Finite Group Databasebeta

← #14765157

Subgroups — #14765157

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622346C211yesmaximal, characteristic
2#13071294C211yesmaximal, characteristic, complemented
3#13071209C211yesmaximal, characteristic
4#13069485C211yesmaximal, characteristic, complemented
5#13069468C211yesmaximal, characteristic, complemented
6#13069311C211yesmaximal, characteristic, complemented
7#13069290C211yesmaximal, characteristic, complemented
8#13069249C211yesmaximal, characteristic, complemented
9#13069242C211yesmaximal, characteristic, complemented
10#13068972C211yesmaximal, characteristic, complemented
11#13068958C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic, complemented
13#13068554C211yesmaximal, characteristic
14#13068384C211yesmaximal, characteristic, complemented
15C11×#1853C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622826—21no—
28#10622826—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622600—21no—
37#10622600—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49#10622558—21no—
50#10622557—21no—
51#10622346C418yescomplemented
52#10622268—21no—
53#10622260—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×#4339—22no—
64C2×#4339—41no—
65C2×#4339—41no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339C2×C414yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90#66979—41no—
91#66979—41no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977C2×C414yes—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×Dic44—41no—
107C2×Dic44—41no—
108C2×Dic44C2×C414yescomplemented
109C2×#4314—41no—
110C2×#4314—41no—
111C2×#4314C2×C414yescomplemented
112#66940—41no—
113#66940—41no—
114C11×#106—41no—
115C11×#106—41no—
116C11×C22⋊C8C2×C414yes—
117C11×#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127#66885C2×C414yescomplemented
128#66880C2×C414yescomplemented
129#66879—41no—
130C8×Dic11—41no—
131#66874—41no—
132#66874—41no—
133#66874—41no—
134#66874—41no—
135#66873—41no—
136#66873—41no—
137#22059—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11—81no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165#4339—44no—
166#4339—44no—
167#4339—44no—
168#4339—44no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44C22×C412yes—
175C2×C4×D11—24no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C22×C412yes—
189C2×Dic22C22×C412yes—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11C22×C412yes—
195C2×C8×C11C22×C412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—42no—
205C11×C22⋊C4—81no—
206C22⋊Dic11—24no—
207C22⋊Dic11—41no—
208C22⋊Dic11—41no—
209(C2×D11)⋊C4—81no—
210(C2×D11)⋊C4—81no—
211(C2×D11)⋊C4—81no—
212(C2×D11)⋊C4—81no—
213C4⋊Dic11—21no—
214C4⋊Dic11—41no—
215C4⋊Dic11—41no—
216C4⋊Dic11C22×C412yes—
217Dic11⋊C4—24no—
218Dic11⋊C4—42no—
219Dic11⋊C4—81no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—42no—
225C4×Dic11—81no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232Dic44—44no—
233#4314—44no—
234C2×#452—111no—
235#2323—111no—
236#2311—111no—
237#1971—111no—
238#1968—111no—
239#1936—111no—
240#1933—111no—
241#1927—111no—
242#1926—111no—
243#1880—111no—
244#1878—111no—
245#1872—111no—
246#1853D1111yescharacteristic, complemented
247#1788—111no—
248#1750—111no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11C4×D412yes—
256C23×C11C22×D411yescharacteristic
257C22×D11—22no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
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×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—84no—
283C2×C4×C11C4×D412yes—
284C2×C4×C11C23×C411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C22⋊D11—48no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312D44—22no—
313D44—22no—
314D44—41no—
315D44—41no—
316C4×D11—48no—
317Dic22—22no—
318Dic22—22no—
319Dic22—22no—
320Dic22—22no—
321Dic22—41no—
322Dic22—41no—
323Dic22—41no—
324Dic22—41no—
325C8×C11—22no—
326C8×C11—22no—
327C11⋊C8—41no—
328C11⋊C8—41no—
329C22×#41—111no—
330C22×Q16—111no—
331C22×SD16—111no—
332C2×C22⋊Q8—111no—
333C2×C4×Q8—111no—
334C2×#117—111no—
335C22×C4⋊C4C2×D1111yescharacteristic
336#452—118no—
337C2×#106C2×D1111yescharacteristic
338C2×#106C2×D1111yescharacteristic
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103—111no—
344C2×#102—111no—
345C2×#102—111no—
346C2×#102—111no—
347C2×C22⋊C8—111no—
348C2×C22⋊C8C2×D1111yescharacteristic
349C2×#97—111no—
350C2×C4×C8—111no—
351#391—111no—
352#391—111no—
353#391—111no—
354#390—111no—
355#390—111no—
356#389—111no—
357#389—221no—
358#388—221no—
359#388—221no—
360#387—221no—
361#386—221no—
362#386—221no—
363#380—221no—
364#380—221no—
365#380C2×D1111yescharacteristic
366C4×C4⋊C4—111no—
367#340—111no—
368#340—111no—
369#340C2×D1111yescharacteristic
370#340C2×D1111yescharacteristic
371#336—111no—
372#336—111no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11C2×C4×D411yescharacteristic
381C22×C11#53411yescharacteristic
382C22×C11#53511yescharacteristic
383C22×C11#57711yescharacteristic
384C22×C11#57711yescharacteristic
385C22×C11#57711yescharacteristic
386C22×C11#57811yescharacteristic
387C2×D11—42no—
388C2×D11—42no—
389C2×D11—42no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—81no—
393C2×D11—81no—
394C4×C11—22no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11#51811yescharacteristic
400C4×C11#51811yescharacteristic
401C4×C11#53811yescharacteristic
402C4×C11#53811yescharacteristic
403Dic11—42no—
404Dic11—42no—
405Dic11—41no—
406Dic11—41no—
407Dic11—41no—
408Dic11—41no—
409Dic11—42no—
410C2×#41—114no—
411C2×#41—222no—
412C2×#41—441no—
413C2×#41—441no—
414C2×#41—441no—
415C2×#41—441no—
416C22×Q8—111no—
417C22×Q8—111no—
418C22×D4—111no—
419C22×D4—221no—
420C23×C4—21no—
421C23×C4—221no—
422C23×C4C22×D1111yescharacteristic
423C2×Q16—114no—
424C2×Q16—441no—
425C2×Q16—441no—
426C2×SD16—114no—
427C2×SD16—441no—
428C2×SD16—441no—
429C22×C8—111no—
430C22×C8—111no—
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C22⋊Q8—114no—
434C22⋊Q8—222no—
435C4×Q8—441no—
436C4×Q8—441no—
437#117—441no—
438#117—441no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—111no—
454C2×C22⋊C4—111no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—221no—
463C2×C42—221no—
464#106—41no—
465#106—41no—
466#103—114no—
467#103—441no—
468#103—441no—
469#103—441no—
470#103—441no—
471#102—114no—
472#102—441no—
473#102—441no—
474C22⋊C8—222no—
475C22⋊C8C4×D1114yes—
476#97—441no—
477C4×C8—441no—
478#95—21no—
479#95—221no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95—221no—
487C2×C11—42no—
488C2×C11#232111yescharacteristic
489C2×C11#294711yescharacteristic
490C2×C11#295211yescharacteristic
491C2×C11#320111yescharacteristic
492C2×C11#320411yescharacteristic
493C2×C11#322211yescharacteristic
494C2×C11#322511yescharacteristic
495D11—82no—
496C24—221no—
497C24D4×D1111yescharacteristic
498#41—444no—
499#41—444no—
500#41—444no—
501#41—444no—
502C2×Q8—112no—
503C2×Q8—112no—
504C2×Q8—221no—
505C2×Q8—221no—
506C2×Q8—221no—
507C2×Q8—221no—
508C2×Q8—221no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×D4—112no—
515C2×D4—224no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—221no—
521C2×D4—442no—
522C2×D4—442no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—111no—
537C22×C4—111no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—224no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4C2×C4×D1112yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4#434312yes—
547C22×C4C23×D1111yescharacteristic
548Q16—444no—
549SD16—444no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8C2×C4×D1112yes—
561C2×C8C2×C4×D1112yes—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—112no—
572C4⋊C4—224no—
573C4⋊C4—221no—
574C4⋊C4—441no—
575C4⋊C4—441no—
576C4⋊C4—442no—
577C4⋊C4—881no—
578C22⋊C4—81no—
579C22⋊C4—224no—
580C22⋊C4—441no—
581C22⋊C4—441no—
582C22⋊C4—881no—
583C22⋊C4—881no—
584C22⋊C4—881no—
585C22⋊C4—881no—
586C42—221no—
587C42—221no—
588C42—221no—
589C42—221no—
590C42—442no—
591C42—881no—
592C11#2205911yescharacteristic, complemented, Sylow
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—222no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23—441no—
604C23—441no—
605C23—441no—
606C23#6694612yes—
607C23C2×D4×D1111yescharacteristic
608Q8—222no—
609Q8—222no—
610Q8—222no—
611Q8—222no—
612Q8—441no—
613Q8—441no—
614Q8—441no—
615Q8—441no—
616D4—222no—
617D4—222no—
618D4—448no—
619D4—441no—
620D4—441no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—448no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4#6694612yes—
663C2×C4C22×C4×D1111yescharacteristic
664C2×C4#6703711yescharacteristic
665C2×C4#6703711yescharacteristic
666C2×C4C2×#434311yescharacteristic
667C2×C4#6704211yescharacteristic
668C2×C4#6704211yescharacteristic
669C8—22no—
670C8—22no—
671C8—441no—
672C8—441no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—442no—
681C22—442no—
682C22—442no—
683C22—881no—
684C22—881no—
685C22—881no—
686C22—881no—
687C22C2×#6694611yescharacteristic
688C22#1062312311yescharacteristic
689C22#1062318411yescharacteristic
690C22#1062329311yescharacteristic
691C22#1062329311yescharacteristic
692C22#1062330611yescharacteristic
693C22#1062331011yescharacteristic
694C4—22no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—442no—
700C4—442no—
701C4—441no—
702C4—441no—
703C4—441no—
704C4—441no—
705C4—442no—
706C4#1062307611yescharacteristic
707C4#1062307611yescharacteristic
708C4#1062317511yescharacteristic
709C4#1062317511yescharacteristic
710C2—42no—
711C2—882no—
712C2#1307127311yescharacteristic
713C2#1307745711yescharacteristic
714C2#1307749911yescharacteristic
715C2#1307950511yescharacteristic
716C2#1307952911yescharacteristic
717C2#1307968411yescharacteristic
718C2#1307972311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#22059
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. #13071294C2semidirect
4. #13069485C2semidirect
5. #13069468C2semidirect
6. #13069311C2semidirect
7. #13069290C2semidirect
8. #13069249C2semidirect
9. #13069242C2semidirect
10. #13068972C2semidirect
11. #13068958C2semidirect
12. #13068923C2semidirect
14. #13068384C2semidirect
15. C11×#1853C2semidirect
51. #10622346C4semidirect
108. C2×Dic44C2×C4semidirect
111. C2×#4314C2×C4semidirect
127. #66885C2×C4semidirect
128. #66880C2×C4semidirect
246. #1853D11semidirect
592. C11#22059semidirect

Maximal subgroups

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

subgroupindex
C2×#106223462
#130712942
#130712092
#130694852
#130694682
#130693112
#130692902
#130692492
#130692422
#130689722
#130689582
#130689232
#130685542
#130683842
C11×#18532
#2205911