Finite Group Databasebeta

← #6461210

Subgroups — #6461210

Order 512.

2078 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34202C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic, complemented
3#29253C214yesmaximal, complemented
4#29247C214yesmaximal, complemented
5#29244C212yesmaximal, complemented
6#29241C212yesmaximal, complemented
7#29237C212yesmaximal, complemented
8#29234C212yesmaximal, complemented
9#23667C212yesmaximal, complemented
10#23616C212yesmaximal, complemented
11#21035C212yesmaximal, complemented
12#20909C211yesmaximal, characteristic
13#20908C211yesmaximal, characteristic
14#20881C212yesmaximal, complemented
15#20846C211yesmaximal, characteristic, complemented
16C2×#1852C211yesmaximal, characteristic, complemented
17#20628C211yesmaximal, characteristic, complemented
18C2×#525C2211yescharacteristic
19C2×#520C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C2×#428C2212yes—
24C22×#107C2212yes—
25C2×#424C2212yes—
26C2×#417C2212yes—
27C2×#416C2212yes—
28C2×#407C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30#2359—22no—
31#2358—22no—
32#2354—21no—
33#2352—21no—
34#2352—21no—
35D4×C4⋊C4—21no—
36#2324C2212yes—
37#2323C2212yes—
38#2317—21no—
39#2317—21no—
40#2317—22no—
41#2317C2212yes—
42#2317C2214yes—
43#2317C2212yes—
44#2317C2211yescharacteristic
45#2311C2211yescharacteristic
46C4×C22⋊Q8C2212yes—
47C4×#121C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#385—22no—
51C2×#384—21no—
52C2×#382—21no—
53C2×#380C2211yescharacteristic
54#2274C2211yescharacteristic
55#2087C2214yescomplemented
56#2087C2214yescomplemented
57#2086C2214yescomplemented
58#2086C2214yescomplemented
59#2068C2214yescomplemented
60#2067C2214yescomplemented
61#2066C2214yescomplemented
62#2065C2214yescomplemented
63#1921C2214yescomplemented
64#1920C2214yescomplemented
65#1919C2214yescomplemented
66#1918C2214yescomplemented
67#1875C2212yes—
68#1874C2211yescharacteristic
69#1874C2212yes—
70#1874C2211yescharacteristic
71#1874C2212yes—
72#1873C2212yes—
73#1872C2211yescharacteristic
74#1872C2212yes—
75#1872C2211yescharacteristic
76#1872C2212yes—
77#1863C2214yescomplemented
78#1863C2214yescomplemented
79#1862C2214yescomplemented
80#1862C2214yescomplemented
81#1854C2214yes—
82#1853C2212yes—
83#1852C2212yes—
84#1852C2212yes—
85#1852C2212yes—
86#1852C2214yes—
87#1798C2214yes—
88#1797C2212yes—
89#1797C2212yes—
90#1736C2212yes—
91#1736C2212yes—
92#1735C2212yes—
93C2×#340C2212yes—
94#1729C2212yes—
95C22×#41C2311yescharacteristic
96C24×C4—21no—
97C24×C4C2311yescharacteristic
98C22×M16C2312yes—
99C23×C8C2312yes—
100#525—24no—
101#525Q818yes—
102C2×#123—21no—
103C2×C22⋊Q8C2311yescharacteristic
104C2×C22⋊Q8C2311yescharacteristic
105C2×#121C2311yescharacteristic
106C2×#121C2311yescharacteristic
107C2×#120—21no—
108#520—44no—
109C2×C4×Q8C2312yes—
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4C2312yes—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—28no—
118C2×#117—21no—
119C2×#117—44no—
120C2×#117D411yescharacteristic
121C2×#117D411yescharacteristic
122C2×#117D412yes—
123C2×#117C2312yes—
124C2×#117C2311yescharacteristic
125C2×#117C2312yes—
126C2×#117C2311yescharacteristic
127C2×#117C2311yescharacteristic
128C2×#117C2312yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—22no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—44no—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D412yes—
148C22×C42—21no—
149C22×C42C2312yes—
150#428—28no—
151C2×#107—44no—
152C2×#107C2314yes—
153C2×#107C2314yes—
154C2×#107C2314yes—
155C2×#106C2314yes—
156#424—44no—
157C2×C4⋊C8C2314yes—
158C2×C4⋊C8C2314yes—
159#417—44no—
160#416—28no—
161C2×#103C2312yes—
162C2×#103C2312yes—
163C2×#103C2314yes—
164C2×#102C2312yes—
165C2×#102C2312yes—
166C2×#102C2314yes—
167#407—24no—
168C2×C22⋊C8—24no—
169C2×C22⋊C8C2311yescharacteristic
170C2×C22⋊C8C2311yescharacteristic
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174#391C2312yes—
175#390—22no—
176#390C2312yes—
177#389—22no—
178#389—22no—
179#389—22no—
180#389—22no—
181#389—22no—
182#389C2314yes—
183#389C2314yes—
184#389C2314yes—
185#389C2314yes—
186#389C2312yes—
187#389C2312yes—
188#388—22no—
189#388—22no—
190#388—22no—
191#388—22no—
192#387—22no—
193#387—22no—
194#386—22no—
195#386—22no—
196#386—22no—
197#385—22no—
198#385—22no—
199#385—24no—
200#385—24no—
201#385—24no—
202#385—24no—
203#385—22no—
204#384—22no—
205#384—22no—
206#384—24no—
207#384—21no—
208#382—22no—
209#382—22no—
210#382—24no—
211#382—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380C2312yes—
217#380C2312yes—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4C2312yes—
222C4×C4⋊C4C2312yes—
223C4×C22⋊C4—22no—
224C4×C22⋊C4—22no—
225C4×C22⋊C4—22no—
226C2×#95—21no—
227C2×#95—22no—
228C2×#95—22no—
229#340C2314yes—
230#340C2314yes—
231#340C2312yes—
232#340C2312yes—
233#340C2314yes—
234#340C2314yes—
235#340C2314yes—
236#340C2314yes—
237#340C2312yes—
238#340C2312yes—
239#336C2314yes—
240#336C2314yes—
241C25C2×D411yescharacteristic
242C2×#41—22no—
243C2×#41—24no—
244C2×#41—24no—
245C2×#41C2×Q814yes—
246C22×Q8C2411yescharacteristic
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C2411yescharacteristic
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—22no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—44no—
263C23×C4—82no—
264C23×C4—82no—
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×Q814yes—
271C23×C4#4114yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C2×M16—24no—
276C2×M16—24no—
277C2×M16—24no—
278C22×C8—24no—
279C22×C8—24no—
280C22×C8—24no—
281C22×C8C2412yes—
282C22×C8C2412yes—
283C22×C8C2414yes—
284#123—28no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8C2×Q814yes—
288C22⋊Q8C2×Q814yes—
289#121—22no—
290#121—22no—
291#121C2×Q814yes—
292#121C2×Q814yes—
293#120—28no—
294C4×Q8—44no—
295C4×D4—28no—
296C4×D4—28no—
297C4×D4—44no—
298C4×D4—48no—
299C4×D4—84no—
300#117—28no—
301#117—28no—
302#117—24no—
303#117—22no—
304#117—24no—
305#117—24no—
306#117—24no—
307#117—24no—
308#117—44no—
309#117—44no—
310#117—42no—
311#117—42no—
312#117—44no—
313#117C2×Q814yes—
314#117#4118yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—84no—
346C2×C4⋊C4—84no—
347C2×C4⋊C4C2×D411yescharacteristic
348C2×C4⋊C4C2×D411yescharacteristic
349C2×C4⋊C4C2×D411yescharacteristic
350C2×C4⋊C4C2×D411yescharacteristic
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4C2414yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2411yescharacteristic
357C2×C4⋊C4C2411yescharacteristic
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
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—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4C2×D412yes—
376C2×C22⋊C4C2×D412yes—
377C2×C22⋊C4C2×D412yes—
378C2×C22⋊C4C2×D412yes—
379C2×C42—28no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—21no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—44no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42C2412yes—
390C2×C42C2412yes—
391#107—28no—
392#107—44no—
393#107—44no—
394#106—28no—
395C4⋊C8—44no—
396C4⋊C8—44no—
397#103—24no—
398#103—24no—
399#103—44no—
400#102—24no—
401#102—24no—
402#102—44no—
403C22⋊C8—22no—
404C22⋊C8—22no—
405C22⋊C8—24no—
406C22⋊C8—24no—
407C22⋊C8—24no—
408#95—22no—
409#95—22no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—41no—
426C24—41no—
427C24C22⋊Q814yes—
428C24C22×D411yescharacteristic
429C24C22×D411yescharacteristic
430C24C22×D411yescharacteristic
431#41—216no—
432#41—48no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8C22×Q812yes—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4C22×Q812yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—82no—
494C22×C4—82no—
495C22×C4—82no—
496C22×C4—82no—
497C22×C4—82no—
498C22×C4—82no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—816no—
504C22×C4C22⋊Q814yes—
505C22×C4C22⋊Q814yes—
506C22×C4C22⋊Q814yes—
507C22×C4C22×D412yes—
508C22×C4C22×D412yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×Q812yes—
515C22×C4C22×Q812yes—
516C22×C4C22×Q812yes—
517C22×C4C2×#4112yes—
518C22×C4C2×#4112yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4114yes—
521C22×C4H(5,𝔽2)14yes—
522C22×C4C2511yescharacteristic
523M16—48no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—24no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—24no—
530C2×C8—24no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—48no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—42no—
556C4⋊C4—44no—
557C4⋊C4—42no—
558C4⋊C4—82no—
559C4⋊C4—84no—
560C4⋊C4—84no—
561C4⋊C4—84no—
562C4⋊C4—84no—
563C4⋊C4—82no—
564C4⋊C4C22×Q812yes—
565C4⋊C4C22×Q812yes—
566C4⋊C4C2×#4114yes—
567C4⋊C4C2×#4114yes—
568C22⋊C4—28no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—28no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—82no—
582C22⋊C4—82no—
583C22⋊C4—82no—
584C42—28no—
585C42—24no—
586C42—28no—
587C42—24no—
588C42—24no—
589C42—42no—
590C42—42no—
591C42—44no—
592C42—82no—
593C42—82no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—28no—
605C23—28no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23C2×C22⋊Q812yes—
623C23C2×C22⋊Q812yes—
624C23C2×C22⋊Q812yes—
625C23#52512yes—
626C23#53412yes—
627C23#57612yes—
628C23#57812yes—
629C23C23×D411yescharacteristic
630Q8—24no—
631Q8—42no—
632D4—24no—
633D4—48no—
634D4—48no—
635D4—42no—
636D4—84no—
637C2×C4—28no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—48no—
666C2×C4—48no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—48no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—88no—
690C2×C4—88no—
691C2×C4—88no—
692C2×C4—164no—
693C2×C4—162no—
694C2×C4—162no—
695C2×C4C2×C22⋊Q812yes—
696C2×C4C2×C22⋊Q812yes—
697C2×C4C2×C22⋊Q812yes—
698C2×C4#52512yes—
699C2×C4#53412yes—
700C2×C4#55318yes—
701C2×C4#55418yes—
702C2×C4C23×Q811yescharacteristic
703C2×C4C22×#4111yescharacteristic
704C2×C4C22×#4112yes—
705C2×C4C2×H(5,𝔽2)12yes—
706C8—42no—
707C8—42no—
708C8—44no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—416no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#257914yes—
737C22#308314yes—
738C22C22×C22⋊Q811yescharacteristic
739C22C2×#52511yescharacteristic
740C22C2×#53411yescharacteristic
741C22C2×#57611yescharacteristic
742C22C2×#57811yescharacteristic
743C22#358511yescharacteristic
744C22#358611yescharacteristic
745C4—22no—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—84no—
757C4—82no—
758C4—82no—
759C4#257914yes—
760C4C2×#55312yes—
761C4C2×#55412yes—
762C2—24no—
763C2—24no—
764C2—42no—
765C2—82no—
766C2C2×#257911yescharacteristic
767C2C2×#308311yescharacteristic
768C2#6049311yescharacteristic
769C2#6058411yescharacteristic
770C2#6058911yescharacteristic
771C2#6075611yescharacteristic
772C2#6075911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2317C2semidirect
3. #29253C2semidirect
4. #29247C2semidirect
5. #29244C2semidirect
6. #29241C2semidirect
7. #29237C2semidirect
8. #29234C2semidirect
9. #23667C2semidirect
10. #23616C2semidirect
11. #21035C2semidirect
14. #20881C2semidirect
15. #20846C2semidirect
16. C2×#1852C2semidirect
17. #20628C2semidirect
55. #2087C22semidirect
56. #2087C22semidirect
57. #2086C22semidirect
58. #2086C22semidirect
59. #2068C22semidirect
60. #2067C22semidirect
61. #2066C22semidirect
62. #2065C22semidirect
63. #1921C22semidirect
64. #1920C22semidirect
65. #1919C22semidirect
66. #1918C22semidirect
77. #1863C22semidirect
78. #1863C22semidirect
79. #1862C22semidirect
80. #1862C22semidirect

Maximal subgroups

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

subgroupindex
#342022
C2×#23172
#292532
#292472
#292442
#292412
#292372
#292342
#236672
#236162
#210352
#209092
#209082
#208812
#208462
C2×#18522
#206282