Finite Group Databasebeta

← #6830700

Subgroups — #6830700

Order 512.

1599 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42975C211yesmaximal, characteristic, complemented
2#42928C211yesmaximal, characteristic, complemented
3#33054C211yesmaximal, characteristic, complemented
4#31848C211yesmaximal, characteristic, complemented
5#31846C211yesmaximal, characteristic, complemented
6#31816C211yesmaximal, characteristic, complemented
7#31802C211yesmaximal, characteristic, complemented
8#31739C211yesmaximal, characteristic, complemented
9#31738C211yesmaximal, characteristic, complemented
10#31725C211yesmaximal, characteristic, complemented
11#31719C211yesmaximal, characteristic, complemented
12#29976C211yesmaximal, characteristic, complemented
13#29727C211yesmaximal, characteristic, complemented
14#29095C211yesmaximal, characteristic, complemented
15#29094C211yesmaximal, characteristic, complemented
16#28931C211yesmaximal, characteristic, complemented
17#28919C211yesmaximal, characteristic, complemented
18#28562C211yesmaximal, characteristic, complemented
19#28560C211yesmaximal, characteristic, complemented
20#27720C211yesmaximal, characteristic, complemented
21#27718C211yesmaximal, characteristic, complemented
22#26227C211yesmaximal, characteristic, complemented
23#26225C211yesmaximal, characteristic, complemented
24#25128C211yesmaximal, characteristic, complemented
25#25108C211yesmaximal, characteristic, complemented
26#23979C211yesmaximal, characteristic, complemented
27#23973C211yesmaximal, characteristic, complemented
28#22498C211yesmaximal, characteristic, complemented
29#22490C211yesmaximal, characteristic, complemented
30#21495C211yesmaximal, characteristic, complemented
31#21091C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#489C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#435C2211yescharacteristic, complemented
41C2×C8×D4C2211yescharacteristic
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C2×#405C2211yescharacteristic
45#2828—21no—
46#2823—21no—
47#2736—21no—
48#2695—21no—
49#2691—21no—
50#2685—21no—
51#2685—21no—
52#2676—21no—
53#2672—21no—
54#2670—21no—
55#2662—21no—
56#2662—21no—
57#2637—21no—
58#2636—21no—
59#2628C2211yescharacteristic
60#2620C2211yescharacteristic
61#2593—21no—
62#2538—21no—
63#2512C2211yescharacteristic
64#2512C2211yescharacteristic
65#2500C2211yescharacteristic
66#2500C2211yescharacteristic
67#2491C2211yescharacteristic
68#2491C2211yescharacteristic
69#2453C2211yescharacteristic, complemented
70#2452C2211yescharacteristic, complemented
71#2441C2211yescharacteristic, complemented
72#2440C2211yescharacteristic, complemented
73#2427C2211yescharacteristic, complemented
74#2426C2211yescharacteristic, complemented
75#2417C2211yescharacteristic
76#2417C2211yescharacteristic, complemented
77#2416C2211yescharacteristic
78#2414C2211yescharacteristic
79#2414C2211yescharacteristic
80#2414C2211yescharacteristic, complemented
81#2408C2211yescharacteristic
82#2408C2211yescharacteristic
83#2392C2211yescharacteristic
84#2354C2211yescharacteristic
85#2354C2211yescharacteristic
86#2317C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2057C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1990C2211yescharacteristic, complemented
131#1989C2211yescharacteristic, complemented
132#1988C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1970C2211yescharacteristic
135#1958C2211yescharacteristic, complemented
136#1954C2211yescharacteristic, complemented
137#1939C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1925C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic, complemented
174#1875C2211yescharacteristic, complemented
175#1874C2211yescharacteristic
176#1874C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1873C2211yescharacteristic, complemented
180#1870C2211yescharacteristic
181#1870C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic, complemented
188#1825C2211yescharacteristic, complemented
189#1825C2211yescharacteristic, complemented
190#1823C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—24no—
213#556—42no—
214#553—24no—
215#553—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260#489—42no—
261#468—42no—
262#466—42no—
263#450—42no—
264#447—42no—
265#435—42no—
266#435—42no—
267C8×D4—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—24no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102—42no—
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310#405—42no—
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397D411yescharacteristic
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396D411yescharacteristic
341#396D411yescharacteristic
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394D411yescharacteristic
361#394D411yescharacteristic
362#394D411yescharacteristic
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392D411yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382C2311yescharacteristic
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#126—44no—
560#126—44no—
561#126—44no—
562#126—82no—
563#126—82no—
564#125—22no—
565#125—41no—
566#124—41no—
567#124—41no—
568#124—44no—
569#124—82no—
570#124—82no—
571#123—44no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—82no—
579C22⋊Q8—82no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—44no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—82no—
596#120—82no—
597#120—82no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—44no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—44no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610#117—22no—
611#117—22no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117#4114yes—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—22no—
778#97—22no—
779#97—41no—
780C4×C8—41no—
781C4×C8—41no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—41no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
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—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2×#4112yes—
941C22×C4H(5,𝔽2)12yes—
942C22×C4C2511yescharacteristic
943SD16—82no—
944SD16—82no—
945D8—82no—
946D8—82no—
947M16—44no—
948M16—82no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—44no—
973C2×C8—82no—
974C2×C8H(5,𝔽2)12yes—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4C2×#4112yes—
1029C4⋊C4C2×#4112yes—
1030C22⋊C4—24no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C42—24no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
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—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—84no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23#54612yes—
1151C23C23×D411yescharacteristic
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—84no—
1157Q8—162no—
1158D4—44no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—84no—
1172D4—82no—
1173D4—82no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
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—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
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—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4#54612yes—
1267C2×C4#57612yes—
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4#58511yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—22no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—168no—
1325C22C2×#54611yescharacteristic
1326C22#349611yescharacteristic
1327C22#350011yescharacteristic
1328C22C2×#57611yescharacteristic
1329C22#358411yescharacteristic
1330C22#358511yescharacteristic
1331C22#358611yescharacteristic
1332C4—22no—
1333C4—22no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—42no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4#346011yescharacteristic
1357C4#349311yescharacteristic
1358C4#353411yescharacteristic
1359C4#356011yescharacteristic
1360C2—42no—
1361C2—81no—
1362C2—81no—
1363C2—161no—
1364C2—161no—
1365C2—161no—
1366C2#3941511yescharacteristic
1367C2#6117111yescharacteristic
1368C2#6118211yescharacteristic
1369C2#6230911yescharacteristic
1370C2#6234911yescharacteristic
1371C2#6260711yescharacteristic
1372C2#6261811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42975C2semidirect
2. #42928C2semidirect
3. #33054C2semidirect
4. #31848C2semidirect
5. #31846C2semidirect
6. #31816C2semidirect
7. #31802C2semidirect
8. #31739C2semidirect
9. #31738C2semidirect
10. #31725C2semidirect
11. #31719C2semidirect
12. #29976C2semidirect
13. #29727C2semidirect
14. #29095C2semidirect
15. #29094C2semidirect
16. #28931C2semidirect
17. #28919C2semidirect
18. #28562C2semidirect
19. #28560C2semidirect
20. #27720C2semidirect
21. #27718C2semidirect
22. #26227C2semidirect
23. #26225C2semidirect
24. #25128C2semidirect
25. #25108C2semidirect
26. #23979C2semidirect
27. #23973C2semidirect
28. #22498C2semidirect
29. #22490C2semidirect
30. #21495C2semidirect
31. #21091C2semidirect
34. C2×#489C22semidirect
40. C2×#435C22semidirect
69. #2453C22semidirect
70. #2452C22semidirect
71. #2441C22semidirect
72. #2440C22semidirect
73. #2427C22semidirect
74. #2426C22semidirect
76. #2417C22semidirect
80. #2414C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2100C22semidirect
91. #2099C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2086C22semidirect
96. #2076C22semidirect
97. #2075C22semidirect
98. #2072C22semidirect
101. #2071C22semidirect
104. #2057C22semidirect
105. #2057C22semidirect
112. #2036C22semidirect
115. #2033C22semidirect
128. #1992C22semidirect
129. #1990C22semidirect
130. #1990C22semidirect
131. #1989C22semidirect
132. #1988C22semidirect
135. #1958C22semidirect
136. #1954C22semidirect
137. #1939C22semidirect
143. #1936C22semidirect
144. #1935C22semidirect
150. #1934C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1925C22semidirect
154. #1923C22semidirect
155. #1923C22semidirect
156. #1921C22semidirect
157. #1918C22semidirect
160. #1895C22semidirect
165. #1892C22semidirect
173. #1875C22semidirect
174. #1875C22semidirect
178. #1873C22semidirect
179. #1873C22semidirect
184. #1836C22semidirect
187. #1825C22semidirect
188. #1825C22semidirect
189. #1825C22semidirect
190. #1823C22semidirect
191. #1803C22semidirect
192. #1802C22semidirect
194. #1771C22semidirect
195. #1762C22semidirect
196. C4×#103C22semidirect
197. #1753C22semidirect
198. #1752C22semidirect
200. #1736C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#429752
#429282
#330542
#318482
#318462
#318162
#318022
#317392
#317382
#317252
#317192
#299762
#297272
#290952
#290942
#289312
#289192
#285622
#285602
#277202
#277182
#262272
#262252
#251282
#251082
#239792
#239732
#224982
#224902
#214952
#210912