Finite Group Databasebeta

← #15869682

Subgroups — #15869682

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718825C211yesmaximal, characteristic, complemented
2C2×#11718783C211yesmaximal, characteristic, complemented
3#13117531C211yesmaximal, characteristic
4#13117520C211yesmaximal, characteristic, complemented
5#13115692C211yesmaximal, characteristic, complemented
6#13115570C211yesmaximal, characteristic, complemented
7#13115535C211yesmaximal, characteristic, complemented
8#13115528C211yesmaximal, characteristic, complemented
9#13115265C211yesmaximal, characteristic
10#13115260C211yesmaximal, characteristic, complemented
11#13114869C211yesmaximal, characteristic, complemented
12#13114735C211yesmaximal, characteristic, complemented
13#103×Dic13C211yesmaximal, characteristic, complemented
14#102×Dic13C211yesmaximal, characteristic, complemented
15C2×C13×#468C211yesmaximal, characteristic
16C22×C13×SD16C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C2×D4×Dic13C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24C13×#468C418yescomplemented
25C2×C13×#107C2211yescharacteristic
26C2×C13×#103C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28#11718891C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31#11718882—21no—
32#11718882C2211yescharacteristic
33#11718881—21no—
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36#11718873C2211yescharacteristic
37#11718873C2211yescharacteristic
38#11718825—24no—
39#11718783—24no—
40C2×#88058C2211yescharacteristic
41C2×#88057C2211yescharacteristic
42C2×#88055C2211yescharacteristic
43C2×#88055C2211yescharacteristic
44C2×C8×Dic13C2211yescharacteristic
45C2×C8×Dic13C2211yescharacteristic
46#11718646—21no—
47#11718646C2211yescharacteristic
48#11718646C2211yescharacteristic
49#11718642—21no—
50C4⋊C4×Dic13C2211yescharacteristic
51C4⋊C4×Dic13C2211yescharacteristic
52#11718612—21no—
53#11718612—21no—
54#11718612—21no—
55#11718611—21no—
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×D4×C13—21no—
64C22×D4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C2×C13×SD16—22no—
68C2×C13×SD16—22no—
69C2×C13×SD16C2×C414yes—
70C2×C13×M16—22no—
71C2×C13×M16—22no—
72C2×C13×M16C2×C414yescomplemented
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8C2×C414yescomplemented
77C13×#121—22no—
78C13×#121C2×C414yes—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13D411yescharacteristic
90C2×C22⋊Dic13D411yescharacteristic
91Q8×Dic13—22no—
92Q8×Dic13—22no—
93D4×Dic13—22no—
94D4×Dic13—22no—
95#88180—22no—
96#88180—22no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13—21no—
100C2×C4⋊Dic13D411yescharacteristic
101C2×C4⋊Dic13D411yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4⋊Dic13C2311yescharacteristic
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4×Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2311yescharacteristic
111C22×#1055—22no—
112C22×#1055—22no—
113C22×#1055—22no—
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C13×#107C2×C414yescomplemented
117C13×#103C2×C414yescomplemented
118C13×#102C2×C414yes—
119#88075—22no—
120#88075—22no—
121#88072—22no—
122#88072—22no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88058—22no—
132#88057—22no—
133#88055—22no—
134#88055D414yescomplemented
135C8×Dic13—22no—
136C8×Dic13—22no—
137#21543—131nomaximal, Sylow
138C24×C13—21no—
139C24×C13C2×D411yescharacteristic
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13C22×C412yes—
146C2×D4×C13—24no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—81no—
153C2×D4×C13—81no—
154C2×D4×C13C22×C412yes—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13C22×C412yes—
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13#4112yes—
165C22×C4×C13C2411yescharacteristic
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—42no—
171C22×Dic13—81no—
172C22×Dic13—81no—
173C22×Dic13C2×D411yescharacteristic
174C22×Dic13C2×D411yescharacteristic
175C22×Dic13C2×D411yescharacteristic
176C22×Dic13C2×D411yescharacteristic
177C13×SD16—28no—
178C13×M16—28no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13C22×C412yes—
182C2×C8×C13C22×C412yes—
183C2×C8×C13C2×D412yes—
184C2×C8×C13#4112yes—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4C22×C412yes—
189C13×C4⋊C4C22×C412yes—
190C13×C22⋊C4—24no—
191C13×C22⋊C4—24no—
192C22⋊Dic13—22no—
193C22⋊Dic13—22no—
194C22⋊Dic13—42no—
195C22⋊Dic13—81no—
196C22⋊Dic13—81no—
197C22⋊Dic13—81no—
198C22⋊Dic13—81no—
199C4⋊Dic13—22no—
200C4⋊Dic13—22no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—42no—
210C4⋊Dic13—81no—
211C4⋊Dic13—81no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—42no—
215C4×Dic13—81no—
216C4×Dic13—81no—
217C4×Dic13C2×D412yes—
218C4×Dic13#4112yes—
219C2×#1055—28no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055C2×D412yes—
225C2×#1055#4112yes—
226C2×#468D1311yescharacteristic
227C2×#440—131no—
228C2×#405—131no—
229#2324—131no—
230#2323—131no—
231#1968—131no—
232#1942—131no—
233#1936—131no—
234#1935—131no—
235#1893—131no—
236#1892—131no—
237#1809—131no—
238#1776—131no—
239C4×#103—131no—
240C4×#102—131no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—22no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13C4×D412yes—
255C23×C13C22×D411yescharacteristic
256Q8×C13—22no—
257Q8×C13—22no—
258Q8×C13—41no—
259Q8×C13—41no—
260D4×C13—22no—
261D4×C13—22no—
262D4×C13—41no—
263D4×C13—41no—
264D4×C13—84no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13C4×D412yes—
281C2×C4×C13C23×C411yescharacteristic
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—21no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—84no—
310C2×Dic13#12112yes—
311C2×Dic13#12112yes—
312C8×C13—22no—
313C8×C13C4×D414yes—
314#1055—22no—
315#1055—22no—
316C22×SD16C2×D1311yescharacteristic
317C22×M16C2×D1311yescharacteristic
318C23×C8—131no—
319C2×C22⋊Q8C2×D1311yescharacteristic
320C2×#121C2×D1311yescharacteristic
321C2×C4×Q8—131no—
322C2×C4×D4—131no—
323C2×#117—131no—
324#468Dic1318yescomplemented
325#440—264no—
326C2×#107—131no—
327C2×#107C2×D1311yescharacteristic
328C2×#106—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#103C2×D1311yescharacteristic
332C2×#102—131no—
333C2×#102—131no—
334C2×#102C2×D1311yescharacteristic
335#405—264no—
336C2×#97—131no—
337C2×#97—131no—
338C2×C4×C8—131no—
339C2×C4×C8—131no—
340#391—131no—
341#390—131no—
342#390—261no—
343#389—131no—
344#389—131no—
345#389—261no—
346#388—261no—
347#388—261no—
348#388—261no—
349#387—261no—
350#386—261no—
351#385—261no—
352#380—131no—
353#380—131no—
354C4×C4⋊C4—131no—
355C4×C4⋊C4—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362C22×C13—22no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—42no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—81no—
373C22×C13—81no—
374C22×C13—81no—
375C22×C13—81no—
376C22×C13C2×C4×D411yescharacteristic
377C22×C13C2×#12111yescharacteristic
378C22×C13#53211yescharacteristic
379C22×C13#57611yescharacteristic
380C22×C13#57711yescharacteristic
381C22×C13#57711yescharacteristic
382C22×C13#57811yescharacteristic
383C4×C13—22no—
384C4×C13—42no—
385C4×C13—42no—
386C4×C13—42no—
387C4×C13C2×C4×D411yescharacteristic
388C4×C13C4×#4111yescharacteristic
389C4×C13#52511yescharacteristic
390C4×C13#52911yescharacteristic
391Dic13—22no—
392Dic13—22no—
393Dic13—41no—
394Dic13—41no—
395Dic13—81no—
396Dic13—81no—
397Dic13—81no—
398Dic13—81no—
399C22×Q8C22×D1311yescharacteristic
400C22×D4—21no—
401C22×D4C22×D1311yescharacteristic
402C23×C4—261no—
403C23×C4C22×D1311yescharacteristic
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16C2×Dic1314yes—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16C2×Dic1314yescomplemented
410C22×C8—131no—
411C22×C8—131no—
412C22×C8—262no—
413C22×C8—262no—
414C22×C8—262no—
415C22×C8C22×D1311yescharacteristic
416C22×C8C22×D1311yescharacteristic
417C22⋊Q8—22no—
418C22⋊Q8C2×Dic1314yescomplemented
419#121—22no—
420#121C2×Dic1314yes—
421C4×Q8—262no—
422C4×Q8—262no—
423C4×D4—262no—
424C4×D4—262no—
425#117—262no—
426#117—262no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—131no—
442C2×C22⋊C4—131no—
443C2×C22⋊C4—261no—
444C2×C22⋊C4—261no—
445C2×C22⋊C4—261no—
446C2×C22⋊C4—261no—
447C2×C22⋊C4—261no—
448C2×C42—131no—
449C2×C42—131no—
450C2×C42—261no—
451C2×C42—261no—
452C2×C42—261no—
453#107—262no—
454#107C2×Dic1314yescomplemented
455#106—262no—
456#103—262no—
457#103—262no—
458#103C2×Dic1314yescomplemented
459#102—262no—
460#102—262no—
461#102C2×Dic1314yes—
462#97—134no—
463#97—262no—
464C4×C8—262no—
465C4×C8—262no—
466#95—261no—
467#95—261no—
468#95—261no—
469#95—261no—
470#95—261no—
471#95—261no—
472#95—261no—
473#95—261no—
474C2×C13—42no—
475C2×C13—82no—
476C2×C13C4×#12111yescharacteristic
477C2×C13#294611yescharacteristic
478C2×C13#294711yescharacteristic
479C2×C13#306211yescharacteristic
480C2×C13#306311yescharacteristic
481C2×C13#317411yescharacteristic
482C2×C13#317511yescharacteristic
483C24—21no—
484C24D4×D1311yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C22×Dic1312yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C22×Dic1312yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—131no—
508C22×C4—131no—
509C22×C4—131no—
510C22×C4—131no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—522no—
516C22×C4—1041no—
517C22×C4—1041no—
518C22×C4D4×D1311yescharacteristic
519C22×C4#612912yes—
520C22×C4C22×Dic1312yes—
521C22×C4C23×D1311yescharacteristic
522SD16—28no—
523M16—28no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—132no—
527C2×C8—132no—
528C2×C8—268no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8D4×D1312yes—
534C2×C8#612912yes—
535C2×C8C22×Dic1312yes—
536C2×C8C22×Dic1312yes—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—262no—
541C4⋊C4—262no—
542C4⋊C4—261no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—522no—
551C4⋊C4—1041no—
552C4⋊C4—1041no—
553C4⋊C4C22×Dic1312yes—
554C4⋊C4C22×Dic1312yes—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—262no—
558C22⋊C4—262no—
559C22⋊C4—522no—
560C22⋊C4—1041no—
561C22⋊C4—1041no—
562C22⋊C4—1041no—
563C22⋊C4—1041no—
564C42—132no—
565C42—132no—
566C42—261no—
567C42—261no—
568C42—522no—
569C42—1041no—
570C42—1041no—
571C13#2154311yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23D4×Dic1312yes—
586C23C2×D4×D1311yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—132no—
612C2×C4—132no—
613C2×C4—261no—
614C2×C4—261no—
615C2×C4—261no—
616C2×C4—261no—
617C2×C4—261no—
618C2×C4—261no—
619C2×C4—261no—
620C2×C4—261no—
621C2×C4—261no—
622C2×C4—261no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—1044no—
636C2×C4D4×Dic1312yes—
637C2×C4C2×D4×D1311yescharacteristic
638C2×C4C2×#612911yescharacteristic
639C2×C4C2×#612911yescharacteristic
640C2×C4#41×D1311yescharacteristic
641C2×C4#41×D1311yescharacteristic
642C2×C4C23×Dic1311yescharacteristic
643C8—22no—
644C8—262no—
645C8—262no—
646C8D4×Dic1314yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22#1171930111yescharacteristic
662C22D13×#12111yescharacteristic
663C22#1171947911yescharacteristic
664C22#1171948011yescharacteristic
665C22#1171948311yescharacteristic
666C22#1171948411yescharacteristic
667C22C2×D4×Dic1311yescharacteristic
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—262no—
673C4—262no—
674C4—521no—
675C4—521no—
676C4—1041no—
677C4—1041no—
678C4—1041no—
679C4—1041no—
680C4#1171930511yescharacteristic
681C4#1171931111yescharacteristic
682C4C2×D4×Dic1311yescharacteristic
683C4#41×Dic1311yescharacteristic
684C2—42no—
685C2—82no—
686C2#121×Dic1311yescharacteristic
687C2#1312366911yescharacteristic
688C2#1312368011yescharacteristic
689C2#1312451111yescharacteristic
690C2#1312452211yescharacteristic
691C2#1312545911yescharacteristic
692C2#1312547011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#468C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenterC2×#468D13
hypocenterC13#21543
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#11718825C2semidirect
2. C2×#11718783C2semidirect
4. #13117520C2semidirect
5. #13115692C2semidirect
6. #13115570C2semidirect
7. #13115535C2semidirect
8. #13115528C2semidirect
10. #13115260C2semidirect
11. #13114869C2semidirect
12. #13114735C2semidirect
13. #103×Dic13C2semidirect
14. #102×Dic13C2semidirect
24. C13×#468C4semidirect
72. C2×C13×M16C2×C4semidirect
76. C13×C22⋊Q8C2×C4semidirect
116. C13×#107C2×C4semidirect
117. C13×#103C2×C4semidirect
134. #88055D4semidirect
324. #468Dic13semidirect
409. C2×M16C2×Dic13semidirect
418. C22⋊Q8C2×Dic13semidirect
454. #107C2×Dic13semidirect
458. #103C2×Dic13semidirect
571. C13#21543semidirect

Maximal subgroups

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

subgroupindex
C2×#117188252
C2×#117187832
#131175312
#131175202
#131156922
#131155702
#131155352
#131155282
#131152652
#131152602
#131148692
#131147352
#103×Dic132
#102×Dic132
C2×C13×#4682
#2154313