Finite Group Databasebeta

← #7518124

Subgroups — #7518124

Order 512.

1924 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3311C211yesmaximal, characteristic
2C2×#3120C211yesmaximal, characteristic, complemented
3#45326C211yesmaximal, characteristic, complemented
4#35987C211yesmaximal, characteristic
5#31226C211yesmaximal, characteristic, complemented
6#31083C211yesmaximal, characteristic, complemented
7#30830C211yesmaximal, characteristic, complemented
8#30620C211yesmaximal, characteristic, complemented
9#27944C211yesmaximal, characteristic, complemented
10#26846C211yesmaximal, characteristic, complemented
11#26577C211yesmaximal, characteristic, complemented
12#26376C211yesmaximal, characteristic, complemented
13#26182C211yesmaximal, characteristic, complemented
14#26169C211yesmaximal, characteristic, complemented
15#26053C211yesmaximal, characteristic, complemented
16#25968C211yesmaximal, characteristic, complemented
17#25511C211yesmaximal, characteristic, complemented
18#25248C211yesmaximal, characteristic, complemented
19#25204C211yesmaximal, characteristic, complemented
20#25156C211yesmaximal, characteristic, complemented
21#25039C211yesmaximal, characteristic, complemented
22#24917C211yesmaximal, characteristic, complemented
23#24617C211yesmaximal, characteristic, complemented
24#24536C211yesmaximal, characteristic, complemented
25#24452C211yesmaximal, characteristic
26#24108C211yesmaximal, characteristic, complemented
27#22903C211yesmaximal, characteristic, complemented
28#22884C211yesmaximal, characteristic, complemented
29#22882C211yesmaximal, characteristic, complemented
30#22671C211yesmaximal, characteristic, complemented
31#20878C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#541C2211yescharacteristic, complemented
35C2×#520C2211yescharacteristic
36#3311—28no—
37C2×#489C2211yescharacteristic
38#3120—28no—
39C2×#484C2211yescharacteristic, complemented
40C2×#485C2211yescharacteristic
41C2×#482C2211yescharacteristic
42C2×#483C2211yescharacteristic, complemented
43C2×#479C2211yescharacteristic, complemented
44C2×#478C2211yescharacteristic
45C2×#476C2211yescharacteristic
46C2×#470C2211yescharacteristic
47C2×#468C2211yescharacteristic
48C2×#465C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#462C2211yescharacteristic, complemented
51C2×#461C2211yescharacteristic
52C2×#452C2211yescharacteristic
53C2×#452C2211yescharacteristic
54C2×#450C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#441C2211yescharacteristic, complemented
57C2×#440C2211yescharacteristic
58C2×#440C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic, complemented
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×#435C2211yescharacteristic
63C2×#433C2211yescharacteristic, complemented
64C2×#428C2211yescharacteristic, complemented
65C2×#417C2211yescharacteristic
66C2×#418C2211yescharacteristic
67C2×#416C2211yescharacteristic
68#2725—21no—
69#2722—21no—
70#2721—21no—
71#2715—21no—
72#2624C2211yescharacteristic
73#2623—21no—
74#2550C2211yescharacteristic, complemented
75#2521—21no—
76#2501C2211yescharacteristic
77#2499C2211yescharacteristic, complemented
78#2498—21no—
79#2496—21no—
80#2487C2211yescharacteristic
81#2482—21no—
82#2462—21no—
83#2453—21no—
84#2451C2211yescharacteristic, complemented
85#2448C2211yescharacteristic
86#2448C2211yescharacteristic
87#2446C2211yescharacteristic, complemented
88#2443—21no—
89#2443—21no—
90#2441C2211yescharacteristic
91#2429C2211yescharacteristic
92#2423C2211yescharacteristic
93#2423C2211yescharacteristic
94#2421C2211yescharacteristic
95#2418—21no—
96#2418—21no—
97#2417C2211yescharacteristic
98#2395C2211yescharacteristic
99C2×#399—21no—
100#2362C2211yescharacteristic
101#2360C2211yescharacteristic, complemented
102Q8×C4⋊C4C2211yescharacteristic, complemented
103D4×C4⋊C4C2211yescharacteristic
104D4×C4⋊C4C2211yescharacteristic
105#2339C2211yescharacteristic
106D4×C22⋊C4C2211yescharacteristic
107D4×C22⋊C4C2211yescharacteristic
108#2316C2211yescharacteristic, complemented
109#2096C2211yescharacteristic, complemented
110#2095C2211yescharacteristic, complemented
111#2093C2211yescharacteristic
112#2092C2211yescharacteristic
113#2088C2211yescharacteristic, complemented
114#2086C2211yescharacteristic, complemented
115#2086C2211yescharacteristic, complemented
116#2084C2211yescharacteristic, complemented
117#2075C2211yescharacteristic
118#2074C2211yescharacteristic, complemented
119#2072C2211yescharacteristic, complemented
120#2072C2211yescharacteristic, complemented
121#2066C2211yescharacteristic, complemented
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2059C2211yescharacteristic, complemented
126#2058C2211yescharacteristic, complemented
127#2058C2211yescharacteristic, complemented
128#2056C2211yescharacteristic, complemented
129#2056C2211yescharacteristic, complemented
130#2055C2211yescharacteristic
131#2043C2211yescharacteristic, complemented
132#2042C2211yescharacteristic
133#2036C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2025C2211yescharacteristic
138#2015C2211yescharacteristic
139#2013C2211yescharacteristic
140#2001C2211yescharacteristic
141#1973C2211yescharacteristic
142#1971C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1948C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1917C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1892C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1870C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1853C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1850C2211yescharacteristic, complemented
191#1847C2211yescharacteristic, complemented
192#1845C2211yescharacteristic, complemented
193#1825C2211yescharacteristic, complemented
194#1809C2211yescharacteristic
195#1804C2211yescharacteristic
196#1803C2211yescharacteristic, complemented
197#1802C2211yescharacteristic
198#1786C2211yescharacteristic
199#1770C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic, complemented
203C2×#340C2211yescharacteristic, complemented
204#1729C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#556—24no—
217#556—42no—
218#546—24no—
219#546—42no—
220#541—24no—
221#541—42no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#126—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244#520—24no—
245#520—42no—
246C2×C4×Q8—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4—21no—
266C22×C4⋊C4—21no—
267C22×C4⋊C4—21no—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272C22×C22⋊C4—21no—
273#489—24no—
274#485—24no—
275#484—24no—
276#483—24no—
277#482—24no—
278#479—24no—
279#478—24no—
280#476—24no—
281#470—24no—
282#468—42no—
283#465—24no—
284#464—24no—
285#462—24no—
286#461—24no—
287#452—24no—
288#452D418yes—
289#450—24no—
290#450—24no—
291#441—24no—
292#440—24no—
293#440—24no—
294C4×Q16—24no—
295C4×SD16—24no—
296C4×SD16—24no—
297#435—24no—
298#433—24no—
299#428—42no—
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319#418—24no—
320#417—24no—
321#416—24no—
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360#400—21no—
361#400—21no—
362#400—21no—
363#400D411yescharacteristic
364#399—21no—
365#399—21no—
366#399—21no—
367#399—21no—
368#399—21no—
369#399—21no—
370#399—21no—
371#399—21no—
372#399—21no—
373#399D411yescharacteristic
374#398—21no—
375#398—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#398—21no—
381#398D411yescharacteristic
382#397—21no—
383#397—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#397D411yescharacteristic
389#397D411yescharacteristic
390#397D411yescharacteristic
391#396—21no—
392#396—21no—
393#396—21no—
394#395—21no—
395#395—21no—
396#394—21no—
397#394—21no—
398#394D411yescharacteristic
399#394D411yescharacteristic
400#391—21no—
401#391—21no—
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—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#387—21no—
449#387—21no—
450#387—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#386—21no—
455#386—21no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#384—21no—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#382C2311yescharacteristic
470#381—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380—21no—
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#379—21no—
481#379—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C22⋊C4—21no—
488C4×C22⋊C4C2311yescharacteristic
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491C2×#95—21no—
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#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25—21no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C2×D414yes—
525C22×Q8—21no—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4C2×D411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16C2×D414yes—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16C2×D414yes—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—41no—
573C2×M16—41no—
574C2×M16—41no—
575C22×C8—22no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—41no—
589C4⋊Q8—41no—
590#126—44no—
591#126—44no—
592#126—44no—
593#126—44no—
594#125—22no—
595#125—41no—
596#125—44no—
597#125—44no—
598#124—22no—
599#124—41no—
600#124—44no—
601#123—44no—
602#123—82no—
603#123—82no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8C2×D414yes—
614#121—22no—
615#121—22no—
616#121—44no—
617#120—44no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—44no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—44no—
644C4×D4—44no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—22no—
649#117—22no—
650#117—41no—
651#117—44no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
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—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—44no—
691C2×C4⋊C4—82no—
692C2×C4⋊C4—82no—
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
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—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4—82no—
740C2×C22⋊C4—82no—
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#107—22no—
766#107—22no—
767#107—22no—
768#107—41no—
769#107—41no—
770#107—41no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—41no—
777#106—41no—
778#106—41no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—41no—
783C4⋊C8—41no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103C2×D414yes—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—41no—
809#102—41no—
810#102C2×D414yes—
811#102#4114yes—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—41no—
816C22⋊C8C2×D414yes—
817#97—22no—
818#97—22no—
819#97—41no—
820C4×C8—22no—
821C4×C8—22no—
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#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861C24—21no—
862C24—21no—
863C24—42no—
864C24—42no—
865C24—42no—
866C24—42no—
867C24—81no—
868C24—81no—
869C24—81no—
870C24C22×D411yescharacteristic
871C24C22×D411yescharacteristic
872#41—28no—
873#41—44no—
874#41—44no—
875#41—44no—
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—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—81no—
895C2×Q8C22×D412yes—
896C2×Q8C22×D412yes—
897C2×D4—24no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—41no—
909C2×D4—41no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—42no—
917C2×D4—82no—
918C2×D4—82no—
919C2×D4—82no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4C22×D412yes—
923C2×D4C2×#4112yes—
924C2×D42−1+412yes—
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—24no—
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—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D412yes—
985C22×C4C22×D411yescharacteristic
986C22×C4H(5,𝔽2)12yes—
987C22×C4C2511yescharacteristic
988Q16—44no—
989Q16—44no—
990SD16—28no—
991SD16—44no—
992SD16—82no—
993SD16—82no—
994M16—44no—
995M16—82no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
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—82no—
1018C2×C8C22×D412yes—
1019C2×C8C22×D412yes—
1020C2×C8C2×#4112yes—
1021C4⋊C4—24no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
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—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
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—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4C22×D412yes—
1083C4⋊C4C2×#4112yes—
1084C22⋊C4—24no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
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—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
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—
1120C22⋊C4—81no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—81no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—22no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—84no—
1168C23—84no—
1169C23—84no—
1170C23—84no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23D4212yes—
1175C23C23×D411yescharacteristic
1176Q8—22no—
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—84no—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—48no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—82no—
1198D4—84no—
1199D4—162no—
1200D4#54714yes—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
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—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—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—48no—
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—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—84no—
1287C2×C4—84no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4D4212yes—
1294C2×C4#57712yes—
1295C2×C4C23×D411yescharacteristic
1296C2×C4C22×#4111yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4C2×2−1+411yescharacteristic
1299C2×C4#58511yescharacteristic
1300C2×C4#58511yescharacteristic
1301C8—22no—
1302C8—22no—
1303C8—22no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C22—22no—
1310C22—24no—
1311C22—22no—
1312C22—22no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—42no—
1318C22—41no—
1319C22—42no—
1320C22—42no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—168no—
1338C22C2×D4211yescharacteristic
1339C22D4×#4111yescharacteristic
1340C22#348911yescharacteristic
1341C22C2×#57711yescharacteristic
1342C22#358511yescharacteristic
1343C22#358611yescharacteristic
1344C22#358611yescharacteristic
1345C4—22no—
1346C4—22no—
1347C4—41no—
1348C4—41no—
1349C4—42no—
1350C4—41no—
1351C4—42no—
1352C4—42no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—42no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4C2×#54711yescharacteristic
1372C4#348511yescharacteristic
1373C4#351311yescharacteristic
1374C4#353511yescharacteristic
1375C2—42no—
1376C2—44no—
1377C2—81no—
1378C2—161no—
1379C2#5899511yescharacteristic
1380C2#6106411yescharacteristic
1381C2#6109511yescharacteristic
1382C2#6151011yescharacteristic
1383C2#6152011yescharacteristic
1384C2#6218911yescharacteristic
1385C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3120C2semidirect
3. #45326C2semidirect
5. #31226C2semidirect
6. #31083C2semidirect
7. #30830C2semidirect
8. #30620C2semidirect
9. #27944C2semidirect
10. #26846C2semidirect
11. #26577C2semidirect
12. #26376C2semidirect
13. #26182C2semidirect
14. #26169C2semidirect
15. #26053C2semidirect
16. #25968C2semidirect
17. #25511C2semidirect
18. #25248C2semidirect
19. #25204C2semidirect
20. #25156C2semidirect
21. #25039C2semidirect
22. #24917C2semidirect
23. #24617C2semidirect
24. #24536C2semidirect
26. #24108C2semidirect
27. #22903C2semidirect
28. #22884C2semidirect
29. #22882C2semidirect
30. #22671C2semidirect
31. #20878C2semidirect
34. C2×#541C22semidirect
39. C2×#484C22semidirect
42. C2×#483C22semidirect
43. C2×#479C22semidirect
50. C2×#462C22semidirect
56. C2×#441C22semidirect
59. C2×C4×Q16C22semidirect
63. C2×#433C22semidirect
64. C2×#428C22semidirect
74. #2550C22semidirect
77. #2499C22semidirect
84. #2451C22semidirect
87. #2446C22semidirect
101. #2360C22semidirect
102. Q8×C4⋊C4C22semidirect
108. #2316C22semidirect
109. #2096C22semidirect
110. #2095C22semidirect
113. #2088C22semidirect
114. #2086C22semidirect
115. #2086C22semidirect
116. #2084C22semidirect
118. #2074C22semidirect
119. #2072C22semidirect
120. #2072C22semidirect
121. #2066C22semidirect
125. #2059C22semidirect
126. #2058C22semidirect
127. #2058C22semidirect
128. #2056C22semidirect
129. #2056C22semidirect
131. #2043C22semidirect
142. #1971C22semidirect
144. #1948C22semidirect
145. #1944C22semidirect
146. #1944C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
150. #1935C22semidirect
152. #1933C22semidirect
153. #1927C22semidirect
157. #1917C22semidirect
158. #1916C22semidirect
160. #1894C22semidirect
161. #1892C22semidirect
165. #1878C22semidirect
172. #1865C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
188. #1853C22semidirect
190. #1850C22semidirect
191. #1847C22semidirect
192. #1845C22semidirect
193. #1825C22semidirect
196. #1803C22semidirect
199. #1770C22semidirect
202. #1753C22semidirect
203. C2×#340C22semidirect
204. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33112
C2×#31202
#453262
#359872
#312262
#310832
#308302
#306202
#279442
#268462
#265772
#263762
#261822
#261692
#260532
#259682
#255112
#252482
#252042
#251562
#250392
#249172
#246172
#245362
#244522
#241082
#229032
#228842
#228822
#226712
#208782