Finite Group Databasebeta

← #29691372

Subgroups — #29691372

Order 15616.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839923C211yesmaximal, characteristic
2#21448504C211yesmaximal, characteristic, complemented
3#21448410C211yesmaximal, characteristic
4#21446703C211yesmaximal, characteristic, complemented
5#21446512C211yesmaximal, characteristic, complemented
6#21446502C211yesmaximal, characteristic, complemented
7#21446463C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic, complemented
9#21446172C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic
14#21445586C211yesmaximal, characteristic, complemented
15C61×#1969C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22#16839923C418yescomplemented
23C2×#14519710C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839659—21no—
38#16839654—21no—
39#16839651—21no—
40#16839644—21no—
41#16839640—21no—
42#16839640—21no—
43#16839621—21no—
44#16839621—21no—
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×Q16×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#391C2211yescharacteristic
60C2×#11758226—22no—
61C2×#11758226—41no—
62C2×#11758226—41no—
63C2×#11758226—41no—
64C2×#11758226—41no—
65C2×#11758226C2×C414yes—
66C22×D244—21no—
67C22×D244C2311yescharacteristic
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61C2311yescharacteristic
71C2×#11758201—41no—
72C2×#11758201—41no—
73C2×#11758201C2×C414yescomplemented
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519753—22no—
77#14519753C2×C414yes—
78Q8×Dic61—41no—
79Q8×Dic61—41no—
80#14519734—41no—
81#14519734—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196D411yescharacteristic
90C2×#11758196D411yescharacteristic
91C4⋊C4×D61—41no—
92C4⋊C4×D61—41no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104#14519710—41no—
105#14519701—41no—
106#14519701—41no—
107#14519701C2×C414yescomplemented
108#14519699—41no—
109#14519699C2×C414yescomplemented
110#14519697—41no—
111#14519689—22no—
112#14519689C2×C414yes—
113#14519688—41no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×Q8×C61C2311yescharacteristic
121C2×Q16×C61—41no—
122C2×Q16×C61—41no—
123C2×Q16×C61C2×C414yescomplemented
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#107×C61—41no—
130#103×C61—41no—
131#103×C61—41no—
132C4×C8×C61—41no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137C23×D61—21no—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C2×Q8×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164#11758226—44no—
165#11758226—44no—
166#11758226—44no—
167#11758226—44no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—24no—
173C2×D244—21no—
174C2×D244—42no—
175C2×D244—42no—
176C2×D244C22×C412yes—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—24no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61C22×C412yes—
188C2×C4×D61#4112yes—
189Q16×C61—44no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C22×C412yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202#11758201—44no—
203#11758198—24no—
204#11758198—41no—
205#11758198—41no—
206#11758198—81no—
207#11758198—81no—
208#11758198—81no—
209#11758198—81no—
210#11758198—81no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—42no—
217C4⋊Dic61C22×C412yes—
218#11758196—24no—
219#11758196—41no—
220#11758196—41no—
221#11758196—42no—
222#11758196—81no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—42no—
226C4×Dic61—81no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418C22×C412yes—
233C23×C61C22×D411yescharacteristic
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—22no—
241C22×D61—41no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61C4×D412yes—
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—22no—
251Q8×C61—22no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255Q8×C61—41no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C23×C411yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61H(5,𝔽2)11yescharacteristic
277C2×C4×C61H(5,𝔽2)11yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—22no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61C4×D412yes—
298D244—22no—
299D244—22no—
300D244—48no—
301D244—41no—
302D244—41no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—48no—
308C4×D61—84no—
309C8×C61—22no—
310C8×C61—41no—
311#92418—22no—
312#92418—41no—
313#22057—611nomaximal, Sylow
314C22×C61C2×C4×D411yescharacteristic
315C22×C61#53411yescharacteristic
316C22×C61#53511yescharacteristic
317C22×C61#57611yescharacteristic
318C22×C61#57711yescharacteristic
319C22×C61#57811yescharacteristic
320C22×C61#57811yescharacteristic
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C2×D61—81no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61#51811yescharacteristic
342C4×C61#51811yescharacteristic
343C4×C61#53811yescharacteristic
344C4×C61#53811yescharacteristic
345Dic61—22no—
346Dic61—41no—
347Dic61—41no—
348Dic61—42no—
349Dic61—81no—
350Dic61—81no—
351C2×#452—611no—
352#2323—611no—
353#2311—611no—
354#1973—611no—
355#1969D6111yescharacteristic, complemented
356#1935—611no—
357#1934—611no—
358#1928—611no—
359#1925—611no—
360#1880—611no—
361#1878—611no—
362#1872—611no—
363#1852—611no—
364#1788—611no—
365#1750—611no—
366C2×C61#232111yescharacteristic
367C2×C61#294711yescharacteristic
368C2×C61#295111yescharacteristic
369C2×C61#320111yescharacteristic
370C2×C61#320311yescharacteristic
371C2×C61#322311yescharacteristic
372C2×C61#322411yescharacteristic
373D61—42no—
374D61—82no—
375C22×#41—611no—
376C22×Q16C2×D6111yescharacteristic
377C22×SD16—611no—
378C2×C22⋊Q8—611no—
379C2×C4×Q8—611no—
380C2×#117—611no—
381C22×C4⋊C4—611no—
382#452—618no—
383C2×#107—611no—
384C2×#107C2×D6111yescharacteristic
385C2×#103—611no—
386C2×#103—611no—
387C2×#103—611no—
388C2×#103C2×D6111yescharacteristic
389C2×#103C2×D6111yescharacteristic
390C2×#102—611no—
391C2×#102—611no—
392C2×#102—611no—
393C2×C22⋊C8—611no—
394C2×C22⋊C8—611no—
395C2×#97—611no—
396C2×C4×C8C2×D6111yescharacteristic
397#391—611no—
398#391C2×D6111yescharacteristic
399#391C2×D6111yescharacteristic
400#390—611no—
401#390—611no—
402#389—611no—
403#389—1221no—
404#388—1221no—
405#388—1221no—
406#387—1221no—
407#386—1221no—
408#386—1221no—
409#380—611no—
410#380—1221no—
411#380—1221no—
412C4×C4⋊C4—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#336—611no—
418#336—611no—
419C61#2205711yescharacteristic, complemented, Sylow
420C2×#41—614no—
421C2×#41—1222no—
422C2×#41—2441no—
423C2×#41—2441no—
424C2×#41—2441no—
425C2×#41—2441no—
426C22×Q8C22×D6111yescharacteristic
427C22×Q8C22×D6111yescharacteristic
428C22×D4—611no—
429C22×D4—1221no—
430C23×C4—611no—
431C23×C4—1221no—
432C23×C4—1221no—
433C2×Q16—41no—
434C2×Q16—41no—
435C2×Q16C4×D6114yescomplemented
436C2×SD16—614no—
437C2×SD16—2441no—
438C2×SD16—2441no—
439C22×C8—611no—
440C22×C8—611no—
441C22×C8C22×D6111yescharacteristic
442C22×C8C22×D6111yescharacteristic
443C22⋊Q8—614no—
444C22⋊Q8—1222no—
445C4×Q8—2441no—
446C4×Q8—2441no—
447#117—2441no—
448#117—2441no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—1221no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—2441no—
459C2×C4⋊C4—2441no—
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C42—611no—
471C2×C42—1221no—
472C2×C42—1221no—
473C2×C42C22×D6111yescharacteristic
474#107—41no—
475#107—2441no—
476#103—41no—
477#103—41no—
478#103—614no—
479#103—2441no—
480#103—2441no—
481#102—614no—
482#102—2441no—
483#102—2441no—
484C22⋊C8—614no—
485C22⋊C8—1222no—
486#97—2441no—
487C4×C8—41no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497C24—611no—
498C24—1221no—
499#41—2444no—
500#41—2444no—
501#41—2444no—
502#41—2444no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C2×C4×D6112yes—
514C2×Q8C2×C4×D6112yes—
515C2×D4—612no—
516C2×D4—1224no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—2442no—
523C2×D4—2442no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—611no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—1224no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—4881no—
542C22×C4—4881no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4—2442no—
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4C23×D6111yescharacteristic
549Q16—44no—
550SD16—2444no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—612no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8C2×C4×D6112yes—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—612no—
568C4⋊C4—1224no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—4881no—
575C4⋊C4—2441no—
576C4⋊C4—2441no—
577C4⋊C4—2442no—
578C4⋊C4—2442no—
579C22⋊C4—1224no—
580C22⋊C4—4881no—
581C22⋊C4—4881no—
582C22⋊C4—4881no—
583C22⋊C4—4881no—
584C22⋊C4—4881no—
585C22⋊C4—2441no—
586C22⋊C4—2441no—
587C42—21no—
588C42—21no—
589C42—1221no—
590C42—1221no—
591C42—4881no—
592C42—2442no—
593C23—612no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—1222no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23C2×D4×D6111yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—1222no—
617D4—1222no—
618D4—2448no—
619D4—2441no—
620D4—2441no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—612no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—4884no—
654C2×C4—2448no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4C22×C4×D6111yescharacteristic
664C2×C4#41×D6111yescharacteristic
665C2×C4#1451982211yescharacteristic
666C2×C4#1451982211yescharacteristic
667C2×C4#1451982211yescharacteristic
668C2×C4#1451982311yescharacteristic
669C8—22no—
670C8—41no—
671C8—1222no—
672C8—2441no—
673C22—1222no—
674C22—1222no—
675C22—1222no—
676C22—4881no—
677C22—4881no—
678C22—4881no—
679C22—4881no—
680C22—2442no—
681C22—2442no—
682C22—2442no—
683C22—2441no—
684C22—2441no—
685C22—2441no—
686C22—2441no—
687C22C4×D4×D6111yescharacteristic
688C22#1684032011yescharacteristic
689C22#1684032511yescharacteristic
690C22#1684056411yescharacteristic
691C22#1684056911yescharacteristic
692C22#1684057511yescharacteristic
693C22#1684057511yescharacteristic
694C4—42no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—1222no—
701C4—4881no—
702C4—4881no—
703C4—2441no—
704C4—2441no—
705C4—2442no—
706C4#1684023411yescharacteristic
707C4#1684023511yescharacteristic
708C4#1684034411yescharacteristic
709C4#1684034611yescharacteristic
710C2—4882no—
711C2—2442no—
712C2#2144847811yescharacteristic
713C2#2145465711yescharacteristic
714C2#2145469411yescharacteristic
715C2#2145670411yescharacteristic
716C2#2145672211yescharacteristic
717C2#2145689511yescharacteristic
718C2#2145690611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1969C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1969D61
hypocenterC61#22057
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. #21448504C2semidirect
4. #21446703C2semidirect
5. #21446512C2semidirect
6. #21446502C2semidirect
7. #21446463C2semidirect
8. #21446438C2semidirect
9. #21446172C2semidirect
10. #21446162C2semidirect
11. #21446123C2semidirect
12. #21446005C2semidirect
14. #21445586C2semidirect
15. C61×#1969C2semidirect
22. #16839923C4semidirect
73. C2×#11758201C2×C4semidirect
107. #14519701C2×C4semidirect
109. #14519699C2×C4semidirect
123. C2×Q16×C61C2×C4semidirect
355. #1969D61semidirect
419. C61#22057semidirect
435. C2×Q16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399232
#214485042
#214484102
#214467032
#214465122
#214465022
#214464632
#214464382
#214461722
#214461622
#214461232
#214460052
#214457582
#214455862
C61×#19692
#2205761