Finite Group Databasebeta

← #7033568

Subgroups — #7033568

Order 512.

1813 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59015C211yesmaximal, characteristic
2#39911C211yesmaximal, characteristic, complemented
3#32210C211yesmaximal, characteristic, complemented
4#31742C211yesmaximal, characteristic, complemented
5#31676C211yesmaximal, characteristic, complemented
6#31566C211yesmaximal, characteristic, complemented
7#31422C211yesmaximal, characteristic, complemented
8#31411C211yesmaximal, characteristic, complemented
9#31336C211yesmaximal, characteristic, complemented
10#30424C211yesmaximal, characteristic, complemented
11#29005C211yesmaximal, characteristic, complemented
12#28857C211yesmaximal, characteristic, complemented
13#28569C211yesmaximal, characteristic, complemented
14#27719C211yesmaximal, characteristic, complemented
15#27518C211yesmaximal, characteristic, complemented
16#27224C211yesmaximal, characteristic, complemented
17#26354C211yesmaximal, characteristic, complemented
18#26229C211yesmaximal, characteristic, complemented
19#25547C211yesmaximal, characteristic, complemented
20#25346C211yesmaximal, characteristic, complemented
21#25217C211yesmaximal, characteristic, complemented
22#24979C211yesmaximal, characteristic, complemented
23#24951C211yesmaximal, characteristic, complemented
24#24794C211yesmaximal, characteristic, complemented
25#24556C211yesmaximal, characteristic, complemented
26#24385C211yesmaximal, characteristic, complemented
27#23642C211yesmaximal, characteristic, complemented
28#23138C211yesmaximal, characteristic, complemented
29#22852C211yesmaximal, characteristic, complemented
30#22500C211yesmaximal, characteristic, complemented
31#21767C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546—21no—
34C22×#121C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic, complemented
40C2×#450C2211yescharacteristic
41C2×#436C2211yescharacteristic, complemented
42C2×#436C2211yescharacteristic, complemented
43C2×#428C2211yescharacteristic, complemented
44C2×#407C2211yescharacteristic
45C2×#407C2211yescharacteristic
46#2848C2211yescharacteristic
47#2765—21no—
48#2751—21no—
49#2736—21no—
50#2685—21no—
51#2672—21no—
52#2671—21no—
53#2653—21no—
54#2597—21no—
55#2589—21no—
56#2563C2211yescharacteristic, complemented
57#2537C2211yescharacteristic
58#2536C2211yescharacteristic
59#2501C2211yescharacteristic
60#2496C2211yescharacteristic
61#2494C2211yescharacteristic, complemented
62#2492C2211yescharacteristic
63#2491C2211yescharacteristic
64#2485C2211yescharacteristic
65#2440C2211yescharacteristic
66#2439C2211yescharacteristic, complemented
67#2437—21no—
68#2430—21no—
69#2425—21no—
70#2423C2211yescharacteristic, complemented
71#2422C2211yescharacteristic
72#2418—21no—
73#2416C2211yescharacteristic
74#2416C2211yescharacteristic
75#2415C2211yescharacteristic, complemented
76#2415C2211yescharacteristic, complemented
77#2408C2211yescharacteristic
78#2405—21no—
79#2362C2211yescharacteristic, complemented
80#2361C2211yescharacteristic
81#2354C2211yescharacteristic, complemented
82D4×C4⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2334—21no—
85C4×#120C2211yescharacteristic
86#2280C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2071C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2058C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic, complemented
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1988C2211yescharacteristic, complemented
131#1968C2211yescharacteristic, complemented
132#1955C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1925C2211yescharacteristic, complemented
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1921C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic, complemented
155#1894C2211yescharacteristic, complemented
156#1894C2211yescharacteristic, complemented
157#1880C2211yescharacteristic, complemented
158#1880C2211yescharacteristic, complemented
159#1877C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic, complemented
166#1875C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1870C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1853C2211yescharacteristic, complemented
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic, complemented
178#1851C2211yescharacteristic, complemented
179#1851C2211yescharacteristic, complemented
180#1836C2211yescharacteristic, complemented
181#1825C2211yescharacteristic, complemented
182#1824C2211yescharacteristic, complemented
183#1824C2211yescharacteristic, complemented
184#1823C2211yescharacteristic
185#1823C2211yescharacteristic
186#1809C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1763C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#547—24no—
215#547—42no—
216#546—48no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#124—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—24no—
238C2×#121—42no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#120—21no—
246C2×#120D411yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265#484—42no—
266#476—42no—
267#468—24no—
268#468—42no—
269#468—42no—
270#450—42no—
271#436—42no—
272#436—42no—
273#428—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307#407—42no—
308#407—42no—
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#401—21no—
324#400—21no—
325#400—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#392—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386D411yescharacteristic
404#386D411yescharacteristic
405#386D411yescharacteristic
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385D411yescharacteristic
415#385D411yescharacteristic
416#385D411yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382C2311yescharacteristic
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443#379—21no—
444#379D411yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C25C2×D411yescharacteristic
496C2×#41—44no—
497C2×#41—44no—
498C2×#41—82no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—44no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575#126—44no—
576#124—44no—
577#123—44no—
578#123—44no—
579#123—44no—
580#123—44no—
581#123—82no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—44no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—44no—
603#121—44no—
604#121—44no—
605#121—44no—
606#121—41no—
607#121—41no—
608#121#4114yes—
609#120—24no—
610#120—44no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—44no—
624C4×D4—44no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629#117—41no—
630#117—41no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—44no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#107—22no—
741#107—22no—
742#107—41no—
743#107—41no—
744#107—41no—
745#107—41no—
746#106—22no—
747#106—41no—
748#106—41no—
749#106—41no—
750C4⋊C8—22no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—41no—
785C4×C8—41no—
786C4×C8—41no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—22no—
824C24—22no—
825C24—21no—
826C24—41no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24—41no—
831C24—42no—
832C24—42no—
833C24—42no—
834C24—42no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—816no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—816no—
901C2×D4C2×#4112yes—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—82no—
959C22×C4—82no—
960C22×C4—82no—
961C22×C4—82no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C2×#4112yes—
980C22×C4H(5,𝔽2)12yes—
981C22×C4C2511yescharacteristic
982SD16—82no—
983SD16—82no—
984M16—44no—
985M16—82no—
986M16—82no—
987M16—82no—
988M16—82no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8H(5,𝔽2)12yes—
1013C4⋊C4—22no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4C2×#4112yes—
1065C22⋊C4—22no—
1066C22⋊C4—24no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4AGL(1,ℤ/8)14yes—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—44no—
1155C23—44no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—82no—
1170C23—82no—
1171C23—82no—
1172C23—84no—
1173C23—84no—
1174C23—82no—
1175C23—82no—
1176C23—84no—
1177C23—84no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23#54612yes—
1182C23C2×AGL(1,ℤ/8)12yes—
1183C23C23×D411yescharacteristic
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—84no—
1189Q8—162no—
1190D4—22no—
1191D4—22no—
1192D4—44no—
1193D4—44no—
1194D4—48no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—82no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—162no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—84no—
1296C2×C4—82no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4#54612yes—
1303C2×C4C2×AGL(1,ℤ/8)12yes—
1304C2×C4C2×AGL(1,ℤ/8)12yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4#58511yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—22no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—88no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—168no—
1363C22C2×#54611yescharacteristic
1364C22#348511yescharacteristic
1365C22#349611yescharacteristic
1366C22C22×AGL(1,ℤ/8)11yescharacteristic
1367C22#358511yescharacteristic
1368C22#358611yescharacteristic
1369C22#358611yescharacteristic
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—42no—
1380C4—41no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4#351411yescharacteristic
1395C4#352111yescharacteristic
1396C4#353411yescharacteristic
1397C4#356011yescharacteristic
1398C2—42no—
1399C2—42no—
1400C2—81no—
1401C2—81no—
1402C2—82no—
1403C2—161no—
1404C2#4348911yescharacteristic
1405C2#6115511yescharacteristic
1406C2#6118111yescharacteristic
1407C2#6171711yescharacteristic
1408C2#6178211yescharacteristic
1409C2#6229411yescharacteristic
1410C2#6229511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59015C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39911C2semidirect
3. #32210C2semidirect
4. #31742C2semidirect
5. #31676C2semidirect
6. #31566C2semidirect
7. #31422C2semidirect
8. #31411C2semidirect
9. #31336C2semidirect
10. #30424C2semidirect
11. #29005C2semidirect
12. #28857C2semidirect
13. #28569C2semidirect
14. #27719C2semidirect
15. #27518C2semidirect
16. #27224C2semidirect
17. #26354C2semidirect
18. #26229C2semidirect
19. #25547C2semidirect
20. #25346C2semidirect
21. #25217C2semidirect
22. #24979C2semidirect
23. #24951C2semidirect
24. #24794C2semidirect
25. #24556C2semidirect
26. #24385C2semidirect
27. #23642C2semidirect
28. #23138C2semidirect
29. #22852C2semidirect
30. #22500C2semidirect
31. #21767C2semidirect
35. C2×#484C22semidirect
36. C2×#476C22semidirect
39. C2×#468C22semidirect
41. C2×#436C22semidirect
42. C2×#436C22semidirect
43. C2×#428C22semidirect
56. #2563C22semidirect
61. #2494C22semidirect
66. #2439C22semidirect
70. #2423C22semidirect
75. #2415C22semidirect
76. #2415C22semidirect
79. #2362C22semidirect
81. #2354C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2092C22semidirect
92. #2086C22semidirect
93. #2083C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
105. #2073C22semidirect
106. #2072C22semidirect
107. #2071C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
110. #2066C22semidirect
111. #2065C22semidirect
112. #2058C22semidirect
113. #2057C22semidirect
114. #2055C22semidirect
115. #2036C22semidirect
118. #2034C22semidirect
119. #2034C22semidirect
122. #2033C22semidirect
123. #2024C22semidirect
124. #2023C22semidirect
127. #2000C22semidirect
128. #1990C22semidirect
129. #1990C22semidirect
130. #1988C22semidirect
131. #1968C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
136. #1936C22semidirect
137. #1936C22semidirect
138. #1934C22semidirect
139. #1933C22semidirect
140. #1926C22semidirect
141. #1925C22semidirect
144. #1921C22semidirect
145. #1919C22semidirect
146. #1919C22semidirect
147. #1918C22semidirect
154. #1895C22semidirect
155. #1894C22semidirect
156. #1894C22semidirect
157. #1880C22semidirect
158. #1880C22semidirect
159. #1877C22semidirect
160. #1877C22semidirect
165. #1875C22semidirect
166. #1875C22semidirect
168. #1872C22semidirect
169. #1872C22semidirect
171. #1870C22semidirect
172. #1870C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
175. #1853C22semidirect
177. #1852C22semidirect
178. #1851C22semidirect
179. #1851C22semidirect
180. #1836C22semidirect
181. #1825C22semidirect
182. #1824C22semidirect
183. #1824C22semidirect
186. #1809C22semidirect
187. #1809C22semidirect
188. #1809C22semidirect
189. #1803C22semidirect
190. #1802C22semidirect
194. #1763C22semidirect
195. C4×#102C22semidirect
196. C4×#102C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#590152
#399112
#322102
#317422
#316762
#315662
#314222
#314112
#313362
#304242
#290052
#288572
#285692
#277192
#275182
#272242
#263542
#262292
#255472
#253462
#252172
#249792
#249512
#247942
#245562
#243852
#236422
#231382
#228522
#225002
#217672