Finite Group Databasebeta

← #25098015

Subgroups — #25098015

Order 11008.

1926 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063349C211yesmaximal, characteristic
2C2×#14583378C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137174C211yesmaximal, characteristic, complemented
6#19134953C211yesmaximal, characteristic, complemented
7#19134951C211yesmaximal, characteristic, complemented
8#19134949C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134941C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C2×#13063349—24no—
19C2×#13063349—24no—
20C2×#13063349C418yescomplemented
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583378—24no—
27#14583378—24no—
28C2×C4×Dic86C2211yescharacteristic, complemented
29C2×#13063290C2211yescharacteristic, complemented
30C2×D4×Dic43C2211yescharacteristic, complemented
31C2×C4×C22⋊D43—21no—
32C2×(C22⋊D43)⋊C4—21no—
33C2×#13063283C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×#13063281—21no—
36C22×Dic43⋊C4—21no—
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582892—24no—
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063248C2211yescharacteristic, complemented
41C2×#13063247C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic, complemented
44C2×#13063245C2211yescharacteristic
45#102×D43—24no—
46#14582802C2211yescharacteristic
47#14582801C2211yescharacteristic
48#14582800C2211yescharacteristic
49#14582799—21no—
50#14582799—21no—
51#14582754—21no—
52#14582754—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59C22×D8×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C43×#390C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C24×D43—21no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900C2×C414yes—
71C2×#10621900D414yes—
72C2×#10621900D414yes—
73C22×Dic86C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—22no—
81C2×D4×D43—22no—
82C2×D4×D43C2×C414yescomplemented
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87#13063349—232no—
88C2×#10621873—22no—
89C2×#10621873—22no—
90C2×#10621873C2×C414yescomplemented
91C2×#10621883—22no—
92C2×#10621883—22no—
93C2×#10621883C2×C414yescomplemented
94C2×#10621882—22no—
95C2×#10621882—22no—
96C2×#10621882C2×C414yescomplemented
97C2×#10621872—22no—
98C2×#10621872—22no—
99C2×#10621872C2×C414yescomplemented
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—22no—
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C4×Dic86—22no—
106C4×Dic86—22no—
107#13063290—22no—
108#13063290—22no—
109D4×Dic43—22no—
110D4×Dic43—22no—
111C4×C22⋊D43—28no—
112(C22⋊D43)⋊C4—28no—
113#13063283—22no—
114#13063283—22no—
115#13063282—22no—
116#13063282—22no—
117#13063281—28no—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—28no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4D411yescharacteristic
125C2×Dic43⋊C4D411yescharacteristic
126C4⋊C4×D43—22no—
127C4⋊C4×D43D414yes—
128C2×C22⋊Dic43—21no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4D411yescharacteristic
137C2×(C2×D43)⋊C4D411yescharacteristic
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43C2311yescharacteristic
142#13063250—22no—
143#13063248—22no—
144#13063247—22no—
145#13063246—22no—
146#13063246—22no—
147#13063245—22no—
148C22×D4×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C2×D8×C43—22no—
152C2×D8×C43—22no—
153C2×D8×C43C2×C414yescomplemented
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C4×D4×C43—22no—
157C4×D4×C43—22no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C42×C43C2311yescharacteristic
164#102×C43—22no—
165#102×C43—22no—
166C24×C43—21no—
167C24×C43—21no—
168C23×D43—21no—
169C23×D43—24no—
170C23×D43—42no—
171C23×D43—42no—
172C23×D43—81no—
173C23×D43—81no—
174C23×D43—81no—
175C23×D43—81no—
176C23×D43C2×D411yescharacteristic
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43C22×C412yes—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43C2×D412yes—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C22×Dic43—24no—
204C22×Dic43—24no—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—81no—
211C22×Dic43—81no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621900—28no—
216#10621900—28no—
217#10621900—28no—
218#10621900C22⋊C4116yescomplemented
219D4×D43—28no—
220D4×D43—28no—
221D4×D43—44no—
222D4×D43—44no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C22×C412yes—
229C2×C4×D43—24no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×C4×D43C22×C412yes—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2×D412yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43#4112yes—
237C2×C4×D43#4112yes—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86C22×C412yes—
242C2×Dic86C2×D412yes—
243C2×Dic86C2×D412yes—
244D8×C43—28no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43C22×C412yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43C2×D412yes—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—81no—
257C22⋊C4×C43—81no—
258C42×C43—21no—
259C42×C43—21no—
260C22⋊Dic43—24no—
261C22⋊Dic43—81no—
262C22⋊Dic43—81no—
263#10621883—28no—
264#10621882—28no—
265(C2×D43)⋊C4—22no—
266(C2×D43)⋊C4—22no—
267(C2×D43)⋊C4—42no—
268(C2×D43)⋊C4—81no—
269(C2×D43)⋊C4—81no—
270(C2×D43)⋊C4—81no—
271(C2×D43)⋊C4—81no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43C2×D412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—22no—
280Dic43⋊C4—22no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43—21no—
284C4×Dic43—21no—
285C4×Dic43—42no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8C22×C412yes—
292#10621873—28no—
293#10621872—28no—
294C8×D43—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43C22×D411yescharacteristic
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—22no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—48no—
322C22×D43—84no—
323C22×D43—84no—
324C22×D43—84no—
325C22×D43—84no—
326C22×D43—84no—
327C22×D43—84no—
328C22×D43C4×D412yes—
329C22×D43#12012yes—
330C22×D43#12112yes—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43C2×C22⋊C414yes—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C22⋊D43—216no—
359C22⋊D43—48no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—216no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—84no—
377C2×Dic43C4×D412yes—
378C2×Dic43#12012yes—
379C2×Dic43#12112yes—
380D172—22no—
381D172—22no—
382D172—41no—
383D172—41no—
384C4×D43—84no—
385C4×D43C2×C22⋊C414yes—
386C4×D43C4×D414yes—
387C4×D43#12114yes—
388C4×D43#12314yes—
389Dic86—22no—
390Dic86—22no—
391Dic86—22no—
392Dic86C2×C22⋊C414yes—
393C8×C43—22no—
394C8×C43—41no—
395C43⋊C8—22no—
396C43⋊C8—41no—
397#20932—431nomaximal, Sylow
398C22×C43—24no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43C2×C4×D411yescharacteristic
413C22×C43C2×#12011yescharacteristic
414C22×C43C2×#12111yescharacteristic
415C22×C43#57611yescharacteristic
416C22×C43#57611yescharacteristic
417C22×C43#57711yescharacteristic
418C22×C43#57711yescharacteristic
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—816no—
429C2×D43—81no—
430C2×D43—81no—
431C2×D43—81no—
432C2×D43—81no—
433C2×D43#38614yes—
434C4×C43—42no—
435C4×C43—41no—
436C4×C43—41no—
437C4×C43—81no—
438C4×C43C22×C22⋊C411yescharacteristic
439C4×C43C2×C4×D411yescharacteristic
440C4×C43C2×#12111yescharacteristic
441C4×C43C2×#12311yescharacteristic
442Dic43—24no—
443Dic43—42no—
444Dic43—41no—
445Dic43—41no—
446Dic43—81no—
447Dic43#38614yes—
448C22×AGL(1,ℤ/8)—431no—
449C2×#520—431no—
450C2×#416—431no—
451C22×#102—431no—
452#2309—431no—
453#1880—431no—
454#1880—431no—
455#1880—431no—
456#1880—431no—
457#1879—431no—
458#1879—431no—
459#1879—431no—
460#1879D4311yescharacteristic, complemented
461#1736—431no—
462#1729—431no—
463C2×C43—44no—
464C2×C43—82no—
465C2×C43C2×#38611yescharacteristic
466C2×C43#294611yescharacteristic
467C2×C43#294611yescharacteristic
468C2×C43#300811yescharacteristic
469C2×C43#301011yescharacteristic
470C2×C43#304511yescharacteristic
471C2×C43#304511yescharacteristic
472D43—24no—
473D43—82no—
474C22×#41—431no—
475C23×D4—431no—
476C2×AGL(1,ℤ/8)—438no—
477C2×AGL(1,ℤ/8)—864no—
478C2×AGL(1,ℤ/8)—864no—
479C22×SD16—431no—
480C22×SD16—431no—
481C22×D8—431no—
482C22×D8C2×D4311yescharacteristic
483C22×M16—431no—
484C23×C8—431no—
485#520—864no—
486#520—864no—
487C2×C4×Q8—431no—
488C2×C4×Q8—431no—
489C2×C4×D4—431no—
490C2×C4×D4—861no—
491C2×C4×D4—861no—
492C2×C4×D4C2×D4311yescharacteristic, complemented
493C2×#117—431no—
494C2×#117—431no—
495C2×#117—861no—
496C22×C4⋊C4—431no—
497C22×C4⋊C4—861no—
498#416—864no—
499C2×#103—431no—
500C2×#103—431no—
501C2×#102—431no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—864no—
506C2×#102C2×D4311yescharacteristic
507C2×#102C2×D4311yescharacteristic, complemented
508#390—431no—
509#390—431no—
510#390—431no—
511#390—861no—
512#390—861no—
513#390C2×D4311yescharacteristic
514#379—861no—
515#379—861no—
516#340—431no—
517#340—431no—
518#340—431no—
519#340C2×D4311yescharacteristic, complemented
520#336—431no—
521#336—431no—
522#336—431no—
523#336C2×D4311yescharacteristic, complemented
524C43#2093211yescharacteristic, complemented, Sylow
525C25—861no—
526C2×#41—434no—
527C2×#41—434no—
528C2×#41—434no—
529C2×#41—862no—
530C2×#41—862no—
531C2×#41—862no—
532C22×Q8—431no—
533C22×D4—434no—
534C22×D4—431no—
535C22×D4—862no—
536C22×D4—862no—
537C22×D4—862no—
538C22×D4—862no—
539C22×D4—862no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4C22×D4311yescharacteristic
543C22×D4C22×D4311yescharacteristic
544C23×C4—21no—
545C23×C4—431no—
546C23×C4—861no—
547C23×C4—861no—
548C23×C4—861no—
549AGL(1,ℤ/8)—8632no—
550C2×SD16—434no—
551C2×SD16—434no—
552C2×SD16—862no—
553C2×SD16—862no—
554C2×SD16—862no—
555C2×SD16—862no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—434no—
559C2×D8—862no—
560C2×D8—862no—
561C2×D8C4×D4314yescomplemented
562C2×M16—434no—
563C2×M16—862no—
564C2×M16—862no—
565C22×C8—431no—
566C22×C8—431no—
567C22×C8—862no—
568C22×C8—862no—
569C22×C8—862no—
570C22×C8C22×D4311yescharacteristic
571C22×C8C22×D4311yescharacteristic
572C4×Q8—862no—
573C4×Q8—862no—
574C4×Q8—862no—
575C4×Q8—862no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—868no—
579C4×D4—862no—
580C4×D4—868no—
581C4×D4—862no—
582#117—862no—
583#117—862no—
584#117—868no—
585#117—862no—
586#117—862no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—434no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—862no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—868no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4C22×D4311yescharacteristic
598C2×C4⋊C4C22×D4311yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—431no—
603C2×C22⋊C4—431no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C42—431no—
613C2×C42—861no—
614C2×C42—861no—
615C2×C42—861no—
616C2×C42C22×D4311yescharacteristic
617#103—862no—
618#103—862no—
619#102—22no—
620#102—22no—
621#102—862no—
622#102—862no—
623#102—862no—
624#102—862no—
625C24—21no—
626C24—21no—
627C24—431no—
628C24—864no—
629C24—861no—
630C24—3441no—
631C24—3441no—
632C24—3441no—
633C24—3441no—
634C24—1722no—
635C24—1722no—
636#41—4316no—
637#41—868no—
638#41—868no—
639#41—868no—
640C2×Q8—432no—
641C2×Q8—432no—
642C2×Q8—432no—
643C2×Q8—861no—
644C2×Q8—861no—
645C2×Q8—861no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—432no—
655C2×D4—868no—
656C2×D4—868no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—1724no—
667C2×D4—1724no—
668C2×D4—1722no—
669C2×D4—1722no—
670C2×D4C2×C4×D4312yes—
671C2×D4C2×C4×D4312yes—
672C2×D4D4×D4312yes—
673C2×D4D4×D4312yes—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—864no—
689C22×C4—864no—
690C22×C4—864no—
691C22×C4—864no—
692C22×C4—861no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—3441no—
697C22×C4—3441no—
698C22×C4—3441no—
699C22×C4—3441no—
700C22×C4D4×D4311yescharacteristic
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4311yescharacteristic
703SD16—868no—
704SD16—868no—
705D8—28no—
706D8—868no—
707M16—868no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—432no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—1724no—
720C2×C8C2×C4×D4312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—432no—
725C4⋊C4—862no—
726C4⋊C4—864no—
727C4⋊C4—862no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4D4×D4312yes—
734C22⋊C4—24no—
735C22⋊C4—81no—
736C22⋊C4—81no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—864no—
740C22⋊C4—3441no—
741C22⋊C4—3441no—
742C22⋊C4—3441no—
743C22⋊C4—3441no—
744C22⋊C4—3441no—
745C22⋊C4—3441no—
746C22⋊C4—1722no—
747C42—21no—
748C42—21no—
749C42—864no—
750C42—864no—
751C42—861no—
752C42—861no—
753C42—1722no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—432no—
769C23—432no—
770C23—432no—
771C23—861no—
772C23—861no—
773C23—861no—
774C23—861no—
775C23—862no—
776C23—3444no—
777C23—3444no—
778C23—3444no—
779C23—3444no—
780C23—3444no—
781C23—3444no—
782C23—1728no—
783C23—1721no—
784C23—1721no—
785C23—1721no—
786C23—1721no—
787C23—1721no—
788C23—1721no—
789C23C2×D4×D4311yescharacteristic
790Q8—434no—
791Q8—862no—
792Q8—862no—
793Q8—862no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—8616no—
802D4—862no—
803D4—862no—
804D4—1728no—
805D4—1721no—
806D4—1721no—
807D4C22⋊C4×D4314yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—432no—
822C2×C4—432no—
823C2×C4—432no—
824C2×C4—434no—
825C2×C4—434no—
826C2×C4—434no—
827C2×C4—434no—
828C2×C4—8616no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—861no—
833C2×C4—862no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—861no—
839C2×C4—3444no—
840C2×C4—3444no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4C22×C4×D4311yescharacteristic
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4C2×D4×D4311yescharacteristic
849C2×C4C2×D4×D4311yescharacteristic
850C2×C4#41×D4311yescharacteristic
851C2×C4#41×D4311yescharacteristic
852C8—22no—
853C8—41no—
854C8—862no—
855C8—1721no—
856C22—24no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—434no—
871C22—862no—
872C22—862no—
873C22—862no—
874C22—862no—
875C22—862no—
876C22—862no—
877C22—34416no—
878C22—3441no—
879C22—3441no—
880C22—3441no—
881C22—3441no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22C4×D4×D4311yescharacteristic
886C22#120×D4311yescharacteristic
887C22#121×D4311yescharacteristic
888C22#1458370011yescharacteristic
889C22#1458370311yescharacteristic
890C22#1458370611yescharacteristic
891C22#1458370911yescharacteristic
892C4—41no—
893C4—42no—
894C4—41no—
895C4—81no—
896C4—434no—
897C4—864no—
898C4—3441no—
899C4—1721no—
900C4—1722no—
901C4—1721no—
902C4C2×C22⋊C4×D4311yescharacteristic
903C4C4×D4×D4311yescharacteristic
904C4#121×D4311yescharacteristic
905C4#123×D4311yescharacteristic
906C2—44no—
907C2—82no—
908C2—864no—
909C2—3442no—
910C2#386×D4311yescharacteristic
911C2#1914342011yescharacteristic
912C2#1914342411yescharacteristic
913C2#1914385811yescharacteristic
914C2#1914387811yescharacteristic
915C2#1914412911yescharacteristic
916C2#1914413511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×#13063349C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#20932
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#14583378C2semidirect
3. C2×#14582892C2semidirect
4. C2×#102×D43C2semidirect
5. #19137174C2semidirect
6. #19134953C2semidirect
7. #19134951C2semidirect
8. #19134949C2semidirect
9. #19134947C2semidirect
10. #19134945C2semidirect
11. #19134943C2semidirect
12. #19134941C2semidirect
13. #19134313C2semidirect
14. #19134290C2semidirect
15. C43×#1879C2semidirect
20. C2×#13063349C4semidirect
28. C2×C4×Dic86C22semidirect
29. C2×#13063290C22semidirect
30. C2×D4×Dic43C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063248C22semidirect
43. C2×#13063246C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582654C22semidirect
57. #14582653C22semidirect
58. #14582653C22semidirect
60. C2×C4×D4×C43C22semidirect
62. C2×#102×C43C22semidirect
64. C43×#340C22semidirect
65. C43×#336C22semidirect
82. C2×D4×D43C2×C4semidirect
90. C2×#10621873C2×C4semidirect
93. C2×#10621883C2×C4semidirect
96. C2×#10621882C2×C4semidirect
99. C2×#10621872C2×C4semidirect
153. C2×D8×C43C2×C4semidirect
218. #10621900C22⋊C4semidirect
460. #1879D43semidirect
492. C2×C4×D4C2×D43semidirect
507. C2×#102C2×D43semidirect
519. #340C2×D43semidirect
523. #336C2×D43semidirect
524. C43#20932semidirect
561. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633492
C2×#145833782
C2×#145828922
C2×#102×D432
#191371742
#191349532
#191349512
#191349492
#191349472
#191349452
#191349432
#191349412
#191343132
#191342902
C43×#18792
#2093243