Finite Group Databasebeta

← C2×#21446194 #29681510

Subgroups — C2×#21446194 #29681510

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519805C211yesmaximal, characteristic
2C2×#16840243C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic, complemented
4C2×#16839768C211yesmaximal, characteristic, complemented
5C2×#16839663C211yesmaximal, characteristic, complemented
6#21446194C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C2×C61×#343C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519805—24no—
12C2×#14519805—22no—
13C2×#14519805C418yescomplemented
14C2×#14519805C2214yes—
15C22×#11758190—21no—
16C22×D488—21no—
17#16840243—22no—
18#16840243—22no—
19#16840243—22no—
20#16840243C2214yescomplemented
21C2×#14519742—21no—
22C2×#14519739—21no—
23C2×C4×C22⋊D61—22no—
24C2×#14519736C2211yescharacteristic
25C2×#14519735—21no—
26C2×C4⋊C4×D61—21no—
27C22×#11758198—22no—
28C22×C4×Dic61C2211yescharacteristic
29C2×#14519703—24no—
30C2×#14519703C2214yescomplemented
31#16839768—22no—
32#16839768C2214yescomplemented
33C2×#14519699—21no—
34C2×#14519699—21no—
35#16839663—22no—
36#16839663C2214yescomplemented
37#16839523C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×C4⋊C4×C61C2211yescharacteristic
41C61×#343C2214yescomplemented
42C24×D61—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222C2×C414yes—
48C2×#11758222D414yes—
49C2×#11758222D412yes—
50C2×#11758222C2312yes—
51C22×Dic122D411yescharacteristic
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244—22no—
56C22×D244—21no—
57C22×D244—22no—
58C22×D244—21no—
59C22×D244—22no—
60C22×D244C2×C414yescomplemented
61C22×D244D411yescharacteristic
62C22×D244C2312yes—
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—22no—
67#14519805—216no—
68#14519805—28no—
69#14519805C2×C4116yescomplemented
70C2×#11758190—28no—
71C2×#11758190—24no—
72C2×D488—28no—
73C2×D488—24no—
74#14519742—24no—
75#14519742—24no—
76#14519739—24no—
77#14519739—24no—
78C4×C22⋊D61—28no—
79C4×C22⋊D61—28no—
80#14519736—21no—
81#14519736—21no—
82#14519736D412yes—
83#14519736C2312yes—
84#14519735—24no—
85#14519735—24no—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61D411yescharacteristic
88C2×#11758196—22no—
89C4⋊C4×D61—24no—
90C4⋊C4×D61—24no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—22no—
93C2×#11758198—28no—
94C2×#11758198—48no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2312yes—
101#14519703—28no—
102#14519699—24no—
103#14519699—24no—
104C23×C4×C61D412yes—
105C23×C4×C61C2311yescharacteristic
106C2×M16×C61—22no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—22no—
110C2×M16×C61—22no—
111C2×M16×C61C2×C414yescomplemented
112C2×M16×C61C2312yes—
113C2×M16×C61C2312yes—
114C22×C8×C61—21no—
115C22×C8×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61D412yes—
121C2×C4⋊C4×C61C2312yes—
122C24×C61C2×D411yescharacteristic
123C23×D61—21no—
124C23×D61—24no—
125C23×D61—22no—
126C23×D61—44no—
127C23×D61—44no—
128C23×D61—41no—
129C23×D61—41no—
130C23×D61—42no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—44no—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2×D414yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61#4112yes—
143C22×C4×C61#4112yes—
144C22×C4×C61C2411yescharacteristic
145C2×C22⋊D61—24no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—24no—
148C2×C22⋊D61—22no—
149C22×Dic61—21no—
150C22×Dic61—24no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156#11758222—24no—
157#11758222—24no—
158#11758222—24no—
159#11758222—24no—
160#11758222—24no—
161#11758222—22no—
162#11758222—22no—
163#11758222C22⋊C418yescomplemented
164#11758222C22×C414yes—
165#11758222C2×D414yes—
166C2×D244—21no—
167C2×D244—22no—
168C2×D244—24no—
169C2×D244—24no—
170C2×D244—24no—
171C2×D244—24no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—24no—
177C2×D244—22no—
178C2×D244—41no—
179C2×D244—41no—
180C2×D244—42no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244—42no—
184C2×D244—42no—
185C2×D244C22⋊C414yescomplemented
186C2×D244C22×C414yescomplemented
187C2×D244C2×D412yes—
188C2×C4×D61—24no—
189C2×C4×D61—22no—
190C2×C4×D61—24no—
191C2×C4×D61—22no—
192C2×C4×D61—28no—
193C2×C4×D61—84no—
194C2×Dic122—21no—
195C2×Dic122—22no—
196C2×Dic122C22⋊C414yescomplemented
197C2×Dic122C2×D412yes—
198M16×C61—24no—
199M16×C61—22no—
200M16×C61—22no—
201M16×C61—22no—
202M16×C61—42no—
203M16×C61C22×C414yescomplemented
204C2×C8×C61—24no—
205C2×C8×C61—22no—
206C2×C8×C61—22no—
207C2×C8×C61—42no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—22no—
211C4⋊C4×C61—22no—
212C22⋊Dic61—22no—
213C22⋊Dic61—22no—
214#11758198—28no—
215#11758198—416no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61C2×D412yes—
219C4⋊Dic61C2×D412yes—
220#11758196—28no—
221C4×Dic61—28no—
222C4×Dic61—22no—
223C4×Dic61—22no—
224C4×Dic61—22no—
225C4×Dic61—22no—
226C4×Dic61—42no—
227D488—216no—
228#11758190—216no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61C4×D412yes—
232C23×C61#12011yescharacteristic
233C23×C61#12011yescharacteristic
234C23×C61#12112yes—
235C23×C61C22×D411yescharacteristic
236C22×D61—22no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—44no—
242C22×D61—416no—
243C22×D61—44no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—44no—
247C22×D61—44no—
248C22×D61—88no—
249C22×D61—82no—
250C22×D61—82no—
251C22×D61—82no—
252C22×D61—82no—
253C2×C4×C61—24no—
254C2×C4×C61—44no—
255C2×C4×C61—44no—
256C2×C4×C61—82no—
257C2×C4×C61C2×C22⋊C412yes—
258C2×C4×C61C2×C22⋊C412yes—
259C2×C4×C61C4×D412yes—
260C2×C4×C61C4×D412yes—
261C2×C4×C61C4×D412yes—
262C2×C4×C61#12011yescharacteristic
263C2×C4×C61#12011yescharacteristic
264C2×C4×C61#12112yes—
265C2×C4×C61#12112yes—
266C2×C4×C61#12112yes—
267C2×C4×C61#12312yes—
268C2×C4×C61#12312yes—
269C2×C4×C61C23×C411yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C22⋊D61—24no—
276C22⋊D61—24no—
277C22⋊D61—28no—
278C2×Dic61—22no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—48no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288D244—24no—
289D244—24no—
290D244—22no—
291D244—24no—
292D244—42no—
293D244—42no—
294D244—44no—
295D244—44no—
296D244C2×C22⋊C414yescomplemented
297C4×D61—24no—
298C4×D61—24no—
299C4×D61—28no—
300C4×D61—88no—
301Dic122—22no—
302Dic122—24no—
303Dic122C2×C22⋊C414yescomplemented
304C8×C61—24no—
305C8×C61—42no—
306C2×#1883—611nomaximal, Sylow
307C22×C61—24no—
308C22×C61—24no—
309C22×C61—21no—
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61#38612yes—
314C22×C61#38612yes—
315C22×C61#45312yes—
316C22×C61#45412yes—
317C22×C61C2×C4×D411yescharacteristic
318C22×C61C2×#12011yescharacteristic
319C22×C61C2×#12111yescharacteristic
320C2×D61—24no—
321C2×D61—48no—
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—48no—
325C2×D61—44no—
326C2×D61—84no—
327C2×D61—88no—
328C2×D61—88no—
329C2×D61—82no—
330C2×D61—82no—
331C4×C61—44no—
332C4×C61#38612yes—
333C4×C61#38612yes—
334C4×C61C22×C22⋊C411yescharacteristic
335C4×C61C2×C4×D411yescharacteristic
336C4×C61C2×#12111yescharacteristic
337C4×C61C2×#12311yescharacteristic
338Dic61—24no—
339Dic61—44no—
340Dic61—42no—
341Dic61—42no—
342C22×AGL(1,ℤ/8)—611no—
343C2×#520—611no—
344C22×#104—611no—
345C2×#418—611no—
346C2×#390—611no—
347#1883—618no—
348C2×#343D6111yescharacteristic, complemented
349C2×#339—611no—
350C2×C61—21no—
351C2×C61—21no—
352C2×C61—22no—
353C2×C61#188314yescomplemented
354C2×C61C2×#38611yescharacteristic
355C2×C61C2×#45311yescharacteristic
356C2×C61C2×#45411yescharacteristic
357D61—44no—
358D61—84no—
359C22×#41—611no—
360C23×D4—611no—
361C2×AGL(1,ℤ/8)—618no—
362C2×AGL(1,ℤ/8)—614no—
363C2×AGL(1,ℤ/8)—1222no—
364C2×AGL(1,ℤ/8)—1224no—
365C22×SD16—1221no—
366C22×D8—1221no—
367C22×M16C2×D6111yescharacteristic
368C22×M16C2×D6111yescharacteristic
369#520—614no—
370#520—1222no—
371#520—1222no—
372#520—1222no—
373C2×C4×Q8—1221no—
374C2×C4×D4—1221no—
375C2×C4×D4—1222no—
376C2×#117—611no—
377C2×#117—1221no—
378C22×C4⋊C4—1221no—
379C22×C4⋊C4C2×D6111yescharacteristic
380C22×C22⋊C4—1222no—
381C22×C42—611no—
382C2×#104—614no—
383C2×#104—1224no—
384#418—614no—
385#418—1222no—
386C2×#102—1221no—
387C2×#102—1221no—
388#390—614no—
389#390—1222no—
390#343C2×D6114yescomplemented
391#339—614no—
392C61C2×#188311yescharacteristic, complemented, Sylow
393C25—1221no—
394C2×#41—614no—
395C2×#41—612no—
396C2×#41—614no—
397C2×#41—612no—
398C2×#41—1221no—
399C2×#41—1222no—
400C2×#41—1221no—
401C2×#41—1222no—
402C22×Q8—611no—
403C22×D4—614no—
404C22×D4—611no—
405C22×D4—612no—
406C22×D4—1221no—
407C22×D4—1221no—
408C22×D4—1222no—
409C22×D4—1221no—
410C22×D4—1221no—
411C22×D4—1222no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1222no—
415C23×C4—1222no—
416C23×C4—1221no—
417C23×C4—1221no—
418C23×C4D24412yes—
419C23×C4C22×D6111yescharacteristic
420AGL(1,ℤ/8)—6116no—
421AGL(1,ℤ/8)—1228no—
422AGL(1,ℤ/8)—12216no—
423C2×SD16—1224no—
424C2×SD16—1228no—
425C2×D8—1224no—
426C2×D8—1228no—
427C2×M16—21no—
428C2×M16—22no—
429C2×M16—21no—
430C2×M16—22no—
431C2×M16—22no—
432C2×M16C4×D6114yescomplemented
433C2×M16C22×D6112yes—
434C2×M16C22×D6112yes—
435C22×C8—21no—
436C22×C8—21no—
437C4×Q8—1224no—
438C4×Q8—1224no—
439C4×D4—1224no—
440C4×D4—1224no—
441C4×D4—1228no—
442C4×D4—1228no—
443#117—612no—
444#117—612no—
445#117—1224no—
446#117—1224no—
447#117—1221no—
448#117—1221no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—1224no—
456C2×C4⋊C4—1224no—
457C2×C4⋊C4—1222no—
458C2×C4⋊C4D24412yes—
459C2×C4⋊C4C22×D6112yes—
460C2×C22⋊C4—1222no—
461C2×C22⋊C4—1221no—
462C2×C22⋊C4—1228no—
463C2×C22⋊C4—2448no—
464C2×C42—612no—
465C2×C42—1222no—
466C2×C42—1221no—
467C2×C42—1222no—
468C2×C42—1222no—
469C2×C42—1221no—
470#104—1228no—
471#102—1224no—
472#102—1224no—
473C24—1221no—
474C24—1222no—
475C24—1224no—
476C24—2444no—
477C24—2444no—
478C24—2441no—
479C24—2441no—
480C24—2442no—
481C24C2×D24411yescharacteristic
482#41—614no—
483#41—614no—
484#41—618no—
485#41—1222no—
486#41—1222no—
487#41—1224no—
488#41—1224no—
489#41—1224no—
490#41—1224no—
491#41—1224no—
492C2×Q8—612no—
493C2×Q8—614no—
494C2×Q8—1221no—
495C2×Q8—1222no—
496C2×D4—614no—
497C2×D4—612no—
498C2×D4—614no—
499C2×D4—1222no—
500C2×D4—1224no—
501C2×D4—1222no—
502C2×D4—1224no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1224no—
509C2×D4—1224no—
510C2×D4—1224no—
511C2×D4—1224no—
512C2×D4—1224no—
513C2×D4—1221no—
514C2×D4—1222no—
515C2×D4—2441no—
516C2×D4—2441no—
517C2×D4—2442no—
518C2×D4—2442no—
519C2×D4—2442no—
520C2×D4—2442no—
521C2×D4—2442no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—44no—
525C22×C4—1228no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—1224no—
529C22×C4—1222no—
530C22×C4—1224no—
531C22×C4—1224no—
532C22×C4—1222no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—4884no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4C2×C4×D6112yes—
539C22×C4C2×D24414yes—
540C22×C4C2×D24411yescharacteristic
541C22×C4#1175822212yes—
542C22×C4D4×D6111yescharacteristic
543C22×C4D4×D6111yescharacteristic
544C22×C4D4×D6112yes—
545C22×C4D4×D6111yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4#1175822612yes—
548C22×C4C23×D6111yescharacteristic
549SD16—12216no—
550D8—12216no—
551M16—22no—
552M16—24no—
553M16—22no—
554M16—22no—
555M16—42no—
556M16C2×C4×D6114yescomplemented
557C2×C8—22no—
558C2×C8—24no—
559C2×C8—22no—
560C2×C8—42no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—612no—
566C4⋊C4—612no—
567C4⋊C4—1228no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C22⋊C4—1228no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—24416no—
574C42—1228no—
575C42—1222no—
576C42—1222no—
577C42—1222no—
578C42—1222no—
579C42—2442no—
580C23—22no—
581C23—22no—
582C23—1222no—
583C23—1224no—
584C23—1224no—
585C23—4882no—
586C23—4888no—
587C23—4882no—
588C23—4882no—
589C23—4882no—
590C23—2444no—
591C23—24416no—
592C23—2444no—
593C23—2442no—
594C23—2442no—
595C23—2444no—
596C23—2444no—
597C23—2442no—
598C23—2442no—
599C23C4×D24412yes—
600C23#1451974711yescharacteristic
601C23#1451974711yescharacteristic
602C23#1451975212yes—
603C23C22×D24411yescharacteristic
604Q8—614no—
605Q8—1222no—
606Q8—1224no—
607D4—614no—
608D4—1224no—
609D4—1224no—
610D4—1228no—
611D4—1224no—
612D4—1224no—
613D4—1222no—
614D4—1224no—
615D4—2442no—
616D4—2442no—
617D4—2444no—
618D4—2444no—
619C2×C4—24no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—82no—
623C2×C4—1222no—
624C2×C4—1224no—
625C2×C4—1224no—
626C2×C4—1224no—
627C2×C4—1228no—
628C2×C4—1224no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—4888no—
632C2×C4—2448no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4C22⋊C4×D6112yes—
638C2×C4C22⋊C4×D6112yes—
639C2×C4#1451973912yes—
640C2×C4#1451973912yes—
641C2×C4C4×D24412yes—
642C2×C4#1451974711yescharacteristic
643C2×C4#1451974711yescharacteristic
644C2×C4#1451975012yes—
645C2×C4#1451975012yes—
646C2×C4#1451975212yes—
647C2×C4#1451976212yes—
648C2×C4#1451976212yes—
649C2×C4C22×C4×D6111yescharacteristic
650C2×C4C2×D4×D6111yescharacteristic
651C2×C4C2×D4×D6111yescharacteristic
652C2×C4C2×D4×D6111yescharacteristic
653C2×C4C2×#1175822211yescharacteristic
654C2×C4C2×#1175822611yescharacteristic
655C8—24no—
656C8—42no—
657C22—21no—
658C22—21no—
659C22—24no—
660C22—24no—
661C22—21no—
662C22—21no—
663C22—1224no—
664C22—4884no—
665C22—4888no—
666C22—4882no—
667C22—4888no—
668C22—4882no—
669C22—2448no—
670C22—2444no—
671C22—2442no—
672C22—2448no—
673C22—2442no—
674C22#1683964012yes—
675C22#1683964012yes—
676C22#1683993212yes—
677C22#1683993712yes—
678C22C2×C4×D24411yescharacteristic
679C22C2×#1451974711yescharacteristic
680C22C2×#1451975211yescharacteristic
681C4—44no—
682C4—1224no—
683C4—2444no—
684C4—2442no—
685C4—2442no—
686C4#1683964012yes—
687C4#1683964012yes—
688C4C2×C22⋊C4×D6111yescharacteristic
689C4C2×#1451973911yescharacteristic
690C4C2×#1451975011yescharacteristic
691C4C2×#1451976211yescharacteristic
692C2—21no—
693C2—22no—
694C2—21no—
695C2—4884no—
696C2—2444no—
697C2#2144619414yesdirect product factor
698C2C2×#1683964011yescharacteristic
699C2C2×#1683993211yescharacteristic
700C2C2×#1683993711yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61#120
prime radicalC22×#14519805C2
cosocleC22×C4×C61C24
hypercenterC2×#343D61
hypocenterC61C2×#1883
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C2×#16840243C2semidirect
3. C22×#14519703C2semidirect
4. C2×#16839768C2semidirect
5. C2×#16839663C2semidirect
6. #21446194C2direct (N × H)
7. C2×#16839523C2semidirect
8. C2×C61×#343C2semidirect
13. C2×#14519805C4semidirect
20. #16840243C22semidirect
30. C2×#14519703C22semidirect
32. #16839768C22semidirect
36. #16839663C22semidirect
37. #16839523C22semidirect
41. C61×#343C22semidirect
60. C22×D244C2×C4semidirect
69. #14519805C2×C4semidirect
111. C2×M16×C61C2×C4semidirect
163. #11758222C22⋊C4semidirect
185. C2×D244C22⋊C4semidirect
186. C2×D244C22×C4semidirect
196. C2×Dic122C22⋊C4semidirect
203. M16×C61C22×C4semidirect
296. D244C2×C22⋊C4semidirect
303. Dic122C2×C22⋊C4semidirect
348. C2×#343D61semidirect
353. C2×C61#1883semidirect
390. #343C2×D61semidirect
392. C61C2×#1883semidirect
432. C2×M16C4×D61semidirect
556. M16C2×C4×D61semidirect
697. C2#21446194direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198052
C2×#168402432
C22×#145197032
C2×#168397682
C2×#168396632
#214461942
C2×#168395232
C2×C61×#3432
C2×#188361