Finite Group Databasebeta

← #25134338

Subgroups — #25134338

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583126C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4C2×#14582895C211yesmaximal, characteristic, complemented
5#19138024C211yesmaximal, characteristic, complemented
6#19135831C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135689C211yesmaximal, characteristic, complemented
9#19135603C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134918C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic, complemented
22C2×#13063284C2211yescharacteristic, complemented
23#14583126—24no—
24#14583061—24no—
25#14583050—24no—
26C2×#13063256C2211yescharacteristic, complemented
27#14582895—24no—
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063249C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582827—21no—
42#14582813—21no—
43#14582805C2211yescharacteristic, complemented
44#14582797C2211yescharacteristic, complemented
45#14582794—21no—
46#14582793—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#546—24no—
55C43×#546—24no—
56C2×#124×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C22⋊C4×C43—21no—
65C22×Dic86C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—41no—
68C2×#10621885—41no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—41no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—41no—
86#13063284—22no—
87#13063284—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99#13063256—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063248—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—41no—
109#13063246D414yescomplemented
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C2×#41×C43D414yes—
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43—22no—
128C22×D4×C43—22no—
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—21no—
132C22×D4×C43—41no—
133C22×D4×C43—41no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141#124×C43—22no—
142#124×C43—22no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146#121×C43—28no—
147#121×C43—22no—
148#121×C43D414yes—
149#120×C43—28no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43D411yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—28no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43—24no—
168C24×C43—21no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177#41×C43—28no—
178#41×C43—44no—
179#41×C43—44no—
180#41×C43—44no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D412yes—
187C2×D4×C43—24no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—22no—
193C2×D4×C43—24no—
194C2×D4×C43—24no—
195C2×D4×C43—22no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—41no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—44no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—81no—
210C2×D4×C43—81no—
211C2×D4×C43C2×D412yes—
212C2×D4×C43C2×D412yes—
213C2×D4×C43C2×D412yes—
214C2×D4×C43#4112yes—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—24no—
220C22×C4×C43—24no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43—81no—
232C22×C4×C43—81no—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2×D412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—22no—
261C42×C43—21no—
262C42×C43—21no—
263C22⋊Dic43—42no—
264C22⋊Dic43—42no—
265C22⋊Dic43—42no—
266C22⋊Dic43—42no—
267#10621885—44no—
268#10621883—44no—
269#10621883—44no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43C2×D412yes—
276Dic43⋊C4—42no—
277Dic43⋊C4—42no—
278Dic43⋊C4—42no—
279C4×Dic43—42no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—44no—
292C2×C43⋊C8C2×D412yes—
293C23×C43—21no—
294C23×C43—22no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—22no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—22no—
309C23×C43—48no—
310C23×C43—48no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—84no—
322C23×C43—84no—
323C23×C43—84no—
324C23×C43—84no—
325C23×C43—84no—
326C23×C43#12012yes—
327C23×C43#13512yes—
328C23×C43C22×D411yescharacteristic
329Q8×C43—22no—
330Q8×C43—22no—
331Q8×C43—41no—
332Q8×C43—41no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—44no—
339D4×C43—48no—
340D4×C43—48no—
341D4×C43—41no—
342D4×C43—41no—
343D4×C43—84no—
344D4×C43#12114yes—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—48no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—84no—
372C2×C4×C43#12012yes—
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C2×#4111yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C2×C4×C43H(5,𝔽2)11yescharacteristic
379C2×Dic43—22no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391Dic86—41no—
392Dic86—41no—
393Dic86—41no—
394Dic86—41no—
395C43⋊C8—22no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398C43⋊C8—41no—
399#24436—431nomaximal, Sylow
400C22×C43—24no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—42no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—42no—
414C22×C43—41no—
415C22×C43—42no—
416C22×C43—41no—
417C22×C43—42no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—816no—
425C22×C43—81no—
426C22×C43—81no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43C2×#12011yescharacteristic
430C22×C43D4211yescharacteristic
431C22×C43#54611yescharacteristic
432C22×C43C2×#13511yescharacteristic
433C22×C43#57511yescharacteristic
434C22×C43#57711yescharacteristic
435C22×C43#57711yescharacteristic
436C4×C43—22no—
437C4×C43—41no—
438C4×C43—42no—
439C4×C43—41no—
440C4×C43—41no—
441C4×C43—42no—
442C4×C43C2×#12111yescharacteristic
443C4×C43#53411yescharacteristic
444C4×C43D4211yescharacteristic
445C4×C43#54611yescharacteristic
446Dic43—42no—
447Dic43—81no—
448Dic43—81no—
449Dic43—81no—
450C2×#546D4311yescharacteristic
451C2×#465—431no—
452C2×#452—431no—
453C2×#450—431no—
454C2×#416—431no—
455#2415—431no—
456#2042—431no—
457#2035—431no—
458#2015—431no—
459#2001—431no—
460#1877—431no—
461#1875—431no—
462#1869—431no—
463#1864—431no—
464#1786—431no—
465C2×C43—42no—
466C2×C43—42no—
467C2×C43—44no—
468C2×C43—82no—
469C2×C43#241011yescharacteristic
470C2×C43#300211yescharacteristic
471C2×C43#300911yescharacteristic
472C2×C43#326711yescharacteristic
473C2×C43#328211yescharacteristic
474C2×C43#329611yescharacteristic
475C2×C43#331111yescharacteristic
476C22×#41C2×D4311yescharacteristic
477C23×D4C2×D4311yescharacteristic
478C22×Q16—431no—
479C22×SD16—431no—
480C22×SD16—431no—
481C23×C8—431no—
482#546—24no—
483#546—24no—
484C2×#124C2×D4311yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8—431no—
487C2×C22⋊Q8—431no—
488C2×C22⋊Q8C2×D4311yescharacteristic
489C2×#121—21no—
490C2×#121C2×D4311yescharacteristic
491C2×#120—21no—
492C2×C4×D4C2×D4311yescharacteristic
493C2×C4×D4C2×D4311yescharacteristic
494C2×#117—431no—
495C22×C22⋊C4—21no—
496#465—864no—
497#452—864no—
498#450—864no—
499C2×#106—431no—
500#416—864no—
501C2×#103—431no—
502C2×#103—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8—431no—
513C2×C22⋊C8—431no—
514#397—861no—
515#394—861no—
516#391—431no—
517#389—431no—
518#389—861no—
519#388—861no—
520#380—431no—
521#340—431no—
522#340—431no—
523#336—431no—
524#336—431no—
525C43#2443611yescharacteristic, complemented, Sylow
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41C22⋊D4314yes—
533C22×Q8—431no—
534C22×Q8C22×D4311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4C22⋊D4311yescharacteristic
545C22×D4C22×D4311yescharacteristic
546C22×D4C22×D4311yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C22×D4311yescharacteristic
550C23×C4C22×D4311yescharacteristic
551C2×Q16—862no—
552C2×Q16—1721no—
553C2×Q16—1721no—
554C2×SD16—862no—
555C2×SD16—862no—
556C2×SD16—862no—
557C2×SD16—862no—
558C2×SD16—862no—
559C2×SD16—1721no—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8—431no—
563C22×C8—431no—
564C22×C8—862no—
565C22×C8—862no—
566C22×C8—1721no—
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—862no—
573C22⋊Q8—862no—
574C22⋊Q8—862no—
575C22⋊Q8—1721no—
576#121—28no—
577#121—22no—
578#121C22⋊D4314yes—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—862no—
585#117—1721no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4C22⋊D4311yescharacteristic
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4C22⋊D4311yescharacteristic
606C2×C22⋊C4C22⋊D4311yescharacteristic
607C2×C42—861no—
608C2×C42C22×D4311yescharacteristic
609#106—862no—
610#103—862no—
611#103—862no—
612#103—862no—
613#103—862no—
614#102—434no—
615#102—862no—
616#102—862no—
617#102—862no—
618#102—862no—
619#102—1721no—
620C22⋊C8—862no—
621C22⋊C8—862no—
622C22⋊C8—1721no—
623#95—861no—
624#95—861no—
625#95—861no—
626#95—861no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×C22⋊D4311yescharacteristic
637C24C2×C22⋊D4311yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—861no—
648C2×Q8—861no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8C2×C22⋊D4312yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4D4×D4312yes—
679C2×D4#1062190012yes—
680C2×D4C2×C22⋊D4312yes—
681C2×D4C2×C22⋊D4312yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—81no—
699C22×C4—81no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4C2×C22⋊D4311yescharacteristic
705C22×C4C2×C22⋊D4311yescharacteristic
706C22×C4C2×C22⋊D4311yescharacteristic
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C2×C22⋊D4312yes—
709C22×C4C2×C22⋊D4312yes—
710C22×C4C23×D4311yescharacteristic
711Q16—1724no—
712SD16—1724no—
713SD16—1724no—
714C2×C8—432no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—861no—
723C2×C8—861no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—1724no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—432no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—1722no—
737C4⋊C4—1722no—
738C4⋊C4—1722no—
739C4⋊C4C2×C22⋊D4312yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—1722no—
748C22⋊C4—1722no—
749C22⋊C4—1722no—
750C22⋊C4—1722no—
751C42—21no—
752C42—21no—
753C42—1722no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—22no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23#1306329412yes—
788C23#1306334512yes—
789C23C22×C22⋊D4311yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—1721no—
795Q8—1721no—
796Q8—1721no—
797Q8—1721no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#1306329714yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—48no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—84no—
837C2×C4—862no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4#1306329412yes—
850C2×C4C2×D4×D4311yescharacteristic
851C2×C4C22×C22⋊D4311yescharacteristic
852C2×C4C22×C22⋊D4311yescharacteristic
853C2×C4C2×#1062190011yescharacteristic
854C2×C4#1306337011yescharacteristic
855C2×C4#1306337011yescharacteristic
856C8—862no—
857C8—1721no—
858C8—1721no—
859C8—1721no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—41no—
878C22—42no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#1306329411yescharacteristic
890C22D4×C22⋊D4311yescharacteristic
891C22#1458354311yescharacteristic
892C22C2×#1306334511yescharacteristic
893C22#1458369711yescharacteristic
894C22#1458371011yescharacteristic
895C22#1458371011yescharacteristic
896C4—22no—
897C4—41no—
898C4—41no—
899C4—42no—
900C4—41no—
901C4—42no—
902C4—3441no—
903C4—3441no—
904C4—3441no—
905C4—1722no—
906C4C2×#1306329711yescharacteristic
907C4#1458345811yescharacteristic
908C4D4×C22⋊D4311yescharacteristic
909C4#1458354311yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2#1913796911yescharacteristic
915C2#1914381311yescharacteristic
916C2#1914387211yescharacteristic
917C2#1914611611yescharacteristic
918C2#1914629811yescharacteristic
919C2#1914643011yescharacteristic
920C2#1914663111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24436
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583126C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14583050C2semidirect
4. C2×#14582895C2semidirect
5. #19138024C2semidirect
6. #19135831C2semidirect
7. #19135788C2semidirect
8. #19135689C2semidirect
9. #19135603C2semidirect
10. #19134929C2semidirect
11. #19134918C2semidirect
12. #19134888C2semidirect
13. #19134856C2semidirect
14. #19134526C2semidirect
16. C22×#10621885C22semidirect
19. C23×C43⋊C8C22semidirect
21. C2×#13063304C22semidirect
22. C2×#13063284C22semidirect
26. C2×#13063256C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063249C22semidirect
31. C2×#13063248C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
43. #14582805C22semidirect
44. #14582797C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
109. #13063246D4semidirect
525. C43#24436semidirect

Maximal subgroups

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

subgroupindex
C2×#145831262
C2×#145830612
C2×#145830502
C2×#145828952
#191380242
#191358312
#191357882
#191356892
#191356032
#191349292
#191349182
#191348882
#191348562
#191345262
C2×C43×#5462
#2443643