Finite Group Databasebeta

← #25144150

Subgroups — #25144150

Order 11008.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583114C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19138172C211yesmaximal, characteristic, complemented
6#19135983C211yesmaximal, characteristic, complemented
7#19135798C211yesmaximal, characteristic, complemented
8#19135784C211yesmaximal, characteristic, complemented
9#19135671C211yesmaximal, characteristic, complemented
10#19135448C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134946C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14#19134856C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C2×#13063313C2211yescharacteristic, complemented
21C2×#13063304C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic, complemented
24#14583114—24no—
25#14583050—24no—
26#14583033—24no—
27C4×#10621882—24no—
28C2×#13063258C2211yescharacteristic, complemented
29C2×#13063256C2211yescharacteristic, complemented
30C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063248C2211yescharacteristic, complemented
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582828—21no—
43#14582814—21no—
44#14582805C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582775—21no—
47#14582758—21no—
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C23×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C22×C22⋊C4×C43—21no—
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#386—21no—
59C43×#386—21no—
60C43×#380C2211yescharacteristic
61C43×#379—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—41no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—41no—
78C2×#10621882D414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063313—22no—
84#13063313—41no—
85#13063304—22no—
86#13063304—41no—
87#13063299—22no—
88#13063299—41no—
89C4×D172—22no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100#13063258—22no—
101#13063256—41no—
102C4⋊(C43⋊C8)—22no—
103#13063248—22no—
104#13063248—41no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246D414yescomplemented
109#13063245—22no—
110#13063245—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—22no—
122C22×D4×C43—21no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—41no—
133C4×D4×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—44no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—24no—
153C24×C43—21no—
154C24×C43—42no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C2×D4×C43—24no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—44no—
177C2×D4×C43C2×D412yes—
178C2×D4×C43C2×D412yes—
179C2×D4×C43#4112yes—
180C2×D4×C43#4112yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43—81no—
194C22×C4×C43—81no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—81no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172C2×D412yes—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—81no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—21no—
239C22⋊Dic43—42no—
240#10621883—44no—
241#10621883—44no—
242#10621882—28no—
243#10621882—44no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—42no—
246(C2×D43)⋊C4—42no—
247(C2×D43)⋊C4—42no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43C2×D412yes—
252Dic43⋊C4—42no—
253Dic43⋊C4—81no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C2×D412yes—
265C2×C43⋊C8C2×D412yes—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—48no—
277C23×C43—48no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—84no—
289C23×C43—84no—
290C23×C43—84no—
291C23×C43—84no—
292C23×C43—84no—
293C23×C43#13512yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—48no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43#12114yes—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—84no—
336C2×C4×C43—84no—
337C2×C4×C43AGL(1,ℤ/8)12yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C22⋊D43—84no—
345C2×Dic43—22no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354D172—22no—
355D172—22no—
356D172—41no—
357D172—41no—
358C4×D43—84no—
359Dic86—41no—
360Dic86—41no—
361Dic86—41no—
362Dic86—41no—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367#25160—431nomaximal, Sylow
368C22×C43—22no—
369C22×C43—24no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—816no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43#52511yescharacteristic
391C22×C43D4211yescharacteristic
392C22×C43D4211yescharacteristic
393C22×C43C2×#13511yescharacteristic
394C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C43#57611yescharacteristic
396C22×C43#57711yescharacteristic
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—81no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C4×C43—22no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43—81no—
410C4×C43—81no—
411C4×C43C2×#12111yescharacteristic
412C4×C43#53811yescharacteristic
413C4×C43#54611yescharacteristic
414C4×C43#54611yescharacteristic
415Dic43—42no—
416Dic43—81no—
417Dic43—81no—
418C2×#463—431no—
419C2×#450—431no—
420C2×#447—431no—
421C2×C4×D8—431no—
422#2427—431no—
423D4×C22⋊C4D4311yescharacteristic, complemented
424#2067—431no—
425#2036—431no—
426#2034—431no—
427#2012—431no—
428#1968—431no—
429#1923—431no—
430#1879—431no—
431#1877—431no—
432#1864—431no—
433C2×C43—42no—
434C2×C43—44no—
435C2×C43—82no—
436C2×C43#242411yescharacteristic
437C2×C43#310511yescharacteristic
438C2×C43#311811yescharacteristic
439C2×C43#326411yescharacteristic
440C2×C43#327211yescharacteristic
441C2×C43#328011yescharacteristic
442C2×C43#328211yescharacteristic
443D43—82no—
444C23×D4C2×D4311yescharacteristic
445C22×SD16—431no—
446C22×SD16—431no—
447C22×D8—431no—
448C22×D8—431no—
449C2×#124—431no—
450C2×C22⋊Q8—431no—
451C2×#121—431no—
452C2×C4×D4—431no—
453C2×C4×D4C2×D4311yescharacteristic
454C2×C4×D4C2×D4311yescharacteristic
455C22×C22⋊C4—21no—
456#463—864no—
457#450—864no—
458#447—864no—
459C4×D8—864no—
460C2×#107—431no—
461C2×#106—431no—
462C2×C4⋊C8—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C4×C8—431no—
474#397—861no—
475#394—861no—
476#391—431no—
477#390C2×D4311yescharacteristic
478#390C2×D4311yescharacteristic
479#389—431no—
480#386—21no—
481#386—21no—
482#386—861no—
483#380—861no—
484#380C2×D4311yescharacteristic
485#379—21no—
486C4×C22⋊C4C2×D4311yescharacteristic
487#340—431no—
488#340—431no—
489#336—431no—
490#336—431no—
491C43#2516011yescharacteristic, complemented, Sylow
492C25—21no—
493C22×Q8—431no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4C22×D4311yescharacteristic
504C22×D4C22×D4311yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C2×SD16—862no—
510C2×SD16—862no—
511C2×SD16—862no—
512C2×SD16—862no—
513C2×SD16—862no—
514C2×SD16—1721no—
515C2×D8—434no—
516C2×D8—862no—
517C2×D8—862no—
518C2×D8—862no—
519C2×D8—862no—
520C2×D8—1721no—
521C22×C8—431no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—431no—
525#124—862no—
526#124—1721no—
527C22⋊Q8—862no—
528C22⋊Q8—1721no—
529#121—862no—
530#121—1721no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—862no—
536C4×D4—1721no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—44no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4C22⋊D4311yescharacteristic
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C42C22×D4311yescharacteristic
559C2×C42C22×D4311yescharacteristic
560#107—862no—
561#106—1721no—
562C4⋊C8—862no—
563#103—862no—
564#103—1721no—
565#102—434no—
566#102—862no—
567#102—862no—
568#102—862no—
569#102—862no—
570#102—862no—
571C22⋊C8—862no—
572C22⋊C8—862no—
573C4×C8—862no—
574#95—21no—
575#95—861no—
576#95—861no—
577#95—861no—
578#95C22⋊D4311yescharacteristic
579#95C22⋊D4311yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24—861no—
590C24C2×C22⋊D4311yescharacteristic
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—432no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—3441no—
619C2×D4—1722no—
620C2×D4—1722no—
621C2×D4#1062189812yes—
622C2×D4#1062189812yes—
623C2×D4D4×D4312yes—
624C2×D4D4×D4312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—3441no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4C2×C22⋊D4311yescharacteristic
646C22×C4C2×C22⋊D4311yescharacteristic
647C22×C4C2×C22⋊D4311yescharacteristic
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C23×D4311yescharacteristic
651SD16—1724no—
652SD16—1724no—
653D8—868no—
654D8—1724no—
655C2×C8—432no—
656C2×C8—432no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—432no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—3441no—
676C4⋊C4—1722no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—1722no—
687C22⋊C4—1722no—
688C22⋊C4—1722no—
689C22⋊C4—1722no—
690C22⋊C4—1722no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—48no—
706C23—48no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—862no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23#1306334512yes—
730C23C22×C22⋊D4311yescharacteristic
731Q8—1721no—
732Q8—1721no—
733Q8—1721no—
734Q8—1721no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—862no—
744D4—862no—
745D4—3444no—
746D4—1721no—
747D4—1721no—
748D4#1306329814yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—862no—
776C2×C4—3444no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4#1306335112yes—
786C2×C4C2×D4×D4311yescharacteristic
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C2×#1062189811yescharacteristic
789C2×C4C2×#1062189811yescharacteristic
790C2×C4#1306337011yescharacteristic
791C2×C4#1306337011yescharacteristic
792C8—862no—
793C8—862no—
794C8—1721no—
795C8—1721no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—816no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—3441no—
819C22—3441no—
820C22—3441no—
821C22—3441no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22#1458341011yescharacteristic
826C22D4×C22⋊D4311yescharacteristic
827C22D4×C22⋊D4311yescharacteristic
828C22C2×#1306334511yescharacteristic
829C22C2×#1306335111yescharacteristic
830C22#1458370211yescharacteristic
831C22#1458371011yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—3441no—
840C4—3441no—
841C4—1722no—
842C4C2×#1306329811yescharacteristic
843C4#1458348711yescharacteristic
844C4#1458353911yescharacteristic
845C4#1458353911yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—3442no—
850C2#1913813111yescharacteristic
851C2#1914464211yescharacteristic
852C2#1914477911yescharacteristic
853C2#1914607111yescharacteristic
854C2#1914619111yescharacteristic
855C2#1914627611yescharacteristic
856C2#1914629811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
hypercenterD4×C22⋊C4D43
hypocenterC43#25160
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583114C2semidirect
2. C2×#14583050C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19138172C2semidirect
6. #19135983C2semidirect
7. #19135798C2semidirect
8. #19135784C2semidirect
9. #19135671C2semidirect
10. #19135448C2semidirect
11. #19135203C2semidirect
12. #19134946C2semidirect
13. #19134929C2semidirect
14. #19134856C2semidirect
15. D4×C22⋊C4×C43C2semidirect
20. C2×#13063313C22semidirect
23. C2×C4×D172C22semidirect
28. C2×#13063258C22semidirect
29. C2×#13063256C22semidirect
30. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×#13063248C22semidirect
32. C2×#13063248C22semidirect
37. C2×#13063245C22semidirect
38. C2×#13063245C22semidirect
41. C2×C4×C43⋊C8C22semidirect
44. #14582805C22semidirect
45. #14582797C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
108. #13063246D4semidirect
423. D4×C22⋊C4D43semidirect
491. C43#25160semidirect

Maximal subgroups

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

subgroupindex
C2×#145831142
C2×#145830502
C2×#145830332
C2×C4×#106218822
#191381722
#191359832
#191357982
#191357842
#191356712
#191354482
#191352032
#191349462
#191349292
#191348562
D4×C22⋊C4×C432
#2516043