Finite Group Databasebeta

← C2×#19146504 #25973027

Subgroups — C2×#19146504 #25973027

Order 11008.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583599C211yesmaximal, characteristic, complemented
2C2×#14583557C211yesmaximal, characteristic, complemented
3#19146504C2116yesmaximal, direct product factor
4C2×#14583253C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583239C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583132C211yesmaximal, characteristic, complemented
9C2×#14583125C211yesmaximal, characteristic, complemented
10C2×#14583041C211yesmaximal, characteristic, complemented
11C2×#14583036C211yesmaximal, characteristic, complemented
12C2×C4×#10621883C211yesmaximal, characteristic, complemented
13C2×#14582964C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583599—24no—
23#14583599C2218yescomplemented
24#14583557—24no—
25#14583557C2218yescomplemented
26C2×#13063318—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063308—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063298—21no—
33C2×#13063298—21no—
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063283C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583253C2218yescomplemented
44#14583239C2218yescomplemented
45#14583216C2218yescomplemented
46#14583207C2218yescomplemented
47#14583132C2218yescomplemented
48#14583125C2218yescomplemented
49#14583041C2218yescomplemented
50#14583036C2218yescomplemented
51C4×#10621883C2218yescomplemented
52#14582964C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56#14582892C2218yescomplemented
57C2×#13063250C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62#103×D43C2218yescomplemented
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C2×Q8×D43—22no—
84C2×Q8×D43—24no—
85C2×Q8×D43—42no—
86C2×Q8×D43C2314yes—
87C22×D172D411yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C23×Dic43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C2×#10621883—24no—
98C2×#10621883C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—42no—
102C2×C8×D43—42no—
103C2×C8×D43C2314yes—
104C2×C8×D43C2314yes—
105#13063318—28no—
106#13063317—22no—
107#13063317C2314yes—
108#13063311—28no—
109#13063308—28no—
110#13063302—28no—
111#13063301—22no—
112#13063301C2314yes—
113#13063298—28no—
114#13063298—28no—
115#13063296—22no—
116#13063296—22no—
117#13063296—22no—
118#13063296C2314yes—
119#13063296C2314yes—
120#13063296C2314yes—
121C4×Dic86—22no—
122C4×Dic86C2314yes—
123C4×D172D414yes—
124C4×D172C2314yes—
125C4×C22⋊D43—28no—
126(C22⋊D43)⋊C4—28no—
127#13063283—22no—
128#13063283C2314yes—
129C2×C4⋊Dic43D411yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149#13063259C2314yes—
150#13063257C2314yes—
151#13063256C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162C4×C43⋊C8C2314yes—
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C2×SD16×C43—42no—
168C2×SD16×C43C2314yes—
169C2×D8×C43—42no—
170C2×D8×C43C2314yes—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173#124×C43—22no—
174#124×C43C2314yes—
175C4×D4×C43—22no—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C23×D43C2×D411yescharacteristic
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43C2412yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—24no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—82no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—44no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—82no—
216C22×Dic43—24no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—44no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224Q8×D43—28no—
225Q8×D43—44no—
226Q8×D43—48no—
227#10621900—28no—
228#10621900—44no—
229#10621900—48no—
230C2×D172—24no—
231C2×D172C2×D414yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—44no—
239C2×C4×D43—82no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2412yes—
243C2×C4×D43C2412yes—
244C2×Dic86—21no—
245C2×Dic86—22no—
246C2×Dic86—24no—
247C2×Dic86—44no—
248C2×Dic86#4114yes—
249C2×Dic86C2412yes—
250SD16×C43—44no—
251D8×C43—44no—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C42×C43C2×D412yes—
262C42×C43C2412yes—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266#10621883—28no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4C2×D414yes—
270(C2×D43)⋊C4C2×D414yes—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43C2×D414yes—
275C4⋊Dic43C2412yes—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283C4×Dic43—24no—
284C4×Dic43—24no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289C8×D43—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43#13514yes—
306C22×D43C22×D412yes—
307C22×D43C22×D412yes—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—42no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—42no—
316D4×C43—42no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—84no—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4112yes—
328C2×C4×C43H(5,𝔽2)12yes—
329C2×C4×C43C2511yescharacteristic
330C22⋊D43—48no—
331C22⋊D43—48no—
332C22⋊D43—48no—
333C22⋊D43—84no—
334C2×Dic43—24no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—48no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347D172—28no—
348C4×D43—24no—
349C4×D43—24no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—48no—
355C4×D43—84no—
356Dic86—24no—
357Dic86—22no—
358Dic86—48no—
359Dic86C2×#4114yes—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3301—431nomaximal, Sylow
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—84no—
372C22×C43—84no—
373C22×C43#54612yes—
374C22×C43C2×#13512yes—
375C22×C43#57712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—22no—
378C2×D43—28no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—44no—
384C2×D43C2×#13514yes—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#54612yes—
390C4×C43C22×#4111yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—24no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×#553—431no—
399C2×#548—431no—
400#3301—4316no—
401C2×#488—431no—
402C2×#481—431no—
403C2×#485—431no—
404C2×#479—431no—
405C2×#466—431no—
406C2×#465—431no—
407C2×#463D4311yescharacteristic, complemented
408C2×#449—431no—
409C2×#448—431no—
410C2×C4×SD16—431no—
411C2×C8×D4—431no—
412C2×#416—431no—
413C22×#103—431no—
414C2×C43—82no—
415C2×C43—82no—
416C2×C43#330114yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C22×#13511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—24no—
421D43—42no—
422C22×#41—431no—
423C23×Q8—431no—
424C22×SD16—431no—
425C22×SD16C2×D4311yescharacteristic
426C22×D8C2×D4311yescharacteristic
427C23×C8—431no—
428C23×C8—431no—
429#553—438no—
430#553—864no—
431#548—438no—
432#548—864no—
433C2×#126—861no—
434C2×#125—431no—
435C2×#124—861no—
436C2×#124C2×D4311yescharacteristic
437C2×#123—861no—
438C2×C22⋊Q8—431no—
439C2×C22⋊Q8—861no—
440C2×#121—431no—
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×C4×D4—861no—
449C2×C4×D4C2×D4311yescharacteristic
450C2×#117—431no—
451C22×C4⋊C4—431no—
452#488—438no—
453#485—438no—
454#481—438no—
455#479—438no—
456#466—438no—
457#465—438no—
458#463C2×D4318yescomplemented
459#449—438no—
460#448—438no—
461C4×SD16—438no—
462C8×D4—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8C2×D4311yescharacteristic
467#416—438no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—438no—
474C2×#103C2×D4311yescharacteristic
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102C2×D4311yescharacteristic
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C4×C8—431no—
482C43C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—862no—
485C2×#41—864no—
486C2×#41—1722no—
487C22×Q8—434no—
488C22×Q8—431no—
489C22×Q8—861no—
490C22×Q8—862no—
491C22×Q8—864no—
492C22×Q8—1722no—
493C22×Q8C22×D4311yescharacteristic
494C22×D4—431no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4C22×D4311yescharacteristic
500C22×D4C22×D4311yescharacteristic
501C23×C4—21no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C2×SD16—42no—
508C2×SD16—434no—
509C2×SD16—864no—
510C2×SD16C22×D4314yes—
511C2×D8—42no—
512C2×D8C22×D4314yes—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—434no—
516C22×C8—434no—
517C22×C8—1722no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#126—868no—
522#125—434no—
523#125—862no—
524#124—22no—
525#124—868no—
526#124C22×D4314yes—
527#123—868no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—862no—
531#121—434no—
532#121—434no—
533#121—434no—
534#121—868no—
535#121—868no—
536#121—862no—
537#121—862no—
538#121—862no—
539C4×Q8—434no—
540C4×Q8—862no—
541C4×D4—22no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—868no—
545C4×D4—868no—
546C4×D4C22×D4314yes—
547#117—434no—
548#117—862no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—434no—
554C2×C4⋊C4—862no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8C22×D4314yes—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103C22×D4314yes—
584#102—434no—
585#102—434no—
586#102—434no—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C4×C8—434no—
591C24—21no—
592C24—21no—
593C24—431no—
594C24—431no—
595#41—868no—
596#41—1724no—
597#41—1728no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—434no—
602C2×Q8—432no—
603C2×Q8—864no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—868no—
607C2×Q8—1724no—
608C2×Q8—1724no—
609C2×Q8—1728no—
610C2×Q8C23×D4312yes—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—434no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—3442no—
624C2×D4—1724no—
625C2×D4—1724no—
626C2×D4—1724no—
627C2×D4C23×D4312yes—
628C2×D4C23×D4312yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—82no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—864no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—3442no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656SD16—44no—
657SD16—868no—
658D8—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—862no—
664C2×C8—862no—
665C2×C8—1724no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—434no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—434no—
687C22⋊C4—434no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C42—864no—
694C42—864no—
695C42D4×D4312yes—
696C42C23×D4312yes—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—434no—
706C23—432no—
707C23—432no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—434no—
718Q8—862no—
719Q8—864no—
720Q8—1728no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—42no—
727D4—868no—
728D4—3444no—
729D4—1728no—
730D4—1728no—
731D4—1728no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—84no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—864no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—3444no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4C2×D4×D4312yes—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337012yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—84no—
778C22—434no—
779C22—868no—
780C22—862no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—1724no—
786C22#1458354612yes—
787C22#135×D4312yes—
788C22#1458370912yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—862no—
795C4—862no—
796C4—864no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4#1458354612yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337011yescharacteristic
803C2—82no—
804C2—82no—
805C2—864no—
806C2—1722no—
807C2#1914650414yesdirect product factor
808C2C2×#1458354611yescharacteristic
809C2C2×#135×D4311yescharacteristic
810C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
hypercenterC2×#463D43
hypocenterC43C2×#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583599C2semidirect
2. C2×#14583557C2semidirect
3. #19146504C2direct (N × H)
4. C2×#14583253C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583239C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583132C2semidirect
9. C2×#14583125C2semidirect
10. C2×#14583041C2semidirect
11. C2×#14583036C2semidirect
12. C2×C4×#10621883C2semidirect
13. C2×#14582964C2semidirect
14. C2×#14582892C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#463C2semidirect
23. #14583599C22semidirect
25. #14583557C22semidirect
43. #14583253C22semidirect
44. #14583239C22semidirect
45. #14583216C22semidirect
46. #14583207C22semidirect
47. #14583132C22semidirect
48. #14583125C22semidirect
49. #14583041C22semidirect
50. #14583036C22semidirect
51. C4×#10621883C22semidirect
52. #14582964C22semidirect
56. #14582892C22semidirect
62. #103×D43C22semidirect
73. C43×#463C22semidirect
407. C2×#463D43semidirect
416. C2×C43#3301semidirect
458. #463C2×D43semidirect
482. C43C2×#3301semidirect
807. C2#19146504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835992
C2×#145835572
#191465042
C2×#145832532
C2×#145832162
C2×#145832392
C2×#145832072
C2×#145831322
C2×#145831252
C2×#145830412
C2×#145830362
C2×C4×#106218832
C2×#145829642
C2×#145828922
C2×#103×D432
C2×C43×#4632
C2×#330143