Finite Group Databasebeta

← #25144030

Subgroups — #25144030

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 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×#10621883C211yesmaximal, characteristic, complemented
5#19138161C211yesmaximal, characteristic, complemented
6#19135969C211yesmaximal, characteristic, complemented
7#19135798C211yesmaximal, characteristic, complemented
8#19135784C211yesmaximal, characteristic, complemented
9#19135671C211yesmaximal, characteristic, complemented
10#19135460C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134953C211yesmaximal, characteristic, complemented
13#19134943C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, 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×Dic86C2211yescharacteristic, complemented
24#14583114—24no—
25#14583050—24no—
26#14583033—24no—
27C4×#10621883—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#14582823—21no—
43#14582814—21no—
44#14582801C2211yescharacteristic, complemented
45#14582799—21no—
46#14582797C2211yescharacteristic, complemented
47#14582788—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—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C2×#10621883D414yescomplemented
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063313—22no—
83#13063313—41no—
84#13063304—22no—
85#13063304—41no—
86#13063299—22no—
87#13063299—41no—
88C4×Dic86—22no—
89C4×Dic86—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
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—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102#13063258—41no—
103#13063256—22no—
104C4⋊(C43⋊C8)—22no—
105#13063248—22no—
106#13063248—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246D414yes—
111#13063245—22no—
112#13063245—41no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—22no—
115C4×C43⋊C8—22no—
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×D172—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86C2×D412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C42×C43—21no—
233C42×C43—21no—
234C42×C43—21no—
235C42×C43—21no—
236C22⋊Dic43—42no—
237#10621883—28no—
238#10621883—44no—
239#10621882—44no—
240#10621882—44no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—81no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43C2×D412yes—
250Dic43⋊C4—42no—
251Dic43⋊C4—42no—
252Dic43⋊C4—81no—
253C4×Dic43—42no—
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—41no—
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—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354D172—41no—
355D172—41no—
356D172—41no—
357D172—41no—
358Dic86—22no—
359Dic86—22no—
360Dic86—41no—
361Dic86—41no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C43⋊C8—41no—
365C43⋊C8—41no—
366#25152—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—24no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—816no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43#52511yescharacteristic
390C22×C43D4211yescharacteristic
391C22×C43D4211yescharacteristic
392C22×C43C2×#13511yescharacteristic
393C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C43#57611yescharacteristic
395C22×C43#57711yescharacteristic
396C2×D43—81no—
397C2×D43—81no—
398C2×D43—81no—
399C2×D43—81no—
400C2×D43—81no—
401C2×D43—81no—
402C2×D43—81no—
403C4×C43—22no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—81no—
409C4×C43—81no—
410C4×C43C2×#12111yescharacteristic
411C4×C43#53811yescharacteristic
412C4×C43#54611yescharacteristic
413C4×C43#54611yescharacteristic
414Dic43—42no—
415Dic43—42no—
416Dic43—81no—
417C2×#463—431no—
418C2×#450—431no—
419C2×#447—431no—
420C2×C4×SD16—431no—
421#2426—431no—
422D4×C22⋊C4D4311yescharacteristic, complemented
423#2065—431no—
424#2036—431no—
425#2034—431no—
426#2012—431no—
427#1970—431no—
428#1923—431no—
429#1880—431no—
430#1879—431no—
431#1862—431no—
432C2×C43—42no—
433C2×C43—44no—
434C2×C43—82no—
435C2×C43#242411yescharacteristic
436C2×C43#310511yescharacteristic
437C2×C43#311811yescharacteristic
438C2×C43#326511yescharacteristic
439C2×C43#327411yescharacteristic
440C2×C43#328011yescharacteristic
441C2×C43#328211yescharacteristic
442D43—161no—
443C23×D4C2×D4311yescharacteristic
444C22×SD16—431no—
445C22×SD16—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#124—431no—
449C2×C22⋊Q8—431no—
450C2×#121—431no—
451C2×C4×Q8—431no—
452C2×C4×D4C2×D4311yescharacteristic
453C2×C4×D4C2×D4311yescharacteristic
454C22×C22⋊C4—21no—
455#463—864no—
456#450—864no—
457#447—864no—
458C4×SD16—864no—
459C2×#107—431no—
460C2×#106—431no—
461C2×C4⋊C8—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×C4×C8—431no—
473#396—861no—
474#394—861no—
475#390—431no—
476#390—861no—
477#390C2×D4311yescharacteristic
478#390C2×D4311yescharacteristic
479#389—431no—
480#388—861no—
481#386—21no—
482#386—21no—
483#380C2×D4311yescharacteristic
484#379—21no—
485C4×C22⋊C4C2×D4311yescharacteristic
486#340—431no—
487#340—431no—
488#336—431no—
489#336—431no—
490C43#2515211yescharacteristic, complemented, Sylow
491C25—21no—
492C22×Q8—431no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4C22×D4311yescharacteristic
503C22×D4C22×D4311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C22×D4311yescharacteristic
507C2×SD16—434no—
508C2×SD16—862no—
509C2×SD16—862no—
510C2×SD16—862no—
511C2×SD16—862no—
512C2×SD16—1721no—
513C2×D8—862no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C2×D8—1721no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—431no—
522C22×C8—431no—
523#124—862no—
524#124—1721no—
525C22⋊Q8—862no—
526C22⋊Q8—1721no—
527#121—862no—
528#121—1721no—
529C4×Q8—862no—
530C4×Q8—1721no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4C22×D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C22⋊C4—21no—
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—44no—
550C2×C22⋊C4—861no—
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×C42—861no—
559C2×C42C22×D4311yescharacteristic
560C2×C42C22×D4311yescharacteristic
561#107—1721no—
562#106—862no—
563C4⋊C8—862no—
564#103—862no—
565#103—862no—
566#102—434no—
567#102—862no—
568#102—862no—
569#102—862no—
570#102—862no—
571#102—1721no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574C4×C8—862no—
575#95—21no—
576#95—861no—
577#95C22⋊D4311yescharacteristic
578#95C22⋊D4311yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—81no—
587C24—81no—
588C24—861no—
589C24C2×C22⋊D4311yescharacteristic
590C2×Q8—432no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—3441no—
618C2×D4—1722no—
619C2×D4—1722no—
620C2×D4#1062189812yes—
621C2×D4#1062189812yes—
622C2×D4D4×D4312yes—
623C2×D4D4×D4312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4C2×C22⋊D4311yescharacteristic
642C22×C4C2×C22⋊D4311yescharacteristic
643C22×C4C2×C22⋊D4311yescharacteristic
644C22×C4C2×C22⋊D4311yescharacteristic
645C22×C4C2×C22⋊D4311yescharacteristic
646C22×C4C23×D4311yescharacteristic
647SD16—868no—
648SD16—1724no—
649D8—1724no—
650D8—1724no—
651C2×C8—432no—
652C2×C8—432no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—432no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—3441no—
672C4⋊C4—1722no—
673C4⋊C4—1722no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C22⋊C4—3441no—
684C22⋊C4—1722no—
685C22⋊C4—1722no—
686C22⋊C4—1722no—
687C22⋊C4—1722no—
688C22⋊C4—1722no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—1722no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—1721no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23#1306334512yes—
729C23C22×C22⋊D4311yescharacteristic
730Q8—862no—
731Q8—862no—
732Q8—1721no—
733Q8—1721no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—3444no—
743D4—1721no—
744D4—1721no—
745D4—1721no—
746D4—1721no—
747D4#1306329814yes—
748C2×C4—21no—
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—41no—
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—84no—
773C2×C4—84no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4#1306335112yes—
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4C2×#1062189811yescharacteristic
787C2×C4C2×#1062189811yescharacteristic
788C2×C4#1306337011yescharacteristic
789C2×C4#1306337011yescharacteristic
790C8—862no—
791C8—862no—
792C8—1721no—
793C8—1721no—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—22no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—3441no—
817C22—3441no—
818C22—3441no—
819C22—3441no—
820C22—3441no—
821C22—3441no—
822C22—3441no—
823C22#1458341011yescharacteristic
824C22D4×C22⋊D4311yescharacteristic
825C22D4×C22⋊D4311yescharacteristic
826C22C2×#1306334511yescharacteristic
827C22C2×#1306335111yescharacteristic
828C22#1458370211yescharacteristic
829C22#1458371011yescharacteristic
830C4—22no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—81no—
836C4—81no—
837C4—3441no—
838C4—1722no—
839C4—1722no—
840C4C2×#1306329811yescharacteristic
841C4#1458348711yescharacteristic
842C4#1458353911yescharacteristic
843C4#1458353911yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—6881no—
848C2#1913813111yescharacteristic
849C2#1914464211yescharacteristic
850C2#1914477911yescharacteristic
851C2#1914608611yescharacteristic
852C2#1914621111yescharacteristic
853C2#1914627611yescharacteristic
854C2#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#25152
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×#10621883C2semidirect
5. #19138161C2semidirect
6. #19135969C2semidirect
7. #19135798C2semidirect
8. #19135784C2semidirect
9. #19135671C2semidirect
10. #19135460C2semidirect
11. #19135203C2semidirect
12. #19134953C2semidirect
13. #19134943C2semidirect
14. #19134842C2semidirect
15. D4×C22⋊C4×C43C2semidirect
20. C2×#13063313C22semidirect
23. C2×C4×Dic86C22semidirect
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. #14582801C22semidirect
46. #14582797C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
71. C2×#10621883D4semidirect
422. D4×C22⋊C4D43semidirect
490. C43#25152semidirect

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×#106218832
#191381612
#191359692
#191357982
#191357842
#191356712
#191354602
#191352032
#191349532
#191349432
#191348422
D4×C22⋊C4×C432
#2515243