Finite Group Databasebeta

← #25134308

Subgroups — #25134308

Order 11008.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583130C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19138035C211yesmaximal, characteristic, complemented
6#19135831C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135672C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic, complemented
22C2×#13063297—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24#14583130—24no—
25#14583044—24no—
26#14583033—24no—
27C2×#13063256C2211yescharacteristic, complemented
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063249C2211yescharacteristic, complemented
31C2×#13063246—24no—
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42#14582821—21no—
43#14582815—21no—
44#14582801C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582776—21no—
47#14582759C2211yescharacteristic, complemented
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×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—41no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C2×#10621882—41no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063299—22no—
86#13063299—22no—
87#13063299—22no—
88#13063299—41no—
89#13063297—44no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102#13063256—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—41no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246D414yescomplemented
112#13063245—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—22no—
115C22⋊(C43⋊C8)—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C25×C43—21no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—41no—
124C2×#41×C43—41no—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—22no—
127C22×D4×C43—22no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C22×D4×C43—21no—
131C22×D4×C43—22no—
132C22×D4×C43—41no—
133C22×D4×C43—41no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43D414yescomplemented
136C22×D4×C43C2311yescharacteristic
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C23×C4×C43—21no—
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142#124×C43—22no—
143#124×C43—22no—
144#123×C43—28no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43D414yescomplemented
147#121×C43—28no—
148#121×C43—22no—
149#121×C43—22no—
150#120×C43—28no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C4×D4×C43—22no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43D411yescharacteristic
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—28no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C22⋊C4×C43D411yescharacteristic
166C2×C42×C43C2311yescharacteristic
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—24no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—42no—
174C24×C43—81no—
175C24×C43—81no—
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178C23×D43—21no—
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182#41×C43—44no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—28no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43—44no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43—81no—
212C2×D4×C43—81no—
213C2×D4×C43C2×D412yes—
214C2×D4×C43C2×D412yes—
215C2×D4×C43C2×D412yes—
216C2×D4×C43#4112yes—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—24no—
222C22×C4×C43—24no—
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—21no—
230C22×C4×C43—21no—
231C22×C4×C43—42no—
232C22×C4×C43—42no—
233C22×C4×C43—81no—
234C22×C4×C43—81no—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C2×C22⋊D43—42no—
243C2×C22⋊D43—42no—
244C2×C22⋊D43—42no—
245C2×C22⋊D43—42no—
246C2×C22⋊D43—42no—
247C2×C22⋊D43—81no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—42no—
252C22×Dic43—42no—
253C22×Dic43—81no—
254C2×D172—21no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—21no—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2×D412yes—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—24no—
271C42×C43—21no—
272C42×C43—21no—
273C22⋊Dic43—42no—
274#10621884—44no—
275#10621882—44no—
276#10621882—44no—
277(C2×D43)⋊C4—42no—
278(C2×D43)⋊C4—42no—
279(C2×D43)⋊C4—42no—
280(C2×D43)⋊C4—81no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—42no—
287C4⋊Dic43C2×D412yes—
288Dic43⋊C4—42no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—44no—
301C2×C43⋊C8C2×D412yes—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—48no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—48no—
329C23×C43—84no—
330C23×C43—84no—
331C23×C43—84no—
332C23×C43—84no—
333C23×C43—84no—
334C23×C43#12012yes—
335C23×C43#13512yes—
336C23×C43AGL(1,ℤ/8)12yes—
337C23×C43C22×D411yescharacteristic
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—41no—
341C22×D43—41no—
342C22×D43—41no—
343C22×D43—41no—
344C22×D43—41no—
345Q8×C43—22no—
346Q8×C43—22no—
347Q8×C43—41no—
348Q8×C43—41no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—48no—
355D4×C43—48no—
356D4×C43—44no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—84no—
360D4×C43#12114yescomplemented
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—22no—
370C2×C4×C43—21no—
371C2×C4×C43—22no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—48no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—84no—
388C2×C4×C43#12012yes—
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C2×#4111yescharacteristic
393C2×C4×C43H(5,𝔽2)11yescharacteristic
394C2×C4×C43H(5,𝔽2)11yescharacteristic
395C22⋊D43—84no—
396C22⋊D43—84no—
397C2×Dic43—22no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—84no—
407D172—41no—
408D172—41no—
409D172—41no—
410D172—41no—
411C43⋊C8—22no—
412C43⋊C8—41no—
413C43⋊C8—41no—
414C43⋊C8—41no—
415#24434—431nomaximal, Sylow
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—22no—
422C22×C43—24no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—42no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—816no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43#44914yescomplemented
445C22×C43C2×#12011yescharacteristic
446C22×C43D4211yescharacteristic
447C22×C43#54611yescharacteristic
448C22×C43C2×#13511yescharacteristic
449C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C43#57611yescharacteristic
451C22×C43#57711yescharacteristic
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C2×D43—81no—
456C2×D43—81no—
457C2×D43—81no—
458C2×D43—81no—
459C4×C43—22no—
460C4×C43—41no—
461C4×C43—42no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—42no—
465C4×C43C2×#12111yescharacteristic
466C4×C43#53411yescharacteristic
467C4×C43D4211yescharacteristic
468C4×C43#54611yescharacteristic
469Dic43—42no—
470Dic43—81no—
471Dic43—81no—
472C2×#546D4311yescharacteristic, complemented
473C2×#465—431no—
474C2×#449—431no—
475C2×#447—431no—
476C22×#102—431no—
477#2416—431no—
478#2042—431no—
479#2034—431no—
480#2012—431no—
481#1999—431no—
482#1879—431no—
483#1872—431no—
484#1869—431no—
485#1864—431no—
486#1788—431no—
487C2×C43—24no—
488C2×C43—44no—
489C2×C43—81no—
490C2×C43—82no—
491C2×C43#241011yescharacteristic
492C2×C43C2×#44911yescharacteristic
493C2×C43#301211yescharacteristic
494C2×C43#326411yescharacteristic
495C2×C43#328211yescharacteristic
496C2×C43#329711yescharacteristic
497C2×C43#330611yescharacteristic
498D43—161no—
499C22×#41C2×D4311yescharacteristic
500C23×D4C2×D4311yescharacteristic
501C22×SD16—431no—
502C22×D8—431no—
503C22×D8—431no—
504C23×C8—431no—
505#546—24no—
506#546—24no—
507C2×#124C2×D4311yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C2×D4311yescharacteristic
510C2×#121—21no—
511C2×#121—431no—
512C2×#121—431no—
513C2×#121—861no—
514C2×#121C2×D4311yescharacteristic
515C2×#120—21no—
516C2×C4×D4C2×D4311yescharacteristic
517C2×C4×D4C2×D4311yescharacteristic
518C22×C4⋊C4—431no—
519C22×C22⋊C4—21no—
520#465—864no—
521#449—864no—
522#447—864no—
523C2×#106—431no—
524C2×#103—431no—
525C2×#103—431no—
526C2×#103—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×#102—431no—
532C2×#102—431no—
533C2×#102—431no—
534C2×#102—864no—
535C2×C22⋊C8—431no—
536C2×C22⋊C8—431no—
537C2×C22⋊C8—431no—
538#396—861no—
539#394—861no—
540#390—431no—
541#389—431no—
542#386—861no—
543#380—431no—
544#340—431no—
545#340—431no—
546#336—431no—
547#336—431no—
548C43#2443411yescharacteristic, complemented, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C22×D4311yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—22no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4—431no—
566C22×D4—861no—
567C22×D4—861no—
568C22×D4C22⋊D4311yescharacteristic
569C22×D4C22⋊D4314yescomplemented
570C22×D4C22×D4311yescharacteristic
571C22×D4C22×D4311yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—861no—
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C2×SD16—862no—
578C2×SD16—862no—
579C2×SD16—1721no—
580C2×D8—862no—
581C2×D8—862no—
582C2×D8—862no—
583C2×D8—862no—
584C2×D8—1721no—
585C2×D8—1721no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—431no—
589C22×C8—431no—
590C22×C8—862no—
591C22×C8—862no—
592C22×C8—1721no—
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8C22⋊D4314yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—862no—
602#121—862no—
603#121—862no—
604#121—1721no—
605#121—1724no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—431no—
615C2×C4⋊C4—862no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—1721no—
619C2×C4⋊C4C22⋊D4311yescharacteristic
620C2×C4⋊C4C22×D4311yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C22⋊C4C22⋊D4311yescharacteristic
633C2×C22⋊C4C22⋊D4311yescharacteristic
634C2×C42C22×D4311yescharacteristic
635#106—862no—
636#103—862no—
637#103—862no—
638#103—1721no—
639#102—434no—
640#102—862no—
641#102—862no—
642#102—862no—
643#102—862no—
644#102—862no—
645#102—862no—
646C22⋊C8—862no—
647C22⋊C8—862no—
648C22⋊C8—1721no—
649#95—861no—
650#95—861no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24—861no—
661C24C2×C22⋊D4311yescharacteristic
662C24C2×C22⋊D4311yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×C22⋊D4312yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—3441no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—1722no—
707C2×D4—1722no—
708C2×D4—1722no—
709C2×D4D4×D4312yes—
710C2×D4#1062190012yes—
711C2×D4C2×C22⋊D4312yes—
712C2×D4C2×C22⋊D4312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—81no—
730C22×C4—81no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—3441no—
735C22×C4—1722no—
736C22×C4—1722no—
737C22×C4C2×C22⋊D4311yescharacteristic
738C22×C4C2×C22⋊D4311yescharacteristic
739C22×C4C2×C22⋊D4311yescharacteristic
740C22×C4C2×C22⋊D4311yescharacteristic
741C22×C4C2×C22⋊D4312yes—
742C22×C4C2×C22⋊D4312yes—
743C22×C4C23×D4311yescharacteristic
744SD16—1724no—
745D8—1724no—
746D8—1724no—
747C2×C8—432no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—861no—
752C2×C8—861no—
753C2×C8—861no—
754C2×C8—861no—
755C2×C8—861no—
756C2×C8—861no—
757C2×C8—861no—
758C2×C8—861no—
759C2×C8—1724no—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—432no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—1722no—
770C4⋊C4—1722no—
771C4⋊C4C2×C22⋊D4312yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—3441no—
780C22⋊C4—1722no—
781C22⋊C4—1722no—
782C22⋊C4—1722no—
783C22⋊C4—1722no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—48no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—1721no—
819C23—1721no—
820C23—1721no—
821C23—1721no—
822C23—1721no—
823C23—1721no—
824C23—1721no—
825C23#1306329412yes—
826C23#1306334512yes—
827C23#1306335012yes—
828C23C22×C22⋊D4311yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—84no—
844D4—3444no—
845D4—3444no—
846D4—1721no—
847D4—1721no—
848D4—1721no—
849D4—1721no—
850D4#1306329714yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—48no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—862no—
879C2×C4—3444no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4#1306329412yes—
889C2×C4C2×D4×D4311yescharacteristic
890C2×C4C22×C22⋊D4311yescharacteristic
891C2×C4C22×C22⋊D4311yescharacteristic
892C2×C4C2×#1062190011yescharacteristic
893C2×C4#1306337011yescharacteristic
894C2×C4#1306337011yescharacteristic
895C8—862no—
896C8—1721no—
897C8—1721no—
898C8—1721no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—3441no—
928C22—3441no—
929C22—3441no—
930C22—3441no—
931C22—3441no—
932C22—3441no—
933C22—3441no—
934C22#1458304414yescomplemented
935C22C2×#1306329411yescharacteristic
936C22D4×C22⋊D4311yescharacteristic
937C22#1458354311yescharacteristic
938C22C2×#1306334511yescharacteristic
939C22C2×#1306335011yescharacteristic
940C22#1458370211yescharacteristic
941C22#1458371011yescharacteristic
942C4—22no—
943C4—41no—
944C4—41no—
945C4—42no—
946C4—41no—
947C4—42no—
948C4—3441no—
949C4—3441no—
950C4—1722no—
951C4C2×#1306329711yescharacteristic
952C4#1458345811yescharacteristic
953C4D4×C22⋊D4311yescharacteristic
954C4#1458354311yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—6881no—
960C2#1913796911yescharacteristic
961C2C2×#1458304411yescharacteristic
962C2#1914389911yescharacteristic
963C2#1914607611yescharacteristic
964C2#1914629811yescharacteristic
965C2#1914644511yescharacteristic
966C2#1914655611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24434
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×#14583130C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583033C2semidirect
4. C22×#13063246C2semidirect
5. #19138035C2semidirect
6. #19135831C2semidirect
7. #19135781C2semidirect
8. #19135672C2semidirect
9. #19135591C2semidirect
10. #19134943C2semidirect
11. #19134903C2semidirect
12. #19134888C2semidirect
13. #19134856C2semidirect
14. #19134535C2semidirect
15. C2×C43×#546C2semidirect
16. C22×#10621884C22semidirect
21. C2×#13063299C22semidirect
27. C2×#13063256C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063249C22semidirect
38. C2×#13063245C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
44. #14582801C22semidirect
45. #14582797C22semidirect
47. #14582759C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
111. #13063246D4semidirect
135. C22×D4×C43D4semidirect
146. C22⋊Q8×C43D4semidirect
360. D4×C43#121semidirect
444. C22×C43#449semidirect
472. C2×#546D43semidirect
548. C43#24434semidirect
569. C22×D4C22⋊D43semidirect
597. C22⋊Q8C22⋊D43semidirect
850. D4#13063297semidirect
934. C22#14583044semidirect

Maximal subgroups

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

subgroupindex
C2×#145831302
C2×#145830442
C2×#145830332
C22×#130632462
#191380352
#191358312
#191357812
#191356722
#191355912
#191349432
#191349032
#191348882
#191348562
#191345352
C2×C43×#5462
#2443443