Finite Group Databasebeta

← #6514125

Subgroups — #6514125

Order 512.

2138 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3246C211yesmaximal, characteristic
2C2×#3103C211yesmaximal, characteristic
3#34953C211yesmaximal, characteristic, complemented
4#34207C211yesmaximal, characteristic
5#28283C212yesmaximal, complemented
6#28252C212yesmaximal, complemented
7#28205C212yesmaximal, complemented
8#28160C212yesmaximal, complemented
9#25202C214yesmaximal, complemented
10#25078C214yesmaximal, complemented
11#24815C212yesmaximal, complemented
12#24730C212yesmaximal, complemented
13#24680C212yesmaximal, complemented
14#24630C212yesmaximal, complemented
15#21972C211yesmaximal, characteristic, complemented
16#21860C211yesmaximal, characteristic, complemented
17C2×#1803C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#520—21no—
21C22×C4×Q8C2211yescharacteristic
22#3246—28no—
23#3103—28no—
24C2×#481C2212yes—
25C2×#475C2211yescharacteristic
26C2×#475C2212yes—
27C2×#475C2211yescharacteristic
28C2×#476C2212yes—
29C2×#465C2214yes—
30C2×#460C2211yescharacteristic
31C2×#460C2212yes—
32C2×#460C2211yescharacteristic
33C2×#461C2212yes—
34C2×#461C2214yes—
35C2×#448C2212yes—
36C2×C4×SD16C2212yes—
37C2×C4×SD16C2212yes—
38C2×#431C2211yescharacteristic
39C22×C4⋊C8C2211yescharacteristic
40C22×#103C2212yes—
41#2584—21no—
42#2584—21no—
43#2583—22no—
44#2567C2211yescharacteristic
45#2567C2211yescharacteristic
46#2546C2211yescharacteristic
47#2546C2211yescharacteristic
48#2502C2212yes—
49#2434C2212yes—
50#2399—22no—
51#2361—22no—
52#2361C2214yes—
53#2354—21no—
54#2354C2212yes—
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2212yes—
57#2326—22no—
58#2311—21no—
59C4×C4⋊Q8C2212yes—
60C4×C4⋊Q8C2212yes—
61C4×C4⋊Q8C2212yes—
62C4×#127C2212yes—
63#2296—21no—
64#2296—21no—
65C2×#384C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#2084C2214yes—
68#2071C2214yes—
69#2066C2214yes—
70#2066C2214yes—
71#2055C2214yes—
72#2055C2214yes—
73#2043C2214yes—
74#2013C2214yes—
75#1990C2212yes—
76#1981C2214yes—
77#1956C2212yes—
78#1948C2214yes—
79#1939C2212yes—
80#1939C2212yes—
81#1927C2214yes—
82#1927C2214yes—
83#1877C2214yes—
84#1877C2214yes—
85#1872C2214yes—
86#1850C2214yes—
87#1842C2212yes—
88#1831C2212yes—
89#1803C2212yes—
90#1803C2212yes—
91#1803C2212yes—
92#1803C2212yes—
93#1803C2212yes—
94#1803C2212yes—
95#1802C2214yes—
96C2×#340C2212yes—
97C22×#41—21no—
98C23×Q8C2311yescharacteristic
99C22×SD16C2312yes—
100C22×SD16C2312yes—
101C22×SD16C2314yes—
102C23×C8C2312yes—
103#533—24no—
104#533—24no—
105#532—24no—
106#532D418yes—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2312yes—
109C2×C4⋊Q8C2312yes—
110C2×C4⋊Q8C2311yescharacteristic
111C2×C4⋊Q8C2311yescharacteristic
112C2×#127C2311yescharacteristic
113C2×#125—21no—
114C2×#124—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8C2312yes—
117C2×#121—21no—
118C2×#121C2312yes—
119#520—48no—
120C2×C4×Q8—22no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—21no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8C2311yescharacteristic
127C2×C4×Q8C2311yescharacteristic
128C2×C4×Q8C2312yes—
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×D4—24no—
132C2×C4×D4—21no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2314yes—
137C2×#117—21no—
138C2×#117—22no—
139C2×#117D411yescharacteristic
140C2×#117D411yescharacteristic
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—22no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C42—21no—
148C22×C42C2311yescharacteristic
149#481—28no—
150#476—28no—
151#475—24no—
152#475—24no—
153#475—28no—
154#465—216no—
155#461—28no—
156#461—48no—
157#460—24no—
158#460—24no—
159#460—28no—
160#448—28no—
161C4×SD16—28no—
162C4×SD16—28no—
163#431—24no—
164C2×#106C2312yes—
165C2×#106C2312yes—
166C2×#106C2314yes—
167C2×C4⋊C8—24no—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2314yes—
173C2×C4⋊C8C2314yes—
174C2×#103—44no—
175C2×#103C2312yes—
176C2×#103C2314yes—
177C2×#103C2312yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102C2312yes—
183C2×#102C2314yes—
184C2×#102C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C4×C8C2312yes—
187#398—22no—
188#398—22no—
189#398—22no—
190#398—22no—
191#395—22no—
192#395—22no—
193#395—22no—
194#395—22no—
195#391—22no—
196#391C2312yes—
197#391C2312yes—
198#391C2312yes—
199#391C2312yes—
200#390—22no—
201#390—22no—
202#390C2314yes—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—22no—
212#389—22no—
213#389—22no—
214#389—22no—
215#389—22no—
216#389C2314yes—
217#388—24no—
218#388—24no—
219#386—24no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#385—24no—
225#385—24no—
226#384—21no—
227#384—21no—
228#384C2312yes—
229#384C2312yes—
230#384C2312yes—
231#384C2312yes—
232#380—22no—
233#380—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4D411yescharacteristic
240C4×C4⋊C4D411yescharacteristic
241C4×C4⋊C4C2314yes—
242C4×C4⋊C4C2311yescharacteristic
243C4×C4⋊C4C2311yescharacteristic
244C4×C22⋊C4D412yes—
245C4×C22⋊C4C2312yes—
246#376D412yes—
247C43C2312yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#336C2314yes—
253#336C2314yes—
254C2×#41—28no—
255C2×#41—44no—
256C2×#41—44no—
257C22×Q8—21no—
258C22×Q8—21no—
259C22×Q8—21no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—41no—
265C22×Q8—41no—
266C22×Q8C2412yes—
267C22×Q8C2411yescharacteristic
268C22×Q8C2411yescharacteristic
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C2412yes—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×SD16—24no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—24no—
285C2×SD16—28no—
286C2×SD16—42no—
287C2×SD16—42no—
288C2×SD16—44no—
289C2×SD16—44no—
290C22×C8—24no—
291C22×C8—42no—
292C22×C8—42no—
293C22×C8C2414yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—42no—
304C4⋊Q8—42no—
305C4⋊Q8C2×D414yes—
306#127—22no—
307#127C2×D414yes—
308#125—44no—
309#124—28no—
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8—44no—
313#121—28no—
314#121—24no—
315#121C2×D418yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—24no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—24no—
326C4×Q8—44no—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×Q8—48no—
330C4×D4—28no—
331C4×D4—24no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—416no—
335C4×D4—48no—
336C4×D4—84no—
337C4×D4C2×D418yes—
338#117—24no—
339#117—44no—
340#117—48no—
341#117SD1618yescomplemented
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—48no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2414yes—
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2411yescharacteristic
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4C2×D412yes—
391C2×C22⋊C4C2×D412yes—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—44no—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D414yes—
405C2×C42C2×D412yes—
406C2×C42#4114yes—
407C2×C42C2412yes—
408C2×C42C2412yes—
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411#106—24no—
412#106—24no—
413#106—28no—
414C4⋊C8—24no—
415C4⋊C8—24no—
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—44no—
419C4⋊C8—44no—
420#103—28no—
421#103—24no—
422#103—24no—
423#103—28no—
424#103—44no—
425#103—44no—
426#103—44no—
427#102—24no—
428#102—24no—
429#102—28no—
430C22⋊C8—24no—
431C4×C8—24no—
432#95—24no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—24no—
442#95C2×D412yes—
443#95C2×D412yes—
444#95C2×D412yes—
445#95C2×D412yes—
446C24—22no—
447C24C22×D411yescharacteristic
448#41—432no—
449C2×Q8—24no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—28no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—81no—
477C2×Q8—81no—
478C2×Q8H(5,𝔽2)12yes—
479C2×Q82−1+412yes—
480C2×D4—28no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C22×D414yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—28no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—84no—
519C22×C4—84no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4#12114yes—
525C22×C4#12114yes—
526C22×C4C2×SD1614yes—
527C22×C4#13714yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C2×#4112yes—
539C22×C4C2511yescharacteristic
540SD16—48no—
541SD16—48no—
542SD16—88no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—24no—
546C2×C8—24no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—24no—
552C2×C8—84no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4C2×SD1614yes—
590C4⋊C4C2×SD1614yes—
591C4⋊C4C22×D414yes—
592C22⋊C4—24no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4C2×SD1618yes—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—42no—
606C42—42no—
607C42—42no—
608C42—42no—
609C42—42no—
610C42—42no—
611C42—44no—
612C42—48no—
613C42#12114yes—
614C42#12114yes—
615C42C2×SD1618yes—
616C42C22×D412yes—
617C42C22×D412yes—
618C42C2×#4112yes—
619C42C2×#4112yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—24no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23C2×#12112yes—
632C23C22×SD1612yes—
633C23C2×#13712yes—
634C23C23×D411yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—48no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—84no—
650D4—24no—
651D4—24no—
652D4—48no—
653D4—416no—
654D4—42no—
655D4—42no—
656D4—48no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—48no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—84no—
705C2×C4—168no—
706C2×C4—164no—
707C2×C4#461116yescomplemented
708C2×C4C2×#12112yes—
709C2×C4C2×#12112yes—
710C2×C4C2×#12112yes—
711C2×C4C2×#12112yes—
712C2×C4C2×#12112yes—
713C2×C4C22×SD1614yes—
714C2×C4C22×SD1614yes—
715C2×C4C22×SD1612yes—
716C2×C4C22×SD1612yes—
717C2×C4C2×#13712yes—
718C2×C4C2×#13712yes—
719C2×C4C23×D411yescharacteristic
720C2×C4C22×#4111yescharacteristic
721C2×C4C2×H(5,𝔽2)11yescharacteristic
722C2×C4C2×2−1+411yescharacteristic
723C2×C4#58511yescharacteristic
724C2×C4#58511yescharacteristic
725C8—44no—
726C8—42no—
727C8—42no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22C2×#46114yes—
742C22C22×#12111yescharacteristic
743C22#348811yescharacteristic
744C22#348911yescharacteristic
745C22C23×SD1611yescharacteristic
746C22C22×#13711yescharacteristic
747C22#358511yescharacteristic
748C22#358611yescharacteristic
749C4—22no—
750C4—22no—
751C4—24no—
752C4—22no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—44no—
759C4—81no—
760C4—81no—
761C4—82no—
762C4—82no—
763C4—84no—
764C4C2×#46114yes—
765C4C2×#46114yes—
766C4#348811yescharacteristic
767C4#348911yescharacteristic
768C4#349211yescharacteristic
769C4#349311yescharacteristic
770C2—24no—
771C2—84no—
772C2#3551811yescharacteristic
773C2C22×#46111yescharacteristic
774C2#6042511yescharacteristic
775C2#6195111yescharacteristic
776C2#6196611yescharacteristic
777C2#6209911yescharacteristic
778C2#6211411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #34953C2semidirect
5. #28283C2semidirect
6. #28252C2semidirect
7. #28205C2semidirect
8. #28160C2semidirect
9. #25202C2semidirect
10. #25078C2semidirect
11. #24815C2semidirect
12. #24730C2semidirect
13. #24680C2semidirect
14. #24630C2semidirect
15. #21972C2semidirect
16. #21860C2semidirect
17. C2×#1803C2semidirect
341. #117SD16semidirect
707. C2×C4#461semidirect

Maximal subgroups

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

subgroupindex
C2×#32462
C2×#31032
#349532
#342072
#282832
#282522
#282052
#281602
#252022
#250782
#248152
#247302
#246802
#246302
#219722
#218602
C2×#18032