Finite Group Databasebeta

← #72318769

Subgroups — #72318769

Order 1024.

1052 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
1#495308C211yesmaximal, characteristic
2C2×#12089C211yesmaximal, characteristic
3C2×#12067C211yesmaximal, characteristic
4#183982C211yesmaximal, characteristic, complemented
5#183975C211yesmaximal, characteristic, complemented
6#129177C211yesmaximal, characteristic, complemented
7#129165C211yesmaximal, characteristic, complemented
8C4×#1368C211yesmaximal, characteristic, complemented
9#128753C211yesmaximal, characteristic, complemented
10#128753C211yesmaximal, characteristic, complemented
11#128719C211yesmaximal, characteristic, complemented
12#128719C211yesmaximal, characteristic, complemented
13#128617C211yesmaximal, characteristic, complemented
14#128617C211yesmaximal, characteristic, complemented
15#126534C211yesmaximal, characteristic, complemented
16C2×#2177C2211yescharacteristic
17#21275C2211yescharacteristic
18#21275C2211yescharacteristic
19#20562—21no—
20#20495—21no—
21C2×#1594C2211yescharacteristic
22C2×#1594C2211yescharacteristic
23C2×#1580C2211yescharacteristic
24C2×#1580C2211yescharacteristic
25#13239C411yescharacteristic
26#13235C411yescharacteristic
27#13167C411yescharacteristic
28#13166C411yescharacteristic
29#13149C411yescharacteristic
30#13149C411yescharacteristic
31#13147C411yescharacteristic
32#13147C411yescharacteristic
33#12674C2211yescharacteristic
34#12637C2211yescharacteristic
35#12637C2211yescharacteristic
36#12591C2211yescharacteristic
37C4×#346C2211yescharacteristic
38#12089C418yescomplemented
39#12067C418yescomplemented
40C2×#1368C2211yescharacteristic
41C2×#1368C2211yescharacteristic
42C2×#1333C2211yescharacteristic
43C2×#1333C2211yescharacteristic
44C2×#1333C2211yescharacteristic
45C2×#1333C2211yescharacteristic
46C2×#1313C2211yescharacteristic
47C2×#1313C2211yescharacteristic
48C2×#1313C2211yescharacteristic
49C2×#1313C2211yescharacteristic
50#8287C2211yescharacteristic
51#8287C2211yescharacteristic
52#8284C2211yescharacteristic
53#8284C2211yescharacteristic
54C4×#334C2211yescharacteristic
55C4×#334C2211yescharacteristic
56#8212—21no—
57#8210—21no—
58#8204—21no—
59#8202—21no—
60#8183—21no—
61#8181—21no—
62#7842C2211yescharacteristic
63#7178C2211yescharacteristic
64#7178C2211yescharacteristic
65#7178C2211yescharacteristic
66#7178C2211yescharacteristic
67#7156C2211yescharacteristic
68#7156C2211yescharacteristic
69C22×D16C2×C411yescharacteristic
70C2×C4×D8C2311yescharacteristic
71C2×C4×D8C2311yescharacteristic
72C2×#436—21no—
73C2×#436—21no—
74C2×C8×D4—21no—
75C2×C8×D4—21no—
76C2×#405—41no—
77#2293—21no—
78#2293—21no—
79#2177C2×C414yes—
80#2177C2×C414yes—
81C2×#367C2×C411yescharacteristic
82C2×#367C2×C411yescharacteristic
83C2×#366C2×C411yescharacteristic
84C2×#357C2×C411yescharacteristic
85C2×#357C2×C411yescharacteristic
86C2×#357C2×C411yescharacteristic
87C2×#357C2×C411yescharacteristic
88C2×#357C2×C411yescharacteristic
89C2×#357C2×C411yescharacteristic
90C2×#346C2×C411yescharacteristic
91C2×#346C2×C411yescharacteristic
92C2×#346C2311yescharacteristic
93C2×#346C2311yescharacteristic
94C2×#346C2311yescharacteristic
95C2×#346C2311yescharacteristic
96C2×C4×C16C2×C411yescharacteristic
97C2×C4×C16C2×C411yescharacteristic
98#1970C2×C411yescharacteristic
99#1970C2×C411yescharacteristic
100#1970C2×C411yescharacteristic
101#1970C2×C411yescharacteristic
102#1942C2×C411yescharacteristic
103#1942C2×C411yescharacteristic
104#1942C2×C411yescharacteristic
105#1942C2×C411yescharacteristic
106#1934—21no—
107#1934—21no—
108#1934—21no—
109#1934—21no—
110C4×#107C2311yescharacteristic
111C4×#107C2311yescharacteristic
112#1770—21no—
113#1770—21no—
114C8×C4⋊C4—21no—
115C8×C4⋊C4—21no—
116C4×C4⋊C8—21no—
117C4×C4⋊C8—21no—
118C4×#102—21no—
119C4×#102—21no—
120#1753—41no—
121#1753—41no—
122#1752—41no—
123C8×C22⋊C4—41no—
124#1750—41no—
125#1750—41no—
126#1744D411yescharacteristic
127#1729—41no—
128C4×#97D411yescharacteristic
129C42×C8C2311yescharacteristic
130#1594—22no—
131#1594—22no—
132#1594C2×C414yes—
133#1594C2×C414yes—
134#1580—22no—
135#1580—22no—
136#1580C2×C414yes—
137#1580C2×C414yes—
138C2×#334C2311yescharacteristic
139C2×#334C2311yescharacteristic
140C2×#334C2311yescharacteristic
141C2×#334C2311yescharacteristic
142C2×D4⋊C8—21no—
143C2×D4⋊C8—21no—
144C2×D4⋊C8—21no—
145C2×D4⋊C8—21no—
146C2×#322D411yescharacteristic
147C2×#322D411yescharacteristic
148C2×#322C2311yescharacteristic
149C2×#322C2311yescharacteristic
150#1380C2×C411yescharacteristic
151#1380C2×C411yescharacteristic
152#1380C2×C411yescharacteristic
153#1380C2×C411yescharacteristic
154#1380C2×C411yescharacteristic
155#1380C2×C411yescharacteristic
156#1374—21no—
157#1374—21no—
158#1368C2×C414yes—
159#1368C2×C414yes—
160#1333C2×C414yes—
161#1333C2×C414yes—
162#1333C2×C414yes—
163#1333C2×C414yes—
164#1313—22no—
165#1313—22no—
166#1313C2×C414yes—
167#1313C2×C414yes—
168#1279—21no—
169#1279—21no—
170#1279—21no—
171#1279—21no—
172#1277—21no—
173#1277—21no—
174C22×D8C22×C411yescharacteristic
175C22×D8C22×C411yescharacteristic
176C22×M16—41no—
177C22×M16—41no—
178C23×C8—41no—
179C23×C8—41no—
180C2×C4×D4—21no—
181C2×C4×D4—21no—
182C2×#117—41no—
183C2×#117—41no—
184C2×D16—22no—
185C2×D16—22no—
186C2×D16C4214yes—
187C22×C16—21no—
188C22×C16—21no—
189C22×C16C22×C411yescharacteristic
190C22×C16C22×C411yescharacteristic
191C22×C16C22×C411yescharacteristic
192C22×C16C22×C411yescharacteristic
193C4×D8—21no—
194C4×D8—21no—
195C4×D8—21no—
196C4×D8—21no—
197C4×D8C22×C412yes—
198C4×D8C22×C412yes—
199C4×D8C22×C412yes—
200C4×D8C22×C412yes—
201#436—24no—
202#436—24no—
203#436—42no—
204#436—42no—
205C8×D4—24no—
206C8×D4—24no—
207C8×D4—42no—
208C8×D4—42no—
209C2×#107C22×C411yescharacteristic
210C2×#107C22×C411yescharacteristic
211C2×#107C22×C411yescharacteristic
212C2×#107C22×C411yescharacteristic
213C2×#107C22×C411yescharacteristic
214C2×#107C22×C411yescharacteristic
215C2×C4⋊C8—21no—
216C2×C4⋊C8—21no—
217C2×C4⋊C8—21no—
218C2×C4⋊C8—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×C22⋊C8—41no—
226C2×C22⋊C8—41no—
227C2×C22⋊C8—41no—
228C2×C22⋊C8—41no—
229#405—84no—
230C2×#97—21no—
231C2×#97—21no—
232C2×#97—41no—
233C2×#97—41no—
234C2×C4×C8—41no—
235C2×C4×C8—41no—
236C2×C4×C8—41no—
237C2×C4×C8—41no—
238C2×C4×C8C22×C411yescharacteristic
239C2×C4×C8C22×C411yescharacteristic
240C2×C4×C8C2×D411yescharacteristic
241C2×C4×C8C2×D411yescharacteristic
242C2×C4×C8C2×D411yescharacteristic
243C2×C4×C8C2×D411yescharacteristic
244C2×C4×C8C2×D411yescharacteristic
245C2×C4×C8#4111yescharacteristic
246C2×C4×C8#4111yescharacteristic
247C2×C4×C8C2411yescharacteristic
248#390—21no—
249#390—21no—
250#390—21no—
251#390—21no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389—21no—
256#388—41no—
257#388—41no—
258#388—41no—
259#388—41no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C22⋊C4—41no—
263C4×C22⋊C4—41no—
264C43C2×D411yescharacteristic
265#367—22no—
266#367C4214yes—
267#366—22no—
268#357—41no—
269#357—41no—
270#357—41no—
271#357—41no—
272#357C4214yes—
273#357C4214yes—
274#346—22no—
275#346—21no—
276#346—21no—
277#346—21no—
278#346—21no—
279#346—41no—
280#346C22×C412yes—
281#346C22×C412yes—
282#346C22×C412yes—
283#346C22×C412yes—
284C4×C16—22no—
285C4×C16—41no—
286#340—21no—
287#340—21no—
288#340—21no—
289#340—21no—
290#340—21no—
291#340—21no—
292#336—21no—
293#336—21no—
294#336—41no—
295#336—41no—
296#336—41no—
297#336—41no—
298#336—41no—
299#336—41no—
300#334—21no—
301#334—21no—
302#334—21no—
303#334—21no—
304#334C22×C412yes—
305#334C22×C412yes—
306#334C22×C412yes—
307#334C22×C412yes—
308D4⋊C8—24no—
309D4⋊C8—24no—
310D4⋊C8—24no—
311D4⋊C8—24no—
312#322—41no—
313#322—41no—
314#322C22×C412yes—
315#322C22×C412yes—
316#322#4112yes—
317#322#4112yes—
318C22×D4—21no—
319C22×D4—21no—
320C23×C4—41no—
321C23×C4—41no—
322C2×D8—21no—
323C2×D8—21no—
324C2×D8—21no—
325C2×D8—21no—
326C2×D8—21no—
327C2×D8—21no—
328C2×D8—21no—
329C2×D8—21no—
330C2×D8—21no—
331C2×D8—21no—
332C2×D8C2×C4212yes—
333C2×D8C2×C4212yes—
334C2×M16—44no—
335C2×M16—44no—
336C2×M16—82no—
337C2×M16—82no—
338C2×M16—161no—
339C2×M16—161no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—44no—
345C22×C8—44no—
346C22×C8—41no—
347C22×C8—41no—
348C22×C8—41no—
349C22×C8—41no—
350C22×C8—82no—
351C22×C8—82no—
352C22×C8—161no—
353C22×C8—161no—
354C22×C8C4×D411yescharacteristic
355C22×C8C4×D411yescharacteristic
356C22×C8C23×C411yescharacteristic
357C22×C8C2×#4111yescharacteristic
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—41no—
363C4×D4—41no—
364C4×D4—41no—
365C4×D4—41no—
366#117—82no—
367#117—82no—
368#117—161no—
369#117—161no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42C4×D411yescharacteristic
393C2×C42C4×D411yescharacteristic
394C2×C42AGL(1,ℤ/8)11yescharacteristic
395C2×C42AGL(1,ℤ/8)11yescharacteristic
396C2×C42AGL(1,ℤ/8)11yescharacteristic
397C2×C42AGL(1,ℤ/8)11yescharacteristic
398C2×C42C22×D411yescharacteristic
399D16—28no—
400C2×C16—21no—
401C2×C16—21no—
402C2×C16—21no—
403C2×C16—21no—
404C2×C16—22no—
405C2×C16—22no—
406C2×C16—21no—
407C2×C16—21no—
408C2×C16—21no—
409C2×C16—21no—
410C2×C16—41no—
411C2×C16—41no—
412C2×C16—41no—
413C2×C16—41no—
414C2×C16C2×C4212yes—
415C2×C16C2×C4212yes—
416C2×C16#13112yes—
417C2×C16#13112yes—
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107—21no—
425#107—21no—
426#107—21no—
427#107—21no—
428#107C2×C4212yes—
429#107C2×C4212yes—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—41no—
435C4⋊C8—41no—
436C4⋊C8—41no—
437C4⋊C8—41no—
438#102—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442#102—81no—
443#102—81no—
444#102—81no—
445#102—81no—
446C22⋊C8—44no—
447C22⋊C8—44no—
448C22⋊C8—44no—
449C22⋊C8—44no—
450#97—42no—
451#97—81no—
452#97—82no—
453#97—161no—
454C4×C8—21no—
455C4×C8—21no—
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—21no—
459C4×C8—21no—
460C4×C8—21no—
461C4×C8—21no—
462C4×C8—21no—
463C4×C8—21no—
464C4×C8—41no—
465C4×C8—41no—
466C4×C8—82no—
467C4×C8—82no—
468C4×C8—161no—
469C4×C8—161no—
470C4×C8C4×D412yes—
471C4×C8C4×D412yes—
472C4×C8C4×D412yes—
473C4×C8C4×D412yes—
474C4×C8C23×C411yescharacteristic
475C4×C8C23×C411yescharacteristic
476C4×C8C2×#4111yescharacteristic
477C4×C8C2×#4111yescharacteristic
478#95—41no—
479#95—41no—
480#95—41no—
481#95—41no—
482#95—41no—
483#95—41no—
484C24—41no—
485C24—41no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4#44211yescharacteristic
517C22×C4#44211yescharacteristic
518C22×C4#44211yescharacteristic
519C22×C4#44211yescharacteristic
520C22×C4C2×C4×D411yescharacteristic
521C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
522C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
523D8—22no—
524D8—22no—
525D8—22no—
526D8—22no—
527D8—41no—
528D8—41no—
529D8—41no—
530D8—41no—
531M16—88no—
532M16—164no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—42no—
554C2×C8—42no—
555C2×C8—42no—
556C2×C8—42no—
557C2×C8—88no—
558C2×C8—81no—
559C2×C8—81no—
560C2×C8—81no—
561C2×C8—81no—
562C2×C8—81no—
563C2×C8—81no—
564C2×C8—81no—
565C2×C8—81no—
566C2×C8—164no—
567C2×C8C22×C4211yescharacteristic
568C2×C8C4×#4111yescharacteristic
569C2×C8C4×#4111yescharacteristic
570C2×C8C4×#4111yescharacteristic
571C2×C8C2×#13111yescharacteristic
572C2×C8C2×#13111yescharacteristic
573C2×C8#56811yescharacteristic
574C2×C8#56811yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—161no—
590C4⋊C4—161no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—82no—
596C22⋊C4—82no—
597C22⋊C4—82no—
598C22⋊C4—82no—
599C22⋊C4—161no—
600C22⋊C4—161no—
601C22⋊C4—161no—
602C22⋊C4—161no—
603C42—21no—
604C42—21no—
605C42—22no—
606C42—21no—
607C42—21no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—81no—
612C42—81no—
613C42—81no—
614C42—81no—
615C42C2×C4×D411yescharacteristic
616C42C2×C4×D411yescharacteristic
617C42#57511yescharacteristic
618C42#57511yescharacteristic
619C16—22no—
620C16—42no—
621C16—42no—
622C16—41no—
623C16—41no—
624C16#40514yescomplemented
625C23—42no—
626C23—42no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23C2×#44211yescharacteristic
640D4—42no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—81no—
645D4—81no—
646D4—81no—
647D4—81no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
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—42no—
664C2×C4—42no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4AGL(1,ℤ/16)12yes—
690C2×C4C42×D411yescharacteristic
691C2×C4#293511yescharacteristic
692C2×C4#293511yescharacteristic
693C2×C4#294311yescharacteristic
694C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
695C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
696C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
697C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
698C2×C4#295711yescharacteristic
699C2×C4#295711yescharacteristic
700C8—21no—
701C8—21no—
702C8—42no—
703C8—42no—
704C8—42no—
705C8—42no—
706C8—41no—
707C8—41no—
708C8—82no—
709C8—82no—
710C8—82no—
711C8—82no—
712C8C2×#40511yescharacteristic
713C8#287511yescharacteristic
714C8#296911yescharacteristic
715C8#296911yescharacteristic
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—82no—
722C22—161no—
723C22—161no—
724C22—161no—
725C22—161no—
726C22—161no—
727C22—161no—
728C22—161no—
729C22—161no—
730C22#1807311yescharacteristic
731C22#1807311yescharacteristic
732C22C4×#44211yescharacteristic
733C22C2×AGL(1,ℤ/16)11yescharacteristic
734C22#3346811yescharacteristic
735C22#3346911yescharacteristic
736C22#3347111yescharacteristic
737C4—22no—
738C4—21no—
739C4—21no—
740C4—21no—
741C4—21no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—82no—
746C4—82no—
747C4—161no—
748C4—161no—
749C4—161no—
750C4—161no—
751C4#1807511yescharacteristic
752C4#1807511yescharacteristic
753C4#2049511yescharacteristic
754C4#2051311yescharacteristic
755C2—162no—
756C2—162no—
757C2#18397511yescharacteristic
758C2#48414011yescharacteristic
759C2#48414111yescharacteristic
760C2#48414411yescharacteristic
761C2#48414711yescharacteristic
762C2C4×AGL(1,ℤ/16)11yescharacteristic
763C2#49325111yescharacteristic
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C22×C42
Frattini, cosocleC2×C4×C8C24
prime radicalC22×D16C2×C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ #7842 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #183982C2semidirect
5. #183975C2semidirect
6. #129177C2semidirect
7. #129165C2semidirect
8. C4×#1368C2semidirect
9. #128753C2semidirect
10. #128753C2semidirect
11. #128719C2semidirect
12. #128719C2semidirect
13. #128617C2semidirect
14. #128617C2semidirect
15. #126534C2semidirect
38. #12089C4semidirect
39. #12067C4semidirect
624. C16#405semidirect

Maximal subgroups

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

subgroupindex
#4953082
C2×#120892
C2×#120672
#1839822
#1839752
#1291772
#1291652
C4×#13682
#1287532
#1287192
#1286172
#1265342