Finite Group Databasebeta

← C2×#19146318 #25971843

Subgroups — C2×#19146318 #25971843

Order 11008.

2858 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063348C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583568C211yesmaximal, characteristic, complemented
4C2×#14583551C211yesmaximal, characteristic, complemented
5#19146318C2116yesmaximal, direct product factor
6C2×#14583270C211yesmaximal, characteristic, complemented
7C2×#14583130C211yesmaximal, characteristic, complemented
8C2×#14583127C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583046C211yesmaximal, characteristic, complemented
13C2×#14583043C211yesmaximal, characteristic, complemented
14C2×#14582984C211yesmaximal, characteristic, complemented
15C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C22×#10621898C2211yescharacteristic
20C2×#13063348—28no—
21C2×#13063348C2218yescomplemented
22C2×#13063345—28no—
23C2×#13063345C2218yescomplemented
24C22×#10621885C2211yescharacteristic
25C22×#10621873C2211yescharacteristic
26C22×#10621883C2211yescharacteristic
27C22×#10621884C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×D344C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C23×C43⋊C8C2211yescharacteristic
32C22×C8×D43C2211yescharacteristic
33#14583568—24no—
34#14583568C2218yescomplemented
35#14583551—24no—
36#14583551C2218yescomplemented
37C2×#13063323C2211yescharacteristic
38C2×#13063321—21no—
39C2×#13063321C2211yescharacteristic
40C2×#13063310—21no—
41C2×#13063307—21no—
42C2×#13063305C2211yescharacteristic
43C2×#13063299—21no—
44C2×#13063299C2211yescharacteristic
45C2×#13063298—21no—
46C2×#13063296—21no—
47C2×#13063296C2211yescharacteristic
48C2×Q8×Dic43C2211yescharacteristic
49C2×#13063287C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×C4⋊C4×D43—21no—
53#14583270C2218yescomplemented
54#14583130C2218yescomplemented
55#14583127C2218yescomplemented
56#14583107C2218yescomplemented
57#14583093C2218yescomplemented
58#14583064C2218yescomplemented
59#14583046C2218yescomplemented
60#14583043C2218yescomplemented
61#14582984C2218yescomplemented
62(C22⋊D43)⋊C8C2218yescomplemented
63C2×#13063256C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic
73C22×SD16×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#452C2218yescomplemented
76C2×#103×C43C2211yescharacteristic
77C2×#102×C43C2211yescharacteristic
78C2×C22⋊C8×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902—42no—
84C2×#10621902—42no—
85C2×#10621902C2314yes—
86C2×#10621902C2314yes—
87C2×#10621898—22no—
88C2×#10621898—24no—
89C2×#10621898—42no—
90C2×#10621898C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×D172—21no—
93C22×D172—21no—
94C22×D172C2311yescharacteristic
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C22⋊D43—21no—
100C22×C22⋊D43—21no—
101C22×C22⋊D43D411yescharacteristic
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43C2311yescharacteristic
107#13063348—232no—
108#13063345—232no—
109C2×#10621885—24no—
110C2×#10621885C2314yes—
111C2×#10621873—42no—
112C2×#10621873C2314yes—
113C2×#10621883—24no—
114C2×#10621883C2314yes—
115C2×#10621884—24no—
116C2×#10621884D418yescomplemented
117C2×#10621884C2314yes—
118C2×#10621884C2314yes—
119C2×D344—24no—
120C2×D344C2314yes—
121C2×#10621882—24no—
122C2×#10621882C2314yes—
123C22×C43⋊C8—24no—
124C22×C43⋊C8C2311yescharacteristic
125C22×C43⋊C8C2314yes—
126C22×C43⋊C8C2311yescharacteristic
127C2×C8×D43—24no—
128C2×C8×D43C2314yes—
129#13063323—22no—
130#13063323C2314yes—
131#13063321—28no—
132#13063321—22no—
133#13063321C2314yes—
134#13063310—28no—
135#13063307—28no—
136#13063305—22no—
137#13063305C2314yes—
138#13063299—22no—
139#13063299—28no—
140#13063299C2314yes—
141#13063298—28no—
142#13063296—22no—
143#13063296—28no—
144#13063296C2314yes—
145Q8×Dic43—22no—
146Q8×Dic43C2314yes—
147#13063287—22no—
148#13063287C2314yes—
149C4×C22⋊D43—28no—
150C4×C22⋊D43D414yes—
151C4×C22⋊D43C2314yes—
152C2×C4⋊Dic43—21no—
153C2×C4⋊Dic43—21no—
154C2×C4⋊Dic43C2311yescharacteristic
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43—28no—
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43D411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063256C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063249C2314yes—
171#13063247C2314yes—
172#13063245C2314yes—
173(C2×D43)⋊C8C2314yes—
174C8×Dic43C2314yes—
175C2×#41×C43—22no—
176C2×#41×C43—24no—
177C2×#41×C43—42no—
178C2×#41×C43C2314yes—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—24no—
186C2×Q16×C43C2314yes—
187C2×SD16×C43—42no—
188C2×SD16×C43C2314yes—
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#102×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43—21no—
203C23×D43C2×D411yescharacteristic
204#41×C43—28no—
205#41×C43—44no—
206#41×C43—48no—
207C2×Q8×C43—21no—
208C2×Q8×C43—21no—
209C2×Q8×C43—22no—
210C2×Q8×C43—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43C2×D414yes—
213C2×Q8×C43C2412yes—
214C2×Q8×C43C2412yes—
215C2×D4×C43—21no—
216C2×D4×C43—24no—
217C2×D4×C43—22no—
218C2×D4×C43—22no—
219C2×D4×C43—44no—
220C2×D4×C43C2412yes—
221C22×C4×C43—22no—
222C22×C4×C43—22no—
223C22×C4×C43—24no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—44no—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2412yes—
231C22×C4×C43C2411yescharacteristic
232C2×C22⋊D43—24no—
233C2×C22⋊D43—24no—
234C2×C22⋊D43—24no—
235C2×C22⋊D43—24no—
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—44no—
239C2×C22⋊D43—44no—
240C2×C22⋊D43—82no—
241C2×C22⋊D43—82no—
242C2×C22⋊D43—82no—
243C2×C22⋊D43C2×D414yes—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248C22×Dic43C2×D411yescharacteristic
249#10621902—28no—
250#10621902—28no—
251#10621902—44no—
252#10621902—44no—
253#10621902—48no—
254#10621902—48no—
255#10621898—28no—
256#10621898—44no—
257#10621898—48no—
258C2×D172—21no—
259C2×D172—22no—
260C2×D172—21no—
261C2×D172—24no—
262C2×D172—24no—
263C2×D172—22no—
264C2×D172—22no—
265C2×D172—44no—
266C2×D172—44no—
267C2×D172C2×D414yes—
268C2×D172C2412yes—
269C2×D172C2412yes—
270C2×C4×D43—22no—
271C2×C4×D43—22no—
272C2×C4×D43—24no—
273C2×C4×D43—24no—
274C2×C4×D43—24no—
275C2×C4×D43—24no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C2×C4×D43—44no—
280C2×C4×D43C2×D412yes—
281C2×C4×D43C2412yes—
282C2×Dic86—22no—
283C2×Dic86—22no—
284C2×Dic86—21no—
285C2×Dic86C2412yes—
286Q16×C43—28no—
287SD16×C43—44no—
288C2×C8×C43—22no—
289C2×C8×C43—22no—
290C2×C8×C43C2412yes—
291C2×C8×C43C2412yes—
292C4⋊C4×C43—24no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43C2412yes—
295C22⋊C4×C43—24no—
296C22⋊Dic43—24no—
297C22⋊Dic43C2×D414yes—
298#10621885—28no—
299#10621884—28no—
300#10621884C2×D4116yescomplemented
301#10621883—28no—
302#10621882—28no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4C2×D414yes—
307C4⋊Dic43—21no—
308C4⋊Dic43—24no—
309C4⋊Dic43—24no—
310C4⋊Dic43C2412yes—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313Dic43⋊C4C2×D414yes—
314C4×Dic43—24no—
315C4×Dic43C2×D412yes—
316C4×Dic43C2412yes—
317C2×C43⋊C8—22no—
318C2×C43⋊C8—28no—
319C2×C43⋊C8C2×D414yes—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322D344—28no—
323#10621873—44no—
324C8×D43—28no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43C22×D412yes—
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—24no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—22no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—42no—
351Q8×C43C22×D414yes—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—48no—
355D4×C43—42no—
356C2×C4×C43—22no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—24no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—48no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43C22×D412yes—
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D412yes—
370C2×C4×C43H(5,𝔽2)12yes—
371C2×C4×C43C2511yescharacteristic
372C22⋊D43—28no—
373C22⋊D43—48no—
374C22⋊D43—48no—
375C22⋊D43—84no—
376C22⋊D43—84no—
377C22⋊D43—84no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384C2×Dic43#13514yescomplemented
385C2×Dic43C22×D412yes—
386C2×Dic43C22×D412yes—
387C2×Dic43C22×D412yes—
388D172—24no—
389D172—22no—
390D172—22no—
391D172—22no—
392D172—48no—
393D172—48no—
394D172—42no—
395D172C22×D414yes—
396C4×D43—24no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—48no—
400C4×D43—48no—
401C4×D43—48no—
402C4×D43—48no—
403Dic86—22no—
404Dic86—22no—
405Dic86—42no—
406C8×C43—22no—
407C8×C43—22no—
408C43⋊C8—22no—
409C43⋊C8C22×D414yes—
410C2×#3284—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—44no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—84no—
419C22×C43D4212yes—
420C22×C43C2×#13512yes—
421C22×C43#57712yes—
422C22×C43C23×D411yescharacteristic
423C2×D43—24no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—44no—
428C2×D43—48no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—84no—
435C4×C43—22no—
436C4×C43—24no—
437C4×C43—42no—
438C4×C43—42no—
439C4×C43D4212yes—
440C4×C43C23×D411yescharacteristic
441C4×C43C2×H(5,𝔽2)11yescharacteristic
442Dic43—22no—
443Dic43—22no—
444Dic43—42no—
445Dic43—42no—
446Dic43C2×#13514yescomplemented
447C22×#135—431no—
448C22×#135—431no—
449C2×#550—431no—
450C2×#547—431no—
451#3284—4316no—
452C2×#492—431no—
453C2×#465—431no—
454C2×#465—431no—
455C2×#462—431no—
456C2×#459—431no—
457C2×#452—431no—
458C2×#452D4311yescharacteristic, complemented
459C2×#449—431no—
460C2×#449—431no—
461C2×C4×SD16—431no—
462C2×C8×D4—431no—
463C2×C43—42no—
464C2×C43—82no—
465C2×C43#328414yescomplemented
466C2×C43C2×D4211yescharacteristic
467C2×C43C22×#13511yescharacteristic
468C2×C43C2×#57711yescharacteristic
469D43—42no—
470D43—44no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41—431no—
475C22×#41C2×D4311yescharacteristic
476C2×#135—438no—
477C2×#135—438no—
478C2×#135—868no—
479C2×#135—868no—
480C22×Q16—431no—
481C22×Q16C2×D4311yescharacteristic
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16C2×D4311yescharacteristic
487C22×D8—431no—
488C22×D8—431no—
489C23×C8—431no—
490C23×C8—431no—
491#550—438no—
492#550—864no—
493#547—438no—
494#547—864no—
495C2×C4⋊Q8—431no—
496C2×#127—431no—
497C2×#127—861no—
498C2×#123—861no—
499C2×#123—861no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8C2×D4311yescharacteristic
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121—861no—
507C2×C4×Q8—431no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×C4×D4—861no—
511C22×C4⋊C4—861no—
512#492—438no—
513#465—438no—
514#465—438no—
515#462—438no—
516#459—438no—
517#452—438no—
518#452C2×D4318yescomplemented
519#449—438no—
520#449—438no—
521C4×SD16—438no—
522C8×D4—438no—
523C2×#106—431no—
524C2×C4⋊C8—431no—
525C2×#103—431no—
526C2×#103—431no—
527C2×#103C2×D4311yescharacteristic
528C2×#102—431no—
529C2×#102—431no—
530C2×#102C2×D4311yescharacteristic
531C2×C22⋊C8—431no—
532C2×C22⋊C8C2×D4311yescharacteristic
533C2×C4×C8—431no—
534C43C2×#328411yescharacteristic, complemented, Sylow
535C2×#41—22no—
536C2×#41—24no—
537C2×#41—42no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—434no—
541C2×#41—864no—
542C2×#41—862no—
543C2×#41—862no—
544C2×#41—862no—
545C2×#41—864no—
546C2×#41—864no—
547C2×#41—1722no—
548C2×#41—1722no—
549C2×#41—1722no—
550C2×#41C22×D4314yes—
551C22×Q8—431no—
552C22×Q8C22×D4311yescharacteristic
553C22×Q8C22×D4311yescharacteristic
554C22×D4—21no—
555C22×D4—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—861no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4C22×D4311yescharacteristic
566C23×C4—21no—
567C23×C4—431no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573#135—8632no—
574#135—8632no—
575C2×Q16—24no—
576C2×Q16—434no—
577C2×Q16—864no—
578C2×Q16C22×D4314yes—
579C2×SD16—42no—
580C2×SD16—438no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—434no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16—1722no—
588C2×SD16C22×D4314yes—
589C2×D8—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—864no—
593C22×C8—431no—
594C22×C8—431no—
595C22×C8—434no—
596C22×C8—434no—
597C22×C8—864no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601C4⋊Q8—434no—
602C4⋊Q8—862no—
603#127—434no—
604#127—862no—
605#127—868no—
606#123—868no—
607#123—868no—
608C22⋊Q8—22no—
609C22⋊Q8—434no—
610C22⋊Q8—862no—
611C22⋊Q8C22×D4314yes—
612#121—434no—
613#121—434no—
614#121—868no—
615#121—868no—
616#121—868no—
617#121—862no—
618#121—862no—
619C4×Q8—434no—
620C4×Q8—862no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—434no—
624C4×D4—862no—
625C4×D4—868no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—868no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C42—431no—
643C2×C42—861no—
644#106—434no—
645C4⋊C8—434no—
646#103—434no—
647#103—434no—
648#103C22×D4314yes—
649#102—434no—
650#102—434no—
651#102C22×D4314yes—
652C22⋊C8—434no—
653C22⋊C8C22×D4314yes—
654C4×C8—434no—
655C24—21no—
656C24—431no—
657C24—861no—
658C24—861no—
659C24D4×D4311yescharacteristic
660#41—28no—
661#41—44no—
662#41—48no—
663#41—868no—
664#41—868no—
665#41—868no—
666#41—1724no—
667#41—1728no—
668#41—1724no—
669#41—1724no—
670#41—1728no—
671#41—1728no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—432no—
678C2×Q8—861no—
679C2×Q8—862no—
680C2×Q8—862no—
681C2×Q8D4×D4314yes—
682C2×Q8C23×D4312yes—
683C2×Q8C23×D4312yes—
684C2×D4—24no—
685C2×D4—22no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—44no—
689C2×D4—434no—
690C2×D4—434no—
691C2×D4—432no—
692C2×D4—432no—
693C2×D4—864no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—861no—
702C2×D4—862no—
703C2×D4—861no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—3442no—
707C2×D4—3442no—
708C2×D4—3442no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4—1724no—
712C2×D4—1724no—
713C2×D4C23×D4312yes—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—24no—
720C22×C4—44no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—864no—
727C22×C4—864no—
728C22×C4—864no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—864no—
734C22×C4—1724no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16—868no—
744SD16—44no—
745SD16—4316no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—868no—
750D8—868no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—434no—
754C2×C8—432no—
755C2×C8—432no—
756C2×C8—868no—
757C2×C8—868no—
758C2×C8—862no—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—434no—
764C4⋊C4—432no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4—864no—
769C4⋊C4—861no—
770C4⋊C4C23×D4312yes—
771C22⋊C4—24no—
772C22⋊C4—434no—
773C22⋊C4—434no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C42—432no—
779C42—432no—
780C42—864no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—432no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—862no—
793C23—864no—
794C23—862no—
795C23—1722no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23C2×D4×D4312yes—
801C23C2×D4×D4311yescharacteristic
802Q8—22no—
803Q8—24no—
804Q8—22no—
805Q8—22no—
806Q8—42no—
807Q8—862no—
808Q8—862no—
809Q8—1722no—
810Q8C2×D4×D4314yes—
811D4—22no—
812D4—22no—
813D4—48no—
814D4—42no—
815D4—434no—
816D4—868no—
817D4—862no—
818D4—862no—
819D4—862no—
820D4—864no—
821D4—3444no—
822D4—3444no—
823D4—3444no—
824D4—1728no—
825D4—1728no—
826D4—1728no—
827D4—1728no—
828D4—1722no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—48no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—434no—
841C2×C4—432no—
842C2×C4—432no—
843C2×C4—432no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—864no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—1728no—
852C2×C4—1728no—
853C2×C4—1728no—
854C2×C4—1728no—
855C2×C4—1722no—
856C2×C4—1722no—
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4312yes—
859C2×C4C2×D4×D4311yescharacteristic
860C2×C4#1306337012yes—
861C2×C4C24×D4311yescharacteristic
862C8—22no—
863C8—22no—
864C8—434no—
865C8—862no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—44no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—84no—
874C22—862no—
875C22—862no—
876C22—862no—
877C22—864no—
878C22—3444no—
879C22—1722no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1724no—
885C22—1728no—
886C22#1458353112yes—
887C22#135×D4312yes—
888C22#1458370812yes—
889C22C22×D4×D4311yescharacteristic
890C4—22no—
891C4—24no—
892C4—42no—
893C4—42no—
894C4—434no—
895C4—862no—
896C4—862no—
897C4—1722no—
898C4—1722no—
899C4#1458353112yes—
900C4C22×D4×D4311yescharacteristic
901C4C2×#1306337011yescharacteristic
902C2—42no—
903C2—82no—
904C2—3442no—
905C2—1722no—
906C2—1724no—
907C2#1914631814yesdirect product factor
908C2C2×#1458353111yescharacteristic
909C2C2×#135×D4311yescharacteristic
910C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#13063348C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583568C2semidirect
4. C2×#14583551C2semidirect
5. #19146318C2direct (N × H)
6. C2×#14583270C2semidirect
7. C2×#14583130C2semidirect
8. C2×#14583127C2semidirect
9. C2×#14583107C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583046C2semidirect
13. C2×#14583043C2semidirect
14. C2×#14582984C2semidirect
15. C2×(C22⋊D43)⋊C8C2semidirect
16. C2×C43×#452C2semidirect
21. C2×#13063348C22semidirect
23. C2×#13063345C22semidirect
34. #14583568C22semidirect
36. #14583551C22semidirect
53. #14583270C22semidirect
54. #14583130C22semidirect
55. #14583127C22semidirect
56. #14583107C22semidirect
57. #14583093C22semidirect
58. #14583064C22semidirect
59. #14583046C22semidirect
60. #14583043C22semidirect
61. #14582984C22semidirect
62. (C22⋊D43)⋊C8C22semidirect
75. C43×#452C22semidirect
116. C2×#10621884D4semidirect
300. #10621884C2×D4semidirect
384. C2×Dic43#135semidirect
446. Dic43C2×#135semidirect
458. C2×#452D43semidirect
465. C2×C43#3284semidirect
518. #452C2×D43semidirect
534. C43C2×#3284semidirect
907. C2#19146318direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633482
C22×#130633452
C2×#145835682
C2×#145835512
#191463182
C2×#145832702
C2×#145831302
C2×#145831272
C2×#145831072
C2×#145830932
C2×#145830642
C2×#145830462
C2×#145830432
C2×#145829842
C2×(C22⋊D43)⋊C82
C2×C43×#4522
C2×#328443