Finite Group Databasebeta

← #29689980

Subgroups — #29689980

Order 15616.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840379C211yesmaximal, characteristic
2C2×#16839788C211yesmaximal, characteristic, complemented
3#21448426C211yesmaximal, characteristic, complemented
4#21446769C211yesmaximal, characteristic, complemented
5#21446765C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446750C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic
9#21446250C211yesmaximal, characteristic, complemented
10#21446242C211yesmaximal, characteristic, complemented
11#21445833C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445823C211yesmaximal, characteristic, complemented
14#21445817C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17#16840379—24no—
18#16840379C418yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519770—21no—
21C2×#14519764—21no—
22C2×#14519764C2211yescharacteristic
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519754—21no—
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16839788—24no—
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519706C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40#16839656—21no—
41#16839650—21no—
42#16839647—21no—
43#16839645—21no—
44#16839631C2211yescharacteristic
45#16839627C2211yescharacteristic
46#16839622C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—41no—
67C2×#11758194—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519776—22no—
71#14519776C2×C414yes—
72#14519770—28no—
73#14519764—28no—
74#14519764—22no—
75#14519764C2×C414yes—
76#14519758—28no—
77#14519756—22no—
78#14519756C2×C414yes—
79#14519754—28no—
80#14519742—22no—
81#14519742C2×C414yes—
82D4×Dic61—22no—
83D4×Dic61C2×C414yes—
84#14519736C2×C414yes—
85#14519736D414yes—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61D411yescharacteristic
102C2×C22⋊Dic61D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108#14519706—22no—
109#14519706—22no—
110#14519706—22no—
111#14519706—22no—
112#14519702—41no—
113#14519702—41no—
114#14519700—41no—
115#14519700—41no—
116#14519698—41no—
117#14519698—41no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×D4×C61—21no—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61—22no—
127C22×C8×C61—41no—
128C22×C8×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61C2×C414yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138#102×C61—41no—
139#102×C61—41no—
140#95×C61—21no—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—24no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—81no—
150C2×D4×C61—81no—
151C2×D4×C61C22×C412yes—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—24no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—81no—
169C22×Dic61—81no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—24no—
180C2×Dic122—81no—
181C2×Dic122—81no—
182C2×Dic122C22×C412yes—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—44no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61C22×C412yes—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—81no—
198C22⋊Dic61—24no—
199C22⋊Dic61—24no—
200C22⋊Dic61—24no—
201C22⋊Dic61—24no—
202C22⋊Dic61—81no—
203C22⋊Dic61C22⋊C414yes—
204C22⋊Dic61C22⋊C414yes—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61C22⋊C414yes—
211C4⋊Dic61C22⋊C414yes—
212C4⋊Dic61C22×C412yes—
213#11758196—24no—
214#11758196—24no—
215#11758196—24no—
216#11758196—81no—
217#11758196—81no—
218C4×Dic61—24no—
219C4×Dic61—81no—
220C4×Dic61—81no—
221C4×Dic61C22×C412yes—
222C4×Dic61C22×C412yes—
223C4×Dic61C2×D412yes—
224C4×Dic61C2×D412yes—
225#11758194—44no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—22no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61C2×C22⋊C412yes—
246C23×C61C22×D411yescharacteristic
247D4×C61—22no—
248D4×C61—22no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—84no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
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×C61—41no—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61H(5,𝔽2)11yescharacteristic
271C2×C4×C61H(5,𝔽2)11yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C2×C4×C612−1+411yescharacteristic
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—84no—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C2×C22⋊C412yes—
297C2×Dic61C2×C22⋊C412yes—
298C2×Dic61C2×C22⋊C412yes—
299Dic122—22no—
300Dic122—22no—
301Dic122—41no—
302Dic122—41no—
303Dic122—84no—
304C8×C61—41no—
305C8×C61—41no—
306#92418—41no—
307#92418—41no—
308#21896—611nomaximal, Sylow
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61C22×C22⋊C411yescharacteristic
324C22×C61#53711yescharacteristic
325C22×C61#53711yescharacteristic
326C22×C61#57611yescharacteristic
327C22×C61#57711yescharacteristic
328C22×C61#57711yescharacteristic
329C22×C61#57811yescharacteristic
330C4×C61—22no—
331C4×C61—42no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61#52011yescharacteristic
335C4×C61#52011yescharacteristic
336C4×C61#53511yescharacteristic
337C4×C61#53611yescharacteristic
338Dic61—22no—
339Dic61—22no—
340Dic61—22no—
341Dic61—22no—
342Dic61—42no—
343Dic61—42no—
344Dic61—81no—
345Dic61—81no—
346C2×#542—611no—
347C2×#424—611no—
348#2314—611no—
349#1988—611no—
350#1987—611no—
351#1983—611no—
352#1983—611no—
353#1895—611no—
354#1894—611no—
355#1893D6111yescharacteristic
356#1892—611no—
357#1805—611no—
358#1804—611no—
359#1803—611no—
360#1802—611no—
361C2×C61—42no—
362C2×C61—82no—
363C2×C61#231111yescharacteristic
364C2×C61#289711yescharacteristic
365C2×C61#289811yescharacteristic
366C2×C61#325711yescharacteristic
367C2×C61#325811yescharacteristic
368C2×C61#326211yescharacteristic
369C2×C61#326311yescharacteristic
370C22×M16—611no—
371C23×C8C2×D6111yescharacteristic
372#542—618no—
373#542—1224no—
374C2×C4⋊Q8—611no—
375C2×#126—1221no—
376C2×#124—611no—
377C2×#124—1221no—
378C2×#123—1221no—
379C2×C22⋊Q8—611no—
380C2×C22⋊Q8—1221no—
381C2×#121C2×D6111yescharacteristic
382C2×C4×Q8—611no—
383C2×C4×D4—611no—
384C2×#117—611no—
385#424—1224no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102C2×D6111yescharacteristic
397C2×#102C2×D6111yescharacteristic
398#388—1221no—
399#388—1221no—
400#387—1221no—
401#387—1221no—
402#384—611no—
403#382—611no—
404#380—611no—
405#380C2×D6111yescharacteristic
406C4×C4⋊C4—611no—
407C4×C4⋊C4—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340C2×D6111yescharacteristic
415#340C2×D6111yescharacteristic
416C61#2189611yescharacteristic, complemented, Sylow
417C22×Q8—611no—
418C22×Q8—1221no—
419C22×D4—21no—
420C22×D4C22×D6111yescharacteristic
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C2×M16—1222no—
424C2×M16—2441no—
425C2×M16—2441no—
426C22×C8—22no—
427C22×C8—41no—
428C22×C8—41no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8C22×D6111yescharacteristic
432C22×C8C22×D6111yescharacteristic
433C4⋊Q8—614no—
434C4⋊Q8—1222no—
435#126—1228no—
436#124—614no—
437#124—1222no—
438#124—1228no—
439#123—1228no—
440C22⋊Q8—614no—
441C22⋊Q8—1228no—
442C22⋊Q8—1222no—
443#121—22no—
444#121C4×D6114yes—
445C4×Q8—614no—
446C4×Q8—1222no—
447C4×D4—614no—
448C4×D4—1222no—
449#117—614no—
450#117—614no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C4⋊C4C22×D6111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—1221no—
476C2×C42—1221no—
477C2×C42—1221no—
478C4⋊C8—1222no—
479C4⋊C8—1222no—
480C4⋊C8—1222no—
481C4⋊C8—1222no—
482#103—2441no—
483#103—2441no—
484#103—2441no—
485#103—2441no—
486#102—41no—
487#102—41no—
488#102—2441no—
489#102—2441no—
490#95—21no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496C24—21no—
497C24D4×D6111yescharacteristic
498C2×Q8—612no—
499C2×Q8—1224no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—4881no—
506C2×Q8—4881no—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C2×C4×D6112yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—1224no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—4881no—
533C22×C4—4881no—
534C22×C4C2×C4×D6112yes—
535C22×C4D4×D6112yes—
536C22×C4D4×D6111yescharacteristic
537C22×C4C23×D6111yescharacteristic
538M16—2444no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—44no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—614no—
558C4⋊C4—614no—
559C4⋊C4—612no—
560C4⋊C4—1224no—
561C4⋊C4—1224no—
562C4⋊C4—1221no—
563C4⋊C4—1224no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—4881no—
569C4⋊C4—4881no—
570C4⋊C4C2×C4×D6112yes—
571C22⋊C4—24no—
572C22⋊C4—81no—
573C22⋊C4—614no—
574C22⋊C4—614no—
575C22⋊C4—1224no—
576C22⋊C4—1224no—
577C22⋊C4—1224no—
578C22⋊C4—1224no—
579C22⋊C4—4881no—
580C42—612no—
581C42—612no—
582C42—612no—
583C42—612no—
584C42—1224no—
585C42—4881no—
586C42—4881no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22⋊C4×D6112yes—
601C23C2×D4×D6111yescharacteristic
602Q8—1222no—
603Q8—1222no—
604Q8—4884no—
605Q8—2441no—
606Q8—2441no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—612no—
628C2×C4—612no—
629C2×C4—612no—
630C2×C4—612no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—4884no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4C22⋊C4×D6112yes—
653C2×C4C22×C4×D6111yescharacteristic
654C2×C4C2×D4×D6111yescharacteristic
655C2×C4#1451982211yescharacteristic
656C2×C4#1451982211yescharacteristic
657C2×C4#1451982411yescharacteristic
658C2×C4#1451982411yescharacteristic
659C8—41no—
660C8—41no—
661C8—2441no—
662C8—2441no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×C22⋊C4×D6111yescharacteristic
678C22#1684033911yescharacteristic
679C22#1684033911yescharacteristic
680C22#1684056311yescharacteristic
681C22#1684056811yescharacteristic
682C22#1684056911yescharacteristic
683C22#1684057611yescharacteristic
684C4—22no—
685C4—42no—
686C4—81no—
687C4—81no—
688C4—1222no—
689C4—1222no—
690C4—1222no—
691C4—1222no—
692C4—4881no—
693C4—4881no—
694C4—2442no—
695C4—2442no—
696C4#1684024111yescharacteristic
697C4#1684024111yescharacteristic
698C4#1684032711yescharacteristic
699C4#1684033411yescharacteristic
700C2—42no—
701C2—82no—
702C2#2144840611yescharacteristic
703C2#2145434011yescharacteristic
704C2#2145434811yescharacteristic
705C2#2145722311yescharacteristic
706C2#2145723811yescharacteristic
707C2#2145727411yescharacteristic
708C2#2145728311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#21896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839788C2semidirect
3. #21448426C2semidirect
4. #21446769C2semidirect
5. #21446765C2semidirect
6. #21446750C2semidirect
7. #21446750C2semidirect
9. #21446250C2semidirect
10. #21446242C2semidirect
11. #21445833C2semidirect
12. #21445827C2semidirect
13. #21445823C2semidirect
14. #21445817C2semidirect
18. #16840379C4semidirect
416. C61#21896semidirect

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168397882
#214484262
#214467692
#214467652
#214467502
#214462582
#214462502
#214462422
#214458332
#214458272
#214458232
#214458172
C61×#18932
#2189661