Finite Group Databasebeta

← #25112358

Subgroups — #25112358

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×#13063351C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19137426C211yesmaximal, characteristic, complemented
5#19135475C211yesmaximal, characteristic, complemented
6#19135448C211yesmaximal, characteristic, complemented
7#19134946C211yesmaximal, characteristic, complemented
8#19134946C211yesmaximal, characteristic, complemented
9#19134929C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063351—24no—
18C2×#13063351—24no—
19C2×#13063351C418yescomplemented
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic, complemented
26C2×C4×D172C2211yescharacteristic, complemented
27#14583009—24no—
28C4×#10621882—24no—
29C2×#13063258C2211yescharacteristic, complemented
30C2×#13063256C2211yescharacteristic, 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×#13063236C2211yescharacteristic, complemented
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582805C2211yescharacteristic, complemented
43#14582805C2211yescharacteristic, complemented
44#14582775—21no—
45#14582775—21no—
46#14582761—21no—
47#14582759C2211yescharacteristic
48#95×D43—21no—
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C22×C22⋊C4×C43—21no—
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#386—21no—
60C43×#386—21no—
61C43×#380C2211yescharacteristic
62C43×#379—21no—
63C4×C22⋊C4×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76#13063351—232no—
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883C2×C414yescomplemented
82C2×#10621883C2×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—
105#13063258—22no—
106#13063256—22no—
107#13063248—41no—
108#13063248—41no—
109#13063246—22no—
110#13063246—22no—
111#13063246—41no—
112#13063246—41no—
113#13063245—22no—
114#13063245—22no—
115C22⋊(C43⋊C8)—22no—
116#13063236—22no—
117C4×C43⋊C8—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C25×C43—21no—
124C22×D4×C43—22no—
125C22×D4×C43—22no—
126C22×D4×C43—21no—
127C22×D4×C43—22no—
128C22×D4×C43—41no—
129C22×D4×C43—41no—
130C22×D4×C43C2×C414yescomplemented
131C22×D4×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43—21no—
135C23×C4×C43C2311yescharacteristic
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C4×D4×C43—41no—
139C4×D4×C43—41no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—44no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43C2311yescharacteristic
153C2×C42×C43C2311yescharacteristic
154#95×C43—21no—
155#95×C43D411yescharacteristic
156#95×C43D411yescharacteristic
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—24no—
160C24×C43—42no—
161C24×C43—42no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—81no—
165C24×C43—81no—
166C24×C43C2×D411yescharacteristic
167C23×D43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—28no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—44no—
181C2×D4×C43—44no—
182C2×D4×C43—44no—
183C2×D4×C43C22×C412yes—
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—21no—
192C22×C4×C43—21no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—81no—
198C22×C4×C43—81no—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43#4112yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213#10621898—28no—
214#10621898—44no—
215#10621898—44no—
216#10621898—44no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22×C412yes—
221C2×D172C2×D412yes—
222C2×D172C2×D412yes—
223C2×C4×D43—24no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22×C412yes—
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—42no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—81no—
250C22⋊C4×C43—81no—
251C42×C43—21no—
252C42×C43—21no—
253C42×C43—21no—
254C42×C43—21no—
255C22⋊Dic43—81no—
256#10621883—28no—
257#10621883—28no—
258#10621882—28no—
259#10621882C22⋊C4116yescomplemented
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
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—22no—
289C23×C43—48no—
290C23×C43—48no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43C4×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—48no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43C2×C22⋊C414yes—
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—21no—
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—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—84no—
348C2×C4×C43—84no—
349C2×C4×C43C4×D412yes—
350C2×C4×C43AGL(1,ℤ/8)12yescomplemented
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C22⋊D43—48no—
358C2×Dic43—22no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172C2×C22⋊C414yescomplemented
371C4×D43—48no—
372C4×D43—84no—
373C4×D43—84no—
374Dic86—22no—
375Dic86—22no—
376Dic86—41no—
377Dic86—41no—
378C43⋊C8—22no—
379C43⋊C8—41no—
380C43⋊C8—41no—
381C43⋊C8C2×C22⋊C414yescomplemented
382#22442—431nomaximal, Sylow
383C22×C43—24no—
384C22×C43—22no—
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×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—816no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C2×C4×D411yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43D4211yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43#57511yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C2×D43—24no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—41no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—81no—
425C4×C43—81no—
426C4×C43C22×C22⋊C411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43#54611yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—42no—
431Dic43—81no—
432Dic43—81no—
433C22×AGL(1,ℤ/8)—431no—
434C2×#442—431no—
435C2×C4×D8—431no—
436#2339—431no—
437D4×C22⋊C4D4311yescharacteristic, complemented
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×C43—82no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
453C2×C43#294611yescharacteristic
454C2×C43#326411yescharacteristic
455C2×C43#326711yescharacteristic
456C2×C43#327211yescharacteristic
457C2×C43#327311yescharacteristic
458D43—44no—
459C22×#41—431no—
460C23×D4C2×D4311yescharacteristic
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
472C2×C4×D4C2×D4311yescharacteristic
473C22×C22⋊C4—21no—
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#391—431no—
490#391—431no—
491#390C2×D4311yescharacteristic
492#390C2×D4311yescharacteristic
493#386—21no—
494#386—21no—
495#386—861no—
496#386—861no—
497#381—861no—
498#380—431no—
499#380C2×D4311yescharacteristic
500#379—21no—
501C4×C22⋊C4C2×D4311yescharacteristic
502C2×#95—861no—
503#340—431no—
504#340—431no—
505#336—431no—
506#336—431no—
507C43#2244211yescharacteristic, complemented, Sylow
508C25—21no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C22×Q8—431no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—431no—
523C22×D4—861no—
524C22×D4C4×D4314yescomplemented
525C22×D4C22×D4311yescharacteristic
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—861no—
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—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—44no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
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—861no—
595#95—861no—
596#95—861no—
597#95—861no—
598#95—861no—
599#95C22⋊D4311yescharacteristic
600#95C22⋊D4311yescharacteristic
601C24—21no—
602C24—21no—
603C24—24no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—81no—
609C24—81no—
610C24—861no—
611C24C2×C22⋊D4311yescharacteristic
612#41—868no—
613#41—1724no—
614#41—1724no—
615#41—1724no—
616C2×Q8—432no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—432no—
638C2×D4—432no—
639C2×D4—432no—
640C2×D4—864no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1722no—
645C2×D4—1722no—
646C2×D4C2×C4×D4312yes—
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—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—861no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—3441no—
667C22×C4—3441no—
668C22×C4—1722no—
669C22×C4—1722no—
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—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C22⋊C4—3441no—
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—22no—
733C23—48no—
734C23—48no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23C4×C22⋊D4312yes—
758C23C22×C22⋊D4311yescharacteristic
759Q8—862no—
760Q8—862no—
761Q8—1721no—
762Q8—1721no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—434no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—1728no—
776D4C22⋊C4×D4314yes—
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—21no—
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—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—862no—
803C2×C4—3444no—
804C2×C4—3444no—
805C2×C4—1728no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4C4×C22⋊D4312yes—
815C2×C4#1306335112yescomplemented
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—22no—
828C22—24no—
829C22—22no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—41no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—864no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22C2×C4×C22⋊D4311yescharacteristic
856C22D4×C22⋊D4311yescharacteristic
857C22D4×C22⋊D4311yescharacteristic
858C22C2×#1306335111yescharacteristic
859C22#1458369711yescharacteristic
860C22#1458370211yescharacteristic
861C22#1458371011yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—81no—
868C4—81no—
869C4—3441no—
870C4—3441no—
871C4—1722no—
872C4C2×C22⋊C4×D4311yescharacteristic
873C4#1458337211yescharacteristic
874C4#1458353911yescharacteristic
875C4#1458353911yescharacteristic
876C2—42no—
877C2—44no—
878C2—82no—
879C2—1724no—
880C2C22⋊C4×C22⋊D4311yescharacteristic
881C2C4×#1306335111yescharacteristic
882C2#1914342711yescharacteristic
883C2#1914607111yescharacteristic
884C2#1914611611yescharacteristic
885C2#1914619111yescharacteristic
886C2#1914620211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063351C2
cosocleC22×C4×C43C24
hypercenterD4×C22⋊C4D43
hypocenterC43#22442
LCSG ▷ C2×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
2. C2×#14583009C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19137426C2semidirect
5. #19135475C2semidirect
6. #19135448C2semidirect
7. #19134946C2semidirect
8. #19134946C2semidirect
9. #19134929C2semidirect
10. #19134929C2semidirect
11. #19134626C2semidirect
12. #19134533C2semidirect
13. #19134526C2semidirect
14. #19134379C2semidirect
15. D4×C22⋊C4×C43C2semidirect
19. C2×#13063351C4semidirect
25. C2×C4×D172C22semidirect
26. C2×C4×D172C22semidirect
29. C2×#13063258C22semidirect
30. C2×#13063256C22semidirect
31. C2×#13063248C22semidirect
32. C2×#13063248C22semidirect
37. C2×#13063245C22semidirect
38. C2×#13063245C22semidirect
40. C2×#13063236C22semidirect
41. C2×C4×C43⋊C8C22semidirect
42. #14582805C22semidirect
43. #14582805C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582654C22semidirect
69. C2×#10621898C2×C4semidirect
81. C2×#10621883C2×C4semidirect
82. C2×#10621883C2×C4semidirect
86. C2×#10621882C2×C4semidirect
91. C2×#10621877C2×C4semidirect
130. C22×D4×C43C2×C4semidirect
259. #10621882C22⋊C4semidirect
350. C2×C4×C43AGL(1,ℤ/8)semidirect
370. D172C2×C22⋊C4semidirect
381. C43⋊C8C2×C22⋊C4semidirect
437. D4×C22⋊C4D43semidirect
507. C43#22442semidirect
524. C22×D4C4×D43semidirect
815. C2×C4#13063351semidirect

Maximal subgroups

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

subgroupindex
C22×#130633512
C2×#145830092
C2×C4×#106218822
#191374262
#191354752
#191354482
#191349462
#191349292
#191346262
#191345332
#191345262
#191343792
D4×C22⋊C4×C432
#2244243