Finite Group Databasebeta

← #29723968

Subgroups — #29723968

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839926C211yesmaximal, characteristic
2C2×C4×#11758190C211yesmaximal, characteristic, complemented
3#21449344C211yesmaximal, characteristic, complemented
4#21448650C211yesmaximal, characteristic
5#21447361C211yesmaximal, characteristic, complemented
6#21447252C211yesmaximal, characteristic, complemented
7#21447142C211yesmaximal, characteristic, complemented
8#21447016C211yesmaximal, characteristic, complemented
9#21446495C211yesmaximal, characteristic, complemented
10#21446159C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446083C211yesmaximal, characteristic, complemented
13#21445820C211yesmaximal, characteristic, complemented
14#21445760C211yesmaximal, characteristic
15C61×#1923C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839926—24no—
24C4×#11758190—24no—
25C2×#14519709C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35#16839698—21no—
36#16839696—21no—
37#16839668C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839655—21no—
42#16839645—21no—
43#16839638—21no—
44#16839638—21no—
45#16839632C2211yescharacteristic
46#16839624—21no—
47#16839622C2211yescharacteristic
48#16839622C2211yescharacteristic
49#95×D61—21no—
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2311yescharacteristic
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×Dic244—22no—
75C2×Dic244—22no—
76C2×Dic244—41no—
77C2×#11758190—22no—
78C2×#11758190—22no—
79C2×#11758190D414yes—
80#14519756—22no—
81#14519756—41no—
82C4×Dic122—22no—
83C4×Dic122—41no—
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—41no—
87C4×D244—41no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104#14519709—22no—
105#14519709—41no—
106#14519702—22no—
107#14519702—22no—
108#14519702—22no—
109#14519702—41no—
110#14519702—41no—
111#14519699—22no—
112#14519699—22no—
113#14519699—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61—41no—
133C22⋊C8×C61—22no—
134C22⋊C8×C61—41no—
135C4×C8×C61—22no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61C2×D411yescharacteristic
139C23×D61—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×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—24no—
153C2×C22⋊D61—42no—
154C2×C22⋊D61—42no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162#11758222—44no—
163#11758222—44no—
164#11758222—44no—
165#11758222—44no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244C2×D412yes—
170C2×D244#4112yes—
171C2×D244#4112yes—
172C2×C4×D61—24no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122C2×D412yes—
192C2×Dic122#4112yes—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C2×D412yes—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—42no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214#11758198—42no—
215#11758198—42no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—81no—
228#11758196—42no—
229#11758196—42no—
230#11758196—81no—
231C4×Dic61—42no—
232Dic244—44no—
233#11758190—28no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61C22×D411yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61#13512yes—
267C2×C4×C61#13712yes—
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C22⋊D61—48no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
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—41no—
295C2×Dic61—41no—
296D244—22no—
297D244—22no—
298D244—22no—
299D244#12314yes—
300C4×D61—48no—
301C4×D61—84no—
302C4×D61—84no—
303Dic122—22no—
304Dic122—22no—
305Dic122—22no—
306Dic122—22no—
307Dic122—41no—
308Dic122—41no—
309Dic122—41no—
310Dic122—41no—
311C8×C61—22no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#24907—611nomaximal, Sylow
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61#52511yescharacteristic
324C22×C61D4211yescharacteristic
325C22×C61#54611yescharacteristic
326C22×C61C2×#13511yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57711yescharacteristic
329C22×C61#57711yescharacteristic
330C2×D61—24no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—42no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—41no—
342C4×C61C2×#12311yescharacteristic
343C4×C61#53811yescharacteristic
344C4×C61#54611yescharacteristic
345C4×C61#55111yescharacteristic
346Dic61—42no—
347Dic61—42no—
348Dic61—81no—
349Dic61—81no—
350Dic61—81no—
351Dic61—81no—
352Dic61—81no—
353C2×#452—611no—
354C2×C4×SD16—611no—
355#2423—611no—
356#2339—611no—
357#2096—611no—
358#2077—611no—
359#2056—611no—
360#2035—611no—
361#1933—611no—
362#1923D6111yescharacteristic, complemented
363#1878—611no—
364#1877—611no—
365#1864—611no—
366#1802—611no—
367#1788—611no—
368C2×C61—81no—
369C2×C61#241811yescharacteristic
370C2×C61#310711yescharacteristic
371C2×C61#312511yescharacteristic
372C2×C61#326611yescharacteristic
373C2×C61#328411yescharacteristic
374C2×C61#329611yescharacteristic
375C2×C61#333111yescharacteristic
376D61—44no—
377C22×#41—611no—
378C22×Q16—611no—
379C22×SD16—611no—
380C2×C22⋊Q8—611no—
381C2×C4×Q8—611no—
382C2×C4×D4—611no—
383C2×C4×D4—611no—
384#452—1224no—
385C4×SD16—1224no—
386C2×#106—611no—
387C2×#106—611no—
388C2×C4⋊C8C2×D6111yescharacteristic
389C2×#103—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×C22⋊C8C2×D6111yescharacteristic
398C2×C22⋊C8C2×D6111yescharacteristic
399C2×C4×C8C2×D6111yescharacteristic
400#399—1221no—
401#398—1221no—
402#391—611no—
403#391—611no—
404#391—611no—
405#389—611no—
406#388—1221no—
407#387—1221no—
408#386—1221no—
409#386—1221no—
410#384—611no—
411#381—1221no—
412#380—611no—
413#380—611no—
414C4×C22⋊C4C2×D6111yescharacteristic
415C2×#95—1221no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#336C2×D6111yescharacteristic
421#336C2×D6111yescharacteristic
422C61#2490711yescharacteristic, complemented, Sylow
423C2×#41—1222no—
424C2×#41—1222no—
425C2×#41—1222no—
426C2×#41—1222no—
427C2×#41—2441no—
428C2×#41—2441no—
429C22×Q8—611no—
430C22×Q8—611no—
431C22×D4—611no—
432C22×D4—1221no—
433C23×C4—1221no—
434C23×C4—1221no—
435C23×C4—1221no—
436C23×C4C22×D6111yescharacteristic
437C2×Q16—1222no—
438C2×Q16—1222no—
439C2×Q16—2441no—
440C2×SD16—614no—
441C2×SD16—1222no—
442C2×SD16—1222no—
443C22×C8C22×D6111yescharacteristic
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C22×C8C22×D6111yescharacteristic
447C22⋊Q8—1222no—
448C22⋊Q8—2441no—
449C4×Q8—1222no—
450C4×Q8—2441no—
451C4×D4—1222no—
452C4×D4—1222no—
453C4×D4—2441no—
454C4×D4—2441no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4D24411yescharacteristic
471C2×C22⋊C4D24411yescharacteristic
472C2×C42—1221no—
473C2×C42C22×D6111yescharacteristic
474C2×C42C22×D6111yescharacteristic
475#106—1222no—
476#106—2441no—
477C4⋊C8—41no—
478#103—1222no—
479#103—1222no—
480#103—1222no—
481#103—2441no—
482#103—2441no—
483#102—1222no—
484#102—1222no—
485#102—1222no—
486C22⋊C8—22no—
487C22⋊C8—41no—
488C4×C8—22no—
489#95—1221no—
490#95—1221no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95D24411yescharacteristic
499#95D24411yescharacteristic
500C24—1221no—
501C24C2×D24411yescharacteristic
502#41—2444no—
503#41—2444no—
504#41—2444no—
505#41—2444no—
506C2×Q8—612no—
507C2×Q8—612no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×Q8—1221no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—1221no—
518C2×D4—612no—
519C2×D4—612no—
520C2×D4—612no—
521C2×D4—1224no—
522C2×D4—1221no—
523C2×D4—1221no—
524C2×D4—1221no—
525C2×D4—2442no—
526C2×D4—2442no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
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×C4—2442no—
547C22×C4—2442no—
548C22×C4—2442no—
549C22×C4C2×D24411yescharacteristic
550C22×C4C2×D24411yescharacteristic
551C22×C4C2×D24411yescharacteristic
552C22×C4C2×D24411yescharacteristic
553C22×C4C2×D24411yescharacteristic
554C22×C4C23×D6111yescharacteristic
555Q16—2444no—
556SD16—1228no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8D4×D6112yes—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—4881no—
580C4⋊C4—4881no—
581C4⋊C4—2442no—
582C4⋊C4—2442no—
583C4⋊C4—2442no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—4881no—
587C22⋊C4—4881no—
588C22⋊C4—2442no—
589C22⋊C4—2442no—
590C22⋊C4—2442no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—2442no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—1222no—
604C23—1222no—
605C23—1222no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23—2441no—
610C23C22×D24411yescharacteristic
611Q8—1222no—
612Q8—1222no—
613Q8—1222no—
614Q8—1222no—
615Q8—2441no—
616Q8—2441no—
617Q8—2441no—
618Q8—2441no—
619D4—614no—
620D4—1222no—
621D4—1222no—
622D4—1222no—
623D4—2448no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—4884no—
644C2×C4—4884no—
645C2×C4—2448no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
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×C4—2441no—
664C2×C4—2441no—
665C2×C4#1451979912yes—
666C2×C4#1451981012yes—
667C2×C4C2×D4×D6111yescharacteristic
668C2×C4#41×D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4#41×D6111yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982311yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—1224no—
685C22—2442no—
686C22—2442no—
687C22—2442no—
688C22—2442no—
689C22—2442no—
690C22—2442no—
691C22#1684027411yescharacteristic
692C22D4×D24411yescharacteristic
693C22#1684040711yescharacteristic
694C22C2×#1451979911yescharacteristic
695C22C2×#1451981011yescharacteristic
696C22#1684057411yescharacteristic
697C22#1684057411yescharacteristic
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—4881no—
704C4—4881no—
705C4—4881no—
706C4—4881no—
707C4—4881no—
708C4—2442no—
709C4—2442no—
710C4#123×D6111yescharacteristic
711C4#1684034611yescharacteristic
712C4#1684040911yescharacteristic
713C4#1684043711yescharacteristic
714C2—81no—
715C2—2444no—
716C2#2144928611yescharacteristic
717C2#2145589111yescharacteristic
718C2#2145609811yescharacteristic
719C2#2145733411yescharacteristic
720C2#2145755111yescharacteristic
721C2#2145765611yescharacteristic
722C2#2145813611yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenter#1923D61
hypocenterC61#24907
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758190C2semidirect
3. #21449344C2semidirect
5. #21447361C2semidirect
6. #21447252C2semidirect
7. #21447142C2semidirect
8. #21447016C2semidirect
9. #21446495C2semidirect
10. #21446159C2semidirect
11. #21446152C2semidirect
12. #21446083C2semidirect
13. #21445820C2semidirect
15. C61×#1923C2semidirect
362. #1923D61semidirect
422. C61#24907semidirect

Maximal subgroups

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

subgroupindex
C2×#168399262
C2×C4×#117581902
#214493442
#214486502
#214473612
#214472522
#214471422
#214470162
#214464952
#214461592
#214461522
#214460832
#214458202
#214457602
C61×#19232
#2490761