Finite Group Databasebeta

← #7339801

Subgroups — #7339801

Order 512.

1380 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#32704C211yesmaximal, characteristic, complemented
2#32699C211yesmaximal, characteristic, complemented
3#32699C211yesmaximal, characteristic, complemented
4#32699C211yesmaximal, characteristic, complemented
5#32697C211yesmaximal, characteristic, complemented
6#31417C211yesmaximal, characteristic, complemented
7#31417C211yesmaximal, characteristic, complemented
8#31415C211yesmaximal, characteristic, complemented
9#31414C211yesmaximal, characteristic, complemented
10#31284C211yesmaximal, characteristic, complemented
11#31282C211yesmaximal, characteristic, complemented
12#30498C211yesmaximal, characteristic, complemented
13#30057C211yesmaximal, characteristic, complemented
14#30056C211yesmaximal, characteristic, complemented
15#29232C211yesmaximal, characteristic, complemented
16#29232C211yesmaximal, characteristic, complemented
17#25748C211yesmaximal, characteristic, complemented
18#25592C211yesmaximal, characteristic, complemented
19#25591C211yesmaximal, characteristic, complemented
20#25198C211yesmaximal, characteristic, complemented
21#25197C211yesmaximal, characteristic, complemented
22#24475C211yesmaximal, characteristic, complemented
23#24472C211yesmaximal, characteristic, complemented
24#24001C211yesmaximal, characteristic, complemented
25#23999C211yesmaximal, characteristic, complemented
26#23993C211yesmaximal, characteristic, complemented
27#23992C211yesmaximal, characteristic, complemented
28#23874C211yesmaximal, characteristic, complemented
29#23362C211yesmaximal, characteristic, complemented
30#22899C211yesmaximal, characteristic, complemented
31#21785C211yesmaximal, characteristic, complemented
32#3585C2211yescharacteristic
33#3510C2211yescharacteristic, complemented
34#3509C2211yescharacteristic, complemented
35#3500C2211yescharacteristic
36#3153C2211yescharacteristic
37#3140C2211yescharacteristic, complemented
38#3138C2211yescharacteristic, complemented
39#3069C2211yescharacteristic
40#3069C2211yescharacteristic, complemented
41#3068C2211yescharacteristic
42#3068C2211yescharacteristic, complemented
43#3040C2211yescharacteristic
44#3040C2211yescharacteristic, complemented
45#3038C2211yescharacteristic
46#3028C2211yescharacteristic
47#3022C2211yescharacteristic
48#3021C2211yescharacteristic
49#3020C2211yescharacteristic
50#3020C2211yescharacteristic
51#3018C2211yescharacteristic
52C2×#456C2211yescharacteristic, complemented
53C2×#454C2211yescharacteristic, complemented
54C2×#455C2211yescharacteristic
55C2×#453C2211yescharacteristic
56#2956C2211yescharacteristic, complemented
57#2956C2211yescharacteristic, complemented
58#2901C2211yescharacteristic
59#2901C2211yescharacteristic
60#2889C2211yescharacteristic, complemented
61#2884C2211yescharacteristic, complemented
62#2858C2211yescharacteristic, complemented
63#2102C2211yescharacteristic, complemented
64#2102C2211yescharacteristic, complemented
65#2102C2211yescharacteristic, complemented
66#2102C2211yescharacteristic, complemented
67#2082C2211yescharacteristic, complemented
68#2082C2211yescharacteristic, complemented
69#2081C2211yescharacteristic, complemented
70#2081C2211yescharacteristic, complemented
71#2081C2211yescharacteristic, complemented
72#2081C2211yescharacteristic, complemented
73#2081C2211yescharacteristic, complemented
74#2081C2211yescharacteristic, complemented
75#2070C2211yescharacteristic, complemented
76#2070C2211yescharacteristic, complemented
77#2050C2211yescharacteristic
78#2050C2211yescharacteristic
79#2049C2211yescharacteristic
80#2049C2211yescharacteristic, complemented
81#2048C2211yescharacteristic
82#2048C2211yescharacteristic
83#2048C2211yescharacteristic
84#2048C2211yescharacteristic, complemented
85#2031C2211yescharacteristic
86#2031C2211yescharacteristic
87#2031C2211yescharacteristic, complemented
88#2031C2211yescharacteristic, complemented
89#2031C2211yescharacteristic, complemented
90#2031C2211yescharacteristic, complemented
91#2031C2211yescharacteristic, complemented
92#2031C2211yescharacteristic, complemented
93#2009C2211yescharacteristic
94#2009C2211yescharacteristic, complemented
95#2008C2211yescharacteristic
96#2008C2211yescharacteristic
97#2008C2211yescharacteristic
98#2008C2211yescharacteristic, complemented
99#2005C2211yescharacteristic
100#2005C2211yescharacteristic, complemented
101#2004C2211yescharacteristic, complemented
102#2004C2211yescharacteristic, complemented
103#2003C2211yescharacteristic
104#2003C2211yescharacteristic
105#2003C2211yescharacteristic
106#2003C2211yescharacteristic
107#2003C2211yescharacteristic, complemented
108#2003C2211yescharacteristic, complemented
109#2002C2211yescharacteristic
110#2002C2211yescharacteristic, complemented
111#1994C2211yescharacteristic, complemented
112#1994C2211yescharacteristic, complemented
113#1967C2211yescharacteristic, complemented
114#1967C2211yescharacteristic, complemented
115#1966C2211yescharacteristic, complemented
116#1962C2211yescharacteristic
117#1932C2211yescharacteristic
118#1932C2211yescharacteristic
119#1932C2211yescharacteristic, complemented
120#1932C2211yescharacteristic, complemented
121#1932C2211yescharacteristic, complemented
122#1932C2211yescharacteristic, complemented
123#1915C2211yescharacteristic
124#1915C2211yescharacteristic, complemented
125#1915C2211yescharacteristic, complemented
126#1912C2211yescharacteristic
127#1912C2211yescharacteristic
128#1912C2211yescharacteristic, complemented
129#1912C2211yescharacteristic, complemented
130#1910C2211yescharacteristic, complemented
131#1910C2211yescharacteristic, complemented
132#1910C2211yescharacteristic, complemented
133#1909C2211yescharacteristic, complemented
134#1906C2211yescharacteristic
135#1906C2211yescharacteristic
136#1906C2211yescharacteristic
137#1906C2211yescharacteristic
138#1906C2211yescharacteristic, complemented
139#1906C2211yescharacteristic, complemented
140#1905C2211yescharacteristic
141#1905C2211yescharacteristic, complemented
142#1905C2211yescharacteristic, complemented
143#1905C2211yescharacteristic, complemented
144#1904C2211yescharacteristic
145#1904C2211yescharacteristic, complemented
146#1904C2211yescharacteristic, complemented
147#1904C2211yescharacteristic, complemented
148#1903C2211yescharacteristic
149#1903C2211yescharacteristic
150#1903C2211yescharacteristic
151#1903C2211yescharacteristic, complemented
152#1902C2211yescharacteristic
153#1902C2211yescharacteristic, complemented
154#1888C2211yescharacteristic, complemented
155#1888C2211yescharacteristic, complemented
156#1888C2211yescharacteristic, complemented
157#1888C2211yescharacteristic, complemented
158#1888C2211yescharacteristic, complemented
159#1887C2211yescharacteristic, complemented
160#1886C2211yescharacteristic, complemented
161#1885C2211yescharacteristic, complemented
162#1884C2211yescharacteristic
163#1884C2211yescharacteristic
164#1884C2211yescharacteristic
165#1861C2211yescharacteristic
166#1861C2211yescharacteristic
167#1861C2211yescharacteristic, complemented
168#1861C2211yescharacteristic, complemented
169#1861C2211yescharacteristic, complemented
170#1861C2211yescharacteristic, complemented
171#1841C2211yescharacteristic, complemented
172#1841C2211yescharacteristic, complemented
173#1841C2211yescharacteristic, complemented
174#1841C2211yescharacteristic, complemented
175#1830C2211yescharacteristic, complemented
176#1830C2211yescharacteristic, complemented
177#1827C2211yescharacteristic, complemented
178#1827C2211yescharacteristic, complemented
179#1827C2211yescharacteristic, complemented
180#1827C2211yescharacteristic, complemented
181#1795C2211yescharacteristic
182#1795C2211yescharacteristic
183#1795C2211yescharacteristic
184C4×#104C2211yescharacteristic, complemented
185C4×#104C2211yescharacteristic, complemented
186C4×#104C2211yescharacteristic, complemented
187#585C2311yescharacteristic
188C2×2−1+4C2311yescharacteristic
189C2×H(5,𝔽2)C2311yescharacteristic
190#577—41no—
191#577—41no—
192#576—41no—
193#576—41no—
194#575—41no—
195#575C2311yescharacteristic
196#575C2311yescharacteristic
197#575C2311yescharacteristic
198#575C2311yescharacteristic
199C2×#137C2311yescharacteristic
200C2×#137C2311yescharacteristic
201C2×#137C2311yescharacteristic
202C2×#137C2311yescharacteristic
203C2×AGL(1,ℤ/8)—41no—
204C2×AGL(1,ℤ/8)C2311yescharacteristic
205C2×AGL(1,ℤ/8)C2311yescharacteristic
206C2×AGL(1,ℤ/8)C2311yescharacteristic
207C2×AGL(1,ℤ/8)C2311yescharacteristic
208C2×AGL(1,ℤ/8)C2311yescharacteristic
209C2×AGL(1,ℤ/8)C2311yescharacteristic
210#568C2311yescharacteristic
211#568C2311yescharacteristic
212#568C2311yescharacteristic
213#568C2311yescharacteristic
214#568C2311yescharacteristic
215#559—41no—
216#557—41no—
217#556—41no—
218#556—41no—
219#552—42no—
220#551—42no—
221#548—41no—
222#546—42no—
223#546—41no—
224#542—41no—
225#541—41no—
226#536—21no—
227#536C2311yescharacteristic
228#536C2311yescharacteristic
229#536C2311yescharacteristic
230#536C2311yescharacteristic
231#535—21no—
232#535C2311yescharacteristic
233#535C2311yescharacteristic
234#533—41no—
235#533C2311yescharacteristic
236#533C2311yescharacteristic
237#532—21no—
238#532C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241#529—41no—
242C2×#124—21no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247#519C2311yescharacteristic
248#519C2311yescharacteristic
249#519C2311yescharacteristic
250#518C2311yescharacteristic
251C4×#41C2311yescharacteristic
252C4×#41C2311yescharacteristic
253C4×#41C2311yescharacteristic
254#497—21no—
255#496—21no—
256#495—21no—
257#495—21no—
258#490—41no—
259#489—41no—
260#488—41no—
261#486—41no—
262#473—41no—
263#473—41no—
264#472—41no—
265#472—41no—
266#471—41no—
267#471—41no—
268#471—41no—
269#471—41no—
270#464—41no—
271#464—41no—
272#463—41no—
273#463—41no—
274#460—41no—
275#459—41no—
276#458—42no—
277#456—21no—
278#456—41no—
279#456—41no—
280#456—41no—
281#456—41no—
282#456—41no—
283#455—21no—
284#455—41no—
285#455—41no—
286#455—41no—
287#454—21no—
288#454—41no—
289#454—41no—
290#454—41no—
291#454—41no—
292#454—41no—
293#453—21no—
294#453—41no—
295#453—41no—
296#453—41no—
297#444—41no—
298#444—41no—
299#443—41no—
300#443—41no—
301#430C2311yescharacteristic
302#430C2311yescharacteristic
303#430C2311yescharacteristic
304#430C2311yescharacteristic
305#430C2311yescharacteristic
306#430C2311yescharacteristic
307#423C2311yescharacteristic
308#423C2311yescharacteristic
309#423C2311yescharacteristic
310#421—41no—
311#421—41no—
312#421C2311yescharacteristic
313#421C2311yescharacteristic
314#421C2311yescharacteristic
315#421C2311yescharacteristic
316#421C2311yescharacteristic
317#421C2311yescharacteristic
318#421C2311yescharacteristic
319#421C2311yescharacteristic
320#421C2311yescharacteristic
321#421C2311yescharacteristic
322#421C2311yescharacteristic
323#421C2311yescharacteristic
324C2×#104—41no—
325C2×#104—41no—
326C2×#104C2311yescharacteristic
327C2×#104C2311yescharacteristic
328C2×#104C2311yescharacteristic
329C2×#104C2311yescharacteristic
330C2×#104C2311yescharacteristic
331C2×#104C2311yescharacteristic
332C2×#104C2311yescharacteristic
333C2×#104C2311yescharacteristic
334C2×#104C2311yescharacteristic
335C2×#104C2311yescharacteristic
336#419C2311yescharacteristic
337#419C2311yescharacteristic
338#419C2311yescharacteristic
339#419C2311yescharacteristic
340#418C2311yescharacteristic
341#418C2311yescharacteristic
342#418C2311yescharacteristic
343#418C2311yescharacteristic
344#418C2311yescharacteristic
345#418C2311yescharacteristic
346#418C2311yescharacteristic
347#418C2311yescharacteristic
348#418C2311yescharacteristic
349#418C2311yescharacteristic
350#413—41no—
351#413C2311yescharacteristic
352#413C2311yescharacteristic
353#413C2311yescharacteristic
354#413C2311yescharacteristic
355#413C2311yescharacteristic
356C2×#101—41no—
357C2×#101C2311yescharacteristic
358C2×#101C2311yescharacteristic
359C2×#101C2311yescharacteristic
360C2×#101C2311yescharacteristic
361C2×#101C2311yescharacteristic
362C2×#101C2311yescharacteristic
363C2×#101C2311yescharacteristic
364C2×#101C2311yescharacteristic
365C2×#100C2311yescharacteristic
366C2×#100C2311yescharacteristic
367C2×#100C2311yescharacteristic
368C2×#100C2311yescharacteristic
369#410—42no—
370#410C2311yescharacteristic
371#410C2311yescharacteristic
372#410C2311yescharacteristic
373#410C2311yescharacteristic
374#410C2311yescharacteristic
375#410C2311yescharacteristic
376#410C2311yescharacteristic
377C4×M16C2311yescharacteristic
378C4×M16C2311yescharacteristic
379C4×M16C2311yescharacteristic
380#390—42no—
381C43C2311yescharacteristic
382#344C2311yescharacteristic
383#344C2311yescharacteristic
384#344C2311yescharacteristic
385#344C2311yescharacteristic
386#344C2311yescharacteristic
387#344C2311yescharacteristic
388#344C2311yescharacteristic
389#344C2311yescharacteristic
390#344C2311yescharacteristic
391#344C2311yescharacteristic
392#344C2311yescharacteristic
393#344C2311yescharacteristic
394#344C2311yescharacteristic
395#344C2311yescharacteristic
396#339C2311yescharacteristic
397#339C2311yescharacteristic
398#339C2311yescharacteristic
399#339C2311yescharacteristic
400#339C2311yescharacteristic
401#339C2311yescharacteristic
402#339C2311yescharacteristic
403#339C2311yescharacteristic
404#339C2311yescharacteristic
405#339C2311yescharacteristic
406#339C2311yescharacteristic
407#339C2311yescharacteristic
408#339C2311yescharacteristic
409#339C2311yescharacteristic
410#338C2311yescharacteristic
411#338C2311yescharacteristic
412H(3,ℤ/4)C2311yescharacteristic
413H(3,ℤ/4)C2311yescharacteristic
414H(3,ℤ/4)C2311yescharacteristic
415H(3,ℤ/4)C2311yescharacteristic
416H(3,ℤ/4)C2311yescharacteristic
417H(3,ℤ/4)C2311yescharacteristic
418H(3,ℤ/4)C2311yescharacteristic
419H(3,ℤ/4)C2311yescharacteristic
4202−1+4—21no—
4212−1+4—21no—
4222−1+4—21no—
4232−1+4—41no—
4242−1+4—41no—
4252−1+4—41no—
4262−1+4—41no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—21no—
429H(5,𝔽2)—21no—
430H(5,𝔽2)—41no—
431H(5,𝔽2)—41no—
432H(5,𝔽2)—41no—
433H(5,𝔽2)—41no—
434H(5,𝔽2)—41no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—22no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41C2411yescharacteristic
444C2×#41C2411yescharacteristic
445C2×#41C2411yescharacteristic
446C2×#41C2411yescharacteristic
447C2×#41C2411yescharacteristic
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8C2411yescharacteristic
451C22×Q8C2411yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—41no—
455C22×D4—41no—
456C22×D4C2411yescharacteristic
457C22×D4C2411yescharacteristic
458#137—21no—
459#137—21no—
460#137—21no—
461#137—21no—
462#137—21no—
463#137—21no—
464#137—21no—
465#137—21no—
466#137—41no—
467#137—41no—
468#137—41no—
469#137—41no—
470#137—41no—
471#137—41no—
472#137—41no—
473#137—41no—
474#137—42no—
475AGL(1,ℤ/8)—21no—
476AGL(1,ℤ/8)—21no—
477AGL(1,ℤ/8)—21no—
478AGL(1,ℤ/8)—21no—
479AGL(1,ℤ/8)—21no—
480AGL(1,ℤ/8)—21no—
481AGL(1,ℤ/8)—21no—
482AGL(1,ℤ/8)—21no—
483AGL(1,ℤ/8)—41no—
484AGL(1,ℤ/8)—41no—
485AGL(1,ℤ/8)—41no—
486AGL(1,ℤ/8)—41no—
487AGL(1,ℤ/8)—41no—
488AGL(1,ℤ/8)—41no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491AGL(1,ℤ/8)—41no—
492AGL(1,ℤ/8)—41no—
493AGL(1,ℤ/8)—41no—
494AGL(1,ℤ/8)—41no—
495AGL(1,ℤ/8)—42no—
496AGL(1,ℤ/8)—42no—
497AGL(1,ℤ/8)—42no—
498#135—41no—
499#135—41no—
500#135—41no—
501#135—41no—
502#135—42no—
503#135—42no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×Q16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—42no—
519C2×D8—21no—
520C2×D8—21no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—42no—
526#131—41no—
527#131—41no—
528#131—41no—
529#131—41no—
530#131—41no—
531#131—41no—
532#131—41no—
533#131—41no—
534#131—41no—
535#131—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16C2411yescharacteristic
542C2×M16C2411yescharacteristic
543C2×M16C2411yescharacteristic
544C2×M16C2411yescharacteristic
545C2×M16C2411yescharacteristic
546C2×M16C2411yescharacteristic
547C2×M16C2411yescharacteristic
548C2×M16C2411yescharacteristic
549C2×M16C2411yescharacteristic
550C2×M16C2411yescharacteristic
551C2×M16C2411yescharacteristic
552C2×M16C2411yescharacteristic
553C4⋊Q8—21no—
554C4⋊Q8—21no—
555C4⋊Q8—21no—
556C4⋊Q8—21no—
557C4⋊Q8—21no—
558C4⋊Q8—21no—
559C4⋊Q8—21no—
560C4⋊Q8—21no—
561C4⋊Q8—41no—
562C4⋊Q8#4111yescharacteristic
563#127—21no—
564#127—21no—
565#127—21no—
566#127—21no—
567#127—41no—
568#127#4111yescharacteristic
569#126—42no—
570#126—42no—
571#126—42no—
572#126—42no—
573#125—21no—
574#125—21no—
575#125—42no—
576#125—42no—
577#125—42no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#124—21no—
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—42no—
597#124—42no—
598#124#4111yescharacteristic
599#124#4111yescharacteristic
600#123—22no—
601#123—22no—
602#123—22no—
603#123—41no—
604#123—42no—
605#123—42no—
606#123—42no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—42no—
614C22⋊Q8—42no—
615C22⋊Q8—42no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—42no—
620#121—42no—
621#120—41no—
622#120—41no—
623#120—42no—
624C4×Q8—21no—
625C4×Q8—21no—
626C4×Q8—21no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—42no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—42no—
646C4×D4—42no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—22no—
651#117—22no—
652#117—41no—
653#117—42no—
654#117—42no—
655#117C2411yescharacteristic
656#117C2411yescharacteristic
657#117C2411yescharacteristic
658#117C2411yescharacteristic
659#117C2411yescharacteristic
660#117C2411yescharacteristic
661#117C2411yescharacteristic
662C2×C4⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—41no—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#108—41no—
677#108—41no—
678#108—41no—
679#108—41no—
680#108—41no—
681#108—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#104—21no—
686#104—21no—
687#104—21no—
688#104—21no—
689#104—21no—
690#104—21no—
691#104—21no—
692#104—21no—
693#104—21no—
694#104—21no—
695#104—21no—
696#104—21no—
697#104—21no—
698#104—21no—
699#104—21no—
700#104—21no—
701#104—21no—
702#104—21no—
703#104—21no—
704#104—21no—
705#104—41no—
706#104—41no—
707#104—41no—
708#104—41no—
709#104—41no—
710#104—41no—
711#104—41no—
712#104—41no—
713#104—41no—
714#104—41no—
715#104—41no—
716#104—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#101—21no—
732#101—21no—
733#101—21no—
734#101—21no—
735#101—21no—
736#101—41no—
737#101—41no—
738#101—41no—
739#101—41no—
740#101—41no—
741#101—41no—
742#101—41no—
743#101—41no—
744#100—21no—
745#100—21no—
746#100—21no—
747#100—21no—
748#100—21no—
749#100—41no—
750#100—41no—
751#100—41no—
752#100—41no—
753#99—41no—
754#99—41no—
755#99—41no—
756#99—41no—
757#99—41no—
758#99—41no—
759#99—41no—
760#97—21no—
761#97—21no—
762#97—21no—
763C4×C8—21no—
764C4×C8—21no—
765C4×C8—21no—
766C24—21no—
767C24—21no—
768C24—41no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—21no—
775#41—21no—
776#41—21no—
777#41—21no—
778#41—21no—
779#41—21no—
780#41—21no—
781#41—21no—
782#41—21no—
783#41—21no—
784#41—21no—
785#41—21no—
786#41—21no—
787#41—21no—
788#41—21no—
789#41—41no—
790#41—41no—
791#41—41no—
792#41—41no—
793#41—41no—
794#41—41no—
795#41—42no—
796#41—82no—
797#41—82no—
798#41—81no—
799#41—81no—
800#41—81no—
801#41—81no—
802#41—81no—
803#41—81no—
804#41—81no—
805#41—81no—
806#41—81no—
807#41—81no—
808#41—81no—
809C2×Q8—22no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—41no—
823C2×Q8—41no—
824C2×Q8—41no—
825C2×Q8—41no—
826C2×Q8—41no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8C2×#4111yescharacteristic
832C2×Q8C2×#4111yescharacteristic
833C2×Q8H(5,𝔽2)11yescharacteristic
834C2×Q8H(5,𝔽2)11yescharacteristic
835C2×Q8H(5,𝔽2)11yescharacteristic
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—22no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—84no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4C2×#4111yescharacteristic
875C2×D4C2×#4111yescharacteristic
876C2×D4H(5,𝔽2)11yescharacteristic
877C2×D4H(5,𝔽2)11yescharacteristic
878C2×D4H(5,𝔽2)11yescharacteristic
879C22×C4—21no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—42no—
895C22×C4—81no—
896C22×C4H(5,𝔽2)12yes—
897C22×C4C2511yescharacteristic
898Q16—41no—
899Q16—41no—
900Q16—41no—
901Q16—41no—
902Q16—81no—
903Q16—81no—
904Q16—81no—
905Q16—81no—
906SD16—41no—
907SD16—41no—
908SD16—41no—
909SD16—41no—
910SD16—41no—
911SD16—41no—
912SD16—41no—
913SD16—41no—
914SD16—42no—
915SD16—42no—
916SD16—81no—
917SD16—81no—
918SD16—81no—
919SD16—81no—
920SD16—81no—
921SD16—81no—
922SD16—81no—
923SD16—81no—
924D8—41no—
925D8—41no—
926D8—41no—
927D8—41no—
928D8—42no—
929D8—42no—
930D8—81no—
931D8—81no—
932D8—81no—
933D8—81no—
934M16—21no—
935M16—21no—
936M16—21no—
937M16—21no—
938M16—21no—
939M16—21no—
940M16—21no—
941M16—21no—
942M16—21no—
943M16—21no—
944M16—21no—
945M16—21no—
946M16—21no—
947M16—21no—
948M16—21no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16—21no—
956M16—21no—
957M16—21no—
958M16—42no—
959M16—81no—
960M16—81no—
961M16—81no—
962M16—81no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—42no—
976C2×C8—81no—
977C2×C8—81no—
978C2×C8—81no—
979C2×C8—81no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—42no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—42no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—41no—
1044C42—41no—
1045C42—41no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—82no—
1050C42C2×#4111yescharacteristic
1051C42C2×#4111yescharacteristic
1052C42H(5,𝔽2)11yescharacteristic
1053C42H(5,𝔽2)11yescharacteristic
1054C42H(5,𝔽2)11yescharacteristic
1055C42H(5,𝔽2)11yescharacteristic
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—81no—
1068C23—82no—
1069C23—82no—
1070C23—82no—
1071C23—162no—
1072C23C2×H(5,𝔽2)11yescharacteristic
1073Q8—21no—
1074Q8—21no—
1075Q8—21no—
1076Q8—21no—
1077Q8—21no—
1078Q8—21no—
1079Q8—21no—
1080Q8—21no—
1081Q8—21no—
1082Q8—21no—
1083Q8—41no—
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—82no—
1092Q8—82no—
1093Q8—81no—
1094Q8—161no—
1095D4—21no—
1096D4—21no—
1097D4—21no—
1098D4—21no—
1099D4—21no—
1100D4—21no—
1101D4—21no—
1102D4—21no—
1103D4—21no—
1104D4—21no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—82no—
1124D4—81no—
1125D4—81no—
1126D4—81no—
1127D4—82no—
1128D4—82no—
1129D4—162no—
1130D4—161no—
1131D4—162no—
1132D4—162no—
1133D4—162no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—82no—
1170C2×C4—81no—
1171C2×C4—81no—
1172C2×C4—82no—
1173C2×C4—82no—
1174C2×C4—81no—
1175C2×C4—81no—
1176C2×C4—81no—
1177C2×C4—82no—
1178C2×C4—161no—
1179C2×C4—161no—
1180C2×C4—162no—
1181C2×C4C22×#4111yescharacteristic
1182C2×C4C2×H(5,𝔽2)11yescharacteristic
1183C2×C4C2×H(5,𝔽2)11yescharacteristic
1184C2×C4C2×H(5,𝔽2)11yescharacteristic
1185C2×C4C2×H(5,𝔽2)11yescharacteristic
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—82no—
1211C22—82no—
1212C22—81no—
1213C22—81no—
1214C22—161no—
1215C22—161no—
1216C22—161no—
1217C22—161no—
1218C22—321no—
1219C22—322no—
1220C22#349011yescharacteristic
1221C22#353211yescharacteristic
1222C22#353211yescharacteristic
1223C4—22no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4#351911yescharacteristic
1244C4#351911yescharacteristic
1245C4#353211yescharacteristic
1246C4#354311yescharacteristic
1247C2—21no—
1248C2—21no—
1249C2—21no—
1250C2—81no—
1251C2—81no—
1252C2—81no—
1253C2—81no—
1254C2—81no—
1255C2—161no—
1256C2—161no—
1257C2#4808811yescharacteristic
subgroupG/H
center, socleC2#48088
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #32704C2semidirect
2. #32699C2semidirect
3. #32699C2semidirect
4. #32699C2semidirect
5. #32697C2semidirect
6. #31417C2semidirect
7. #31417C2semidirect
8. #31415C2semidirect
9. #31414C2semidirect
10. #31284C2semidirect
11. #31282C2semidirect
12. #30498C2semidirect
13. #30057C2semidirect
14. #30056C2semidirect
15. #29232C2semidirect
16. #29232C2semidirect
17. #25748C2semidirect
18. #25592C2semidirect
19. #25591C2semidirect
20. #25198C2semidirect
21. #25197C2semidirect
22. #24475C2semidirect
23. #24472C2semidirect
24. #24001C2semidirect
25. #23999C2semidirect
26. #23993C2semidirect
27. #23992C2semidirect
28. #23874C2semidirect
29. #23362C2semidirect
30. #22899C2semidirect
31. #21785C2semidirect
33. #3510C22semidirect
34. #3509C22semidirect
37. #3140C22semidirect
38. #3138C22semidirect
40. #3069C22semidirect
42. #3068C22semidirect
44. #3040C22semidirect
52. C2×#456C22semidirect
53. C2×#454C22semidirect
56. #2956C22semidirect
57. #2956C22semidirect
60. #2889C22semidirect
61. #2884C22semidirect
62. #2858C22semidirect
63. #2102C22semidirect
64. #2102C22semidirect
65. #2102C22semidirect
66. #2102C22semidirect
67. #2082C22semidirect
68. #2082C22semidirect
69. #2081C22semidirect
70. #2081C22semidirect
71. #2081C22semidirect
72. #2081C22semidirect
73. #2081C22semidirect
74. #2081C22semidirect
75. #2070C22semidirect
76. #2070C22semidirect
80. #2049C22semidirect
84. #2048C22semidirect
87. #2031C22semidirect
88. #2031C22semidirect
89. #2031C22semidirect
90. #2031C22semidirect
91. #2031C22semidirect
92. #2031C22semidirect
94. #2009C22semidirect
98. #2008C22semidirect
100. #2005C22semidirect
101. #2004C22semidirect
102. #2004C22semidirect
107. #2003C22semidirect
108. #2003C22semidirect
110. #2002C22semidirect
111. #1994C22semidirect
112. #1994C22semidirect
113. #1967C22semidirect
114. #1967C22semidirect
115. #1966C22semidirect
119. #1932C22semidirect
120. #1932C22semidirect
121. #1932C22semidirect
122. #1932C22semidirect
124. #1915C22semidirect
125. #1915C22semidirect
128. #1912C22semidirect
129. #1912C22semidirect
130. #1910C22semidirect
131. #1910C22semidirect
132. #1910C22semidirect
133. #1909C22semidirect
138. #1906C22semidirect
139. #1906C22semidirect
141. #1905C22semidirect
142. #1905C22semidirect
143. #1905C22semidirect
145. #1904C22semidirect
146. #1904C22semidirect
147. #1904C22semidirect
151. #1903C22semidirect
153. #1902C22semidirect
154. #1888C22semidirect
155. #1888C22semidirect
156. #1888C22semidirect
157. #1888C22semidirect
158. #1888C22semidirect
159. #1887C22semidirect
160. #1886C22semidirect
161. #1885C22semidirect
167. #1861C22semidirect
168. #1861C22semidirect
169. #1861C22semidirect
170. #1861C22semidirect
171. #1841C22semidirect
172. #1841C22semidirect
173. #1841C22semidirect
174. #1841C22semidirect
175. #1830C22semidirect
176. #1830C22semidirect
177. #1827C22semidirect
178. #1827C22semidirect
179. #1827C22semidirect
180. #1827C22semidirect
184. C4×#104C22semidirect
185. C4×#104C22semidirect
186. C4×#104C22semidirect

Maximal subgroups

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

subgroupindex
#327042
#326992
#326972
#314172
#314152
#314142
#312842
#312822
#304982
#300572
#300562
#292322
#257482
#255922
#255912
#251982
#251972
#244752
#244722
#240012
#239992
#239932
#239922
#238742
#233622
#228992
#217852