Finite Group Databasebeta

← #7506764

Subgroups — #7506764

Order 512.

2262 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2#34742C211yesmaximal, characteristic, complemented
3#31960C214yesmaximal, complemented
4#31958C214yesmaximal, complemented
5#31932C214yesmaximal, complemented
6#31930C214yesmaximal, complemented
7#23734C211yesmaximal, characteristic, complemented
8#23658C211yesmaximal, characteristic, complemented
9#23628C211yesmaximal, characteristic, complemented
10#23618C211yesmaximal, characteristic, complemented
11#23480C211yesmaximal, characteristic, complemented
12#23391C211yesmaximal, characteristic
13#21236C211yesmaximal, characteristic, complemented
14#21049C211yesmaximal, characteristic, complemented
15#20928C211yesmaximal, characteristic, complemented
16#20909C211yesmaximal, characteristic, complemented
17#20844C211yesmaximal, characteristic, complemented
18#20764C211yesmaximal, characteristic, complemented
19#20648C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×#123—22no—
23C22×#121C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#423C2211yescharacteristic
30C2×#417C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#418C2211yescharacteristic
36C2×#407C2211yescharacteristic
37C2×#407C2211yescharacteristic
38C2×C4×M16C2211yescharacteristic
39#2501—22no—
40#2501—22no—
41#2501C2214yes—
42#2501C2214yes—
43#2423C2212yescomplemented
44#2422C2212yescomplemented
45#2421C2212yescomplemented
46#2420C2212yescomplemented
47#2419—22no—
48#2418—22no—
49#2395—22no—
50C2×#399—22no—
51C4×#123—22no—
52#2297C2211yescharacteristic
53#2296C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56#2285C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59#2280C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61#2096C2212yescomplemented
62#2095C2212yescomplemented
63#2094C2212yescomplemented
64#2093C2212yescomplemented
65#2084C2214yescomplemented
66#2083C2214yescomplemented
67#2073C2214yescomplemented
68#2071C2214yescomplemented
69#2067C2214yescomplemented
70#2065C2214yescomplemented
71#2034C2214yes—
72#2033C2214yes—
73#2000C2214yes—
74#1999C2214yes—
75#1973C2212yescomplemented
76#1972C2212yescomplemented
77#1970C2212yescomplemented
78#1968C2212yescomplemented
79#1924C2214yescomplemented
80#1923C2214yescomplemented
81#1880C2214yescomplemented
82#1879C2214yescomplemented
83#1874C2214yescomplemented
84#1872C2214yescomplemented
85#1853C2214yescomplemented
86#1852C2214yescomplemented
87#1836C2214yescomplemented
88#1834C2214yescomplemented
89#1803C2214yescomplemented
90#1802C2214yescomplemented
91#1736C2211yescharacteristic
92#1736C2211yescharacteristic
93#1736C2211yescharacteristic
94#1736C2211yescharacteristic
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4C2311yescharacteristic
104C2×AGL(1,ℤ/8)—24no—
105C2×AGL(1,ℤ/8)—24no—
106C2×AGL(1,ℤ/8)—42no—
107C22×SD16C2312yes—
108C22×D8C2312yes—
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C22×M16C2311yescharacteristic
112C22×M16C2311yescharacteristic
113#525—24no—
114#525—42no—
115C2×#123—21no—
116C2×#123—24no—
117C2×#123—24no—
118C2×#123—24no—
119C2×#123—24no—
120C2×#123—22no—
121C2×#123—416no—
122C2×C22⋊Q8C2312yes—
123C2×#121—22no—
124C2×#121—42no—
125C2×#121—42no—
126C2×#121C2312yes—
127C2×#121C2314yes—
128C2×#120—21no—
129C4×#41—24no—
130C4×#41—42no—
131C2×C4×Q8C2312yes—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4C2312yes—
135C2×#117—21no—
136C2×#117C2311yescharacteristic
137C2×#117C2311yescharacteristic
138C2×#117C2311yescharacteristic
139C22×C4⋊C4—21no—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—22no—
142C22×C4⋊C4—22no—
143C22×C4⋊C4—42no—
144C22×C4⋊C4—42no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—22no—
151C22×C22⋊C4—22no—
152C22×C22⋊C4D412yes—
153C22×C42—21no—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#428—42no—
157#428—42no—
158#428—42no—
159C2×#107C2312yes—
160C2×#107C2312yes—
161C2×#107C2312yes—
162C2×#106C2312yes—
163C2×#106C2312yes—
164C2×#106C2312yes—
165#423—42no—
166C2×C4⋊C8C2314yes—
167#418—42no—
168#418—42no—
169#418—42no—
170#417—42no—
171#417—42no—
172#417—42no—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#102C2312yes—
177C2×#102C2312yes—
178C2×#102C2312yes—
179C2×#102C2314yes—
180C2×#102C2312yes—
181C2×#102C2314yes—
182C2×#102C2312yes—
183#407—24no—
184#407—42no—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C4×M16—24no—
188C2×#97C2312yes—
189C2×C4×C8C2312yes—
190#400—22no—
191#399—22no—
192#399—24no—
193#399—24no—
194#399—24no—
195#399—24no—
196#398—22no—
197#397—22no—
198#397—22no—
199#397—22no—
200#394—22no—
201#394—22no—
202#391C2311yescharacteristic
203#391C2311yescharacteristic
204#390—21no—
205#390—22no—
206#390—21no—
207#390C2314yes—
208#390C2312yes—
209#390C2312yes—
210#390C2311yescharacteristic
211#390C2311yescharacteristic
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#386—22no—
219#386—22no—
220#385—22no—
221#385—22no—
222#384—21no—
223#384—22no—
224#384—21no—
225#384C2314yes—
226#384C2312yes—
227#384C2312yes—
228#384C2312yes—
229#382C2312yes—
230#381—21no—
231#381—22no—
232#380—22no—
233#380C2312yes—
234#380C2312yes—
235#379—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—21no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4D412yes—
242C4×C22⋊C4D412yes—
243C4×C22⋊C4C2312yes—
244C4×C22⋊C4C2312yes—
245C2×#95D412yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#336C2312yes—
253#336C2312yes—
254#336C2314yes—
255C25—21no—
256C25C2×D411yescharacteristic
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41#4114yes—
263C22×Q8C2411yescharacteristic
264C22×D4—21no—
265C22×D4—24no—
266C22×D4—22no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—44no—
275C22×D4—48no—
276C22×D4C2412yes—
277C22×D4C2411yescharacteristic
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—44no—
291C23×C4—48no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298AGL(1,ℤ/8)—416no—
299C2×SD16—24no—
300C2×SD16—24no—
301C2×SD16—42no—
302C2×D8—24no—
303C2×D8—24no—
304C2×D8—42no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16#4114yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321#123—416no—
322#123—416no—
323#123—416no—
324#123—44no—
325#123—48no—
326#123—416no—
327C22⋊Q8—24no—
328C22⋊Q8—42no—
329#121—24no—
330#121—44no—
331#121—44no—
332#121—42no—
333#121—48no—
334#120—44no—
335C4×Q8—24no—
336C4×Q8—42no—
337C4×D4—24no—
338C4×D4—42no—
339C4×D4—48no—
340C4×D4—48no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—44no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—48no—
372C2×C4⋊C4—48no—
373C2×C4⋊C4—48no—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2411yescharacteristic
381C2×C22⋊C4—28no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—48no—
399C2×C22⋊C4—48no—
400C2×C22⋊C4C2×D412yes—
401C2×C22⋊C4C2×D412yes—
402C2×C22⋊C4C2×D412yes—
403C2×C22⋊C4C2×D412yes—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—22no—
412C2×C42—44no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D412yes—
415C2×C42C2×D411yescharacteristic
416C2×C42C2412yes—
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419#107—42no—
420#107—42no—
421#107—42no—
422#106—42no—
423#106—42no—
424#106—42no—
425C4⋊C8—44no—
426#103—42no—
427#103—42no—
428#103—42no—
429#102—42no—
430#102—42no—
431#102—42no—
432#102—42no—
433#102—42no—
434#102—44no—
435#102—44no—
436C22⋊C8—28no—
437C22⋊C8—44no—
438#97—24no—
439C4×C8—24no—
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#95C2×D412yes—
449#95C2×D412yes—
450#95C2×D412yes—
451#95C2×D412yes—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—22no—
458C24—42no—
459C24—44no—
460C24—44no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24C22×D412yes—
465C24C22×D411yescharacteristic
466#41—28no—
467#41—28no—
468#41—44no—
469#41—44no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8C2×#4112yes—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—82no—
503C2×D4—816no—
504C2×D4C2×#4112yes—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—48no—
548C22×C4—44no—
549C22×C4—82no—
550C22×C4—816no—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D411yescharacteristic
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C42−1+412yes—
563C22×C4C2511yescharacteristic
564SD16—48no—
565D8—48no—
566M16—28no—
567M16—44no—
568M16—44no—
569M16—44no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8C2×#4114yes—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4AGL(1,ℤ/8)18yescomplemented
629C42—22no—
630C42—22no—
631C42—24no—
632C42—21no—
633C42—21no—
634C42—22no—
635C42—22no—
636C42—21no—
637C42—21no—
638C42—44no—
639C42—42no—
640C42—42no—
641C42—42no—
642C23—22no—
643C23—22no—
644C23—28no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—48no—
654C23—44no—
655C23—44no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—84no—
666C23—88no—
667C23—84no—
668C23—88no—
669C23—84no—
670C23#53512yes—
671C23#54612yes—
672C23#54712yes—
673C23C2×AGL(1,ℤ/8)14yes—
674C23C23×D411yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—41no—
678Q8—41no—
679D4—22no—
680D4—22no—
681D4—48no—
682D4—42no—
683D4—41no—
684D4—42no—
685D4—42no—
686D4—41no—
687D4—42no—
688D4—88no—
689D4—816no—
690D4—84no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—48no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—88no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4—816no—
736C2×C4—84no—
737C2×C4#53512yes—
738C2×C4#53914yes—
739C2×C4#54014yes—
740C2×C4#54612yes—
741C2×C4#54712yes—
742C2×C4#55114yes—
743C2×C4#56214yes—
744C2×C4C2×AGL(1,ℤ/8)14yes—
745C2×C4C2×AGL(1,ℤ/8)14yes—
746C2×C4C22×#4111yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×2−1+411yescharacteristic
752C8—24no—
753C8—42no—
754C8—42no—
755C8—42no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—416no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—44no—
770C22—82no—
771C22—81no—
772C22—81no—
773C22—84no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—84no—
778C22—168no—
779C22#270614yes—
780C22C2×#53511yescharacteristic
781C22C2×#54611yescharacteristic
782C22C2×#54711yescharacteristic
783C22C22×AGL(1,ℤ/8)12yes—
784C22#358612yes—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—81no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—81no—
796C4—82no—
797C4—82no—
798C4#270614yes—
799C4C2×#53911yescharacteristic
800C4C2×#54011yescharacteristic
801C4C2×#55111yescharacteristic
802C4C2×#56211yescharacteristic
803C2—24no—
804C2—44no—
805C2—82no—
806C2—162no—
807C2C2×#270611yescharacteristic
808C2#6079811yescharacteristic
809C2#6080711yescharacteristic
810C2#6116112yes—
811C2#6125212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23391C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2501C2semidirect
2. #34742C2semidirect
3. #31960C2semidirect
4. #31958C2semidirect
5. #31932C2semidirect
6. #31930C2semidirect
7. #23734C2semidirect
8. #23658C2semidirect
9. #23628C2semidirect
10. #23618C2semidirect
11. #23480C2semidirect
13. #21236C2semidirect
14. #21049C2semidirect
15. #20928C2semidirect
16. #20909C2semidirect
17. #20844C2semidirect
18. #20764C2semidirect
19. #20648C2semidirect
43. #2423C22semidirect
44. #2422C22semidirect
45. #2421C22semidirect
46. #2420C22semidirect
61. #2096C22semidirect
62. #2095C22semidirect
63. #2094C22semidirect
64. #2093C22semidirect
65. #2084C22semidirect
66. #2083C22semidirect
67. #2073C22semidirect
68. #2071C22semidirect
69. #2067C22semidirect
70. #2065C22semidirect
75. #1973C22semidirect
76. #1972C22semidirect
77. #1970C22semidirect
78. #1968C22semidirect
79. #1924C22semidirect
80. #1923C22semidirect
81. #1880C22semidirect
82. #1879C22semidirect
83. #1874C22semidirect
84. #1872C22semidirect
85. #1853C22semidirect
86. #1852C22semidirect
87. #1836C22semidirect
88. #1834C22semidirect
89. #1803C22semidirect
90. #1802C22semidirect
628. C22⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
#347422
#319602
#319582
#319322
#319302
#237342
#236582
#236282
#236182
#234802
#233912
#212362
#210492
#209282
#209092
#208442
#207642
#206482