Finite Group Databasebeta

← #7647858

Subgroups — #7647858

Order 512.

6918 conjugacy classes of subgroups.

The subgroup lattice has 1539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42172C214yesmaximal, complemented
4#42170C214yesmaximal, complemented
5#40607C214yesmaximal, complemented
6#40600C214yesmaximal, complemented
7#39613C212yesmaximal, complemented
8#39483C212yesmaximal, complemented
9#39161C212yesmaximal, complemented
10#38948C212yesmaximal, complemented
11#38095C212yesmaximal, complemented
12#38089C212yesmaximal, complemented
13#37870C212yesmaximal, complemented
14#37869C212yesmaximal, complemented
15#37639C211yesmaximal, characteristic, complemented
16#37634C211yesmaximal, characteristic, complemented
17#37632C211yesmaximal, characteristic, complemented
18#37616C211yesmaximal, characteristic, complemented
19#37280C214yesmaximal, complemented
20#37272C214yesmaximal, complemented
21#35520C214yesmaximal, complemented
22#35279C211yesmaximal, characteristic, complemented
23#35258C214yesmaximal, complemented
24#35249C211yesmaximal, characteristic, complemented
25#35238C211yesmaximal, characteristic, complemented
26#35201C211yesmaximal, characteristic, complemented
27#35190C211yesmaximal, characteristic, complemented
28#35179C211yesmaximal, characteristic, complemented
29#34977C211yesmaximal, characteristic, complemented
30#34947C211yesmaximal, characteristic, complemented
31#34060C211yesmaximal, characteristic, complemented
32#3511—216no—
33#3480—216no—
34C2×#559C2212yes—
35C2×#559C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#556C2212yes—
38C2×#556C2212yes—
39C2×#556C2211yescharacteristic
40C2×#555C2212yes—
41C2×#554C2212yes—
42C2×#553C2212yes—
43C2×#553C2211yescharacteristic
44C2×#553C2212yes—
45C2×#553C2212yes—
46C2×#553C2212yes—
47C2×#553C2211yescharacteristic
48C2×#550C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2212yes—
51C2×#548C2212yes—
52C2×#548C2211yescharacteristic
53C2×#547C2212yes—
54C2×#542C2212yes—
55C2×#542C2212yes—
56C2×#537C2212yes—
57C2×#533C2211yescharacteristic
58C2×#533C2211yescharacteristic
59C2×#532C2211yescharacteristic
60C2×#532C2211yescharacteristic
61C2×#532C2211yescharacteristic
62C2×#532C2211yescharacteristic
63C2×#532C2212yes—
64C22×C4⋊Q8C2211yescharacteristic
65C2×#529C2211yescharacteristic
66C2×#529C2211yescharacteristic
67C2×#529C2212yes—
68C2×#529C2212yes—
69C2×#520C2212yes—
70C2×C4×#41C2211yescharacteristic
71C2×C4×#41C2211yescharacteristic
72C2×C4×#41C2212yes—
73C2×C4×#41C2211yescharacteristic
74C22×C4×Q8C2211yescharacteristic
75#2861C2212yes—
76#2859C2212yes—
77#2857C2214yes—
78#2856C2212yes—
79#2855C2214yes—
80#2854C2214yes—
81#2850C2214yes—
82#2850C2212yes—
83#2821C2214yes—
84#2819C2214yes—
85#2816C2214yes—
86#2813C2214yes—
87#2730C2218yes—
88#2729C2218yes—
89#2727C2218yes—
90#2712C2218yes—
91#2704C2218yes—
92#2702C2218yes—
93#2699C2218yes—
94#2695C2218yes—
95#2688C2218yes—
96#2686C2218yes—
97#2682C2218yes—
98#2681C2218yes—
99#2673C2218yes—
100#2672C2218yes—
101#2671C2218yes—
102#2671C2218yes—
103#2663C2214yes—
104#2662C2214yes—
105#2660C2212yes—
106#2660C2212yes—
107#2641C2212yes—
108#2640C2212yes—
109#2636C2214yes—
110#2635C2214yes—
111#2632C2214yes—
112#2632C2214yes—
113#2628C2214yes—
114#2628C2214yes—
115#2627C2214yes—
116#2620C2212yes—
117#2620C2214yes—
118#2619C2212yes—
119#2619C2212yes—
120#2619C2212yes—
121#2616C2214yes—
122#2615C2214yes—
123#2615C2214yes—
124#2614C2214yes—
125#2610C2214yes—
126#2604C2214yes—
127#2598C2214yes—
128#2582C2214yes—
129#2581C2214yes—
130#2580C2214yes—
131#2568C2211yescharacteristic
132#2568C2211yescharacteristic
133#2568C2212yes—
134#2567C2211yescharacteristic
135#2567C2211yescharacteristic
136#2567C2211yescharacteristic
137#2567C2211yescharacteristic
138#2566C2212yes—
139#2566C2212yes—
140#2566C2212yes—
141#2565C2212yes—
142#2565C2212yes—
143#2565C2212yes—
144#2564C2214yes—
145#2563C2211yescharacteristic
146#2563C2211yescharacteristic
147#2563C2211yescharacteristic
148#2563C2211yescharacteristic
149#2563C2212yes—
150#2548C2211yescharacteristic
151#2548C2211yescharacteristic
152#2544C2212yes—
153#2544C2212yes—
154#2542C2211yescharacteristic
155#2542C2211yescharacteristic
156#2542C2212yes—
157#2541C2211yescharacteristic
158#2541C2211yescharacteristic
159#2541C2212yes—
160#2537C2214yes—
161#2536C2214yes—
162#2503C2212yes—
163#2501C2212yes—
164#2501C2212yes—
165#2500C2212yes—
166#2500C2212yes—
167#2500C2212yes—
168#2500C2212yes—
169#2500C2212yes—
170#2499C2212yes—
171#2487C2214yes—
172#2486C2214yes—
173#2479C2218yes—
174#2477C2218yes—
175#2473C2218yes—
176#2469C2218yes—
177#2468C2218yes—
178#2467C2218yes—
179#2465C2218yes—
180#2464C2218yes—
181#2463C2218yes—
182#2461C2218yes—
183#2459C2218yes—
184#2459C2218yes—
185#2457C2218yes—
186#2455C2218yes—
187#2455C2218yes—
188#2443C2218yes—
189#2436C2212yes—
190#2431C2212yes—
191#2431C2212yes—
192#2430C2214yes—
193#2417C2214yes—
194#2416C2214yes—
195#2415C2214yes—
196#2414C2214yes—
197#2409C2214yes—
198#2407C2214yes—
199#2407C2214yes—
200#2406C2214yes—
201#2396C2214yes—
202#2388C2214yes—
203#2328C2212yes—
204#2326C2212yes—
205#2326C2212yes—
206#2326C2212yes—
207#2324C2214yes—
208#2323C2214yes—
209#2320C2212yes—
210#2319C2212yes—
211#2318C2212yes—
212#2318C2212yes—
213#2317C2212yes—
214#2317C2212yes—
215#2317C2212yes—
216#2314C2212yes—
217#2314C2212yes—
218#2311C2212yes—
219#2311C2212yes—
220#2310C2212yes—
221C4×#127C2212yes—
222C4×#124C2212yes—
223C4×C22⋊Q8C2214yes—
224C4×#121C2214yes—
225#2297C2212yes—
226#2295C2212yes—
227#2293C2212yes—
228#2290C2212yes—
229#2290C2212yes—
230#2285C2211yescharacteristic
231#2285C2211yescharacteristic
232#2285C2212yes—
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic
235C4×#117C2211yescharacteristic
236C2×C4×C4⋊C4C2211yescharacteristic
237C22×#41C2311yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2312yes—
240C22×#41C2312yes—
241C22×#41C2312yes—
242C22×#41C2312yes—
243C22×#41C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245C23×Q8C2312yes—
246#559—28no—
247#559—216no—
248#557—28no—
249#556—216no—
250#556—216no—
251#556—28no—
252#555—216no—
253#554—216no—
254#553—28no—
255#553—28no—
256#553—216no—
257#553—216no—
258#553—216no—
259#553—216no—
260#550—28no—
261#548—28no—
262#548—28no—
263#548—216no—
264#548—216no—
265#547—216no—
266#542—216no—
267#542—216no—
268#537—216no—
269#533—28no—
270#533—28no—
271#532—216no—
272#532—28no—
273#532—28no—
274#532—28no—
275#532—28no—
276C2×C4⋊Q8—28no—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2312yes—
285C2×#127C2311yescharacteristic
286C2×#127C2312yes—
287C2×#127C2311yescharacteristic
288C2×#127C2312yes—
289C2×#127C2312yes—
290#529—216no—
291#529—216no—
292#529—28no—
293#529—28no—
294C2×#126C2312yes—
295C2×#126C2312yes—
296C2×#126C2312yes—
297C2×#126C2312yes—
298C2×#126C2312yes—
299C2×#126C2312yes—
300C2×#126C2314yes—
301C2×#126C2314yes—
302C2×#125C2312yes—
303C2×#125C2312yes—
304C2×#125C2311yescharacteristic
305C2×#125C2311yescharacteristic
306C2×#125C2312yes—
307C2×#125C2312yes—
308C2×#124C2312yes—
309C2×#124C2312yes—
310C2×#124C2312yes—
311C2×#124C2312yes—
312C2×#124C2311yescharacteristic
313C2×#124C2312yes—
314C2×#124C2311yescharacteristic
315C2×#124C2312yes—
316C2×#124C2312yes—
317C2×#124C2314yes—
318C2×#124C2312yes—
319C2×#124C2312yes—
320C2×#124C2314yes—
321C2×#124C2312yes—
322C2×#123C2312yes—
323C2×#123C2312yes—
324C2×#123C2314yes—
325C2×#123C2312yes—
326C2×#123C2312yes—
327C2×#123C2312yes—
328C2×#123C2312yes—
329C2×#123C2314yes—
330C2×#123C2318yes—
331C2×#123C2318yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2318yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2311yescharacteristic
350C2×#121C2311yescharacteristic
351C2×#121C2312yes—
352C2×#121C2311yescharacteristic
353C2×#121C2311yescharacteristic
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2314yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2314yes—
366C2×#121C2314yes—
367C2×#121C2314yes—
368C2×#121C2318yes—
369C2×#121C2318yes—
370#520—216no—
371C4×#41—216no—
372C4×#41—28no—
373C4×#41—28no—
374C4×#41D4116yescomplemented
375C2×C4×Q8—28no—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2311yescharacteristic
391C2×C4×Q8C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2318yes—
418C2×C4×D4C2311yescharacteristic
419C2×C4×D4C2311yescharacteristic
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2311yescharacteristic
423C2×C4×D4C2311yescharacteristic
424C2×#117C2312yes—
425C2×#117C2311yescharacteristic
426C2×#117C2312yes—
427C2×#117C2312yes—
428C2×#117C2312yes—
429C2×#117C2312yes—
430C2×#117C2311yescharacteristic
431C2×#117C2314yes—
432C2×#117C2312yes—
433C2×#117C2312yes—
434C2×#117C2312yes—
435C2×#117C2312yes—
436C2×#117C2311yescharacteristic
437C2×#117C2311yescharacteristic
438C2×#117C2311yescharacteristic
439C22×C4⋊C4C2312yes—
440C22×C4⋊C4C2311yescharacteristic
441C22×C4⋊C4C2312yes—
442C22×C4⋊C4C2312yes—
443C22×C4⋊C4C2314yes—
444C22×C4⋊C4C2312yes—
445C22×C42C2312yes—
446C22×C42C2312yes—
447C22×C42C2312yes—
448C22×C42C2312yes—
449C22×C42C2311yescharacteristic
450C22×C42C2311yescharacteristic
451C22×C42C2311yescharacteristic
452#400C2314yes—
453#400C2318yes—
454#400C2314yes—
455#400C2318yes—
456#399C2314yes—
457#399C2314yes—
458#399C2318yes—
459#399C2318yes—
460#399C2318yes—
461#398C2318yes—
462#398C2318yes—
463#398C2318yes—
464#398C2318yes—
465#398C2318yes—
466#397C2318yes—
467#397C2318yes—
468#396C2318yes—
469#396C2318yes—
470#396C2318yes—
471#396C2318yes—
472#395C2314yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2318yes—
477#395C2318yes—
478#394C2318yes—
479#394C2318yes—
480#394C2318yes—
481#394C2318yes—
482#394C2318yes—
483#394C2314yes—
484#394C2318yes—
485#394C2318yes—
486#394C2318yes—
487#394C2318yes—
488#394C2314yes—
489#394C2318yes—
490#394C2318yes—
491#394C2318yes—
492#394C2318yes—
493#393C2314yes—
494#393C2314yes—
495#393C2314yes—
496#393C2314yes—
497#393C2318yes—
498#393C2318yes—
499#393C2318yes—
500#392C2314yes—
501#392C2314yes—
502#392C2318yes—
503#392C2318yes—
504#392C2318yes—
505#392C2318yes—
506#392C2318yes—
507#392C2318yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2318yes—
514#391C2314yes—
515#391C2312yes—
516#391C2314yes—
517#391C2314yes—
518#391C2318yes—
519#390C2312yes—
520#390C2312yes—
521#390C2318yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2318yes—
532#390C2314yes—
533#390C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2318yes—
541#389C2318yes—
542#389C2318yes—
543#389C2318yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2318yes—
549#388C2318yes—
550#388C2318yes—
551#388C2318yes—
552#388C2318yes—
553#388C2318yes—
554#388C2318yes—
555#388C2318yes—
556#388C2318yes—
557#388C2318yes—
558#388C2318yes—
559#388C2318yes—
560#387C2318yes—
561#387C2318yes—
562#387C2318yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2318yes—
568#386C2318yes—
569#386C2314yes—
570#386C2314yes—
571#386C2318yes—
572#386C2318yes—
573#386C2318yes—
574#386C2318yes—
575#386C2318yes—
576#386C2318yes—
577#386C2318yes—
578#386C2318yes—
579#386C2318yes—
580#385C2318yes—
581#385C2318yes—
582#385C2318yes—
583#385C2314yes—
584#385C2314yes—
585#385C2318yes—
586#385C2318yes—
587#385C2318yes—
588#385C2318yes—
589#385C2318yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2312yes—
598#383C2312yes—
599#383C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2312yes—
610#381C2312yes—
611#381C2318yes—
612#381C2312yes—
613#381C2318yes—
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2318yes—
618#380C2314yes—
619#380C2318yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2318yes—
625#380C2312yes—
626#380C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2311yescharacteristic
629C4×C4⋊C4C2311yescharacteristic
630C4×C4⋊C4C2311yescharacteristic
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2318yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2318yes—
640C4×C22⋊C4C2318yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644#376C2312yes—
645#376C2312yes—
646#376C2312yes—
647C2×#95C2312yes—
648C43C2312yes—
649C2×#41—24no—
650C2×#41—24no—
651C2×#41—28no—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—28no—
655C2×#41—28no—
656C2×#41—28no—
657C2×#41—44no—
658C2×#41—48no—
659C2×#41—42no—
660C2×#41—42no—
661C2×#41—48no—
662C2×#41—84no—
663C2×#41—84no—
664C2×#41C2×D418yes—
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8—28no—
668C22×Q8—42no—
669C22×Q8—84no—
670C22×Q8C2412yes—
671C22×Q8C2411yescharacteristic
672C22×Q8C2412yes—
673C22×Q8C2411yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2414yes—
678C22×Q8C2411yescharacteristic
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2411yescharacteristic
682C22×D4C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2412yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2418yes—
696C22×D4C2418yes—
697C22×D4C2411yescharacteristic
698C22×D4C2411yescharacteristic
699C22×D4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2411yescharacteristic
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C4⋊Q8—28no—
723C4⋊Q8—24no—
724C4⋊Q8—24no—
725C4⋊Q8—28no—
726C4⋊Q8—28no—
727C4⋊Q8—28no—
728C4⋊Q8—24no—
729C4⋊Q8—24no—
730#127—28no—
731#127—24no—
732#127—24no—
733#127—44no—
734#127—44no—
735#126—28no—
736#126—28no—
737#126—216no—
738#126—216no—
739#126—28no—
740#126—28no—
741#126—28no—
742#126—28no—
743#125—28no—
744#125—28no—
745#125—24no—
746#125—24no—
747#125—28no—
748#125—28no—
749#124—28no—
750#124—28no—
751#124—28no—
752#124—28no—
753#124—28no—
754#124—216no—
755#124—216no—
756#124—24no—
757#124—24no—
758#124—28no—
759#124—28no—
760#124—28no—
761#124—28no—
762#124—44no—
763#123—28no—
764#123—28no—
765#123—28no—
766#123—28no—
767#123—28no—
768#123—28no—
769#123—216no—
770#123—216no—
771#123—88no—
772#123—88no—
773C22⋊Q8—216no—
774C22⋊Q8—24no—
775C22⋊Q8—24no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—28no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—216no—
783C22⋊Q8—216no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—88no—
787#121—28no—
788#121—28no—
789#121—28no—
790#121—28no—
791#121—216no—
792#121—216no—
793#121—216no—
794#121—24no—
795#121—24no—
796#121—28no—
797#121—28no—
798#121—28no—
799#121—24no—
800#121—24no—
801#121—28no—
802#121—28no—
803#121—28no—
804#121—28no—
805#121—28no—
806#121—28no—
807#121—48no—
808#121—48no—
809#121—88no—
810#121—88no—
811C4×Q8—28no—
812C4×Q8—28no—
813C4×Q8—24no—
814C4×Q8—28no—
815C4×Q8—24no—
816C4×Q8—24no—
817C4×Q8—24no—
818C4×Q8—28no—
819C4×Q8—24no—
820C4×Q8—24no—
821C4×Q8—28no—
822C4×Q8—28no—
823C4×Q8—28no—
824C4×Q8—28no—
825C4×Q8C2×D418yes—
826C4×Q8C2×D418yes—
827C4×D4—28no—
828C4×D4—28no—
829C4×D4—28no—
830C4×D4—28no—
831C4×D4—28no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—28no—
835C4×D4—28no—
836C4×D4—28no—
837C4×D4—28no—
838C4×D4—28no—
839C4×D4—216no—
840C4×D4—216no—
841C4×D4—24no—
842C4×D4—24no—
843C4×D4—24no—
844C4×D4—24no—
845C4×D4—28no—
846C4×D4—28no—
847C4×D4—28no—
848C4×D4—28no—
849C4×D4—28no—
850C4×D4—28no—
851C4×D4—28no—
852C4×D4—88no—
853C4×D4C2×D418yes—
854C4×D4C2×D418yes—
855C4×D4C2×D418yes—
856C4×D4C2×D418yes—
857C4×D4C2×D418yes—
858C4×D4C2×D418yes—
859#117—24no—
860#117—24no—
861#117—28no—
862#117—28no—
863#117—216no—
864#117—28no—
865#117—28no—
866#117—28no—
867#117—28no—
868#117—44no—
869#117—44no—
870#117—44no—
871#117C2×D418yes—
872#117C2×D418yes—
873#117C2×D418yes—
874C2×C4⋊C4—28no—
875C2×C4⋊C4—24no—
876C2×C4⋊C4—28no—
877C2×C4⋊C4—28no—
878C2×C4⋊C4—216no—
879C2×C4⋊C4—44no—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2418yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2418yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2418yes—
922C2×C4⋊C4C2418yes—
923C2×C4⋊C4C2418yes—
924C2×C4⋊C4C2418yes—
925C2×C4⋊C4C2411yescharacteristic
926C2×C4⋊C4C2411yescharacteristic
927C2×C4⋊C4C2411yescharacteristic
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2411yescharacteristic
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2418yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2418yes—
960C2×C22⋊C4C2418yes—
961C2×C22⋊C4C2418yes—
962C2×C22⋊C4C2418yes—
963C2×C22⋊C4C2418yes—
964C2×C22⋊C4C2418yes—
965C2×C22⋊C4C2418yes—
966C2×C22⋊C4C2418yes—
967C2×C22⋊C4C2418yes—
968C2×C22⋊C4C2418yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2418yes—
972C2×C22⋊C4C2411yescharacteristic
973C2×C22⋊C4C2411yescharacteristic
974C2×C22⋊C4C2411yescharacteristic
975C2×C22⋊C4C2411yescharacteristic
976C2×C22⋊C4C2411yescharacteristic
977C2×C22⋊C4C2411yescharacteristic
978C2×C42—28no—
979C2×C42—28no—
980C2×C42—28no—
981C2×C42—44no—
982C2×C42C2×D418yes—
983C2×C42C2×D418yes—
984C2×C42C2×D418yes—
985C2×C42C2412yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2414yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2411yescharacteristic
1011C2×C42C2411yescharacteristic
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2418yes—
1023#95C2418yes—
1024#95C2418yes—
1025#95C2418yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2418yes—
1029#95C2414yes—
1030#95C2418yes—
1031#95C2414yes—
1032#95C2418yes—
1033#95C2418yes—
1034#95C2418yes—
1035#95C2418yes—
1036#95C2418yes—
1037#95C2418yes—
1038C24C2514yes—
1039C24C2512yes—
1040C24C2512yes—
1041C24C2511yescharacteristic
1042C24C2511yescharacteristic
1043C24C2511yescharacteristic
1044#41—416no—
1045#41—416no—
1046#41—416no—
1047#41—432no—
1048#41—432no—
1049#41—816no—
1050#41—816no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—22no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—28no—
1059C2×Q8—24no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—28no—
1063C2×Q8—22no—
1064C2×Q8—42no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—42no—
1068C2×Q8—44no—
1069C2×Q8—48no—
1070C2×Q8—416no—
1071C2×Q8—816no—
1072C2×Q8C22×D414yes—
1073C2×Q82−1+414yes—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—28no—
1082C2×D4—28no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—22no—
1094C2×D4—22no—
1095C2×D4—28no—
1096C2×D4—24no—
1097C2×D4—22no—
1098C2×D4—22no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—48no—
1108C2×D4—44no—
1109C2×D4—48no—
1110C2×D4—48no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—48no—
1114C2×D4—44no—
1115C2×D4—48no—
1116C2×D4—48no—
1117C2×D4—48no—
1118C2×D4—48no—
1119C2×D4—48no—
1120C2×D4C22×D414yes—
1121C2×D4C22×D414yes—
1122C2×D4C22×D414yes—
1123C22×C4—22no—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—22no—
1129C22×C4—22no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—28no—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—28no—
1140C22×C4—24no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—28no—
1144C22×C4—28no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—28no—
1148C22×C4—28no—
1149C22×C4—42no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4—48no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—48no—
1160C22×C4—44no—
1161C22×C4—48no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—48no—
1165C22×C4C22×D414yes—
1166C22×C4C22×D414yes—
1167C22×C4C22×D414yes—
1168C22×C4C22×D414yes—
1169C22×C4C22×D414yes—
1170C22×C4C22×D414yes—
1171C22×C4C22×D414yes—
1172C22×C4C22×D414yes—
1173C22×C4C22×D414yes—
1174C22×C4C2514yes—
1175C22×C4C2514yes—
1176C22×C4C2514yes—
1177C22×C4C2512yes—
1178C22×C4C2514yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2511yescharacteristic
1196C22×C4C2512yes—
1197C22×C4C2511yescharacteristic
1198C22×C4C2511yescharacteristic
1199C4⋊C4—28no—
1200C4⋊C4—24no—
1201C4⋊C4—22no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—28no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—28no—
1228C4⋊C4—28no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—24no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—48no—
1237C4⋊C4—44no—
1238C4⋊C4—48no—
1239C4⋊C4—48no—
1240C4⋊C4—48no—
1241C4⋊C4—44no—
1242C4⋊C4—48no—
1243C4⋊C4—48no—
1244C4⋊C4C22×D414yes—
1245C4⋊C4C22×D414yes—
1246C4⋊C4C22×D414yes—
1247C4⋊C4C22×D414yes—
1248C4⋊C4C22×D414yes—
1249C4⋊C4C22×D414yes—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—24no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—28no—
1274C22⋊C4—216no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—48no—
1279C22⋊C4—48no—
1280C22⋊C4—48no—
1281C22⋊C4—48no—
1282C22⋊C4—48no—
1283C22⋊C4—48no—
1284C22⋊C4—48no—
1285C22⋊C4—48no—
1286C22⋊C4—48no—
1287C22⋊C4—48no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—48no—
1291C22⋊C4C22×D414yes—
1292C22⋊C4C22×D414yes—
1293C22⋊C4C22×D414yes—
1294C22⋊C4C22×D414yes—
1295C22⋊C4C22×D414yes—
1296C22⋊C4C22×D414yes—
1297C42—24no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—28no—
1306C42—28no—
1307C42—24no—
1308C42—24no—
1309C42—24no—
1310C42—24no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42C22×D414yes—
1315C42C22×D414yes—
1316C42C22×D414yes—
1317C42C22×D414yes—
1318C42C22×D414yes—
1319C42C22×D414yes—
1320C42C22×D414yes—
1321C42C22×D414yes—
1322C42C22×D414yes—
1323C42C22×D414yes—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—22no—
1330C23—21no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—24no—
1339C23—24no—
1340C23—22no—
1341C23—22no—
1342C23—24no—
1343C23—24no—
1344C23—28no—
1345C23—24no—
1346C23—22no—
1347C23—22no—
1348C23—24no—
1349C23—24no—
1350C23—28no—
1351C23C23×D412yes—
1352C23C23×D412yes—
1353C23C23×D412yes—
1354C23C2611yescharacteristic
1355Q8—28no—
1356Q8—44no—
1357Q8—48no—
1358Q8—48no—
1359Q8—48no—
1360Q8—48no—
1361Q8—48no—
1362Q8—44no—
1363Q8—88no—
1364D4—44no—
1365D4—44no—
1366D4—44no—
1367D4—48no—
1368D4—48no—
1369D4—48no—
1370D4—48no—
1371D4—48no—
1372D4—48no—
1373D4—416no—
1374D4—48no—
1375D4—48no—
1376D4—44no—
1377D4—44no—
1378D4—84no—
1379D4—84no—
1380D4—84no—
1381D4—88no—
1382D4—88no—
1383D4—816no—
1384D4—168no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—28no—
1401C2×C4—28no—
1402C2×C4—28no—
1403C2×C4—28no—
1404C2×C4—28no—
1405C2×C4—28no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—28no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—24no—
1433C2×C4—28no—
1434C2×C4—28no—
1435C2×C4—44no—
1436C2×C4—44no—
1437C2×C4—44no—
1438C2×C4—48no—
1439C2×C4—48no—
1440C2×C4—48no—
1441C2×C4—416no—
1442C2×C4—48no—
1443C2×C4—48no—
1444C2×C4—84no—
1445C2×C4—84no—
1446C2×C4—88no—
1447C2×C4—88no—
1448C2×C4—84no—
1449C2×C4—88no—
1450C2×C4—88no—
1451C2×C4C23×D412yes—
1452C2×C4C23×D412yes—
1453C2×C4C23×D412yes—
1454C2×C4C23×D412yes—
1455C2×C4C23×D412yes—
1456C2×C4C23×D412yes—
1457C2×C4C23×D412yes—
1458C2×C4C23×D412yes—
1459C2×C4C23×D412yes—
1460C2×C4C23×D412yes—
1461C2×C4C23×D412yes—
1462C2×C4C23×D412yes—
1463C2×C4C2×2−1+414yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4#58514yes—
1466C2×C4#58512yes—
1467C22—22no—
1468C22—22no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—22no—
1473C22—22no—
1474C22—22no—
1475C22—22no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—44no—
1485C22—44no—
1486C22—42no—
1487C22—42no—
1488C22—44no—
1489C22—48no—
1490C22—44no—
1491C22—44no—
1492C22—42no—
1493C22—42no—
1494C22—48no—
1495C22—44no—
1496C22—44no—
1497C22C24×D411yescharacteristic
1498C22C22×2−1+411yescharacteristic
1499C22C2×#58511yescharacteristic
1500C22C2×#58512yes—
1501C22H(7,𝔽2)12yes—
1502C4—22no—
1503C4—22no—
1504C4—22no—
1505C4—24no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—22no—
1510C4—22no—
1511C4—22no—
1512C4—22no—
1513C4—42no—
1514C4—42no—
1515C4—44no—
1516C4—44no—
1517C4—42no—
1518C4—44no—
1519C4—44no—
1520C4—44no—
1521C4—42no—
1522C4—42no—
1523C4—44no—
1524C4—44no—
1525C4#344914yes—
1526C4#348914yes—
1527C2—42no—
1528C2—42no—
1529C2—42no—
1530C2—82no—
1531C2—82no—
1532C2—84no—
1533C2C2×#344911yescharacteristic
1534C2C2×#348911yescharacteristic
1535C2#6285211yescharacteristic
1536C2#6293812yes—
1537C2#6295212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3511C2semidirect
2. C2×#3480C2semidirect
3. #42172C2semidirect
4. #42170C2semidirect
5. #40607C2semidirect
6. #40600C2semidirect
7. #39613C2semidirect
8. #39483C2semidirect
9. #39161C2semidirect
10. #38948C2semidirect
11. #38095C2semidirect
12. #38089C2semidirect
13. #37870C2semidirect
14. #37869C2semidirect
15. #37639C2semidirect
16. #37634C2semidirect
17. #37632C2semidirect
18. #37616C2semidirect
19. #37280C2semidirect
20. #37272C2semidirect
21. #35520C2semidirect
22. #35279C2semidirect
23. #35258C2semidirect
24. #35249C2semidirect
25. #35238C2semidirect
26. #35201C2semidirect
27. #35190C2semidirect
28. #35179C2semidirect
29. #34977C2semidirect
30. #34947C2semidirect
31. #34060C2semidirect
374. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34802
#421722
#421702
#406072
#406002
#396132
#394832
#391612
#389482
#380952
#380892
#378702
#378692
#376392
#376342
#376322
#376162
#372802
#372722
#355202
#352792
#352582
#352492
#352382
#352012
#351902
#351792
#349772
#349472
#340602