Finite Group Databasebeta

← #25097961

Subgroups — #25097961

Order 11008.

1802 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic
4C2×#14582906C211yesmaximal, characteristic, complemented
5#19137084C211yesmaximal, characteristic
6#19134951C211yesmaximal, characteristic, complemented
7#19134950C211yesmaximal, characteristic, complemented
8#19134949C211yesmaximal, characteristic, complemented
9#19134948C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134938C211yesmaximal, characteristic, complemented
12#19134933C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×#13063357—24no—
19C2×#13063357—24no—
20C2×#13063357C418yescomplemented
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×#10621872C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063290—21no—
30C2×#13063290C2211yescharacteristic
31C4×Q8×D43—24no—
32C4×Q8×D43—24no—
33C2×#13063283C2211yescharacteristic
34C2×C4⋊C4×D43—21no—
35C2×C4⋊C4×D43C2211yescharacteristic
36C2×C42×D43—21no—
37C2×C42×D43C2211yescharacteristic
38#14582906—24no—
39#14582899—24no—
40C2×#13063250C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582801C2211yescharacteristic
48#14582800C2211yescharacteristic
49#14582777—21no—
50#14582777—21no—
51#14582746—21no—
52#14582746—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57#14582653C2211yescharacteristic
58#14582653C2211yescharacteristic
59C22×Q16×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C43×#391C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902—22no—
70C2×#10621902—22no—
71C2×#10621902C2×C414yes—
72C22×Dic86—21no—
73C22×Dic86C2311yescharacteristic
74C2×Q8×D43—22no—
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43C2×C414yes—
78C2×Q8×D43D414yes—
79C2×Q8×D43D414yes—
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43D411yescharacteristic
86C22×C4×D43D411yescharacteristic
87C22×C4×D43C2311yescharacteristic
88#13063357—232no—
89C2×#10621885—22no—
90C2×#10621885—22no—
91C2×#10621885C2×C414yescomplemented
92C2×#10621873—22no—
93C2×#10621873—22no—
94C2×#10621873C2×C414yescomplemented
95C2×#10621884—22no—
96C2×#10621884—22no—
97C2×#10621884C2×C414yescomplemented
98C2×#10621872—22no—
99C2×#10621872—22no—
100C2×#10621872—22no—
101C2×#10621872—22no—
102C2×#10621872—22no—
103C2×#10621872C2×C414yes—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106Q8×Dic43—22no—
107Q8×Dic43—22no—
108C4×Dic86—28no—
109C4×Dic86—22no—
110C4×Dic86—22no—
111#13063290—28no—
112#13063290—22no—
113#13063290—22no—
114#13063283—22no—
115#13063283—22no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2311yescharacteristic
119C2×Dic43⋊C4—21no—
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C4⋊C4×D43—28no—
123C4⋊C4×D43—22no—
124C4⋊C4×D43D414yes—
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4—21no—
127C2×(C2×D43)⋊C4—21no—
128C2×(C2×D43)⋊C4—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×C4×Dic43—21no—
131C2×C4×Dic43—21no—
132C2×C4×Dic43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43D411yescharacteristic
135C2×C4×Dic43D411yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C42×D43—28no—
138C42×D43—22no—
139C42×D43—22no—
140#13063250—22no—
141#13063249—22no—
142#13063249—22no—
143#13063248—22no—
144#13063247—22no—
145#13063245—22no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×Q8×C43C2311yescharacteristic
149C22×Q8×C43C2311yescharacteristic
150C2×Q16×C43—22no—
151C2×Q16×C43—22no—
152C2×Q16×C43C2×C414yescomplemented
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C4×Q8×C43—22no—
156C4×Q8×C43—22no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C42×C43—21no—
161C2×C42×C43C2311yescharacteristic
162#103×C43—22no—
163#103×C43—22no—
164#95×C43—21no—
165#95×C43—21no—
166C23×D43—21no—
167C23×D43C2×D411yescharacteristic
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43C22×C412yes—
177C2×Q8×C43C22×C412yes—
178C2×Q8×C43C2×D412yes—
179C2×Q8×C43C2×D412yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193#10621902—28no—
194#10621902—28no—
195#10621902—44no—
196#10621902—44no—
197Q8×D43—28no—
198Q8×D43—28no—
199Q8×D43—28no—
200Q8×D43C22⋊C4116yescomplemented
201C2×D172—21no—
202C2×D172—24no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—42no—
208C2×D172—42no—
209C2×D172C22×C412yes—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—22no—
215C2×C4×D43—24no—
216C2×C4×D43—22no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—41no—
220C2×C4×D43—41no—
221C2×C4×D43—42no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43C22×C412yes—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2×D412yes—
228C2×C4×D43C2×D412yes—
229C2×C4×D43#4112yes—
230C2×C4×D43#4112yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—24no—
235C2×Dic86—24no—
236C2×Dic86—24no—
237C2×Dic86C22×C412yes—
238C2×Dic86C2×D412yes—
239C2×Dic86C2×D412yes—
240Q16×C43—28no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43C22×C412yes—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C2×D412yes—
252C42×C43—24no—
253C42×C43—21no—
254C42×C43—21no—
255#10621885—28no—
256#10621884—28no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43C2×D412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C4×Dic43—24no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—22no—
276C4×Dic43—22no—
277C4×Dic43—42no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8C22×C412yes—
284#10621873—28no—
285#10621872—28no—
286#10621872—44no—
287C23×C43C22×D411yescharacteristic
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—22no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43C4×D412yes—
300C22×D43#12012yes—
301C22×D43#12112yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—41no—
308Q8×C43—41no—
309Q8×C43C2×C22⋊C414yes—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43#13712yescomplemented
328C2×C4×C43C23×C411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×Dic43—22no—
335C2×Dic43—21no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43C4×D412yes—
349C2×Dic43#12012yes—
350C2×Dic43#12112yes—
351C2×Dic43#13712yescomplemented
352D172—22no—
353D172—22no—
354D172—48no—
355D172—41no—
356D172—41no—
357C4×D43—28no—
358C4×D43—216no—
359C4×D43—44no—
360C4×D43—48no—
361C4×D43—48no—
362C4×D43C2×C22⋊C414yes—
363C4×D43C4×D414yes—
364C4×D43#12114yes—
365C4×D43#12314yes—
366Dic86—22no—
367Dic86—22no—
368Dic86—22no—
369Dic86—216no—
370Dic86C2×C22⋊C414yes—
371C8×C43—22no—
372C8×C43—41no—
373C43⋊C8—22no—
374C43⋊C8—41no—
375#20926—431nomaximal, Sylow
376C22×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43C2×#12111yescharacteristic
379C22×C43C2×#13711yescharacteristic
380C22×C43C2×#13711yescharacteristic
381C22×C43#57511yescharacteristic
382C22×C43#57511yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C2×D43—81no—
396C2×D43#38614yes—
397C4×C43—22no—
398C4×C43—24no—
399C4×C43—41no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—81no—
403C4×C43C22×C22⋊C411yescharacteristic
404C4×C43C2×C4×D411yescharacteristic
405C4×C43C2×#12111yescharacteristic
406C4×C43C2×#12311yescharacteristic
407Dic43—22no—
408Dic43—24no—
409Dic43—41no—
410Dic43—42no—
411Dic43—81no—
412Dic43#38614yes—
413C22×#137—431no—
414C22×C4×Q8—431no—
415C2×#417—431no—
416C2×#419—431no—
417#2297—431no—
418#1880—431no—
419#1880—431no—
420#1880—431no—
421#1880—431no—
422#1878—431no—
423#1878—431no—
424#1878—431no—
425#1878D4311yescharacteristic, complemented
426#1736—431no—
427#1728—431no—
428C2×C43C2×#38611yescharacteristic
429C2×C43C4×#13711yescharacteristic
430C2×C43C4×#13711yescharacteristic
431C2×C43#300411yescharacteristic
432C2×C43#300511yescharacteristic
433C2×C43#303711yescharacteristic
434C2×C43#303711yescharacteristic
435D43—24no—
436D43—82no—
437C22×#41—431no—
438C23×Q8—431no—
439C2×#137—438no—
440C2×#137—864no—
441C2×#137—864no—
442C22×Q16—431no—
443C22×Q16C2×D4311yescharacteristic
444C22×SD16—431no—
445C22×SD16—431no—
446C22×M16—431no—
447C22×M16—431no—
448C2×C4×Q8—431no—
449C2×C4×Q8—431no—
450C2×C4×Q8—431no—
451C2×C4×Q8—861no—
452C2×C4×Q8—861no—
453C2×C4×Q8—864no—
454C2×C4×Q8—864no—
455C2×C4×Q8C2×D4311yescharacteristic
456C2×#117—431no—
457C22×C4⋊C4—431no—
458C22×C4⋊C4—861no—
459C22×C42—431no—
460C22×C42—861no—
461#419—864no—
462#417—864no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103C2×D4311yescharacteristic
468C2×#103C2×D4311yescharacteristic
469C2×#102—431no—
470C2×#102—431no—
471#391—431no—
472#391C2×D4311yescharacteristic
473#390—431no—
474#390—431no—
475#386—861no—
476#386—861no—
477C4×C22⋊C4—861no—
478C4×C22⋊C4—861no—
479#340—431no—
480#340—431no—
481#340—431no—
482#340C2×D4311yescharacteristic
483#336—431no—
484#336—431no—
485#336—431no—
486#336C2×D4311yescharacteristic
487C43#2092611yescharacteristic, complemented, Sylow
488C2×#41—434no—
489C2×#41—862no—
490C2×#41—862no—
491C2×#41—862no—
492C2×#41—862no—
493C2×#41—862no—
494C22×Q8—434no—
495C22×Q8—434no—
496C22×Q8—434no—
497C22×Q8—431no—
498C22×Q8—861no—
499C22×Q8—862no—
500C22×Q8—862no—
501C22×Q8—862no—
502C22×Q8C22×D4311yescharacteristic
503C22×Q8C22×D4311yescharacteristic
504C22×D4—431no—
505C22×D4—861no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512#137—8632no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—434no—
516C2×Q16—862no—
517C2×Q16—862no—
518C2×Q16C4×D4314yescomplemented
519C2×SD16—434no—
520C2×SD16—434no—
521C2×SD16—862no—
522C2×SD16—862no—
523C2×SD16—862no—
524C2×SD16—862no—
525C2×M16—434no—
526C2×M16—862no—
527C2×M16—862no—
528C2×M16—862no—
529C2×M16—862no—
530C2×M16—862no—
531C22×C8—431no—
532C22×C8—431no—
533C22×C8C22×D4311yescharacteristic
534C22×C8C22×D4311yescharacteristic
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—862no—
538C4×Q8—862no—
539C4×Q8—868no—
540C4×Q8—862no—
541C4×Q8—868no—
542C4×Q8—862no—
543C4×Q8—862no—
544C4×Q8—862no—
545#117—862no—
546#117—862no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—862no—
552C2×C4⋊C4—868no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C42—21no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—862no—
569C2×C42—862no—
570C2×C42—868no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42—861no—
574C2×C42—861no—
575C2×C42C22×D4311yescharacteristic
576#103—22no—
577#103—22no—
578#103—862no—
579#103—862no—
580#103—862no—
581#103—862no—
582#102—862no—
583#102—862no—
584#95—21no—
585#95—21no—
586#95—861no—
587#95—861no—
588C24—431no—
589C24—861no—
590#41—868no—
591#41—868no—
592#41—1724no—
593#41—1724no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—4316no—
603C2×Q8—432no—
604C2×Q8—432no—
605C2×Q8—432no—
606C2×Q8—864no—
607C2×Q8—864no—
608C2×Q8—864no—
609C2×Q8—868no—
610C2×Q8—868no—
611C2×Q8—868no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8C2×C4×D4312yes—
616C2×Q8C2×C4×D4312yes—
617C2×Q8D4×D4312yes—
618C2×Q8D4×D4312yes—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—1722no—
627C2×D4—1722no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—431no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—862no—
642C22×C4—864no—
643C22×C4—862no—
644C22×C4—864no—
645C22×C4—864no—
646C22×C4—864no—
647C22×C4—864no—
648C22×C4—862no—
649C22×C4—861no—
650C22×C4—862no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—1721no—
654C22×C4—1721no—
655C22×C4—1722no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4D4×D4311yescharacteristic
660C22×C4D4×D4311yescharacteristic
661C22×C4C23×D4311yescharacteristic
662Q16—28no—
663Q16—868no—
664SD16—868no—
665SD16—868no—
666M16—868no—
667M16—1724no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—432no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8C2×C4×D4312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—432no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4D4×D4312yes—
693C22⋊C4—1722no—
694C22⋊C4—1722no—
695C22⋊C4—1722no—
696C22⋊C4—1722no—
697C22⋊C4—1722no—
698C42—24no—
699C42—21no—
700C42—21no—
701C42—862no—
702C42—862no—
703C42—864no—
704C42—864no—
705C42—864no—
706C42—861no—
707C42—861no—
708C42—1722no—
709C23—432no—
710C23—432no—
711C23—432no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—862no—
717C23—1721no—
718C23—1721no—
719C23—1721no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—41no—
730Q8—41no—
731Q8—434no—
732Q8—8616no—
733Q8—862no—
734Q8—862no—
735Q8—862no—
736Q8C22⋊C4×D4314yes—
737D4—862no—
738D4—862no—
739D4—1728no—
740D4—1721no—
741D4—1721no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—432no—
760C2×C4—432no—
761C2×C4—432no—
762C2×C4—434no—
763C2×C4—434no—
764C2×C4—434no—
765C2×C4—434no—
766C2×C4—432no—
767C2×C4—8616no—
768C2×C4—868no—
769C2×C4—862no—
770C2×C4—861no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—862no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—1728no—
779C2×C4—1724no—
780C2×C4—1728no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306335712yescomplemented
787C2×C4C22×C4×D4311yescharacteristic
788C2×C4C2×D4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C8—22no—
794C8—41no—
795C8—862no—
796C8—1721no—
797C22—434no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—3441no—
805C22—3441no—
806C22—3441no—
807C22—3441no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22C4×D4×D4311yescharacteristic
812C22#120×D4311yescharacteristic
813C22#121×D4311yescharacteristic
814C22#137×D4311yescharacteristic
815C22C2×#1306335711yescharacteristic
816C22#1458369611yescharacteristic
817C22#1458369811yescharacteristic
818C4—22no—
819C4—24no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—81no—
824C4—434no—
825C4—862no—
826C4—864no—
827C4—3441no—
828C4—1721no—
829C4—1722no—
830C4C2×C22⋊C4×D4311yescharacteristic
831C4C4×D4×D4311yescharacteristic
832C4#121×D4311yescharacteristic
833C4#123×D4311yescharacteristic
834C2—864no—
835C2—3442no—
836C2#386×D4311yescharacteristic
837C2#1914341111yescharacteristic
838C2C4×#1306335711yescharacteristic
839C2#1914383011yescharacteristic
840C2#1914383811yescharacteristic
841C2#1914406511yescharacteristic
842C2#1914406811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1878D43
hypocenterC43#20926
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D43C2semidirect
4. C2×#14582906C2semidirect
6. #19134951C2semidirect
7. #19134950C2semidirect
8. #19134949C2semidirect
9. #19134948C2semidirect
10. #19134939C2semidirect
11. #19134938C2semidirect
12. #19134933C2semidirect
13. #19134313C2semidirect
14. #19134287C2semidirect
15. C43×#1878C2semidirect
20. C2×#13063357C4semidirect
91. C2×#10621885C2×C4semidirect
94. C2×#10621873C2×C4semidirect
97. C2×#10621884C2×C4semidirect
152. C2×Q16×C43C2×C4semidirect
200. Q8×D43C22⋊C4semidirect
327. C2×C4×C43#137semidirect
351. C2×Dic43#137semidirect
425. #1878D43semidirect
487. C43#20926semidirect
518. C2×Q16C4×D43semidirect
786. C2×C4#13063357semidirect

Maximal subgroups

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

subgroupindex
C22×#130633572
C2×C4×Q8×D432
C2×#145828992
C2×#145829062
#191370842
#191349512
#191349502
#191349492
#191349482
#191349392
#191349382
#191349332
#191343132
#191342872
C43×#18782
#2092643