Finite Group Databasebeta

← #6375860

Subgroups — #6375860

Order 512.

2384 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3036C211yesmaximal, characteristic
2#34207C211yesmaximal, characteristic, complemented
3#34058C211yesmaximal, characteristic, complemented
4#22161C214yesmaximal, complemented
5#22157C214yesmaximal, complemented
6#22152C212yesmaximal, complemented
7#22151C212yesmaximal, complemented
8#22146C212yesmaximal, complemented
9#22145C212yesmaximal, complemented
10#21257C211yesmaximal, characteristic, complemented
11#21235C212yesmaximal, complemented
12#21171C211yesmaximal, characteristic, complemented
13#21092C212yesmaximal, complemented
14#20932C212yesmaximal, complemented
15#20878C212yesmaximal, complemented
16C2×#1802C211yesmaximal, characteristic, complemented
17#20431C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2212yes—
19C2×#532C2211yescharacteristic
20C2×#520C2212yes—
21C22×C4×D4C2211yescharacteristic
22#3036C4116yescomplemented
23C2×#463C2214yes—
24C2×#461C2212yes—
25C2×#459C2212yes—
26C2×#428C2212yes—
27C2×#423C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#417C2212yes—
30C2×#416C2212yes—
31C2×#416C2212yes—
32C22×#102C2212yes—
33C2×#405C2212yes—
34#2361—22no—
35#2361—22no—
36#2354—21no—
37#2354—21no—
38D4×C4⋊C4—21no—
39D4×C4⋊C4—21no—
40#2326C2214yescomplemented
41#2319—21no—
42#2319—21no—
43#2319C2212yes—
44#2319C2212yes—
45#2316C2211yescharacteristic
46#2316C2211yescharacteristic
47#2312—22no—
48#2311C2212yes—
49#2309C2211yescharacteristic
50#2309C2211yescharacteristic
51C4×C4⋊Q8C2212yescomplemented
52C4×#127C2212yescomplemented
53#2293—21no—
54#2293—21no—
55#2293C2212yes—
56#2293C2212yes—
57C2×#384C2211yescharacteristic
58#2280—22no—
59C4×#117C2211yescharacteristic
60C4×#117C2211yescharacteristic
61#1983C2212yescomplemented
62#1983C2212yescomplemented
63#1982C2211yescharacteristic, complemented
64#1982C2211yescharacteristic, complemented
65#1981C2211yescharacteristic, complemented
66#1981C2211yescharacteristic, complemented
67#1973C2214yes—
68#1972C2214yes—
69#1970C2214yes—
70#1968C2214yes—
71#1948C2212yescomplemented
72#1948C2212yescomplemented
73#1947C2212yescomplemented
74#1947C2212yescomplemented
75#1936C2214yescomplemented
76#1935C2214yescomplemented
77#1934C2214yescomplemented
78#1933C2214yescomplemented
79#1880C2214yes—
80#1880C2214yes—
81#1879C2214yes—
82#1879C2214yes—
83#1865C2214yescomplemented
84#1864C2214yescomplemented
85#1863C2214yescomplemented
86#1862C2214yescomplemented
87#1802C2212yes—
88#1802C2212yes—
89#1802C2214yes—
90#1768C2214yescomplemented
91#1767C2212yescomplemented
92C4×C4⋊C8C2212yescomplemented
93#1736C2212yes—
94C2×#340C2212yes—
95#1729C2212yes—
96C22×#41C2312yes—
97C23×D4C2311yescharacteristic
98C24×C4—21no—
99C2×AGL(1,ℤ/8)—44no—
100C2×AGL(1,ℤ/8)—44no—
101C2×AGL(1,ℤ/8)C2×C4116yescomplemented
102C22×SD16C2314yes—
103C22×D8C2314yes—
104C22×M16C2312yes—
105C23×C8C2312yes—
106#532—24no—
107#532C2×C418yes—
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#124C2312yes—
111C2×#121—21no—
112C2×#121—21no—
113#520—44no—
114#520—44no—
115C2×C4×Q8C2314yes—
116C2×C4×D4—24no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—24no—
124C2×C4×D4C2×C418yescomplemented
125C2×C4×D4C2312yes—
126C2×C4×D4C2312yes—
127C2×C4×D4C2314yes—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117C2311yescharacteristic
132C2×#117C2311yescharacteristic
133C2×#117C2311yescharacteristic
134C2×#117C2311yescharacteristic
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—22no—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C42C2311yescharacteristic
142#463C2×C4132yescomplemented
143#461C2×C4116yescomplemented
144#459C2×C4116yescomplemented
145#428—44no—
146C2×#107C2314yes—
147C2×#106C2314yes—
148#423C2×C418yescomplemented
149C2×C4⋊C8—24no—
150C2×C4⋊C8C2311yescharacteristic
151C2×C4⋊C8C2311yescharacteristic
152C2×C4⋊C8C2312yes—
153C2×C4⋊C8C2312yes—
154C2×C4⋊C8C2312yes—
155#417C2×C4116yescomplemented
156#416—44no—
157#416—44no—
158C2×#103C2312yes—
159C2×#103C2312yes—
160C2×#103C2312yes—
161C2×#103C2312yes—
162C2×#103C2314yes—
163C2×#102—44no—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2312yes—
167C2×#102C2312yes—
168C2×#102C2312yes—
169C2×#102C2312yes—
170C2×#102C2314yes—
171#405—44no—
172C2×#97C2314yes—
173C2×C4×C8C2314yes—
174#391C2314yes—
175#390—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—22no—
180#390—22no—
181#390C2314yes—
182#390C2312yes—
183#390C2312yes—
184#390C2312yes—
185#390C2312yes—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—22no—
191#389—22no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—24no—
205#388—24no—
206#386—24no—
207#385—24no—
208#385—24no—
209#384—21no—
210#384—21no—
211#384C2312yes—
212#384C2312yes—
213#381—22no—
214#381—22no—
215#380—22no—
216#380—22no—
217#380—22no—
218#380—22no—
219#380—22no—
220#380—22no—
221#379—22no—
222#379—22no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4—22no—
225C4×C4⋊C4D411yescharacteristic
226C4×C4⋊C4D411yescharacteristic
227C4×C4⋊C4D411yescharacteristic
228C4×C4⋊C4D411yescharacteristic
229C4×C4⋊C4C2311yescharacteristic
230C4×C4⋊C4C2311yescharacteristic
231C4×C4⋊C4C2311yescharacteristic
232C4×C4⋊C4C2311yescharacteristic
233C4×C22⋊C4—21no—
234C4×C22⋊C4—21no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4D412yes—
238C4×C22⋊C4D412yes—
239#376—21no—
240#376C2312yes—
241C43—21no—
242C43C2312yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#336C2314yes—
248#336C2314yes—
249C25—21no—
250C2×#41—24no—
251C2×#41—24no—
252C2×#41—24no—
253C2×#41—24no—
254C2×#41—24no—
255C2×#41C22×C418yes—
256C22×Q8C2412yes—
257C22×D4—22no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4C22×C414yes—
267C22×D4C2412yes—
268C22×D4C2412yes—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—28no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—82no—
277C23×C4—82no—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2411yescharacteristic
281AGL(1,ℤ/8)—432no—
282C2×SD16—44no—
283C2×SD16—44no—
284C2×SD16C22×C4116yes—
285C2×D8—44no—
286C2×D8—44no—
287C2×D8C22×C4116yes—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16C22×C418yes—
291C22×C8—24no—
292C22×C8—24no—
293C22×C8—24no—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2414yes—
297C4⋊Q8—22no—
298C4⋊Q8C22×C414yes—
299#127—22no—
300#127C22×C414yes—
301#124—24no—
302#124C22×C418yes—
303#121—28no—
304#121—28no—
305C4×Q8—44no—
306C4×Q8—44no—
307C4×D4—28no—
308C4×D4—28no—
309C4×D4—28no—
310C4×D4—28no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—44no—
314C4×D4—44no—
315C4×D4—416no—
316C4×D4—84no—
317C4×D4—84no—
318C4×D4C22×C418yes—
319C4×D4C22×C418yes—
320#117—22no—
321#117—22no—
322#117—22no—
323#117—22no—
324#117—22no—
325#117—22no—
326#117—22no—
327#117—22no—
328#117—48no—
329#117—84no—
330#117—84no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—48no—
348C2×C4⋊C4—82no—
349C2×C4⋊C4—82no—
350C2×C4⋊C4C22×C414yes—
351C2×C4⋊C4C2×D411yescharacteristic
352C2×C4⋊C4C2×D411yescharacteristic
353C2×C4⋊C4C2×D411yescharacteristic
354C2×C4⋊C4C2×D411yescharacteristic
355C2×C4⋊C4C2414yes—
356C2×C4⋊C4C2411yescharacteristic
357C2×C4⋊C4C2411yescharacteristic
358C2×C4⋊C4C2411yescharacteristic
359C2×C4⋊C4C2411yescharacteristic
360C2×C4⋊C4C2412yes—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4C2×D412yes—
380C2×C22⋊C4C2×D412yes—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—24no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42C22×C414yes—
389C2×C42C2×D412yes—
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42#4114yes—
396C2×C42C2412yes—
397C2×C42C2412yes—
398C2×C42C2411yescharacteristic
399C2×C42C2411yescharacteristic
400#107—44no—
401#106—44no—
402C4⋊C8—24no—
403C4⋊C8—22no—
404C4⋊C8—22no—
405C4⋊C8C22×C418yes—
406C4⋊C8C22×C418yes—
407#103—42no—
408#103—42no—
409#103—42no—
410#103—42no—
411#103C22×C4116yes—
412#102—44no—
413#102—44no—
414#102—42no—
415#102—42no—
416#102—42no—
417#102—42no—
418#102C22×C4116yes—
419#97—44no—
420C4×C8—44no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431#95C2×D412yes—
432#95C2×D412yes—
433#95C2×D412yes—
434#95C2×D412yes—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—42no—
439C24—42no—
440C24—81no—
441C24—81no—
442C24—81no—
443C24—81no—
444C24C22×D411yescharacteristic
445#41—216no—
446#41—216no—
447#41—48no—
448#41—48no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8C23×C414yes—
455C2×D4—28no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4C23×C414yes—
482C2×D4C23×C414yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—816no—
505C22×C4—82no—
506C22×C4—82no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—82no—
512C22×C4—82no—
513C22×C4C4×D414yes—
514C22×C4C4×D414yes—
515C22×C4C23×C412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2×#4112yes—
526C22×C4H(5,𝔽2)12yes—
527C22×C4H(5,𝔽2)12yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C42−1+412yes—
530C22×C4C2511yescharacteristic
531SD16—416no—
532D8—416no—
533M16—216no—
534C2×C8—24no—
535C2×C8—24no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—48no—
543C2×C8C23×C418yes—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—48no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—82no—
567C4⋊C4—82no—
568C4⋊C4—82no—
569C4⋊C4—82no—
570C4⋊C4—82no—
571C4⋊C4—82no—
572C4⋊C4C23×C414yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—48no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—82no—
583C22⋊C4—82no—
584C22⋊C4—82no—
585C22⋊C4—82no—
586C22⋊C4—82no—
587C22⋊C4—82no—
588C22⋊C4—82no—
589C22⋊C4—82no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C42—24no—
593C42—24no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—42no—
599C42—42no—
600C42—48no—
601C42—42no—
602C42—42no—
603C42—42no—
604C42—42no—
605C42—81no—
606C42—81no—
607C42C4×D414yes—
608C42C4×D414yes—
609C42C23×C412yes—
610C42C23×C412yes—
611C42C2×#4112yes—
612C42C2×#4112yes—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—24no—
618C23—24no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—48no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23C2×C4×D412yes—
639C23#53512yes—
640C23#53712yes—
641C23C23×D411yescharacteristic
642Q8—24no—
643Q8—24no—
644Q8—42no—
645Q8—42no—
646D4—24no—
647D4—24no—
648D4—24no—
649D4—24no—
650D4—48no—
651D4—416no—
652D4—48no—
653D4—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—48no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—416no—
685C2×C4—416no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—88no—
702C2×C4—84no—
703C2×C4—168no—
704C2×C4—164no—
705C2×C4C2×C4×D412yes—
706C2×C4C2×C4×D412yes—
707C2×C4C2×C4×D412yes—
708C2×C4C2×C4×D412yes—
709C2×C4C2×C4×D412yes—
710C2×C4#51814yes—
711C2×C4#52014yes—
712C2×C4#53512yes—
713C2×C4#53712yes—
714C2×C4#54014yes—
715C2×C4#54214yes—
716C2×C4#57612yes—
717C2×C4#57712yes—
718C2×C4C24×C411yescharacteristic
719C2×C4C22×#4111yescharacteristic
720C2×C4C2×H(5,𝔽2)11yescharacteristic
721C2×C4C2×H(5,𝔽2)11yescharacteristic
722C2×C4C2×H(5,𝔽2)11yescharacteristic
723C2×C4C2×2−1+411yescharacteristic
724C8—28no—
725C8—42no—
726C8—42no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—816no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22#232414yes—
749C22C22×C4×D411yescharacteristic
750C22C2×#53511yescharacteristic
751C22C2×#53711yescharacteristic
752C22C2×#57611yescharacteristic
753C22C2×#57711yescharacteristic
754C22#358511yescharacteristic
755C22#358611yescharacteristic
756C4—22no—
757C4—22no—
758C4—22no—
759C4—42no—
760C4—42no—
761C4—44no—
762C4—42no—
763C4—42no—
764C4—44no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4—84no—
769C4—81no—
770C4#232414yes—
771C4#294614yes—
772C4C2×#51811yescharacteristic
773C4C2×#52011yescharacteristic
774C4C2×#54011yescharacteristic
775C4C2×#54211yescharacteristic
776C2—24no—
777C2—84no—
778C2—84no—
779C2C2×#232411yescharacteristic
780C2C2×#294611yescharacteristic
781C2#6017011yescharacteristic
782C2#6083211yescharacteristic
783C2#6083611yescharacteristic
784C2#6092811yescharacteristic
785C2#6092911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3036C2
LCSG ▷ C2×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
2. #34207C2semidirect
3. #34058C2semidirect
4. #22161C2semidirect
5. #22157C2semidirect
6. #22152C2semidirect
7. #22151C2semidirect
8. #22146C2semidirect
9. #22145C2semidirect
10. #21257C2semidirect
11. #21235C2semidirect
12. #21171C2semidirect
13. #21092C2semidirect
14. #20932C2semidirect
15. #20878C2semidirect
16. C2×#1802C2semidirect
17. #20431C2semidirect
22. #3036C4semidirect
40. #2326C22semidirect
51. C4×C4⋊Q8C22semidirect
52. C4×#127C22semidirect
61. #1983C22semidirect
62. #1983C22semidirect
63. #1982C22semidirect
64. #1982C22semidirect
65. #1981C22semidirect
66. #1981C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1947C22semidirect
74. #1947C22semidirect
75. #1936C22semidirect
76. #1935C22semidirect
77. #1934C22semidirect
78. #1933C22semidirect
83. #1865C22semidirect
84. #1864C22semidirect
85. #1863C22semidirect
86. #1862C22semidirect
90. #1768C22semidirect
91. #1767C22semidirect
92. C4×C4⋊C8C22semidirect
101. C2×AGL(1,ℤ/8)C2×C4semidirect
124. C2×C4×D4C2×C4semidirect
142. #463C2×C4semidirect
143. #461C2×C4semidirect
144. #459C2×C4semidirect
148. #423C2×C4semidirect
155. #417C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30362
#342072
#340582
#221612
#221572
#221522
#221512
#221462
#221452
#212572
#212352
#211712
#210922
#209322
#208782
C2×#18022
#204312