Finite Group Databasebeta

← #6377994

Subgroups — #6377994

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60846C211yesmaximal, characteristic
2#60207C211yesmaximal, characteristic
3C2×#2961C211yesmaximal, characteristic, complemented
4#22258C212yesmaximal, complemented
5#22236C212yesmaximal, complemented
6#22132C214yesmaximal, complemented
7#22096C212yesmaximal, complemented
8#22095C212yesmaximal, complemented
9#21993C211yesmaximal, characteristic, complemented
10#21857C211yesmaximal, characteristic
11#21845C211yesmaximal, characteristic, complemented
12#21733C212yesmaximal, complemented
13#21659C212yesmaximal, complemented
14#21629C214yesmaximal, complemented
15#21593C212yesmaximal, complemented
16#21592C212yesmaximal, complemented
17#20481C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19C2×#533C2211yescharacteristic
20#3233C414yescomplemented
21#3232C412yescomplemented
22#3232C412yescomplemented
23#3231C412yescomplemented
24#3230C411yescharacteristic, complemented
25#3229C411yescharacteristic, complemented
26#3228C412yescomplemented
27#3227C411yescharacteristic, complemented
28#3226C411yescharacteristic, complemented
29#3160C2212yes—
30#3131C2212yes—
31#3091C2212yes—
32#3091C2212yes—
33#3076C2214yes—
34#2970—22no—
35#2970—22no—
36#2968—22no—
37#2968—22no—
38#2961—22no—
39#2961—22no—
40#2961C2212yes—
41#2961C2212yes—
42#2961C2212yes—
43#2961C2212yes—
44#2961C2211yescharacteristic
45#2961C2211yescharacteristic
46C2×#446—22no—
47C2×#446—22no—
48#2932C2211yescharacteristic
49#2932C2211yescharacteristic
50#2929C2212yes—
51#2929C2212yes—
52#2923C2212yes—
53#2920C2211yescharacteristic
54C2×#431C2211yescharacteristic
55C2×#424C2212yes—
56C2×#423C2211yescharacteristic
57#2875C2212yes—
58C2×#405C2212yes—
59C22×#97C2211yescharacteristic
60#2283C2211yescharacteristic
61#1995C2212yes—
62#1995C2212yes—
63#1995C2212yes—
64#1986C2214yes—
65#1963C2212yes—
66#1950C2214yes—
67#1946C2214yes—
68#1945C2214yes—
69#1938C2214yes—
70#1937C2214yes—
71#1929C2214yes—
72#1929C2214yes—
73#1922C2214yes—
74#1922C2214yes—
75#1922C2214yes—
76#1922C2214yes—
77#1871C2212yes—
78#1871C2212yes—
79#1866C2214yes—
80#1866C2214yes—
81#1855C2212yes—
82#1855C2212yes—
83#1848C2212yes—
84#1837C2212yes—
85#1826C2212yes—
86#1826C2212yes—
87#1806C2214yes—
88#1773C2214yes—
89#1772C2214yes—
90#1771C2212yes—
91#1771C2212yes—
92#1765C2214yes—
93#1764C2214yes—
94#1752C2211yescharacteristic
95#1752C2211yescharacteristic
96C8×C22⋊C4C2211yescharacteristic
97C8×C22⋊C4C2211yescharacteristic
98#1746C2212yes—
99#1726C2212yes—
100C2×#131C2312yes—
101C2×#131C2312yes—
102C22×M16C2312yes—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105#533—21no—
106#533—21no—
107#533—21no—
108#533—21no—
109#533C2×C411yescharacteristic
110#533C2×C411yescharacteristic
111#533C2×C412yes—
112#533C2×C412yes—
113#533C2312yes—
114#533C2312yes—
115#533C2311yescharacteristic
116#532C2×C411yescharacteristic
117#532C2×C411yescharacteristic
118#532C2311yescharacteristic
119C2×C4⋊Q8C2×C411yescharacteristic
120C2×C4⋊Q8C2×C411yescharacteristic
121#529—21no—
122#529—21no—
123#529—21no—
124#529—21no—
125#529C2×C412yes—
126#529C2×C412yes—
127C2×#125C2×C412yes—
128#525—21no—
129#525—21no—
130#525C2312yes—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C4×#41—21no—
134C4×#41—21no—
135C4×#41C2312yes—
136C2×C4×Q8—21no—
137C2×C4×Q8—21no—
138C2×#117C2312yes—
139C22×C42C2311yescharacteristic
140#500C2×C412yes—
141#500C2×C412yes—
142#499C2×C414yes—
143#499C2×C414yes—
144#498C2×C412yes—
145#498C2×C412yes—
146#488C2×C414yes—
147#488C2×C414yes—
148#487C2×C412yes—
149#487C2×C412yes—
150#486C2×C412yes—
151#486C2×C412yes—
152#485C2×C414yes—
153#485C2×C414yes—
154#484C2×C412yes—
155#484C2×C412yes—
156#483C2×C412yes—
157#483C2×C412yes—
158#482C2×C414yes—
159#482C2×C414yes—
160#481C2×C412yes—
161#481C2×C412yes—
162#480C2×C412yes—
163#480C2×C412yes—
164#479C2×C414yes—
165#479C2×C414yes—
166#478C2×C414yes—
167#478C2×C414yes—
168#477C2×C414yes—
169#476C2×C414yes—
170#475C2×C414yes—
171#474C2×C414yes—
172#446—24no—
173#446—24no—
174#446—24no—
175#446—24no—
176#446—24no—
177#446—24no—
178#446—24no—
179#446—24no—
180#446—22no—
181#446—22no—
182#446—22no—
183#446—22no—
184#435—22no—
185#435—22no—
186#435—22no—
187#435—22no—
188#435—22no—
189#435—22no—
190#435—22no—
191#435—22no—
192C8×D4—22no—
193C8×D4—22no—
194C8×D4—22no—
195C8×D4—22no—
196#433—22no—
197#433—22no—
198#432—21no—
199#432—21no—
200#432—22no—
201#432—22no—
202#431—21no—
203#431—21no—
204#431C2×C411yescharacteristic
205#431C2×C411yescharacteristic
206#431C2×C412yes—
207#431C2×C411yescharacteristic
208#431C2×C411yescharacteristic
209#431C2×C412yes—
210C2×#108C2314yes—
211C2×#108C2314yes—
212#427C2314yes—
213#427C2314yes—
214#424—24no—
215#424C2314yes—
216#424C2314yes—
217#424C2312yes—
218#424C2312yes—
219#423—21no—
220#423—21no—
221#423C2312yes—
222#423C2311yescharacteristic
223#423C2312yes—
224#423C2311yescharacteristic
225C2×C4⋊C8—24no—
226C2×C4⋊C8—21no—
227C2×C4⋊C8—21no—
228C2×C4⋊C8C2312yes—
229C2×#104C2314yes—
230C2×#104C2314yes—
231#416C2314yes—
232#416C2314yes—
233#408C2312yes—
234#408C2312yes—
235#407C2312yes—
236C2×C22⋊C8C2311yescharacteristic
237C2×C22⋊C8C2311yescharacteristic
238#405—22no—
239#405—22no—
240#405—22no—
241#405—22no—
242#405C2314yes—
243#405C2314yes—
244#405C2312yes—
245#405C2312yes—
246C4×M16—22no—
247C4×M16C2312yes—
248C2×#97—22no—
249C2×#97—22no—
250C2×#97D412yes—
251C2×#97D412yes—
252C2×#97D412yes—
253C2×#97D412yes—
254C2×#97C2312yes—
255C2×#97C2312yes—
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×C4×C8—22no—
261C2×C4×C8C2312yes—
262C2×C4×C8C2312yes—
263C2×C4×C8C2312yes—
264#383—21no—
265#382—21no—
266#381—21no—
267#380—21no—
268C4×C4⋊C4C2312yes—
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271#376C2312yes—
272#341C2314yes—
273#341C2314yes—
274#339C2314yes—
275#339C2314yes—
276#339C2314yes—
277#339C2314yes—
278#339C2314yes—
279#339C2314yes—
280#336C2312yes—
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284C2×#41—21no—
285C2×#41—21no—
286C2×#41C2412yes—
287C22×Q8—21no—
288C22×Q8—21no—
289C23×C4#4111yescharacteristic
290C23×C4#4111yescharacteristic
291C23×C4C2411yescharacteristic
292#131—28no—
293#131—44no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—44no—
298C2×M16C2414yes—
299C2×M16C2412yes—
300C2×M16C2412yes—
301C22×C8—24no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—42no—
306C22×C8C2×D412yes—
307C22×C8C2×D412yes—
308C22×C8C2×D412yes—
309C22×C8C2×D412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2411yescharacteristic
313C22×C8C2411yescharacteristic
314C22×C8C2411yescharacteristic
315C22×C8C2411yescharacteristic
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8C22×C411yescharacteristic
321C4⋊Q8C22×C412yes—
322C4⋊Q8C22×C412yes—
323C4⋊Q8C22×C412yes—
324C4⋊Q8C22×C412yes—
325C4⋊Q8C22×C411yescharacteristic
326C4⋊Q8C22×C411yescharacteristic
327#127C22×C411yescharacteristic
328#126—22no—
329#126—22no—
330#125—22no—
331#125—22no—
332#125—21no—
333#125—21no—
334#125C22×C414yes—
335#125C22×C414yes—
336#125C22×C412yes—
337#124—21no—
338#124—21no—
339#124C22×C412yes—
340#123—22no—
341#123—22no—
342#123—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8C22×C412yes—
356C22⋊Q8C22×C412yes—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—21no—
361#121C22×C412yes—
362#121C22×C412yes—
363#120—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C22×C412yes—
377C4×Q8C22×C412yes—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C22×C412yes—
389C4×D4C22×C412yes—
390#117—21no—
391#117—21no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117C22×C414yes—
398#117C2414yes—
399#117C2412yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4C22×C412yes—
406C2×C4⋊C4C22×C412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42#4111yescharacteristic
421C2×C42#4111yescharacteristic
422C2×C42C2412yes—
423C2×C42C2412yes—
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#108—44no—
427#108—44no—
428#107C22×C414yes—
429#107C22×C414yes—
430#107C22×C414yes—
431#107C22×C414yes—
432#106C22×C414yes—
433#106C22×C414yes—
434#106C22×C414yes—
435#106C22×C414yes—
436C4⋊C8—28no—
437C4⋊C8—28no—
438C4⋊C8—22no—
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8C22×C412yes—
451C4⋊C8C22×C412yes—
452C4⋊C8C22×C412yes—
453C4⋊C8C22×C412yes—
454#104—44no—
455#104—44no—
456#103C22×C414yes—
457#103C22×C414yes—
458#103C22×C414yes—
459#103C22×C414yes—
460#102C22×C414yes—
461#102C22×C414yes—
462#102C22×C414yes—
463#102C22×C414yes—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470C22⋊C8C22×C411yescharacteristic
471C22⋊C8C22×C411yescharacteristic
472C22⋊C8C22×C411yescharacteristic
473C22⋊C8C22×C411yescharacteristic
474C22⋊C8C22×C412yes—
475C22⋊C8C22×C412yes—
476#97—22no—
477#97—22no—
478#97—24no—
479#97—24no—
480#97—24no—
481#97—22no—
482#97—42no—
483#97C2×D412yes—
484#97C2×D412yes—
485#97C2×D412yes—
486#97C2×D412yes—
487#97C2×D412yes—
488#97C2×D412yes—
489#97C2×D412yes—
490#97C2×D412yes—
491C4×C8—24no—
492C4×C8—24no—
493C4×C8—22no—
494C4×C8—22no—
495C4×C8—24no—
496C4×C8—22no—
497C4×C8—42no—
498C4×C8C22×C412yes—
499C4×C8C22×C412yes—
500C4×C8C22×C412yes—
501C4×C8C22×C412yes—
502#95—22no—
503#95—22no—
504#95—21no—
505#95—21no—
506#95—22no—
507C24C2×#4111yescharacteristic
508#41—24no—
509#41—24no—
510#41—82no—
511#41—82no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—82no—
519C2×Q8—82no—
520C2×Q8C23×C412yes—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4C23×C412yes—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—42no—
537C22×C4—81no—
538C22×C4C4×D411yescharacteristic
539C22×C4C4×D411yescharacteristic
540C22×C4C4×D411yescharacteristic
541C22×C4C4×D411yescharacteristic
542C22×C4C4×D411yescharacteristic
543C22×C4C4×D411yescharacteristic
544C22×C4C4×D411yescharacteristic
545C22×C4C4×D411yescharacteristic
546C22×C4C23×C411yescharacteristic
547C22×C4C23×C411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555C22×C4C2511yescharacteristic
556M16—24no—
557M16—24no—
558M16—24no—
559M16—24no—
560M16—44no—
561M16—44no—
562M16—44no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—24no—
575C2×C8—42no—
576C2×C8—42no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8—44no—
580C2×C8C23×C412yes—
581C2×C8C23×C412yes—
582C2×C8C23×C412yes—
583C2×C8C23×C412yes—
584C2×C8C22×D412yes—
585C2×C8C22×D412yes—
586C2×C8C22×D412yes—
587C2×C8C22×D412yes—
588C2×C82−1+414yes—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—82no—
610C4⋊C4C23×C414yes—
611C4⋊C4C23×C414yes—
612C4⋊C4C23×C412yes—
613C4⋊C4C23×C412yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C42—22no—
628C42—22no—
629C42—24no—
630C42—22no—
631C42—24no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42C4×D411yescharacteristic
637C42C4×D411yescharacteristic
638C42C4×D411yescharacteristic
639C42C4×D411yescharacteristic
640C42C4×D411yescharacteristic
641C42C4×D411yescharacteristic
642C42C4×D411yescharacteristic
643C42C4×D411yescharacteristic
644C42C23×C411yescharacteristic
645C42C23×C411yescharacteristic
646C42C23×C411yescharacteristic
647C42C23×C411yescharacteristic
648C42C22×D411yescharacteristic
649C42C22×D411yescharacteristic
650C42C22×D411yescharacteristic
651C42C22×D411yescharacteristic
652C23—22no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23C2×C4×D411yescharacteristic
657C23C2×C4×D411yescharacteristic
658C23C22×#4111yescharacteristic
659Q8—24no—
660Q8—82no—
661Q8—82no—
662Q8—82no—
663Q8—82no—
664Q8—81no—
665Q8—81no—
666D4—24no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—81no—
671D4—81no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C2×C4×D411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C2×C4×D411yescharacteristic
717C2×C4C2×C4×D411yescharacteristic
718C2×C4C24×C411yescharacteristic
719C2×C4C23×D411yescharacteristic
720C2×C4C2×2−1+412yes—
721C2×C4#58512yes—
722C8—22no—
723C8—22no—
724C8—22no—
725C8—22no—
726C8—22no—
727C8—22no—
728C8—22no—
729C8—42no—
730C8—42no—
731C8—44no—
732C8#53614yes—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22#295712yes—
745C22C22×C4×D411yescharacteristic
746C22#346112yes—
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—44no—
758C4—42no—
759C4—44no—
760C4—42no—
761C4—42no—
762C4—82no—
763C4—82no—
764C4C4×2−1+412yes—
765C4C2×#53611yescharacteristic
766C4#344911yescharacteristic
767C2—22no—
768C2—22no—
769C2—41no—
770C2—82no—
771C2C4×#53611yescharacteristic
772C2C2×#295711yescharacteristic
773C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#3444C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×#97 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2961C2semidirect
4. #22258C2semidirect
5. #22236C2semidirect
6. #22132C2semidirect
7. #22096C2semidirect
8. #22095C2semidirect
9. #21993C2semidirect
11. #21845C2semidirect
12. #21733C2semidirect
13. #21659C2semidirect
14. #21629C2semidirect
15. #21593C2semidirect
16. #21592C2semidirect
17. #20481C2semidirect
20. #3233C4semidirect
21. #3232C4semidirect
22. #3232C4semidirect
23. #3231C4semidirect
24. #3230C4semidirect
25. #3229C4semidirect
26. #3228C4semidirect
27. #3227C4semidirect
28. #3226C4semidirect

Maximal subgroups

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

subgroupindex
#608462
#602072
C2×#29612
#222582
#222362
#221322
#220962
#220952
#219932
#218572
#218452
#217332
#216592
#216292
#215932
#215922
#204812