Finite Group Databasebeta

← #10822323

Subgroups — #10822323

Order 768.

2282 conjugacy classes of subgroups.

The subgroup lattice has 748 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×#5832C211yesmaximal, characteristic, complemented
3C22×#932C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5C2×#5221C211yesmaximal, characteristic, complemented
6C2×#5133C211yesmaximal, characteristic, complemented
7#72057C212yesmaximal, complemented
8#72055C212yesmaximal, complemented
9#72045C212yesmaximal, complemented
10#72044C212yesmaximal, complemented
11#71979C211yesmaximal, characteristic, complemented
12#23428—31nomaximal, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×#235C2211yescharacteristic
16C2×C3×AGL(1,ℤ/8)—24no—
17C2×C3×AGL(1,ℤ/8)—24no—
18C2×C3×AGL(1,ℤ/8)—24no—
19C22×C3×SD16C2212yes—
20C22×C3×D8C2212yes—
21C22×C3×M16C2211yescharacteristic
22C22×#217—22no—
23#5832—24no—
24#5832—24no—
25C2×#947C2211yescharacteristic, complemented
26C2×#944C2211yescharacteristic, complemented
27C2×#940C2211yescharacteristic, complemented
28C2×#939—22no—
29C2×#936C2211yescharacteristic, complemented
30C22×#214C2212yes—
31C2×#932—24no—
32C2×#932—24no—
33C2×#932—24no—
34C22×#213C2212yes—
35C2×C4×#67—22no—
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×#208C2211yescharacteristic
39#5232—24no—
40C2×#835C2212yescomplemented
41#5221—22no—
42#5221C2212yes—
43#5221C2212yes—
44C2×#832C2212yescomplemented
45#5133—24no—
46C2×#821C2212yescomplemented
47C2×#816C2212yescomplemented
48#4550C2212yescomplemented
49#4550C2212yescomplemented
50C22×AGL(1,ℤ/8)—31no—
51C22×AGL(1,ℤ/8)D311yescharacteristic, complemented
52C2×#532—31no—
53C2×#417—31no—
54C2×#417—31no—
55C2×#390—31no—
56#2013—32no—
57#2012—32no—
58#2012—32no—
59#2011—32no—
60#1728—31no—
61C25×C3—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41D414yes—
68C22×C3×Q8C2311yescharacteristic
69C22×C3×D4—21no—
70C22×C3×D4—22no—
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—21no—
75C22×C3×D4—22no—
76C22×C3×D4D414yescomplemented
77C22×C3×D4C2311yescharacteristic
78C22×C3×D4C2312yes—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—22no—
83C23×Dic3—21no—
84C23×Dic3D412yes—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235D414yes—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×Dic6C2311yescharacteristic
94C3×AGL(1,ℤ/8)—232no—
95C2×C3×SD16—24no—
96C2×C3×SD16—24no—
97C2×C3×SD16—24no—
98C2×C3×D8—24no—
99C2×C3×D8—24no—
100C2×C3×D8—24no—
101C2×C3×M16—22no—
102C2×C3×M16—22no—
103C2×C3×M16D414yescomplemented
104C22×C3×C8C2312yes—
105C2×#217—22no—
106C2×#217—24no—
107C2×#217—24no—
108C2×#217—48no—
109#947—22no—
110#947—22no—
111#944—22no—
112#944—22no—
113#940—22no—
114#940—22no—
115#939—216no—
116#936—22no—
117#936—22no—
118C2×#214—24no—
119C2×#214—24no—
120C2×#214—24no—
121#932—232no—
122C2×#213—24no—
123C2×#213—24no—
124C2×#213—24no—
125C4×#67—216no—
126C2×(C2×D3)⋊C4—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2312yes—
131C2×Dic3⋊C4—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3D412yes—
135C2×C4×Dic3C2311yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C2×#208—22no—
138C2×#208—22no—
139C2×#208D414yescomplemented
140C22×C3⋊C8C2312yes—
141#835—24no—
142#832—24no—
143#821—24no—
144#816—24no—
145C22×#41—31no—
146C22×#41C2×D311yescharacteristic
147C23×D4C2×D311yescharacteristic
148C2×AGL(1,ℤ/8)—24no—
149C2×AGL(1,ℤ/8)—24no—
150C2×AGL(1,ℤ/8)—24no—
151C2×AGL(1,ℤ/8)—64no—
152C2×AGL(1,ℤ/8)—64no—
153C2×AGL(1,ℤ/8)—64no—
154C22×SD16—32no—
155C22×SD16C2×D312yes—
156C22×D8—32no—
157C22×D8C2×D312yes—
158C22×M16—31no—
159C22×M16C2×D311yescharacteristic
160#532—64no—
161#532—64no—
162C2×C4⋊Q8—31no—
163C2×#127—31no—
164C2×#124—31no—
165C2×#124—31no—
166C2×#121—62no—
167C2×C4×D4—62no—
168C22×C4⋊C4—31no—
169C22×C22⋊C4—62no—
170C22×C42—31no—
171#417—64no—
172#417—64no—
173C2×#103—32no—
174C2×#103—32no—
175C2×#102—32no—
176C2×#102—32no—
177#390—32no—
178#390—32no—
179#390—62no—
180#336—32no—
181#336—32no—
182C24×C3—24no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—44no—
186C24×C3—44no—
187C24×C3—42no—
188C24×C3—42no—
189C24×C3C2×D411yescharacteristic
190C23×D3—21no—
191C3×#41—28no—
192C3×#41—28no—
193C3×#41—44no—
194C3×#41—44no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8C2×D412yes—
201C2×C3×D4—24no—
202C2×C3×D4—28no—
203C2×C3×D4—28no—
204C2×C3×D4—24no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—42no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—44no—
219C2×C3×D4—44no—
220C2×C3×D4—42no—
221C2×C3×D4C2×D414yes—
222C2×C3×D4C2×D412yes—
223C22×C3×C4—21no—
224C22×C3×C4—24no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4#4112yes—
234C22×C3×C4C2411yescharacteristic
235C2×#67—28no—
236C2×#67—24no—
237C2×#67—44no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—44no—
241C22×Dic3—24no—
242C22×Dic3—21no—
243C22×Dic3—24no—
244C22×Dic3—22no—
245C22×Dic3—42no—
246C22×Dic3—44no—
247C22×Dic3—42no—
248C22×Dic3C2×D412yes—
249C22×Dic3C2×D412yes—
250#235—28no—
251#235—28no—
252#235—44no—
253#235—44no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12C2×D412yes—
260C2×C4×D3—24no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6C2×D412yes—
269C3×SD16—216no—
270C3×D8—216no—
271C3×M16—28no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8C2×D414yes—
275#217—28no—
276#217—48no—
277#217—48no—
278#214—216no—
279#213—216no—
280(C2×D3)⋊C4—28no—
281C4⋊Dic3—22no—
282C4⋊Dic3—22no—
283C4⋊Dic3—42no—
284Dic3⋊C4—28no—
285C4×Dic3—24no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3—21no—
289C4×Dic3—21no—
290#208—28no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C2×D414yes—
294C25—21no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—34no—
301C2×#41—62no—
302C2×#41—62no—
303C2×#41—62no—
304C2×#41—62no—
305C2×#41—62no—
306C2×#41#6714yes—
307C22×Q8—31no—
308C22×Q8C22×D311yescharacteristic
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—31no—
317C22×D4—62no—
318C22×D4—61no—
319C22×D4#6714yescomplemented
320C22×D4C22×D311yescharacteristic
321C22×D4C22×D312yes—
322C23×C4—21no—
323C23×C4—32no—
324C23×C4—61no—
325C23×C4—61no—
326C23×C4C22×D311yescharacteristic
327AGL(1,ℤ/8)—232no—
328AGL(1,ℤ/8)—632no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—64no—
333C2×SD16—64no—
334C2×SD16—64no—
335C2×D8—24no—
336C2×D8—24no—
337C2×D8—24no—
338C2×D8—64no—
339C2×D8—64no—
340C2×D8—64no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—34no—
344C2×M16—62no—
345C2×M16—62no—
346C2×M16#6714yescomplemented
347C22×C8—32no—
348C22×C8C22×D312yes—
349C4⋊Q8—62no—
350C4⋊Q8—62no—
351#127—62no—
352#127—62no—
353#124—62no—
354#124—62no—
355#124—62no—
356#124—62no—
357#121—616no—
358C4×D4—616no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—61no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—128no—
369C2×C42—32no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—62no—
373C2×C42—62no—
374#103—64no—
375#103—64no—
376#102—64no—
377#102—64no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—24no—
382C23×C3—416no—
383C23×C3—42no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—42no—
387C23×C3—44no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—44no—
391C23×C3—48no—
392C23×C3—84no—
393C23×C3—84no—
394C23×C3—88no—
395C23×C3#12012yes—
396C23×C3#12112yes—
397C23×C3#12712yes—
398C23×C3C22×D411yescharacteristic
399C22×D3—22no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—42no—
403C22×D3—42no—
404C3×Q8—22no—
405C3×Q8—22no—
406C3×Q8—41no—
407C3×Q8—41no—
408C3×D4—24no—
409C3×D4—22no—
410C3×D4—24no—
411C3×D4—22no—
412C3×D4—48no—
413C3×D4—41no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—41no—
417C3×D4—48no—
418C2×C3×C4—22no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—48no—
422C2×C3×C4#12014yes—
423C2×C3×C4#12012yes—
424C2×C3×C4#12014yes—
425C2×C3×C4#12114yes—
426C2×C3×C4#12114yes—
427C2×C3×C4#12112yes—
428C2×C3×C4#12712yes—
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C22×D411yescharacteristic
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435#67—416no—
436#67—48no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—48no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—44no—
448C2×Dic3—84no—
449C2×Dic3AGL(1,ℤ/8)14yescomplemented
450D12—22no—
451D12—22no—
452D12—41no—
453D12—41no—
454C4×D3—48no—
455Dic6—22no—
456Dic6—22no—
457Dic6—41no—
458Dic6—41no—
459C3×C8—24no—
460C3⋊C8—24no—
461C24—24no—
462C24—22no—
463C24—21no—
464C24—44no—
465C24—44no—
466C24—42no—
467C24—42no—
468C24—61no—
469C24D3×D411yescharacteristic
470#41—28no—
471#41—28no—
472#41—44no—
473#41—44no—
474#41—68no—
475#41—68no—
476#41—124no—
477#41—124no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—32no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×Q8C2×#6712yes—
490C2×D4—24no—
491C2×D4—28no—
492C2×D4—24no—
493C2×D4—28no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—32no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—68no—
512C2×D4—64no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—124no—
519C2×D4—124no—
520C2×D4—122no—
521C2×D4—122no—
522C2×D4C2×#6712yes—
523C2×D4C2×#6714yes—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—61no—
533C22×C4—64no—
534C22×C4—62no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4—124no—
539C22×C4—122no—
540C22×C4D3×D412yes—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D412yes—
543C22×C4#23712yes—
544C22×C4C2×#6712yes—
545C22×C4C2×#6712yes—
546C22×C4C2×#6712yes—
547C22×C4C23×D311yescharacteristic
548SD16—216no—
549SD16—616no—
550D8—216no—
551D8—616no—
552M16—28no—
553M16—68no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—34no—
557C2×C8—62no—
558C2×C8—62no—
559C2×C8C2×#6714yes—
560C4⋊C4—68no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—122no—
564C22⋊C4—68no—
565C22⋊C4—68no—
566C22⋊C4—128no—
567C22⋊C4—128no—
568C42—64no—
569C42—61no—
570C42—61no—
571C42—61no—
572C42—61no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—24no—
576C22×C3—24no—
577C22×C3—42no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—48no—
581C22×C3—816no—
582C22×C3—81no—
583C22×C3—82no—
584C22×C3—81no—
585C22×C3—82no—
586C22×C3—84no—
587C22×C3—82no—
588C22×C3#39214yes—
589C22×C3C2×#12011yescharacteristic
590C22×C3C2×#12111yescharacteristic
591C22×C3C2×#12711yescharacteristic
592C22×C3C2×AGL(1,ℤ/8)12yes—
593C22×C3#57512yes—
594C2×D3—42no—
595C2×D3—44no—
596C2×D3—81no—
597C2×D3—81no—
598C2×D3—82no—
599C3×C4—42no—
600C3×C4#39214yes—
601C3×C4C2×#12011yescharacteristic
602C3×C4C2×#12011yescharacteristic
603C3×C4C2×#12111yescharacteristic
604C3×C4C2×#12111yescharacteristic
605Dic3—24no—
606Dic3—42no—
607Dic3—42no—
608Dic3—82no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—416no—
614C23—48no—
615C23—44no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—62no—
624C23—84no—
625C23—84no—
626C23—88no—
627C23—122no—
628C23—122no—
629C23—121no—
630C23—121no—
631C23#93712yes—
632C23#93912yes—
633C23#94012yes—
634C23C2×D3×D411yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—62no—
640Q8—62no—
641Q8—121no—
642Q8—121no—
643D4—24no—
644D4—22no—
645D4—22no—
646D4—24no—
647D4—48no—
648D4—48no—
649D4—41no—
650D4—42no—
651D4—41no—
652D4—42no—
653D4—62no—
654D4—62no—
655D4—1216no—
656D4—128no—
657D4—121no—
658D4—121no—
659C2×C4—22no—
660C2×C4—34no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—48no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—128no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—128no—
674C2×C4—124no—
675C2×C4—122no—
676C2×C4—244no—
677C2×C4#93712yes—
678C2×C4#93714yes—
679C2×C4#93814yes—
680C2×C4#93912yes—
681C2×C4#93914yes—
682C2×C4#94012yes—
683C2×C4#95314yes—
684C2×C4C2×D3×D411yescharacteristic
685C2×C4C2×D3×D411yescharacteristic
686C2×C4C2×#23711yescharacteristic
687C2×C4C22×#6711yescharacteristic
688C2×C4C22×#6711yescharacteristic
689C2×C4C22×#6711yescharacteristic
690C8—24no—
691C8—64no—
692C2×C3—24no—
693C2×C3—82no—
694C2×C3—84no—
695C2×C3C2×#39211yescharacteristic
696C2×C3#300612yes—
697C2×C3#303612yes—
698C2×C3#315111yescharacteristic
699C2×C3#315311yescharacteristic
700D3—82no—
701C22—24no—
702C22—22no—
703C22—22no—
704C22—24no—
705C22—42no—
706C22—44no—
707C22—48no—
708C22—44no—
709C22—816no—
710C22—82no—
711C22—82no—
712C22—81no—
713C22—82no—
714C22—81no—
715C22—84no—
716C22—122no—
717C22—124no—
718C22—242no—
719C22—241no—
720C22—241no—
721C22#522314yes—
722C22D3×AGL(1,ℤ/8)12yes—
723C22#577312yes—
724C22C2×#93711yescharacteristic
725C22C2×#93911yescharacteristic
726C22C2×#94011yescharacteristic
727C4—42no—
728C4—64no—
729C4—122no—
730C4—122no—
731C4—242no—
732C4#522314yes—
733C4C2×#93711yescharacteristic
734C4C2×#93811yescharacteristic
735C4C2×#93911yescharacteristic
736C4C2×#95311yescharacteristic
737C3#2342811yescharacteristic, complemented, Sylow
738C2—24no—
739C2—84no—
740C2—82no—
741C2—242no—
742C2#8393112yes—
743C2#8393711yescharacteristic
744C2#8393811yescharacteristic
745C2#8394612yes—
746C2C2×#522311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×AGL(1,ℤ/8)C2
socleC23×C3C22×D4
hypercenterC22×AGL(1,ℤ/8)D3
hypocenterC3#23428
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ 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×#5832C2semidirect
3. C22×#932C2semidirect
4. C2×#5232C2semidirect
5. C2×#5221C2semidirect
6. C2×#5133C2semidirect
7. #72057C2semidirect
8. #72055C2semidirect
9. #72045C2semidirect
10. #72044C2semidirect
11. #71979C2semidirect
25. C2×#947C22semidirect
26. C2×#944C22semidirect
27. C2×#940C22semidirect
29. C2×#936C22semidirect
40. C2×#835C22semidirect
44. C2×#832C22semidirect
46. C2×#821C22semidirect
47. C2×#816C22semidirect
48. #4550C22semidirect
49. #4550C22semidirect
51. C22×AGL(1,ℤ/8)D3semidirect
76. C22×C3×D4D4semidirect
103. C2×C3×M16D4semidirect
139. C2×#208D4semidirect
319. C22×D4#67semidirect
346. C2×M16#67semidirect
449. C2×Dic3AGL(1,ℤ/8)semidirect
737. C3#23428semidirect

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×#58322
C22×#9322
C2×#52322
C2×#52212
C2×#51332
#720572
#720552
#720452
#720442
#719792
#234283