Finite Group Databasebeta

← #6462015

Subgroups — #6462015

Order 512.

2002 conjugacy classes of subgroups.

The subgroup lattice has 755 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#533C211yesmaximal, characteristic, complemented
2C2×#2293C211yesmaximal, characteristic
3#29537C214yesmaximal, complemented
4#29389C212yesmaximal, complemented
5#29369C212yesmaximal, complemented
6#29241C212yesmaximal, complemented
7#28120C212yesmaximal
8#27610C211yesmaximal, characteristic, complemented
9#27582C211yesmaximal, characteristic
10#24063C211yesmaximal, characteristic, complemented
11#23933C211yesmaximal, characteristic
12#23781C212yesmaximal, complemented
13#23683C212yesmaximal, complemented
14#21579C212yesmaximal, complemented
15#21453C212yesmaximal
16#21124C214yesmaximal, complemented
17#20778C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117—21no—
21C2×#483C2212yes—
22C2×#450C2212yes—
23C2×#440C2214yes—
24C4×C4⋊Q8C2211yescharacteristic, complemented
25C4×C4⋊Q8C2211yescharacteristic, complemented
26C4×C4⋊Q8C2211yescharacteristic, complemented
27C4×C4⋊Q8C2211yescharacteristic, complemented
28C4×#125—21no—
29C4×#125—21no—
30C4×C22⋊Q8—21no—
31C4×C22⋊Q8—21no—
32C4×C22⋊Q8C2212yes—
33C4×C22⋊Q8C2212yes—
34#2296—21no—
35#2295—21no—
36#2295C2212yescomplemented
37#2293—21no—
38#2293—21no—
39#2293—21no—
40#2293—21no—
41#2293C2212yes—
42#2293C2212yes—
43#2293C2212yes—
44#2293C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388—21no—
50C2×#388—21no—
51#2285C2211yescharacteristic
52C42×Q8—21no—
53C42×Q8C2212yescomplemented
54C4×#117—21no—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4—21no—
57C2×C43C2211yescharacteristic
58#2099C2212yescomplemented
59#2093C2212yes—
60#2087C2214yescomplemented
61#2083C2212yescomplemented
62#2071C2212yes—
63#2068C2214yescomplemented
64#2065C2214yes—
65#2058C2212yescomplemented
66#2055C2214yes—
67#2043C2212yescomplemented
68#2023C2212yes—
69#2013C2212yes—
70#1928C2214yescomplemented
71#1926C2214yes—
72#1925C2214yes—
73#1921C2214yescomplemented
74#1919C2214yescomplemented
75#1918C2214yescomplemented
76#1880C2214yes—
77#1880C2214yes—
78#1877C2214yes—
79#1872C2212yes—
80#1872C2212yes—
81#1865C2214yescomplemented
82#1863C2214yescomplemented
83#1862C2214yes—
84#1852C2212yes—
85#1852C2212yes—
86#1839C2212yescomplemented
87#1831C2212yescomplemented
88#1823C2212yes—
89#1817C2211yescharacteristic
90#1817C2211yescharacteristic
91#1797C2212yes—
92#1786C2212yes—
93#1776C2214yescomplemented
94#1767C2212yescomplemented
95#1763C2214yescomplemented
96#1762C2214yes—
97#1749C2212yes—
98#1745C2212yescomplemented
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C22×SD16C2314yes—
102#533—28no—
103C2×C4⋊Q8C2311yescharacteristic
104C2×C4⋊Q8C2311yescharacteristic
105C2×#125—21no—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8C2312yes—
108C2×C4×Q8—21no—
109C2×C4×Q8—21no—
110C2×C4×Q8—21no—
111C2×C4×Q8C2312yes—
112C2×C4×Q8C2312yes—
113C2×C4×Q8C2312yes—
114C2×C4×D4—28no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4C2312yes—
118C2×C4×D4C2312yes—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—22no—
125C2×#117—48no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C42—21no—
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#483—28no—
145#450—28no—
146#440—216no—
147C2×#107C2314yes—
148C2×#107C2314yes—
149C2×#106C2314yes—
150C2×C4⋊C8C2314yes—
151C2×#103C2314yes—
152C2×#103C2314yes—
153C2×#103C2314yes—
154C2×#102C2314yes—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×C22⋊C8C2312yes—
158C2×C22⋊C8C2312yes—
159C2×#97C2314yes—
160#391—21no—
161#391—21no—
162#391C2312yes—
163#391C2312yes—
164#390—21no—
165#390—21no—
166#390—21no—
167#390—21no—
168#390C2312yes—
169#390C2312yes—
170#390C2312yes—
171#390C2312yes—
172#389—21no—
173#389—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389C2312yes—
183#389C2312yes—
184#389C2312yes—
185#389C2312yes—
186#389C2312yes—
187#389C2312yes—
188#388—22no—
189#388—22no—
190#388—22no—
191#388—22no—
192#388—22no—
193#388—22no—
194#388—22no—
195#388—22no—
196#387—22no—
197#387—22no—
198#387—22no—
199#387—22no—
200#385—22no—
201#385—22no—
202#384C2311yescharacteristic
203#384C2311yescharacteristic
204#382—21no—
205#380—21no—
206#380C2312yes—
207C4×C4⋊C4—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4—21no—
210C4×C4⋊C4—21no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—22no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4—22no—
222C4×C4⋊C4C2312yes—
223C4×C4⋊C4C2312yes—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C22⋊C4—22no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233#376—22no—
234C2×#95—21no—
235C2×#95—21no—
236C2×#95—21no—
237C43—22no—
238C43D411yescharacteristic
239C43D411yescharacteristic
240C43D411yescharacteristic
241C43D411yescharacteristic
242C43C2311yescharacteristic
243C43C2311yescharacteristic
244C43C2311yescharacteristic
245C43C2311yescharacteristic
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#336C2314yes—
253#336C2312yes—
254#336C2312yes—
255#336C2312yes—
256#336C2312yes—
257#336C2314yes—
258C25—21no—
259C22×Q8—21no—
260C22×Q8C2412yes—
261C22×D4—24no—
262C22×D4—21no—
263C22×D4—24no—
264C22×D4—42no—
265C22×D4C2412yes—
266C23×C4—28no—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×SD16—28no—
282C2×SD16—28no—
283C2×SD16—44no—
284C22×C8C2414yes—
285C22×C8C2414yes—
286C4⋊Q8—24no—
287C4⋊Q8—24no—
288#125—28no—
289C22⋊Q8—28no—
290C22⋊Q8—24no—
291C22⋊Q8#4118yes—
292C4×Q8—28no—
293C4×Q8—24no—
294C4×Q8—24no—
295C4×Q8—28no—
296C4×Q8—44no—
297C4×Q8—44no—
298C4×Q8—44no—
299C4×D4—28no—
300C4×D4—28no—
301C4×D4—24no—
302C4×D4—24no—
303C4×D4—24no—
304C4×D4#4118yes—
305#117—28no—
306#117—48no—
307#117—48no—
308#117—48no—
309#117—48no—
310#117—44no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2412yes—
337C2×C4⋊C4C2412yes—
338C2×C4⋊C4C2412yes—
339C2×C4⋊C4C2412yes—
340C2×C4⋊C4C2412yes—
341C2×C4⋊C4C2412yes—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—44no—
375C2×C42C2×D411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D411yescharacteristic
379C2×C42C2×D411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2411yescharacteristic
398C2×C42C2411yescharacteristic
399C2×C42C2411yescharacteristic
400C2×C42C2411yescharacteristic
401C2×C42C2411yescharacteristic
402C2×C42C2411yescharacteristic
403#107—28no—
404#107—44no—
405#106—28no—
406C4⋊C8—44no—
407#103—28no—
408#103—28no—
409#103—44no—
410#102—28no—
411#102—28no—
412#102—44no—
413C22⋊C8—24no—
414C22⋊C8—24no—
415#97—28no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432C24—24no—
433C24—22no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24C22×D411yescharacteristic
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—24no—
444C2×Q8—24no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8C2×#4114yes—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—416no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4C2×#4114yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—28no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—432no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4AGL(1,ℤ/8)14yes—
498C22×C4#13714yes—
499C22×C4C22×D411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C2×#4114yes—
513C22×C4C2511yescharacteristic
514SD16—416no—
515C2×C8—24no—
516C2×C8—24no—
517C2×C8—24no—
518C2×C8—24no—
519C2×C8—24no—
520C2×C8—24no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—28no—
525C4⋊C4—24no—
526C4⋊C4—28no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—42no—
534C4⋊C4—44no—
535C4⋊C4—44no—
536C4⋊C4—42no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—42no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—44no—
546C4⋊C4—42no—
547C4⋊C4C2×#4114yes—
548C4⋊C4C2×#4114yes—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—28no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—44no—
557C22⋊C4—44no—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C42—28no—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—44no—
590C42—44no—
591C42—44no—
592C42—44no—
593C42—44no—
594C42—44no—
595C42—44no—
596C42C2×#4114yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—24no—
602C23—48no—
603C23—48no—
604C23—48no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—84no—
612C23—84no—
613C23—84no—
614C23—84no—
615C23#52512yes—
616C23C2×AGL(1,ℤ/8)12yes—
617C23C2×#13712yes—
618C23C23×D411yescharacteristic
619Q8—28no—
620Q8—48no—
621Q8—44no—
622D4—28no—
623D4—48no—
624D4—44no—
625C2×C4—28no—
626C2×C4—28no—
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—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—28no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—416no—
665C2×C4—416no—
666C2×C4—44no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4#52512yes—
689C2×C4#52512yes—
690C2×C4#52512yes—
691C2×C4C2×AGL(1,ℤ/8)12yes—
692C2×C4C2×AGL(1,ℤ/8)12yes—
693C2×C4C2×#13712yes—
694C2×C4C2×#13712yes—
695C2×C4#57512yes—
696C2×C4#57512yes—
697C2×C4C22×#4112yes—
698C2×C4C22×#4112yes—
699C2×C4#58512yes—
700C8—44no—
701C8—44no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—816no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22#311214yes—
717C22C2×#52511yescharacteristic
718C22C2×#52511yescharacteristic
719C22#344911yescharacteristic
720C22C22×AGL(1,ℤ/8)11yescharacteristic
721C22C22×#13711yescharacteristic
722C22C2×#57511yescharacteristic
723C22C2×#57511yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—44no—
736C4—44no—
737C4—41no—
738C4—41no—
739C4—44no—
740C4—82no—
741C4—82no—
742C4—82no—
743C4—82no—
744C4#347514yes—
745C2—24no—
746C2—84no—
747C2#3487511yescharacteristic
748C2C2×#311211yescharacteristic
749C2#6055811yescharacteristic
750C2#6056211yescharacteristic
751C2#6056311yescharacteristic
752C2#6096011yescharacteristic
753C2#6096511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C4×#533C2semidirect
3. #29537C2semidirect
4. #29389C2semidirect
5. #29369C2semidirect
6. #29241C2semidirect
8. #27610C2semidirect
10. #24063C2semidirect
12. #23781C2semidirect
13. #23683C2semidirect
14. #21579C2semidirect
16. #21124C2semidirect
17. #20778C2semidirect
24. C4×C4⋊Q8C22semidirect
25. C4×C4⋊Q8C22semidirect
26. C4×C4⋊Q8C22semidirect
27. C4×C4⋊Q8C22semidirect
36. #2295C22semidirect
53. C42×Q8C22semidirect
58. #2099C22semidirect
60. #2087C22semidirect
61. #2083C22semidirect
63. #2068C22semidirect
65. #2058C22semidirect
67. #2043C22semidirect
70. #1928C22semidirect
73. #1921C22semidirect
74. #1919C22semidirect
75. #1918C22semidirect
81. #1865C22semidirect
82. #1863C22semidirect
86. #1839C22semidirect
87. #1831C22semidirect
93. #1776C22semidirect
94. #1767C22semidirect
95. #1763C22semidirect
98. #1745C22semidirect

Maximal subgroups

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

subgroupindex
C4×#5332
C2×#22932
#295372
#293892
#293692
#292412
#281202
#276102
#275822
#240632
#239332
#237812
#236832
#215792
#214532
#211242
#207782