Finite Group Databasebeta

← #6488712

Subgroups — #6488712

Order 512.

1914 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35291C211yesmaximal, characteristic, complemented
2#34210C211yesmaximal, characteristic
3#33018C214yesmaximal, complemented
4#30138C214yesmaximal, complemented
5#29377C214yesmaximal, complemented
6#29192C211yesmaximal, characteristic, complemented
7#29190C211yesmaximal, characteristic, complemented
8#28613C211yesmaximal, characteristic, complemented
9#28613C211yesmaximal, characteristic, complemented
10#28130C214yesmaximal, complemented
11#27962C211yesmaximal, characteristic, complemented
12#27908C211yesmaximal, characteristic, complemented
13#25855C211yesmaximal, characteristic
14#25717C211yesmaximal, characteristic
15#22268C211yesmaximal, characteristic, complemented
16#22268C211yesmaximal, characteristic, complemented
17#22220C211yesmaximal, characteristic, complemented
18#22219C211yesmaximal, characteristic, complemented
19#20782C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C2×#518C2212yes—
22C2×#492C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#485C2214yes—
27C2×#450C2214yes—
28#2862C2211yescharacteristic, complemented
29#2859C2211yescharacteristic, complemented
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2645C2212yescomplemented
33#2625C2212yes—
34#2514—21no—
35#2509—21no—
36#2508—21no—
37#2495—21no—
38#2494—21no—
39#2489—21no—
40#2453—21no—
41#2421—21no—
42#2366—21no—
43#2366—21no—
44#2366—21no—
45#2366—21no—
46D4×C22⋊C4—21no—
47D4×C22⋊C4—21no—
48D4×C22⋊C4—21no—
49D4×C22⋊C4—21no—
50#2328C2212yes—
51#2328C2212yes—
52#2323C2212yes—
53#2320C2212yescomplemented
54#2309C2212yes—
55C4×C4⋊Q8C2211yescharacteristic, complemented
56C4×C4⋊Q8C2211yescharacteristic, complemented
57C4×#127C2211yescharacteristic
58C4×#127C2211yescharacteristic
59C4×#127C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C4×#117C2211yescharacteristic
63#2101C2214yescomplemented
64#2097C2214yescomplemented
65#2067C2214yescomplemented
66#2065C2214yescomplemented
67#2055C2214yescomplemented
68#2055C2214yescomplemented
69#2041C2214yes—
70#2014C2214yes—
71#1990C2211yescharacteristic, complemented
72#1990C2211yescharacteristic, complemented
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1956C2211yescharacteristic, complemented
78#1956C2211yescharacteristic, complemented
79#1926C2214yescomplemented
80#1925C2214yescomplemented
81#1880C2214yescomplemented
82#1880C2214yescomplemented
83#1877C2214yescomplemented
84#1877C2214yescomplemented
85#1877C2214yescomplemented
86#1877C2214yescomplemented
87#1864C2214yescomplemented
88#1864C2214yescomplemented
89#1862C2214yescomplemented
90#1862C2214yescomplemented
91#1845C2211yescharacteristic, complemented
92#1844C2211yescharacteristic, complemented
93#1840C2212yescomplemented
94#1834C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1832C2212yescomplemented
97#1825C2214yes—
98#1818C2212yes—
99#1798C2212yes—
100#1786C2214yes—
101C4×C4⋊C8C2211yescharacteristic, complemented
102C4×C4⋊C8C2211yescharacteristic, complemented
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1744C2211yescharacteristic, complemented
106#1744C2211yescharacteristic, complemented
107C23×D4—21no—
108C23×D4—21no—
109C23×D4C2312yes—
110C22×SD16C2314yes—
111C22×SD16C2314yes—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127—24no—
115C2×#127—24no—
116C2×#127—21no—
117C2×#127—21no—
118C2×#127C2312yes—
119C2×#127C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8C2312yes—
124#518—48no—
125C2×C4×Q8—21no—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×#117C2312yes—
142C2×#117C2311yescharacteristic
143C2×#117C2311yescharacteristic
144C22×C22⋊C4—22no—
145C22×C22⋊C4—22no—
146C22×C42C2311yescharacteristic
147#492—24no—
148#492—24no—
149#486—24no—
150#486—24no—
151#485—48no—
152#450—48no—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C4×C8C2311yescharacteristic
168C2×C4×C8C2311yescharacteristic
169C2×C4×C8C2311yescharacteristic
170C2×C4×C8C2311yescharacteristic
171#401—22no—
172#400—22no—
173#400—22no—
174#400—22no—
175#400—22no—
176#398—22no—
177#397—22no—
178#397—22no—
179#391—21no—
180#391—21no—
181#391—21no—
182#391—21no—
183#391C2312yes—
184#391C2312yes—
185#391C2312yes—
186#391C2312yes—
187#390—22no—
188#390—22no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390C2312yes—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#389—22no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#383—22no—
232#382—21no—
233#382—21no—
234#382—21no—
235#382—22no—
236#382C2312yes—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380C2312yes—
243#379—22no—
244#379—22no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4D411yescharacteristic
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4C2312yes—
255C4×C22⋊C4D411yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259#376C2311yescharacteristic
260#376C2311yescharacteristic
261C43C2311yescharacteristic
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#336C2312yes—
268#336C2312yes—
269#336C2312yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275C25—22no—
276C22×Q8—21no—
277C22×Q8C2412yes—
278C22×D4—28no—
279C22×D4—28no—
280C22×D4—24no—
281C22×D4—24no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—28no—
290C22×D4—44no—
291C22×D4—82no—
292C22×D4—82no—
293C22×D4—82no—
294C22×D4—82no—
295C22×D4C2412yes—
296C22×D4C2412yes—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×SD16—44no—
309C2×SD16—44no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318#127—28no—
319#127—28no—
320#127—24no—
321#127—24no—
322#127—22no—
323#127—22no—
324#127#4114yes—
325#127#4114yes—
326#125—82no—
327C22⋊Q8—28no—
328C22⋊Q8—82no—
329C4×Q8—44no—
330C4×Q8—82no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4—48no—
336C4×D4—48no—
337C4×D4—82no—
338C4×D4—82no—
339C4×D4—82no—
340C4×D4—82no—
341C4×D4—82no—
342C4×D4—82no—
343C4×D4—82no—
344C4×D4—82no—
345#117—24no—
346#117—28no—
347#117—42no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C2×D411yescharacteristic
366C2×C4⋊C4C2×D411yescharacteristic
367C2×C4⋊C4C2×D411yescharacteristic
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—48no—
390C2×C22⋊C4—48no—
391C2×C22⋊C4C2×D411yescharacteristic
392C2×C22⋊C4C2×D411yescharacteristic
393C2×C22⋊C4C2×D411yescharacteristic
394C2×C22⋊C4C2×D411yescharacteristic
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416#107—44no—
417#106—44no—
418C4⋊C8—42no—
419C4⋊C8—42no—
420#103—44no—
421#103—44no—
422#102—28no—
423#102—28no—
424#102—44no—
425#102—44no—
426#102—44no—
427#102—44no—
428C22⋊C8—24no—
429C22⋊C8—24no—
430C4×C8—22no—
431C4×C8—22no—
432C4×C8—22no—
433C4×C8—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95C2×D411yescharacteristic
451#95C2×D411yescharacteristic
452#95C2×D411yescharacteristic
453#95C2×D411yescharacteristic
454#95C2×D411yescharacteristic
455#95C2×D411yescharacteristic
456#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458C24—28no—
459C24—22no—
460C24—22no—
461C24—44no—
462C24—44no—
463C24—82no—
464C24—82no—
465C24—82no—
466C24—82no—
467C24C22×D411yescharacteristic
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—82no—
501C2×D4—82no—
502C2×D4—82no—
503C2×D4—82no—
504C2×D4—816no—
505C2×D4—816no—
506C2×D4C2×#4114yes—
507C2×D4C2×#4114yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—82no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4H(5,𝔽2)14yes—
549C22×C4C2511yescharacteristic
550SD16—88no—
551SD16—88no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—44no—
627C42—44no—
628C42—82no—
629C42C2×#4112yes—
630C42C2×#4112yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—24no—
638C23—24no—
639C23—416no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—88no—
653C23—88no—
654C23—164no—
655C23—164no—
656C23—164no—
657C23—164no—
658C23#53512yes—
659C23C23×D411yescharacteristic
660Q8—44no—
661Q8—44no—
662Q8—84no—
663D4—28no—
664D4—28no—
665D4—416no—
666D4—48no—
667D4—48no—
668D4—48no—
669D4—48no—
670D4—44no—
671D4—44no—
672D4—88no—
673D4—88no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—164no—
729C2×C4—164no—
730C2×C4—164no—
731C2×C4—164no—
732C2×C4#52512yes—
733C2×C4#52512yes—
734C2×C4#53512yes—
735C2×C4#57612yes—
736C2×C4#57712yes—
737C2×C4#57712yes—
738C2×C4#57712yes—
739C2×C4C22×#4111yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C2×H(5,𝔽2)12yes—
742C2×C4#58512yes—
743C8—42no—
744C8—42no—
745C8—42no—
746C8—42no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—1616no—
769C22C2×#52511yescharacteristic
770C22C2×#53511yescharacteristic
771C22#344911yescharacteristic
772C22C2×#57611yescharacteristic
773C22C2×#57711yescharacteristic
774C22C2×#57711yescharacteristic
775C22C2×#57711yescharacteristic
776C4—22no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4#311814yes—
794C4#312314yes—
795C4#351312yes—
796C4#351312yes—
797C2—42no—
798C2—84no—
799C2—84no—
800C2#3523311yescharacteristic
801C2C2×#311811yescharacteristic
802C2C2×#312311yescharacteristic
803C2#6081811yescharacteristic
804C2#6082211yescharacteristic
805C2#6100611yescharacteristic
806C2#6101211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35291C2semidirect
3. #33018C2semidirect
4. #30138C2semidirect
5. #29377C2semidirect
6. #29192C2semidirect
7. #29190C2semidirect
8. #28613C2semidirect
9. #28613C2semidirect
10. #28130C2semidirect
11. #27962C2semidirect
12. #27908C2semidirect
15. #22268C2semidirect
16. #22268C2semidirect
17. #22220C2semidirect
18. #22219C2semidirect
19. #20782C2semidirect
28. #2862C22semidirect
29. #2859C22semidirect
32. #2645C22semidirect
53. #2320C22semidirect
55. C4×C4⋊Q8C22semidirect
56. C4×C4⋊Q8C22semidirect
63. #2101C22semidirect
64. #2097C22semidirect
65. #2067C22semidirect
66. #2065C22semidirect
67. #2055C22semidirect
68. #2055C22semidirect
71. #1990C22semidirect
72. #1990C22semidirect
77. #1956C22semidirect
78. #1956C22semidirect
79. #1926C22semidirect
80. #1925C22semidirect
81. #1880C22semidirect
82. #1880C22semidirect
83. #1877C22semidirect
84. #1877C22semidirect
85. #1877C22semidirect
86. #1877C22semidirect
87. #1864C22semidirect
88. #1864C22semidirect
89. #1862C22semidirect
90. #1862C22semidirect
91. #1845C22semidirect
92. #1844C22semidirect
93. #1840C22semidirect
94. #1834C22semidirect
95. #1834C22semidirect
96. #1832C22semidirect
101. C4×C4⋊C8C22semidirect
102. C4×C4⋊C8C22semidirect
105. #1744C22semidirect
106. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#352912
#342102
#330182
#301382
#293772
#291922
#291902
#286132
#281302
#279622
#279082
#258552
#257172
#222682
#222202
#222192
#207822