Finite Group Databasebeta

← #6673645

Subgroups — #6673645

Order 512.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3356C211yesmaximal, characteristic, complemented
2C2×#3081C211yesmaximal, characteristic, complemented
3#42436C211yesmaximal, characteristic, complemented
4#36075C211yesmaximal, characteristic
5#33018C211yesmaximal, characteristic, complemented
6#31244C211yesmaximal, characteristic, complemented
7#31240C211yesmaximal, characteristic, complemented
8#31136C211yesmaximal, characteristic, complemented
9#31128C211yesmaximal, characteristic, complemented
10#30954C211yesmaximal, characteristic, complemented
11#30947C211yesmaximal, characteristic, complemented
12#30930C211yesmaximal, characteristic, complemented
13#30927C211yesmaximal, characteristic, complemented
14#29786C211yesmaximal, characteristic, complemented
15#29648C211yesmaximal, characteristic, complemented
16#28361C211yesmaximal, characteristic, complemented
17#28110C211yesmaximal, characteristic
18#26893C211yesmaximal, characteristic, complemented
19#26892C211yesmaximal, characteristic, complemented
20#26813C211yesmaximal, characteristic, complemented
21#26799C211yesmaximal, characteristic, complemented
22#26478C211yesmaximal, characteristic, complemented
23#26468C211yesmaximal, characteristic, complemented
24#26363C211yesmaximal, characteristic, complemented
25#26357C211yesmaximal, characteristic, complemented
26#24586C211yesmaximal, characteristic, complemented
27#24477C211yesmaximal, characteristic, complemented
28#24096C211yesmaximal, characteristic, complemented
29#23969C211yesmaximal, characteristic
30#22624C211yesmaximal, characteristic, complemented
31#22074C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#518C2211yescharacteristic
36#3356—28no—
37C2×#498C2211yescharacteristic, complemented
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic, complemented
41C2×#483C2211yescharacteristic
42C2×#483C2211yescharacteristic, complemented
43#3081—28no—
44C2×#477C2211yescharacteristic, complemented
45C2×#475C2211yescharacteristic, complemented
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#476C2211yescharacteristic
51C2×#476C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#470C2211yescharacteristic
55C2×#470C2211yescharacteristic, complemented
56C2×#450C2211yescharacteristic
57C2×C4×Q16C2211yescharacteristic, complemented
58C2×#436C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#428C2211yescharacteristic, complemented
61C2×#427C2211yescharacteristic
62C2×#424C2211yescharacteristic
63C2×#418C2211yescharacteristic
64C22×#102C2211yescharacteristic
65#2817—21no—
66#2719—21no—
67#2713—21no—
68#2690—21no—
69#2677—21no—
70#2638—21no—
71#2636—21no—
72#2625C2211yescharacteristic
73#2625C2211yescharacteristic
74#2621—21no—
75#2603—21no—
76#2551C2211yescharacteristic, complemented
77#2550C2211yescharacteristic, complemented
78#2536—21no—
79#2499C2211yescharacteristic
80#2492C2211yescharacteristic, complemented
81#2489C2211yescharacteristic, complemented
82#2485C2211yescharacteristic
83#2480—21no—
84#2480—21no—
85#2472—21no—
86#2472—21no—
87#2453C2211yescharacteristic, complemented
88#2452C2211yescharacteristic
89#2452C2211yescharacteristic
90#2451C2211yescharacteristic, complemented
91#2442C2211yescharacteristic, complemented
92#2440C2211yescharacteristic, complemented
93#2435C2211yescharacteristic
94#2427C2211yescharacteristic
95#2427C2211yescharacteristic
96#2415—21no—
97#2408C2211yescharacteristic
98#2398—21no—
99#2395C2211yescharacteristic
100#2367C2211yescharacteristic
101#2367C2211yescharacteristic
102#2363C2211yescharacteristic
103#2363C2211yescharacteristic
104#2346C2211yescharacteristic
105#2344C2211yescharacteristic
106#2094C2211yescharacteristic
107#2092C2211yescharacteristic
108#2088C2211yescharacteristic, complemented
109#2088C2211yescharacteristic, complemented
110#2085C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2068C2211yescharacteristic, complemented
114#2068C2211yescharacteristic, complemented
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic, complemented
117#2066C2211yescharacteristic, complemented
118#2066C2211yescharacteristic, complemented
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic, complemented
123#2059C2211yescharacteristic, complemented
124#2058C2211yescharacteristic, complemented
125#2058C2211yescharacteristic, complemented
126#2058C2211yescharacteristic, complemented
127#2057C2211yescharacteristic, complemented
128#2056C2211yescharacteristic, complemented
129#2056C2211yescharacteristic, complemented
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2036C2211yescharacteristic, complemented
133#2035C2211yescharacteristic, complemented
134#2034C2211yescharacteristic
135#2033C2211yescharacteristic
136#2026C2211yescharacteristic, complemented
137#2026C2211yescharacteristic, complemented
138#2024C2211yescharacteristic, complemented
139#2024C2211yescharacteristic, complemented
140#2023C2211yescharacteristic
141#2023C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1973C2211yescharacteristic
149#1968C2211yescharacteristic
150#1959C2211yescharacteristic
151#1958C2211yescharacteristic
152#1949C2211yescharacteristic, complemented
153#1947C2211yescharacteristic, complemented
154#1944C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1940C2211yescharacteristic, complemented
157#1939C2211yescharacteristic, complemented
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1928C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1895C2211yescharacteristic
173#1895C2211yescharacteristic
174#1892C2211yescharacteristic
175#1892C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1874C2211yescharacteristic
183#1874C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1854C2211yescharacteristic, complemented
192#1854C2211yescharacteristic, complemented
193#1851C2211yescharacteristic, complemented
194#1851C2211yescharacteristic, complemented
195#1850C2211yescharacteristic
196#1825C2211yescharacteristic
197#1825C2211yescharacteristic
198#1824C2211yescharacteristic
199#1818C2211yescharacteristic
200#1809C2211yescharacteristic
201#1786C2211yescharacteristic
202#1776C2211yescharacteristic, complemented
203C4×#107C2211yescharacteristic, complemented
204#1753C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—24no—
213#556—42no—
214#554—24no—
215#554—42no—
216#544—24no—
217#544—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247#518—24no—
248#518—42no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269#498—24no—
270#485—24no—
271#485—24no—
272#485—42no—
273#483—24no—
274#483—24no—
275#478—24no—
276#478—24no—
277#478—24no—
278#478—24no—
279#477—24no—
280#476—24no—
281#476—24no—
282#475—24no—
283#474—24no—
284#474—24no—
285#470—24no—
286#470—24no—
287#450—42no—
288C4×Q16—24no—
289#436—24no—
290#428—24no—
291#428D418yescomplemented
292#427—24no—
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310#424—24no—
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318#418—24no—
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#102—24no—
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#400—21no—
359#400—21no—
360#400D411yescharacteristic
361#399D411yescharacteristic
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398D411yescharacteristic
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397D411yescharacteristic
381#397D411yescharacteristic
382#397D411yescharacteristic
383#396—21no—
384#396—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394D411yescharacteristic
397#394D411yescharacteristic
398#393—21no—
399#393—21no—
400#393—21no—
401#392—21no—
402#391—21no—
403#391—21no—
404#391—21no—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#390—21no—
412#390—21no—
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
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#388—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#384C2311yescharacteristic
459#382—21no—
460#382—21no—
461#382C2311yescharacteristic
462#381—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#379—21no—
471#379—21no—
472#379—21no—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#376—21no—
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×Q16—22no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16C2×D414yes—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—44no—
577C4⋊Q8—82no—
578#126—44no—
579#126—44no—
580#125—22no—
581#125—22no—
582#125—41no—
583#125—41no—
584#125—44no—
585#125—44no—
586#124—22no—
587#124—22no—
588#124—41no—
589#124—41no—
590#124—44no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—44no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—82no—
604C22⋊Q8—82no—
605C22⋊Q8—82no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#120—82no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—44no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—44no—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—41no—
636#117—82no—
637#117C2×D414yes—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
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—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—41no—
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D414yes—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×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—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—44no—
719C2×C22⋊C4—44no—
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—22no—
747#107—41no—
748#107—41no—
749#107C2×D414yes—
750#107C2×D414yes—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—22no—
757#106—41no—
758#106—41no—
759#106C2×D414yes—
760#106C2×D414yes—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—22no—
765C4⋊C8—22no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799#97—41no—
800C4×C8—22no—
801C4×C8—41no—
802#95—21no—
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
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844C24—21no—
845C24—21no—
846C24—42no—
847C24—42no—
848C24—42no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C2×Q8—21no—
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—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×D4—28no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—41no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—44no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D42−1+412yes—
906C2×D42−1+412yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—24no—
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—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D412yes—
961C22×C4C22×D411yescharacteristic
962C22×C4H(5,𝔽2)12yes—
963C22×C4C2511yescharacteristic
964Q16—44no—
965SD16—82no—
966SD16—82no—
967M16—44no—
968M16—44no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—44no—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4C22×D412yes—
1050C4⋊C4C22×D412yes—
1051C4⋊C4C22×D412yes—
1052C4⋊C4C22×D412yes—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—24no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—22no—
1122C23—22no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—48no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23D4212yes—
1146C23C23×D411yescharacteristic
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—84no—
1156Q8—162no—
1157Q8—162no—
1158Q8—162no—
1159D4—22no—
1160D4—22no—
1161D4—22no—
1162D4—22no—
1163D4—44no—
1164D4—48no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—162no—
1170D4—162no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
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—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
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—84no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4D4212yes—
1262C2×C4#57712yes—
1263C2×C4C23×D411yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4C2×2−1+411yescharacteristic
1266C2×C4C2×2−1+411yescharacteristic
1267C2×C4#58511yescharacteristic
1268C2×C4#58511yescharacteristic
1269C8—22no—
1270C8—22no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—42no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22C2×D4211yescharacteristic
1307C22#348911yescharacteristic
1308C22#348911yescharacteristic
1309C22C2×#57711yescharacteristic
1310C22#358411yescharacteristic
1311C22#358511yescharacteristic
1312C22#358611yescharacteristic
1313C4—22no—
1314C4—22no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—41no—
1328C4—41no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4#344911yescharacteristic
1340C4#348611yescharacteristic
1341C4#353511yescharacteristic
1342C4#353511yescharacteristic
1343C2—42no—
1344C2—81no—
1345C2—82no—
1346C2—82no—
1347C2#3765311yescharacteristic
1348C2#6107511yescharacteristic
1349C2#6109211yescharacteristic
1350C2#6217911yescharacteristic
1351C2#6219611yescharacteristic
1352C2#6221611yescharacteristic
1353C2#6222711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
1. C2×#3356C2semidirect
2. C2×#3081C2semidirect
3. #42436C2semidirect
5. #33018C2semidirect
6. #31244C2semidirect
7. #31240C2semidirect
8. #31136C2semidirect
9. #31128C2semidirect
10. #30954C2semidirect
11. #30947C2semidirect
12. #30930C2semidirect
13. #30927C2semidirect
14. #29786C2semidirect
15. #29648C2semidirect
16. #28361C2semidirect
18. #26893C2semidirect
19. #26892C2semidirect
20. #26813C2semidirect
21. #26799C2semidirect
22. #26478C2semidirect
23. #26468C2semidirect
24. #26363C2semidirect
25. #26357C2semidirect
26. #24586C2semidirect
27. #24477C2semidirect
28. #24096C2semidirect
30. #22624C2semidirect
31. #22074C2semidirect
37. C2×#498C22semidirect
40. C2×#485C22semidirect
42. C2×#483C22semidirect
44. C2×#477C22semidirect
45. C2×#475C22semidirect
55. C2×#470C22semidirect
57. C2×C4×Q16C22semidirect
60. C2×#428C22semidirect
76. #2551C22semidirect
77. #2550C22semidirect
80. #2492C22semidirect
81. #2489C22semidirect
87. #2453C22semidirect
90. #2451C22semidirect
91. #2442C22semidirect
92. #2440C22semidirect
108. #2088C22semidirect
109. #2088C22semidirect
110. #2085C22semidirect
111. #2084C22semidirect
112. #2068C22semidirect
113. #2068C22semidirect
114. #2068C22semidirect
116. #2066C22semidirect
117. #2066C22semidirect
118. #2066C22semidirect
122. #2059C22semidirect
123. #2059C22semidirect
124. #2058C22semidirect
125. #2058C22semidirect
126. #2058C22semidirect
127. #2057C22semidirect
128. #2056C22semidirect
129. #2056C22semidirect
132. #2036C22semidirect
133. #2035C22semidirect
136. #2026C22semidirect
137. #2026C22semidirect
138. #2024C22semidirect
139. #2024C22semidirect
152. #1949C22semidirect
153. #1947C22semidirect
154. #1944C22semidirect
155. #1941C22semidirect
156. #1940C22semidirect
157. #1939C22semidirect
160. #1928C22semidirect
161. #1927C22semidirect
164. #1924C22semidirect
165. #1923C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1919C22semidirect
169. #1918C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
185. #1865C22semidirect
188. #1863C22semidirect
191. #1854C22semidirect
192. #1854C22semidirect
193. #1851C22semidirect
194. #1851C22semidirect
202. #1776C22semidirect
203. C4×#107C22semidirect
291. #428D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33562
C2×#30812
#424362
#360752
#330182
#312442
#312402
#311362
#311282
#309542
#309472
#309302
#309272
#297862
#296482
#283612
#281102
#268932
#268922
#268132
#267992
#264782
#264682
#263632
#263572
#245862
#244772
#240962
#239692
#226242
#220742