Finite Group Databasebeta

← C2×#80960 #11675671

Subgroups — C2×#80960 #11675671

Order 768.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5722C211yesmaximal, characteristic, complemented
2C2×#5539C211yesmaximal, characteristic
3C2×C3×#474C211yesmaximal, characteristic
4C2×#5081C211yesmaximal, characteristic, complemented
5C2×#5018C211yesmaximal, characteristic
6#80960C2116yesmaximal, direct product factor
7C2×#4877C211yesmaximal, characteristic, complemented
8C2×#4875C211yesmaximal, characteristic, complemented
9C2×#4876C211yesmaximal, characteristic, complemented
10C2×#4874C211yesmaximal, characteristic, complemented
11C2×#4829C211yesmaximal, characteristic, complemented
12C2×#4828C211yesmaximal, characteristic, complemented
13C2×#4761C211yesmaximal, characteristic
14C2×#4759C211yesmaximal, characteristic
15C2×#4757C211yesmaximal, characteristic
16C2×#4758C211yesmaximal, characteristic
17C2×#3385—31nomaximal, Sylow
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#944—21no—
21C2×#944—21no—
22C2×D4×Dic3C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×#924—21no—
26C22×Dic3⋊C4—21no—
27#5722—24no—
28#5722C2218yescomplemented
29#5539—24no—
30#5539C2218yes—
31C2×#890C2211yescharacteristic
32C2×#888—21no—
33C2×#888C2211yescharacteristic
34C2×#888C2211yescharacteristic
35C2×#888C2211yescharacteristic
36C2×#887—21no—
37C2×#887C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×#878—21no—
40C2×#878—21no—
41C2×#870C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C3×#474C2218yes—
45C2×C3×#107C2211yescharacteristic
46C2×C3×#107C2211yescharacteristic
47C2×C3×C4⋊C8C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#818C2211yescharacteristic
52C2×#817C2211yescharacteristic
53C2×#816C2211yescharacteristic
54C2×#816C2211yescharacteristic
55C2×#815C2211yescharacteristic
56C2×Dic3⋊C8C2211yescharacteristic
57C2×Dic3⋊C8C2211yescharacteristic
58C2×C8×Dic3C2211yescharacteristic
59#5081C2218yescomplemented
60#5018C2218yes—
61C2×#810C2211yescharacteristic
62C2×#808C2211yescharacteristic
63C2×#808C2211yescharacteristic
64C2×#807C2211yescharacteristic
65C2×#807C2211yescharacteristic
66C2×#807C2211yescharacteristic
67C2×#803C2211yescharacteristic
68#4877C2218yescomplemented
69#4876C2218yescomplemented
70#4875C2218yescomplemented
71#4874C2218yescomplemented
72#4829C2218yescomplemented
73#4828C2218yescomplemented
74#4761C2218yes—
75#4759C2218yes—
76#4758C2218yes—
77#4757C2218yes—
78C2×Q82—31no—
79C2×#554—31no—
80#3385—316no—
81C2×#501—31no—
82C2×#501—31no—
83C2×#500—31no—
84C2×#479—31no—
85C2×#479—31no—
86C2×#477—31no—
87C2×#476—31no—
88C2×#474—31no—
89C2×#474D311yescharacteristic
90C2×#446—31no—
91C2×#440—31no—
92C2×#440—31no—
93C2×C4×SD16—31no—
94C22×C3×Q8—21no—
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×Dic3—21no—
98C23×Dic3—21no—
99C22×Dic6—21no—
100C22×Dic6—21no—
101C22×Dic6—21no—
102C22×Dic6D411yescharacteristic
103C22×Dic6C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8C2314yes—
108C3×C4×D4—22no—
109C3×C4×D4C2314yes—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117C2×#217—21no—
118#944—28no—
119#944—28no—
120D4×Dic3—22no—
121D4×Dic3—22no—
122D4×Dic3C2314yes—
123D4×Dic3C2314yes—
124C2×#214Q818yescomplemented
125C2×#214C2314yes—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—28no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—28no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×Dic3⋊C4D411yescharacteristic
144C2×C4×Dic3—21no—
145C2×C4×Dic3—21no—
146C2×C4×Dic3—21no—
147C2×C4×Dic3C2311yescharacteristic
148C2×C4×Dic3C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151#890—22no—
152#890C2314yes—
153#888—28no—
154#888—22no—
155#888—22no—
156#888—22no—
157#888C2314yes—
158#888C2314yes—
159#888C2314yes—
160#887—28no—
161#887—22no—
162#887—22no—
163#887C2314yes—
164#887C2314yes—
165#878—28no—
166#878—28no—
167#870—22no—
168#870C2314yes—
169C4×Dic6—22no—
170C4×Dic6D414yes—
171C4×Dic6C2314yes—
172C4×Dic6C2314yes—
173C3×#107C2314yes—
174C3×#107C2314yes—
175C3×C4⋊C8C2314yes—
176C3×#102C2314yes—
177C3×#102C2314yes—
178#832C2314yes—
179#818C2314yes—
180#817C2314yes—
181#816C2314yes—
182#816C2314yes—
183#815C2314yes—
184Dic3⋊C8C2314yes—
185Dic3⋊C8C2314yes—
186C8×Dic3C2314yes—
187#810C2314yes—
188#808C2314yes—
189#808C2314yes—
190#807C2314yes—
191#807C2314yes—
192#807C2314yes—
193#803C2314yes—
194C22×SD16—31no—
195Q82—38no—
196Q82—64no—
197#554—38no—
198#554—64no—
199C2×C4⋊Q8—31no—
200C2×C4⋊Q8—31no—
201C2×C4⋊Q8—31no—
202C2×C4⋊Q8—61no—
203C2×C4⋊Q8—61no—
204C2×C4⋊Q8—61no—
205C2×C4⋊Q8C2×D311yescharacteristic
206C2×#125—31no—
207C2×#125—31no—
208C2×C22⋊Q8—61no—
209C2×C22⋊Q8—61no—
210C2×C22⋊Q8—61no—
211C2×C4×Q8—31no—
212C2×C4×Q8—31no—
213C2×C4×Q8—31no—
214C2×C4×Q8—31no—
215C2×C4×Q8—61no—
216C2×C4×D4—31no—
217C2×C4×D4—31no—
218C2×C4×D4C2×D311yescharacteristic
219C22×C4⋊C4—61no—
220#501—38no—
221#501—38no—
222#500—38no—
223#479—38no—
224#479—38no—
225#477—38no—
226#476—38no—
227#474—38no—
228#474C2×D318yes—
229#446—38no—
230#440—38no—
231#440—38no—
232C4×SD16—38no—
233C2×#107—31no—
234C2×#107—31no—
235C2×#107—31no—
236C2×#107—31no—
237C2×#107C2×D311yescharacteristic
238C2×#107C2×D311yescharacteristic
239C2×#106—31no—
240C2×#106—31no—
241C2×#106—31no—
242C2×C4⋊C8—31no—
243C2×C4⋊C8—31no—
244C2×C4⋊C8C2×D311yescharacteristic
245C2×#103—31no—
246C2×#103—31no—
247C2×#103—31no—
248C2×#102—31no—
249C2×#102C2×D311yescharacteristic
250C2×#102C2×D311yescharacteristic
251C2×#97—31no—
252C2×#97—31no—
253C2×C4×C8—31no—
254C24×C3—21no—
255C2×C3×Q8—24no—
256C2×C3×Q8—82no—
257C2×C3×D4—21no—
258C2×C3×D4—22no—
259C2×C3×D4C2×Q814yes—
260C2×C3×D4C2412yes—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—24no—
265C22×C3×C4—82no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—24no—
274C22×Dic3—24no—
275C22×Dic3—44no—
276C22×Dic3—82no—
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C2×Dic6—21no—
282C2×Dic6—22no—
283C2×Dic6—24no—
284C2×Dic6—24no—
285C2×Dic6—24no—
286C2×Dic6—24no—
287C2×Dic6—82no—
288C2×Dic6—82no—
289C2×Dic6—82no—
290C2×Dic6C2×D414yes—
291C2×Dic6C2×Q814yes—
292C2×Dic6C2412yes—
293C2×C3×C8—22no—
294C2×C3×C8—22no—
295C2×C3×C8C2412yes—
296C2×C3×C8C2412yes—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C2412yes—
302C3×C4⋊C4C2412yes—
303C3×C4⋊C4C2412yes—
304C3×C22⋊C4—24no—
305C3×C42C2×D412yes—
306C3×C42C2412yes—
307#217—24no—
308#217—24no—
309#214C2×Q8116yescomplemented
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—24no—
314C4⋊Dic3C2×D414yes—
315C4⋊Dic3C2412yes—
316C4⋊Dic3C2412yes—
317C4⋊Dic3C2412yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—24no—
325Dic3⋊C4—24no—
326Dic3⋊C4—24no—
327Dic3⋊C4C2×D414yes—
328Dic3⋊C4C2×D414yes—
329C4×Dic3—24no—
330C4×Dic3—24no—
331C4×Dic3—24no—
332C4×Dic3C2×D412yes—
333C4×Dic3C2×D412yes—
334C4×Dic3C2412yes—
335C4×Dic3C2412yes—
336C2×C3⋊C8—22no—
337C2×C3⋊C8C2×Q814yes—
338C2×C3⋊C8C2412yes—
339C2×C3⋊C8C2412yes—
340C22×Q8—21no—
341C22×Q8—31no—
342C22×Q8—31no—
343C22×Q8—61no—
344C22×Q8—61no—
345C22×Q8—61no—
346C22×D4C22×D311yescharacteristic
347C23×C4—21no—
348C23×C4—61no—
349C23×C4—61no—
350C2×SD16—38no—
351C2×SD16—34no—
352C22×C8—31no—
353C22×C8—31no—
354C22×C8C22×D311yescharacteristic
355C22×C8C22×D311yescharacteristic
356C4⋊Q8—22no—
357C4⋊Q8—34no—
358C4⋊Q8—34no—
359C4⋊Q8—34no—
360C4⋊Q8—62no—
361C4⋊Q8—62no—
362C4⋊Q8—62no—
363C4⋊Q8—68no—
364C4⋊Q8—68no—
365C4⋊Q8—68no—
366C4⋊Q8C22×D314yes—
367#125—34no—
368#125—34no—
369#125—62no—
370#125—62no—
371C22⋊Q8—68no—
372C22⋊Q8—68no—
373C22⋊Q8—68no—
374C4×Q8—34no—
375C4×Q8—34no—
376C4×Q8—34no—
377C4×Q8—34no—
378C4×Q8—34no—
379C4×Q8—62no—
380C4×Q8—62no—
381C4×Q8—68no—
382C4×Q8—62no—
383C4×D4—22no—
384C4×D4—34no—
385C4×D4—34no—
386C4×D4—62no—
387C4×D4—62no—
388C4×D4C22×D314yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—68no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—61no—
416C2×C42—61no—
417C2×C42—61no—
418C2×C42C22×D311yescharacteristic
419#107—34no—
420#107—34no—
421#107—34no—
422#107—34no—
423#107C22×D314yes—
424#107C22×D314yes—
425#106—34no—
426#106—34no—
427#106—34no—
428C4⋊C8—34no—
429C4⋊C8—34no—
430C4⋊C8C22×D314yes—
431#103—34no—
432#103—34no—
433#103—34no—
434#102—34no—
435#102C22×D314yes—
436#102C22×D314yes—
437#97—34no—
438#97—34no—
439C4×C8—34no—
440C23×C3—24no—
441C23×C3—22no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3C22×D411yescharacteristic
445C3×Q8—84no—
446C3×D4—24no—
447C3×D4—22no—
448C3×D4C22×Q814yes—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—84no—
458C2×C3×C4C22×D412yes—
459C2×C3×C4C22×D412yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×Q812yes—
462C2×C3×C42−1+412yes—
463C2×C3×C4C2511yescharacteristic
464C2×Dic3—24no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—48no—
476C2×Dic3—84no—
477C2×Dic3#13714yes—
478C2×Dic3C22×D412yes—
479C2×Dic3C22×D412yes—
480C2×Dic3C22×D412yes—
481C2×Dic3C22×D412yes—
482Dic6—24no—
483Dic6—22no—
484Dic6—28no—
485Dic6—84no—
486Dic6—84no—
487Dic6—84no—
488Dic6C22×Q814yes—
489C3×C8—22no—
490C3×C8—22no—
491C3⋊C8—22no—
492C3⋊C8C22×Q814yes—
493C24—21no—
494C2×Q8—24no—
495C2×Q8—34no—
496C2×Q8—34no—
497C2×Q8—32no—
498C2×Q8—64no—
499C2×Q8—64no—
500C2×Q8—64no—
501C2×Q8—64no—
502C2×Q8—61no—
503C2×Q8—62no—
504C2×Q8—82no—
505C2×Q8—242no—
506C2×Q8—242no—
507C2×Q8—242no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4D3×Q814yes—
511C2×D4C23×D312yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—64no—
521C22×C4—64no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—82no—
527C22×C4—124no—
528C22×C4—242no—
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4C23×D311yescharacteristic
532SD16—316no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—34no—
536C2×C8—32no—
537C2×C8—32no—
538C2×C8—62no—
539C2×C8C23×D312yes—
540C2×C8C23×D312yes—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—34no—
548C4⋊C4—32no—
549C4⋊C4—32no—
550C4⋊C4—32no—
551C4⋊C4—64no—
552C4⋊C4—64no—
553C4⋊C4—64no—
554C4⋊C4—64no—
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4C23×D312yes—
565C4⋊C4C23×D312yes—
566C4⋊C4C23×D312yes—
567C22⋊C4—24no—
568C22⋊C4—64no—
569C22⋊C4—64no—
570C42—32no—
571C42—32no—
572C42—32no—
573C42—32no—
574C42—64no—
575C42—64no—
576C42—64no—
577C42D3×D412yes—
578C42C23×D312yes—
579C22×C3—24no—
580C22×C3—48no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3D4×Q812yes—
584C22×C3C2×#13712yes—
585C22×C3#57612yes—
586C22×C3C23×D411yescharacteristic
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—42no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4D4×Q812yes—
593C3×C4C23×Q811yescharacteristic
594C3×C4C2×2−1+411yescharacteristic
595Dic3—24no—
596Dic3—22no—
597Dic3—22no—
598Dic3—22no—
599Dic3—42no—
600Dic3—42no—
601Dic3—42no—
602Dic3C2×#13714yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C2×D3×D411yescharacteristic
608Q8—34no—
609Q8—68no—
610Q8—64no—
611Q8—62no—
612Q8—84no—
613Q8—244no—
614Q8—244no—
615Q8—244no—
616D4—24no—
617D4—22no—
618D4C2×D3×Q814yes—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—32no—
625C2×C4—34no—
626C2×C4—32no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—64no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—84no—
641C2×C4—128no—
642C2×C4—122no—
643C2×C4—122no—
644C2×C4—122no—
645C2×C4—244no—
646C2×C4C2×D3×D412yes—
647C2×C4C2×D3×D412yes—
648C2×C4C2×D3×D411yescharacteristic
649C2×C4C2×D3×Q812yes—
650C2×C4#101012yes—
651C2×C4C24×D311yescharacteristic
652C8—22no—
653C8—22no—
654C8—34no—
655C8—62no—
656C2×C3—44no—
657C2×C3#338514yescomplemented
658C2×C3C2×D4×Q811yescharacteristic
659C2×C3C22×#13711yescharacteristic
660C2×C3C2×#57611yescharacteristic
661C22—24no—
662C22—48no—
663C22—42no—
664C22—42no—
665C22#563212yes—
666C22#575712yes—
667C22D3×#13712yes—
668C22C22×D3×D411yescharacteristic
669C4—22no—
670C4—22no—
671C4—34no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—62no—
676C4—62no—
677C4—62no—
678C4—64no—
679C4—122no—
680C4—122no—
681C4—122no—
682C4#563212yes—
683C4C22×D3×Q811yescharacteristic
684C4C2×#101011yescharacteristic
685C3C2×#338511yescharacteristic, complemented, Sylow
686C2—44no—
687C2#8096014yesdirect product factor
688C2C2×#563211yescharacteristic
689C2C2×#575711yescharacteristic
690C2C2×D3×#13711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#474C2
socleC23×C3C22×D4
prime radicalC22×C3×D4C23
hypercenterC2×#474D3
hypocenterC3C2×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#5722C2semidirect
4. C2×#5081C2semidirect
6. #80960C2direct (N × H)
7. C2×#4877C2semidirect
8. C2×#4875C2semidirect
9. C2×#4876C2semidirect
10. C2×#4874C2semidirect
11. C2×#4829C2semidirect
12. C2×#4828C2semidirect
28. #5722C22semidirect
59. #5081C22semidirect
68. #4877C22semidirect
69. #4876C22semidirect
70. #4875C22semidirect
71. #4874C22semidirect
72. #4829C22semidirect
73. #4828C22semidirect
124. C2×#214Q8semidirect
309. #214C2×Q8semidirect
657. C2×C3#3385semidirect
685. C3C2×#3385semidirect
687. C2#80960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#57222
C2×#55392
C2×C3×#4742
C2×#50812
C2×#50182
#809602
C2×#48772
C2×#48752
C2×#48762
C2×#48742
C2×#48292
C2×#48282
C2×#47612
C2×#47592
C2×#47572
C2×#47582
C2×#33853