Finite Group Databasebeta

← #6994537

Subgroups — #6994537

Order 512.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45325C211yesmaximal, characteristic, complemented
2#42916C211yesmaximal, characteristic
3#31950C211yesmaximal, characteristic, complemented
4#31841C211yesmaximal, characteristic, complemented
5#31566C211yesmaximal, characteristic, complemented
6#31397C211yesmaximal, characteristic, complemented
7#31388C211yesmaximal, characteristic, complemented
8#31025C211yesmaximal, characteristic, complemented
9#30929C211yesmaximal, characteristic, complemented
10#30405C211yesmaximal, characteristic, complemented
11#28979C211yesmaximal, characteristic, complemented
12#28153C211yesmaximal, characteristic, complemented
13#28098C211yesmaximal, characteristic, complemented
14#27721C211yesmaximal, characteristic, complemented
15#26965C211yesmaximal, characteristic, complemented
16#26660C211yesmaximal, characteristic, complemented
17#26636C211yesmaximal, characteristic, complemented
18#25951C211yesmaximal, characteristic, complemented
19#25127C211yesmaximal, characteristic, complemented
20#24962C211yesmaximal, characteristic, complemented
21#24566C211yesmaximal, characteristic, complemented
22#24532C211yesmaximal, characteristic, complemented
23#24392C211yesmaximal, characteristic, complemented
24#24123C211yesmaximal, characteristic, complemented
25#23968C211yesmaximal, characteristic, complemented
26#23865C211yesmaximal, characteristic, complemented
27#23394C211yesmaximal, characteristic, complemented
28#22847C211yesmaximal, characteristic, complemented
29#22445C211yesmaximal, characteristic, complemented
30#22417C211yesmaximal, characteristic, complemented
31#21772C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#537C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#441C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C2×#416C2211yescharacteristic
50C22×#103C2211yescharacteristic
51C2×#408C2211yescharacteristic
52C2×#408C2211yescharacteristic
53#2814—21no—
54#2716—21no—
55#2712—21no—
56#2705—21no—
57#2701—21no—
58#2701—21no—
59#2695—21no—
60#2682—21no—
61#2682—21no—
62#2661—21no—
63#2618—21no—
64#2616C2211yescharacteristic
65#2583—21no—
66#2557—21no—
67#2538C2211yescharacteristic
68#2538C2211yescharacteristic
69#2536C2211yescharacteristic
70#2521—21no—
71#2502C2211yescharacteristic
72#2499C2211yescharacteristic
73#2492C2211yescharacteristic
74#2486C2211yescharacteristic
75#2458—21no—
76#2451—21no—
77#2439C2211yescharacteristic
78#2429C2211yescharacteristic
79#2429C2211yescharacteristic
80#2423C2211yescharacteristic
81#2422C2211yescharacteristic
82#2422C2211yescharacteristic
83#2417C2211yescharacteristic
84#2415C2211yescharacteristic
85#2409C2211yescharacteristic
86#2407C2211yescharacteristic
87#2407C2211yescharacteristic
88#2388C2211yescharacteristic
89#2360C2211yescharacteristic
90#2354C2211yescharacteristic
91#2341C2211yescharacteristic
92Q8×C22⋊C4C2211yescharacteristic
93#2311C2211yescharacteristic
94#2100C2211yescharacteristic
95#2099C2211yescharacteristic
96#2099C2211yescharacteristic
97#2092C2211yescharacteristic
98#2083C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2074C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2024C2211yescharacteristic
119#2023C2211yescharacteristic
120#2016C2211yescharacteristic
121#2016C2211yescharacteristic
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1990C2211yescharacteristic
135#1981C2211yescharacteristic
136#1973C2211yescharacteristic
137#1968C2211yescharacteristic
138#1956C2211yescharacteristic
139#1954C2211yescharacteristic
140#1935C2211yescharacteristic
141#1933C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1919C2211yescharacteristic
147#1919C2211yescharacteristic
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic
152#1893C2211yescharacteristic
153#1892C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1874C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1872C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic
178#1863C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1851C2211yescharacteristic
183#1850C2211yescharacteristic
184#1836C2211yescharacteristic
185#1825C2211yescharacteristic
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1823C2211yescharacteristic
189#1809C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1802C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1787C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C2×#137—24no—
208C2×#137—42no—
209C2×#137—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221#556—42no—
222#556—42no—
223#547—24no—
224#547—42no—
225#537—24no—
226#537—42no—
227#536—42no—
228#536—42no—
229C2×C4⋊Q8—21no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×#126—21no—
233C2×#126—21no—
234C2×#124—21no—
235C2×#124—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×#121—21no—
257C2×#121—21no—
258C2×#121—21no—
259C2×#121—21no—
260C2×#121C2311yescharacteristic
261C2×#121C2311yescharacteristic
262C2×C4×Q8—21no—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C22×C4⋊C4—21no—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277#483—42no—
278#475—42no—
279#470—42no—
280#467—42no—
281#452—42no—
282#452—42no—
283#451—42no—
284#441—42no—
285C4×Q16—42no—
286#435—42no—
287C8×D4—42no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297#416—42no—
298#416—42no—
299C2×#103—42no—
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328#408—42no—
329#408—42no—
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344#400—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#395—21no—
369#395—21no—
370#395D411yescharacteristic
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394D411yescharacteristic
381#394D411yescharacteristic
382#394D411yescharacteristic
383#393—21no—
384#393—21no—
385#393—21no—
386#393D411yescharacteristic
387#392—21no—
388#392—21no—
389#392D411yescharacteristic
390#392D411yescharacteristic
391#392D411yescharacteristic
392#391—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#390—21no—
404#390—21no—
405#390—21no—
406#390—21no—
407#390—21no—
408#390—21no—
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#382C2311yescharacteristic
453#381—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467C4×C4⋊C4—21no—
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41#4114yes—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8—22no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8C2×D411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4C2×D411yescharacteristic
541C22×D4C2×D411yescharacteristic
542C22×D4C2×D411yescharacteristic
543C22×D4C2×D411yescharacteristic
544C22×D4C2×D411yescharacteristic
545C22×D4C2×D411yescharacteristic
546C22×D4C2411yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557#137—416no—
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×Q16—41no—
569C2×Q16—41no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×M16—22no—
577C2×M16—22no—
578C2×M16—41no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16—41no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8—41no—
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C4⋊Q8—22no—
600C4⋊Q8—22no—
601C4⋊Q8—41no—
602C4⋊Q8—41no—
603C4⋊Q8—44no—
604#126—44no—
605#126—44no—
606#124—44no—
607#124—44no—
608#123—44no—
609#123—44no—
610#123—44no—
611#123—44no—
612#123—82no—
613#123—82no—
614#123—82no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—44no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—41no—
644#121—44no—
645#121—44no—
646#121—44no—
647#121—44no—
648C4×Q8—22no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8—41no—
656C4×Q8—44no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665#117—22no—
666#117—22no—
667#117—41no—
668#117—41no—
669#117—41no—
670#117—41no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
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—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—44no—
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
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—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C42—21no—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776#107—41no—
777#107—41no—
778#106—22no—
779#106—22no—
780#106—41no—
781#106—41no—
782C4⋊C8—41no—
783C4⋊C8—41no—
784C4⋊C8—41no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
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#103—41no—
805#103—41no—
806#103—41no—
807#102—22no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102—41no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—41no—
819C22⋊C8—41no—
820C22⋊C8—41no—
821C22⋊C8—41no—
822C22⋊C8—41no—
823C22⋊C8—41no—
824#97—22no—
825C4×C8—41no—
826C4×C8—41no—
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#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862C24—21no—
863C24C22×D411yescharacteristic
864C24C22×D411yescharacteristic
865C24C22×D411yescharacteristic
866C24C22×D411yescharacteristic
867#41—44no—
868#41—44no—
869#41—44no—
870#41—82no—
871#41—82no—
872#41—82no—
873#41—82no—
874#41—82no—
875#41—82no—
876#41—82no—
877#41—82no—
878#41—82no—
879C2×Q8—22no—
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—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—41no—
903C2×Q8—41no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—81no—
911C2×Q8—81no—
912C2×Q8—82no—
913C2×Q8—82no—
914C2×Q8C2×#4112yes—
915C2×Q8H(5,𝔽2)12yes—
916C2×D4—22no—
917C2×D4—24no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—41no—
929C2×D4—41no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—41no—
933C2×D4—41no—
934C2×D4—41no—
935C2×D4—41no—
936C2×D4—41no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—41no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4C2×#4112yes—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—24no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4—81no—
1006C22×C4—81no—
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C2×#4112yes—
1018C22×C4H(5,𝔽2)12yes—
1019C22×C4C2511yescharacteristic
1020Q16—28no—
1021Q16—44no—
1022Q16—82no—
1023Q16—82no—
1024SD16—44no—
1025SD16—44no—
1026M16—44no—
1027M16—82no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—82no—
1052C2×C8—82no—
1053C2×C8—82no—
1054C2×C8H(5,𝔽2)12yes—
1055C4⋊C4—24no—
1056C4⋊C4—22no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C4⋊C4—81no—
1099C4⋊C4—81no—
1100C4⋊C4—81no—
1101C4⋊C4—81no—
1102C4⋊C4—81no—
1103C4⋊C4—81no—
1104C4⋊C4—81no—
1105C4⋊C4—81no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4H(5,𝔽2)12yes—
1111C22⋊C4—24no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C22⋊C4—81no—
1151C22⋊C4—81no—
1152C22⋊C4—81no—
1153C22⋊C4—81no—
1154C22⋊C4—81no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—21no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—81no—
1166C42—81no—
1167C42—81no—
1168C42—81no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—22no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23#54612yes—
1204C23C23×D411yescharacteristic
1205Q8—22no—
1206Q8—22no—
1207Q8—22no—
1208Q8—22no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—82no—
1222Q8—84no—
1223Q8—84no—
1224D4—22no—
1225D4—22no—
1226D4—44no—
1227D4—41no—
1228D4—41no—
1229D4—82no—
1230D4—82no—
1231D4—82no—
1232D4—82no—
1233D4—84no—
1234D4—82no—
1235D4—84no—
1236D4—162no—
1237D4—162no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—84no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—84no—
1330C2×C4—162no—
1331C2×C4—162no—
1332C2×C4#54612yes—
1333C2×C4#57712yes—
1334C2×C4#57812yes—
1335C2×C4C22×#4111yescharacteristic
1336C2×C4C2×H(5,𝔽2)11yescharacteristic
1337C2×C4C2×H(5,𝔽2)11yescharacteristic
1338C2×C4C2×H(5,𝔽2)11yescharacteristic
1339C2×C4C2×H(5,𝔽2)11yescharacteristic
1340C2×C4#58511yescharacteristic
1341C8—22no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C8—41no—
1347C8—41no—
1348C8—41no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—42no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—42no—
1377C22—41no—
1378C22—41no—
1379C22—41no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22C2×#54611yescharacteristic
1385C22#348411yescharacteristic
1386C22#349611yescharacteristic
1387C22C2×#57711yescharacteristic
1388C22C2×#57811yescharacteristic
1389C22#358411yescharacteristic
1390C22#358611yescharacteristic
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—42no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—42no—
1402C4—42no—
1403C4—41no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4#349011yescharacteristic
1417C4#350511yescharacteristic
1418C4#353411yescharacteristic
1419C4#354311yescharacteristic
1420C2—42no—
1421C2—81no—
1422C2—81no—
1423C2—81no—
1424C2—82no—
1425C2#4299711yescharacteristic
1426C2#6117211yescharacteristic
1427C2#6121011yescharacteristic
1428C2#6164211yescharacteristic
1429C2#6168611yescharacteristic
1430C2#6230911yescharacteristic
1431C2#6234311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42916C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45325C2semidirect
3. #31950C2semidirect
4. #31841C2semidirect
5. #31566C2semidirect
6. #31397C2semidirect
7. #31388C2semidirect
8. #31025C2semidirect
9. #30929C2semidirect
10. #30405C2semidirect
11. #28979C2semidirect
12. #28153C2semidirect
13. #28098C2semidirect
14. #27721C2semidirect
15. #26965C2semidirect
16. #26660C2semidirect
17. #26636C2semidirect
18. #25951C2semidirect
19. #25127C2semidirect
20. #24962C2semidirect
21. #24566C2semidirect
22. #24532C2semidirect
23. #24392C2semidirect
24. #24123C2semidirect
25. #23968C2semidirect
26. #23865C2semidirect
27. #23394C2semidirect
28. #22847C2semidirect
29. #22445C2semidirect
30. #22417C2semidirect
31. #21772C2semidirect

Maximal subgroups

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

subgroupindex
#453252
#429162
#319502
#318412
#315662
#313972
#313882
#310252
#309292
#304052
#289792
#281532
#280982
#277212
#269652
#266602
#266362
#259512
#251272
#249622
#245662
#245322
#243922
#241232
#239682
#238652
#233942
#228472
#224452
#224172
#217722