Finite Group Databasebeta

← #6463808

Subgroups — #6463808

Order 512.

2174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C212yesmaximal, complemented
2C4×#533C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#28209C212yesmaximal, complemented
5#28208C214yesmaximal, complemented
6#28207C212yesmaximal, complemented
7#28206C211yesmaximal, characteristic, complemented
8#28205C211yesmaximal, characteristic, complemented
9#28204C212yesmaximal, complemented
10#28203C212yesmaximal, complemented
11#28202C211yesmaximal, characteristic, complemented
12#28201C211yesmaximal, characteristic, complemented
13#23656C212yesmaximal, complemented
14#23504C212yesmaximal
15#21058C214yesmaximal, complemented
16C2×#1831C211yesmaximal, characteristic, complemented
17#20645C212yesmaximal, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×C4×#41C2212yes—
21#3076—216no—
22C2×#479C2214yes—
23C2×#477C2212yes—
24C2×#475C2212yes—
25C2×#478C2214yes—
26C2×#476C2212yes—
27C2×#474C2212yes—
28C2×#427C2214yes—
29C22×C4⋊C8C2212yes—
30C2×#416C2214yes—
31C2×#416C2214yes—
32C4×C4⋊Q8C2211yescharacteristic
33C4×C4⋊Q8C2211yescharacteristic
34C4×C4⋊Q8C2211yescharacteristic
35C4×C4⋊Q8C2211yescharacteristic
36C4×C4⋊Q8C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic
38C4×#127C2211yescharacteristic
39C4×#127C2211yescharacteristic
40C4×#125C2212yes—
41C4×#125C2212yes—
42C4×#124C2212yes—
43C4×#124C2212yes—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121—21no—
52#2297C2212yes—
53#2296C2212yes—
54#2295—21no—
55#2295—21no—
56#2293—21no—
57#2293—21no—
58#2285C2211yescharacteristic
59#2285C2211yescharacteristic
60C42×Q8—21no—
61C42×Q8—21no—
62C42×D4—21no—
63C42×D4—21no—
64C4×#117C2212yes—
65C2×C43C2211yescharacteristic
66#2085C2214yes—
67#2085C2214yes—
68#2084C2212yes—
69#2084C2212yes—
70#2083C2212yes—
71#2083C2212yes—
72#2043C2212yes—
73#2043C2212yes—
74#2042C2214yes—
75#2042C2214yes—
76#2041C2212yes—
77#2041C2212yes—
78#1928C2214yes—
79#1928C2214yes—
80#1927C2214yes—
81#1927C2214yes—
82#1926C2214yes—
83#1926C2214yes—
84#1925C2214yes—
85#1925C2214yes—
86#1831C2211yescharacteristic
87#1831C2211yescharacteristic
88#1831C2212yes—
89#1831C2212yes—
90#1831C2212yes—
91#1805C2214yes—
92#1804C2214yes—
93#1803C2212yes—
94#1803C2212yes—
95#1802C2212yes—
96#1802C2212yes—
97#1735C2214yes—
98C2×#336C2212yes—
99C2×#336C2212yes—
100C22×#41C2312yes—
101C23×C8C2314yes—
102#533—24no—
103#533D418yescomplemented
104#532—28no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#125C2312yes—
110C2×#124C2312yes—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×#121—21no—
114C2×#121—21no—
115C4×#41—28no—
116C4×#41—28no—
117C2×C4×Q8—21no—
118C2×C4×Q8—21no—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8C2312yes—
124C2×C4×Q8C2312yes—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4C2312yes—
134C2×C4×D4C2312yes—
135C2×#117—22no—
136C2×#117C2312yes—
137C2×#117C2312yes—
138C2×#117C2312yes—
139C22×C42—22no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#479—216no—
148#478—216no—
149#477—28no—
150#476—28no—
151#475—28no—
152#474—28no—
153#427—216no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8—28no—
159C2×C4⋊C8C2314yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162#416—216no—
163#416—216no—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391C2312yes—
177#391C2312yes—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#386—22no—
205#386—22no—
206#385—22no—
207#385—22no—
208#384C2311yescharacteristic
209#384C2311yescharacteristic
210#384C2311yescharacteristic
211#384C2311yescharacteristic
212#382C2312yes—
213#382C2312yes—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218C4×C4⋊C4—22no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4—22no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#376—22no—
249C43—22no—
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43D411yescharacteristic
253C43D411yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256C43C2311yescharacteristic
257C43C2311yescharacteristic
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#336C2312yes—
263#336C2312yes—
264#336C2314yes—
265#336C2312yes—
266#336C2314yes—
267#336C2312yes—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—24no—
272C2×#41—24no—
273C2×#41#4118yes—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8C2412yes—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4C2412yes—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2411yescharacteristic
291C22×C8—28no—
292C22×C8—28no—
293C22×C8—28no—
294C22×C8C2414yes—
295C22×C8C2414yes—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8C2×D414yes—
300C4⋊Q8C2×D414yes—
301#127—24no—
302#125—24no—
303#125C2×D418yes—
304#124—24no—
305#124—24no—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308#121—28no—
309#121—28no—
310C4×Q8—28no—
311C4×Q8—28no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—24no—
315C4×Q8—24no—
316C4×Q8—44no—
317C4×Q8—44no—
318C4×Q8—44no—
319C4×Q8—44no—
320C4×D4—28no—
321C4×D4—28no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—44no—
329C4×D4—48no—
330C4×D4—48no—
331C4×D4—44no—
332#117—24no—
333#117—24no—
334#117—24no—
335#117—28no—
336#117—48no—
337#117C2×D418yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—48no—
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D414yes—
413C2×C42C2×D411yescharacteristic
414C2×C42#4114yes—
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421#107—28no—
422#107—28no—
423#106—28no—
424#106—28no—
425C4⋊C8—24no—
426C4⋊C8—24no—
427C4⋊C8—28no—
428#103—28no—
429#103—28no—
430#103—28no—
431#103—28no—
432#102—28no—
433#102—28no—
434#102—28no—
435#102—28no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452C24—22no—
453C24C22×D411yescharacteristic
454#41—216no—
455#41—216no—
456#41—48no—
457#41—48no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8C2×#4114yes—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—28no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4C2×#4114yes—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4#12114yes—
518C22×C4#12114yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D412yes—
532C22×C4C22×D411yescharacteristic
533C22×C4C2×#4112yes—
534C22×C4C2×#4114yes—
535C22×C42−1+414yes—
536C22×C4C2511yescharacteristic
537C2×C8—24no—
538C2×C8—24no—
539C2×C8—24no—
540C2×C8—24no—
541C2×C8—24no—
542C2×C8—24no—
543C2×C8—416no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—42no—
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4—42no—
572C4⋊C4C22×D414yes—
573C4⋊C4C22×D414yes—
574C22⋊C4—28no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—44no—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C42—28no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—44no—
610C42—44no—
611C42—44no—
612C42—44no—
613C42—44no—
614C42—44no—
615C42—44no—
616C42—44no—
617C42#12114yes—
618C42#12114yes—
619C42#13514yes—
620C42C22×D412yes—
621C42C22×D412yes—
622C42C2×#4112yes—
623C42C2×#4112yes—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—24no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23C2×#12112yes—
636C23#52512yes—
637C23#53612yes—
638C23C23×D411yescharacteristic
639Q8—24no—
640Q8—24no—
641Q8—48no—
642Q8—42no—
643Q8—42no—
644Q8—48no—
645D4—24no—
646D4—24no—
647D4—48no—
648D4—48no—
649D4—416no—
650D4—42no—
651D4—42no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—28no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—24no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—416no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—88no—
707C2×C4—88no—
708C2×C4C2×#12112yes—
709C2×C4C2×#12112yes—
710C2×C4C2×#12112yes—
711C2×C4C2×#12112yes—
712C2×C4C2×#12112yes—
713C2×C4#52512yes—
714C2×C4#53612yes—
715C2×C4#54818yes—
716C2×C4#55218yes—
717C2×C4C2×#13512yes—
718C2×C4C2×#13512yes—
719C2×C4C2×#13512yes—
720C2×C4#57512yes—
721C2×C4#57512yes—
722C2×C4#57512yes—
723C2×C4C23×D411yescharacteristic
724C2×C4C22×#4112yes—
725C2×C4C22×#4111yescharacteristic
726C2×C4C2×2−1+412yes—
727C8—44no—
728C8—44no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22#253614yes—
743C22C22×#12111yescharacteristic
744C22C2×#52511yescharacteristic
745C22C2×#53611yescharacteristic
746C22C22×#13511yescharacteristic
747C22C2×#57511yescharacteristic
748C22C2×#57511yescharacteristic
749C22C2×#57511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—44no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—44no—
763C4—44no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4#253614yes—
769C4#303514yes—
770C4C2×#54812yes—
771C4C2×#55212yes—
772C2—24no—
773C2—84no—
774C2C2×#253611yescharacteristic
775C2C2×#303511yescharacteristic
776C2#6041511yescharacteristic
777C2#6053611yescharacteristic
778C2#6054611yescharacteristic
779C2#6084611yescharacteristic
780C2#6085411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3076C2semidirect
2. C4×#533C2semidirect
4. #28209C2semidirect
5. #28208C2semidirect
6. #28207C2semidirect
7. #28206C2semidirect
8. #28205C2semidirect
9. #28204C2semidirect
10. #28203C2semidirect
11. #28202C2semidirect
12. #28201C2semidirect
13. #23656C2semidirect
15. #21058C2semidirect
16. C2×#1831C2semidirect
17. #20645C2semidirect
103. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
C4×#5332
C4×#5322
#282092
#282082
#282072
#282062
#282052
#282042
#282032
#282022
#282012
#236562
#235042
#210582
C2×#18312
#206452