Finite Group Databasebeta

← #6449858

Subgroups — #6449858

Order 512.

2164 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C211yesmaximal, characteristic, complemented
2C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
3#35172C211yesmaximal, characteristic, complemented
4#34188C211yesmaximal, characteristic, complemented
5#24689C214yesmaximal, complemented
6#24688C214yesmaximal, complemented
7#24679C212yesmaximal, complemented
8#24678C212yesmaximal, complemented
9#24677C212yesmaximal, complemented
10#24676C212yesmaximal, complemented
11#23634C212yesmaximal, complemented
12#23544C212yesmaximal
13#21322C211yesmaximal, characteristic, complemented
14#21175C212yesmaximal, complemented
15#21145C211yesmaximal, characteristic, complemented
16#21065C212yesmaximal, complemented
17C2×#1802C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×#533C2211yescharacteristic
20C2×C4×#41C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#3076—28no—
23C2×#479C2212yescomplemented
24C2×#477C2211yescharacteristic, complemented
25C2×#475C2211yescharacteristic, complemented
26C2×#478C2212yescomplemented
27C2×#476C2211yescharacteristic, complemented
28C2×#474C2211yescharacteristic, complemented
29C4×AGL(1,ℤ/8)—28no—
30C2×#442C2212yes—
31C2×#440C2212yes—
32C2×C4×SD16C2212yes—
33C2×C4×D8C2212yes—
34C2×#428C2211yescharacteristic
35C2×#427C2212yes—
36C2×#424C2212yes—
37C22×C4⋊C8C2211yescharacteristic
38C2×#417C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C2×#416C2212yes—
41C22×#102C2212yes—
42C2×C4×M16C2211yescharacteristic
43#2848—22no—
44#2626—22no—
45#2580—22no—
46#2566C2214yes—
47#2563C2212yes—
48#2542C2212yes—
49#2538—21no—
50#2538—21no—
51#2355C2212yescomplemented
52#2355C2212yescomplemented
53#2354C2212yescomplemented
54#2354C2212yescomplemented
55#2352—22no—
56#2352—22no—
57#2317C2212yes—
58#2314—22no—
59#2311C2212yes—
60#2309C2212yes—
61#2285—21no—
62#2285—21no—
63#2285C2211yescharacteristic
64C2×#384C2211yescharacteristic
65#2274C2212yes—
66#2074C2214yescomplemented
67#2073C2214yescomplemented
68#2072C2214yescomplemented
69#2071C2214yescomplemented
70#2055C2214yes—
71#2055C2214yes—
72#2054C2214yes—
73#2054C2214yes—
74#1992C2214yescomplemented
75#1990C2212yescomplemented
76#1990C2212yescomplemented
77#1949C2214yescomplemented
78#1949C2214yescomplemented
79#1948C2214yescomplemented
80#1947C2214yescomplemented
81#1940C2214yescomplemented
82#1939C2212yescomplemented
83#1939C2212yescomplemented
84#1926C2214yes—
85#1926C2214yes—
86#1925C2214yes—
87#1925C2214yes—
88#1802C2212yes—
89#1802C2212yes—
90#1802C2214yes—
91#1736C2212yes—
92#1736C2212yes—
93C2×#340C2212yes—
94#1729C2212yes—
95C22×#41C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4—21no—
98C2×AGL(1,ℤ/8)—24no—
99C2×AGL(1,ℤ/8)—24no—
100C2×AGL(1,ℤ/8)—24no—
101C22×SD16C2312yes—
102C22×D8C2312yes—
103C22×M16C2311yescharacteristic
104C22×M16C2311yescharacteristic
105C23×C8C2312yes—
106#533—24no—
107#533—24no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#125C2312yes—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C4×#41—24no—
116C4×#41D418yes—
117C2×C4×Q8—21no—
118C2×C4×Q8—21no—
119C2×C4×Q8C2311yescharacteristic
120C2×C4×Q8C2311yescharacteristic
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4C2312yes—
128C2×C4×D4C2312yes—
129C2×C4×D4C2311yescharacteristic
130C2×C4×D4C2311yescharacteristic
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—21no—
134C2×#117C2312yes—
135C2×#117C2311yescharacteristic
136C2×#117C2312yes—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C42—21no—
143C22×C42C2311yescharacteristic
144#479—28no—
145#478—28no—
146#477—24no—
147#476—24no—
148#475—24no—
149#474—24no—
150#442—28no—
151#440—28no—
152C4×SD16—28no—
153C4×D8—28no—
154#428—24no—
155#427—28no—
156C2×#107C2312yes—
157C2×#107C2312yes—
158C2×#107C2312yes—
159C2×#106C2312yes—
160C2×#106C2312yes—
161C2×#106C2312yes—
162#424—28no—
163C2×C4⋊C8—24no—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2314yes—
168C2×C4⋊C8C2314yes—
169#418—24no—
170#417—24no—
171#416—28no—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#102—28no—
176C2×#102C2312yes—
177C2×#102C2312yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C4×M16—24no—
184C2×#97C2312yes—
185C2×C4×C8C2312yes—
186#399—24no—
187#396—24no—
188#396—24no—
189#393—24no—
190#391C2314yes—
191#390—22no—
192#390—22no—
193#390C2314yes—
194#390C2314yes—
195#390C2314yes—
196#389—22no—
197#389—22no—
198#388—24no—
199#388—24no—
200#387—24no—
201#387—24no—
202#386—24no—
203#385—24no—
204#385—24no—
205#385—24no—
206#384—21no—
207#384—21no—
208#384D411yescharacteristic
209#384D411yescharacteristic
210#384C2314yes—
211#384C2312yes—
212#384C2312yes—
213#382—22no—
214#382—22no—
215#382D412yes—
216#382C2314yes—
217#380—22no—
218#380—22no—
219#380—22no—
220#380—22no—
221#380—22no—
222#380—22no—
223#380D412yes—
224#380D412yes—
225#379—24no—
226C4×C4⋊C4—22no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4C2314yes—
231C4×C4⋊C4C2314yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—24no—
235#340C2314yes—
236#340C2314yes—
237#340C2314yes—
238#340C2314yes—
239#340C2314yes—
240#340C2314yes—
241#336C2314yes—
242#336C2314yes—
243C25—21no—
244C2×#41—22no—
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41C2×D414yes—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8C2411yescharacteristic
253C22×D4—21no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4#4114yes—
261C22×D4C2411yescharacteristic
262C22×D4C2412yes—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—44no—
271C23×C4—82no—
272C23×C4—82no—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2411yescharacteristic
276AGL(1,ℤ/8)—232no—
277C2×SD16—24no—
278C2×SD16—24no—
279C2×SD16—24no—
280C2×D8—24no—
281C2×D8—24no—
282C2×D8—24no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16#4114yes—
289C22×C8—24no—
290C22×C8—24no—
291C22×C8—24no—
292C22×C8C2412yes—
293C22×C8C2412yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300#125—24no—
301#125—24no—
302C22⋊Q8—44no—
303C22⋊Q8—44no—
304C22⋊Q8—84no—
305C22⋊Q8—84no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—44no—
309C4×Q8—44no—
310C4×Q8C2×D414yes—
311C4×Q8C2×D414yes—
312C4×D4—28no—
313C4×D4—28no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—44no—
321C4×D4—44no—
322C4×D4C2×D414yes—
323C4×D4C2×D414yes—
324#117—22no—
325#117—24no—
326#117—24no—
327#117—28no—
328#117—24no—
329#117—24no—
330#117—84no—
331#117—84no—
332#117C2×D414yes—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—82no—
352C2×C4⋊C4—82no—
353C2×C4⋊C4C2×D412yes—
354C2×C4⋊C4C2×D412yes—
355C2×C4⋊C4C2×D412yes—
356C2×C4⋊C4C2×D412yes—
357C2×C4⋊C4C2×D412yes—
358C2×C4⋊C4C2×D412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2414yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2411yescharacteristic
364C2×C4⋊C4C2411yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D414yes—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—28no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D414yes—
389C2×C42#4114yes—
390C2×C42C2414yes—
391C2×C42C2411yescharacteristic
392C2×C42C2411yescharacteristic
393#107—24no—
394#107—24no—
395#107—24no—
396#106—24no—
397#106—24no—
398#106—24no—
399C4⋊C8—28no—
400C4⋊C8—28no—
401C4⋊C8—22no—
402C4⋊C8—22no—
403C4⋊C8—24no—
404#103—24no—
405#103—24no—
406#103—24no—
407#102—24no—
408#102—24no—
409#102—24no—
410#102—28no—
411#102—28no—
412#102—24no—
413#102—24no—
414#97—24no—
415C4×C8—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95C2×D414yes—
423#95C2×D414yes—
424C24—21no—
425C24—22no—
426C24—24no—
427C24—42no—
428C24—42no—
429C24—81no—
430C24—81no—
431C24—81no—
432C24—81no—
433C24C22×D411yescharacteristic
434#41—28no—
435#41—28no—
436#41—44no—
437#41—44no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8—81no—
449C2×Q8C22×D412yes—
450C2×D4—24no—
451C2×D4—28no—
452C2×D4—24no—
453C2×D4—28no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—44no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4C22×D412yes—
471C2×D4C2×#4114yes—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—82no—
499C22×C4—82no—
500C22×C4—816no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4#12114yes—
506C22×C4#12114yes—
507C22×C4C22×D414yes—
508C22×C4C22×D414yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D412yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C42−1+412yes—
519C22×C42−1+412yes—
520C22×C4C2511yescharacteristic
521SD16—216no—
522D8—216no—
523M16—28no—
524M16—44no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—48no—
537C2×C8C2×#4114yes—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—24no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—44no—
557C4⋊C4—42no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—82no—
565C4⋊C4—82no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4C22×D412yes—
569C4⋊C4C22×D412yes—
570C22⋊C4—24no—
571C22⋊C4—28no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—84no—
578C22⋊C4—84no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C22⋊C4—84no—
583C42—24no—
584C42—24no—
585C42—24no—
586C42—24no—
587C42—24no—
588C42—44no—
589C42—84no—
590C42—84no—
591C42#12114yes—
592C42#12114yes—
593C42C22×D412yes—
594C42C22×D412yes—
595C42C2×#4112yes—
596C42C2×#4112yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—24no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—48no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—84no—
617C23—84no—
618C23—84no—
619C23—84no—
620C23—84no—
621C23—84no—
622C23C2×#12112yes—
623C23#54712yes—
624C23#54812yes—
625C23C23×D411yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—84no—
631Q8—84no—
632D4—22no—
633D4—24no—
634D4—22no—
635D4—24no—
636D4—48no—
637D4—48no—
638D4—42no—
639D4—41no—
640D4—42no—
641D4—41no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—44no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—48no—
667C2×C4—48no—
668C2×C4—44no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—88no—
681C2×C4—84no—
682C2×C4—88no—
683C2×C4—164no—
684C2×C4C2×#12112yes—
685C2×C4C2×#12112yes—
686C2×C4C2×#12112yes—
687C2×C4C2×#12112yes—
688C2×C4C2×#12112yes—
689C2×C4#52514yes—
690C2×C4#53614yes—
691C2×C4#54712yes—
692C2×C4#54812yes—
693C2×C4#55214yes—
694C2×C4#55614yes—
695C2×C4#57612yes—
696C2×C4#57712yes—
697C2×C4C23×D411yescharacteristic
698C2×C4C22×#4111yescharacteristic
699C2×C4C22×#4111yescharacteristic
700C2×C4C22×#4111yescharacteristic
701C2×C4C2×2−1+411yescharacteristic
702C2×C4C2×2−1+411yescharacteristic
703C8—24no—
704C8—42no—
705C8—42no—
706C8—42no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—816no—
720C22—82no—
721C22—82no—
722C22—81no—
723C22—82no—
724C22—81no—
725C22—82no—
726C22—81no—
727C22—81no—
728C22#241514yes—
729C22C22×#12111yescharacteristic
730C22C2×#54711yescharacteristic
731C22C2×#54811yescharacteristic
732C22C2×#57611yescharacteristic
733C22C2×#57711yescharacteristic
734C22#358511yescharacteristic
735C22#358611yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—42no—
741C4—44no—
742C4—44no—
743C4—42no—
744C4—82no—
745C4—82no—
746C4—82no—
747C4—84no—
748C4#241514yes—
749C4#304514yes—
750C4C2×#52511yescharacteristic
751C4C2×#53611yescharacteristic
752C4C2×#55211yescharacteristic
753C4C2×#55611yescharacteristic
754C2—24no—
755C2—82no—
756C2—84no—
757C2C2×#241511yescharacteristic
758C2C2×#304511yescharacteristic
759C2#6042511yescharacteristic
760C2#6127811yescharacteristic
761C2#6127911yescharacteristic
762C2#6133911yescharacteristic
763C2#6134011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3076C2semidirect
3. #35172C2semidirect
4. #34188C2semidirect
5. #24689C2semidirect
6. #24688C2semidirect
7. #24679C2semidirect
8. #24678C2semidirect
9. #24677C2semidirect
10. #24676C2semidirect
11. #23634C2semidirect
13. #21322C2semidirect
14. #21175C2semidirect
15. #21145C2semidirect
16. #21065C2semidirect
17. C2×#1802C2semidirect
23. C2×#479C22semidirect
24. C2×#477C22semidirect
25. C2×#475C22semidirect
26. C2×#478C22semidirect
27. C2×#476C22semidirect
28. C2×#474C22semidirect
51. #2355C22semidirect
52. #2355C22semidirect
53. #2354C22semidirect
54. #2354C22semidirect
66. #2074C22semidirect
67. #2073C22semidirect
68. #2072C22semidirect
69. #2071C22semidirect
74. #1992C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1949C22semidirect
78. #1949C22semidirect
79. #1948C22semidirect
80. #1947C22semidirect
81. #1940C22semidirect
82. #1939C22semidirect
83. #1939C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
C2×C4×AGL(1,ℤ/8)2
#351722
#341882
#246892
#246882
#246792
#246782
#246772
#246762
#236342
#235442
#213222
#211752
#211452
#210652
C2×#18022