Finite Group Databasebeta

← #224774

Subgroups — #224774

Order 512.

938 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#556C211yesmaximal, characteristic
2#22722C211yesmaximal, characteristic, complemented
3#21340C211yesmaximal, characteristic, complemented
4#9677C211yesmaximal, characteristic, complemented
5#9676C211yesmaximal, characteristic
6#9675C211yesmaximal, characteristic
7#9646C211yesmaximal, characteristic
8#9643C211yesmaximal, characteristic, complemented
9#9640C211yesmaximal, characteristic
10#8564C211yesmaximal, characteristic, complemented
11#8564C211yesmaximal, characteristic, complemented
12#8563C211yesmaximal, characteristic
13#8174C211yesmaximal, characteristic
14#8173C211yesmaximal, characteristic, complemented
15#8171C211yesmaximal, characteristic, complemented
16C2×#556C411yescharacteristic
17C2×#446—21no—
18#2373—21no—
19#2373—21no—
20#2367C411yescharacteristic
21#2367C411yescharacteristic
22#2365C411yescharacteristic
23#2362—21no—
24#2356C411yescharacteristic
25#2356C411yescharacteristic
26#2355C411yescharacteristic
27#2354C411yescharacteristic
28#2347—21no—
29C4×C4⋊Q8C2211yescharacteristic
30C4×#126—21no—
31C4×#126—21no—
32C4×#124C2211yescharacteristic
33C4×#124C2211yescharacteristic
34C4×C22⋊Q8—21no—
35C42×Q8C2211yescharacteristic
36C42×Q8C2211yescharacteristic
37C42×Q8C2211yescharacteristic
38C42×D4C2211yescharacteristic
39C4×#117—21no—
40#1985—21no—
41#1940—21no—
42#1940—21no—
43#1940—21no—
44#1939—21no—
45#1917—21no—
46#1917—21no—
47#1842C2211yescharacteristic
48#1842C2211yescharacteristic
49#1842C2211yescharacteristic
50#1767C2211yescharacteristic
51#1767C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56#1744C2211yescharacteristic
57#1744C2211yescharacteristic
58C4×#97C2211yescharacteristic
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2211yescharacteristic
64C2×Q8⋊C8C2211yescharacteristic
65C2×Q8⋊C8C2211yescharacteristic
66C2×Q8⋊C8C2211yescharacteristic
67C2×D4⋊C8C2211yescharacteristic
68C2×D4⋊C8C2211yescharacteristic
69C2×D4⋊C8C2211yescharacteristic
70C2×D4⋊C8C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#556—24no—
76#556—24no—
77C2×C4⋊Q8C2×C411yescharacteristic
78C2×#126—21no—
79C2×#126—21no—
80C2×#124C2×C411yescharacteristic
81C2×#124C2×C411yescharacteristic
82C2×C22⋊Q8—21no—
83C2×C4×Q8C2×C411yescharacteristic
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×Q8C2×C411yescharacteristic
86C2×C4×Q8C2×C411yescharacteristic
87C2×C4×Q8C2×C411yescharacteristic
88C2×C4×Q8D411yescharacteristic
89C2×C4×Q8D411yescharacteristic
90C2×C4×Q8C2311yescharacteristic
91C2×C4×Q8C2311yescharacteristic
92C2×C4×D4C2×C411yescharacteristic
93C2×C4×D4C2×C411yescharacteristic
94C2×C4×D4C2311yescharacteristic
95C2×#117—21no—
96C2×#117—21no—
97C22×C42—21no—
98#446—44no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8C2311yescharacteristic
109C2×C4⋊C8C2311yescharacteristic
110C2×C4⋊C8C2311yescharacteristic
111C2×C4⋊C8C2311yescharacteristic
112C2×#97—21no—
113C2×#97—21no—
114C2×#97—21no—
115C2×#97—21no—
116C2×C4×C8—21no—
117C2×C4×C8C2311yescharacteristic
118C2×C4×C8C2311yescharacteristic
119C2×C4×C8C2311yescharacteristic
120C2×C4×C8C2311yescharacteristic
121#391—21no—
122#391C2×C411yescharacteristic
123#391C2×C411yescharacteristic
124#391C2×C411yescharacteristic
125#391C2×C411yescharacteristic
126#390C2×C411yescharacteristic
127#390C2×C411yescharacteristic
128#389—21no—
129#389—21no—
130#389—21no—
131#388—21no—
132#388—21no—
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#385—21no—
150#385—21no—
151#384C2×C411yescharacteristic
152#383—21no—
153#383—21no—
154#382C2×C411yescharacteristic
155#382C2×C411yescharacteristic
156#380—21no—
157C4×C4⋊C4—21no—
158C4×C4⋊C4—21no—
159C4×C4⋊C4—21no—
160C4×C4⋊C4—21no—
161C4×C4⋊C4—21no—
162C4×C4⋊C4—21no—
163C4×C4⋊C4—21no—
164C4×C4⋊C4—21no—
165C4×C4⋊C4—21no—
166C4×C4⋊C4—21no—
167C4×C4⋊C4C2×C411yescharacteristic
168C4×C4⋊C4C2×C411yescharacteristic
169C4×C4⋊C4C2×C411yescharacteristic
170C4×C4⋊C4C2×C411yescharacteristic
171C4×C4⋊C4C2×C411yescharacteristic
172C4×C4⋊C4C2×C411yescharacteristic
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4D411yescharacteristic
177C4×C4⋊C4D411yescharacteristic
178C4×C4⋊C4D411yescharacteristic
179C4×C4⋊C4D411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4C2311yescharacteristic
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192#376—21no—
193#376—21no—
194C43—21no—
195C43—21no—
196C43C2311yescharacteristic
197C43C2311yescharacteristic
198C43C2311yescharacteristic
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209Q8⋊C8—22no—
210Q8⋊C8—22no—
211Q8⋊C8—22no—
212Q8⋊C8—22no—
213Q8⋊C8—41no—
214Q8⋊C8—41no—
215Q8⋊C8—41no—
216Q8⋊C8—41no—
217D4⋊C8—22no—
218D4⋊C8—22no—
219D4⋊C8—41no—
220D4⋊C8—41no—
221C22×Q8C22⋊C411yescharacteristic
222C22×Q8C22×C411yescharacteristic
223C22×Q8C22×C411yescharacteristic
224C22×D4C22×C411yescharacteristic
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C4⋊Q8—22no—
237C4⋊Q8—22no—
238#126—28no—
239#126—28no—
240#124—22no—
241#124—22no—
242#124—22no—
243#124M1614yes—
244C22⋊Q8—28no—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×Q8—22no—
253C4×Q8—22no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—42no—
263C4×Q8—41no—
264C4×Q8—41no—
265C4×Q8M1614yes—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—41no—
274#117—28no—
275#117—44no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4C22⋊C411yescharacteristic
287C2×C4⋊C4C22⋊C411yescharacteristic
288C2×C4⋊C4C22⋊C411yescharacteristic
289C2×C4⋊C4C22⋊C411yescharacteristic
290C2×C4⋊C4C22⋊C411yescharacteristic
291C2×C4⋊C4C22⋊C411yescharacteristic
292C2×C4⋊C4C22⋊C411yescharacteristic
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C4⋊C4C22×C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42C22×C411yescharacteristic
327C2×C42C22×C411yescharacteristic
328C2×C42C22×C411yescharacteristic
329C2×C42C22×C411yescharacteristic
330C2×C42C22×C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C2×D411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2411yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—42no—
353C4⋊C8—42no—
354C4⋊C8—42no—
355C4⋊C8—42no—
356C4⋊C8—42no—
357C4⋊C8—42no—
358C4⋊C8—81no—
359C4⋊C8—81no—
360C4⋊C8—81no—
361C4⋊C8#4112yes—
362#97—42no—
363#97—42no—
364#97—42no—
365#97—42no—
366C4×C8—21no—
367C4×C8—21no—
368C4×C8—21no—
369C4×C8—21no—
370C4×C8—21no—
371C4×C8—21no—
372C4×C8—21no—
373C4×C8—42no—
374C4×C8#4112yes—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400C24—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—41no—
414C2×Q8C2×M1612yes—
415C2×Q8C2×M1612yes—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×M1612yes—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—81no—
441C22×C4C2×C22⋊C411yescharacteristic
442C22×C4C2×C22⋊C411yescharacteristic
443C22×C4C2×C22⋊C411yescharacteristic
444C22×C4C2×C22⋊C411yescharacteristic
445C22×C4C2×C22⋊C411yescharacteristic
446C22×C4C2×C22⋊C411yescharacteristic
447C22×C4C2×C22⋊C411yescharacteristic
448C22×C4C2×C22⋊C411yescharacteristic
449C22×C4C2×C22⋊C411yescharacteristic
450C22×C4C2×C22⋊C411yescharacteristic
451C22×C4C2×C22⋊C411yescharacteristic
452C22×C4C2×C22⋊C411yescharacteristic
453C22×C4C23×C411yescharacteristic
454C22×C4C22×D411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—81no—
509C4⋊C4C2×M1612yes—
510C4⋊C4#13112yes—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—24no—
545C42—22no—
546C42—41no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—42no—
552C42—42no—
553C42—42no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—42no—
561C42—42no—
562C42—42no—
563C42—81no—
564C42—81no—
565C42C2×M1612yes—
566C42C2×M1612yes—
567C42AGL(1,ℤ/8)12yes—
568C42#13712yes—
569C42C2×#4111yescharacteristic
570C42C2×#4111yescharacteristic
571C42H(5,𝔽2)11yescharacteristic
572C422−1+411yescharacteristic
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23C22×C22⋊C411yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—44no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—48no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4#40712yes—
655C2×C4#40712yes—
656C2×C4#41712yes—
657C2×C4#41712yes—
658C2×C4#42112yes—
659C2×C4C4×#4111yescharacteristic
660C2×C4#52011yescharacteristic
661C2×C4#54811yescharacteristic
662C2×C4#54811yescharacteristic
663C2×C4#55011yescharacteristic
664C2×C4#55011yescharacteristic
665C2×C4C22×M1611yescharacteristic
666C2×C4C22×M1611yescharacteristic
667C2×C4C2×#13111yescharacteristic
668C2×C4#56811yescharacteristic
669C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
670C2×C4C2×#13711yescharacteristic
671C2×C4#57711yescharacteristic
672C2×C4#57811yescharacteristic
673C8—42no—
674C8—42no—
675C8—42no—
676C8—81no—
677C8—81no—
678C8—81no—
679C8—81no—
680C8—81no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22#234111yescharacteristic
689C22C2×#40711yescharacteristic
690C22#288011yescharacteristic
691C22C2×#41711yescharacteristic
692C22#289811yescharacteristic
693C22C2×#42111yescharacteristic
694C22#290111yescharacteristic
695C4—21no—
696C4—21no—
697C4—22no—
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—41no—
705C4—42no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—42no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4#296511yescharacteristic
717C4#297011yescharacteristic
718C4#298911yescharacteristic
719C4#299011yescharacteristic
720C4#336711yescharacteristic
721C4#336911yescharacteristic
722C4#339711yescharacteristic
723C4#339811yescharacteristic
724C2—82no—
725C2#1745111yescharacteristic
726C2#1745411yescharacteristic
727C2#1751211yescharacteristic
728C2#1752411yescharacteristic
729C2#2253211yescharacteristic
730C2#2254411yescharacteristic
731C2#2255111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×Q8 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22722C2semidirect
3. #21340C2semidirect
4. #9677C2semidirect
8. #9643C2semidirect
10. #8564C2semidirect
11. #8564C2semidirect
14. #8173C2semidirect
15. #8171C2semidirect

Maximal subgroups

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

subgroupindex
C4×#5562
#227222
#213402
#96772
#96762
#96752
#96462
#96432
#96402
#85642
#85632
#81742
#81732
#81712