Finite Group Databasebeta

← #14797663

Subgroups — #14797663

Order 2816.

986 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×#10622852C211yesmaximal, characteristic
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3#13072119C211yesmaximal, characteristic, complemented
4#13070164C211yesmaximal, characteristic, complemented
5#13070052C211yesmaximal, characteristic, complemented
6#13069938C211yesmaximal, characteristic, complemented
7#13069819C211yesmaximal, characteristic, complemented
8#13069295C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13068960C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068863C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic
15C11×#2339C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#386—21no—
26C11×#386—21no—
27C11×#381—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×C11×#95—21no—
31#10622852—24no—
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C4×#4324—24no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622565—21no—
47#10622558—21no—
48#10622549C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622271—21no—
54#10622265—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×Dic22C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—41no—
78C4×D4×C11—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×#4326—22no—
91C2×#4326—22no—
92C2×#4326—41no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324D414yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977—41no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C4×Dic22—22no—
110C4×Dic22—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120#66899—41no—
121#66896—22no—
122#66896—22no—
123#66896—22no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—41no—
132#66874—22no—
133#66874—41no—
134#66872—22no—
135#66871—41no—
136C4⋊(C11⋊C8)—41no—
137C4×C11⋊C8—22no—
138#24903—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11#4112yes—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11C2×D412yes—
158C2×D4×C11#4112yes—
159C2×D4×C11#4112yes—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C2×D412yes—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—81no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C22⋊Dic11—42no—
208C22⋊Dic11—42no—
209#4326—44no—
210#4324—28no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—42no—
220C4×Dic11—42no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8C2×D412yes—
233C2×#452—111no—
234C2×C4×SD16—111no—
235#2421—111no—
236#2339D1111yescharacteristic
237#2097—111no—
238#2077—111no—
239#2056—111no—
240#2036—111no—
241#1933—111no—
242#1923—111no—
243#1878—111no—
244#1877—111no—
245#1862—111no—
246#1804—111no—
247#1788—111no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11C22×D411yescharacteristic
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—41no—
266Q8×C11—41no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—48no—
271D4×C11#12314yes—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—48no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—84no—
301C2×C4×C11—84no—
302C2×C4×C11#13512yes—
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×Dic11—22no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321Dic22—22no—
322Dic22—22no—
323Dic22—41no—
324Dic22—41no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C11⋊C8—41no—
328C11⋊C8—41no—
329C22×#41C2×D1111yescharacteristic
330C22×Q16—111no—
331C22×SD16—111no—
332C2×C22⋊Q8—111no—
333C2×C4×Q8—111no—
334C2×C4×D4C2×D1111yescharacteristic
335C2×C4×D4C2×D1111yescharacteristic
336#452—224no—
337C4×SD16—224no—
338C2×#107—111no—
339C2×#106—111no—
340C2×C4⋊C8—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103—111no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#102—111no—
347C2×#102—111no—
348C2×#102—111no—
349C2×C22⋊C8—111no—
350C2×C22⋊C8—111no—
351C2×C4×C8—111no—
352#400—221no—
353#397—221no—
354#391—111no—
355#391C2×D1111yescharacteristic
356#391C2×D1111yescharacteristic
357#389—111no—
358#388—221no—
359#387—221no—
360#386—21no—
361#386—21no—
362#382—111no—
363#381—21no—
364#380—111no—
365#380C2×D1111yescharacteristic
366C4×C22⋊C4C2×D1111yescharacteristic
367C2×#95—21no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#336—111no—
373#336—111no—
374C22×C11—24no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11#52511yescharacteristic
389C22×C11D4211yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11C2×#13511yescharacteristic
392C22×C11#57511yescharacteristic
393C22×C11#57711yescharacteristic
394C22×C11#57811yescharacteristic
395C4×C11—22no—
396C4×C11—41no—
397C4×C11—42no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11C2×#12311yescharacteristic
404C4×C11#53811yescharacteristic
405C4×C11#54611yescharacteristic
406C4×C11#55111yescharacteristic
407Dic11—42no—
408Dic11—81no—
409Dic11—81no—
410Dic11—81no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C22×Q8—111no—
418C22×Q8C22×D1111yescharacteristic
419C22×D4—21no—
420C22×D4C22×D1111yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C22×D1111yescharacteristic
425C2×Q16—222no—
426C2×Q16—222no—
427C2×Q16—441no—
428C2×SD16—114no—
429C2×SD16—222no—
430C2×SD16—222no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C22×C8—111no—
435C22⋊Q8—222no—
436C22⋊Q8—441no—
437C4×Q8—222no—
438C4×Q8—441no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—41no—
442C4×D4—41no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4—221no—
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4C22⋊D1111yescharacteristic
457C2×C22⋊C4C22⋊D1111yescharacteristic
458C2×C42—221no—
459C2×C42C22×D1111yescharacteristic
460C2×C42C22×D1111yescharacteristic
461#107—441no—
462#106—222no—
463C4⋊C8—441no—
464#103—222no—
465#103—222no—
466#103—222no—
467#103—441no—
468#103—441no—
469#102—222no—
470#102—222no—
471#102—222no—
472C22⋊C8—222no—
473C22⋊C8—441no—
474C4×C8—222no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95C22⋊D1111yescharacteristic
487#95C22⋊D1111yescharacteristic
488C2×C11—44no—
489C2×C11—81no—
490C2×C11#241811yescharacteristic
491C2×C11#310211yescharacteristic
492C2×C11#312011yescharacteristic
493C2×C11#326911yescharacteristic
494C2×C11#328211yescharacteristic
495C2×C11#330211yescharacteristic
496C2×C11#332311yescharacteristic
497C24—21no—
498C24C2×C22⋊D1111yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—112no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×Q8#433912yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4#433912yes—
522C2×D4D4×D1112yes—
523C2×D4#434112yes—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552Q16—444no—
553SD16—228no—
554C2×C8—112no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—221no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—442no—
577C4⋊C4—442no—
578C4⋊C4—442no—
579C22⋊C4—22no—
580C22⋊C4—41no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—442no—
585C22⋊C4—442no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—442no—
591C11#2490311yescharacteristic, complemented, Sylow
592C23—22no—
593C23—22no—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×C22⋊D1111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—222no—
612Q8—222no—
613Q8—441no—
614Q8—441no—
615D4—22no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4#6693614yes—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—222no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4#6700312yes—
663C2×C4C2×#433911yescharacteristic
664C2×C4C2×#433911yescharacteristic
665C2×C4C2×D4×D1111yescharacteristic
666C2×C4C2×#434111yescharacteristic
667C2×C4#6703711yescharacteristic
668C2×C4#6703711yescharacteristic
669C8—222no—
670C8—441no—
671C8—441no—
672C8—441no—
673C22—24no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22#1062332211yescharacteristic
688C22D4×C22⋊D1111yescharacteristic
689C22#1062333711yescharacteristic
690C22C2×#6700311yescharacteristic
691C22#1062335311yescharacteristic
692C22#1062336711yescharacteristic
693C22#1062336911yescharacteristic
694C4—22no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—81no—
701C4—81no—
702C4—442no—
703C4—881no—
704C4—881no—
705C4—881no—
706C4C2×#6693611yescharacteristic
707C4#1062302111yescharacteristic
708C4#1062302511yescharacteristic
709C4#1062302611yescharacteristic
710C2—44no—
711C2—81no—
712C2#1307207811yescharacteristic
713C2#1307863411yescharacteristic
714C2#1307883011yescharacteristic
715C2#1308016711yescharacteristic
716C2#1308031911yescharacteristic
717C2#1308053311yescharacteristic
718C2#1308083211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2339C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#2339D11
hypocenterC11#24903
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4324C2semidirect
3. #13072119C2semidirect
4. #13070164C2semidirect
5. #13070052C2semidirect
6. #13069938C2semidirect
7. #13069819C2semidirect
8. #13069295C2semidirect
9. #13069224C2semidirect
10. #13068960C2semidirect
11. #13068950C2semidirect
12. #13068863C2semidirect
13. #13068626C2semidirect
591. C11#24903semidirect

Maximal subgroups

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

subgroupindex
C2×#106228522
C2×C4×#43242
#130721192
#130701642
#130700522
#130699382
#130698192
#130692952
#130692242
#130689602
#130689502
#130688632
#130686262
#130685562
C11×#23392
#2490311