Finite Group Databasebeta

← #25117245

Subgroups — #25117245

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583032C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3C2×#14582903C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135277C211yesmaximal, characteristic, complemented
7#19135215C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2363C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23#14583032C418yescomplemented
24C4×#10621882—24no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27#14582903—24no—
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic, complemented
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38C2×C4×C43⋊C8C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582777—21no—
42#14582777—21no—
43#14582759C2211yescharacteristic
44#14582754—21no—
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C43×#390—21no—
55C43×#390C2211yescharacteristic, complemented
56C43×#389C2211yescharacteristic, complemented
57C43×#388—21no—
58C43×#386—21no—
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C4×C22⋊C4×C43—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C24×D43—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2×C414yescomplemented
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C2×#10621882—41no—
78C2×#10621882C2×C414yes—
79C2×#10621882C2×C414yescomplemented
80C2×#10621877—22no—
81C2×#10621877—22no—
82C2×#10621877—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—41no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C22⋊C4×D43—44no—
101#13063258—22no—
102#13063256—41no—
103#13063246—22no—
104#13063246—41no—
105#13063245—22no—
106#13063245—22no—
107#13063245—22no—
108#13063245C2×C414yescomplemented
109#13063245C2×C414yescomplemented
110#13063245D414yescomplemented
111C22⋊(C43⋊C8)C2×C414yescomplemented
112#13063236—41no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119#121×C43—22no—
120#121×C43C2×C414yescomplemented
121C4×D4×C43—22no—
122C4×D4×C43—41no—
123#117×C43—22no—
124#117×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#95×C43—21no—
141#95×C43—21no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—24no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—81no—
154C23×D43—81no—
155C2×D4×C43—21no—
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43C22×C412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43—81no—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43#4112yes—
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—21no—
183C22×Dic43—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—24no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—28no—
194C2×D172—42no—
195C2×D172—42no—
196C2×D172—44no—
197C2×D172—44no—
198C2×D172—44no—
199C2×D172C22×C412yes—
200C2×D172C22×C412yes—
201C2×D172C2×D412yes—
202C2×D172#4112yes—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—81no—
208C2×C4×D43—81no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—81no—
214C4⋊C4×C43C22×C412yes—
215C4⋊C4×C43C2×D412yes—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—41no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—81no—
223C42×C43—21no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—42no—
228C42×C43—81no—
229C22⋊Dic43—42no—
230#10621882—28no—
231#10621882—44no—
232(C2×D43)⋊C4—42no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—81no—
237(C2×D43)⋊C4—81no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242#10621877—44no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C22×C412yes—
253C2×C43⋊C8C22×C412yes—
254C2×C43⋊C8C2×D412yes—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43C4×D412yes—
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—48no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—48no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43—84no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—84no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—84no—
323C2×C4×C43C4×D412yes—
324C2×C4×C43AGL(1,ℤ/8)12yes—
325C2×C4×C43C23×C411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337D172—22no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—48no—
343D172—41no—
344D172—41no—
345D172C4×D414yes—
346C4×D43—84no—
347C4×D43—84no—
348C43⋊C8—22no—
349C43⋊C8—22no—
350C43⋊C8—22no—
351C43⋊C8—41no—
352#22880—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43C2×C4×D411yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43#54611yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43#57511yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C2×D43—24no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—816no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—81no—
397C4×C43C2×C4×D411yescharacteristic
398C4×C43#51811yescharacteristic
399C4×C43#54611yescharacteristic
400C4×C43#55111yescharacteristic
401Dic43—81no—
402Dic43—81no—
403C2×#447—431no—
404C2×C4×D8—431no—
405C2×#418—431no—
406#2363D4311yescharacteristic, complemented
407D4×C22⋊C4—431no—
408#1972—431no—
409#1934—431no—
410#1925—431no—
411#1895—431no—
412#1879—431no—
413#1879—431no—
414#1864—431no—
415#1854—431no—
416#1762—431no—
417#1753—431no—
418C2×C43—42no—
419C2×C43—82no—
420C2×C43#235811yescharacteristic
421C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C43#294811yescharacteristic
423C2×C43#326411yescharacteristic
424C2×C43#326811yescharacteristic
425C2×C43#332211yescharacteristic
426C2×C43#332511yescharacteristic
427D43—44no—
428D43—82no—
429C23×D4—431no—
430C22×D8—431no—
431C22×D8—431no—
432C22×M16—431no—
433C2×#121C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4C2×D4311yescharacteristic, complemented
437C2×#117C2×D4311yescharacteristic
438C22×C22⋊C4—861no—
439#447—438no—
440C4×D8—864no—
441C2×#107—431no—
442C2×#106—431no—
443#418—864no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×C22⋊C8—431no—
453C2×#97—431no—
454C2×C4×C8—431no—
455#390—21no—
456#390—431no—
457#390—431no—
458#390C2×D4311yescharacteristic, complemented
459#389C2×D4311yescharacteristic, complemented
460#388—21no—
461#386—21no—
462#386—861no—
463#386—861no—
464#380—431no—
465#379—861no—
466C4×C4⋊C4C2×D4311yescharacteristic, complemented
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2×D4311yescharacteristic
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473#336—431no—
474#336—431no—
475C43#2288011yescharacteristic, complemented, Sylow
476C25—861no—
477C22×D4—21no—
478C22×D4—434no—
479C22×D4—431no—
480C22×D4—431no—
481C22×D4—862no—
482C22×D4—862no—
483C22×D4—862no—
484C22×D4—861no—
485C22×D4—1721no—
486C22×D4—1721no—
487C22×D4C22×D4311yescharacteristic
488C23×C4—21no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×D8—434no—
493C2×D8—434no—
494C2×D8—862no—
495C2×D8—862no—
496C2×D8—1721no—
497C2×D8—1721no—
498C2×M16—862no—
499C2×M16—862no—
500C2×M16—1721no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505#121—22no—
506#121C4×D4314yescomplemented
507C4×D4—22no—
508C4×D4—41no—
509C4×D4—862no—
510C4×D4—862no—
511C4×D4—1721no—
512C4×D4—1721no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—1724no—
534C2×C22⋊C4C22⋊D4311yescharacteristic
535C2×C22⋊C4C22⋊D4311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C22×D4311yescharacteristic
539C2×C42C22×D4311yescharacteristic
540#107—862no—
541#106—1721no—
542#102—434no—
543#102—434no—
544#102—434no—
545#102—862no—
546#102—862no—
547#102—862no—
548#102—862no—
549#102—1721no—
550C22⋊C8—434no—
551#97—1721no—
552C4×C8—862no—
553#95—21no—
554#95—21no—
555#95—861no—
556#95C22⋊D4311yescharacteristic
557#95C22⋊D4311yescharacteristic
558C24—21no—
559C24—861no—
560C24—864no—
561C24—861no—
562C24—3441no—
563C24—3441no—
564C24—1722no—
565C24—1722no—
566C24—1722no—
567C24—1722no—
568C24C2×C22⋊D4311yescharacteristic
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—432no—
578C2×D4—432no—
579C2×D4—432no—
580C2×D4—432no—
581C2×D4—868no—
582C2×D4—864no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—1724no—
592C2×D4—1724no—
593C2×D4—1724no—
594C2×D4—1722no—
595C2×D4—1722no—
596C2×D4C2×C4×D4312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—81no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—3441no—
610C22×C4—3441no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4C2×C4×D4312yes—
616C22×C4#1062189812yes—
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622C22×C4C23×D4311yescharacteristic
623D8—868no—
624D8—1724no—
625M16—1724no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—432no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4C2×C4×D4312yes—
648C4⋊C4D4×D4312yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—3441no—
657C22⋊C4—3441no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C22⋊C4—1722no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—862no—
686C23—3444no—
687C23—3444no—
688C23—3444no—
689C23—3444no—
690C23—3444no—
691C23—1728no—
692C23—1728no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23C4×C22⋊D4312yes—
704C23C22×C22⋊D4311yescharacteristic
705D4—22no—
706D4—22no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—434no—
711D4—862no—
712D4—862no—
713D4—862no—
714D4—862no—
715D4—862no—
716D4—1728no—
717D4—1721no—
718D4—1721no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—84no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4C4×C22⋊D4312yes—
755C2×C4#1306335012yes—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C2×C4C2×#1062189811yescharacteristic
760C2×C4#1306337011yescharacteristic
761C2×C4#1306337111yescharacteristic
762C8—862no—
763C8—862no—
764C8—862no—
765C8—1721no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—864no—
781C22—34416no—
782C22—3441no—
783C22—3441no—
784C22—3441no—
785C22—3441no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22C2×C4×C22⋊D4311yescharacteristic
796C22D4×C22⋊D4311yescharacteristic
797C22#1458353711yescharacteristic
798C22C2×#1306335011yescharacteristic
799C22#1458369711yescharacteristic
800C22#1458370211yescharacteristic
801C22#1458370211yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—81no—
810C4—3441no—
811C4—3441no—
812C4C4×D4×D4311yescharacteristic
813C4#1458337111yescharacteristic
814C4#1458354511yescharacteristic
815C4#1458357811yescharacteristic
816C2—42no—
817C2—82no—
818C2—3442no—
819C2—1724no—
820C2#1913757211yescharacteristic
821C2C4×#1306335011yescharacteristic
822C2#1914344511yescharacteristic
823C2#1914607611yescharacteristic
824C2#1914613611yescharacteristic
825C2#1914679011yescharacteristic
826C2#1914683111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2363C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#2363D43
hypocenterC43#22880
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C2×#14582903C2semidirect
4. C22⋊C4×D172C2semidirect
5. #19135470C2semidirect
6. #19135277C2semidirect
7. #19135215C2semidirect
8. #19135034C2semidirect
9. #19134946C2semidirect
10. #19134943C2semidirect
11. #19134855C2semidirect
12. #19134794C2semidirect
13. #19134423C2semidirect
14. #19134379C2semidirect
15. C43×#2363C2semidirect
23. #14583032C4semidirect
25. C2×#13063258C22semidirect
26. C2×#13063256C22semidirect
28. C2×#13063246C22semidirect
29. C2×#13063246C22semidirect
37. C2×#13063236C22semidirect
38. C2×C4×C43⋊C8C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582654C22semidirect
50. #14582654C22semidirect
52. C2×C4×D4×C43C22semidirect
55. C43×#390C22semidirect
56. C43×#389C22semidirect
59. C4×C4⋊C4×C43C22semidirect
69. C22×D172C2×C4semidirect
79. C2×#10621882C2×C4semidirect
108. #13063245C2×C4semidirect
109. #13063245C2×C4semidirect
110. #13063245D4semidirect
111. C22⋊(C43⋊C8)C2×C4semidirect
120. #121×C43C2×C4semidirect
406. #2363D43semidirect
436. C2×C4×D4C2×D43semidirect
458. #390C2×D43semidirect
459. #389C2×D43semidirect
466. C4×C4⋊C4C2×D43semidirect
475. C43#22880semidirect
506. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
C2×C4×#106218822
C2×#145829032
C22⋊C4×D1722
#191354702
#191352772
#191352152
#191350342
#191349462
#191349432
#191348552
#191347942
#191344232
#191343792
C43×#23632
#2288043