Finite Group Databasebeta

← #29737497

Subgroups — #29737497

Order 15616.

1032 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×#16840051C211yesmaximal, characteristic, complemented
2C2×#16839764C211yesmaximal, characteristic
3#21449522C211yesmaximal, characteristic, complemented
4#21448647C211yesmaximal, characteristic
5#21447359C211yesmaximal, characteristic, complemented
6#21447209C211yesmaximal, characteristic, complemented
7#21447201C211yesmaximal, characteristic, complemented
8#21446959C211yesmaximal, characteristic, complemented
9#21446081C211yesmaximal, characteristic, complemented
10#21446063C211yesmaximal, characteristic, complemented
11#21446011C211yesmaximal, characteristic, complemented
12#21446002C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic
15C61×#1809C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519754—21no—
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16840051—24no—
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27#16839764—24no—
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839696—21no—
38#16839683—21no—
39#16839667C2211yescharacteristic
40#16839667C2211yescharacteristic
41#16839661C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839638—21no—
44#16839638—21no—
45#16839634—21no—
46#16839631C2211yescharacteristic
47#16839624—21no—
48C4×C22⋊Dic61C2211yescharacteristic
49#95×D61—21no—
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×#107×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222Q814yescomplemented
67C22×Dic122—21no—
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519776—22no—
78#14519776—41no—
79#14519754—44no—
80#14519739—22no—
81#14519739—22no—
82#14519739—41no—
83#14519739—41no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61D411yescharacteristic
95C2×C22⋊Dic61D411yescharacteristic
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519708—22no—
101#14519708—41no—
102#14519706—22no—
103#14519706—41no—
104#14519702—22no—
105#14519702—22no—
106#14519700—41no—
107#14519700—41no—
108#14519699—22no—
109#14519699D414yes—
110#14519697—22no—
111#14519697—22no—
112C22⋊#92418—22no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—41no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133#107×C61—41no—
134#106×C61—22no—
135#95×C61—21no—
136#95×C61—21no—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×Q812yes—
149C22×C4×C61#4112yes—
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—24no—
152C2×C22⋊D61—42no—
153C2×C22⋊D61—42no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C22×Dic61—81no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164#11758222—28no—
165#11758222—44no—
166#11758222—44no—
167#11758222—44no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244C2×D412yes—
172C2×D244C2×Q812yes—
173C2×D244#4112yes—
174C2×C4×D61—24no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—81no—
182C2×C4×D61—81no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—42no—
189C2×Dic122—42no—
190C2×Dic122—81no—
191C2×Dic122C2×Q812yes—
192M16×C61—44no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61C2×D412yes—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—81no—
209C22⋊Dic61—22no—
210C22⋊Dic61—22no—
211#11758198—42no—
212#11758198—42no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—42no—
217C4⋊Dic61—42no—
218C4⋊Dic61C2×D412yes—
219#11758196—42no—
220#11758196—42no—
221#11758196—42no—
222#11758196—81no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61C22⋊Q812yes—
240C23×C61C22×D411yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61C22⋊Q812yes—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×Q811yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61H(5,𝔽2)11yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C22⋊D61—48no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—21no—
280C2×Dic61—22no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—84no—
294C2×Dic61AGL(1,ℤ/8)12yes—
295C2×Dic61#13712yes—
296D244—22no—
297D244—22no—
298D244—22no—
299D244C22⋊Q814yescomplemented
300C4×D61—48no—
301C4×D61—84no—
302C4×D61—84no—
303Dic122—22no—
304Dic122—22no—
305Dic122—41no—
306Dic122—41no—
307Dic122—84no—
308C8×C61—22no—
309C8×C61—41no—
310#92418—41no—
311#92418—41no—
312#25978—611nomaximal, Sylow
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61C2×C22⋊Q811yescharacteristic
321C22×C61D4211yescharacteristic
322C22×C61#54611yescharacteristic
323C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C61C2×#13711yescharacteristic
325C22×C61#57711yescharacteristic
326C22×C61#57711yescharacteristic
327C2×D61—24no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—42no—
334C4×C61—22no—
335C4×C61—81no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61—81no—
339C4×C61C2×C22⋊Q811yescharacteristic
340C4×C61#54311yescharacteristic
341C4×C61#54611yescharacteristic
342C4×C61#55111yescharacteristic
343Dic61—22no—
344Dic61—22no—
345Dic61—41no—
346Dic61—42no—
347Dic61—41no—
348Dic61—42no—
349Dic61—81no—
350C2×#476—611no—
351C2×#417—611no—
352#2440—611no—
353#2339—611no—
354#2096—611no—
355#2068—611no—
356#2066—611no—
357#2024—611no—
358#1864—611no—
359#1862—611no—
360#1853—611no—
361#1851—611no—
362#1809D6111yescharacteristic, complemented
363#1802—611no—
364#1788—611no—
365C2×C61—42no—
366C2×C61#243711yescharacteristic
367C2×C61#307911yescharacteristic
368C2×C61#308411yescharacteristic
369C2×C61#326611yescharacteristic
370C2×C61#327211yescharacteristic
371C2×C61#330611yescharacteristic
372C2×C61#333111yescharacteristic
373D61—44no—
374C22×#41—611no—
375C22×M16C2×D6111yescharacteristic
376C2×C4⋊Q8—611no—
377C2×C22⋊Q8—1221no—
378C2×C4×D4—611no—
379C2×C4×D4—611no—
380C22×C4⋊C4—611no—
381#476—1224no—
382C2×#107C2×D6111yescharacteristic
383C2×#106—611no—
384C2×#106—611no—
385C2×#106C2×D6111yescharacteristic
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388#417—1224no—
389C2×#103—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#102—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×C22⋊C8—611no—
398#398—1221no—
399#395—1221no—
400#391—611no—
401#391—611no—
402#389—611no—
403#389—611no—
404#386—1221no—
405#386—1221no—
406#385—1221no—
407#384—611no—
408#381—1221no—
409#380C2×D6111yescharacteristic
410#380C2×D6111yescharacteristic
411C4×C22⋊C4—611no—
412C2×#95—1221no—
413#340—611no—
414#340—611no—
415#340C2×D6111yescharacteristic
416#340C2×D6111yescharacteristic
417#336—611no—
418#336—611no—
419C61#2597811yescharacteristic, complemented, Sylow
420C2×#41—614no—
421C2×#41—1222no—
422C2×#41—1222no—
423C2×#41—1222no—
424C2×#41—2441no—
425C2×#41—2441no—
426C22×Q8—611no—
427C22×Q8—1221no—
428C22×D4—611no—
429C22×D4—1221no—
430C23×C4—1221no—
431C23×C4—1221no—
432C23×C4—1221no—
433C23×C4—1221no—
434C23×C4C22×D6111yescharacteristic
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8—611no—
439C22×C8—611no—
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C4⋊Q8—1222no—
443C4⋊Q8—2441no—
444C22⋊Q8—2444no—
445C4×D4—1222no—
446C4×D4—1222no—
447C4×D4—2441no—
448C4×D4—2441no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—1222no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4—1221no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—2441no—
459C2×C4⋊C4C22×D6111yescharacteristic
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C42—611no—
470C2×C42—611no—
471#107—41no—
472#106—22no—
473#106—1222no—
474#106—2441no—
475C4⋊C8—1222no—
476C4⋊C8—2441no—
477#103—1222no—
478#103—1222no—
479#103—2441no—
480#103—2441no—
481#102—614no—
482#102—1222no—
483#102—1222no—
484#102—1222no—
485C22⋊C8—1222no—
486#95—21no—
487#95—21no—
488#95—611no—
489#95—611no—
490#95—1221no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496C24—1221no—
497C24D4×D6111yescharacteristic
498#41—1228no—
499#41—2444no—
500#41—2444no—
501#41—2444no—
502C2×Q8—612no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—4881no—
509C2×Q8—2442no—
510C2×Q8—2442no—
511C2×D4—612no—
512C2×D4—612no—
513C2×D4—612no—
514C2×D4—1224no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—1221no—
518C2×D4—2442no—
519C2×D4—2442no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1224no—
535C22×C4—1221no—
536C22×C4—4881no—
537C22×C4—4881no—
538C22×C4—4881no—
539C22×C4—2442no—
540C22×C4—2442no—
541C22×C4—2442no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4—2442no—
546C22×C4—2442no—
547C22×C4#1175822212yes—
548C22×C4D4×D6111yescharacteristic
549C22×C4Q8×D6112yes—
550C22×C4C23×D6111yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8D4×D6112yes—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—612no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—1221no—
576C4⋊C4—4881no—
577C4⋊C4—2442no—
578C4⋊C4—2442no—
579C4⋊C4—2442no—
580C4⋊C4—2442no—
581C4⋊C4—2442no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—2442no—
587C22⋊C4—2442no—
588C42—1221no—
589C42—1221no—
590C42—1221no—
591C42—1221no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1222no—
599C23—1222no—
600C23—1222no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23—2441no—
605C23#1451975512yes—
606C23C2×D4×D6111yescharacteristic
607Q8—1222no—
608Q8—1222no—
609Q8—4884no—
610Q8—2441no—
611Q8—2441no—
612D4—614no—
613D4—1222no—
614D4—1222no—
615D4—1222no—
616D4—2448no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1222no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1222no—
648C2×C4—1221no—
649C2×C4—4884no—
650C2×C4—4884no—
651C2×C4—4884no—
652C2×C4—2448no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4#1451975512yes—
661C2×C4C2×D4×D6111yescharacteristic
662C2×C4C2×Q8×D6111yescharacteristic
663C2×C4#41×D6111yescharacteristic
664C2×C4C2×#1175822211yescharacteristic
665C2×C4#1451982211yescharacteristic
666C2×C4#1451982311yescharacteristic
667C8—22no—
668C8—41no—
669C8—2441no—
670C8—2441no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—1224no—
679C22—2442no—
680C22—2442no—
681C22—2442no—
682C22—2442no—
683C22—2442no—
684C22—2442no—
685C22C2×#1451975511yescharacteristic
686C22#1684039611yescharacteristic
687C22#1684040111yescharacteristic
688C22AGL(1,ℤ/8)×D6111yescharacteristic
689C22#137×D6111yescharacteristic
690C22#1684057111yescharacteristic
691C22#1684057211yescharacteristic
692C4—22no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—1222no—
698C4—1222no—
699C4—4881no—
700C4—2441no—
701C4—2442no—
702C4—2442no—
703C4—2441no—
704C4C22⋊Q8×D6111yescharacteristic
705C4#1684038711yescharacteristic
706C4#1684040211yescharacteristic
707C4#1684043611yescharacteristic
708C2—42no—
709C2—2444no—
710C2#2144948711yescharacteristic
711C2#2145563211yescharacteristic
712C2#2145568011yescharacteristic
713C2#2145733611yescharacteristic
714C2#2145741611yescharacteristic
715C2#2145777511yescharacteristic
716C2#2145813011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1809C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenter#1809D61
hypocenterC61#25978
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C2×#16840051C2semidirect
3. #21449522C2semidirect
5. #21447359C2semidirect
6. #21447209C2semidirect
7. #21447201C2semidirect
8. #21446959C2semidirect
9. #21446081C2semidirect
10. #21446063C2semidirect
11. #21446011C2semidirect
12. #21446002C2semidirect
13. #21445818C2semidirect
15. C61×#1809C2semidirect
66. C2×#11758222Q8semidirect
299. D244C22⋊Q8semidirect
362. #1809D61semidirect
419. C61#25978semidirect

Maximal subgroups

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

subgroupindex
C2×#168400512
C2×#168397642
#214495222
#214486472
#214473592
#214472092
#214472012
#214469592
#214460812
#214460632
#214460112
#214460022
#214458182
#214457572
C61×#18092
#2597861