Finite Group Databasebeta

← #6997679

Subgroups — #6997679

Order 512.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59130C211yesmaximal, characteristic
2#40005C211yesmaximal, characteristic, complemented
3#32092C211yesmaximal, characteristic, complemented
4#32085C211yesmaximal, characteristic, complemented
5#32043C211yesmaximal, characteristic, complemented
6#32041C211yesmaximal, characteristic, complemented
7#31305C211yesmaximal, characteristic, complemented
8#31304C211yesmaximal, characteristic, complemented
9#30659C211yesmaximal, characteristic, complemented
10#30654C211yesmaximal, characteristic, complemented
11#29165C211yesmaximal, characteristic, complemented
12#29061C211yesmaximal, characteristic, complemented
13#29055C211yesmaximal, characteristic, complemented
14#28112C211yesmaximal, characteristic, complemented
15#28110C211yesmaximal, characteristic, complemented
16#27285C211yesmaximal, characteristic, complemented
17#27278C211yesmaximal, characteristic, complemented
18#26766C211yesmaximal, characteristic, complemented
19#26761C211yesmaximal, characteristic, complemented
20#25864C211yesmaximal, characteristic, complemented
21#24890C211yesmaximal, characteristic, complemented
22#24880C211yesmaximal, characteristic, complemented
23#24053C211yesmaximal, characteristic, complemented
24#24051C211yesmaximal, characteristic, complemented
25#24050C211yesmaximal, characteristic, complemented
26#24047C211yesmaximal, characteristic, complemented
27#23506C211yesmaximal, characteristic, complemented
28#23121C211yesmaximal, characteristic, complemented
29#22430C211yesmaximal, characteristic, complemented
30#22427C211yesmaximal, characteristic, complemented
31#22083C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#489C2211yescharacteristic
38C2×#484C2211yescharacteristic, complemented
39C2×#485C2211yescharacteristic
40C2×#482C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#436C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#419C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#419C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48C2×#418C2211yescharacteristic
49#2857C2211yescharacteristic
50#2786—21no—
51#2750—21no—
52#2690—21no—
53#2681—21no—
54#2676—21no—
55#2674—21no—
56#2650—21no—
57#2590—21no—
58#2558—21no—
59#2545C2211yescharacteristic
60#2540C2211yescharacteristic
61#2509C2211yescharacteristic, complemented
62#2506C2211yescharacteristic, complemented
63#2497C2211yescharacteristic, complemented
64#2497C2211yescharacteristic, complemented
65#2491—21no—
66#2486C2211yescharacteristic, complemented
67#2485C2211yescharacteristic
68#2485C2211yescharacteristic
69#2485C2211yescharacteristic, complemented
70#2472—21no—
71#2461—21no—
72#2440C2211yescharacteristic, complemented
73#2439C2211yescharacteristic, complemented
74#2437—21no—
75#2436C2211yescharacteristic
76#2432C2211yescharacteristic
77#2427C2211yescharacteristic
78#2426C2211yescharacteristic
79#2424—21no—
80#2409C2211yescharacteristic
81#2408C2211yescharacteristic
82#2367C2211yescharacteristic
83#2358—21no—
84#2354C2211yescharacteristic
85#2352C2211yescharacteristic
86#2332—21no—
87C4×C22⋊Q8C2211yescharacteristic
88C4×#121C2211yescharacteristic
89#2296C2211yescharacteristic
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2074C2211yescharacteristic, complemented
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic, complemented
99#2065C2211yescharacteristic
100#2057C2211yescharacteristic, complemented
101#2043C2211yescharacteristic, complemented
102#2043C2211yescharacteristic, complemented
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1981C2211yescharacteristic, complemented
132#1959C2211yescharacteristic
133#1959C2211yescharacteristic
134#1958C2211yescharacteristic
135#1956C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1924C2211yescharacteristic, complemented
150#1921C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1894C2211yescharacteristic, complemented
163#1894C2211yescharacteristic, complemented
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1870C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1825C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic, complemented
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1787C2211yescharacteristic, complemented
193#1787C2211yescharacteristic, complemented
194#1787C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211D4×Q8—24no—
212D4×Q8—42no—
213#548—42no—
214#548—42no—
215#546—24no—
216#546—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—42no—
225C2×#124—42no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—21no—
244C2×#121D411yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#120—21no—
249C2×#120—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C42C2311yescharacteristic
266#489—42no—
267#489—42no—
268#485—24no—
269#484—42no—
270#482—42no—
271#436—42no—
272#436—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#419—42no—
284#419—42no—
285#419—42no—
286#418—42no—
287#418—42no—
288#417—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#400—21no—
346#399—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#395—21no—
362#395—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#393—21no—
372#393—21no—
373#393—21no—
374#393—21no—
375#392—21no—
376#392—21no—
377#391—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390D411yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389D411yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388D411yescharacteristic
417#388D411yescharacteristic
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386D411yescharacteristic
434#386D411yescharacteristic
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#380—21no—
448#380—21no—
449#380D411yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—22no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4C2×D411yescharacteristic
536C22×D4C2×D411yescharacteristic
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—44no—
575#125—82no—
576#124—22no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—22no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—44no—
587#124—44no—
588#124—44no—
589#123—44no—
590#123—82no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—44no—
595C22⋊Q8—44no—
596C22⋊Q8—44no—
597C22⋊Q8—44no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—82no—
603C22⋊Q8#4114yes—
604#121—22no—
605#121—22no—
606#121—42no—
607#121—44no—
608#121—44no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#120—44no—
614#120—44no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—44no—
628C4×D4—44no—
629#117—22no—
630#117—22no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
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—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
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—44no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—44no—
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#107—22no—
742#107—41no—
743#107—41no—
744#107—41no—
745#106—22no—
746#106—41no—
747#106—41no—
748#106—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799#97—41no—
800#97—41no—
801C4×C8—41no—
802C4×C8—41no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
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#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—21no—
841C24—21no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—44no—
853#41—82no—
854#41—82no—
855#41—82no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×Q8—42no—
879C2×Q8—44no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8—82no—
885C2×Q8—82no—
886C2×Q8—82no—
887C2×Q8—82no—
888C2×Q8—82no—
889C2×Q8C2×#4112yes—
890C2×Q8H(5,𝔽2)12yes—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—22no—
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—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—41no—
910C2×D4—41no—
911C2×D4—41no—
912C2×D4—41no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—82no—
922C2×D4—82no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4H(5,𝔽2)12yes—
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—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C2×#4112yes—
994C22×C4H(5,𝔽2)12yes—
995C22×C4C2511yescharacteristic
996M16—82no—
997M16—82no—
998M16—82no—
999M16—82no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C4⋊C4—24no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4C2×#4112yes—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—41no—
1129C42—41no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C42—81no—
1137C42—81no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—22no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—84no—
1173C23—84no—
1174C23—84no—
1175C23—84no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23#54612yes—
1180C23C23×D411yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—22no—
1184Q8—22no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—84no—
1194Q8—84no—
1195Q8—162no—
1196D4—22no—
1197D4—22no—
1198D4—44no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—84no—
1206D4—82no—
1207D4—82no—
1208D4—84no—
1209D4—84no—
1210D4—162no—
1211D4—162no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
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—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—82no—
1298C2×C4—82no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4#54612yes—
1305C2×C4#57512yes—
1306C2×C4C22×#4111yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—42no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—168no—
1356C22C2×#54611yescharacteristic
1357C22#348411yescharacteristic
1358C22#350011yescharacteristic
1359C22C2×#57511yescharacteristic
1360C22#358511yescharacteristic
1361C22#358611yescharacteristic
1362C22#358611yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—42no—
1376C4—42no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4#351311yescharacteristic
1389C4#351311yescharacteristic
1390C4#353411yescharacteristic
1391C4#353411yescharacteristic
1392C2—42no—
1393C2—81no—
1394C2—81no—
1395C2—82no—
1396C2—161no—
1397C2#4300511yescharacteristic
1398C2#6115811yescharacteristic
1399C2#6122211yescharacteristic
1400C2#6159011yescharacteristic
1401C2#6165511yescharacteristic
1402C2#6256911yescharacteristic
1403C2#6259311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59130C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #40005C2semidirect
3. #32092C2semidirect
4. #32085C2semidirect
5. #32043C2semidirect
6. #32041C2semidirect
7. #31305C2semidirect
8. #31304C2semidirect
9. #30659C2semidirect
10. #30654C2semidirect
11. #29165C2semidirect
12. #29061C2semidirect
13. #29055C2semidirect
14. #28112C2semidirect
15. #28110C2semidirect
16. #27285C2semidirect
17. #27278C2semidirect
18. #26766C2semidirect
19. #26761C2semidirect
20. #25864C2semidirect
21. #24890C2semidirect
22. #24880C2semidirect
23. #24053C2semidirect
24. #24051C2semidirect
25. #24050C2semidirect
26. #24047C2semidirect
27. #23506C2semidirect
28. #23121C2semidirect
29. #22430C2semidirect
30. #22427C2semidirect
31. #22083C2semidirect
38. C2×#484C22semidirect
46. C2×#419C22semidirect
61. #2509C22semidirect
62. #2506C22semidirect
63. #2497C22semidirect
64. #2497C22semidirect
66. #2486C22semidirect
69. #2485C22semidirect
72. #2440C22semidirect
73. #2439C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2096C22semidirect
94. #2074C22semidirect
96. #2068C22semidirect
98. #2066C22semidirect
100. #2057C22semidirect
101. #2043C22semidirect
102. #2043C22semidirect
117. #2036C22semidirect
118. #2036C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
129. #2024C22semidirect
131. #1981C22semidirect
135. #1956C22semidirect
136. #1944C22semidirect
137. #1943C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
142. #1933C22semidirect
143. #1933C22semidirect
144. #1928C22semidirect
145. #1927C22semidirect
148. #1924C22semidirect
149. #1924C22semidirect
150. #1921C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1916C22semidirect
155. #1916C22semidirect
161. #1894C22semidirect
162. #1894C22semidirect
163. #1894C22semidirect
167. #1873C22semidirect
168. #1872C22semidirect
171. #1870C22semidirect
172. #1870C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
186. #1803C22semidirect
192. #1787C22semidirect
193. #1787C22semidirect
194. #1787C22semidirect
197. C4×#103C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#591302
#400052
#320922
#320852
#320432
#320412
#313052
#313042
#306592
#306542
#291652
#290612
#290552
#281122
#281102
#272852
#272782
#267662
#267612
#258642
#248902
#248802
#240532
#240512
#240502
#240472
#235062
#231212
#224302
#224272
#220832