Finite Group Databasebeta

← #17067663

Subgroups — #17067663

Order 4352.

1104 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763147C211yesmaximal, characteristic, complemented
2C2×#11763130C211yesmaximal, characteristic
3#14531267C211yesmaximal, characteristic, complemented
4#14530119C211yesmaximal, characteristic, complemented
5#14530119C211yesmaximal, characteristic, complemented
6#14530020C211yesmaximal, characteristic, complemented
7#14530020C211yesmaximal, characteristic, complemented
8#14529107C211yesmaximal, characteristic
9#14529097C211yesmaximal, characteristic, complemented
10#14529052C211yesmaximal, characteristic, complemented
11#14529045C211yesmaximal, characteristic, complemented
12#14529038C211yesmaximal, characteristic, complemented
13#14529031C211yesmaximal, characteristic, complemented
14#14528852C211yesmaximal, characteristic, complemented
15C2×C17×#529C211yesmaximal, characteristic
16C2×#10587612C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18#11763147—24no—
19#11763130—24no—
20C2×#10587478C2211yescharacteristic
21C2×#10587478C2211yescharacteristic
22C2×#10587479C2211yescharacteristic
23C2×#10587479C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762707C2211yescharacteristic
36#11762707C2211yescharacteristic
37#11762707C2211yescharacteristic
38#11762682—21no—
39#11762682—21no—
40C4×#63225—21no—
41C4×#63225—21no—
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762564C2211yescharacteristic
49#11762564C2211yescharacteristic
50C17×#529—24no—
51C17×#529—24no—
52C2×C17×#126—21no—
53C2×C17×#125C2211yescharacteristic
54C2×C17×#124C2211yescharacteristic
55C2×C17×#123—21no—
56C2×C17×C22⋊Q8C2211yescharacteristic
57C2×C17×#121C2211yescharacteristic
58C2×C4×Q8×C17C2211yescharacteristic
59C2×C4×D4×C17—21no—
60C2×C4×D4×C17C2211yescharacteristic
61C2×C17×#117—21no—
62C22×C42×C17C2211yescharacteristic
63C22×Q8×C17C2311yescharacteristic
64C22×D4×C17—21no—
65C22×D4×C17C2311yescharacteristic
66C23×C4×C17—21no—
67C23×C4×C17D411yescharacteristic
68C23×C4×C17D411yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C17×#126—28no—
71C17×#125—22no—
72C17×#125—22no—
73C17×#124—22no—
74C17×#124—22no—
75C17×#123—28no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8D414yes—
78C17×#121—22no—
79C17×#121D414yes—
80C4×Q8×C17—22no—
81C4×Q8×C17—22no—
82C4×D4×C17—28no—
83C4×D4×C17—22no—
84C4×D4×C17—22no—
85C17×#117—28no—
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17C2311yescharacteristic
91C2×C4⋊C4×C17C2311yescharacteristic
92C2×C22⋊C4×C17—21no—
93C2×C22⋊C4×C17—21no—
94C2×C22⋊C4×C17—21no—
95C2×C22⋊C4×C17—21no—
96C2×C22⋊C4×C17—21no—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C42×C17—21no—
100C2×C42×C17D411yescharacteristic
101C2×C42×C17D411yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C42×C17C2311yescharacteristic
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106#10587612—22no—
107#10587612—22no—
108#10587612—22no—
109#10587612—22no—
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×#63225—21no—
115C2×#63225—21no—
116C2×#63225—21no—
117C2×#63225—21no—
118C2×C4×Dic17—21no—
119C2×C4×Dic17—21no—
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C22×#3622C2311yescharacteristic
124#10587506—22no—
125#10587506—22no—
126#10587506—22no—
127#10587506—22no—
128#10587503—22no—
129#10587503—22no—
130#10587503—22no—
131#10587503—22no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136C22⋊#3622—22no—
137C22⋊#3622—22no—
138#10587479—22no—
139#10587479—22no—
140#10587478—22no—
141#10587478—22no—
142C24×C17—21no—
143C24×C17C2×D411yescharacteristic
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17C2×D412yes—
150C2×D4×C17—24no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—42no—
157C2×D4×C17—42no—
158C2×D4×C17C2×D412yes—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—24no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—22no—
170C22×C4×C17—41no—
171C22×C4×C17—41no—
172C22×C4×C17—41no—
173C22×C4×C17—42no—
174C22×C4×C17—42no—
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D412yes—
180C22×C4×C17C2×D412yes—
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2411yescharacteristic
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C4⋊C4×C17—24no—
188C4⋊C4×C17—24no—
189C4⋊C4×C17—24no—
190C4⋊C4×C17—24no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17C2×D412yes—
194C4⋊C4×C17C2×D412yes—
195C22⋊C4×C17—24no—
196C22⋊C4×C17—24no—
197C22⋊C4×C17—24no—
198C22⋊C4×C17—24no—
199C22⋊C4×C17—24no—
200C42×C17—24no—
201C42×C17—22no—
202C42×C17—22no—
203C42×C17—21no—
204C42×C17—21no—
205C42×C17—21no—
206C42×C17—21no—
207C22⋊Dic17—24no—
208C22⋊Dic17—42no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17#4112yes—
216C4⋊Dic17#4112yes—
217#63225—42no—
218#63225—42no—
219#63225—42no—
220#63225—42no—
221C4×Dic17—24no—
222C4×Dic17—42no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235#24068—171nomaximal, Sylow
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—22no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17#12012yes—
250C23×C17C22×D411yescharacteristic
251Q8×C17—22no—
252Q8×C17—22no—
253Q8×C17—41no—
254Q8×C17—41no—
255D4×C17—22no—
256D4×C17—22no—
257D4×C17—48no—
258D4×C17—41no—
259D4×C17—41no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
263C2×C4×C17—21no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—44no—
281C2×C4×C17—48no—
282C2×C4×C17—44no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17#12012yes—
290C2×C4×C17#13512yes—
291C2×C4×C17C22×D411yescharacteristic
292C2×C4×C17C22×D411yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17C2×#4111yescharacteristic
295C2×C4×C172−1+411yescharacteristic
296C2×C4×C172−1+411yescharacteristic
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309#3622—41no—
310#3622—41no—
311#3622—41no—
312#3622—41no—
313C2×#529D1711yescharacteristic
314C2×#485—171no—
315C2×#482—171no—
316#2296—171no—
317#2059—171no—
318#2059—171no—
319#2042—171no—
320#2042—171no—
321#1875—171no—
322#1873—171no—
323#1865—171no—
324#1864—171no—
325#1863—171no—
326#1862—171no—
327#1817—171no—
328C22×C17—22no—
329C22×C17—22no—
330C22×C17—22no—
331C22×C17—41no—
332C22×C17—41no—
333C22×C17—41no—
334C22×C17—41no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17—42no—
338C22×C17—81no—
339C22×C17—81no—
340C22×C17—81no—
341C22×C17—81no—
342C22×C17C2×#12011yescharacteristic
343C22×C17#52511yescharacteristic
344C22×C17#53611yescharacteristic
345C22×C17C2×#13511yescharacteristic
346C22×C17#57511yescharacteristic
347C22×C17#57511yescharacteristic
348C22×C17#57511yescharacteristic
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—42no—
352C4×C17—41no—
353C4×C17—42no—
354C4×C17—41no—
355C4×C17—41no—
356C4×C17—42no—
357C4×C17#54711yescharacteristic
358C4×C17#54711yescharacteristic
359C4×C17#54711yescharacteristic
360C4×C17#54711yescharacteristic
361Dic17—42no—
362Dic17—42no—
363Dic17—81no—
364Dic17—81no—
365#529—24no—
366#529—24no—
367C2×#126—21no—
368C2×#125C2×D1711yescharacteristic
369C2×#124C2×D1711yescharacteristic
370C2×#123—21no—
371C2×C22⋊Q8C2×D1711yescharacteristic
372C2×#121C2×D1711yescharacteristic
373C2×C4×Q8C2×D1711yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C2×D1711yescharacteristic
376C2×#117—21no—
377C2×#117—171no—
378C2×#117—171no—
379C22×C42C2×D1711yescharacteristic
380#485—344no—
381#482—344no—
382C2×#107—171no—
383C2×#107—171no—
384C2×#106—171no—
385C2×#106—171no—
386C2×#103—171no—
387C2×#103—171no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#102—171no—
391C2×#102—171no—
392C2×#102—171no—
393C2×#102—171no—
394C2×C22⋊C8—171no—
395C2×C22⋊C8—171no—
396#389—171no—
397#389—171no—
398#389—171no—
399#389—171no—
400#385—341no—
401#385—341no—
402C4×C4⋊C4—341no—
403C4×C4⋊C4—341no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#336—171no—
409#336—171no—
410#336—171no—
411#336—171no—
412C2×C17—42no—
413C2×C17—82no—
414C2×C17#240611yescharacteristic
415C2×C17#300211yescharacteristic
416C2×C17#300511yescharacteristic
417C2×C17#310211yescharacteristic
418C2×C17#311111yescharacteristic
419C2×C17#323311yescharacteristic
420C2×C17#324011yescharacteristic
421C22×Q8C22×D1711yescharacteristic
422C22×D4—21no—
423C22×D4C22×D1711yescharacteristic
424C23×C4—21no—
425C23×C4C22⋊D1711yescharacteristic
426C23×C4C22⋊D1711yescharacteristic
427C23×C4C22×D1711yescharacteristic
428C22×C8—171no—
429C22×C8—171no—
430C22×C8—171no—
431C22×C8—171no—
432#126—28no—
433#125—22no—
434#125—22no—
435#124—22no—
436#124—22no—
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8C22⋊D1714yes—
440#121—22no—
441#121C22⋊D1714yes—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×D4—28no—
445C4×D4—22no—
446C4×D4—22no—
447#117—28no—
448#117—342no—
449#117—342no—
450#117—342no—
451#117—342no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—171no—
457C2×C4⋊C4—171no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—341no—
461C2×C4⋊C4—341no—
462C2×C4⋊C4—341no—
463C2×C4⋊C4—341no—
464C2×C4⋊C4C22×D1711yescharacteristic
465C2×C4⋊C4C22×D1711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—341no—
472C2×C22⋊C4—341no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—341no—
477C2×C42—341no—
478C2×C42C22⋊D1711yescharacteristic
479C2×C42C22⋊D1711yescharacteristic
480C2×C42C22×D1711yescharacteristic
481C2×C42C22×D1711yescharacteristic
482#107—342no—
483#107—342no—
484#106—342no—
485#106—342no—
486#103—342no—
487#103—342no—
488#103—342no—
489#103—342no—
490#102—342no—
491#102—342no—
492#102—342no—
493#102—342no—
494C22⋊C8—342no—
495C22⋊C8—342no—
496#95—341no—
497#95—341no—
498#95—341no—
499#95—341no—
500C17#2406811yescharacteristic, complemented, Sylow
501C24—21no—
502C24C2×C22⋊D1711yescharacteristic
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8C2×C22⋊D1712yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×C22⋊D1712yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—341no—
535C22×C4—341no—
536C22×C4—341no—
537C22×C4—341no—
538C22×C4C2×C22⋊D1711yescharacteristic
539C22×C4C2×C22⋊D1711yescharacteristic
540C22×C4C2×C22⋊D1711yescharacteristic
541C22×C4C2×C22⋊D1712yes—
542C22×C4C2×C22⋊D1712yes—
543C22×C4C2×C22⋊D1711yescharacteristic
544C22×C4C2×C22⋊D1711yescharacteristic
545C22×C4C23×D1711yescharacteristic
546C2×C8—341no—
547C2×C8—341no—
548C2×C8—341no—
549C2×C8—341no—
550C2×C8—341no—
551C2×C8—341no—
552C2×C8—341no—
553C2×C8—341no—
554C2×C8—341no—
555C2×C8—341no—
556C2×C8—341no—
557C2×C8—341no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—24no—
564C4⋊C4—172no—
565C4⋊C4—172no—
566C4⋊C4—341no—
567C4⋊C4—341no—
568C4⋊C4—341no—
569C4⋊C4—341no—
570C4⋊C4—341no—
571C4⋊C4—341no—
572C4⋊C4—682no—
573C4⋊C4—682no—
574C4⋊C4—682no—
575C4⋊C4—682no—
576C4⋊C4C2×C22⋊D1712yes—
577C4⋊C4C2×C22⋊D1712yes—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—344no—
584C22⋊C4—682no—
585C42—24no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—22no—
591C42—22no—
592C42—344no—
593C42—682no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#1058763912yes—
608C23C22×C22⋊D1711yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—44no—
639C2×C4—48no—
640C2×C4—44no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—681no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4#1058763612yes—
660C2×C4#1058763912yes—
661C2×C4#41×D1711yescharacteristic
662C2×C4#41×D1711yescharacteristic
663C2×C4#1058769711yescharacteristic
664C2×C4#1058769711yescharacteristic
665C2×C4C22×C22⋊D1711yescharacteristic
666C2×C4C22×C22⋊D1711yescharacteristic
667C8—681no—
668C8—681no—
669C8—681no—
670C8—681no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#1058763911yescharacteristic
686C22#1176331611yescharacteristic
687C22#1176338011yescharacteristic
688C22C2×#1058763611yescharacteristic
689C22#1176360711yescharacteristic
690C22#1176360711yescharacteristic
691C22#1176360711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—682no—
701C4—682no—
702C4—1361no—
703C4—1361no—
704C4#1176345811yescharacteristic
705C4#1176345811yescharacteristic
706C4#1176345811yescharacteristic
707C4#1176345811yescharacteristic
708C2—42no—
709C2—82no—
710C2#1453211511yescharacteristic
711C2#1453800211yescharacteristic
712C2#1453802611yescharacteristic
713C2#1453879611yescharacteristic
714C2#1453888711yescharacteristic
715C2#1453995911yescharacteristic
716C2#1454002011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#529C2
socleC23×C17C22×D4
prime radicalC2×C17×#121C22
hypercenterC2×#529D17
hypocenterC17#24068
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#11763147C2semidirect
3. #14531267C2semidirect
4. #14530119C2semidirect
5. #14530119C2semidirect
6. #14530020C2semidirect
7. #14530020C2semidirect
9. #14529097C2semidirect
10. #14529052C2semidirect
11. #14529045C2semidirect
12. #14529038C2semidirect
13. #14529031C2semidirect
14. #14528852C2semidirect
500. C17#24068semidirect

Maximal subgroups

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

subgroupindex
C2×#117631472
C2×#117631302
#145312672
#145301192
#145300202
#145291072
#145290972
#145290522
#145290452
#145290382
#145290312
#145288522
C2×C17×#5292
#2406817