Finite Group Databasebeta

← #25112363

Subgroups — #25112363

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063350C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic, complemented
5#19135479C211yesmaximal, characteristic, complemented
6#19135452C211yesmaximal, characteristic, complemented
7#19134943C211yesmaximal, characteristic, complemented
8#19134943C211yesmaximal, characteristic, complemented
9#19134932C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2339C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063350—24no—
18C2×#13063350—24no—
19C2×#13063350C418yescomplemented
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C22⋊C4×D43—21no—
28#14583009—24no—
29C4×#10621882—24no—
30C2×#13063258C2211yescharacteristic, complemented
31C2×#13063256C2211yescharacteristic, complemented
32C2×#13063249C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063236C2211yescharacteristic, complemented
42C2×C4×C43⋊C8C2211yescharacteristic, complemented
43#14582801C2211yescharacteristic
44#14582801C2211yescharacteristic
45#14582777—21no—
46#14582777—21no—
47#14582759C2211yescharacteristic
48#14582754—21no—
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C22×#41×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic, complemented
55C2×C4×D4×C43C2211yescharacteristic, complemented
56C43×#391C2211yescharacteristic, complemented
57C43×#391C2211yescharacteristic, complemented
58C43×#386—21no—
59C43×#386—21no—
60C43×#381—21no—
61C43×#380C2211yescharacteristic
62C4×C22⋊C4×C43C2211yescharacteristic
63C2×#95×C43—21no—
64C24×D43—21no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—21no—
68C22×D172—22no—
69C22×D172—41no—
70C22×D172—41no—
71C22×D172C2×C414yescomplemented
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76#13063350—232no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884—22no—
80C2×#10621884—22no—
81C2×#10621884C2×C414yescomplemented
82C2×#10621884C2×C414yescomplemented
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882C2×C414yes—
86C2×#10621882C2×C414yescomplemented
87C2×#10621882D414yes—
88C2×#10621882D414yes—
89C2×#10621877—22no—
90C2×#10621877—22no—
91C2×#10621877C2×C414yescomplemented
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C4×D172—22no—
97C4×D172—22no—
98C4×D172—41no—
99C4×D172—41no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C22⋊C4×D43—44no—
110#13063258—22no—
111#13063256—22no—
112#13063249—41no—
113#13063249—41no—
114#13063246—22no—
115#13063246—22no—
116#13063245—22no—
117#13063245—22no—
118#13063245—41no—
119#13063245—41no—
120C22⋊(C43⋊C8)—22no—
121#13063236—22no—
122C4×C43⋊C8—22no—
123C43⋊#95—21no—
124C2×#41×C43—22no—
125C2×#41×C43—22no—
126C2×#41×C43—22no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C2×#41×C43C2×C414yescomplemented
130C22×Q8×C43C2311yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43—21no—
135C23×C4×C43—21no—
136C23×C4×C43C2311yescharacteristic
137C4×D4×C43—22no—
138C4×D4×C43—22no—
139C4×D4×C43—41no—
140C4×D4×C43—41no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154#95×C43—21no—
155#95×C43D411yescharacteristic
156#95×C43D411yescharacteristic
157C24×C43—21no—
158C24×C43C2×D411yescharacteristic
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168#41×C43—28no—
169#41×C43—44no—
170#41×C43—44no—
171#41×C43—44no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43C22×C412yes—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—24no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43C22×C412yes—
185C2×D4×C43C2×D412yes—
186C2×D4×C43C2×D412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43—42no—
201C22×C4×C43—81no—
202C22×C4×C43—81no—
203C22×C4×C43C22×C412yes—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43#4112yes—
210C22×C4×C43C2411yescharacteristic
211C22×Dic43—21no—
212C22×Dic43—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—24no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—28no—
223C2×D172—42no—
224C2×D172—42no—
225C2×D172—44no—
226C2×D172—44no—
227C2×D172—44no—
228C2×D172C22×C412yes—
229C2×D172C22×C412yes—
230C2×D172C2×D412yes—
231C2×D172C2×D412yes—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—41no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—81no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43—21no—
251C22⋊Dic43—42no—
252#10621884—28no—
253#10621884—28no—
254#10621882—28no—
255#10621882C22⋊C4116yescomplemented
256(C2×D43)⋊C4—42no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4—81no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266#10621877—28no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8C22×C412yes—
276C2×C43⋊C8C22×C412yes—
277C2×C43⋊C8C2×D412yes—
278C2×C43⋊C8C2×D412yes—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43C4×D412yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—48no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—48no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—41no—
318Q8×C43—41no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43C2×C22⋊C414yescomplemented
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—48no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—84no—
352C2×C4×C43—84no—
353C2×C4×C43C4×D412yes—
354C2×C4×C43AGL(1,ℤ/8)12yescomplemented
355C2×C4×C43C23×C411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43H(5,𝔽2)11yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—22no—
371D172—22no—
372D172—48no—
373D172—41no—
374D172—41no—
375D172C2×C22⋊C414yes—
376C4×D43—84no—
377C4×D43—84no—
378C43⋊C8—22no—
379C43⋊C8—41no—
380C43⋊C8—41no—
381C43⋊C8C2×C22⋊C414yescomplemented
382#22442—431nomaximal, Sylow
383C22×C43—22no—
384C22×C43—24no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43C2×C4×D411yescharacteristic
398C22×C43D4211yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C43#57511yescharacteristic
402C22×C43#57611yescharacteristic
403C22×C43#57711yescharacteristic
404C2×D43—24no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—816no—
415C2×D43—81no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—41no—
425C4×C43—81no—
426C4×C43—81no—
427C4×C43C22×C22⋊C411yescharacteristic
428C4×C43#51811yescharacteristic
429C4×C43#54611yescharacteristic
430C4×C43#54611yescharacteristic
431Dic43—81no—
432Dic43—81no—
433C22×AGL(1,ℤ/8)—431no—
434C2×#442—431no—
435C2×C4×D8—431no—
436#2339D4311yescharacteristic, complemented
437D4×C22⋊C4—431no—
438#1973—431no—
439#1968—431no—
440#1879—431no—
441#1879—431no—
442#1877—431no—
443#1877—431no—
444#1809—431no—
445#1788—431no—
446#1786—431no—
447#1753—431no—
448C2×C43—42no—
449C2×C43—44no—
450C2×C43D4×C22⋊C411yescharacteristic
451C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C43#294611yescharacteristic
453C2×C43#326411yescharacteristic
454C2×C43#326711yescharacteristic
455C2×C43#327211yescharacteristic
456C2×C43#327311yescharacteristic
457D43—44no—
458D43—82no—
459C22×#41C2×D4311yescharacteristic
460C23×D4—431no—
461C2×AGL(1,ℤ/8)—438no—
462C2×AGL(1,ℤ/8)—864no—
463C2×AGL(1,ℤ/8)—864no—
464C22×SD16—431no—
465C22×SD16—431no—
466C22×D8—431no—
467C22×D8—431no—
468C22×M16—431no—
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C2×C4×D4C2×D4311yescharacteristic, complemented
472C2×C4×D4C2×D4311yescharacteristic, complemented
473C22×C22⋊C4—861no—
474#442—864no—
475C4×D8—864no—
476C2×#107—431no—
477C2×#106—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×C22⋊C8—431no—
487C2×#97—431no—
488C2×C4×C8—431no—
489#391C2×D4311yescharacteristic, complemented
490#391C2×D4311yescharacteristic, complemented
491#390—431no—
492#390—431no—
493#386—21no—
494#386—21no—
495#386—861no—
496#386—861no—
497#381—21no—
498#380—431no—
499#380C2×D4311yescharacteristic
500#379—861no—
501C4×C22⋊C4C2×D4311yescharacteristic
502C2×#95—21no—
503#340—431no—
504#340—431no—
505#336—431no—
506#336—431no—
507C43#2244211yescharacteristic, complemented, Sylow
508C25—861no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C4×D4314yescomplemented
515C22×Q8C22×D4311yescharacteristic
516C22×D4—21no—
517C22×D4—434no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—862no—
521C22×D4—862no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—1721no—
525C22×D4—1721no—
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—861no—
531C23×C4—861no—
532C23×C4C22×D4311yescharacteristic
533AGL(1,ℤ/8)—8632no—
534C2×SD16—434no—
535C2×SD16—434no—
536C2×SD16—862no—
537C2×SD16—862no—
538C2×SD16—862no—
539C2×SD16—862no—
540C2×D8—434no—
541C2×D8—434no—
542C2×D8—434no—
543C2×D8—434no—
544C2×D8—862no—
545C2×D8—862no—
546C2×M16—434no—
547C2×M16—862no—
548C2×M16—862no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—431no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—862no—
558C4×D4—862no—
559C4×D4—1721no—
560C4×D4—1721no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—1724no—
576C2×C22⋊C4C22⋊D4311yescharacteristic
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C42C22×D4311yescharacteristic
579C2×C42C22×D4311yescharacteristic
580#107—862no—
581#106—862no—
582#103—1721no—
583#103—1721no—
584#102—862no—
585#102—862no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590C22⋊C8—862no—
591#97—862no—
592C4×C8—862no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—861no—
599#95C22⋊D4311yescharacteristic
600#95C22⋊D4311yescharacteristic
601C24—21no—
602C24—861no—
603C24—864no—
604C24—861no—
605C24—3441no—
606C24—3441no—
607C24—1722no—
608C24—1722no—
609C24—1722no—
610C24—1722no—
611C24C2×C22⋊D4311yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×C4×D4312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4312yes—
648C2×D4D4×D4312yes—
649C2×D4D4×D4312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—81no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—3441no—
669C22×C4—3441no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4C2×C4×D4312yes—
675C22×C4#1062189812yes—
676C22×C4C2×C22⋊D4311yescharacteristic
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4311yescharacteristic
681C22×C4C23×D4311yescharacteristic
682SD16—868no—
683SD16—868no—
684D8—4316no—
685D8—868no—
686M16—868no—
687C2×C8—432no—
688C2×C8—432no—
689C2×C8—432no—
690C2×C8—432no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—81no—
712C22⋊C4—3441no—
713C22⋊C4—3441no—
714C22⋊C4—1722no—
715C22⋊C4—1722no—
716C22⋊C4—1722no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—862no—
737C23—862no—
738C23—862no—
739C23—862no—
740C23—3444no—
741C23—3444no—
742C23—3444no—
743C23—3444no—
744C23—3444no—
745C23—1728no—
746C23—1728no—
747C23—1721no—
748C23—1721no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23C4×C22⋊D4312yes—
758C23C22×C22⋊D4311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—434no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—1728no—
774D4—1721no—
775D4—1721no—
776D4C22⋊C4×D4314yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—3444no—
807C2×C4—3444no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4C4×C22⋊D4312yes—
815C2×C4#1306335012yescomplemented
816C2×C4C22×C4×D4311yescharacteristic
817C2×C4C2×D4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×#1062189811yescharacteristic
820C2×C4#1306337011yescharacteristic
821C2×C4#1306337011yescharacteristic
822C8—434no—
823C8—862no—
824C8—1721no—
825C8—1721no—
826C22—22no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—864no—
841C22—34416no—
842C22—3441no—
843C22—3441no—
844C22—3441no—
845C22—3441no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22C2×C4×C22⋊D4311yescharacteristic
856C22D4×C22⋊D4311yescharacteristic
857C22D4×C22⋊D4311yescharacteristic
858C22C2×#1306335011yescharacteristic
859C22#1458369711yescharacteristic
860C22#1458370211yescharacteristic
861C22#1458370711yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—3441no—
871C4—3441no—
872C4C2×C22⋊C4×D4311yescharacteristic
873C4#1458337211yescharacteristic
874C4#1458353911yescharacteristic
875C4#1458353911yescharacteristic
876C2—42no—
877C2—44no—
878C2—3442no—
879C2—1724no—
880C2C22⋊C4×C22⋊D4311yescharacteristic
881C2C4×#1306335011yescharacteristic
882C2#1914342311yescharacteristic
883C2#1914607611yescharacteristic
884C2#1914612111yescharacteristic
885C2#1914619511yescharacteristic
886C2#1914620211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2339C2
socleC23×C43C22×D4
prime radicalC22×#13063350C2
cosocleC22×C4×C43C24
hypercenter#2339D43
hypocenterC43#22442
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C2×C4×#10621882C2semidirect
4. C22⋊C4×D172C2semidirect
5. #19135479C2semidirect
6. #19135452C2semidirect
7. #19134943C2semidirect
8. #19134943C2semidirect
9. #19134932C2semidirect
10. #19134932C2semidirect
11. #19134626C2semidirect
12. #19134535C2semidirect
13. #19134525C2semidirect
14. #19134379C2semidirect
15. C43×#2339C2semidirect
19. C2×#13063350C4semidirect
30. C2×#13063258C22semidirect
31. C2×#13063256C22semidirect
32. C2×#13063249C22semidirect
33. C2×#13063249C22semidirect
34. C2×#13063246C22semidirect
35. C2×#13063246C22semidirect
41. C2×#13063236C22semidirect
42. C2×C4×C43⋊C8C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582654C22semidirect
54. C2×C4×D4×C43C22semidirect
55. C2×C4×D4×C43C22semidirect
56. C43×#391C22semidirect
57. C43×#391C22semidirect
71. C22×D172C2×C4semidirect
81. C2×#10621884C2×C4semidirect
82. C2×#10621884C2×C4semidirect
86. C2×#10621882C2×C4semidirect
91. C2×#10621877C2×C4semidirect
129. C2×#41×C43C2×C4semidirect
255. #10621882C22⋊C4semidirect
323. D4×C43C2×C22⋊C4semidirect
354. C2×C4×C43AGL(1,ℤ/8)semidirect
381. C43⋊C8C2×C22⋊C4semidirect
436. #2339D43semidirect
471. C2×C4×D4C2×D43semidirect
472. C2×C4×D4C2×D43semidirect
489. #391C2×D43semidirect
490. #391C2×D43semidirect
507. C43#22442semidirect
514. C2×#41C4×D43semidirect
776. D4C22⋊C4×D43semidirect
815. C2×C4#13063350semidirect

Maximal subgroups

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

subgroupindex
C22×#130633502
C2×#145830092
C2×C4×#106218822
C22⋊C4×D1722
#191354792
#191354522
#191349432
#191349322
#191346262
#191345352
#191345252
#191343792
C43×#23392
#2244243