Finite Group Databasebeta

← #25132168

Subgroups — #25132168

Order 11008.

1510 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583111C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583038C211yesmaximal, characteristic, complemented
4C2×#14582997C211yesmaximal, characteristic, complemented
5#19139508C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135394C211yesmaximal, characteristic, complemented
12#19134600C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×C43×#548C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063296—21no—
22C2×C4×D172C2211yescharacteristic
23#14583111—24no—
24#14583044—24no—
25#14583038—24no—
26#14582997—24no—
27C2×#13063258C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
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
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×#13063236C2211yescharacteristic
44#14582815—21no—
45#14582815—21no—
46#14582769C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756—21no—
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C43×#548—24no—
55C43×#548—24no—
56C2×#124×C43—21no—
57C2×#124×C43C2211yescharacteristic
58C2×C22⋊Q8×C43—21no—
59C2×C22⋊Q8×C43C2211yescharacteristic
60C2×#121×C43—21no—
61C2×#121×C43C2211yescharacteristic
62C2×C4×Q8×C43C2211yescharacteristic
63C2×C4×D4×C43—21no—
64C2×C4×D4×C43C2211yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C4×D43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884—41no—
74C2×#10621884D414yescomplemented
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063299—22no—
83#13063299—22no—
84#13063299—41no—
85#13063299—41no—
86#13063296—44no—
87C4×D172—22no—
88C4×D172—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99#13063258—22no—
100C4⋊(C43⋊C8)—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—41no—
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110#13063245—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—41no—
114C22⋊(C43⋊C8)—41no—
115#13063236—22no—
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—41no—
123C2×#41×C43—41no—
124C22×Q8×C43—22no—
125C22×Q8×C43—22no—
126C22×Q8×C43—21no—
127C22×Q8×C43—22no—
128C22×Q8×C43—22no—
129C22×Q8×C43—41no—
130C22×Q8×C43—41no—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×D4×C43—21no—
134C22×D4×C43—21no—
135C22×D4×C43D411yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141#124×C43—28no—
142#124×C43—22no—
143#124×C43D414yescomplemented
144C22⋊Q8×C43—28no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147#121×C43—28no—
148#121×C43—22no—
149#121×C43—22no—
150C4×Q8×C43—22no—
151C4×Q8×C43D414yescomplemented
152C4×D4×C43—28no—
153C4×D4×C43—22no—
154C4×D4×C43—22no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43D411yescharacteristic
158C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
166C2×C42×C43C2311yescharacteristic
167C24×C43—21no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C23×D43—21no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175C2×Q8×C43—24no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—42no—
185C2×Q8×C43—42no—
186C2×Q8×C43—44no—
187C2×Q8×C43—44no—
188C2×Q8×C43—44no—
189C2×Q8×C43—44no—
190C2×Q8×C43C2×D412yes—
191C2×Q8×C43C2×D412yes—
192C2×Q8×C43C2×D412yes—
193C2×Q8×C43#4112yes—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—41no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43C2×D412yes—
209C22×C4×C43—24no—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
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—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—42no—
227C22×C4×C43—42no—
228C22×C4×C43—42no—
229C22×C4×C43—42no—
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—81no—
240C2×C22⋊D43—81no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172C2×D412yes—
250C2×C4×D43—42no—
251C2×C4×D43—42no—
252C2×C4×D43—42no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—22no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2×D412yes—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C42×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2×D412yes—
267C22⋊Dic43—42no—
268C22⋊Dic43—42no—
269#10621884—28no—
270#10621884—44no—
271#10621882—44no—
272(C2×D43)⋊C4—42no—
273(C2×D43)⋊C4—42no—
274(C2×D43)⋊C4—42no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—42no—
282C4⋊Dic43—81no—
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—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8C2×D412yes—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—22no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43AGL(1,ℤ/8)12yes—
316C23×C43C22×D411yescharacteristic
317C22×D43—22no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—48no—
330Q8×C43—41no—
331Q8×C43—41no—
332Q8×C43#12114yescomplemented
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—44no—
336D4×C43—48no—
337D4×C43—48no—
338D4×C43—41no—
339D4×C43—41no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—48no—
356C2×C4×C43—48no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
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#12012yes—
370C2×C4×C43#12012yes—
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C2×C4×C43H(5,𝔽2)11yescharacteristic
376C2×C4×C43H(5,𝔽2)11yescharacteristic
377C22⋊D43—84no—
378C22⋊D43—84no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388D172—22no—
389D172—22no—
390D172—41no—
391D172—41no—
392C4×D43—84no—
393C43⋊C8—22no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397#24256—431nomaximal, Sylow
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—42no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—81no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43C2×#12011yescharacteristic
420C22×C43D4211yescharacteristic
421C22×C43#54611yescharacteristic
422C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C43#57511yescharacteristic
424C22×C43#57711yescharacteristic
425C22×C43#57811yescharacteristic
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—81no—
430C2×D43—81no—
431C2×D43—81no—
432C2×D43—81no—
433C4×C43—24no—
434C4×C43—22no—
435C4×C43—22no—
436C4×C43—41no—
437C4×C43—41no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43C2×#12111yescharacteristic
441C4×C43#53511yescharacteristic
442C4×C43D4211yescharacteristic
443C4×C43#54611yescharacteristic
444Dic43—81no—
445Dic43—81no—
446Dic43—81no—
447C2×#548D4311yescharacteristic, complemented
448C2×#463—431no—
449C2×#449—431no—
450C2×#448—431no—
451C2×#440—431no—
452#2537—431no—
453#2036—431no—
454#2033—431no—
455#2000—431no—
456#1999—431no—
457#1959—431no—
458#1955—431no—
459#1803—431no—
460#1788—431no—
461#1787—431no—
462C2×C43—42no—
463C2×C43—81no—
464C2×C43—82no—
465C2×C43#240811yescharacteristic
466C2×C43#300611yescharacteristic
467C2×C43#301311yescharacteristic
468C2×C43#326511yescharacteristic
469C2×C43#326911yescharacteristic
470C2×C43#330811yescharacteristic
471C2×C43#332111yescharacteristic
472D43—82no—
473C22×#41C2×D4311yescharacteristic
474C23×Q8C2×D4311yescharacteristic
475C22×SD16—431no—
476C22×SD16—431no—
477C22×D8—431no—
478#548—24no—
479#548—24no—
480C2×#124—21no—
481C2×#124C2×D4311yescharacteristic
482C2×C22⋊Q8—21no—
483C2×C22⋊Q8C2×D4311yescharacteristic
484C2×#121—21no—
485C2×#121—431no—
486C2×#121—431no—
487C2×#121—861no—
488C2×#121C2×D4311yescharacteristic
489C2×C4×Q8C2×D4311yescharacteristic
490C2×C4×D4—21no—
491C2×C4×D4—431no—
492C2×C4×D4C2×D4311yescharacteristic
493#463—864no—
494#449—864no—
495#448—864no—
496#440—864no—
497C2×#107—431no—
498C2×C4⋊C8—431no—
499C2×#103—431no—
500C2×#103—431no—
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×C22⋊C8—431no—
510C2×C22⋊C8—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8—431no—
513C2×#97—431no—
514#394—861no—
515#394—861no—
516#384—431no—
517#380—431no—
518#380—431no—
519#380—861no—
520#340—431no—
521#340—431no—
522C43#2425611yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
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—861no—
548C23×C4C22×D4311yescharacteristic
549C23×C4C22×D4311yescharacteristic
550C2×SD16—434no—
551C2×SD16—862no—
552C2×SD16—862no—
553C2×SD16—862no—
554C2×SD16—862no—
555C2×SD16—1721no—
556C2×D8—862no—
557C2×D8—862no—
558C2×D8—1721no—
559C22×C8—431no—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8—431no—
563#124—28no—
564#124—22no—
565#124C22⋊D4314yescomplemented
566C22⋊Q8—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569#121—28no—
570#121—22no—
571#121—22no—
572#121—862no—
573#121—862no—
574#121—1721no—
575#121—1721no—
576#121—1724no—
577C4×Q8—22no—
578C4×Q8C22⋊D4314yescomplemented
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—862no—
583C4×D4—862no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4C22⋊D4311yescharacteristic
592C2×C4⋊C4C22×D4311yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4C22⋊D4311yescharacteristic
603C2×C22⋊C4C22⋊D4311yescharacteristic
604C2×C42—21no—
605C2×C42C22×D4311yescharacteristic
606#107—862no—
607C4⋊C8—862no—
608#103—862no—
609#103—862no—
610#103—862no—
611#103—862no—
612#103—862no—
613#103—1721no—
614#102—862no—
615#102—862no—
616#102—862no—
617#102—1721no—
618C22⋊C8—862no—
619C22⋊C8—862no—
620C22⋊C8—1721no—
621C22⋊C8—1721no—
622#97—862no—
623#95—861no—
624#95—861no—
625C24—21no—
626C24—861no—
627C24C2×C22⋊D4311yescharacteristic
628C24C2×C22⋊D4311yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8D4×D4312yes—
649C2×Q8#1062190012yes—
650C2×Q8C2×C22⋊D4312yes—
651C2×Q8C2×C22⋊D4312yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—41no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—432no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—3441no—
673C2×D4—3441no—
674C2×D4—1722no—
675C2×D4—1722no—
676C2×D4—1722no—
677C2×D4—1722no—
678C2×D4C2×C22⋊D4312yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
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—42no—
699C22×C4—42no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—1722no—
704C22×C4—1722no—
705C22×C4—1722no—
706C22×C4C2×C22⋊D4311yescharacteristic
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C2×C22⋊D4311yescharacteristic
709C22×C4C2×C22⋊D4311yescharacteristic
710C22×C4C23×D4311yescharacteristic
711SD16—868no—
712SD16—1724no—
713D8—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—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—3441no—
737C4⋊C4—1722no—
738C4⋊C4C2×C22⋊D4312yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—1722no—
746C22⋊C4—1722no—
747C22⋊C4—1722no—
748C22⋊C4—1722no—
749C22⋊C4—1722no—
750C42—24no—
751C42C2×C22⋊D4312yes—
752C42C2×C22⋊D4312yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—862no—
774C23—1721no—
775C23—1721no—
776C23—1721no—
777C23—1721no—
778C23—1721no—
779C23—1721no—
780C23#1306335012yes—
781C23C22×C22⋊D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8#1306329614yescomplemented
791D4—22no—
792D4—22no—
793D4—44no—
794D4—48no—
795D4—48no—
796D4—41no—
797D4—41no—
798D4—862no—
799D4—862no—
800D4—3444no—
801D4—3444no—
802D4—1721no—
803D4—1721no—
804C2×C4—22no—
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—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
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—3444no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4#1306329412yes—
844C2×C4#1306329412yes—
845C2×C4C2×D4×D4311yescharacteristic
846C2×C4C22×C22⋊D4311yescharacteristic
847C2×C4C22×C22⋊D4311yescharacteristic
848C2×C4C2×#1062190011yescharacteristic
849C2×C4#1306337011yescharacteristic
850C2×C4#1306337011yescharacteristic
851C8—862no—
852C8—1721no—
853C8—1721no—
854C8—1721no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—3441no—
877C22—3441no—
878C22—3441no—
879C22—3441no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22C2×#1306329411yescharacteristic
884C22D4×C22⋊D4311yescharacteristic
885C22#1458354311yescharacteristic
886C22C2×#1306335011yescharacteristic
887C22#1458369711yescharacteristic
888C22#1458370711yescharacteristic
889C22#1458371411yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—3441no—
898C4—3441no—
899C4—3441no—
900C4C2×#1306329611yescharacteristic
901C4#1458346611yescharacteristic
902C4D4×C22⋊D4311yescharacteristic
903C4#1458354311yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—3442no—
908C2#1913794511yescharacteristic
909C2#1914384711yescharacteristic
910C2#1914391011yescharacteristic
911C2#1914609111yescharacteristic
912C2#1914615111yescharacteristic
913C2#1914658611yescharacteristic
914C2#1914678111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#548C2
socleC23×C43C22×D4
hypercenterC2×#548D43
hypocenterC43#24256
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#14583111C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583038C2semidirect
4. C2×#14582997C2semidirect
5. #19139508C2semidirect
6. #19135795C2semidirect
7. #19135774C2semidirect
8. #19135596C2semidirect
9. #19135591C2semidirect
10. #19135412C2semidirect
11. #19135394C2semidirect
12. #19134600C2semidirect
13. #19134535C2semidirect
14. #19134530C2semidirect
15. C2×C43×#548C2semidirect
74. C2×#10621884D4semidirect
143. #124×C43D4semidirect
151. C4×Q8×C43D4semidirect
332. Q8×C43#121semidirect
447. C2×#548D43semidirect
522. C43#24256semidirect
565. #124C22⋊D43semidirect
578. C4×Q8C22⋊D43semidirect
790. Q8#13063296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831112
C2×#145830442
C2×#145830382
C2×#145829972
#191395082
#191357952
#191357742
#191355962
#191355912
#191354122
#191353942
#191346002
#191345352
#191345302
C2×C43×#5482
#2425643