Finite Group Databasebeta

← #25112356

Subgroups — #25112356

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×#13063349C211yesmaximal, characteristic
2C2×D8×Dic43C211yesmaximal, characteristic, complemented
3#19137420C211yesmaximal, characteristic, complemented
4D4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19135476C211yesmaximal, characteristic, complemented
6#19135447C211yesmaximal, characteristic, complemented
7#19134943C211yesmaximal, characteristic, complemented
8#19134941C211yesmaximal, characteristic, complemented
9#19134929C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134625C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C2×C43×#442C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C2×#13063349—24no—
19C2×#13063349—24no—
20C2×#13063349C418yescomplemented
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic, complemented
27C22×(C2×D43)⋊C4—21no—
28D8×Dic43—24no—
29C2×#13063259C2211yescharacteristic, complemented
30C2×#13063250C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063245C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic, complemented
38#14582805C2211yescharacteristic, complemented
39#14582804C2211yescharacteristic, complemented
40#14582801C2211yescharacteristic
41#14582800C2211yescharacteristic
42#14582778—21no—
43#14582778—21no—
44#14582776—21no—
45#14582776—21no—
46#14582760—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582754—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C2×C43⋊#95—21no—
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582654C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C22×D8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic, complemented
59C43×#442—24no—
60C2×#106×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C2×#97×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—41no—
69C2×#10621900—41no—
70C2×#10621900C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C2×D4×D43—22no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—41no—
79C2×D4×D43—41no—
80C2×D4×D43C2×C414yescomplemented
81C23×Dic43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063349—232no—
86C2×#10621873—22no—
87C2×#10621873—22no—
88C2×#10621873C2×C414yescomplemented
89C2×#10621883—22no—
90C2×#10621883—22no—
91C2×#10621883C2×C414yescomplemented
92C2×#10621882—22no—
93C2×#10621882—22no—
94C2×#10621882C2×C414yescomplemented
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872C2×C414yescomplemented
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100D4×Dic43—22no—
101D4×Dic43—22no—
102D4×Dic43—41no—
103D4×Dic43—41no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—44no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118#13063259—22no—
119#13063250—41no—
120#13063248—41no—
121#13063247—41no—
122#13063246—22no—
123#13063246—22no—
124#13063245—41no—
125(C2×D43)⋊C8—22no—
126C8×Dic43—22no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95D411yescharacteristic
134C43⋊#95D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C2×D8×C43C2×C414yes—
140C2×D8×C43D414yes—
141C2×D8×C43D414yes—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C4×D4×C43—22no—
145C4×D4×C43—22no—
146C4×D4×C43—41no—
147C4×D4×C43—41no—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C42×C43C2311yescharacteristic
153#106×C43—22no—
154#102×C43—22no—
155#102×C43—22no—
156#97×C43—22no—
157C24×C43—21no—
158C24×C43—21no—
159C23×D43—21no—
160C23×D43—24no—
161C23×D43—42no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—81no—
166C23×D43—81no—
167C23×D43C2×D411yescharacteristic
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C22×C412yes—
176C2×D4×C43C2×D412yes—
177C2×D4×C43C2×D412yes—
178C2×D4×C43C2×D412yes—
179C2×D4×C43C2×D412yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—81no—
187C22×C4×C43—81no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C22×Dic43—24no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212#10621900—28no—
213#10621900—44no—
214#10621900—44no—
215#10621900—44no—
216D4×D43—28no—
217D4×D43—44no—
218D4×D43—44no—
219D4×D43—44no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C22×C412yes—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43C22×C412yes—
231C2×C4×D43#4112yes—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22×C412yes—
238D8×C43C22⋊C4116yescomplemented
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43C22×C412yes—
243C2×C8×C43C2×D412yes—
244C2×C8×C43C2×D412yes—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C42×C43—21no—
252C42×C43—21no—
253C22⋊Dic43—42no—
254C22⋊Dic43—42no—
255#10621883—28no—
256#10621882—28no—
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—41no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—81no—
263(C2×D43)⋊C4—81no—
264(C2×D43)⋊C4—81no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8C22×C412yes—
277#10621873—28no—
278#10621872—28no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43C22×D411yescharacteristic
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—48no—
302C22×D43—48no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43C4×D412yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43C2×C22⋊C414yes—
322D4×C43C2×C22⋊C414yescomplemented
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—48no—
344C22⋊D43—48no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—48no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—84no—
363C2×Dic43—84no—
364C2×Dic43C4×D412yes—
365C2×Dic43AGL(1,ℤ/8)12yescomplemented
366D172—22no—
367D172—22no—
368D172—41no—
369D172—41no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374Dic86—22no—
375Dic86—22no—
376Dic86—41no—
377Dic86—41no—
378C8×C43—41no—
379C8×C43C2×C22⋊C414yescomplemented
380C43⋊C8—22no—
381C43⋊C8—41no—
382#22442—431nomaximal, Sylow
383C22×C43—24no—
384C22×C43—24no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
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—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
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—41no—
420C4×C43—41no—
421C4×C43—81no—
422C4×C43—81no—
423C4×C43C22×C22⋊C411yescharacteristic
424C4×C43#51811yescharacteristic
425C4×C43#54611yescharacteristic
426C4×C43#54611yescharacteristic
427Dic43—22no—
428Dic43—22no—
429Dic43—42no—
430Dic43—41no—
431Dic43—81no—
432Dic43—81no—
433C22×AGL(1,ℤ/8)—431no—
434C2×#442D4311yescharacteristic, complemented
435C2×C4×D8—431no—
436#2339—431no—
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—44no—
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—42no—
458D43—82no—
459C22×#41—431no—
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×D8C2×D4311yescharacteristic
468C22×M16—431no—
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C2×C4×D4C2×D4311yescharacteristic
472C2×C4×D4C2×D4311yescharacteristic, complemented
473C22×C22⋊C4—861no—
474#442—24no—
475C4×D8—864no—
476C2×#107—431no—
477C2×#106C2×D4311yescharacteristic, complemented
478C2×#103—431no—
479C2×#103—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102C2×D4311yescharacteristic
485C2×#102C2×D4311yescharacteristic, complemented
486C2×C22⋊C8—431no—
487C2×#97C2×D4311yescharacteristic, complemented
488C2×C4×C8—431no—
489#391—431no—
490#391—431no—
491#390—431no—
492#390—431no—
493#386—861no—
494#386—861no—
495#386—861no—
496#386—861no—
497#381—861no—
498#380—431no—
499#380—431no—
500#379—861no—
501C4×C22⋊C4—431no—
502C2×#95—861no—
503#340—431no—
504#340—431no—
505#336—431no—
506#336—431no—
507C43#2244211yescharacteristic, complemented, Sylow
508C25—861no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C22×Q8—431no—
516C22×D4—434no—
517C22×D4—431no—
518C22×D4—862no—
519C22×D4—861no—
520C22×D4—862no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4—1721no—
524C22×D4—1721no—
525C22×D4C22×D4311yescharacteristic
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—431no—
530C23×C4—861no—
531C23×C4—861no—
532C23×C4—861no—
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—862no—
542C2×D8—862no—
543C2×D8C4×D4314yes—
544C2×D8D17214yes—
545C2×D8C22⋊D4314yes—
546C2×M16—434no—
547C2×M16—862no—
548C2×M16—862no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8C22×D4311yescharacteristic
552C22×C8C22×D4311yescharacteristic
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—431no—
568C2×C22⋊C4—431no—
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—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—1724no—
578C2×C42—431no—
579C2×C42C22×D4311yescharacteristic
580#107—862no—
581#106—22no—
582#103—1721no—
583#103—1721no—
584#102—22no—
585#102—22no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590C22⋊C8—862no—
591#97—22no—
592C4×C8—862no—
593#95—431no—
594#95—431no—
595#95—861no—
596#95—861no—
597#95—861no—
598#95—861no—
599#95—861no—
600#95—861no—
601C24—21no—
602C24—21no—
603C24—431no—
604C24—864no—
605C24—861no—
606C24—3441no—
607C24—3441no—
608C24—1722no—
609C24—1722no—
610C24—1722no—
611C24—1722no—
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—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—432no—
629C2×D4—864no—
630C2×D4—868no—
631C2×D4—864no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—1724no—
638C2×D4—1724no—
639C2×D4—1724no—
640C2×D4—1722no—
641C2×D4—1722no—
642C2×D4—1722no—
643C2×D4—1722no—
644C2×D4C2×C4×D4312yes—
645C2×D4C2×C4×D4312yes—
646C2×D4C2×D17212yes—
647C2×D4C2×D17212yes—
648C2×D4C2×C22⋊D4312yes—
649C2×D4C2×C22⋊D4312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—431no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—3441no—
672C22×C4—3441no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4—1722no—
679C22×C4D4×D4311yescharacteristic
680C22×C4D4×D4311yescharacteristic
681C22×C4C23×D4311yescharacteristic
682SD16—868no—
683SD16—868no—
684D8—868no—
685D8(C2×D43)⋊C4116yescomplemented
686M16—868no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—432no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8C2×C4×D4312yes—
697C2×C8C2×D17212yes—
698C2×C8C2×C22⋊D4312yes—
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—42no—
708C22⋊C4—42no—
709C22⋊C4—862no—
710C22⋊C4—3441no—
711C22⋊C4—3441no—
712C22⋊C4—3441no—
713C22⋊C4—1721no—
714C22⋊C4—1722no—
715C22⋊C4—1722no—
716C22⋊C4—1722no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C42—21no—
720C42—21no—
721C42—861no—
722C42—861no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—432no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—862no—
745C23—3444no—
746C23—3444no—
747C23—3444no—
748C23—3444no—
749C23—3444no—
750C23—1728no—
751C23—1728no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23C2×D4×D4311yescharacteristic
759Q8—862no—
760Q8—862no—
761Q8—1721no—
762Q8—1721no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—862no—
770D4—862no—
771D4—1728no—
772D4—1728no—
773D4—1721no—
774D4—1721no—
775D4C2×(C2×D43)⋊C414yes—
776D4C2×(C2×D43)⋊C414yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—432no—
792C2×C4—432no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—3444no—
806C2×C4—3444no—
807C2×C4—1728no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4C22×C4×D4311yescharacteristic
817C2×C4C22×C22⋊D4311yescharacteristic
818C2×C4C22×D17211yescharacteristic
819C2×C4#41×D4311yescharacteristic
820C2×C4#1306337011yescharacteristic
821C2×C4#1306337111yescharacteristic
822C8—41no—
823C8—862no—
824C8—1721no—
825C8C2×(C2×D43)⋊C414yescomplemented
826C22—24no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—862no—
841C22—862no—
842C22—862no—
843C22—34416no—
844C22—3441no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1721no—
852C22—1721no—
853C22—1721no—
854C22—1721no—
855C22C4×D4×D4311yescharacteristic
856C22D4×C22⋊D4311yescharacteristic
857C22D4×D17211yescharacteristic
858C22AGL(1,ℤ/8)×D4311yescharacteristic
859C22#1458369511yescharacteristic
860C22#1458370311yescharacteristic
861C22#1458370911yescharacteristic
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—862no—
867C4—862no—
868C4—3441no—
869C4—3441no—
870C4—1722no—
871C4—1721no—
872C4C22×(C2×D43)⋊C411yescharacteristic
873C4#1458337111yescharacteristic
874C4#1458353711yescharacteristic
875C4#1458354411yescharacteristic
876C2—44no—
877C2—44no—
878C2—3442no—
879C2—1722no—
880C2D4×(C2×D43)⋊C411yescharacteristic
881C2#1914340611yescharacteristic
882C2#1914342411yescharacteristic
883C2#1914607711yescharacteristic
884C2#1914612211yescharacteristic
885C2#1914618911yescharacteristic
886C2#1914620011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC22×#13063349C2
cosocleC22×C4×C43C24
hypercenterC2×#442D43
hypocenterC43#22442
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic43C2semidirect
3. #19137420C2semidirect
4. D4×(C2×D43)⋊C4C2semidirect
5. #19135476C2semidirect
6. #19135447C2semidirect
7. #19134943C2semidirect
8. #19134941C2semidirect
9. #19134929C2semidirect
10. #19134927C2semidirect
11. #19134625C2semidirect
12. #19134532C2semidirect
13. #19134524C2semidirect
14. #19134380C2semidirect
15. C2×C43×#442C2semidirect
20. C2×#13063349C4semidirect
26. C2×D4×Dic43C22semidirect
29. C2×#13063259C22semidirect
30. C2×#13063250C22semidirect
31. C2×#13063248C22semidirect
34. C2×#13063246C22semidirect
37. C2×C8×Dic43C22semidirect
38. #14582805C22semidirect
39. #14582804C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582654C22semidirect
55. #14582653C22semidirect
58. C2×C4×D4×C43C22semidirect
60. C2×#106×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×#97×C43C22semidirect
70. C2×#10621900C2×C4semidirect
80. C2×D4×D43C2×C4semidirect
88. C2×#10621873C2×C4semidirect
91. C2×#10621883C2×C4semidirect
94. C2×#10621882C2×C4semidirect
97. C2×#10621872C2×C4semidirect
238. D8×C43C22⋊C4semidirect
322. D4×C43C2×C22⋊C4semidirect
365. C2×Dic43AGL(1,ℤ/8)semidirect
379. C8×C43C2×C22⋊C4semidirect
434. C2×#442D43semidirect
472. C2×C4×D4C2×D43semidirect
477. C2×#106C2×D43semidirect
485. C2×#102C2×D43semidirect
487. C2×#97C2×D43semidirect
507. C43#22442semidirect
685. D8(C2×D43)⋊C4semidirect
776. D4C2×(C2×D43)⋊C4semidirect
825. C8C2×(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633492
C2×D8×Dic432
#191374202
D4×(C2×D43)⋊C42
#191354762
#191354472
#191349432
#191349412
#191349292
#191349272
#191346252
#191345322
#191345242
#191343802
C2×C43×#4422
#2244243