Finite Group Databasebeta

← #29647440

Subgroups — #29647440

Order 15616.

1272 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840307C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3#21448213C211yesmaximal, characteristic, complemented
4#21444377C214yesmaximal, complemented
5#21444364C214yesmaximal, complemented
6#21444336C211yesmaximal, characteristic, complemented
7#21444335C211yesmaximal, characteristic, complemented
8#21444334C211yesmaximal, characteristic, complemented
9C61×#1507C211yesmaximal, characteristic, complemented
10C22×#11758224—21no—
11#16840307—21no—
12#16840307—21no—
13#16840307—21no—
14#16840307—21no—
15#16840307C412yescomplemented
16#16840307C412yescomplemented
17#16840307C2212yes—
18#16840307C2212yes—
19C2×#14519776C411yescharacteristic, complemented
20C2×#14519773C411yescharacteristic, complemented
21C2×#14519763—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×D4×Dic61C411yescharacteristic, complemented
25C2×#14519739C411yescharacteristic, complemented
26C2×#14519737—21no—
27C22×C4×Dic61C2211yescharacteristic
28#16839816—21no—
29#16839816C2212yescomplemented
30#16839812—21no—
31#16839812C2212yescomplemented
32#16839785—21no—
33#16839726C2211yescharacteristic
34M16×Dic61—21no—
35#16839629C2212yescomplemented
36#16839626C2212yescomplemented
37#16839623—21no—
38#16839620—21no—
39C4×#11758196—21no—
40C4×C22⋊Dic61C2211yescharacteristic
41#16839608—21no—
42#16839497C2214yescomplemented
43#16839496C2214yescomplemented
44#16839495C2214yescomplemented
45C2×#121×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#327C2214yescomplemented
49C2×#11758224—22no—
50C2×#11758224—22no—
51C2×#11758224—22no—
52C2×#11758224—22no—
53C2×#11758224—48no—
54C22×Dic122—21no—
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C23×Dic61—21no—
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—21no—
63C2×#11758194—21no—
64#14519776—21no—
65#14519776—21no—
66#14519776C2×C412yes—
67#14519776C2×C412yes—
68#14519773—21no—
69#14519773—21no—
70#14519773C2×C412yes—
71#14519773C2×C412yes—
72#14519763—22no—
73#14519763—22no—
74#14519763—22no—
75#14519763—22no—
76#14519751—21no—
77#14519751—21no—
78#14519751C2×C412yes—
79#14519751C2312yes—
80#14519749—22no—
81#14519749—22no—
82#14519749—22no—
83#14519749—22no—
84D4×Dic61—21no—
85D4×Dic61—21no—
86D4×Dic61C2×C412yes—
87D4×Dic61C2×C412yes—
88#14519739—21no—
89#14519739—21no—
90#14519739C2×C412yes—
91#14519739C2×C412yes—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—22no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120#14519687—22no—
121C8×Dic61—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684C2312yes—
126C22×D4×C61—21no—
127C22×D4×C61C2×C411yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61C2×C412yes—
133#121×C61C2312yes—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2312yes—
140#95×C61C2312yes—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—44no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—42no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—44no—
166C2×C22⋊D61—44no—
167C2×C22⋊D61—44no—
168C22×Dic61—24no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—42no—
174C22×Dic61—44no—
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22⋊C411yescharacteristic
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187#11758224—48no—
188#11758224—48no—
189#11758224—48no—
190#11758224—48no—
191C2×D244—21no—
192C2×D244—42no—
193C2×D244C22×C412yes—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—44no—
197C2×Dic122—22no—
198C2×Dic122—22no—
199C2×Dic122—44no—
200M16×C61—42no—
201C2×C8×C61—22no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61C22×C412yes—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—42no—
207C42×C61—42no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—42no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215C4⋊Dic61—21no—
216C4⋊Dic61C22×C412yes—
217#11758196—22no—
218#11758196—22no—
219#11758196—44no—
220C4×Dic61—42no—
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22×C411yescharacteristic
230C4×Dic61C22×C411yescharacteristic
231C4×Dic61C22×C411yescharacteristic
232C4×Dic61C22×C411yescharacteristic
233C4×Dic61C2×D411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237#11758194—42no—
238C2×#92418—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—41no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C2×C22⋊C411yescharacteristic
248C23×C61C22×D411yescharacteristic
249C22×D61—22no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253D4×C61—42no—
254D4×C61—44no—
255D4×C61—44no—
256D4×C61—42no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61C2×C22⋊C411yescharacteristic
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×C4×C61C23×C411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C22⋊D61—44no—
273C22⋊D61—44no—
274C22⋊D61—44no—
275C22⋊D61—44no—
276C22⋊D61—44no—
277C22⋊D61—44no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—44no—
291C2×Dic61—42no—
292C2×Dic61—44no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61C2×C22⋊C411yescharacteristic
297C2×Dic61C2×C22⋊C411yescharacteristic
298C2×Dic61C2×C22⋊C411yescharacteristic
299C2×Dic61C2×C22⋊C411yescharacteristic
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61AGL(1,ℤ/8)14yes—
305D244—42no—
306D244—42no—
307C4×D61—44no—
308C4×D61—44no—
309Dic122—44no—
310Dic122—44no—
311C8×C61—42no—
312#92418—42no—
313#17583—611nomaximal, Sylow
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—44no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—84no—
326C22×C61#42112yes—
327C22×C61C22×C22⋊C411yescharacteristic
328C22×C61C2×AGL(1,ℤ/8)12yes—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—42no—
332C2×D61—84no—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—42no—
337C4×C61—82no—
338C4×C61#41012yes—
339Dic61—21no—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—21no—
345Dic61—42no—
346Dic61—82no—
347Dic61#41812yes—
348Dic61#41812yes—
349C2×#532—611no—
350#2920—611no—
351#2283—611no—
352#1517—614no—
353#1514—614no—
354#1507—611no—
355#1507—611no—
356#1507—611no—
357#1507D6111yescharacteristic, complemented
358C2×C61—22no—
359C2×C61—22no—
360C2×C61—41no—
361C2×C61—82no—
362C2×C61C2×#41011yescharacteristic
363C2×C61C2×#41811yescharacteristic
364C2×C61C2×#42111yescharacteristic
365D61—82no—
366C22×#41—1221no—
367#532—612no—
368#532—612no—
369#532—612no—
370#532—612no—
371#532—1221no—
372#532—1221no—
373#532—1221no—
374#532—1221no—
375C2×C4⋊Q8—611no—
376C2×#127—611no—
377C2×#124—1221no—
378C2×#121—611no—
379C2×#121—1221no—
380C2×#121C2×D6111yescharacteristic
381C2×C4×D4—611no—
382C2×C4×D4—611no—
383C2×C4×D4—1221no—
384C22×C42—611no—
385#432—612no—
386#432—1221no—
387#431—612no—
388#431—1221no—
389#423—1221no—
390#407—611no—
391#407C2×D6111yescharacteristic
392C4×M16—1221no—
393#383—612no—
394#382—612no—
395#381—1221no—
396#380—1221no—
397C4×C4⋊C4—1221no—
398C4×C22⋊C4—611no—
399C4×C22⋊C4C2×D6111yescharacteristic
400#376—1221no—
401#327—614no—
402#327—614no—
403#327—614no—
404#327C2×D6114yescomplemented
405C61#1758311yescharacteristic, complemented, Sylow
406C2×#41—1222no—
407C2×#41—1222no—
408C2×#41—1222no—
409C2×#41—1222no—
410C2×#41—2448no—
411C22×Q8—1221no—
412C22×D4—21no—
413C22×D4—611no—
414C22×D4—1221no—
415C22×D4—1221no—
416C22×D4—1221no—
417C22×D4C4×D6111yescharacteristic
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—1221no—
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C2×M16—21no—
424C2×M16—1221no—
425C4⋊Q8—612no—
426C4⋊Q8—612no—
427C4⋊Q8—1221no—
428C4⋊Q8—1221no—
429#127—612no—
430#127—612no—
431#127—1221no—
432#127—1221no—
433#124—1222no—
434#124—1222no—
435#124—1222no—
436#124—1222no—
437#121—21no—
438#121—21no—
439#121—612no—
440#121—612no—
441#121—1222no—
442#121—1222no—
443#121—1222no—
444#121—1222no—
445#121—1221no—
446#121—1221no—
447#121C4×D6112yes—
448#121C22×D6112yes—
449C4×D4—612no—
450C4×D4—612no—
451C4×D4—612no—
452C4×D4—612no—
453C4×D4—1222no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1221no—
458C4×D4—1221no—
459C4×D4—1221no—
460C4×D4—1221no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1222no—
464C2×C4⋊C4C4×D6111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C42—21no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—1221no—
485C4⋊C8—1222no—
486C4⋊C8—1222no—
487C22⋊C8—21no—
488C22⋊C8—612no—
489C22⋊C8—1221no—
490C22⋊C8C22×D6112yes—
491#97—1222no—
492C4×C8—1222no—
493#95—612no—
494#95—1222no—
495#95—1222no—
496#95—1222no—
497#95C22×D6112yes—
498C24—21no—
499C24—1221no—
500C24D4×D6111yescharacteristic
501#41—2448no—
502#41—2448no—
503#41—2448no—
504#41—2448no—
505C2×Q8—1222no—
506C2×Q8—1222no—
507C2×Q8—2444no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—44no—
513C2×D4—612no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1221no—
521C2×D4—2442no—
522C2×D4—2444no—
523C2×D4—2444no—
524C2×D4—2444no—
525C2×D4C2×C4×D6112yes—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1224no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1221no—
547C22×C4—1222no—
548C22×C4—2444no—
549C22×C4—2442no—
550C22×C4—2444no—
551C22×C4C2×C4×D6111yescharacteristic
552C22×C4C2×C4×D6111yescharacteristic
553C22×C4D4×D6111yescharacteristic
554C22×C4D4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556C22×C4C23×D6111yescharacteristic
557M16—42no—
558M16—2442no—
559C2×C8—22no—
560C2×C8—1222no—
561C4⋊C4—21no—
562C4⋊C4—612no—
563C4⋊C4—1222no—
564C4⋊C4—1222no—
565C4⋊C4—1221no—
566C4⋊C4—2444no—
567C4⋊C4C2×C4×D6112yes—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—42no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—2442no—
578C42—42no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42—611no—
593C42—611no—
594C42—611no—
595C42—2442no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—1222no—
604C23—2442no—
605C23—2442no—
606C23—2442no—
607C23C22⋊C4×D6111yescharacteristic
608C23C22⋊C4×D6111yescharacteristic
609C23C2×D4×D6111yescharacteristic
610Q8—2444no—
611Q8—2444no—
612D4—42no—
613D4—44no—
614D4—44no—
615D4—42no—
616D4—2442no—
617D4—2444no—
618D4—2444no—
619D4—2444no—
620D4—2444no—
621D4—2444no—
622D4—2444no—
623D4—2442no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—614no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—2444no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2444no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4C22⋊C4×D6111yescharacteristic
665C2×C4C22⋊C4×D6111yescharacteristic
666C2×C4C22×C4×D6111yescharacteristic
667C2×C4C2×D4×D6111yescharacteristic
668C8—42no—
669C8—2442no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—44no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22—4884no—
683C22—2442no—
684C22—2442no—
685C22—2442no—
686C22#1683977712yes—
687C22C2×C22⋊C4×D6111yescharacteristic
688C22AGL(1,ℤ/8)×D6112yes—
689C4—21no—
690C4—21no—
691C4—21no—
692C4—42no—
693C4—82no—
694C4—612no—
695C4—612no—
696C4—1221no—
697C4—1221no—
698C4—1221no—
699C4—1221no—
700C4—1221no—
701C4—1221no—
702C4—4882no—
703C4—2442no—
704C4#1683973412yes—
705C2—22no—
706C2—22no—
707C2—41no—
708C2—82no—
709C2—4882no—
710C2C2×#1683973411yescharacteristic
711C2#418×D6111yescharacteristic
712C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1507C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840307C2
cosocleC22×C4×C61C24
hypercenter#1507D61
hypocenterC61#17583
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. #21448213C2semidirect
4. #21444377C2semidirect
5. #21444364C2semidirect
6. #21444336C2semidirect
7. #21444335C2semidirect
8. #21444334C2semidirect
9. C61×#1507C2semidirect
15. #16840307C4semidirect
16. #16840307C4semidirect
19. C2×#14519776C4semidirect
20. C2×#14519773C4semidirect
24. C2×D4×Dic61C4semidirect
25. C2×#14519739C4semidirect
29. #16839816C22semidirect
31. #16839812C22semidirect
35. #16839629C22semidirect
36. #16839626C22semidirect
42. #16839497C22semidirect
43. #16839496C22semidirect
44. #16839495C22semidirect
48. C61×#327C22semidirect
357. #1507D61semidirect
404. #327C2×D61semidirect
405. C61#17583semidirect

Maximal subgroups

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

subgroupindex
C2×#168403072
#214544482
#214482132
#214443772
#214443642
#214443362
#214443352
#214443342
C61×#15072
#1758361