Finite Group Databasebeta

← C2×#19146447 #25972966

Subgroups — C2×#19146447 #25972966

Order 11008.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583545C211yesmaximal, characteristic, complemented
3#19146447C2116yesmaximal, direct product factor
4C2×#14583254C211yesmaximal, characteristic, complemented
5C2×#14583235C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583200C211yesmaximal, characteristic, complemented
8C2×#14583135C211yesmaximal, characteristic, complemented
9C2×#14583128C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic, complemented
12C2×#14583035C211yesmaximal, characteristic, complemented
13C2×C4×D344C211yesmaximal, characteristic, complemented
14C2×#14582896C211yesmaximal, characteristic, complemented
15C22×#13063247C211yesmaximal, characteristic, complemented
16C2×C8×D4×C43C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic, complemented
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583595—24no—
23#14583595C2218yescomplemented
24#14583545—24no—
25#14583545C2218yescomplemented
26C2×#13063320—21no—
27C2×#13063317C2211yescharacteristic, complemented
28C2×#13063313C2211yescharacteristic
29C2×#13063310—21no—
30C2×#13063307—21no—
31C2×#13063304C2211yescharacteristic
32C2×#13063299C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063299C2211yescharacteristic, complemented
35C2×#13063298—21no—
36C2×#13063297—21no—
37C2×#13063293—21no—
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic, complemented
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063284C2211yescharacteristic, complemented
42C22×C4⋊Dic43C2211yescharacteristic
43C2×C22⋊C4×D43—21no—
44#14583254C2218yescomplemented
45#14583235C2218yescomplemented
46#14583224C2218yescomplemented
47#14583200C2218yescomplemented
48#14583135C2218yescomplemented
49#14583128C2218yescomplemented
50#14583115C2218yescomplemented
51#14583046C2218yescomplemented
52#14583035C2218yescomplemented
53C4×D344C2218yescomplemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57#14582896C2218yescomplemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2218yescomplemented
68C2×#13063247C2211yescharacteristic, complemented
69C23×C8×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×C4×D4×C43C2211yescharacteristic
72C8×D4×C43C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic, complemented
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic, complemented
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—24no—
80C2×#10621898—42no—
81C2×#10621898C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×D172—24no—
84C22×D172—21no—
85C22×D172—22no—
86C22×D172—42no—
87C22×D172C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×D172C2314yes—
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C2×#10621873—42no—
100C2×#10621873C2314yescomplemented
101C2×D344—24no—
102C2×D344—42no—
103C2×D344C2314yes—
104C2×D344C2314yes—
105#13063320—28no—
106#13063317—22no—
107#13063317C2314yescomplemented
108#13063313—22no—
109#13063313C2314yes—
110#13063310—28no—
111#13063307—28no—
112#13063304—22no—
113#13063304C2314yes—
114#13063299—22no—
115#13063299—22no—
116#13063299—22no—
117#13063299C2314yes—
118#13063299C2314yes—
119#13063299C2314yescomplemented
120#13063298—28no—
121#13063297—28no—
122#13063293—28no—
123C4×D172—22no—
124C4×D172—22no—
125C4×D172C2314yes—
126C4×D172C2314yescomplemented
127(C22⋊D43)⋊C4—28no—
128#13063284—22no—
129#13063284C2314yescomplemented
130C2×C4⋊Dic43—22no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2314yes—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C22⋊C4×D43—28no—
150C2×C4×Dic43—21no—
151#13063259C2314yescomplemented
152#13063259C2314yescomplemented
153#13063257C2314yescomplemented
154#13063250C2314yescomplemented
155#13063250C2314yescomplemented
156#13063250C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163#13063247C2314yescomplemented
164C22×D4×C43D411yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C22×C8×C43—42no—
168C22×C8×C43—42no—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2314yes—
174C22×C8×C43C2314yescomplemented
175C4×D4×C43D414yes—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C4⋊C8×C43C2314yescomplemented
182C22⋊C8×C43C2314yes—
183C22⋊C8×C43C2314yescomplemented
184C4×C8×C43C2314yescomplemented
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—24no—
191C23×D43—44no—
192C23×D43—44no—
193C23×D43—82no—
194C2×D4×C43—24no—
195C2×D4×C43C2×D414yes—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43—82no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—24no—
223C22×Dic43—82no—
224#10621898—28no—
225#10621898—44no—
226#10621898—48no—
227C2×D172—21no—
228C2×D172—22no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—28no—
237C2×D172—44no—
238C2×D172—44no—
239C2×D172—48no—
240C2×D172#4114yes—
241C2×D172C2412yes—
242C2×D172C2412yes—
243C2×D172C2412yes—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—24no—
247C2×C4×D43—44no—
248C2×C4×D43—82no—
249C2×C4×D43—82no—
250C2×Dic86—22no—
251C2×Dic86—22no—
252C2×Dic86—21no—
253C2×Dic86C2412yes—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—44no—
259C2×C8×C43—44no—
260C2×C8×C43C2412yes—
261C2×C8×C43C2412yes—
262C2×C8×C43C2412yes—
263C2×C8×C43C2412yes—
264C4⋊C4×C43C2×D414yes—
265C22⋊C4×C43C2×D414yes—
266C22⋊C4×C43C2×D414yes—
267C42×C43C2×D412yes—
268C42×C43C2412yes—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43C2412yes—
284C4⋊Dic43C2412yes—
285C4⋊Dic43C2412yes—
286C4⋊Dic43C2412yes—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290C4×Dic43—24no—
291D344—28no—
292D344—44no—
293#10621873—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43#13514yes—
300C23×C43C22×D412yes—
301C23×C43C22×D412yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—24no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—48no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—48no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—84no—
318C22×D43—816no—
319D4×C43—28no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—24no—
325C2×C4×C43—24no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4112yes—
336C2×C4×C43H(5,𝔽2)12yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—48no—
339C22⋊D43—48no—
340C22⋊D43—84no—
341C22⋊D43—84no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—84no—
353D172—24no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—22no—
359D172—48no—
360D172—42no—
361D172—42no—
362D172C2×#4114yes—
363C4×D43—48no—
364C4×D43—84no—
365C4×D43—84no—
366Dic86—22no—
367Dic86—22no—
368Dic86—42no—
369C8×C43—22no—
370C8×C43—22no—
371C8×C43—22no—
372C8×C43—22no—
373C2×#3297—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—28no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—44no—
381C22×C43#54612yes—
382C22×C43C2×#13514yes—
383C22×C43C2×#13512yes—
384C22×C43#57612yes—
385C22×C43C23×D411yescharacteristic
386C2×D43—24no—
387C2×D43—48no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—816no—
397C2×D43—84no—
398C2×D43—84no—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—22no—
403C4×C43#54612yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—42no—
407Dic43—42no—
408Dic43—42no—
409Dic43—42no—
410Dic43—42no—
411C2×#553—431no—
412C2×#546—431no—
413#3297—4316no—
414C2×#488—431no—
415C2×#484—431no—
416C2×#482—431no—
417C2×#478—431no—
418C2×#466—431no—
419C2×#465—431no—
420C2×#463—431no—
421C2×#449—431no—
422C2×#447—431no—
423C2×C4×D8—431no—
424C2×C8×D4D4311yescharacteristic, complemented
425C2×#416—431no—
426C22×#102—431no—
427C2×C43—24no—
428C2×C43—42no—
429C2×C43#329714yescomplemented
430C2×C43C2×#54611yescharacteristic
431C2×C43C22×#13511yescharacteristic
432C2×C43C2×#57611yescharacteristic
433D43—44no—
434D43—82no—
435D43—82no—
436C22×#41—431no—
437C23×D4—431no—
438C22×SD16—431no—
439C22×D8—431no—
440C22×D8—431no—
441C23×C8C2×D4311yescharacteristic
442C23×C8C2×D4311yescharacteristic, complemented
443#553—438no—
444#553—864no—
445#546—438no—
446#546—864no—
447C2×#126—861no—
448C2×#125—431no—
449C2×#124—431no—
450C2×#123—861no—
451C2×#123—861no—
452C2×C22⋊Q8—431no—
453C2×#121—431no—
454C2×#121—431no—
455C2×#121—431no—
456C2×#121—861no—
457C2×#121—861no—
458C2×#120—861no—
459C2×C4×D4—431no—
460C2×C4×D4—431no—
461C2×C4×D4—861no—
462C2×C4×D4C2×D4311yescharacteristic
463C2×#117—431no—
464C22×C4⋊C4—431no—
465C22×C22⋊C4—861no—
466#488—438no—
467#484—438no—
468#482—438no—
469#478—438no—
470#466—438no—
471#465—438no—
472#463—438no—
473#449—438no—
474#447—438no—
475C4×D8—438no—
476C8×D4C2×D4318yescomplemented
477C2×#107—431no—
478C2×#107—431no—
479C2×#106—431no—
480C2×C4⋊C8C2×D4311yescharacteristic, complemented
481#416—438no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—438no—
492C2×#102—431no—
493C2×C22⋊C8C2×D4311yescharacteristic
494C2×C22⋊C8C2×D4311yescharacteristic, complemented
495C2×C4×C8C2×D4311yescharacteristic, complemented
496C43C2×#329711yescharacteristic, complemented, Sylow
497C25—861no—
498C2×#41—434no—
499C2×#41—864no—
500C2×#41—862no—
501C2×#41—1722no—
502C22×Q8—431no—
503C22×D4—431no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—434no—
507C22×D4—864no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—862no—
514C22×D4—1722no—
515C22×D4D17211yescharacteristic
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4C22×D4311yescharacteristic
521C23×C4C22×D4311yescharacteristic
522C2×SD16—434no—
523C2×SD16—1722no—
524C2×D8—434no—
525C2×D8—434no—
526C2×D8—864no—
527C2×D8—1722no—
528C22×C8—42no—
529C22×C8—42no—
530C22×C8C22×D4311yescharacteristic
531C22×C8C22×D4311yescharacteristic
532C22×C8C22×D4311yescharacteristic
533C22×C8C22×D4311yescharacteristic
534C22×C8C22×D4314yes—
535C22×C8C22×D4314yescomplemented
536#126—868no—
537#125—434no—
538#125—862no—
539#124—434no—
540#124—862no—
541#123—868no—
542#123—868no—
543C22⋊Q8—434no—
544C22⋊Q8—862no—
545#121—434no—
546#121—434no—
547#121—434no—
548#121—868no—
549#121—862no—
550#121—862no—
551#121—862no—
552#121—868no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—868no—
557C4×D4—862no—
558C4×D4—862no—
559C4×D4D17214yes—
560C4×D4C22×D4314yes—
561#117—434no—
562#117—862no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—434no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4D17211yescharacteristic
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—868no—
584C2×C22⋊C4D17211yescharacteristic
585C2×C22⋊C4D17211yescharacteristic
586C2×C42—861no—
587C2×C42C22×D4311yescharacteristic
588#107—434no—
589#107—434no—
590#106—434no—
591C4⋊C8C22×D4314yescomplemented
592#103—434no—
593#103—434no—
594#103—434no—
595#102—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600#102—434no—
601#102—434no—
602C22⋊C8C22×D4314yes—
603C22⋊C8C22×D4314yescomplemented
604C4×C8C22×D4314yescomplemented
605C24—861no—
606C24—864no—
607C24—861no—
608C24—861no—
609C24—3442no—
610C24—1724no—
611C24—1724no—
612C24C2×D17211yescharacteristic
613C24C2×D17211yescharacteristic
614#41—868no—
615#41—1724no—
616#41—1728no—
617C2×Q8—432no—
618C2×Q8—861no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×D4—24no—
622C2×D4—434no—
623C2×D4—432no—
624C2×D4—432no—
625C2×D4—432no—
626C2×D4—868no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—3442no—
641C2×D4—3442no—
642C2×D4—1724no—
643C2×D4—1728no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4C2×D17214yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—864no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—864no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—3442no—
662C22×C4—3442no—
663C22×C4—3442no—
664C22×C4—1724no—
665C22×C4C2×D17212yes—
666C22×C4C2×D17212yes—
667C22×C4C2×D17211yescharacteristic
668C22×C4C2×D17211yescharacteristic
669C22×C4C2×D17211yescharacteristic
670C22×C4C2×D17211yescharacteristic
671C22×C4C23×D4312yes—
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674SD16—1724no—
675D8—868no—
676D8—1724no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—44no—
682C2×C8—44no—
683C2×C8C23×D4312yes—
684C2×C8C23×D4312yes—
685C2×C8C23×D4312yes—
686C2×C8C23×D4312yes—
687C4⋊C4—432no—
688C4⋊C4—432no—
689C4⋊C4—432no—
690C4⋊C4—432no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—864no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4C2×D17214yes—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4C2×D17214yes—
710C22⋊C4C2×D17214yes—
711C42—864no—
712C42C2×D17212yes—
713C42C23×D4312yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—862no—
720C23—864no—
721C23—862no—
722C23—862no—
723C23—34416no—
724C23—3444no—
725C23—1728no—
726C23—1722no—
727C23—1728no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23#1306334714yes—
736C23C22×D17212yes—
737C23C22×D17212yes—
738C23C22×D17211yescharacteristic
739Q8—862no—
740Q8—862no—
741Q8—1722no—
742D4—28no—
743D4—434no—
744D4—862no—
745D4—862no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—864no—
750D4—3444no—
751D4—3444no—
752D4—1728no—
753D4—1728no—
754D4—1728no—
755D4—1722no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—3444no—
773C2×C4—3444no—
774C2×C4—3444no—
775C2×C4—1728no—
776C2×C4—1722no—
777C2×C4—1722no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4C22×D17212yes—
782C2×C4C22×D17212yes—
783C2×C4C22×D17212yes—
784C2×C4C22×D17212yes—
785C2×C4C22×D17211yescharacteristic
786C2×C4#41×D4312yes—
787C2×C4#1306337012yes—
788C2×C4C24×D4311yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—864no—
801C22—34416no—
802C22—3444no—
803C22—3444no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1728no—
813C22#1458354412yes—
814C22C2×#1306334714yes—
815C22C2×#1306334712yes—
816C22#1458370412yes—
817C22C23×D17211yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—1722no—
823C4—1722no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4#1458354412yes—
828C4C2×#41×D4311yescharacteristic
829C4C2×#1306337011yescharacteristic
830C2—24no—
831C2—42no—
832C2—3442no—
833C2—3442no—
834C2—1724no—
835C2#1914644714yesdirect product factor
836C2C2×#1458354411yescharacteristic
837C2C22×#1306334711yescharacteristic
838C2C2×#1458370411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C8×D4×C43C2
socleC23×C43C22×D4
hypercenterC2×C8×D4D43
hypocenterC43C2×#3297
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583545C2semidirect
3. #19146447C2direct (N × H)
4. C2×#14583254C2semidirect
5. C2×#14583235C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583200C2semidirect
8. C2×#14583135C2semidirect
9. C2×#14583128C2semidirect
10. C2×#14583115C2semidirect
11. C2×#14583046C2semidirect
12. C2×#14583035C2semidirect
13. C2×C4×D344C2semidirect
14. C2×#14582896C2semidirect
15. C22×#13063247C2semidirect
16. C2×C8×D4×C43C2semidirect
19. C22×#10621873C22semidirect
23. #14583595C22semidirect
25. #14583545C22semidirect
27. C2×#13063317C22semidirect
34. C2×#13063299C22semidirect
39. C2×C4×D172C22semidirect
41. C2×#13063284C22semidirect
44. #14583254C22semidirect
45. #14583235C22semidirect
46. #14583224C22semidirect
47. #14583200C22semidirect
48. #14583135C22semidirect
49. #14583128C22semidirect
50. #14583115C22semidirect
51. #14583046C22semidirect
52. #14583035C22semidirect
53. C4×D344C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063257C22semidirect
57. #14582896C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
67. C2×#13063247C22semidirect
68. C2×#13063247C22semidirect
70. C23×C8×C43C22semidirect
72. C8×D4×C43C22semidirect
73. C2×C4⋊C8×C43C22semidirect
75. C2×C22⋊C8×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
100. C2×#10621873C23semidirect
107. #13063317C23semidirect
119. #13063299C23semidirect
126. C4×D172C23semidirect
129. #13063284C23semidirect
151. #13063259C23semidirect
152. #13063259C23semidirect
153. #13063257C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063250C23semidirect
163. #13063247C23semidirect
174. C22×C8×C43C23semidirect
181. C4⋊C8×C43C23semidirect
183. C22⋊C8×C43C23semidirect
184. C4×C8×C43C23semidirect
424. C2×C8×D4D43semidirect
429. C2×C43#3297semidirect
442. C23×C8C2×D43semidirect
476. C8×D4C2×D43semidirect
480. C2×C4⋊C8C2×D43semidirect
494. C2×C22⋊C8C2×D43semidirect
495. C2×C4×C8C2×D43semidirect
496. C43C2×#3297semidirect
535. C22×C8C22×D43semidirect
591. C4⋊C8C22×D43semidirect
603. C22⋊C8C22×D43semidirect
604. C4×C8C22×D43semidirect
835. C2#19146447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145835452
#191464472
C2×#145832542
C2×#145832352
C2×#145832242
C2×#145832002
C2×#145831352
C2×#145831282
C2×#145831152
C2×#145830462
C2×#145830352
C2×C4×D3442
C2×#145828962
C22×#130632472
C2×C8×D4×C432
C2×#329743