Finite Group Databasebeta

← #6519892

Subgroups — #6519892

Order 512.

1807 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3252C211yesmaximal, characteristic, complemented
2C2×#2995C211yesmaximal, characteristic, complemented
3#37622C211yesmaximal, characteristic, complemented
4#35234C211yesmaximal, characteristic
5#28569C211yesmaximal, characteristic, complemented
6#28568C211yesmaximal, characteristic, complemented
7#28559C211yesmaximal, characteristic, complemented
8#28558C211yesmaximal, characteristic, complemented
9#25488C211yesmaximal, characteristic, complemented
10#25484C211yesmaximal, characteristic, complemented
11#25403C211yesmaximal, characteristic, complemented
12#25399C211yesmaximal, characteristic, complemented
13#25357C211yesmaximal, characteristic, complemented
14#25353C211yesmaximal, characteristic, complemented
15#25311C211yesmaximal, characteristic, complemented
16#25307C211yesmaximal, characteristic, complemented
17#24851C211yesmaximal, characteristic, complemented
18#24849C211yesmaximal, characteristic, complemented
19#24794C211yesmaximal, characteristic, complemented
20#24793C211yesmaximal, characteristic, complemented
21#24791C211yesmaximal, characteristic, complemented
22#24789C211yesmaximal, characteristic, complemented
23#24766C211yesmaximal, characteristic, complemented
24#24764C211yesmaximal, characteristic, complemented
25#24716C211yesmaximal, characteristic, complemented
26#24714C211yesmaximal, characteristic, complemented
27#24666C211yesmaximal, characteristic, complemented
28#24664C211yesmaximal, characteristic, complemented
29#21868C211yesmaximal, characteristic, complemented
30#21394C211yesmaximal, characteristic, complemented
31#21170C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#3252—28no—
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#470C2211yescharacteristic
42C2×#470C2211yescharacteristic
43C2×#468C2211yescharacteristic
44C2×#468C2211yescharacteristic
45C2×#468C2211yescharacteristic
46C2×#467C2211yescharacteristic
47C2×#465C2211yescharacteristic
48C2×#464C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#462C2211yescharacteristic
51C2×#461C2211yescharacteristic
52#2995—28no—
53C2×#446C2211yescharacteristic
54C2×#446C2211yescharacteristic
55C2×#436C2211yescharacteristic
56C2×#436C2211yescharacteristic
57C2×#435C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×#435C2211yescharacteristic
61C2×#433C2211yescharacteristic
62C2×#433C2211yescharacteristic
63C2×#432C2211yescharacteristic
64C2×#428C2211yescharacteristic
65C2×#428C2211yescharacteristic
66C2×#424C2211yescharacteristic
67C2×#424C2211yescharacteristic
68C2×#423C2211yescharacteristic
69#2854—21no—
70#2854—21no—
71#2814—21no—
72#2814—21no—
73#2664—21no—
74#2664—21no—
75#2664—21no—
76#2662—21no—
77#2628C2211yescharacteristic
78#2628C2211yescharacteristic
79#2625—21no—
80#2624—21no—
81#2621C2211yescharacteristic
82#2621C2211yescharacteristic
83#2601—21no—
84#2601—21no—
85#2592—21no—
86#2592C2211yescharacteristic
87#2584—21no—
88#2584C2211yescharacteristic
89#2582C2211yescharacteristic
90#2582C2211yescharacteristic
91#2564—21no—
92#2562C2211yescharacteristic
93#2543—21no—
94#2540C2211yescharacteristic
95#2538C2211yescharacteristic
96#2538C2211yescharacteristic
97#2417C2211yescharacteristic
98#2417C2211yescharacteristic
99#2416C2211yescharacteristic
100#2416C2211yescharacteristic
101#2415C2211yescharacteristic
102#2415C2211yescharacteristic
103#2415C2211yescharacteristic
104#2415C2211yescharacteristic
105#2324C2211yescharacteristic
106#2324C2211yescharacteristic
107#2323C2211yescharacteristic
108#2323C2211yescharacteristic
109#2285C2211yescharacteristic
110C2×C4×C4⋊C4C2211yescharacteristic
111#2088C2211yescharacteristic
112#2088C2211yescharacteristic
113#2087C2211yescharacteristic
114#2086C2211yescharacteristic
115#2077C2211yescharacteristic
116#2077C2211yescharacteristic
117#2076C2211yescharacteristic
118#2075C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2067C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2066C2211yescharacteristic
126#2065C2211yescharacteristic
127#2056C2211yescharacteristic
128#2056C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2036C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2034C2211yescharacteristic
138#2033C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#1992C2211yescharacteristic
144#1992C2211yescharacteristic
145#1988C2211yescharacteristic
146#1988C2211yescharacteristic
147#1981C2211yescharacteristic
148#1981C2211yescharacteristic
149#1973C2211yescharacteristic
150#1971C2211yescharacteristic
151#1969C2211yescharacteristic
152#1968C2211yescharacteristic
153#1959C2211yescharacteristic
154#1959C2211yescharacteristic
155#1949C2211yescharacteristic
156#1949C2211yescharacteristic
157#1949C2211yescharacteristic
158#1949C2211yescharacteristic
159#1948C2211yescharacteristic
160#1948C2211yescharacteristic
161#1947C2211yescharacteristic
162#1947C2211yescharacteristic
163#1944C2211yescharacteristic
164#1943C2211yescharacteristic
165#1942C2211yescharacteristic
166#1941C2211yescharacteristic
167#1936C2211yescharacteristic
168#1935C2211yescharacteristic
169#1935C2211yescharacteristic
170#1935C2211yescharacteristic
171#1934C2211yescharacteristic
172#1933C2211yescharacteristic
173#1933C2211yescharacteristic
174#1933C2211yescharacteristic
175#1895C2211yescharacteristic
176#1894C2211yescharacteristic
177#1894C2211yescharacteristic
178#1894C2211yescharacteristic
179#1893C2211yescharacteristic
180#1892C2211yescharacteristic
181#1892C2211yescharacteristic
182#1892C2211yescharacteristic
183#1875C2211yescharacteristic
184#1875C2211yescharacteristic
185#1873C2211yescharacteristic
186#1873C2211yescharacteristic
187#1872C2211yescharacteristic
188#1872C2211yescharacteristic
189#1872C2211yescharacteristic
190#1872C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1808C2211yescharacteristic
194#1807C2211yescharacteristic
195#1805C2211yescharacteristic
196#1805C2211yescharacteristic
197#1804C2211yescharacteristic
198#1804C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203#1736C2211yescharacteristic
204#1736C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#533—24no—
216#533—24no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219#529—24no—
220#529—24no—
221#529—24no—
222#529—24no—
223C2×#126—21no—
224C2×#126D411yescharacteristic
225C2×#126D411yescharacteristic
226C2×#125—21no—
227C2×#125D411yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#124D411yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123D411yescharacteristic
233C2×#123D411yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×#121—21no—
246C2×#121—21no—
247C2×#121D411yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×C4×Q8—21no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C42—21no—
270C22×C42C2311yescharacteristic
271#479—24no—
272#479—24no—
273#477—24no—
274#476—24no—
275#470—24no—
276#470—24no—
277#470—42no—
278#468—24no—
279#468—24no—
280#468—42no—
281#467—42no—
282#465—42no—
283#464—24no—
284#464—24no—
285#462—24no—
286#461—24no—
287#446—24no—
288#446—24no—
289#436—24no—
290#436—24no—
291#435—24no—
292#435—24no—
293#435—24no—
294#435—24no—
295#433—24no—
296#433—24no—
297#432—24no—
298#428—42no—
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
312#424—24no—
313#424—24no—
314#423D418yescomplemented
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361#400—21no—
362#400—21no—
363#400—21no—
364#399—21no—
365#399—21no—
366#399—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398—21no—
376#398—21no—
377#398—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#397—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#396—21no—
388#396—21no—
389#396—21no—
390#396—21no—
391#396—21no—
392#396—21no—
393#396—21no—
394#396—21no—
395#395—21no—
396#395—21no—
397#395—21no—
398#394—21no—
399#394—21no—
400#394—21no—
401#394—21no—
402#394—21no—
403#394—21no—
404#394—21no—
405#393—21no—
406#393—21no—
407#393—21no—
408#392—21no—
409#391—21no—
410#391—21no—
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#390—21no—
418#390—21no—
419#390—21no—
420#390—21no—
421#390—21no—
422#390—21no—
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389—21no—
430#389—21no—
431#389—21no—
432#389—21no—
433#389—21no—
434#389—21no—
435#389—21no—
436#389—21no—
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#389C2311yescharacteristic
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#389C2311yescharacteristic
443#389C2311yescharacteristic
444#389C2311yescharacteristic
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#388—21no—
450#388—21no—
451#388—21no—
452#388—21no—
453#388—21no—
454#388—21no—
455#388—21no—
456#388—21no—
457#388—21no—
458#388—21no—
459#387—21no—
460#387—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#386—21no—
466#386—21no—
467#385—21no—
468#385—21no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#380—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482#380C2311yescharacteristic
483#380C2311yescharacteristic
484#380C2311yescharacteristic
485C4×C4⋊C4—21no—
486C4×C4⋊C4—21no—
487C4×C4⋊C4—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C2×#95—21no—
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#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518C22×Q8—21no—
519C22×Q8C2×D411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
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×M16C2×D414yes—
561C2×M16C2×D414yes—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580#126—24no—
581#126—24no—
582#126—44no—
583#125—24no—
584#125—22no—
585#125—22no—
586#125—44no—
587#124—24no—
588#124—22no—
589#124—22no—
590#123—24no—
591#123—24no—
592#123—44no—
593C22⋊Q8—24no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—44no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613#121—24no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—41no—
619#121—41no—
620#121—82no—
621#121—82no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×Q8—22no—
628C4×Q8—22no—
629C4×Q8—22no—
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—22no—
639C4×D4—44no—
640#117—22no—
641#117—22no—
642#117—22no—
643#117—22no—
644#117—44no—
645#117—44no—
646#117—41no—
647#117—41no—
648#117—41no—
649#117—41no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
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—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—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—82no—
756C2×C42C2×D411yescharacteristic
757C2×C42C2×D411yescharacteristic
758C2×C42C2×D414yes—
759C2×C42#4114yes—
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—41no—
769#107—41no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—41no—
775#106—41no—
776C4⋊C8—22no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8C2×D414yes—
783C4⋊C8C2×D414yes—
784C4⋊C8C2×D414yes—
785C4⋊C8C2×D414yes—
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—22no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#102—22no—
805#102—22no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810C22⋊C8—22no—
811C22⋊C8—22no—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816#97—22no—
817#97—22no—
818#97—22no—
819#97—22no—
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#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858C24—21no—
859C24C22×D411yescharacteristic
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862C2×Q8—22no—
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—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—41no—
882C2×Q8—41no—
883C2×Q8—42no—
884C2×Q8—81no—
885C2×Q8—81no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
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—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4#12114yes—
955C22×C4#12114yes—
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
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×D412yes—
968C22×C4C2×#4112yes—
969C22×C4C2511yescharacteristic
970Q16—82no—
971Q16—82no—
972SD16—82no—
973SD16—82no—
974M16—44no—
975M16—44no—
976M16—82no—
977M16—82no—
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—
1002C2×C8C22×D412yes—
1003C2×C8C22×D412yes—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
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—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
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—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4H(5,𝔽2)12yes—
1068C4⋊C42−1+412yes—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
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—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
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—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—81no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42#12114yes—
1122C42#12114yes—
1123C42C22×D412yes—
1124C42C22×D412yes—
1125C42C2×#4112yes—
1126C42C2×#4112yes—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23C2×#12112yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—82no—
1169Q8—84no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—82no—
1175D4—82no—
1176D4—82no—
1177D4—84no—
1178D4—162no—
1179D4—162no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
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—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
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×C4C2×#12112yes—
1271C2×C4C2×#12112yes—
1272C2×C4C2×#12112yes—
1273C2×C4C2×#12112yes—
1274C2×C4C2×#12112yes—
1275C2×C4C23×D411yescharacteristic
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×2−1+411yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C8—22no—
1282C8—22no—
1283C8—22no—
1284C8—22no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22C22×#12111yescharacteristic
1318C22#348811yescharacteristic
1319C22#348911yescharacteristic
1320C22#358511yescharacteristic
1321C22#358611yescharacteristic
1322C22#358611yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—42no—
1335C4—41no—
1336C4—41no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4#349611yescharacteristic
1351C4#349711yescharacteristic
1352C4#351111yescharacteristic
1353C4#351211yescharacteristic
1354C2—42no—
1355C2—81no—
1356C2—81no—
1357C2—161no—
1358C2#3556411yescharacteristic
1359C2#6045511yescharacteristic
1360C2#6045611yescharacteristic
1361C2#6208411yescharacteristic
1362C2#6208611yescharacteristic
1363C2#6223211yescharacteristic
1364C2#6223411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35234C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3252C2semidirect
2. C2×#2995C2semidirect
3. #37622C2semidirect
5. #28569C2semidirect
6. #28568C2semidirect
7. #28559C2semidirect
8. #28558C2semidirect
9. #25488C2semidirect
10. #25484C2semidirect
11. #25403C2semidirect
12. #25399C2semidirect
13. #25357C2semidirect
14. #25353C2semidirect
15. #25311C2semidirect
16. #25307C2semidirect
17. #24851C2semidirect
18. #24849C2semidirect
19. #24794C2semidirect
20. #24793C2semidirect
21. #24791C2semidirect
22. #24789C2semidirect
23. #24766C2semidirect
24. #24764C2semidirect
25. #24716C2semidirect
26. #24714C2semidirect
27. #24666C2semidirect
28. #24664C2semidirect
29. #21868C2semidirect
30. #21394C2semidirect
31. #21170C2semidirect
314. #423D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32522
C2×#29952
#376222
#352342
#285692
#285682
#285592
#285582
#254882
#254842
#254032
#253992
#253572
#253532
#253112
#253072
#248512
#248492
#247942
#247932
#247912
#247892
#247662
#247642
#247162
#247142
#246662
#246642
#218682
#213942
#211702