Finite Group Databasebeta

← C2×#19144131 #25963519

Subgroups — C2×#19144131 #25963519

Order 11008.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic, complemented
2C22×#13063346C211yesmaximal, characteristic, complemented
3C2×#14583462C211yesmaximal, characteristic, complemented
4C2×#14583381C211yesmaximal, characteristic, complemented
5#19144131C2116yesmaximal, direct product factor
6C2×#14583121C211yesmaximal, characteristic, complemented
7C2×#14583119C211yesmaximal, characteristic, complemented
8C2×#14583097C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583113C211yesmaximal, characteristic, complemented
11C2×#14583093C211yesmaximal, characteristic, complemented
12C2×#14583091C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#460C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C2×#13063352—28no—
21C2×#13063352C2218yescomplemented
22C2×#13063346—28no—
23C2×#13063346C2218yescomplemented
24C22×#10621885C2211yescharacteristic, complemented
25C22×#10621873C2211yescharacteristic, complemented
26C22×#10621884C2211yescharacteristic
27C22×D344C2211yescharacteristic
28C22×#10621882C2211yescharacteristic
29C22×#10621882C2211yescharacteristic, complemented
30C22×#10621872C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583462—24no—
33#14583462C2218yescomplemented
34C2×#13063321C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063312C2211yescharacteristic
37C2×#13063297—21no—
38C2×#13063297—21no—
39C2×#13063293—21no—
40C2×#13063293—21no—
41#14583381—24no—
42#14583381C2218yescomplemented
43C2×Q8×Dic43C2211yescharacteristic, complemented
44C2×C4×D172—21no—
45C2×C4×D172C2211yescharacteristic, complemented
46C2×#13063287—21no—
47C2×#13063287C2211yescharacteristic, complemented
48C2×#13063282—21no—
49C2×#13063282C2211yescharacteristic
50C2×C4⋊C4×D43—21no—
51C2×C4⋊C4×D43C2211yescharacteristic
52#14583121C2218yescomplemented
53#14583119C2218yescomplemented
54#14583115C2218yescomplemented
55#14583113C2218yescomplemented
56#14583097C2218yescomplemented
57#14583093C2218yescomplemented
58#14583091C2218yescomplemented
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
61C2×Dic43⋊C8C2211yescharacteristic, complemented
62C2×Dic43⋊C8C2211yescharacteristic, complemented
63#14582897C2218yescomplemented
64C2×#13063250C2211yescharacteristic, complemented
65C2×#13063248C2211yescharacteristic, complemented
66C2×#13063247C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063246C2211yescharacteristic, complemented
69C2×#13063245C2211yescharacteristic
70#102×D43C2218yescomplemented
71C22×SD16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic, complemented
73C2×#127×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic, complemented
75C43×#460C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic, complemented
77C2×#102×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902D418yescomplemented
83C2×#10621902C2314yes—
84C2×#10621900—24no—
85C2×#10621900—22no—
86C2×#10621900—24no—
87C2×#10621900C2314yes—
88C22×Dic86C2311yescharacteristic
89C22×D172—21no—
90C22×D172C2311yescharacteristic
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C2×D4×D43—24no—
97C2×D4×D43—22no—
98C2×D4×D43—24no—
99C2×D4×D43C2314yes—
100C23×Dic43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106#13063352—232no—
107#13063346—232no—
108C2×#10621885—24no—
109C2×#10621885C2314yescomplemented
110C2×#10621873—24no—
111C2×#10621873C2314yescomplemented
112C2×#10621884—24no—
113C2×#10621884C2314yes—
114C2×D344—24no—
115C2×D344C2314yes—
116C2×#10621882—24no—
117C2×#10621882—24no—
118C2×#10621882C2314yes—
119C2×#10621882C2314yescomplemented
120C2×#10621872—24no—
121C2×#10621872C2314yes—
122C22×C43⋊C8C2311yescharacteristic
123C22×C43⋊C8C2311yescharacteristic
124C2×C8×D43—24no—
125C2×C8×D43C2314yes—
126#13063321—22no—
127#13063321C2314yes—
128#13063313—22no—
129#13063313C2314yes—
130#13063312—22no—
131#13063312C2314yes—
132#13063297—28no—
133#13063297—28no—
134#13063293—28no—
135#13063293—28no—
136Q8×Dic43—22no—
137Q8×Dic43C2314yescomplemented
138C4×D172—22no—
139C4×D172—28no—
140C4×D172C2314yescomplemented
141#13063287—28no—
142#13063287—22no—
143#13063287C2314yescomplemented
144#13063282—28no—
145#13063282D414yes—
146#13063282C2314yes—
147C2×C4⋊Dic43—21no—
148C2×C4⋊Dic43C2311yescharacteristic
149C2×Dic43⋊C4—21no—
150C2×Dic43⋊C4D411yescharacteristic
151C2×Dic43⋊C4D411yescharacteristic
152C4⋊C4×D43—22no—
153C4⋊C4×D43—28no—
154C4⋊C4×D43C2314yes—
155C2×C22⋊Dic43—21no—
156C2×C22⋊Dic43—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4D411yescharacteristic
162C2×(C2×D43)⋊C4D411yescharacteristic
163C2×C4×Dic43—21no—
164C2×C4×Dic43C2311yescharacteristic
165C4⋊(C43⋊C8)C2314yescomplemented
166Dic43⋊C8C2314yescomplemented
167Dic43⋊C8C2314yescomplemented
168#13063250C2314yescomplemented
169#13063248C2314yescomplemented
170#13063247C2314yes—
171#13063246C2314yes—
172#13063246C2314yescomplemented
173#13063245C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×D4×C43—21no—
176C22×D4×C43—21no—
177C22×D4×C43C2311yescharacteristic
178C22×D4×C43C2311yescharacteristic
179C2×SD16×C43—24no—
180C2×SD16×C43—24no—
181C2×SD16×C43C2314yes—
182C2×SD16×C43C2314yescomplemented
183C22×C8×C43C2311yescharacteristic
184C22×C8×C43C2311yescharacteristic
185#127×C43—22no—
186#127×C43C2314yes—
187C4×Q8×C43—22no—
188C4×Q8×C43C2314yescomplemented
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yescomplemented
194#102×C43C2314yes—
195#102×C43C2314yescomplemented
196C24×C43—21no—
197C24×C43—21no—
198C23×D43—21no—
199C23×D43—21no—
200C23×D43—24no—
201C23×D43—44no—
202C23×D43—82no—
203C23×D43—82no—
204C23×D43C2×D411yescharacteristic
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43C2×D414yes—
208C2×Q8×C43C2412yes—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—24no—
212C2×D4×C43—24no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43—22no—
216C2×D4×C43—22no—
217C2×D4×C43—82no—
218C2×D4×C43—82no—
219C2×D4×C43C2412yes—
220C2×D4×C43C2412yes—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
232C2×C22⋊D43—82no—
233C2×C22⋊D43—82no—
234C22×Dic43—24no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—44no—
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241#10621902—216no—
242#10621902—28no—
243#10621902C2×D4116yescomplemented
244#10621900—28no—
245#10621900—28no—
246#10621900—48no—
247D4×D43—28no—
248D4×D43—28no—
249D4×D43—48no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—21no—
253C2×D172—28no—
254C2×D172—24no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172C2×D414yes—
258C2×D172C2412yes—
259C2×D172C2412yes—
260C2×C4×D43—28no—
261C2×C4×D43—24no—
262C2×C4×D43—24no—
263C2×C4×D43—24no—
264C2×C4×D43—24no—
265C2×C4×D43—82no—
266C2×C4×D43—82no—
267C2×C4×D43—82no—
268C2×C4×D43C2×D414yes—
269C2×C4×D43C2×D412yes—
270C2×C4×D43#4114yes—
271C2×C4×D43C2412yes—
272C2×Dic86—22no—
273C2×Dic86—22no—
274C2×Dic86—21no—
275C2×Dic86C2412yes—
276SD16×C43—28no—
277SD16×C43—28no—
278C2×C8×C43—22no—
279C2×C8×C43—22no—
280C2×C8×C43C2412yes—
281C2×C8×C43C2412yes—
282C4⋊C4×C43—24no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C2412yes—
285C42×C43—24no—
286C42×C43C2×D412yes—
287C42×C43C2412yes—
288C22⋊Dic43—24no—
289C22⋊Dic43—24no—
290#10621885—28no—
291#10621884—28no—
292#10621882—28no—
293#10621882—28no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4C2×D414yes—
299(C2×D43)⋊C4C2×D414yes—
300C4⋊Dic43—21no—
301C4⋊Dic43—24no—
302C4⋊Dic43C2412yes—
303Dic43⋊C4—24no—
304Dic43⋊C4C2×D414yes—
305Dic43⋊C4C2×D414yes—
306C4×Dic43—24no—
307C4×Dic43C2×D412yes—
308C4×Dic43C2412yes—
309C2×C43⋊C8—22no—
310C2×C43⋊C8—22no—
311C2×C43⋊C8C2412yes—
312C2×C43⋊C8C2412yes—
313D344—28no—
314#10621873—28no—
315#10621872—28no—
316C8×D43—28no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—42no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43—42no—
323C23×C43—42no—
324C23×C43—42no—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—24no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—42no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43—48no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—816no—
340C22×D43#12114yes—
341C22×D43C22×D412yes—
342Q8×C43—24no—
343Q8×C43—22no—
344Q8×C43C22×D414yes—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—42no—
350D4×C43—42no—
351D4×C43—84no—
352D4×C43—84no—
353C2×C4×C43—24no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—42no—
359C2×C4×C43C22×D412yes—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D412yes—
363C2×C4×C43C2×#4112yes—
364C2×C4×C43C2511yescharacteristic
365C22⋊D43—48no—
366C22⋊D43—48no—
367C22⋊D43—84no—
368C22⋊D43—84no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375C2×Dic43—48no—
376C2×Dic43#12114yes—
377C2×Dic43C22×D412yes—
378C2×Dic43C22×D412yes—
379C2×Dic43C22×D412yes—
380D172—216no—
381D172—24no—
382D172—22no—
383D172—22no—
384D172—22no—
385D172—42no—
386D172C22×D414yes—
387C4×D43—216no—
388C4×D43—84no—
389C4×D43—84no—
390C4×D43—84no—
391C4×D43#12118yes—
392C4×D43C22×D414yes—
393C4×D43C2×#4114yes—
394Dic86—22no—
395Dic86—22no—
396Dic86—42no—
397C8×C43—22no—
398C8×C43—22no—
399C43⋊C8—22no—
400C43⋊C8—22no—
401C2×#3045—431nomaximal, Sylow
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—84no—
409C22×C43—84no—
410C22×C43C2×#12112yes—
411C22×C43#57612yes—
412C22×C43#57712yes—
413C22×C43C23×D411yescharacteristic
414C2×D43—28no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—24no—
418C2×D43—48no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—816no—
425C2×D43—84no—
426C2×D43C2×#12114yes—
427C4×C43—24no—
428C4×C43—22no—
429C4×C43—22no—
430C4×C43—42no—
431C4×C43C2×#12112yes—
432C4×C43C23×D411yescharacteristic
433C4×C43C22×#4111yescharacteristic
434Dic43—22no—
435Dic43—22no—
436Dic43—42no—
437Dic43—42no—
438Dic43C2×#12114yes—
439C22×AGL(1,ℤ/8)—431no—
440C22×#135—431no—
441C2×#535—431no—
442C2×#520—431no—
443#3045—4316no—
444C2×#464—431no—
445C2×#464—431no—
446C2×#460—431no—
447C2×#460D4311yescharacteristic, complemented
448C2×#463—431no—
449C2×#463—431no—
450C2×#459—431no—
451C2×#459—431no—
452C2×#424—431no—
453C2×#417—431no—
454C22×#102—431no—
455C2×C43—82no—
456C2×C43—82no—
457C2×C43#304514yescomplemented
458C2×C43C22×#12111yescharacteristic
459C2×C43C2×#57611yescharacteristic
460C2×C43C2×#57711yescharacteristic
461D43—24no—
462D43—44no—
463D43—82no—
464C22×#41—431no—
465C22×#41—431no—
466C23×D4—431no—
467C2×AGL(1,ℤ/8)—438no—
468C2×AGL(1,ℤ/8)—868no—
469C2×#135—438no—
470C2×#135—868no—
471C22×Q16—431no—
472C22×SD16—431no—
473C22×SD16—431no—
474C22×SD16C2×D4311yescharacteristic
475C22×SD16C2×D4311yescharacteristic, complemented
476C22×D8—431no—
477C22×D8—431no—
478C22×D8—431no—
479C22×M16—431no—
480C23×C8—431no—
481#535—438no—
482#535—864no—
483C2×#127—431no—
484C2×#127C2×D4311yescharacteristic
485C2×#124—431no—
486C2×#124—431no—
487C2×#121—861no—
488C2×#121—861no—
489C2×#120—861no—
490C2×#120—861no—
491#520—438no—
492#520—864no—
493C2×C4×Q8—431no—
494C2×C4×Q8C2×D4311yescharacteristic, complemented
495C2×C4×D4—431no—
496C2×C4×D4—431no—
497C2×C4×D4—861no—
498C2×C4×D4—861no—
499C2×#117—431no—
500C2×#117—861no—
501C22×C4⋊C4—431no—
502C22×C4⋊C4—861no—
503#464—438no—
504#464—438no—
505#463—438no—
506#463—438no—
507#460—438no—
508#460C2×D4318yescomplemented
509#459—438no—
510#459—438no—
511#424—438no—
512C2×C4⋊C8—431no—
513C2×C4⋊C8—431no—
514C2×C4⋊C8—431no—
515C2×C4⋊C8C2×D4311yescharacteristic, complemented
516#417—438no—
517C2×#103—431no—
518C2×#103—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—438no—
524C2×#102C2×D4311yescharacteristic
525C2×#102C2×D4311yescharacteristic, complemented
526C43C2×#304511yescharacteristic, complemented, Sylow
527C25—861no—
528C2×#41—438no—
529C2×#41—434no—
530C2×#41—434no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—864no—
534C2×#41—864no—
535C2×#41—864no—
536C22×Q8—431no—
537C22×Q8C22×D4311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—434no—
541C22×D4—431no—
542C22×D4—431no—
543C22×D4—861no—
544C22×D4—864no—
545C22×D4—864no—
546C22×D4—862no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4—861no—
550C22×D4—861no—
551C22×D4C22×D4311yescharacteristic
552C22×D4C22×D4311yescharacteristic
553C23×C4—431no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4—861no—
557C23×C4—861no—
558C23×C4—861no—
559AGL(1,ℤ/8)—8632no—
560#135—8632no—
561C2×Q16—434no—
562C2×Q16—864no—
563C2×SD16—24no—
564C2×SD16—24no—
565C2×SD16—434no—
566C2×SD16—434no—
567C2×SD16—864no—
568C2×SD16—864no—
569C2×SD16C22×D4314yes—
570C2×SD16C22×D4314yescomplemented
571C2×D8—434no—
572C2×D8—434no—
573C2×D8—434no—
574C2×D8—864no—
575C2×D8—864no—
576C2×D8—864no—
577C2×M16—434no—
578C2×M16—864no—
579C22×C8—431no—
580C22×C8—431no—
581C22×C8—434no—
582C22×C8—864no—
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585#127—22no—
586#127—434no—
587#127—862no—
588#127C22×D4314yes—
589#124—434no—
590#124—434no—
591#124—862no—
592#124—862no—
593#121—868no—
594#121—868no—
595#120—868no—
596#120—868no—
597C4×Q8—22no—
598C4×Q8—434no—
599C4×Q8—862no—
600C4×Q8C22×D4314yescomplemented
601C4×D4—434no—
602C4×D4—434no—
603C4×D4—868no—
604C4×D4—862no—
605C4×D4—868no—
606C4×D4—862no—
607#117—434no—
608#117—434no—
609#117—868no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—868no—
616C2×C4⋊C4—862no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4C22×D4311yescharacteristic
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C42—21no—
629C2×C42—431no—
630C2×C42—861no—
631C2×C42C22×D4311yescharacteristic
632C4⋊C8—434no—
633C4⋊C8—434no—
634C4⋊C8—434no—
635C4⋊C8C22×D4314yescomplemented
636#103—434no—
637#103—434no—
638#102—434no—
639#102—434no—
640#102—434no—
641#102—434no—
642#102C22×D4314yes—
643#102C22×D4314yescomplemented
644C24—21no—
645C24—21no—
646C24—431no—
647C24—864no—
648C24—861no—
649C24—861no—
650C24—3442no—
651C24—3442no—
652C24—1724no—
653#41—4316no—
654#41—8616no—
655#41—868no—
656#41—868no—
657#41—868no—
658#41—1728no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—432no—
662C2×Q8—861no—
663C2×Q8—862no—
664C2×Q8—862no—
665C2×Q8D4×D4314yes—
666C2×Q8C23×D4312yes—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—434no—
678C2×D4—432no—
679C2×D4—432no—
680C2×D4—864no—
681C2×D4—868no—
682C2×D4—868no—
683C2×D4—868no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—864no—
688C2×D4—861no—
689C2×D4—862no—
690C2×D4—861no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—3442no—
694C2×D4—3442no—
695C2×D4—1728no—
696C2×D4—1724no—
697C2×D4—1724no—
698C2×D4C23×D4312yes—
699C2×D4C23×D4312yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—431no—
703C22×C4—432no—
704C22×C4—434no—
705C22×C4—434no—
706C22×C4—432no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—864no—
710C22×C4—868no—
711C22×C4—864no—
712C22×C4—864no—
713C22×C4—864no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—864no—
717C22×C4—3442no—
718C22×C4—3442no—
719C22×C4—3442no—
720C22×C4—1724no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724Q16—868no—
725SD16—28no—
726SD16—28no—
727SD16—868no—
728SD16—868no—
729D8—868no—
730D8—868no—
731D8—868no—
732M16—868no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—432no—
736C2×C8—432no—
737C2×C8—868no—
738C2×C8—862no—
739C2×C8—862no—
740C2×C8C23×D4312yes—
741C2×C8C23×D4312yes—
742C4⋊C4—24no—
743C4⋊C4—21no—
744C4⋊C4—434no—
745C4⋊C4—434no—
746C4⋊C4—432no—
747C4⋊C4—864no—
748C4⋊C4—864no—
749C4⋊C4—861no—
750C4⋊C4C23×D4312yes—
751C22⋊C4—434no—
752C22⋊C4—434no—
753C22⋊C4—864no—
754C22⋊C4—864no—
755C22⋊C4—864no—
756C22⋊C4—864no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C42—24no—
760C42—432no—
761C42—432no—
762C42—864no—
763C42D4×D4312yes—
764C42C23×D4312yes—
765C23—22no—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—434no—
774C23—432no—
775C23—862no—
776C23—862no—
777C23—864no—
778C23—862no—
779C23—862no—
780C23—3444no—
781C23—3444no—
782C23—34416no—
783C23—1728no—
784C23—1722no—
785C23—1722no—
786C23—1722no—
787C23—1722no—
788C23—1722no—
789C23C2×D4×D4311yescharacteristic
790Q8—24no—
791Q8—22no—
792Q8—862no—
793Q8—862no—
794Q8—1722no—
795Q8C2×D4×D4314yes—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—42no—
801D4—42no—
802D4—84no—
803D4—84no—
804D4—434no—
805D4—8616no—
806D4—864no—
807D4—862no—
808D4—862no—
809D4—862no—
810D4—3444no—
811D4—3444no—
812D4—1728no—
813D4—1728no—
814D4—1722no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—434no—
822C2×C4—432no—
823C2×C4—438no—
824C2×C4—434no—
825C2×C4—434no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—8616no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—862no—
833C2×C4—3444no—
834C2×C4—3444no—
835C2×C4—3444no—
836C2×C4—1728no—
837C2×C4—1722no—
838C2×C4—1722no—
839C2×C4C2×D4×D4312yes—
840C2×C4C2×D4×D4312yes—
841C2×C4C2×D4×D4311yescharacteristic
842C2×C4C2×D4×D4312yes—
843C2×C4#41×D4312yes—
844C2×C4C24×D4311yescharacteristic
845C8—22no—
846C8—22no—
847C8—862no—
848C8—862no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—84no—
856C22—84no—
857C22—434no—
858C22—862no—
859C22—862no—
860C22—868no—
861C22—864no—
862C22—34416no—
863C22—3444no—
864C22—1722no—
865C22—1722no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1728no—
870C22#121×D4312yes—
871C22#1458370312yes—
872C22#1458370512yes—
873C22C22×D4×D4311yescharacteristic
874C4—22no—
875C4—24no—
876C4—22no—
877C4—42no—
878C4—434no—
879C4—862no—
880C4—862no—
881C4—1722no—
882C4—1722no—
883C4#121×D4312yes—
884C4C22×D4×D4311yescharacteristic
885C4C2×#41×D4311yescharacteristic
886C2—82no—
887C2—82no—
888C2—864no—
889C2—3442no—
890C2—1724no—
891C2#1914413114yesdirect product factor
892C2C2×#121×D4311yescharacteristic
893C2C2×#1458370311yescharacteristic
894C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
hypercenterC2×#460D43
hypocenterC43C2×#3045
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C22×#13063352C2semidirect
2. C22×#13063346C2semidirect
3. C2×#14583462C2semidirect
4. C2×#14583381C2semidirect
5. #19144131C2direct (N × H)
6. C2×#14583121C2semidirect
7. C2×#14583119C2semidirect
8. C2×#14583097C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583113C2semidirect
11. C2×#14583093C2semidirect
12. C2×#14583091C2semidirect
13. C2×#14582924C2semidirect
14. C2×#14582897C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#460C2semidirect
21. C2×#13063352C22semidirect
23. C2×#13063346C22semidirect
24. C22×#10621885C22semidirect
25. C22×#10621873C22semidirect
29. C22×#10621882C22semidirect
33. #14583462C22semidirect
42. #14583381C22semidirect
43. C2×Q8×Dic43C22semidirect
45. C2×C4×D172C22semidirect
47. C2×#13063287C22semidirect
52. #14583121C22semidirect
53. #14583119C22semidirect
54. #14583115C22semidirect
55. #14583113C22semidirect
56. #14583097C22semidirect
57. #14583093C22semidirect
58. #14583091C22semidirect
59. #14582924C22semidirect
60. C2×C4⋊(C43⋊C8)C22semidirect
61. C2×Dic43⋊C8C22semidirect
62. C2×Dic43⋊C8C22semidirect
63. #14582897C22semidirect
64. C2×#13063250C22semidirect
65. C2×#13063248C22semidirect
68. C2×#13063246C22semidirect
70. #102×D43C22semidirect
72. C22×SD16×C43C22semidirect
74. C2×C4×Q8×C43C22semidirect
75. C43×#460C22semidirect
76. C2×C4⋊C8×C43C22semidirect
78. C2×#102×C43C22semidirect
82. C2×#10621902D4semidirect
109. C2×#10621885C23semidirect
111. C2×#10621873C23semidirect
119. C2×#10621882C23semidirect
137. Q8×Dic43C23semidirect
140. C4×D172C23semidirect
143. #13063287C23semidirect
165. C4⋊(C43⋊C8)C23semidirect
166. Dic43⋊C8C23semidirect
167. Dic43⋊C8C23semidirect
168. #13063250C23semidirect
169. #13063248C23semidirect
172. #13063246C23semidirect
182. C2×SD16×C43C23semidirect
188. C4×Q8×C43C23semidirect
193. C4⋊C8×C43C23semidirect
195. #102×C43C23semidirect
243. #10621902C2×D4semidirect
447. C2×#460D43semidirect
457. C2×C43#3045semidirect
475. C22×SD16C2×D43semidirect
494. C2×C4×Q8C2×D43semidirect
508. #460C2×D43semidirect
515. C2×C4⋊C8C2×D43semidirect
525. C2×#102C2×D43semidirect
526. C43C2×#3045semidirect
570. C2×SD16C22×D43semidirect
600. C4×Q8C22×D43semidirect
635. C4⋊C8C22×D43semidirect
643. #102C22×D43semidirect
891. C2#19144131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633522
C22×#130633462
C2×#145834622
C2×#145833812
#191441312
C2×#145831212
C2×#145831192
C2×#145830972
C2×#145831152
C2×#145831132
C2×#145830932
C2×#145830912
C2×#145829242
C2×#145828972
C2×#102×D432
C2×C43×#4602
C2×#304543