Finite Group Databasebeta

← #14814351

Subgroups — #14814351

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072054C211yesmaximal, characteristic
2#13071516C211yesmaximal, characteristic, complemented
3#13070041C211yesmaximal, characteristic, complemented
4#13070020C211yesmaximal, characteristic, complemented
5#13069801C211yesmaximal, characteristic, complemented
6#13069237C211yesmaximal, characteristic, complemented
7#13069184C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2099C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66948—21no—
18C2×#66948C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66946—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33#10622607—21no—
34#10622602—21no—
35#10622602—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622586—21no—
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622285—21no—
46#10622278—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—22no—
98C2×C8×D11—41no—
99C2×C8×D11—41no—
100#66948—22no—
101#66948—22no—
102#66948—22no—
103#66948—41no—
104#66948—44no—
105#66946—44no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—41no—
110C4⋊C4×D11—41no—
111C4⋊C4×D11—41no—
112C4×D44—22no—
113C4×D44—22no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—41no—
121(C2×D11)⋊C8—22no—
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124#66882—41no—
125#66873—41no—
126#66873—41no—
127#66871—22no—
128#26198—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11C2×D411yescharacteristic
131C23×D11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44—81no—
158C2×D44D814yes—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×C4×D11—81no—
178C2×C4×D11#4112yes—
179C2×C4×D11#4112yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—81no—
196C11×C4⋊C4#4112yes—
197C42×C11—21no—
198C42×C11—21no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—42no—
206(C2×D11)⋊C4—42no—
207(C2×D11)⋊C4—81no—
208C4⋊Dic11—22no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11#4112yes—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—42no—
218C4×Dic11—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C8×D11—44no—
226#2416—111no—
227D4×C4⋊C4—111no—
228#2099D1111yescharacteristic, complemented
229#2075—111no—
230#2071—111no—
231#2033—111no—
232#1925—111no—
233#1918—111no—
234#1893—111no—
235#1874—111no—
236#1874—111no—
237#1869—111no—
238#1852—111no—
239#1823—111no—
240C2×#340—111no—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11#12312yes—
260C22×D11C2×D812yes—
261C22×D11C2×D812yes—
262C22×D11#13712yes—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11C2×D812yes—
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11#12312yes—
302D44—28no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—84no—
308D44—84no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—22no—
313C4×D11—41no—
314C4×D11—41no—
315C4×D11—41no—
316C4×D11—41no—
317C4×D11—84no—
318C4×D11—84no—
319C4×D11—84no—
320C8×C11—41no—
321C8×C11—41no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C23×C8—111no—
325C2×#121—111no—
326C2×#121—111no—
327C2×#121—221no—
328C2×C4×D4—111no—
329C2×C4×D4—221no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C2×#107—111no—
334C2×#107—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342#396—221no—
343#394—221no—
344#390—111no—
345#389—221no—
346#389C2×D1111yescharacteristic
347#386—221no—
348#385—221no—
349#385—221no—
350#384C2×D1111yescharacteristic
351#380—111no—
352#380—111no—
353#380—111no—
354C4×C4⋊C4—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#340C2×D1111yescharacteristic
363#340C2×D1111yescharacteristic
364#340C2×D1111yescharacteristic
365#336—111no—
366#336C2×D1111yescharacteristic
367C22×C11C2×#12311yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11C22×D811yescharacteristic
371C22×C11C2×#13711yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—41no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—81no—
393C2×D11—81no—
394C2×D11#48014yes—
395C4×C11—22no—
396C4×C11—41no—
397C4×C11—42no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11#52911yescharacteristic
402C4×C11#53811yescharacteristic
403C4×C11#55311yescharacteristic
404C4×C11#55311yescharacteristic
405Dic11—22no—
406Dic11—41no—
407Dic11—42no—
408Dic11—81no—
409Dic11—81no—
410C22×D4—111no—
411C22×D4—111no—
412C22×D4—221no—
413C22×D4—221no—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—221no—
417C23×C4—221no—
418C23×C4—221no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—222no—
422C22×C8—441no—
423C22×C8—441no—
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1111yescharacteristic
426#121—222no—
427#121—222no—
428#121—222no—
429#121—441no—
430#121—444no—
431C4×D4—222no—
432C4×D4—222no—
433C4×D4—444no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—441no—
448C2×C4⋊C4—441no—
449C2×C4⋊C4—441no—
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C4⋊C4C22×D1111yescharacteristic
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C22⋊C4—221no—
461C2×C22⋊C4—221no—
462C2×C22⋊C4—221no—
463C2×C42—221no—
464C2×C42C22×D1111yescharacteristic
465#107—222no—
466#107—441no—
467#102—222no—
468#102—441no—
469#102—441no—
470#102—441no—
471C22⋊C8—222no—
472C22⋊C8—441no—
473C22⋊C8—441no—
474#95—21no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11#244411yescharacteristic
480C2×C11C2×#48011yescharacteristic
481C2×C11#309911yescharacteristic
482C2×C11#329411yescharacteristic
483C2×C11#329411yescharacteristic
484C2×C11#331611yescharacteristic
485C2×C11#332011yescharacteristic
486D11—24no—
487D11—42no—
488D11—161no—
489C24—111no—
490C24—111no—
491C24—221no—
492C2×D4—114no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—442no—
502C2×D4—442no—
503C2×D4—442no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—881no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—111no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—881no—
535C22×C4—881no—
536C22×C4—881no—
537C22×C4D4×D1111yescharacteristic
538C22×C4D4×D1111yescharacteristic
539C22×C4C23×D1111yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—444no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C4⋊C4—112no—
564C4⋊C4—222no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4—221no—
570C4⋊C4—442no—
571C4⋊C4—442no—
572C4⋊C4—442no—
573C4⋊C4#434312yes—
574C22⋊C4—222no—
575C22⋊C4—222no—
576C22⋊C4—442no—
577C22⋊C4—442no—
578C22⋊C4—442no—
579C22⋊C4—442no—
580C22⋊C4—442no—
581C22⋊C4—442no—
582C22⋊C4—881no—
583C42—21no—
584C42—21no—
585C42—442no—
586C11#2619811yescharacteristic, complemented, Sylow
587C23—112no—
588C23—112no—
589C23—112no—
590C23—112no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—221no—
595C23—221no—
596C23—221no—
597C23—221no—
598C23—221no—
599C23—221no—
600C23—221no—
601C23—441no—
602C23—441no—
603C23—441no—
604C23—441no—
605C23—441no—
606C23—441no—
607C23—441no—
608C23C2×D4×D1111yescharacteristic
609D4—228no—
610D4—441no—
611D4—441no—
612D4—441no—
613D4—441no—
614D4—884no—
615D4—884no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—112no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—222no—
643C2×C4—221no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—884no—
657C2×C4—884no—
658C2×C4—884no—
659C2×C4D8×D1112yes—
660C2×C4C2×#434311yescharacteristic
661C2×C4#41×D1111yescharacteristic
662C2×C4#41×D1111yescharacteristic
663C2×C4#41×D1111yescharacteristic
664C2×C4#6704211yescharacteristic
665C2×C4#6704211yescharacteristic
666C8—41no—
667C8—41no—
668C8—441no—
669C8—441no—
670C22—114no—
671C22—222no—
672C22—222no—
673C22—222no—
674C22—222no—
675C22—222no—
676C22—222no—
677C22—222no—
678C22—222no—
679C22—222no—
680C22—441no—
681C22—441no—
682C22—441no—
683C22—441no—
684C22—881no—
685C22—881no—
686C22—881no—
687C22—881no—
688C22—881no—
689C22—881no—
690C22—881no—
691C22#1062316111yescharacteristic
692C22D11×#12311yescharacteristic
693C22#1062320711yescharacteristic
694C22C2×D8×D1111yescharacteristic
695C22#1062329311yescharacteristic
696C22D11×#13711yescharacteristic
697C22#1062330911yescharacteristic
698C4—22no—
699C4—41no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—222no—
705C4—442no—
706C4—441no—
707C4—881no—
708C4—881no—
709C4#1062322211yescharacteristic
710C4#1062322611yescharacteristic
711C4#1062323511yescharacteristic
712C4#1062324011yescharacteristic
713C2—224no—
714C2—442no—
715C2—1761no—
716C2#1307236711yescharacteristic
717C2D11×#48011yescharacteristic
718C2#1307860011yescharacteristic
719C2#1308042611yescharacteristic
720C2#1308042811yescharacteristic
721C2#1308072411yescharacteristic
722C2#1308078611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radical#13072054C2
hypercenter#2099D11
hypocenterC11#26198
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
2. #13071516C2semidirect
3. #13070041C2semidirect
4. #13070020C2semidirect
5. #13069801C2semidirect
6. #13069237C2semidirect
7. #13069184C2semidirect
8. #13069043C2semidirect
9. #13068932C2semidirect
10. #13068932C2semidirect
11. #13068907C2semidirect
12. #13068805C2semidirect
13. #13068701C2semidirect
14. D11×#340C2semidirect
15. C11×#2099C2semidirect
228. #2099D11semidirect
586. C11#26198semidirect

Maximal subgroups

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

subgroupindex
#130720542
#130715162
#130700412
#130700202
#130698012
#130692372
#130691842
#130690432
#130689322
#130689072
#130688052
#130687012
D11×#3402
C11×#20992
#2619811