#67—44no—
472C2×Dic3—22no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475D12—22no—
476D12—22no—
477D12—41no—
478D12—41no—
479C4×D3—44no—
480C4×D3—44no—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3×C8—24no—
486C3⋊C8—24no—
487C3⋊C8—24no—
488C3⋊C8C22×D418yes—
489C24—21no—
490C24—24no—
491C24—22no—
492C24—42no—
493C24—41no—
494C24—41no—
495C24—61no—
496C24—84no—
497C24#23711yescharacteristic
498#41—24no—
499#41—24no—
500#41—24no—
501#41—22no—
502#41—24no—
503#41—24no—
504#41—22no—
505#41—64no—
506#41—64no—
507#41—64no—
508#41—64no—
509#41—122no—
510#41—122no—
511#41—122no—
512#41—122no—
513#41C2×#6718yes—
514#41C2×#6714yes—
515#41C23×D314yes—
516C2×Q8—22no—
517C2×Q8—21no—
518C2×Q8—32no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8C2×#6712yes—
525C2×Q8C2×#6714yes—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—24no—
539C2×D4—22no—
540C2×D4—24no—
541C2×D4—22no—
542C2×D4—32no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—64no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—122no—
557C2×D4—121no—
558C2×D4—121no—
559C2×D4C2×#6712yes—
560C2×D4C2×#6714yes—
561C2×D4C23×D314yes—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—61no—
568C22×C4—64no—
569C22×C4—122no—
570C22×C4—121no—
571C22×C4—121no—
572C22×C4D3×D411yescharacteristic
573C22×C4D3×D411yescharacteristic
574C22×C4D3×D412yes—
575C22×C4#23711yescharacteristic
576C22×C4#23712yes—
577C22×C4C2×#6711yescharacteristic
578C22×C4C2×#6711yescharacteristic
579C22×C4C2×#6712yes—
580C22×C4C23×D311yescharacteristic
581C22×C4C23×D312yes—
582Q16—68no—
583SD16—216no—
584SD16—616no—
585SD16—68no—
586SD16—68no—
587D8—216no—
588D8—616no—
589D8—68no—
590M16—24no—
591M16—22no—
592M16—38no—
593M16—38no—
594M16—34no—
595M16—34no—
596M16—616no—
597M16—64no—
598M16—62no—
599M16—64no—
600M16—62no—
601M16C23×D314yes—
602C2×C8—24no—
603C2×C8—22no—
604C2×C8—34no—
605C2×C8—34no—
606C2×C8—34no—
607C2×C8—616no—
608C2×C8—62no—
609C2×C8—64no—
610C2×C8—62no—
611C2×C8—64no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—24no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—84no—
621C22×C3—84no—
622C22×C3—88no—
623C22×C3—84no—
624C22×C3—88no—
625C22×C3—84no—
626C22×C3C2×#12111yescharacteristic
627C22×C3C2×#12112yes—
628C22×C3C2×#12112yes—
629C22×C3C2×#12111yescharacteristic
630C22×C3C22×#4111yescharacteristic
631C2×D3—42no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C3×C4—24no—
636C3×C4C2×#12111yescharacteristic
637C3×C4C2×#12111yescharacteristic
638C3×C4C2×#12112yes—
639C3×C4C2×#12112yes—
640C3×C4C23×D411yescharacteristic
641C3×C4C23×D411yescharacteristic
642Dic3—42no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—42no—
647C23—44no—
648C23—42no—
649C23—44no—
650C23—42no—
651C23—62no—
652C23—82no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—88no—
657C23—88no—
658C23—121no—
659C23—121no—
660C23—242no—
661C23#93911yescharacteristic
662C23#93911yescharacteristic
663C23#93912yes—
664C23C2×#23711yescharacteristic
665C23C2×#23712yes—
666Q8—24no—
667Q8—22no—
668Q8—62no—
669Q8—62no—
670Q8—121no—
671Q8—121no—
672Q8C22×#6714yes—
673D4—24no—
674D4—24no—
675D4—28no—
676D4—24no—
677D4—24no—
678D4—24no—
679D4—22no—
680D4—44no—
681D4—42no—
682D4—44no—
683D4—42no—
684D4—62no—
685D4—62no—
686D4—124no—
687D4—124no—
688D4—121no—
689D4—121no—
690D4C22×#6714yes—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—62no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—124no—
700C2×C4—124no—
701C2×C4#93912yes—
702C2×C4#93912yes—
703C2×C4#93912yes—
704C2×C4#93912yes—
705C2×C4#93912yes—
706C2×C4#93911yescharacteristic
707C2×C4#93911yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4C2×D3×D412yes—
710C2×C4C2×D3×D412yes—
711C2×C4C2×D3×D411yescharacteristic
712C2×C4C2×#23712yes—
713C2×C4C2×#23711yescharacteristic
714C2×C4C22×#6712yes—
715C2×C4C22×#6712yes—
716C2×C4C22×#6711yescharacteristic
717C2×C4C22×#6711yescharacteristic
718C2×C4C24×D311yescharacteristic
719C8—24no—
720C8—38no—
721C8—64no—
722C8—64no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—22no—
726C2×C3—22no—
727C2×C3—44no—
728C2×C3—84no—
729C2×C3#306812yescomplemented
730C2×C3C22×#12111yescharacteristic
731D3—82no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—44no—
739C22—44no—
740C22—84no—
741C22—84no—
742C22—88no—
743C22—84no—
744C22—88no—
745C22—84no—
746C22—122no—
747C22—242no—
748C22—242no—
749C22—242no—
750C22C2×#93912yes—
751C22C2×#93911yescharacteristic
752C22C2×#93912yes—
753C22C2×#93911yescharacteristic
754C22C22×#23711yescharacteristic
755C4—24no—
756C4—122no—
757C4C2×#93912yes—
758C4C2×#93911yescharacteristic
759C4C2×#93912yes—
760C4C2×#93911yescharacteristic
761C4C22×D3×D411yescharacteristic
762C4C23×#6711yescharacteristic
763C3C2×#306811yescharacteristic, complemented, Sylow
764C2—22no—
765C2—21no—
766C2—21no—
767C2—22no—
768C2—44no—
769C2—84no—
770C2—242no—
771C2#8394312yesdirect product factor
772C2C22×#93911yescharacteristic
subgroupG/H
centerC22C2×#939
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×AGL(1,ℤ/8)C2
socleC22×C3C2×#121
hypercenterC22×AGL(1,ℤ/8)D3
hypocenterC3C2×#3068
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C2×#5822C2semidirect
3. C2×#5819C2semidirect
4. C22×#932C2semidirect
5. C22×#833C2semidirect
6. #83943C2direct (N × H)
7. C2×#5199C2semidirect
8. C2×#5200C2semidirect
9. C2×#5132C2semidirect
10. C2×#5124C2semidirect
18. C2×C3×AGL(1,ℤ/8)C22semidirect
22. C2×#951C22semidirect
24. #5822C22semidirect
26. C2×#949C22semidirect
28. #5819C22semidirect
30. C2×#948C22semidirect
32. C22×#214C22semidirect
37. C2×#932C22semidirect
38. C22×#213C22semidirect
43. C2×#833C22semidirect
44. C2×#833C22semidirect
45. #5200C22semidirect
46. #5199C22semidirect
47. C2×#824C22semidirect
48. #5132C22semidirect
49. C2×#823C22semidirect
50. #5124C22semidirect
51. C2×#822C22semidirect
54. C22×AGL(1,ℤ/8)D3semidirect
111. #951C23semidirect
114. #949C23semidirect
117. #948C23semidirect
124. C2×#214C23semidirect
131. C2×#213C23semidirect
150. #833C23semidirect
151. #824C23semidirect
152. #823C23semidirect
153. #822C23semidirect
170. C2×AGL(1,ℤ/8)C2×D3semidirect
729. C2×C3#3068semidirect
763. C3C2×#3068semidirect
771. C2#83943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
C2×#58222
C2×#58192
C22×#9322
C22×#8332
#839432
C2×#51992
C2×#52002
C2×#51322
C2×#51242
C2×#30683