Finite Group Databasebeta

← #11662174

Subgroups — #11662174

Order 768.

2870 conjugacy classes of subgroups.

The subgroup lattice has 732 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
2#87260C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4C2×#5805C211yesmaximal, characteristic, complemented
5C2×#5215C211yesmaximal, characteristic, complemented
6#83936C218yesmaximal, complemented
7#83933C214yesmaximal, complemented
8#83932C214yesmaximal, complemented
9#83849C214yesmaximal, complemented
10#83826C214yesmaximal, complemented
11#83768C211yesmaximal, characteristic, complemented
12#83750C211yesmaximal, characteristic, complemented
13#60426—31nomaximal, Sylow
14C22×C3×#41C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C22×#235C2211yescharacteristic
17C2×C3×AGL(1,ℤ/8)—28no—
18C2×C3×AGL(1,ℤ/8)C2214yes—
19C2×C3×AGL(1,ℤ/8)C2214yescomplemented
20C22×C3×SD16C2212yescomplemented
21C22×C3×D8C2212yescomplemented
22C22×C3×M16C2211yescharacteristic
23C2×#953—22no—
24#5827—22no—
25#5827C2214yescomplemented
26Dic3×#41—22no—
27Dic3×#41C2214yescomplemented
28C2×#951C2212yescomplemented
29#5822—28no—
30C2×#950C2214yescomplemented
31C2×#949C2212yescomplemented
32#5812C2212yescomplemented
33C2×#942C2212yescomplemented
34#5805—22no—
35#5805—22no—
36#5805C2214yes—
37#5805C2214yescomplemented
38C2×#940C2212yescomplemented
39C2×#938—22no—
40#5798—22no—
41#5798C2212yescomplemented
42C2×#936C2212yescomplemented
43C2×#932C2212yescomplemented
44C2×#926—22no—
45C2×#926C2211yescharacteristic
46C2×#926C2211yescharacteristic
47C22×#208C2211yescharacteristic
48#5215C2214yescomplemented
49#5215C2214yescomplemented
50C2×#832C2214yescomplemented
51#5166C22116yescomplemented
52#5163C22116yescomplemented
53#5153C22116yescomplemented
54#5150C22116yescomplemented
55#5133C2214yescomplemented
56#5131C2212yescomplemented
57#5120C2212yescomplemented
58#5119C2214yescomplemented
59#5118C2214yescomplemented
60#5113C2214yescomplemented
61#5102C2214yescomplemented
62C2×#575—31no—
63C22×AGL(1,ℤ/8)D311yescharacteristic, complemented
64C2×#535—31no—
65#3428—31no—
66#3045—38no—
67#3043—34no—
68#3041—34no—
69#3040—34no—
70#3038—34no—
71#2905—31no—
72#2896—31no—
73C2×#418—31no—
74C25×C3—21no—
75C2×C3×#41—21no—
76C2×C3×#41—21no—
77C2×C3×#41—24no—
78C2×C3×#41D418yescomplemented
79C2×C3×#41C2312yes—
80C2×C3×#41C2312yes—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4—24no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4—24no—
88C22×C3×D4C2312yes—
89C22×C3×D4C2312yes—
90C22×C3×D4C2312yes—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—24no—
96C2×#235—21no—
97C2×#235—21no—
98C2×#235—24no—
99C2×#235—24no—
100C2×#235C2312yes—
101C2×#235C2312yes—
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×Dic6C2311yescharacteristic
105C3×AGL(1,ℤ/8)—216no—
106C3×AGL(1,ℤ/8)—216no—
107C2×C3×SD16—28no—
108C2×C3×SD16C2318yes—
109C2×C3×D8—28no—
110C2×C3×D8C2318yes—
111C2×C3×M16—24no—
112C2×C3×M16C2312yes—
113C2×C3×M16C2312yes—
114C22×C3×C8C2312yes—
115#953—28no—
116#953—28no—
117C2×#217—21no—
118C2×#217—24no—
119C2×#217—24no—
120C2×#217D412yes—
121#951—28no—
122#950—216no—
123#949—28no—
124Q8×Dic3—24no—
125Q8×Dic3C2318yescomplemented
126C2×#216C2314yescomplemented
127#942—28no—
128C2×#215C2314yescomplemented
129#940—24no—
130#940C2318yes—
131#938—28no—
132#938—28no—
133#936—24no—
134#936C2318yes—
135D4×Dic3—28no—
136D4×Dic3—28no—
137D4×Dic3—24no—
138D4×Dic3C2318yescomplemented
139C2×#214C2314yescomplemented
140#932—28no—
141C2×#213C2314yescomplemented
142#926—21no—
143#926—21no—
144#926—24no—
145#926—24no—
146#926—24no—
147#926D412yes—
148#926D412yes—
149#926C2312yes—
150#926C2312yes—
151#926C2312yes—
152#926C2312yes—
153C2×C4⋊Dic3—24no—
154C2×C4⋊Dic3D412yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—24no—
158C2×C4×Dic3C2312yes—
159C2×#208—24no—
160C2×#208C2312yes—
161C2×#208C2312yes—
162C22×C3⋊C8C2312yes—
163#832C23116yes—
164#821C2318yescomplemented
165#816C2318yescomplemented
166Dic3⋊C8C23116yescomplemented
167C22×#41—31no—
168C22×#41C2×D311yescharacteristic
169C23×D4C2×D311yescharacteristic
170#575—68no—
171C2×#137—32no—
172C2×#137—32no—
173C2×AGL(1,ℤ/8)—28no—
174C2×AGL(1,ℤ/8)—32no—
175C2×AGL(1,ℤ/8)—32no—
176C2×AGL(1,ℤ/8)C2×D314yes—
177C2×AGL(1,ℤ/8)C2×D314yescomplemented
178C2×#135—34no—
179C22×SD16C2×D312yescomplemented
180C22×D8C2×D312yescomplemented
181C22×M16—31no—
182C22×M16C2×D311yescharacteristic
183#535—34no—
184#535—34no—
185#535—62no—
186#535—62no—
187C2×#127—32no—
188C2×#124—32no—
189C2×#121—62no—
190C2×#120—62no—
191#520—34no—
192#520—62no—
193#519—32no—
194#518—32no—
195#518—62no—
196C4×#41—34no—
197C4×#41—62no—
198C2×#117—31no—
199C2×#117—31no—
200C2×#117—62no—
201#464—316no—
202#463—316no—
203#460—316no—
204#459—316no—
205#424—34no—
206#424—34no—
207#423—34no—
208#419—32no—
209#418—34no—
210#418—34no—
211#418—32no—
212#417—34no—
213#416—34no—
214C2×#102—34no—
215C24×C3—21no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—44no—
220C24×C3—84no—
221C24×C3C2×D411yescharacteristic
222C23×D3—21no—
223C3×#41—28no—
224C3×#41—28no—
225C3×#41—24no—
226C3×#41—24no—
227C3×#41C2×D418yes—
228C3×#41C2×D418yescomplemented
229C2×C3×Q8—21no—
230C2×C3×Q8—22no—
231C2×C3×Q8C2×D414yescomplemented
232C2×C3×Q8C2412yes—
233C2×C3×D4—28no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—21no—
237C2×C3×D4—24no—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—44no—
248C2×C3×D4—44no—
249C2×C3×D4—44no—
250C2×C3×D4C2×D414yescomplemented
251C2×C3×D4C2414yes—
252C2×C3×D4C2412yes—
253C22×C3×C4—21no—
254C22×C3×C4—28no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D414yes—
261C22×C3×C4#4114yes—
262C22×C3×C4C2411yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C2×#67—22no—
266C2×#67—22no—
267C2×#67—216no—
268C2×#67—44no—
269C2×#67—88no—
270C22×Dic3—21no—
271C22×Dic3—22no—
272C22×Dic3—28no—
273C22×Dic3C2×D414yes—
274#235—24no—
275#235—24no—
276#235—24no—
277#235—24no—
278#235—44no—
279#235—44no—
280C2×D12—22no—
281C2×D12—22no—
282C2×D12—21no—
283C2×D12C2412yes—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—44no—
287C2×Dic6—22no—
288C2×Dic6—22no—
289C2×Dic6—21no—
290C2×Dic6C2412yes—
291C3×SD16—216no—
292C3×D8—216no—
293C3×M16—24no—
294C3×M16—24no—
295C2×C3×C8—24no—
296C2×C3×C8C2414yes—
297#217—22no—
298#217—22no—
299#217—28no—
300#217—216no—
301#217C2×D414yes—
302#217C2×D414yes—
303#216—28no—
304#215—28no—
305#214—28no—
306#213—28no—
307C4⋊Dic3—22no—
308C4⋊Dic3—28no—
309C4⋊Dic3C2×D414yes—
310C4⋊Dic3C2×D414yes—
311C4⋊Dic3C2414yes—
312C4×Dic3—22no—
313C4×Dic3—22no—
314C4×Dic3—28no—
315C4×Dic3C2×D414yes—
316C4×Dic3C2414yes—
317#208—24no—
318#208—24no—
319C2×C3⋊C8—24no—
320C2×C3⋊C8C2414yes—
321C25—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—24no—
325C2×#41—32no—
326C2×#41—32no—
327C2×#41—61no—
328C2×#41—61no—
329C2×#41—64no—
330C2×#41—64no—
331C2×#41#6718yescomplemented
332C2×#41C22×D312yes—
333C2×#41C22×D312yes—
334C22×Q8—31no—
335C22×Q8C22×D311yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—31no—
343C22×D4—64no—
344C22×D4—61no—
345C22×D4C22×D312yes—
346C22×D4C22×D312yes—
347C22×D4C22×D312yes—
348C22×D4C22×D311yescharacteristic
349C23×C4—21no—
350C23×C4—61no—
351C23×C4C22×D311yescharacteristic
352#137—68no—
353#137—68no—
354AGL(1,ℤ/8)—216no—
355AGL(1,ℤ/8)—216no—
356AGL(1,ℤ/8)—68no—
357AGL(1,ℤ/8)—68no—
358#135—616no—
359C2×Q16—34no—
360C2×SD16—28no—
361C2×SD16—34no—
362C2×SD16—34no—
363C2×SD16C22×D318yes—
364C2×D8—28no—
365C2×D8—34no—
366C2×D8C22×D318yes—
367C2×M16—24no—
368C2×M16—32no—
369C2×M16—32no—
370C2×M16—64no—
371C2×M16C22×D312yes—
372C2×M16C22×D312yes—
373C22×C8—32no—
374C22×C8C22×D312yes—
375#127—38no—
376#127—64no—
377#124—38no—
378#124—64no—
379#121—68no—
380#121—68no—
381#120—68no—
382#120—68no—
383C4×Q8—38no—
384C4×Q8—64no—
385C4×D4—38no—
386C4×D4—68no—
387C4×D4—64no—
388C4×D4—68no—
389#117—32no—
390#117—32no—
391#117—32no—
392#117—32no—
393#117—32no—
394#117—32no—
395#117—64no—
396#117—64no—
397#117—64no—
398#117—61no—
399#117—61no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—64no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—64no—
405C2×C22⋊C4—64no—
406C2×C22⋊C4—61no—
407C2×C42—32no—
408C2×C42—64no—
409C2×C42—61no—
410C4⋊C8—316no—
411#103—38no—
412#102—316no—
413#102—38no—
414C23×C3—22no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—42no—
418C23×C3—48no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3—44no—
422C23×C3—82no—
423C23×C3—84no—
424C23×C3—84no—
425C23×C3—816no—
426C23×C3#12114yes—
427C23×C3C22×D411yescharacteristic
428C23×C3C22×D411yescharacteristic
429C23×C3C22×D411yescharacteristic
430C22×D3—22no—
431C22×D3—44no—
432C22×D3—42no—
433C3×Q8—24no—
434C3×Q8—22no—
435C3×Q8C22×D414yes—
436C3×D4—28no—
437C3×D4—28no—
438C3×D4—24no—
439C3×D4—24no—
440C3×D4—22no—
441C3×D4—24no—
442C3×D4—44no—
443C3×D4—44no—
444C3×D4—44no—
445C3×D4C22×D414yes—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4#12114yes—
451C2×C3×C4#12114yes—
452C2×C3×C4#12114yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D412yes—
457C2×C3×C4C22×D412yes—
458C2×C3×C4C22×D412yes—
459C2×C3×C4C2×#4112yes—
460C2×C3×C4C2×#4112yes—
461C2×C3×C4C2×#4112yes—
462C2×C3×C4C2511yescharacteristic
463#67—44no—
464#67—44no—
465#67—816no—
466C2×Dic3—24no—
467C2×Dic3—22no—
468C2×Dic3—44no—
469C2×Dic3—42no—
470C2×Dic3—88no—
471C2×Dic3—82no—
472C2×Dic3C22×D418yes—
473D12—22no—
474D12—22no—
475D12—42no—
476C4×D3—44no—
477C4×D3—44no—
478Dic6—22no—
479Dic6—22no—
480Dic6—42no—
481C3×C8—24no—
482C3⋊C8—24no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—44no—
488C24—61no—
489C24—84no—
490C24D3×D411yescharacteristic
491#41—28no—
492#41—28no—
493#41—24no—
494#41—24no—
495#41—64no—
496#41—64no—
497#41—64no—
498#41—64no—
499#41—124no—
500#41—124no—
501#41C2×#6718yes—
502#41C2×#6718yescomplemented
503C2×Q8—21no—
504C2×Q8—22no—
505C2×Q8—32no—
506C2×Q8—61no—
507C2×Q8—62no—
508C2×Q8—62no—
509C2×Q8C2×#6714yescomplemented
510C2×Q8C23×D312yes—
511C2×D4—28no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—32no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—616no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—61no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—124no—
536C2×D4—248no—
537C2×D4C2×#6714yescomplemented
538C2×D4C23×D314yes—
539C2×D4C23×D312yes—
540C22×C4—21no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—34no—
545C22×C4—68no—
546C22×C4—61no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—124no—
551C22×C4D3×D411yescharacteristic
552C22×C4D3×D411yescharacteristic
553C22×C4D3×D411yescharacteristic
554C22×C4#23714yes—
555C22×C4C2×#6714yes—
556C22×C4C23×D311yescharacteristic
557C22×C4C23×D311yescharacteristic
558C22×C4C23×D311yescharacteristic
559Q16—68no—
560SD16—216no—
561SD16—68no—
562SD16—68no—
563D8—216no—
564D8—68no—
565M16—24no—
566M16—24no—
567M16—64no—
568M16—64no—
569C2×C8—24no—
570C2×C8—34no—
571C2×C8—64no—
572C2×C8C23×D314yes—
573C4⋊C4—34no—
574C4⋊C4—34no—
575C4⋊C4—34no—
576C4⋊C4—68no—
577C4⋊C4—62no—
578C22⋊C4—34no—
579C22⋊C4—34no—
580C22⋊C4—68no—
581C22⋊C4—616no—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C42—34no—
585C42—34no—
586C42—68no—
587C42—62no—
588C42—62no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—24no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—48no—
596C22×C3—44no—
597C22×C3—84no—
598C22×C3—88no—
599C22×C3—88no—
600C22×C3—88no—
601C22×C3C2×#12112yes—
602C22×C3C2×#12112yes—
603C22×C3C2×#12112yes—
604C22×C3C23×D411yescharacteristic
605C2×D3—44no—
606C2×D3—42no—
607C2×D3—84no—
608C3×C4—24no—
609C3×C4C2×#12112yes—
610C3×C4C2×#12112yes—
611C3×C4C2×#12112yes—
612C3×C4C23×D411yescharacteristic
613C3×C4C22×#4111yescharacteristic
614Dic3—28no—
615Dic3—44no—
616Dic3—42no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—42no—
621C23—48no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—62no—
626C23—84no—
627C23—84no—
628C23—82no—
629C23—816no—
630C23—124no—
631C23—122no—
632C23#93914yes—
633C23C2×D3×D411yescharacteristic
634C23C2×D3×D411yescharacteristic
635C23C2×D3×D411yescharacteristic
636Q8—22no—
637Q8—24no—
638Q8—62no—
639Q8—62no—
640Q8—122no—
641Q8C22×#6714yes—
642D4—28no—
643D4—28no—
644D4—22no—
645D4—24no—
646D4—24no—
647D4—24no—
648D4—44no—
649D4—44no—
650D4—44no—
651D4—62no—
652D4—62no—
653D4—124no—
654D4—124no—
655D4—122no—
656D4—2416no—
657D4C22×#6714yes—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—38no—
663C2×C4—64no—
664C2×C4—62no—
665C2×C4—124no—
666C2×C4—122no—
667C2×C4—124no—
668C2×C4—124no—
669C2×C4—248no—
670C2×C4—242no—
671C2×C4#93914yes—
672C2×C4#93914yes—
673C2×C4#93914yes—
674C2×C4C2×D3×D411yescharacteristic
675C2×C4C2×D3×D411yescharacteristic
676C2×C4C2×D3×D411yescharacteristic
677C2×C4C2×#23712yes—
678C2×C4C2×#23712yes—
679C2×C4C2×#23712yes—
680C2×C4C22×#6712yes—
681C2×C4C22×#6712yes—
682C2×C4C22×#6712yes—
683C2×C4C24×D311yescharacteristic
684C8—24no—
685C8—64no—
686C2×C3—22no—
687C2×C3—22no—
688C2×C3—22no—
689C2×C3—44no—
690C2×C3—84no—
691C2×C3C22×#12111yescharacteristic
692C2×C3#358512yes—
693D3—82no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—44no—
699C22—44no—
700C22—48no—
701C22—44no—
702C22—84no—
703C22—88no—
704C22—88no—
705C22—88no—
706C22—124no—
707C22—122no—
708C22—244no—
709C22C2×#93912yes—
710C22C2×#93912yes—
711C22C2×#93912yes—
712C22C22×D3×D411yescharacteristic
713C4—24no—
714C4—68no—
715C4—124no—
716C4—122no—
717C4C2×#93912yes—
718C4C2×#93912yes—
719C4C2×#93912yes—
720C4C22×#23711yescharacteristic
721C4C23×#6711yescharacteristic
722C3#6042611yescharacteristic, complemented, Sylow
723C2—22no—
724C2—22no—
725C2—22no—
726C2—44no—
727C2—84no—
728C2—242no—
729C2#8719212yes—
730C2C22×#93911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
hypercenterC22×AGL(1,ℤ/8)D3
hypocenterC3#60426
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. #87260C2semidirect
3. C2×#5822C2semidirect
4. C2×#5805C2semidirect
5. C2×#5215C2semidirect
6. #83936C2semidirect
7. #83933C2semidirect
8. #83932C2semidirect
9. #83849C2semidirect
10. #83826C2semidirect
11. #83768C2semidirect
12. #83750C2semidirect
19. C2×C3×AGL(1,ℤ/8)C22semidirect
20. C22×C3×SD16C22semidirect
21. C22×C3×D8C22semidirect
25. #5827C22semidirect
27. Dic3×#41C22semidirect
28. C2×#951C22semidirect
30. C2×#950C22semidirect
31. C2×#949C22semidirect
32. #5812C22semidirect
33. C2×#942C22semidirect
37. #5805C22semidirect
38. C2×#940C22semidirect
41. #5798C22semidirect
42. C2×#936C22semidirect
43. C2×#932C22semidirect
48. #5215C22semidirect
49. #5215C22semidirect
50. C2×#832C22semidirect
51. #5166C22semidirect
52. #5163C22semidirect
53. #5153C22semidirect
54. #5150C22semidirect
55. #5133C22semidirect
56. #5131C22semidirect
57. #5120C22semidirect
58. #5119C22semidirect
59. #5118C22semidirect
60. #5113C22semidirect
61. #5102C22semidirect
63. C22×AGL(1,ℤ/8)D3semidirect
78. C2×C3×#41D4semidirect
125. Q8×Dic3C23semidirect
126. C2×#216C23semidirect
128. C2×#215C23semidirect
138. D4×Dic3C23semidirect
139. C2×#214C23semidirect
141. C2×#213C23semidirect
164. #821C23semidirect
165. #816C23semidirect
166. Dic3⋊C8C23semidirect
177. C2×AGL(1,ℤ/8)C2×D3semidirect
179. C22×SD16C2×D3semidirect
180. C22×D8C2×D3semidirect
228. C3×#41C2×D4semidirect
231. C2×C3×Q8C2×D4semidirect
250. C2×C3×D4C2×D4semidirect
331. C2×#41#67semidirect
502. #41C2×#67semidirect
509. C2×Q8C2×#67semidirect
537. C2×D4C2×#67semidirect
722. C3#60426semidirect

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
#872602
C2×#58222
C2×#58052
C2×#52152
#839362
#839332
#839322
#838492
#838262
#837682
#837502
#604263