Finite Group Databasebeta

← C83×#26313 #35254137

Subgroups — C83×#26313 #35254137

Order 21248.

742 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2563C211yesmaximal, characteristic
2C83×#2352C211yesmaximal, characteristic
3C83×#2077C211yesmaximal, characteristic, complemented
4C83×#2076C211yesmaximal, characteristic, complemented
5C83×#2076C211yesmaximal, characteristic, complemented
6C83×#2075C211yesmaximal, characteristic, complemented
7C83×#1993C211yesmaximal, characteristic, complemented
8C83×#1988C211yesmaximal, characteristic, complemented
9C83×#1955C211yesmaximal, characteristic
10C83×#1949C211yesmaximal, characteristic, complemented
11C83×#1854C211yesmaximal, characteristic, complemented
12C83×#1853C211yesmaximal, characteristic, complemented
13C83×#1825C211yesmaximal, characteristic, complemented
14C83×#1823C211yesmaximal, characteristic, complemented
15C83×#1776C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C83C2211yescharacteristic
17C2×C4×D4×C83C2211yescharacteristic
18C2×#117×C83C2211yescharacteristic
19C22×C4⋊C4×C83C2211yescharacteristic
20C2×#107×C83C2211yescharacteristic
21C2×#107×C83C2211yescharacteristic
22C2×#106×C83C2211yescharacteristic
23C2×#106×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C22⋊C8×C83C2211yescharacteristic
26C2×C22⋊C8×C83C2211yescharacteristic
27C2×C22⋊C8×C83C2211yescharacteristic
28C2×C22⋊C8×C83C2211yescharacteristic
29C2×#97×C83C2211yescharacteristic
30#393×C83—21no—
31#393×C83—21no—
32#390×C83—21no—
33#388×C83—21no—
34#387×C83—21no—
35#386×C83—21no—
36#382×C83—21no—
37#382×C83C2211yescharacteristic
38#380×C83C2211yescharacteristic
39#380×C83C2211yescharacteristic
40#380×C83C2211yescharacteristic
41#380×C83C2211yescharacteristic
42#380×C83C2211yescharacteristic
43#380×C83C2211yescharacteristic
44C4×C4⋊C4×C83C2211yescharacteristic
45C4×C4⋊C4×C83C2211yescharacteristic
46C4×C22⋊C4×C83—21no—
47#340×C83C2211yescharacteristic
48#340×C83C2211yescharacteristic
49#340×C83C2211yescharacteristic
50#340×C83C2211yescharacteristic
51#340×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59C22×Q8×C83—21no—
60C22×D4×C83D411yescharacteristic
61C23×C4×C83—21no—
62C23×C4×C83C2311yescharacteristic
63C23×C4×C83C2311yescharacteristic
64C22×C8×C83C2311yescharacteristic
65C22×C8×C83C2311yescharacteristic
66C22×C8×C83C2311yescharacteristic
67C22×C8×C83C2311yescharacteristic
68C4⋊Q8×C83—22no—
69C4⋊Q8×C83—22no—
70C4×D4×C83—22no—
71C4×D4×C83—22no—
72#117×C83—22no—
73#117×C83—41no—
74C2×C4⋊C4×C83—22no—
75C2×C4⋊C4×C83—21no—
76C2×C4⋊C4×C83—21no—
77C2×C4⋊C4×C83—41no—
78C2×C4⋊C4×C83D411yescharacteristic
79C2×C4⋊C4×C83C2311yescharacteristic
80C2×C4⋊C4×C83C2311yescharacteristic
81C2×C4⋊C4×C83C2311yescharacteristic
82C2×C4⋊C4×C83C2311yescharacteristic
83C2×C4⋊C4×C83C2311yescharacteristic
84C2×C4⋊C4×C83C2311yescharacteristic
85C2×C4⋊C4×C83C2311yescharacteristic
86C2×C4⋊C4×C83C2311yescharacteristic
87C2×C22⋊C4×C83—21no—
88C2×C22⋊C4×C83—21no—
89C2×C22⋊C4×C83—21no—
90C2×C22⋊C4×C83—21no—
91C2×C22⋊C4×C83—21no—
92C2×C22⋊C4×C83—21no—
93C2×C22⋊C4×C83—21no—
94C2×C22⋊C4×C83D411yescharacteristic
95C2×C22⋊C4×C83D411yescharacteristic
96C2×C42×C83—21no—
97C2×C42×C83—21no—
98C2×C42×C83—21no—
99C2×C42×C83C2311yescharacteristic
100#107×C83—22no—
101#107×C83—41no—
102#106×C83—22no—
103#106×C83—41no—
104C4⋊C8×C83—22no—
105C22⋊C8×C83—22no—
106C22⋊C8×C83—22no—
107C22⋊C8×C83—41no—
108C22⋊C8×C83—41no—
109#97×C83—22no—
110#95×C83—21no—
111#95×C83—21no—
112#95×C83—21no—
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83—21no—
119#95×C83—21no—
120C24×C83C2×D411yescharacteristic
121C24×C83C2×D411yescharacteristic
122C2×Q8×C83—42no—
123C2×Q8×C83—81no—
124C2×Q8×C83—81no—
125C2×D4×C83—22no—
126C2×D4×C83—22no—
127C2×D4×C83—41no—
128C22×C4×C83—21no—
129C22×C4×C83—21no—
130C22×C4×C83—21no—
131C22×C4×C83—21no—
132C22×C4×C83—21no—
133C22×C4×C83—21no—
134C22×C4×C83—21no—
135C22×C4×C83—21no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—21no—
139C22×C4×C83—21no—
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83—21no—
144C22×C4×C83—21no—
145C22×C4×C83—21no—
146C22×C4×C83—21no—
147C22×C4×C83—21no—
148C22×C4×C83—42no—
149C22×C4×C83—42no—
150C22×C4×C83—81no—
151C22×C4×C83C2×D411yescharacteristic
152C22×C4×C83C2×D411yescharacteristic
153C22×C4×C83C2×D411yescharacteristic
154C22×C4×C83C2×D411yescharacteristic
155C22×C4×C83C2411yescharacteristic
156C2×C8×C83—21no—
157C2×C8×C83—21no—
158C2×C8×C83—21no—
159C2×C8×C83—21no—
160C2×C8×C83—21no—
161C2×C8×C83—21no—
162C2×C8×C83—21no—
163C2×C8×C83—21no—
164C2×C8×C83—21no—
165C2×C8×C83—21no—
166C2×C8×C83—21no—
167C2×C8×C83#4112yes—
168C4⋊C4×C83—22no—
169C4⋊C4×C83—21no—
170C4⋊C4×C83—21no—
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—42no—
185C4⋊C4×C83—42no—
186C4⋊C4×C83#4112yes—
187C22⋊C4×C83—22no—
188C22⋊C4×C83—22no—
189C22⋊C4×C83—42no—
190C22⋊C4×C83—42no—
191C22⋊C4×C83—81no—
192C22⋊C4×C83—81no—
193C22⋊C4×C83—81no—
194C22⋊C4×C83—81no—
195C22⋊C4×C83—81no—
196C42×C83—42no—
197C42×C83—42no—
198C42×C83—81no—
199C42×C83#4112yes—
200C42×C83#4112yes—
201C23×C83—21no—
202C23×C83—21no—
203C23×C83—21no—
204C23×C83—21no—
205C23×C83—21no—
206C23×C83—21no—
207C23×C83—21no—
208C23×C83—21no—
209C23×C83—21no—
210C23×C83—21no—
211C23×C83—21no—
212C23×C83—21no—
213C23×C83—21no—
214C23×C83#13712yes—
215C23×C83C22×D411yescharacteristic
216Q8×C83—84no—
217D4×C83—44no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—22no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—41no—
250C2×C4×C83—41no—
251C2×C4×C83—41no—
252C2×C4×C83—41no—
253C2×C4×C83—41no—
254C2×C4×C83—41no—
255C2×C4×C83—41no—
256C2×C4×C83—41no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—84no—
261C2×C4×C83#12312yes—
262C2×C4×C83#12312yes—
263C2×C4×C83C2×#4111yescharacteristic
264C2×C4×C83C2×#4111yescharacteristic
265C2×C4×C83C2×#4111yescharacteristic
266C2×C4×C83C2×#4111yescharacteristic
267C2×C4×C83H(5,𝔽2)11yescharacteristic
268C2×C4×C832−1+411yescharacteristic
269C8×C83—22no—
270C8×C83—41no—
271C8×C83—41no—
272C8×C83—41no—
273C22×C83—22no—
274C22×C83—22no—
275C22×C83—22no—
276C22×C83—41no—
277C22×C83—41no—
278C22×C83—41no—
279C22×C83—41no—
280C22×C83—41no—
281C22×C83—41no—
282C22×C83—41no—
283C22×C83—41no—
284C22×C83—41no—
285C22×C83—41no—
286C22×C83—41no—
287C22×C83C2×#12311yescharacteristic
288C22×C83#54611yescharacteristic
289C22×C83#54711yescharacteristic
290C22×C83C2×#13711yescharacteristic
291C22×C83#57511yescharacteristic
292C22×C83#57611yescharacteristic
293C22×C83#57711yescharacteristic
294C4×C83—22no—
295C4×C83—22no—
296C4×C83—41no—
297C4×C83—41no—
298C4×C83—42no—
299C4×C83—81no—
300C4×C83—81no—
301C4×C83—81no—
302C4×C83—81no—
303C4×C83—81no—
304C4×C83—81no—
305C4×C83—81no—
306C4×C83#52911yescharacteristic
307C4×C83#54211yescharacteristic
308C4×C83#55611yescharacteristic
309C4×C83#55911yescharacteristic
310#26313C8311yesmaximal, characteristic, direct product factor, Sylow
311C2×C83—42no—
312C2×C83—81no—
313C2×C83#244711yescharacteristic
314C2×C83#309511yescharacteristic
315C2×C83#309611yescharacteristic
316C2×C83#331411yescharacteristic
317C2×C83#332111yescharacteristic
318C2×C83#334411yescharacteristic
319C2×C83#334711yescharacteristic
320#2563C2×C8311yescharacteristic
321#2352C2×C8311yescharacteristic
322#2077C2×C8311yescharacteristic, complemented
323#2076C2×C8311yescharacteristic, complemented
324#2076C2×C8311yescharacteristic, complemented
325#2075C2×C8311yescharacteristic, complemented
326#1993C2×C8311yescharacteristic, complemented
327#1988C2×C8311yescharacteristic, complemented
328#1955C2×C8311yescharacteristic
329#1949C2×C8311yescharacteristic, complemented
330#1854C2×C8311yescharacteristic, complemented
331#1853C2×C8311yescharacteristic, complemented
332#1825C2×C8311yescharacteristic, complemented
333#1823C2×C8311yescharacteristic, complemented
334#1776C2×C8311yescharacteristic, complemented
335C83#2631311yescharacteristic, direct product factor, Sylow
336C2×C4⋊Q8C22×C8311yescharacteristic
337C2×C4×D4C22×C8311yescharacteristic
338C2×#117C22×C8311yescharacteristic
339C22×C4⋊C4C22×C8311yescharacteristic
340C2×#107C22×C8311yescharacteristic
341C2×#107C22×C8311yescharacteristic
342C2×#106C22×C8311yescharacteristic
343C2×#106C22×C8311yescharacteristic
344C2×C4⋊C8C22×C8311yescharacteristic
345C2×C22⋊C8C22×C8311yescharacteristic
346C2×C22⋊C8C22×C8311yescharacteristic
347C2×C22⋊C8C22×C8311yescharacteristic
348C2×C22⋊C8C22×C8311yescharacteristic
349C2×#97C22×C8311yescharacteristic
350#393—21no—
351#393—21no—
352#390—21no—
353#388—21no—
354#387—21no—
355#386—21no—
356#382—21no—
357#382C22×C8311yescharacteristic
358#380C22×C8311yescharacteristic
359#380C22×C8311yescharacteristic
360#380C22×C8311yescharacteristic
361#380C22×C8311yescharacteristic
362#380C22×C8311yescharacteristic
363#380C22×C8311yescharacteristic
364C4×C4⋊C4C22×C8311yescharacteristic
365C4×C4⋊C4C22×C8311yescharacteristic
366C4×C22⋊C4—21no—
367#340C22×C8311yescharacteristic
368#340C22×C8311yescharacteristic
369#340C22×C8311yescharacteristic
370#340C22×C8311yescharacteristic
371#340C22×C8311yescharacteristic
372#340C22×C8311yescharacteristic
373#340C22×C8311yescharacteristic
374#340C22×C8311yescharacteristic
375#340C22×C8311yescharacteristic
376#340C22×C8311yescharacteristic
377#340C22×C8311yescharacteristic
378#340C22×C8311yescharacteristic
379C22×Q8—21no—
380C22×D4D4×C8311yescharacteristic
381C23×C4—21no—
382C23×C4C23×C8311yescharacteristic
383C23×C4C23×C8311yescharacteristic
384C22×C8C23×C8311yescharacteristic
385C22×C8C23×C8311yescharacteristic
386C22×C8C23×C8311yescharacteristic
387C22×C8C23×C8311yescharacteristic
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390C4×D4—22no—
391C4×D4—22no—
392#117—22no—
393#117—41no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4D4×C8311yescharacteristic
399C2×C4⋊C4C23×C8311yescharacteristic
400C2×C4⋊C4C23×C8311yescharacteristic
401C2×C4⋊C4C23×C8311yescharacteristic
402C2×C4⋊C4C23×C8311yescharacteristic
403C2×C4⋊C4C23×C8311yescharacteristic
404C2×C4⋊C4C23×C8311yescharacteristic
405C2×C4⋊C4C23×C8311yescharacteristic
406C2×C4⋊C4C23×C8311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4D4×C8311yescharacteristic
415C2×C22⋊C4D4×C8311yescharacteristic
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C23×C8311yescharacteristic
420#107—22no—
421#107—41no—
422#106—22no—
423#106—41no—
424C4⋊C8—22no—
425C22⋊C8—22no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C22⋊C8—41no—
429#97—22no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440C24C2×D4×C8311yescharacteristic
441C24C2×D4×C8311yescharacteristic
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—81no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—41no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—81no—
471C22×C4C2×D4×C8311yescharacteristic
472C22×C4C2×D4×C8311yescharacteristic
473C22×C4C2×D4×C8311yescharacteristic
474C22×C4C2×D4×C8311yescharacteristic
475C22×C4C24×C8311yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8#41×C8312yes—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4#41×C8312yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C42—42no—
517C42—42no—
518C42—81no—
519C42#41×C8312yes—
520C42#41×C8312yes—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23#137×C8312yes—
535C23C22×D4×C8311yescharacteristic
536Q8—84no—
537D4—44no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4#123×C8312yes—
582C2×C4#123×C8312yes—
583C2×C4C2×#41×C8311yescharacteristic
584C2×C4C2×#41×C8311yescharacteristic
585C2×C4C2×#41×C8311yescharacteristic
586C2×C4C2×#41×C8311yescharacteristic
587C2×C4H(5,𝔽2)×C8311yescharacteristic
588C2×C42−1+4×C8311yescharacteristic
589C8—22no—
590C8—41no—
591C8—41no—
592C8—41no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22C2×#123×C8311yescharacteristic
608C22#546×C8311yescharacteristic
609C22#547×C8311yescharacteristic
610C22C2×#137×C8311yescharacteristic
611C22#575×C8311yescharacteristic
612C22#576×C8311yescharacteristic
613C22#577×C8311yescharacteristic
614C4—22no—
615C4—22no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4#529×C8311yescharacteristic
627C4#542×C8311yescharacteristic
628C4#556×C8311yescharacteristic
629C4#559×C8311yescharacteristic
630C2—42no—
631C2—81no—
632C2C83×#244711yescharacteristic
633C2C83×#309511yescharacteristic
634C2C83×#309611yescharacteristic
635C2C83×#331411yescharacteristic
636C2C83×#332111yescharacteristic
637C2C83×#334411yescharacteristic
638C2C83×#334711yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC22×D4×C83D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#2077C2semidirect
4. C83×#2076C2semidirect
5. C83×#2076C2semidirect
6. C83×#2075C2semidirect
7. C83×#1993C2semidirect
8. C83×#1988C2semidirect
10. C83×#1949C2semidirect
11. C83×#1854C2semidirect
12. C83×#1853C2semidirect
13. C83×#1825C2semidirect
14. C83×#1823C2semidirect
15. C83×#1776C2semidirect
310. #26313C83direct (N × H)
322. #2077C2×C83semidirect
323. #2076C2×C83semidirect
324. #2076C2×C83semidirect
325. #2075C2×C83semidirect
326. #1993C2×C83semidirect
327. #1988C2×C83semidirect
329. #1949C2×C83semidirect
330. #1854C2×C83semidirect
331. #1853C2×C83semidirect
332. #1825C2×C83semidirect
333. #1823C2×C83semidirect
334. #1776C2×C83semidirect
335. C83#26313direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25632
C83×#23522
C83×#20772
C83×#20762
C83×#20752
C83×#19932
C83×#19882
C83×#19552
C83×#19492
C83×#18542
C83×#18532
C83×#18252
C83×#18232
C83×#17762
#2631383