Finite Group Databasebeta

← C2×#19144171 #25963698

Subgroups — C2×#19144171 #25963698

Order 11008.

3046 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063346C211yesmaximal, characteristic, complemented
2C23×C8×D43C211yesmaximal, characteristic, complemented
3C2×#14583412C211yesmaximal, characteristic, complemented
4C2×#14583409C211yesmaximal, characteristic, complemented
5#19144171C2116yesmaximal, direct product factor
6C2×#14583139C211yesmaximal, characteristic, complemented
7C2×#14583138C211yesmaximal, characteristic, complemented
8C2×#14583134C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583129C211yesmaximal, characteristic, complemented
11C2×#14583128C211yesmaximal, characteristic, complemented
12C2×#14583125C211yesmaximal, characteristic, complemented
13C2×#14582934C211yesmaximal, characteristic, complemented
14C2×#14582894C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#465C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063346—28no—
21C2×#13063346C2218yescomplemented
22C22×#10621885C2211yescharacteristic, complemented
23C22×#10621873C2211yescharacteristic, complemented
24C22×#10621882C2211yescharacteristic, complemented
25C23×C43⋊C8C2211yescharacteristic
26C22×C8×D43—28no—
27C22×C8×D43C2211yescharacteristic
28C22×C8×D43C2211yescharacteristic
29C22×C8×D43C2211yescharacteristic
30C22×C8×D43C2211yescharacteristic
31C22×C8×D43C2218yescomplemented
32#14583412—24no—
33#14583412C2218yescomplemented
34#14583409—24no—
35#14583409C2218yescomplemented
36C2×#13063310—21no—
37C2×#13063307—21no—
38C2×#13063305C2211yescharacteristic
39C2×#13063304C2211yescharacteristic
40C2×#13063301C2211yescharacteristic
41C2×#13063300C2211yescharacteristic
42C2×#13063299C2211yescharacteristic
43C2×#13063296C2211yescharacteristic
44C2×#13063295—21no—
45C2×#13063293—21no—
46C2×D4×Dic43—21no—
47C2×#13063287—21no—
48C2×(C22⋊D43)⋊C4—21no—
49C2×(C22⋊D43)⋊C4—21no—
50C2×#13063283C2211yescharacteristic
51C2×#13063283C2211yescharacteristic
52#14583139C2218yescomplemented
53#14583138C2218yescomplemented
54#14583134C2218yescomplemented
55#14583133C2218yescomplemented
56#14583129C2218yescomplemented
57#14583128C2218yescomplemented
58#14583125C2218yescomplemented
59#14582934C2218yescomplemented
60C2×#13063258C2211yescharacteristic, complemented
61C2×#13063258C2211yescharacteristic, complemented
62C2×#13063257C2211yescharacteristic, complemented
63#14582894C2218yescomplemented
64#14582892C2218yescomplemented
65C2×#13063250C2211yescharacteristic, complemented
66C2×#13063249C2211yescharacteristic, complemented
67C2×#13063248C2211yescharacteristic, complemented
68C2×#13063247C2211yescharacteristic, complemented
69C2×#13063246C2211yescharacteristic, complemented
70C2×#13063245C2211yescharacteristic, complemented
71C22×SD16×C43C2211yescharacteristic, complemented
72C23×C8×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×#121×C43C2211yescharacteristic
75C43×#465C2218yescomplemented
76C2×#106×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×#102×C43C2211yescharacteristic, complemented
79C24×D43D411yescharacteristic
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902C2314yes—
84C2×#10621900—24no—
85C2×#10621900—22no—
86C2×#10621900—24no—
87C2×#10621900C2314yes—
88C22×Dic86C2311yescharacteristic
89C22×D172—21no—
90C22×D172—21no—
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C23×Dic43—21no—
96C23×Dic43D411yescharacteristic
97C22×C4×D43—24no—
98C22×C4×D43—24no—
99C22×C4×D43—21no—
100C22×C4×D43D411yescharacteristic
101C22×C4×D43D411yescharacteristic
102C22×C4×D43D414yes—
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2314yes—
105C22×C4×D43C2311yescharacteristic
106#13063346—232no—
107C2×#10621885—24no—
108C2×#10621885C2314yescomplemented
109C2×#10621873—24no—
110C2×#10621873C2314yescomplemented
111C2×#10621882—24no—
112C2×#10621882C2314yescomplemented
113C22×C43⋊C8—24no—
114C22×C43⋊C8C2314yes—
115C22×C43⋊C8C2311yescharacteristic
116C22×C43⋊C8C2311yescharacteristic
117C2×C8×D43—24no—
118C2×C8×D43—24no—
119C2×C8×D43—24no—
120C2×C8×D43—232no—
121C2×C8×D43D418yescomplemented
122C2×C8×D43C2314yes—
123C2×C8×D43C2314yes—
124C2×C8×D43C2314yes—
125C2×C8×D43C2314yes—
126#13063310—28no—
127#13063307—28no—
128#13063305—22no—
129#13063305C2314yes—
130#13063304—22no—
131#13063304C2314yes—
132#13063301—22no—
133#13063301C2314yes—
134#13063300—22no—
135#13063300C2314yes—
136#13063299—22no—
137#13063299C2314yes—
138#13063296—22no—
139#13063296C2314yes—
140#13063295—28no—
141#13063293—28no—
142D4×Dic43—28no—
143#13063287—28no—
144(C22⋊D43)⋊C4—28no—
145(C22⋊D43)⋊C4—28no—
146#13063283—22no—
147#13063283—22no—
148#13063283C2314yes—
149#13063283C2314yes—
150C2×C4⋊Dic43—21no—
151C2×C4⋊Dic43C2311yescharacteristic
152C2×C4⋊Dic43C2311yescharacteristic
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
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)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165#13063258C2314yescomplemented
166#13063258C2314yescomplemented
167#13063257C2314yescomplemented
168#13063250C2314yescomplemented
169#13063249C2314yescomplemented
170#13063248C2314yescomplemented
171#13063247C2314yescomplemented
172#13063246C2314yescomplemented
173#13063245C2314yescomplemented
174C22×Q8×C43C2311yescharacteristic
175C22×D4×C43—21no—
176C22×D4×C43C2311yescharacteristic
177C23×C4×C43C2311yescharacteristic
178C2×SD16×C43—24no—
179C2×SD16×C43C2314yescomplemented
180C22×C8×C43—24no—
181C22×C8×C43C2314yes—
182C22×C8×C43C2311yescharacteristic
183C22×C8×C43C2311yescharacteristic
184C22⋊Q8×C43—22no—
185C22⋊Q8×C43C2314yes—
186#121×C43—22no—
187#121×C43C2314yes—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C22⋊C4×C43—21no—
192C2×C22⋊C4×C43—21no—
193#106×C43C2314yescomplemented
194#103×C43C2314yescomplemented
195#102×C43C2314yescomplemented
196C24×C43—21no—
197C24×C43C2×D411yescharacteristic
198C23×D43—24no—
199C23×D43—24no—
200C23×D43—24no—
201C23×D43—21no—
202C23×D43C2×D414yes—
203C23×D43C2×D411yescharacteristic
204C23×D43C2×D411yescharacteristic
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43C2412yes—
209C2×D4×C43—21no—
210C2×D4×C43—24no—
211C2×D4×C43—22no—
212C2×D4×C43—22no—
213C2×D4×C43—44no—
214C2×D4×C43C2412yes—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C22×Dic43—24no—
231C22×Dic43—24no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—44no—
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D414yes—
238C22×Dic43C2×D411yescharacteristic
239#10621902—28no—
240#10621902—28no—
241#10621902—48no—
242#10621900—28no—
243#10621900—28no—
244#10621900—48no—
245C2×D172—21no—
246C2×D172—24no—
247C2×D172—24no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—44no—
251C2×D172—44no—
252C2×D172C2412yes—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—24no—
256C2×C4×D43—216no—
257C2×C4×D43—28no—
258C2×C4×D43—28no—
259C2×C4×D43—24no—
260C2×C4×D43—24no—
261C2×C4×D43—44no—
262C2×C4×D43C2×D414yes—
263C2×C4×D43C2×D414yes—
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2×D414yes—
266C2×C4×D43C2×D412yes—
267C2×C4×D43#4114yes—
268C2×C4×D43C2412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—21no—
273C2×Dic86C2412yes—
274SD16×C43—28no—
275C2×C8×C43—22no—
276C2×C8×C43—28no—
277C2×C8×C43C2×D414yes—
278C2×C8×C43C2412yes—
279C2×C8×C43C2412yes—
280C4⋊C4×C43—24no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43C2412yes—
284C4⋊C4×C43C2412yes—
285C22⋊C4×C43—24no—
286C22⋊C4×C43—24no—
287C22⋊Dic43—24no—
288C22⋊Dic43—24no—
289#10621885—28no—
290#10621882—28no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—24no—
300C4⋊Dic43C2412yes—
301C4⋊Dic43C2412yes—
302Dic43⋊C4—24no—
303Dic43⋊C4—24no—
304C4×Dic43—24no—
305C4×Dic43—24no—
306C2×C43⋊C8—22no—
307C2×C43⋊C8—28no—
308C2×C43⋊C8C2×D414yes—
309C2×C43⋊C8C2412yes—
310C2×C43⋊C8C2412yes—
311#10621873—28no—
312C8×D43—28no—
313C8×D43—28no—
314C8×D43—28no—
315C8×D43C2×D4116yescomplemented
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—42no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43#13514yescomplemented
323C23×C43C22×D412yes—
324C23×C43C22×D411yescharacteristic
325C22×D43—232no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—28no—
331C22×D43—28no—
332C22×D43—28no—
333C22×D43—22no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43#12114yes—
338C22×D43#13514yescomplemented
339C22×D43C22×D412yes—
340C22×D43C22×D412yes—
341Q8×C43—22no—
342Q8×C43—22no—
343Q8×C43—42no—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—48no—
347D4×C43—42no—
348C2×C4×C43—22no—
349C2×C4×C43—24no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—42no—
358C2×C4×C43C22×D412yes—
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D412yes—
361C2×C4×C43C2×#4112yes—
362C2×C4×C43C2511yescharacteristic
363C22⋊D43—48no—
364C22⋊D43—48no—
365C22⋊D43—48no—
366C2×Dic43—22no—
367C2×Dic43—28no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—48no—
375C2×Dic43#12114yes—
376C2×Dic43C22×D412yes—
377C2×Dic43C22×D412yes—
378D172—22no—
379D172—22no—
380D172—48no—
381D172—48no—
382D172—42no—
383C4×D43—28no—
384C4×D43—24no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—28no—
388C4×D43—48no—
389C4×D43#12118yes—
390C4×D43C22×D414yes—
391C4×D43C2×#4114yes—
392Dic86—22no—
393Dic86—22no—
394Dic86—42no—
395C8×C43—22no—
396C8×C43C22×D414yes—
397C43⋊C8—22no—
398C43⋊C8C22×D414yes—
399C2×#3050—431nomaximal, Sylow
400C22×C43—22no—
401C22×C43—28no—
402C22×C43—22no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—84no—
407C22×C43C2×#12112yes—
408C22×C43C2×#13512yes—
409C22×C43C2×#13512yes—
410C22×C43C2×#13514yescomplemented
411C22×C43C23×D411yescharacteristic
412C2×D43—232no—
413C2×D43—22no—
414C2×D43—28no—
415C2×D43—28no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—84no—
423C2×D43C2×#12114yes—
424C2×D43C2×#13514yescomplemented
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43C2×#12112yes—
430C4×C43C23×D411yescharacteristic
431C4×C43C22×#4111yescharacteristic
432Dic43—22no—
433Dic43—42no—
434Dic43—42no—
435Dic43—42no—
436Dic43C2×#12114yes—
437C22×#135—431no—
438C24×C8—431no—
439C2×#525—431no—
440C2×#525—431no—
441#3050—4316no—
442C2×#467—431no—
443C2×#467—431no—
444C2×#466—431no—
445C2×#466—431no—
446C2×#465—431no—
447C2×#465—431no—
448C2×#465—431no—
449C2×#465D4311yescharacteristic, complemented
450C2×#427—431no—
451C2×#416—431no—
452C2×#416—431no—
453C2×C43—24no—
454C2×C43—82no—
455C2×C43#305014yescomplemented
456C2×C43C22×#12111yescharacteristic
457C2×C43C22×#13511yescharacteristic
458C2×C43C22×#13511yescharacteristic
459D43—24no—
460D43—24no—
461D43—82no—
462C22×#41—431no—
463C22×#41—431no—
464C24×C4—431no—
465C2×#135—438no—
466C2×#135—868no—
467C22×Q16—431no—
468C22×SD16—431no—
469C22×SD16C2×D4311yescharacteristic, complemented
470C22×D8—431no—
471C23×C8—431no—
472C23×C8—431no—
473C23×C8—431no—
474C23×C8—431no—
475C23×C8—431no—
476C23×C8—438no—
477C23×C8—868no—
478C23×C8C2×D4311yescharacteristic
479#525—438no—
480#525—438no—
481#525—864no—
482#525—864no—
483C2×#123—861no—
484C2×#123—861no—
485C2×C22⋊Q8—431no—
486C2×C22⋊Q8—431no—
487C2×C22⋊Q8—431no—
488C2×C22⋊Q8C2×D4311yescharacteristic
489C2×#121—431no—
490C2×#121—431no—
491C2×#121—431no—
492C2×#121C2×D4311yescharacteristic
493C2×#120—861no—
494C2×#120—861no—
495C2×C4×D4—861no—
496C2×C4×D4—861no—
497C2×C4×D4—861no—
498C2×C4×D4—861no—
499C2×#117—431no—
500C2×#117—431no—
501#467—438no—
502#467—438no—
503#466—438no—
504#466—438no—
505#465—438no—
506#465—438no—
507#465—438no—
508#465C2×D4318yescomplemented
509#427—438no—
510C2×#107—431no—
511C2×#107—431no—
512C2×#106—431no—
513C2×#106C2×D4311yescharacteristic, complemented
514#416—438no—
515#416—438no—
516C2×#103—431no—
517C2×#103—431no—
518C2×#103—431no—
519C2×#103C2×D4311yescharacteristic, complemented
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102C2×D4311yescharacteristic, complemented
524C43C2×#305011yescharacteristic, complemented, Sylow
525C25—431no—
526C2×#41—434no—
527C2×#41—434no—
528C2×#41—862no—
529C2×#41—862no—
530C2×#41—864no—
531C2×#41—864no—
532C2×#41—864no—
533C2×#41—864no—
534C22×Q8—431no—
535C22×Q8C22×D4311yescharacteristic
536C22×D4—21no—
537C22×D4—431no—
538C22×D4—861no—
539C22×D4—861no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4C22×D4311yescharacteristic
544C23×C4—431no—
545C23×C4—431no—
546C23×C4—431no—
547C23×C4—431no—
548C23×C4—434no—
549C23×C4—431no—
550C23×C4—434no—
551C23×C4—864no—
552C23×C4—864no—
553C23×C4—861no—
554C23×C4—861no—
555C23×C4C22×D4311yescharacteristic
556#135—8632no—
557C2×Q16—434no—
558C2×Q16—864no—
559C2×SD16—24no—
560C2×SD16—434no—
561C2×SD16—864no—
562C2×SD16C22×D4314yescomplemented
563C2×D8—434no—
564C2×D8—864no—
565C22×C8—24no—
566C22×C8—431no—
567C22×C8—438no—
568C22×C8—434no—
569C22×C8—431no—
570C22×C8—434no—
571C22×C8—434no—
572C22×C8—434no—
573C22×C8—434no—
574C22×C8—864no—
575C22×C8—8632no—
576C22×C8—864no—
577C22×C8—864no—
578C22×C8—864no—
579C22×C8C22×D4311yescharacteristic
580C22×C8C22×D4314yes—
581C22×C8C22×D4311yescharacteristic
582#123—868no—
583#123—868no—
584C22⋊Q8—22no—
585C22⋊Q8—434no—
586C22⋊Q8—434no—
587C22⋊Q8—434no—
588C22⋊Q8—862no—
589C22⋊Q8—862no—
590C22⋊Q8—862no—
591C22⋊Q8C22×D4314yes—
592#121—22no—
593#121—434no—
594#121—434no—
595#121—434no—
596#121—862no—
597#121—862no—
598#121—862no—
599#121C22×D4314yes—
600#120—868no—
601#120—868no—
602C4×D4—868no—
603C4×D4—868no—
604C4×D4—868no—
605C4×D4—868no—
606#117—434no—
607#117—434no—
608#117—862no—
609#117—862no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
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—861no—
629C2×C42—861no—
630#107—434no—
631#107—434no—
632#106—434no—
633#106C22×D4314yescomplemented
634#103—434no—
635#103—434no—
636#103—434no—
637#103C22×D4314yescomplemented
638#102—434no—
639#102—434no—
640#102—434no—
641#102C22×D4314yescomplemented
642C24—21no—
643C24—431no—
644C24—431no—
645C24—434no—
646C24—864no—
647C24—864no—
648C24—864no—
649C24—861no—
650C24D4×D4311yescharacteristic
651#41—868no—
652#41—868no—
653#41—868no—
654#41—868no—
655#41—1728no—
656#41—1728no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—432no—
661C2×Q8—861no—
662C2×Q8—862no—
663C2×Q8—862no—
664C2×Q8C23×D4312yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—432no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—864no—
676C2×D4—862no—
677C2×D4—861no—
678C2×D4—862no—
679C2×D4—1724no—
680C2×D4—1724no—
681C2×D4—1724no—
682C2×D4—1724no—
683C2×D4—1724no—
684C2×D4C23×D4312yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—431no—
691C22×C4—432no—
692C22×C4—434no—
693C22×C4—434no—
694C22×C4—432no—
695C22×C4—434no—
696C22×C4—431no—
697C22×C4—434no—
698C22×C4—432no—
699C22×C4—434no—
700C22×C4—432no—
701C22×C4—868no—
702C22×C4—864no—
703C22×C4—8616no—
704C22×C4—868no—
705C22×C4—864no—
706C22×C4—864no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—1724no—
715C22×C4—1724no—
716C22×C4D4×D4312yes—
717C22×C4D4×D4311yescharacteristic
718C22×C4C23×D4312yes—
719C22×C4C23×D4311yescharacteristic
720Q16—868no—
721SD16—28no—
722SD16—868no—
723D8—868no—
724C2×C8—22no—
725C2×C8—28no—
726C2×C8—434no—
727C2×C8—432no—
728C2×C8—4316no—
729C2×C8—432no—
730C2×C8—868no—
731C2×C8—868no—
732C2×C8—868no—
733C2×C8—862no—
734C2×C8—868no—
735C2×C8D4×D4314yes—
736C2×C8C23×D4312yes—
737C2×C8C23×D4312yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—432no—
742C4⋊C4—432no—
743C4⋊C4—864no—
744C4⋊C4—864no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—864no—
748C4⋊C4C23×D4312yes—
749C4⋊C4C23×D4312yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—864no—
753C22⋊C4—864no—
754C22⋊C4—864no—
755C22⋊C4—864no—
756C22⋊C4—864no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C22⋊C4—864no—
760C42—864no—
761C42—864no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—434no—
769C23—434no—
770C23—432no—
771C23—432no—
772C23—868no—
773C23—868no—
774C23—8632no—
775C23—862no—
776C23—862no—
777C23—862no—
778C23—862no—
779C23—868no—
780C23—862no—
781C23—1722no—
782C23—1722no—
783C23—1722no—
784C23#1306334614yescomplemented
785C23C2×D4×D4312yes—
786C23C2×D4×D4311yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—862no—
791Q8—862no—
792Q8—1722no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—862no—
798D4—862no—
799D4—1728no—
800D4—1728no—
801D4—1728no—
802D4—1728no—
803D4—1728no—
804D4—1722no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—434no—
816C2×C4—432no—
817C2×C4—438no—
818C2×C4—434no—
819C2×C4—434no—
820C2×C4—432no—
821C2×C4—868no—
822C2×C4—868no—
823C2×C4—868no—
824C2×C4—862no—
825C2×C4—864no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—1728no—
832C2×C4—1728no—
833C2×C4—1722no—
834C2×C4—1722no—
835C2×C4—1722no—
836C2×C4C2×D4×D4312yes—
837C2×C4C2×D4×D4311yescharacteristic
838C2×C4C2×D4×D4312yes—
839C2×C4#41×D4312yes—
840C2×C4C24×D4311yescharacteristic
841C8—22no—
842C8—434no—
843C8—862no—
844C8C2×D4×D4314yes—
845C22—22no—
846C22—22no—
847C22—28no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—434no—
853C22—434no—
854C22—8632no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—868no—
860C22—868no—
861C22—3444no—
862C22—1722no—
863C22—1722no—
864C22—1722no—
865C22#121×D4312yes—
866C22#135×D4312yes—
867C22C2×#1306334612yes—
868C22C2×#1306334614yescomplemented
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—434no—
875C4—862no—
876C4—1722no—
877C4—1722no—
878C4—1722no—
879C4#121×D4312yes—
880C4C22×D4×D4311yescharacteristic
881C4C2×#41×D4311yescharacteristic
882C2—24no—
883C2—82no—
884C2—864no—
885C2—864no—
886C2—3442no—
887C2#1914417114yesdirect product factor
888C2C2×#121×D4311yescharacteristic
889C2C2×#135×D4311yescharacteristic
890C2C22×#1306334611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#465C2
socleC23×C43C22×D4
hypercenterC2×#465D43
hypocenterC43C2×#3050
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#13063346C2semidirect
2. C23×C8×D43C2semidirect
3. C2×#14583412C2semidirect
4. C2×#14583409C2semidirect
5. #19144171C2direct (N × H)
6. C2×#14583139C2semidirect
7. C2×#14583138C2semidirect
8. C2×#14583134C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583129C2semidirect
11. C2×#14583128C2semidirect
12. C2×#14583125C2semidirect
13. C2×#14582934C2semidirect
14. C2×#14582894C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#465C2semidirect
21. C2×#13063346C22semidirect
22. C22×#10621885C22semidirect
23. C22×#10621873C22semidirect
24. C22×#10621882C22semidirect
31. C22×C8×D43C22semidirect
33. #14583412C22semidirect
35. #14583409C22semidirect
52. #14583139C22semidirect
53. #14583138C22semidirect
54. #14583134C22semidirect
55. #14583133C22semidirect
56. #14583129C22semidirect
57. #14583128C22semidirect
58. #14583125C22semidirect
59. #14582934C22semidirect
60. C2×#13063258C22semidirect
61. C2×#13063258C22semidirect
62. C2×#13063257C22semidirect
63. #14582894C22semidirect
64. #14582892C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063249C22semidirect
67. C2×#13063248C22semidirect
68. C2×#13063247C22semidirect
69. C2×#13063246C22semidirect
70. C2×#13063245C22semidirect
71. C22×SD16×C43C22semidirect
75. C43×#465C22semidirect
76. C2×#106×C43C22semidirect
77. C2×#103×C43C22semidirect
78. C2×#102×C43C22semidirect
108. C2×#10621885C23semidirect
110. C2×#10621873C23semidirect
112. C2×#10621882C23semidirect
121. C2×C8×D43D4semidirect
165. #13063258C23semidirect
166. #13063258C23semidirect
167. #13063257C23semidirect
168. #13063250C23semidirect
169. #13063249C23semidirect
170. #13063248C23semidirect
171. #13063247C23semidirect
172. #13063246C23semidirect
173. #13063245C23semidirect
179. C2×SD16×C43C23semidirect
193. #106×C43C23semidirect
194. #103×C43C23semidirect
195. #102×C43C23semidirect
315. C8×D43C2×D4semidirect
322. C23×C43#135semidirect
338. C22×D43#135semidirect
410. C22×C43C2×#135semidirect
424. C2×D43C2×#135semidirect
449. C2×#465D43semidirect
455. C2×C43#3050semidirect
469. C22×SD16C2×D43semidirect
508. #465C2×D43semidirect
513. C2×#106C2×D43semidirect
519. C2×#103C2×D43semidirect
523. C2×#102C2×D43semidirect
524. C43C2×#3050semidirect
562. C2×SD16C22×D43semidirect
633. #106C22×D43semidirect
637. #103C22×D43semidirect
641. #102C22×D43semidirect
784. C23#13063346semidirect
868. C22C2×#13063346semidirect
887. C2#19144171direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633462
C23×C8×D432
C2×#145834122
C2×#145834092
#191441712
C2×#145831392
C2×#145831382
C2×#145831342
C2×#145831332
C2×#145831292
C2×#145831282
C2×#145831252
C2×#145829342
C2×#145828942
C2×#145828922
C2×C43×#4652
C2×#305043