Finite Group Databasebeta

← #25134608

Subgroups — #25134608

Order 11008.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583147C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic, complemented
4C2×#14582900C211yesmaximal, characteristic, complemented
5#19138035C211yesmaximal, characteristic, complemented
6#19135838C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135678C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134893C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#547C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063297—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24#14583147—24no—
25#14583044—24no—
26#14583044—24no—
27C2×#13063258C2211yescharacteristic
28#14582900—24no—
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42#14582821—21no—
43#14582815—21no—
44#14582801C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582776—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C43×#547—24no—
55C43×#547—24no—
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×#123×C43—21no—
59C2×C22⋊Q8×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×#121×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C4⋊C4×C43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884—41no—
73C2×#10621884—41no—
74C2×#10621884—41no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—22no—
78C2×#10621877—22no—
79C2×#10621877—22no—
80C2×#10621877—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#13063258—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—41no—
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—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C2×#41×C43D414yescomplemented
130C22×Q8×C43C2311yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C22×D4×C43—21no—
133C22×D4×C43—21no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C4⋊Q8×C43—22no—
142C4⋊Q8×C43—22no—
143#123×C43—28no—
144#123×C43—28no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43—22no—
148C22⋊Q8×C43D414yescomplemented
149#121×C43—28no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43—28no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43—21no—
159C2×C4⋊C4×C43D411yescharacteristic
160C2×C4⋊C4×C43C2311yescharacteristic
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×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C23×D43—21no—
171#41×C43—28no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178#41×C43—44no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43C2×D412yes—
190C2×Q8×C43C2×D412yes—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—24no—
198C2×D4×C43—41no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43C2×D412yes—
204C2×D4×C43C2×D412yes—
205C2×D4×C43#4112yes—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—24no—
211C22×C4×C43—24no—
212C22×C4×C43—24no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43—42no—
227C22×C4×C43—42no—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—42no—
236C2×C22⋊D43—42no—
237C2×C22⋊D43—42no—
238C2×C22⋊D43—42no—
239C2×C22⋊D43—42no—
240C2×C22⋊D43—81no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—42no—
245C22×Dic43—42no—
246C22×Dic43—81no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—21no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2×D412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—22no—
265C42×C43—21no—
266C42×C43—21no—
267C22⋊Dic43—42no—
268#10621884—44no—
269#10621884—44no—
270#10621882—44no—
271(C2×D43)⋊C4—42no—
272(C2×D43)⋊C4—42no—
273(C2×D43)⋊C4—42no—
274(C2×D43)⋊C4—81no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—42no—
281C4⋊Dic43C2×D412yes—
282Dic43⋊C4—42no—
283#10621877—44no—
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—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8C2×D412yes—
296C23×C43—22no—
297C23×C43—21no—
298C23×C43—22no—
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—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43#12012yes—
317C23×C43C22×D411yescharacteristic
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—41no—
330Q8×C43—41no—
331Q8×C43—41no—
332Q8×C43—41no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—44no—
337D4×C43—48no—
338D4×C43—48no—
339D4×C43#12114yescomplemented
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—48no—
358C2×C4×C43—48no—
359C2×C4×C43—48no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
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#12012yes—
371C2×C4×C43AGL(1,ℤ/8)12yes—
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C2×#4111yescharacteristic
376C2×C4×C43H(5,𝔽2)11yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C22⋊D43—84no—
379C22⋊D43—84no—
380C2×Dic43—22no—
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—84no—
390D172—41no—
391D172—41no—
392D172—41no—
393D172—41no—
394C43⋊C8—22no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#24454—431nomaximal, Sylow
399C22×C43—24no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—42no—
411C22×C43—41no—
412C22×C43—42no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43C2×#12011yescharacteristic
421C22×C43D4211yescharacteristic
422C22×C43#54611yescharacteristic
423C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C43#57511yescharacteristic
425C22×C43#57711yescharacteristic
426C22×C43#57811yescharacteristic
427C2×D43—81no—
428C2×D43—81no—
429C2×D43—81no—
430C2×D43—81no—
431C2×D43—81no—
432C2×D43—81no—
433C2×D43—81no—
434C4×C43—22no—
435C4×C43—22no—
436C4×C43—41no—
437C4×C43—42no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—41no—
441C4×C43C2×#12111yescharacteristic
442C4×C43#53411yescharacteristic
443C4×C43D4211yescharacteristic
444C4×C43#54611yescharacteristic
445Dic43—42no—
446Dic43—81no—
447Dic43—81no—
448C2×#547D4311yescharacteristic, complemented
449C2×#468—431no—
450C2×#449—431no—
451C2×#449—431no—
452C2×#417—431no—
453#2416—431no—
454#2043—431no—
455#2036—431no—
456#2013—431no—
457#2000—431no—
458#1879—431no—
459#1872—431no—
460#1870—431no—
461#1862—431no—
462#1788—431no—
463C2×C43—42no—
464C2×C43—44no—
465C2×C43—81no—
466C2×C43#241011yescharacteristic
467C2×C43#300611yescharacteristic
468C2×C43#301311yescharacteristic
469C2×C43#326911yescharacteristic
470C2×C43#327211yescharacteristic
471C2×C43#330711yescharacteristic
472C2×C43#333011yescharacteristic
473D43—161no—
474C22×#41C2×D4311yescharacteristic
475C22×#41C2×D4311yescharacteristic
476C22×SD16—431no—
477C22×SD16—431no—
478C22×D8—431no—
479C22×M16—431no—
480#547—24no—
481#547—24no—
482C2×C4⋊Q8C2×D4311yescharacteristic
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C2×D4311yescharacteristic
486C2×C22⋊Q8C2×D4311yescharacteristic
487C2×#121—21no—
488C2×#121—431no—
489C2×#121—431no—
490C2×#121—861no—
491C2×C4×D4C2×D4311yescharacteristic
492C2×C4×D4C2×D4311yescharacteristic
493C22×C4⋊C4—21no—
494C22×C4⋊C4—431no—
495#468—864no—
496#449—864no—
497#449—864no—
498C2×#107—431no—
499#417—864no—
500C2×#103—431no—
501C2×#103—431no—
502C2×#103—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#103—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×C22⋊C8—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8—431no—
513#396—861no—
514#394—861no—
515#390—431no—
516#389—431no—
517#386—861no—
518#380—431no—
519#340—431no—
520#340—431no—
521#336—431no—
522#336—431no—
523C43#2445411yescharacteristic, complemented, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41C22⋊D4314yescomplemented
536C22×Q8C22×D4311yescharacteristic
537C22×Q8C22×D4311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—431no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4C22⋊D4311yescharacteristic
544C22×D4C22×D4311yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—861no—
549C23×C4C22×D4311yescharacteristic
550C23×C4C22×D4311yescharacteristic
551C2×SD16—862no—
552C2×SD16—862no—
553C2×SD16—862no—
554C2×SD16—1721no—
555C2×SD16—1721no—
556C2×SD16—1721no—
557C2×D8—862no—
558C2×D8—862no—
559C2×D8—862no—
560C2×M16—862no—
561C2×M16—862no—
562C2×M16—1721no—
563C22×C8—431no—
564C22×C8—431no—
565C22×C8—431no—
566C22×C8—431no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#123—28no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8C22⋊D4314yescomplemented
575#121—28no—
576#121—862no—
577#121—862no—
578#121—862no—
579#121—1721no—
580#121—1724no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—1721no—
597C2×C4⋊C4C22⋊D4311yescharacteristic
598C2×C4⋊C4C22×D4311yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4C22⋊D4311yescharacteristic
608C2×C22⋊C4C22⋊D4311yescharacteristic
609C2×C42C22×D4311yescharacteristic
610#107—862no—
611#103—862no—
612#103—862no—
613#103—862no—
614#103—862no—
615#103—862no—
616#103—1721no—
617#102—434no—
618#102—862no—
619#102—862no—
620#102—862no—
621C22⋊C8—862no—
622C22⋊C8—862no—
623C22⋊C8—1721no—
624#95—861no—
625#95—861no—
626C24—21no—
627C24—861no—
628C24C2×C22⋊D4311yescharacteristic
629C24C2×C22⋊D4311yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×C22⋊D4312yes—
649C2×Q8C2×C22⋊D4312yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—41no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—861no—
668C2×D4—3441no—
669C2×D4—1722no—
670C2×D4—1722no—
671C2×D4—1722no—
672C2×D4—1722no—
673C2×D4—1722no—
674C2×D4D4×D4312yes—
675C2×D4#1062190012yes—
676C2×D4C2×C22⋊D4312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—3441no—
703C22×C4—1722no—
704C22×C4—1722no—
705C22×C4C2×C22⋊D4311yescharacteristic
706C22×C4C2×C22⋊D4311yescharacteristic
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C2×C22⋊D4312yes—
709C22×C4C2×C22⋊D4312yes—
710C22×C4C2×C22⋊D4311yescharacteristic
711C22×C4C23×D4311yescharacteristic
712SD16—1724no—
713SD16—1724no—
714D8—1724no—
715M16—1724no—
716C2×C8—432no—
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—861no—
727C2×C8—861no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—432no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—1722no—
741C4⋊C4—1722no—
742C4⋊C4C2×C22⋊D4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—3441no—
749C22⋊C4—1722no—
750C22⋊C4—1722no—
751C22⋊C4—1722no—
752C22⋊C4—1722no—
753C42—21no—
754C42—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—1721no—
776C23—1721no—
777C23—1721no—
778C23—1721no—
779C23—1721no—
780C23—1721no—
781C23—1721no—
782C23#1306329412yes—
783C23C22×C22⋊D4311yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—3444no—
799D4—3444no—
800D4—1721no—
801D4—1721no—
802D4—1721no—
803D4—1721no—
804D4#1306329714yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—862no—
836C2×C4—3444no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4#1306329412yes—
846C2×C4#1306335012yes—
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4C22×C22⋊D4311yescharacteristic
849C2×C4C22×C22⋊D4311yescharacteristic
850C2×C4C2×#1062190011yescharacteristic
851C2×C4#1306337011yescharacteristic
852C2×C4#1306337011yescharacteristic
853C8—862no—
854C8—1721no—
855C8—1721no—
856C8—1721no—
857C22—22no—
858C22—22no—
859C22—24no—
860C22—22no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—42no—
868C22—41no—
869C22—42no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—3441no—
879C22—3441no—
880C22—3441no—
881C22—3441no—
882C22—3441no—
883C22—3441no—
884C22—3441no—
885C22C2×#1306329411yescharacteristic
886C22D4×C22⋊D4311yescharacteristic
887C22#1458354311yescharacteristic
888C22C2×#1306335011yescharacteristic
889C22#1458369711yescharacteristic
890C22#1458370711yescharacteristic
891C22#1458371411yescharacteristic
892C4—22no—
893C4—22no—
894C4—42no—
895C4—41no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—3441no—
900C4—3441no—
901C4—1722no—
902C4C2×#1306329711yescharacteristic
903C4#1458345811yescharacteristic
904C4D4×C22⋊D4311yescharacteristic
905C4#1458354311yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—6881no—
910C2#1913796911yescharacteristic
911C2#1914384711yescharacteristic
912C2#1914391011yescharacteristic
913C2#1914614611yescharacteristic
914C2#1914619511yescharacteristic
915C2#1914657111yescharacteristic
916C2#1914690011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43#24454
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583147C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583044C2semidirect
4. C2×#14582900C2semidirect
5. #19138035C2semidirect
6. #19135838C2semidirect
7. #19135795C2semidirect
8. #19135678C2semidirect
9. #19135596C2semidirect
10. #19134943C2semidirect
11. #19134903C2semidirect
12. #19134893C2semidirect
13. #19134842C2semidirect
14. #19134535C2semidirect
15. C2×C43×#547C2semidirect
111. #13063246D4semidirect
129. C2×#41×C43D4semidirect
148. C22⋊Q8×C43D4semidirect
339. D4×C43#121semidirect
448. C2×#547D43semidirect
523. C43#24454semidirect
535. C2×#41C22⋊D43semidirect
574. C22⋊Q8C22⋊D43semidirect
804. D4#13063297semidirect

Maximal subgroups

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

subgroupindex
C2×#145831472
C2×#145830442
C2×#145829002
#191380352
#191358382
#191357952
#191356782
#191355962
#191349432
#191349032
#191348932
#191348422
#191345352
C2×C43×#5472
#2445443