Finite Group Databasebeta

← C4×#14583167 #25103473

Subgroups — C4×#14583167 #25103473

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583167C211yesmaximal, characteristic
2C4×#13063350C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4C4×#13063332C211yesmaximal, characteristic, complemented
5#19135504C211yesmaximal, characteristic, complemented
6#19135377C211yesmaximal, characteristic, complemented
7#19135260C211yesmaximal, characteristic, complemented
8#19135256C211yesmaximal, characteristic, complemented
9#19135105C211yesmaximal, characteristic, complemented
10#19135101C211yesmaximal, characteristic, complemented
11#19134657C211yesmaximal, characteristic, complemented
12C4×#13063260C211yesmaximal, characteristic, complemented
13C4×#13063241C211yesmaximal, characteristic, complemented
14C4×#13063242C211yesmaximal, characteristic, complemented
15C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583167C418yesdirect product factor
22#14583009—21no—
23#14582997—21no—
24C4×#10621884—21no—
25C4×#10621882—21no—
26C4×#10621882—21no—
27C4×#10621882—21no—
28C4×#10621882—21no—
29C4×#10621882—21no—
30C2×#13063260C2211yescharacteristic
31C2×#13063260C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34#14582903C2211yescharacteristic
35#14582900C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063242C2211yescharacteristic
39C2×#13063242C2211yescharacteristic
40C2×#13063241C2211yescharacteristic
41C2×#13063241C2211yescharacteristic
42#14582855—21no—
43#14582855—21no—
44#14582855C2211yescharacteristic
45#14582855C2211yescharacteristic
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49C2×C4×C43⋊C8—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582663C2211yescharacteristic
57C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C43×#442—21no—
61C43×#440—21no—
62C4×SD16×C43—21no—
63C4×D8×C43—21no—
64C43×#428C2211yescharacteristic
65C43×#418C2211yescharacteristic
66C43×#417C2211yescharacteristic
67C4×M16×C43C2211yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70#13063350—22no—
71#13063350C2×C414yescomplemented
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—22no—
77C2×#10621882C2×C414yescomplemented
78#13063332—22no—
79#13063332—22no—
80#13063332—22no—
81#13063332C2×C414yescomplemented
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C22×C43⋊C8—21no—
89C22×C43⋊C8—21no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C4×D172—21no—
93C4×D172—21no—
94C4×D172—21no—
95C4×D172—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98#13063260—22no—
99#13063260C2×C414yescomplemented
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063256—21no—
104#13063249—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245—21no—
112#13063242—22no—
113#13063242C2×C414yescomplemented
114#13063241—22no—
115#13063241C2×C414yescomplemented
116#13063236—21no—
117#13063236—21no—
118#13063236—21no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8D411yescharacteristic
125C4×C43⋊C8D411yescharacteristic
126C4×C43⋊C8D411yescharacteristic
127C4×C43⋊C8D411yescharacteristic
128C2×#41×C43C2311yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131AGL(1,ℤ/8)×C43—22no—
132AGL(1,ℤ/8)×C43C2×C414yescomplemented
133C2×SD16×C43—21no—
134C2×D8×C43—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C4×Q8×C43D411yescharacteristic
138C4×Q8×C43D411yescharacteristic
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C4×D4×C43D411yescharacteristic
146C4×D4×C43D411yescharacteristic
147#117×C43—21no—
148#117×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153#107×C43—21no—
154#106×C43—21no—
155#103×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#102×C43—21no—
159#97×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C23×D43—21no—
163#41×C43—21no—
164#41×C43—21no—
165#41×C43C22×C412yes—
166#41×C43#4112yes—
167C2×Q8×C43C2×D411yescharacteristic
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C2×D411yescharacteristic
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43—82no—
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—41no—
194C2×C4×D43—41no—
195C2×C4×D43—82no—
196SD16×C43—24no—
197D8×C43—24no—
198M16×C43—21no—
199M16×C43—21no—
200M16×C43—21no—
201M16×C43C22×C412yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221C42×C43C2×D411yescharacteristic
222#10621884—24no—
223#10621882—24no—
224#10621882—24no—
225#10621882—24no—
226(C2×D43)⋊C4—41no—
227(C2×D43)⋊C4—41no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230#10621877—24no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—24no—
235#10621877—21no—
236#10621877—21no—
237#10621877C22×C412yes—
238#10621877C22×C412yes—
239#10621877#4112yes—
240C2×C43⋊C8—24no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—24no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8C22×C412yes—
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251C2×C43⋊C8C2×D411yescharacteristic
252C2×C43⋊C8C2×D411yescharacteristic
253C2×C43⋊C8#4112yes—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—81no—
259C23×C43—81no—
260C23×C43C2×#4111yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—81no—
265C22×D43—81no—
266Q8×C43—21no—
267Q8×C43C4×D412yes—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—21no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43C4×D412yes—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—41no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—41no—
286C2×C4×C43—82no—
287C2×C4×C43—82no—
288C2×C4×C43—81no—
289C2×C4×C43#12111yescharacteristic
290C2×C4×C43#12111yescharacteristic
291C2×C4×C43#12111yescharacteristic
292C2×C4×C43#12111yescharacteristic
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×Dic43—41no—
300C2×Dic43—81no—
301D172—22no—
302D172—22no—
303D172—41no—
304D172—41no—
305C4×D43—82no—
306C4×D43—82no—
307C8×C43—22no—
308C8×C43—41no—
309C43⋊C8—22no—
310C43⋊C8—22no—
311C43⋊C8—21no—
312C43⋊C8—22no—
313C43⋊C8—21no—
314C43⋊C8—41no—
315C43⋊C8C4×D412yes—
316C43⋊C8C4×D412yes—
317C4×#472—431nomaximal, Sylow
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—42no—
324C22×C43—82no—
325C22×C43—82no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43C4×#4111yescharacteristic
329C22×C43C2×#12111yescharacteristic
330C22×C43#52911yescharacteristic
331C2×D43—42no—
332C2×D43—82no—
333C2×D43—81no—
334C2×D43—81no—
335C2×D43—82no—
336C4×C43—21no—
337C4×C43—21no—
338C4×C43—21no—
339C4×C43—22no—
340C4×C43—41no—
341C4×C43—41no—
342C4×C43—81no—
343C4×C43#47212yescomplemented
344C4×C43C2×C4×D411yescharacteristic
345C4×C43C2×C4×D411yescharacteristic
346C4×C43#52511yescharacteristic
347C4×C43#53211yescharacteristic
348Dic43—81no—
349C2×#472—431no—
350C4×AGL(1,ℤ/8)—431no—
351C4×AGL(1,ℤ/8)D4311yescharacteristic, complemented
352C2×C4×D8—431no—
353C4×#131—431no—
354#1978—431no—
355#1952—431no—
356#1931—431no—
357#1931—431no—
358#1907—431no—
359#1907—431no—
360#1816—431no—
361C4×#108—431no—
362C4×#100—431no—
363C4×#100—431no—
364C2×C43—21no—
365C2×C43—21no—
366C2×C43—42no—
367C2×C43—82no—
368C2×C43C4×#12111yescharacteristic
369C2×C43C2×#47211yescharacteristic
370C2×C43#306711yescharacteristic
371D43—82no—
372C2×AGL(1,ℤ/8)—431no—
373C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
374C22×D8—431no—
375C2×#131—431no—
376C2×#131—431no—
377C4×#41C2×D4311yescharacteristic
378C2×C4×D4—431no—
379C2×C4×D4C2×D4311yescharacteristic
380#472—438no—
381#442—21no—
382#442—861no—
383#440—21no—
384#440—861no—
385C4×SD16—21no—
386C4×SD16—861no—
387C4×D8—21no—
388C4×D8—861no—
389C4×D8—861no—
390C4×D8—861no—
391C4×D8—861no—
392C4×D8—861no—
393C2×#108—431no—
394C2×#108—431no—
395#428—431no—
396#428C2×D4311yescharacteristic
397C2×#107—431no—
398#418—431no—
399#418C2×D4311yescharacteristic
400#417—431no—
401#417C2×D4311yescharacteristic
402C2×#102—431no—
403C2×#102—431no—
404C2×#100—431no—
405C2×#100—431no—
406C2×#100—431no—
407C2×#100—431no—
408#405—431no—
409#405—431no—
410#405—861no—
411#405—861no—
412C4×M16—431no—
413C4×M16—431no—
414C4×M16—861no—
415C4×M16C2×D4311yescharacteristic
416C2×C4×C8—431no—
417C2×C4×C8—861no—
418#343—431no—
419#343—431no—
420#343—431no—
421#343—431no—
422#341—431no—
423#341—431no—
424C43C4×#47211yescharacteristic, complemented, Sylow
425C2×#41C22×D4311yescharacteristic
426C22×D4—431no—
427C22×D4C22×D4311yescharacteristic
428C23×C4—21no—
429C23×C4—861no—
430AGL(1,ℤ/8)—22no—
431AGL(1,ℤ/8)—434no—
432AGL(1,ℤ/8)—862no—
433AGL(1,ℤ/8)C4×D4314yescomplemented
434C2×SD16—21no—
435C2×SD16—861no—
436C2×D8—21no—
437C2×D8—434no—
438C2×D8—862no—
439C2×D8—861no—
440C2×D8—861no—
441C2×D8—861no—
442#131—434no—
443#131—862no—
444#131—862no—
445#131—862no—
446C2×M16—431no—
447C2×M16—431no—
448C2×M16—431no—
449C2×M16—431no—
450C2×M16—861no—
451C2×M16—861no—
452C2×M16C22×D4311yescharacteristic
453C2×M16C22×D4311yescharacteristic
454C22×C8—431no—
455C22×C8—431no—
456C22×C8—861no—
457C22×C8—861no—
458C4×Q8C22⋊D4311yescharacteristic
459C4×Q8C22⋊D4311yescharacteristic
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—861no—
467C4×D4—861no—
468C4×D4—861no—
469C4×D4—861no—
470C4×D4C22⋊D4311yescharacteristic
471C4×D4C22⋊D4311yescharacteristic
472#117—21no—
473#117C22×D4311yescharacteristic
474C2×C4⋊C4—431no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—861no—
478C2×C42—21no—
479C2×C42C22×D4311yescharacteristic
480#108—434no—
481#108—862no—
482#107—21no—
483#107—861no—
484#107—861no—
485#107—861no—
486#106—21no—
487#106—861no—
488#103—21no—
489#103—861no—
490#102—21no—
491#102—21no—
492#102—21no—
493#102—861no—
494#102—861no—
495#102—861no—
496#102—861no—
497#102—861no—
498#102—861no—
499#102—861no—
500#100—434no—
501#100—434no—
502#100—862no—
503#100—862no—
504#97—21no—
505#97—861no—
506#97—861no—
507#97—861no—
508#97—861no—
509C4×C8—21no—
510C4×C8—431no—
511C4×C8—431no—
512C4×C8—431no—
513C4×C8—431no—
514C4×C8—861no—
515C4×C8—861no—
516C4×C8—861no—
517C4×C8—861no—
518C24—21no—
519C24—861no—
520#41—21no—
521#41—21no—
522#41C2×C4×D4312yes—
523#41#1062189812yes—
524C2×Q8C2×C22⋊D4311yescharacteristic
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—432no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4C2×C4×D4312yes—
538C2×D4C2×C22⋊D4311yescharacteristic
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—82no—
546C22×C4—861no—
547C22×C4—3442no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4#1062190011yescharacteristic
551C22×C4#1062190011yescharacteristic
552C22×C4C23×D4311yescharacteristic
553SD16—24no—
554SD16—864no—
555D8—24no—
556D8—864no—
557D8—864no—
558D8—864no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—432no—
563M16—432no—
564M16—432no—
565M16—864no—
566M16—864no—
567M16—861no—
568M16—861no—
569M16—861no—
570M16—861no—
571M16—861no—
572M16C2×C4×D4312yes—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—432no—
576C2×C8—431no—
577C2×C8—431no—
578C2×C8—432no—
579C2×C8—431no—
580C2×C8—431no—
581C2×C8—864no—
582C2×C8—864no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4C2×C22⋊D4311yescharacteristic
596C4⋊C4C2×C22⋊D4311yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—1721no—
603C22⋊C4—1721no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42D4×D4311yescharacteristic
608C42D4×D4311yescharacteristic
609C42C2×C22⋊D4311yescharacteristic
610C42C2×C22⋊D4311yescharacteristic
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—81no—
616C23—81no—
617C23—862no—
618C23—3441no—
619C23—3441no—
620C23—1721no—
621C23—1721no—
622C23C2×#1062190011yescharacteristic
623Q8—21no—
624Q8C4×C22⋊D4312yes—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—21no—
630D4—41no—
631D4—41no—
632D4—862no—
633D4—862no—
634D4—1721no—
635D4—1721no—
636D4C4×C22⋊D4312yes—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4—81no—
650C2×C4—3442no—
651C2×C4—3442no—
652C2×C4—3441no—
653C2×C4—1721no—
654C2×C4#1306329711yescharacteristic
655C2×C4#1306329711yescharacteristic
656C2×C4#1306329711yescharacteristic
657C2×C4#1306329711yescharacteristic
658C2×C4C22×C4×D4311yescharacteristic
659C2×C4C2×D4×D4311yescharacteristic
660C2×C4C22×C22⋊D4311yescharacteristic
661C2×C4#41×D4311yescharacteristic
662C2×C4#41×D4311yescharacteristic
663C2×C4C2×#1062189811yescharacteristic
664C8—22no—
665C8—41no—
666C8—432no—
667C8—432no—
668C8—862no—
669C8—862no—
670C8—861no—
671C8—861no—
672C8—862no—
673C8—1721no—
674C22—21no—
675C22—21no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—42no—
680C22—82no—
681C22—82no—
682C22—81no—
683C22—81no—
684C22—3442no—
685C22—3442no—
686C22—3441no—
687C22—3441no—
688C22—1722no—
689C22C4×#1062190011yescharacteristic
690C22C2×#1306329711yescharacteristic
691C22#1458342911yescharacteristic
692C4—22no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—3441no—
700C4#1458316712yesdirect product factor
701C4C4×D4×D4311yescharacteristic
702C4C2×C4×C22⋊D4311yescharacteristic
703C4#1458340811yescharacteristic
704C4#1458344511yescharacteristic
705C2—21no—
706C2—21no—
707C2—42no—
708C2—82no—
709C2—3442no—
710C2C4×#1306329711yescharacteristic
711C2C2×#1458316711yescharacteristic
712C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C2×#121
prime radicalC2×#14583167C2
cosocleC22×C4×C43C24
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43C4×#472
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. C4×#13063350C2semidirect
3. C2×C4×#10621882C2semidirect
4. C4×#13063332C2semidirect
5. #19135504C2semidirect
6. #19135377C2semidirect
7. #19135260C2semidirect
8. #19135256C2semidirect
9. #19135105C2semidirect
10. #19135101C2semidirect
11. #19134657C2semidirect
12. C4×#13063260C2semidirect
13. C4×#13063241C2semidirect
14. C4×#13063242C2semidirect
15. C4×AGL(1,ℤ/8)×C43C2semidirect
21. #14583167C4direct (N × H)
71. #13063350C2×C4semidirect
77. C2×#10621882C2×C4semidirect
81. #13063332C2×C4semidirect
99. #13063260C2×C4semidirect
113. #13063242C2×C4semidirect
115. #13063241C2×C4semidirect
132. AGL(1,ℤ/8)×C43C2×C4semidirect
343. C4×C43#472semidirect
351. C4×AGL(1,ℤ/8)D43semidirect
424. C43C4×#472semidirect
433. AGL(1,ℤ/8)C4×D43semidirect
700. C4#14583167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831672
C4×#130633502
C2×C4×#106218822
C4×#130633322
#191355042
#191353772
#191352602
#191352562
#191351052
#191351012
#191346572
C4×#130632602
C4×#130632412
C4×#130632422
C4×AGL(1,ℤ/8)×C432
C4×#47243