Finite Group Databasebeta

← #7173442

Subgroups — #7173442

Order 512.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3364C211yesmaximal, characteristic, complemented
2C2×#3296C211yesmaximal, characteristic
3#59416C211yesmaximal, characteristic
4#39955C211yesmaximal, characteristic, complemented
5#31087C211yesmaximal, characteristic, complemented
6#31082C211yesmaximal, characteristic, complemented
7#30997C211yesmaximal, characteristic, complemented
8#30996C211yesmaximal, characteristic, complemented
9#30640C211yesmaximal, characteristic, complemented
10#30633C211yesmaximal, characteristic, complemented
11#30600C211yesmaximal, characteristic, complemented
12#30594C211yesmaximal, characteristic, complemented
13#28721C211yesmaximal, characteristic, complemented
14#28513C211yesmaximal, characteristic, complemented
15#27261C211yesmaximal, characteristic, complemented
16#27256C211yesmaximal, characteristic, complemented
17#25953C211yesmaximal, characteristic, complemented
18#25950C211yesmaximal, characteristic, complemented
19#25890C211yesmaximal, characteristic
20#25654C211yesmaximal, characteristic, complemented
21#25473C211yesmaximal, characteristic, complemented
22#25343C211yesmaximal, characteristic, complemented
23#25033C211yesmaximal, characteristic, complemented
24#25031C211yesmaximal, characteristic, complemented
25#24904C211yesmaximal, characteristic, complemented
26#24901C211yesmaximal, characteristic, complemented
27#24334C211yesmaximal, characteristic, complemented
28#24127C211yesmaximal, characteristic, complemented
29#23681C211yesmaximal, characteristic, complemented
30#23204C211yesmaximal, characteristic, complemented
31#22150C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#556C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×#546C2211yescharacteristic
36#3364—28no—
37#3296—28no—
38C2×#488C2211yescharacteristic
39C2×#488C2211yescharacteristic
40C2×#488C2211yescharacteristic
41C2×#487C2211yescharacteristic, complemented
42C2×#482C2211yescharacteristic
43C2×#483C2211yescharacteristic
44C2×#479C2211yescharacteristic, complemented
45C2×#479C2211yescharacteristic, complemented
46C2×#479C2211yescharacteristic, complemented
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#474C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#462C2211yescharacteristic, complemented
55C2×#452C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×C8×Q8C2211yescharacteristic, complemented
58C2×C4×Q16C2211yescharacteristic, complemented
59C2×C4×Q16C2211yescharacteristic, complemented
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C8×D4C2211yescharacteristic
63C2×#416C2211yescharacteristic
64C22×#102C2211yescharacteristic
65#2859C2211yescharacteristic, complemented
66#2719—21no—
67#2713—21no—
68#2694—21no—
69#2687—21no—
70#2685—21no—
71#2674—21no—
72#2664—21no—
73#2611—21no—
74#2604—21no—
75#2584C2211yescharacteristic, complemented
76#2580C2211yescharacteristic
77#2562C2211yescharacteristic
78#2559—21no—
79#2553—21no—
80#2536C2211yescharacteristic
81#2480—21no—
82#2476—21no—
83#2472—21no—
84#2442C2211yescharacteristic
85#2441C2211yescharacteristic, complemented
86#2440C2211yescharacteristic
87#2439C2211yescharacteristic, complemented
88#2435C2211yescharacteristic
89#2432C2211yescharacteristic
90#2429C2211yescharacteristic
91#2427C2211yescharacteristic
92#2423C2211yescharacteristic
93#2423C2211yescharacteristic, complemented
94#2421C2211yescharacteristic
95#2421C2211yescharacteristic
96#2421C2211yescharacteristic, complemented
97#2420C2211yescharacteristic
98#2342—21no—
99#2341C2211yescharacteristic
100D4×C22⋊C4C2211yescharacteristic
101#2323—21no—
102C4×#124C2211yescharacteristic
103C4×#124C2211yescharacteristic
104C4×#124C2211yescharacteristic
105#2295C2211yescharacteristic, complemented
106#2096C2211yescharacteristic, complemented
107#2095C2211yescharacteristic, complemented
108#2094C2211yescharacteristic
109#2093C2211yescharacteristic
110#2088C2211yescharacteristic, complemented
111#2087C2211yescharacteristic, complemented
112#2085C2211yescharacteristic, complemented
113#2077C2211yescharacteristic
114#2075C2211yescharacteristic, complemented
115#2074C2211yescharacteristic, complemented
116#2074C2211yescharacteristic, complemented
117#2074C2211yescharacteristic, complemented
118#2073C2211yescharacteristic
119#2073C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic, complemented
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic, complemented
125#2058C2211yescharacteristic, complemented
126#2056C2211yescharacteristic, complemented
127#2055C2211yescharacteristic
128#2043C2211yescharacteristic, complemented
129#2043C2211yescharacteristic, complemented
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2036C2211yescharacteristic
134#2036C2211yescharacteristic, complemented
135#2036C2211yescharacteristic, complemented
136#2035C2211yescharacteristic
137#2035C2211yescharacteristic
138#2035C2211yescharacteristic
139#2034C2211yescharacteristic
140#2033C2211yescharacteristic
141#2025C2211yescharacteristic
142#2023C2211yescharacteristic
143#2015C2211yescharacteristic
144#2001C2211yescharacteristic
145#2001C2211yescharacteristic, complemented
146#1991C2211yescharacteristic, complemented
147#1991C2211yescharacteristic, complemented
148#1984C2211yescharacteristic, complemented
149#1983C2211yescharacteristic
150#1969C2211yescharacteristic, complemented
151#1968C2211yescharacteristic
152#1958C2211yescharacteristic
153#1958C2211yescharacteristic
154#1954C2211yescharacteristic
155#1949C2211yescharacteristic, complemented
156#1942C2211yescharacteristic, complemented
157#1941C2211yescharacteristic, complemented
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1933C2211yescharacteristic, complemented
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1877C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic, complemented
186#1846C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic, complemented
200C4×C4⋊C8C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202C4×#102C2211yescharacteristic
203C8×C22⋊C4C2211yescharacteristic
204C8×C22⋊C4C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#557—24no—
214#557—42no—
215#556—24no—
216#556—42no—
217#552—24no—
218#552—42no—
219#546—24no—
220#546—42no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124D411yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#123—21no—
238C2×#123—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#120—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267#488—24no—
268#488—24no—
269#488—24no—
270#487—24no—
271#483—24no—
272#482—24no—
273#479—24no—
274#479—24no—
275#479—42no—
276#478—24no—
277#478—42no—
278#474—24no—
279#467—24no—
280#465—24no—
281#464—24no—
282#464D418yes—
283#462—24no—
284#452—24no—
285#450—24no—
286C8×Q8—24no—
287C4×Q16—24no—
288C4×Q16—24no—
289C4×SD16—24no—
290C4×SD16—24no—
291C8×D4—24no—
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310#416—24no—
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#102—24no—
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356#400—21no—
357#400—21no—
358#400—21no—
359#400—21no—
360#400—21no—
361#399—21no—
362#399—21no—
363#399—21no—
364#399—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#395—21no—
381#395—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#393—21no—
391#393—21no—
392#391—21no—
393#391D411yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#390—21no—
399#390—21no—
400#390D411yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388D411yescharacteristic
436#388D411yescharacteristic
437#388D411yescharacteristic
438#388D411yescharacteristic
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#382D411yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#381—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#379—21no—
476#379—21no—
477#379—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488C4×C22⋊C4C2311yescharacteristic
489#376—21no—
490C43C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C22×Q8—21no—
523C22×Q8C2×D411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4C2×D411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16C2×D414yes—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16C2×D414yes—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—44no—
577#126—44no—
578#126—44no—
579#126—44no—
580#125—22no—
581#125—22no—
582#125—22no—
583#125—22no—
584#125—22no—
585#125—41no—
586#125—44no—
587#125—44no—
588#125—44no—
589#124—24no—
590#124—22no—
591#124—22no—
592#124—22no—
593#124—41no—
594#124—41no—
595#124C2×D414yes—
596#123—44no—
597#123—44no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—44no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—44no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610#121—22no—
611#121—44no—
612#121—41no—
613#120—44no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—44no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8C2×D414yes—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637#117—22no—
638#117—44no—
639#117—44no—
640#117—41no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—44no—
722C2×C22⋊C4—44no—
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750#107—22no—
751#107—22no—
752#107—22no—
753#107—41no—
754#107—41no—
755#107—41no—
756#106—22no—
757#106—22no—
758#106—22no—
759#106—41no—
760#106—41no—
761#106—41no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—22no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767C4⋊C8C2×D414yes—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103C2×D414yes—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102C2×D414yes—
800C22⋊C8—22no—
801C22⋊C8—22no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C4×C8—22no—
807C4×C8—22no—
808C4×C8—22no—
809C4×C8—22no—
810C4×C8—41no—
811C4×C8—41no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866C2×Q8—22no—
867C2×Q8—22no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—41no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—81no—
888C2×Q8C22×D412yes—
889C2×Q8C22×D412yes—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—41no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4C22×D412yes—
917C2×D42−1+412yes—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C2511yescharacteristic
972Q16—44no—
973Q16—44no—
974SD16—44no—
975SD16—44no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—82no—
999C2×C8—82no—
1000C2×C8C22×D412yes—
1001C2×C8C22×D412yes—
1002C4⋊C4—24no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4C22×D412yes—
1061C22⋊C4—22no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4#13514yes—
1101C42—24no—
1102C42—22no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—41no—
1112C42—41no—
1113C42—41no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42C22×D412yes—
1122C42H(5,𝔽2)12yes—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—84no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23C2×#13512yes—
1158C23C23×D411yescharacteristic
1159Q8—22no—
1160Q8—22no—
1161Q8—22no—
1162Q8—22no—
1163Q8—44no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—84no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—22no—
1177D4—44no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—84no—
1183D4—84no—
1184D4—162no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4D4212yes—
1273C2×C4D4212yes—
1274C2×C4C2×#13512yes—
1275C2×C4C2×#13512yes—
1276C2×C4C23×D411yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×2−1+411yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C8—22no—
1283C8—22no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—42no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—42no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—168no—
1319C22C2×D4211yescharacteristic
1320C22#348911yescharacteristic
1321C22#350011yescharacteristic
1322C22C22×#13511yescharacteristic
1323C22#358411yescharacteristic
1324C22#358411yescharacteristic
1325C22#358611yescharacteristic
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—42no—
1335C4—41no—
1336C4—42no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#348511yescharacteristic
1353C4#348911yescharacteristic
1354C4#356111yescharacteristic
1355C4#356211yescharacteristic
1356C2—42no—
1357C2—81no—
1358C2—82no—
1359C2—82no—
1360C2#4513411yescharacteristic
1361C2D4×#13511yescharacteristic
1362C2#6109611yescharacteristic
1363C2#6209711yescharacteristic
1364C2#6220811yescharacteristic
1365C2#6253311yescharacteristic
1366C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3364C2semidirect
4. #39955C2semidirect
5. #31087C2semidirect
6. #31082C2semidirect
7. #30997C2semidirect
8. #30996C2semidirect
9. #30640C2semidirect
10. #30633C2semidirect
11. #30600C2semidirect
12. #30594C2semidirect
13. #28721C2semidirect
14. #28513C2semidirect
15. #27261C2semidirect
16. #27256C2semidirect
17. #25953C2semidirect
18. #25950C2semidirect
20. #25654C2semidirect
21. #25473C2semidirect
22. #25343C2semidirect
23. #25033C2semidirect
24. #25031C2semidirect
25. #24904C2semidirect
26. #24901C2semidirect
27. #24334C2semidirect
28. #24127C2semidirect
29. #23681C2semidirect
30. #23204C2semidirect
31. #22150C2semidirect
32. C2×#557C22semidirect
41. C2×#487C22semidirect
44. C2×#479C22semidirect
45. C2×#479C22semidirect
46. C2×#479C22semidirect
54. C2×#462C22semidirect
57. C2×C8×Q8C22semidirect
58. C2×C4×Q16C22semidirect
59. C2×C4×Q16C22semidirect
65. #2859C22semidirect
75. #2584C22semidirect
85. #2441C22semidirect
87. #2439C22semidirect
93. #2423C22semidirect
96. #2421C22semidirect
105. #2295C22semidirect
106. #2096C22semidirect
107. #2095C22semidirect
110. #2088C22semidirect
111. #2087C22semidirect
112. #2085C22semidirect
114. #2075C22semidirect
115. #2074C22semidirect
116. #2074C22semidirect
117. #2074C22semidirect
122. #2066C22semidirect
124. #2059C22semidirect
125. #2058C22semidirect
126. #2056C22semidirect
128. #2043C22semidirect
129. #2043C22semidirect
134. #2036C22semidirect
135. #2036C22semidirect
145. #2001C22semidirect
146. #1991C22semidirect
147. #1991C22semidirect
148. #1984C22semidirect
150. #1969C22semidirect
155. #1949C22semidirect
156. #1942C22semidirect
157. #1941C22semidirect
161. #1933C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
167. #1892C22semidirect
170. #1878C22semidirect
172. #1873C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
182. #1854C22semidirect
185. #1850C22semidirect
186. #1846C22semidirect
187. #1846C22semidirect
189. #1807C22semidirect
190. #1805C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
199. C4×C4⋊C8C22semidirect
200. C4×C4⋊C8C22semidirect
201. C4×#103C22semidirect
204. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33642
C2×#32962
#594162
#399552
#310872
#310822
#309972
#309962
#306402
#306332
#306002
#305942
#287212
#285132
#272612
#272562
#259532
#259502
#258902
#256542
#254732
#253432
#250332
#250312
#249042
#249012
#243342
#241272
#236812
#232042
#221502