Finite Group Databasebeta

← #25002035

Subgroups — #25002035

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2C2×#14582881C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4#19134316C211yesmaximal, characteristic, complemented
5#19134315C211yesmaximal, characteristic, complemented
6#19134304C211yesmaximal, characteristic, complemented
7C43×#1733C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583379—22no—
11#14583379—22no—
12#14583379—22no—
13#14583379—22no—
14C2×C4×Dic86—21no—
15C2×C4×D172—21no—
16C2×(C22⋊D43)⋊C4—22no—
17C2×#13063284C2211yescharacteristic
18C2×#13063283C412yescomplemented
19C22×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊C4×D43C412yescomplemented
21#14582881—22no—
22#14582881C414yescomplemented
23C2×#13063243—21no—
24C2×#13063241—21no—
25#14582872—22no—
26#14582872C414yescomplemented
27C2×#13063239—22no—
28#14582662—22no—
29#14582661—22no—
30#14582658—22no—
31C22×M16×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#339—22no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898C2×C412yes—
44C2×#10621898C2×C412yes—
45C2×#10621898D412yes—
46C2×#10621898Q812yes—
47C22×Dic86D411yescharacteristic
48C22×D172D411yescharacteristic
49C22×C22⋊D43D412yes—
50C23×Dic43—21no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C412yes—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877C2×C412yescomplemented
59C22×C43⋊C8—21no—
60C4×Dic86—24no—
61C4×Dic86—24no—
62C4×D172—24no—
63C4×D172—24no—
64(C22⋊D43)⋊C4—28no—
65(C22⋊D43)⋊C4—28no—
66#13063284—21no—
67#13063284—21no—
68#13063284—21no—
69#13063284C2×C412yescomplemented
70#13063283—24no—
71#13063283—24no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2×C412yes—
77C2×C4⋊Dic43D412yes—
78C2×C4⋊Dic43D412yes—
79C2×Dic43⋊C4—22no—
80C4⋊C4×D43—24no—
81C4⋊C4×D43—24no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—22no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—21no—
86#13063243—24no—
87#13063241—24no—
88#13063239—28no—
89C23×C4×C43C2311yescharacteristic
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43C2×C412yescomplemented
96C22×C8×C43—21no—
97#117×C43—21no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102#117×C43C2×C412yescomplemented
103#117×C43D412yes—
104#117×C43D412yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2×C411yescharacteristic
107C2×C4⋊C4×C43C2×C411yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43C22⋊C412yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—41no—
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×Q811yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C2×C22⋊D43—22no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43C22⋊C414yes—
136C2×C22⋊D43C4⋊C414yes—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—41no—
141C22×Dic43—82no—
142C22×Dic43C22⋊C412yes—
143#10621898—22no—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149#10621898—22no—
150#10621898—22no—
151#10621898—22no—
152#10621898—22no—
153#10621898—22no—
154#10621898—22no—
155#10621898—22no—
156#10621898—22no—
157#10621898—22no—
158#10621898—22no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22⋊C412yes—
164C2×D172C4⋊C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—28no—
170C2×C4×D43—84no—
171C2×C4×D43C4214yes—
172C2×C4×D43C4⋊C414yes—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C22⋊C412yes—
178C2×Dic86C4⋊C412yes—
179M16×C43—22no—
180M16×C43—22no—
181M16×C43—41no—
182M16×C43—41no—
183C2×C8×C43—22no—
184C2×C8×C43—41no—
185C2×C8×C43—41no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43C22⋊C412yes—
191C4⋊C4×C43C22⋊C412yes—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—41no—
196C42×C43—22no—
197C42×C43—22no—
198C42×C43—22no—
199C42×C43—41no—
200C22⋊Dic43—22no—
201C22⋊Dic43—41no—
202(C2×D43)⋊C4—28no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43—41no—
208C4⋊Dic43C22⋊C414yes—
209Dic43⋊C4—28no—
210C4×Dic43—28no—
211C4×Dic43—22no—
212C4×Dic43—41no—
213#10621877—22no—
214#10621877—22no—
215#10621877—41no—
216#10621877—41no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—41no—
219C2×C43⋊C8—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C2×C22⋊C411yescharacteristic
223C23×C43C2×C22⋊C411yescharacteristic
224C23×C43C2×C4⋊C411yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12011yescharacteristic
227C23×C43#12311yescharacteristic
228C23×C43#12311yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—42no—
232C22×D43—42no—
233C22×D43#9514yes—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—81no—
240C2×C4×C43—81no—
241C2×C4×C43C2×C4211yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C4⋊C411yescharacteristic
246C2×C4×C43C2×C4⋊C411yescharacteristic
247C2×C4×C43#11711yescharacteristic
248C2×C4×C43#11711yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C4×D411yescharacteristic
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C4×D411yescharacteristic
256C2×C4×C43C4×D411yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43C22⋊Q811yescharacteristic
264C2×C4×C43C22⋊Q811yescharacteristic
265C2×C4×C43C22⋊Q811yescharacteristic
266C2×C4×C43C22⋊Q811yescharacteristic
267C2×C4×C43#12311yescharacteristic
268C2×C4×C43#12311yescharacteristic
269C22⋊D43—24no—
270C22⋊D43—24no—
271C22⋊D43—24no—
272C22⋊D43—24no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—24no—
276C2×Dic43—44no—
277C2×Dic43—42no—
278C2×Dic43—82no—
279C2×Dic43—82no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43#9514yes—
283D172—22no—
284D172—22no—
285D172—22no—
286D172—22no—
287C4×D43—24no—
288C4×D43—24no—
289C4×D43—24no—
290C4×D43—24no—
291C4×D43—88no—
292Dic86—22no—
293Dic86—22no—
294Dic86—22no—
295Dic86—22no—
296C8×C43—42no—
297C43⋊C8—42no—
298#10765—431nomaximal, Sylow
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43C2×#9511yescharacteristic
310C22×C43#37911yescharacteristic
311C22×C43#38111yescharacteristic
312C22×C43#38511yescharacteristic
313C22×C43#38511yescharacteristic
314C22×C43#38611yescharacteristic
315C22×C43#38611yescharacteristic
316C2×D43—24no—
317C2×D43—44no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—44no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—82no—
324C4×C43C4×C22⋊C411yescharacteristic
325C4×C43C4×C22⋊C411yescharacteristic
326C4×C43#38011yescharacteristic
327C4×C43#38011yescharacteristic
328C4×C43#38511yescharacteristic
329C4×C43#38511yescharacteristic
330C4×C43#38611yescharacteristic
331C4×C43#38611yescharacteristic
332Dic43—24no—
333Dic43—44no—
334Dic43—82no—
335C2×#520—431no—
336C2×#413—431no—
337C2×#410—431no—
338#1736—431no—
339#1736—431no—
340#1733—431no—
341#1733D4311yescharacteristic, complemented
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43—21no—
348C2×C43C22⋊#9511yescharacteristic
349C2×C43#179511yescharacteristic
350C2×C43#179611yescharacteristic
351D43—44no—
352C22×#41—431no—
353C22×M16—431no—
354C22×M16C2×D4311yescharacteristic
355#520—862no—
356#520—862no—
357#520—862no—
358#520—862no—
359C2×C4×Q8—861no—
360C2×C4×D4—861no—
361C2×C4×D4—862no—
362C2×#117—432no—
363C2×#117—431no—
364C2×#117C2×D4311yescharacteristic
365C2×#117C2×D4311yescharacteristic
366C22×C4⋊C4—431no—
367C22×C4⋊C4—432no—
368#413—434no—
369#413—862no—
370C2×#101—861no—
371C2×#100—861no—
372#410—434no—
373#410—862no—
374C2×#99—862no—
375#340—862no—
376#340—862no—
377#339—22no—
378#339—862no—
379C43#1076511yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—432no—
382C2×#41—432no—
383C2×#41—432no—
384C2×#41—861no—
385C2×#41—861no—
386C2×#41—861no—
387C2×#41—861no—
388C2×#41—861no—
389C2×#41—861no—
390C2×#41—861no—
391C2×#41—861no—
392C22×Q8—431no—
393C22×D4—432no—
394C22×D4—431no—
395C23×C4—432no—
396C23×C4—862no—
397C23×C4—861no—
398C23×C4C22×D4311yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—432no—
405C2×M16—861no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—861no—
409C2×M16—861no—
410C2×M16C4×D4312yescomplemented
411C22×C8—21no—
412C22×C8—861no—
413C4×Q8—864no—
414C4×Q8—864no—
415C4×D4—864no—
416C4×D4—864no—
417C4×D4—868no—
418C4×D4—868no—
419#117—21no—
420#117—21no—
421#117—21no—
422#117—21no—
423#117—21no—
424#117—432no—
425#117—864no—
426#117—864no—
427#117—861no—
428#117—861no—
429#117—861no—
430#117C4×D4312yescomplemented
431#117D17212yes—
432#117C22⋊D4312yes—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—432no—
435C2×C4⋊C4—432no—
436C2×C4⋊C4—432no—
437C2×C4⋊C4—864no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—864no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C4×D4311yescharacteristic
445C2×C4⋊C4C4×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—861no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—862no—
453C2×C42—861no—
454#101—864no—
455#100—864no—
456#99—868no—
457C24—432no—
458C24D4×D4311yescharacteristic
459#41—862no—
460#41—862no—
461#41—862no—
462#41—862no—
463#41—862no—
464#41—862no—
465#41—862no—
466#41—862no—
467#41—862no—
468#41—862no—
469#41—862no—
470#41—862no—
471#41—862no—
472#41—862no—
473#41—862no—
474#41—862no—
475C2×Q8—432no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—434no—
482C2×D4—434no—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—862no—
488C2×D4—862no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—432no—
497C22×C4—434no—
498C22×C4—434no—
499C22×C4—868no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—3444no—
508C22×C4—3442no—
509C22×C4—1721no—
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4C2×C4×D4311yescharacteristic
512C22×C4C2×C4×D4311yescharacteristic
513C22×C4C2×D17211yescharacteristic
514C22×C4#1062189811yescharacteristic
515C22×C4#1062189811yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4#1062190011yescharacteristic
521C22×C4Q8×D4311yescharacteristic
522C22×C4#1062190211yescharacteristic
523C22×C4C2×C22⋊D4311yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—862no—
529M16—862no—
530M16—1721no—
531M16—1721no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—862no—
536C2×C8—1721no—
537C2×C8—1721no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—41no—
542C4⋊C4—434no—
543C4⋊C4—868no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—1721no—
549C4⋊C4(C2×D43)⋊C412yes—
550C4⋊C4(C2×D43)⋊C412yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—868no—
556C22⋊C4—862no—
557C22⋊C4—1721no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—41no—
562C42—868no—
563C42—862no—
564C42—1721no—
565C23—41no—
566C23—41no—
567C23—434no—
568C23—862no—
569C23—862no—
570C23—1722no—
571C23—1722no—
572C23C22⋊C4×D4311yescharacteristic
573C23C22⋊C4×D4311yescharacteristic
574C23C4⋊C4×D4311yescharacteristic
575C23#1306329311yescharacteristic
576C23#1306329511yescharacteristic
577C23#1306330711yescharacteristic
578C23#1306331011yescharacteristic
579Q8—862no—
580Q8—862no—
581Q8—862no—
582Q8—862no—
583D4—864no—
584D4—864no—
585D4—864no—
586D4—864no—
587D4—862no—
588D4—862no—
589D4—862no—
590D4—862no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—434no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—3448no—
607C2×C4—3441no—
608C2×C4—3441no—
609C2×C4—3442no—
610C2×C4—3442no—
611C2×C4—1722no—
612C2×C4—1724no—
613C2×C4C42×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22⋊C4×D4311yescharacteristic
616C2×C4C2×(C2×D43)⋊C411yescharacteristic
617C2×C4C4⋊C4×D4311yescharacteristic
618C2×C4C4⋊C4×D4311yescharacteristic
619C2×C4#1306328211yescharacteristic
620C2×C4#1306328311yescharacteristic
621C2×C4(C22⋊D43)⋊C411yescharacteristic
622C2×C4(C22⋊D43)⋊C411yescharacteristic
623C2×C4C4×C22⋊D4311yescharacteristic
624C2×C4C4×C22⋊D4311yescharacteristic
625C2×C4#1306328711yescharacteristic
626C2×C4#1306328711yescharacteristic
627C2×C4C4×D17211yescharacteristic
628C2×C4C4×D17211yescharacteristic
629C2×C4#1306329311yescharacteristic
630C2×C4#1306329511yescharacteristic
631C2×C4#1306329611yescharacteristic
632C2×C4#1306329811yescharacteristic
633C2×C4#1306329811yescharacteristic
634C2×C4#1306330011yescharacteristic
635C2×C4#1306330111yescharacteristic
636C2×C4#1306330311yescharacteristic
637C2×C4#1306330311yescharacteristic
638C2×C4#1306330511yescharacteristic
639C2×C4#1306330711yescharacteristic
640C2×C4#1306331011yescharacteristic
641C8—42no—
642C8—1722no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—864no—
654C22—1724no—
655C22—1724no—
656C22—1722no—
657C22—1722no—
658C22#95×D4311yescharacteristic
659C22#1458275411yescharacteristic
660C22#1458276111yescharacteristic
661C22#1458277011yescharacteristic
662C22#1458277311yescharacteristic
663C22#1458277511yescharacteristic
664C22#1458277711yescharacteristic
665C4—42no—
666C4—42no—
667C4—82no—
668C4—864no—
669C4—3442no—
670C4—1724no—
671C4#1458274611yescharacteristic
672C4C4×(C2×D43)⋊C411yescharacteristic
673C4#1458275611yescharacteristic
674C4#1458275811yescharacteristic
675C4#1458277011yescharacteristic
676C4#1458277311yescharacteristic
677C4#1458277511yescharacteristic
678C4#1458277711yescharacteristic
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—1724no—
686C2(C2×D43)⋊#9511yescharacteristic
687C2#1913456411yescharacteristic
688C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1733C2
socleC22×C43#379
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1733D43
hypocenterC43#10765
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #19134316C2semidirect
5. #19134315C2semidirect
6. #19134304C2semidirect
7. C43×#1733C2semidirect
18. C2×#13063283C4semidirect
20. C2×C4⋊C4×D43C4semidirect
22. #14582881C4semidirect
26. #14582872C4semidirect
58. C2×#10621877C2×C4semidirect
69. #13063284C2×C4semidirect
95. C2×M16×C43C2×C4semidirect
102. #117×C43C2×C4semidirect
341. #1733D43semidirect
379. C43#10765semidirect
410. C2×M16C4×D43semidirect
430. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C2×#145828812
C2×#145828722
#191343162
#191343152
#191343042
C43×#17332
#1076543