Finite Group Databasebeta

← C151×#21624 #50326549

Subgroups — C151×#21624 #50326549

Order 38656.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C151C211yesmaximal, characteristic
2#2331×C151C211yesmaximal, characteristic, complemented
3#2275×C151C211yesmaximal, characteristic
4#1987×C151C211yesmaximal, characteristic, complemented
5#1949×C151C211yesmaximal, characteristic, complemented
6#1921×C151C211yesmaximal, characteristic, complemented
7#1918×C151C211yesmaximal, characteristic, complemented
8#1864×C151C211yesmaximal, characteristic
9#1862×C151C211yesmaximal, characteristic
10#1804×C151C211yesmaximal, characteristic
11#1776×C151C211yesmaximal, characteristic, complemented
12C4×#107×C151C211yesmaximal, characteristic, complemented
13#1768×C151C211yesmaximal, characteristic, complemented
14#1762×C151C211yesmaximal, characteristic
15C4×#102×C151C211yesmaximal, characteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20#474×C151C418yescomplemented
21C2×#107×C151C2211yescharacteristic
22C2×#107×C151C2211yescharacteristic
23C2×#107×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#97×C151C2211yescharacteristic
32C2×C4×C8×C151C2211yescharacteristic
33#391×C151—21no—
34#391×C151—21no—
35#389×C151C2211yescharacteristic
36#389×C151C2211yescharacteristic
37#387×C151—21no—
38#387×C151—21no—
39#382×C151C2211yescharacteristic
40C4×C4⋊C4×C151C2211yescharacteristic
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C4⋊C4×C151C2211yescharacteristic
43C4×C4⋊C4×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C22⋊C4×C151—21no—
46C4×C22⋊C4×C151—21no—
47C4×C22⋊C4×C151—21no—
48#376×C151C2211yescharacteristic
49C2×#95×C151—21no—
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60C22×Q8×C151—21no—
61C22×D4×C151C2311yescharacteristic
62C23×C4×C151—21no—
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151C2×C414yescomplemented
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C4×D4×C151C2×C414yes—
76C4×D4×C151Q814yescomplemented
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151—21no—
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98#107×C151—22no—
99#107×C151C2×C414yescomplemented
100#107×C151C2×C414yescomplemented
101#106×C151—22no—
102C4⋊C8×C151—22no—
103C4⋊C8×C151C2×C414yescomplemented
104#102×C151—22no—
105#102×C151—22no—
106#102×C151C2×C414yes—
107#102×C151C2×C414yes—
108#97×C151—22no—
109C4×C8×C151—22no—
110#95×C151—21no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118#95×C151—21no—
119#95×C151D411yescharacteristic
120#95×C151D411yescharacteristic
121#95×C151D411yescharacteristic
122#95×C151D411yescharacteristic
123C24×C151—21no—
124C2×Q8×C151—24no—
125C2×Q8×C151—81no—
126C2×Q8×C151—81no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151C22×C412yes—
131C2×D4×C151C2×Q812yes—
132C2×D4×C151#4112yes—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—24no—
139C22×C4×C151—24no—
140C22×C4×C151—24no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—81no—
144C22×C4×C151—81no—
145C22×C4×C151—81no—
146C22×C4×C151—81no—
147C22×C4×C151—81no—
148C22×C4×C151—81no—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2411yescharacteristic
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151C22×C412yes—
167C2×C8×C151C22×C412yes—
168C4⋊C4×C151—24no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—81no—
179C4⋊C4×C151—81no—
180C4⋊C4×C151C22×C412yes—
181C4⋊C4×C151C22×C412yes—
182C4⋊C4×C151C22×C412yes—
183C4⋊C4×C151C2×Q812yes—
184C4⋊C4×C151#4112yes—
185C22⋊C4×C151—24no—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—24no—
188C42×C151—21no—
189C42×C151—21no—
190C42×C151—81no—
191C42×C151—81no—
192C42×C151—81no—
193C42×C151—81no—
194C42×C151—81no—
195C42×C151C22×C412yes—
196C42×C151C2×Q812yes—
197C42×C151#4112yes—
198C42×C151#4112yes—
199C23×C151—22no—
200C23×C151—22no—
201C23×C151—22no—
202C23×C151—41no—
203C23×C151—41no—
204C23×C151—41no—
205C23×C151—41no—
206C23×C151C22×D411yescharacteristic
207Q8×C151—84no—
208D4×C151—22no—
209D4×C151—22no—
210D4×C151—22no—
211D4×C151C4×Q814yes—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—22no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—84no—
248C2×C4×C151—84no—
249C2×C4×C151—84no—
250C2×C4×C151C4×D412yes—
251C2×C4×C151C4×D412yes—
252C2×C4×C151C22⋊Q812yes—
253C2×C4×C151C22⋊Q812yes—
254C2×C4×C151C23×C411yescharacteristic
255C2×C4×C151C22×Q811yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C2×C4×C151C2×#4111yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C8×C151—22no—
261C8×C151—22no—
262C8×C151—41no—
263C8×C151—41no—
264C22×C151—24no—
265C22×C151—42no—
266C22×C151—42no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151C2×C4×D411yescharacteristic
272C22×C151C2×C22⋊Q811yescharacteristic
273C22×C151#52511yescharacteristic
274C22×C151#57611yescharacteristic
275C22×C151#57611yescharacteristic
276C22×C151#57711yescharacteristic
277C22×C151#57811yescharacteristic
278C4×C151—22no—
279C4×C151—22no—
280C4×C151—22no—
281C4×C151—22no—
282C4×C151—42no—
283C4×C151—41no—
284C4×C151—42no—
285C4×C151—41no—
286C4×C151—42no—
287C4×C151—42no—
288C4×C151—42no—
289C4×C151—81no—
290C4×C151—81no—
291C4×C151C2×C4×Q811yescharacteristic
292C4×C151C4×#4111yescharacteristic
293C4×C151#52911yescharacteristic
294C4×C151#53311yescharacteristic
295C2×C151—44no—
296C2×C151C4×C22⋊Q811yescharacteristic
297C2×C151#294711yescharacteristic
298C2×C151#294811yescharacteristic
299C2×C151#308111yescharacteristic
300C2×C151#308311yescharacteristic
301C2×C151#311811yescharacteristic
302C2×C151#312411yescharacteristic
303#21624C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#2162411yescharacteristic, direct product factor, Sylow
305C2×#474C2×C15111yescharacteristic
306#2331C2×C15111yescharacteristic, complemented
307#2275C2×C15111yescharacteristic
308#1987C2×C15111yescharacteristic, complemented
309#1949C2×C15111yescharacteristic, complemented
310#1921C2×C15111yescharacteristic, complemented
311#1918C2×C15111yescharacteristic, complemented
312#1864C2×C15111yescharacteristic
313#1862C2×C15111yescharacteristic
314#1804C2×C15111yescharacteristic
315#1776C2×C15111yescharacteristic, complemented
316C4×#107C2×C15111yescharacteristic, complemented
317#1768C2×C15111yescharacteristic, complemented
318#1762C2×C15111yescharacteristic
319C4×#102C2×C15111yescharacteristic
320C2×C4⋊Q8C22×C15111yescharacteristic
321C2×C4×D4C22×C15111yescharacteristic
322C2×C4×D4C22×C15111yescharacteristic
323C2×C4×D4C22×C15111yescharacteristic
324#474C4×C15118yescomplemented
325C2×#107C22×C15111yescharacteristic
326C2×#107C22×C15111yescharacteristic
327C2×#107C22×C15111yescharacteristic
328C2×#106C22×C15111yescharacteristic
329C2×C4⋊C8C22×C15111yescharacteristic
330C2×C4⋊C8C22×C15111yescharacteristic
331C2×#102C22×C15111yescharacteristic
332C2×#102C22×C15111yescharacteristic
333C2×#102C22×C15111yescharacteristic
334C2×#102C22×C15111yescharacteristic
335C2×#97C22×C15111yescharacteristic
336C2×C4×C8C22×C15111yescharacteristic
337#391—21no—
338#391—21no—
339#389C22×C15111yescharacteristic
340#389C22×C15111yescharacteristic
341#387—21no—
342#387—21no—
343#382C22×C15111yescharacteristic
344C4×C4⋊C4C22×C15111yescharacteristic
345C4×C4⋊C4C22×C15111yescharacteristic
346C4×C4⋊C4C22×C15111yescharacteristic
347C4×C4⋊C4C22×C15111yescharacteristic
348C4×C4⋊C4C22×C15111yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—21no—
352#376C22×C15111yescharacteristic
353C2×#95—21no—
354#340C22×C15111yescharacteristic
355#340C22×C15111yescharacteristic
356#340C22×C15111yescharacteristic
357#340C22×C15111yescharacteristic
358#340C22×C15111yescharacteristic
359#340C22×C15111yescharacteristic
360#340C22×C15111yescharacteristic
361#340C22×C15111yescharacteristic
362#336C22×C15111yescharacteristic
363#336C22×C15111yescharacteristic
364C22×Q8—21no—
365C22×D4C23×C15111yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C22×C8C23×C15111yescharacteristic
370C22×C8C23×C15111yescharacteristic
371C22×C8C23×C15111yescharacteristic
372C22×C8C23×C15111yescharacteristic
373C4⋊Q8—22no—
374C4⋊Q8C2×C4×C15114yescomplemented
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4C2×C4×C15114yes—
380C4×D4Q8×C15114yescomplemented
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C23×C15111yescharacteristic
385C2×C4⋊C4C23×C15111yescharacteristic
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C4⋊C4C23×C15111yescharacteristic
388C2×C4⋊C4C23×C15111yescharacteristic
389C2×C4⋊C4C23×C15111yescharacteristic
390C2×C4⋊C4C23×C15111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C23×C15111yescharacteristic
400C2×C42C23×C15111yescharacteristic
401C2×C42C23×C15111yescharacteristic
402#107—22no—
403#107C2×C4×C15114yescomplemented
404#107C2×C4×C15114yescomplemented
405#106—22no—
406C4⋊C8—22no—
407C4⋊C8C2×C4×C15114yescomplemented
408#102—22no—
409#102—22no—
410#102C2×C4×C15114yes—
411#102C2×C4×C15114yes—
412#97—22no—
413C4×C8—22no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95D4×C15111yescharacteristic
424#95D4×C15111yescharacteristic
425#95D4×C15111yescharacteristic
426#95D4×C15111yescharacteristic
427C24—21no—
428C2×Q8—24no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C22×C4×C15112yes—
435C2×D4C2×Q8×C15112yes—
436C2×D4#41×C15112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15111yescharacteristic
456C22×C4C2×D4×C15111yescharacteristic
457C22×C4C2×D4×C15111yescharacteristic
458C22×C4C2×D4×C15111yescharacteristic
459C22×C4C24×C15111yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C22×C4×C15112yes—
471C2×C8C22×C4×C15112yes—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4C22×C4×C15112yes—
485C4⋊C4C22×C4×C15112yes—
486C4⋊C4C22×C4×C15112yes—
487C4⋊C4C2×Q8×C15112yes—
488C4⋊C4#41×C15112yes—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—81no—
496C42—81no—
497C42—81no—
498C42—81no—
499C42C22×C4×C15112yes—
500C42C2×Q8×C15112yes—
501C42#41×C15112yes—
502C42#41×C15112yes—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C22×D4×C15111yescharacteristic
511Q8—84no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4C4×Q8×C15114yes—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4—84no—
553C2×C4—84no—
554C2×C4C4×D4×C15112yes—
555C2×C4C4×D4×C15112yes—
556C2×C4C22⋊Q8×C15112yes—
557C2×C4C22⋊Q8×C15112yes—
558C2×C4C23×C4×C15111yescharacteristic
559C2×C4C22×Q8×C15111yescharacteristic
560C2×C4C2×#41×C15111yescharacteristic
561C2×C4C2×#41×C15111yescharacteristic
562C2×C4C2×#41×C15111yescharacteristic
563C2×C4C2×#41×C15111yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22C2×C4×D4×C15111yescharacteristic
576C22C2×C22⋊Q8×C15111yescharacteristic
577C22#525×C15111yescharacteristic
578C22#576×C15111yescharacteristic
579C22#576×C15111yescharacteristic
580C22#577×C15111yescharacteristic
581C22#578×C15111yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4C2×C4×Q8×C15111yescharacteristic
596C4C4×#41×C15111yescharacteristic
597C4#529×C15111yescharacteristic
598C4#533×C15111yescharacteristic
599C2—44no—
600C2C4×C22⋊Q8×C15111yescharacteristic
601C2#2947×C15111yescharacteristic
602C2#2948×C15111yescharacteristic
603C2#3081×C15111yescharacteristic
604C2#3083×C15111yescharacteristic
605C2#3118×C15111yescharacteristic
606C2#3124×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2331×C151C2semidirect
4. #1987×C151C2semidirect
5. #1949×C151C2semidirect
6. #1921×C151C2semidirect
7. #1918×C151C2semidirect
11. #1776×C151C2semidirect
12. C4×#107×C151C2semidirect
13. #1768×C151C2semidirect
20. #474×C151C4semidirect
70. C4⋊Q8×C151C2×C4semidirect
76. C4×D4×C151Q8semidirect
99. #107×C151C2×C4semidirect
100. #107×C151C2×C4semidirect
103. C4⋊C8×C151C2×C4semidirect
303. #21624C151direct (N × H)
304. C151#21624direct (N × H)
306. #2331C2×C151semidirect
308. #1987C2×C151semidirect
309. #1949C2×C151semidirect
310. #1921C2×C151semidirect
311. #1918C2×C151semidirect
315. #1776C2×C151semidirect
316. C4×#107C2×C151semidirect
317. #1768C2×C151semidirect
324. #474C4×C151semidirect
374. C4⋊Q8C2×C4×C151semidirect
380. C4×D4Q8×C151semidirect
403. #107C2×C4×C151semidirect
404. #107C2×C4×C151semidirect
407. C4⋊C8C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1512
#2331×C1512
#2275×C1512
#1987×C1512
#1949×C1512
#1921×C1512
#1918×C1512
#1864×C1512
#1862×C1512
#1804×C1512
#1776×C1512
C4×#107×C1512
#1768×C1512
#1762×C1512
C4×#102×C1512
#21624151