Finite Group Databasebeta

← #25130384

Subgroups — #25130384

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic
2C2×#14583240C211yesmaximal, characteristic, complemented
3#19138886C211yesmaximal, characteristic
4#19135935C211yesmaximal, characteristic, complemented
5#19135931C211yesmaximal, characteristic, complemented
6#19135800C211yesmaximal, characteristic, complemented
7#19135793C211yesmaximal, characteristic, complemented
8#19135028C211yesmaximal, characteristic, complemented
9#19134892C211yesmaximal, characteristic
10#19134860C211yesmaximal, characteristic, complemented
11#19134846C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic, complemented
13#19134791C211yesmaximal, characteristic, complemented
14#19134685C211yesmaximal, characteristic, complemented
15C2×C43×#428C211yesmaximal, characteristic, complemented
16#14583584—24no—
17#14583584—24no—
18C2×#13063320—21no—
19C2×#13063316C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063308—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063290C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063284—21no—
27C2×#13063283C2211yescharacteristic
28#14583240—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38#14582827—21no—
39#14582814—21no—
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582790—21no—
43#14582783—21no—
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C43×#428—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#107×C43C2211yescharacteristic
61C2×#106×C43C2211yescharacteristic
62C2×#106×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063320—28no—
69#13063316—22no—
70#13063316—22no—
71#13063315—28no—
72#13063308—28no—
73#13063305—22no—
74#13063305—22no—
75#13063304—22no—
76#13063304D414yes—
77#13063290—22no—
78#13063290—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81#13063284—28no—
82#13063283—22no—
83#13063283—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43D411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—22no—
107#13063256—22no—
108#13063250—22no—
109#13063250—22no—
110#13063248—22no—
111#13063248—22no—
112C22⋊(C43⋊C8)—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—22no—
123C2×M16×C43—22no—
124C2×M16×C43—22no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#117×C43—22no—
128#117×C43—22no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43D414yes—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138#107×C43—22no—
139#107×C43—22no—
140#106×C43—22no—
141#106×C43—22no—
142C24×C43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—24no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—22no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86C2×D412yes—
181M16×C43—28no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43#4112yes—
187C2×C8×C43#4112yes—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C4⋊C4×C43C2×D412yes—
197C22⋊C4×C43—42no—
198C42×C43—42no—
199C22⋊Dic43—24no—
200C22⋊Dic43—22no—
201C22⋊Dic43—81no—
202(C2×D43)⋊C4—24no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—42no—
206(C2×D43)⋊C4—81no—
207C4⋊Dic43—24no—
208C4⋊Dic43—24no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C2×D412yes—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—22no—
219Dic43⋊C4—42no—
220Dic43⋊C4—81no—
221C4×Dic43—24no—
222C4×Dic43—24no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43#12012yes—
238C23×C43C22×D411yescharacteristic
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—48no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43#12012yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C22⋊D43—44no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C4×D43—41no—
295C4×D43—41no—
296C4×D43—41no—
297C4×D43—41no—
298Dic86—22no—
299Dic86—22no—
300Dic86—41no—
301Dic86—41no—
302C8×C43—22no—
303C8×C43—22no—
304C43⋊C8—41no—
305C43⋊C8—41no—
306#24106—431nomaximal, Sylow
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43C2×#12011yescharacteristic
315C22×C43#54711yescharacteristic
316C22×C43#54711yescharacteristic
317C22×C43#57511yescharacteristic
318C22×C43#57511yescharacteristic
319C22×C43#57711yescharacteristic
320C22×C43#57811yescharacteristic
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C2×D43—41no—
327C2×D43—41no—
328C4×C43—22no—
329C4×C43—42no—
330C4×C43—42no—
331C4×C43—81no—
332C4×C43—81no—
333C4×C43#52511yescharacteristic
334C4×C43#53611yescharacteristic
335C4×C43#54711yescharacteristic
336C4×C43#54711yescharacteristic
337Dic43—42no—
338Dic43—41no—
339Dic43—41no—
340Dic43—41no—
341Dic43—42no—
342Dic43—81no—
343Dic43—81no—
344C2×#552—431no—
345C2×#485—431no—
346C2×#428D4311yescharacteristic, complemented
347#2485—431no—
348#2059—431no—
349#2059—431no—
350#2036—431no—
351#2035—431no—
352#1894—431no—
353#1870—431no—
354#1865—431no—
355#1863—431no—
356#1854—431no—
357#1854—431no—
358#1824—431no—
359C2×C43—42no—
360C2×C43#240611yescharacteristic
361C2×C43#300511yescharacteristic
362C2×C43#301311yescharacteristic
363C2×C43#334811yescharacteristic
364C2×C43#334911yescharacteristic
365C2×C43#335111yescharacteristic
366C2×C43#335211yescharacteristic
367D43—81no—
368C22×M16C2×D4311yescharacteristic
369#552—864no—
370#552—864no—
371C2×#126—861no—
372C2×#125—431no—
373C2×#125—861no—
374C2×#123—861no—
375C2×C22⋊Q8—431no—
376C2×C22⋊Q8—431no—
377C2×C4×Q8—431no—
378C2×C4×D4—431no—
379C2×#117—431no—
380C2×#117—861no—
381C2×#117C2×D4311yescharacteristic
382C22×C4⋊C4C2×D4311yescharacteristic
383#485—864no—
384#428—24no—
385C2×#107—431no—
386C2×#107C2×D4311yescharacteristic
387C2×#107C2×D4311yescharacteristic
388C2×#106—431no—
389C2×#106C2×D4311yescharacteristic
390C2×#106C2×D4311yescharacteristic
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×#103—431no—
395C2×C22⋊C8—431no—
396C2×C22⋊C8—431no—
397C2×C22⋊C8—431no—
398#397—861no—
399#394—861no—
400#389—431no—
401#389—431no—
402#388—861no—
403#387—861no—
404#380—431no—
405#380—431no—
406#380—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#336—431no—
414#336—431no—
415C43#2410611yescharacteristic, complemented, Sylow
416C22×Q8—431no—
417C22×D4—431no—
418C23×C4—21no—
419C23×C4—431no—
420C23×C4C22×D4311yescharacteristic
421C2×M16—22no—
422C2×M16—22no—
423C2×M16—22no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428#126—868no—
429#125—862no—
430#125—868no—
431#125—862no—
432#123—868no—
433C22⋊Q8—434no—
434C22⋊Q8—862no—
435C22⋊Q8—862no—
436C22⋊Q8—862no—
437C4×Q8—862no—
438C4×Q8—862no—
439C4×D4—862no—
440C4×D4—862no—
441#117—22no—
442#117—22no—
443#117—862no—
444#117—868no—
445#117—862no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4C22⋊D4314yes—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4—431no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C42—21no—
474C2×C42—431no—
475C2×C42—861no—
476C2×C42—861no—
477#107—22no—
478#107—22no—
479#107—862no—
480#106—22no—
481#106—22no—
482#106—862no—
483#103—862no—
484#103—862no—
485#103—862no—
486#103—862no—
487C22⋊C8—862no—
488C22⋊C8—862no—
489C22⋊C8—862no—
490#95—861no—
491#95—861no—
492#95—861no—
493#95—861no—
494#95—861no—
495C24—431no—
496C24D4×D4311yescharacteristic
497C2×Q8—432no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×D4—862no—
504C2×D4—1721no—
505C2×D4—1721no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4312yes—
532C22×C4C2×C22⋊D4312yes—
533C22×C4C23×D4311yescharacteristic
534M16—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8#1062189812yes—
546C2×C8#1062189812yes—
547C4⋊C4—24no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—432no—
555C4⋊C4—864no—
556C4⋊C4—864no—
557C4⋊C4—864no—
558C4⋊C4—864no—
559C4⋊C4—862no—
560C4⋊C4—864no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—3441no—
567C4⋊C4—1722no—
568C4⋊C4C2×C22⋊D4312yes—
569C4⋊C4C2×C22⋊D4312yes—
570C22⋊C4—42no—
571C22⋊C4—864no—
572C22⋊C4—864no—
573C22⋊C4—862no—
574C22⋊C4—864no—
575C22⋊C4—862no—
576C22⋊C4—3441no—
577C22⋊C4—3441no—
578C22⋊C4—1722no—
579C42—42no—
580C42—864no—
581C42—864no—
582C42—861no—
583C42—861no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—861no—
591C23—861no—
592C23—861no—
593C23—861no—
594C23—861no—
595C23—861no—
596C23—861no—
597C23#1306329312yes—
598C23C2×D4×D4311yescharacteristic
599Q8—862no—
600Q8—862no—
601Q8—1721no—
602Q8—1721no—
603D4—1724no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4#1306329312yes—
649C2×C4C2×D4×D4311yescharacteristic
650C2×C4C22×C22⋊D4311yescharacteristic
651C2×C4C2×#1062189811yescharacteristic
652C2×C4C2×#1062189811yescharacteristic
653C2×C4#1306337311yescharacteristic
654C2×C4#1306337311yescharacteristic
655C8—22no—
656C8—22no—
657C8—1721no—
658C8—1721no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—1721no—
667C22—1721no—
668C22—1721no—
669C22—1721no—
670C22—1721no—
671C22—1721no—
672C22—1721no—
673C22C2×#1306329311yescharacteristic
674C22#1458355011yescharacteristic
675C22#1458355011yescharacteristic
676C22#1458369511yescharacteristic
677C22#1458369511yescharacteristic
678C22#1458370811yescharacteristic
679C22#1458371511yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—3441no—
686C4—3441no—
687C4—1721no—
688C4—1722no—
689C4—1721no—
690C4—1721no—
691C4—1722no—
692C4#1458341011yescharacteristic
693C4#1458347311yescharacteristic
694C4#1458355011yescharacteristic
695C4#1458355011yescharacteristic
696C2—42no—
697C2—3441no—
698C2#1913793011yescharacteristic
699C2#1914383411yescharacteristic
700C2#1914390911yescharacteristic
701C2#1914711111yescharacteristic
702C2#1914712611yescharacteristic
703C2#1914715111yescharacteristic
704C2#1914716611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#428D43
hypocenterC43#24106
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
4. #19135935C2semidirect
5. #19135931C2semidirect
6. #19135800C2semidirect
7. #19135793C2semidirect
8. #19135028C2semidirect
10. #19134860C2semidirect
11. #19134846C2semidirect
12. #19134793C2semidirect
13. #19134791C2semidirect
14. #19134685C2semidirect
15. C2×C43×#428C2semidirect
346. C2×#428D43semidirect
415. C43#24106semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×#145832402
#191388862
#191359352
#191359312
#191358002
#191357932
#191350282
#191348922
#191348602
#191348462
#191347932
#191347912
#191346852
C2×C43×#4282
#2410643