Finite Group Databasebeta

← C2×#19146562 #25973113

Subgroups — C2×#19146562 #25973113

Order 11008.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583549C211yesmaximal, characteristic, complemented
2C2×#14583540C211yesmaximal, characteristic, complemented
3#19146562C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583227C211yesmaximal, characteristic, complemented
7C2×#14583188C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583116C211yesmaximal, characteristic, complemented
10C2×#14583043C211yesmaximal, characteristic, complemented
11C2×#14583032C211yesmaximal, characteristic, complemented
12C2×#14583008C211yesmaximal, characteristic, complemented
13C2×#14582970C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C22×#13063247C211yesmaximal, characteristic, complemented
16C2×C43×#465C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900—21no—
19C23×D172C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621872C2211yescharacteristic, complemented
23#14583549—24no—
24#14583549C2218yescomplemented
25#14583540—24no—
26#14583540C2218yescomplemented
27C2×#13063324C2211yescharacteristic, complemented
28C2×#13063314C2211yescharacteristic
29C2×#13063310—21no—
30C2×#13063307—21no—
31C2×#13063306—21no—
32C2×#13063302—21no—
33C2×#13063300—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063296C2211yescharacteristic, complemented
36C2×#13063295—21no—
37C2×D4×Dic43C2211yescharacteristic, complemented
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43C2211yescharacteristic
40C22×C4⋊Dic43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—21no—
43#14583260C2218yescomplemented
44#14583227C2218yescomplemented
45#14583219C2218yescomplemented
46#14583188C2218yescomplemented
47#14583151C2218yescomplemented
48#14583116C2218yescomplemented
49#14583043C2218yescomplemented
50#14583032C2218yescomplemented
51#14583008C2218yescomplemented
52#14582970C2218yescomplemented
53C2×#13063256C2211yescharacteristic, complemented
54C2×#13063256C2211yescharacteristic, complemented
55C2×Dic43⋊C8C2211yescharacteristic, complemented
56#14582899C2218yescomplemented
57C2×#13063249C2211yescharacteristic, complemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063247C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2218yescomplemented
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063235C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic, complemented
70C23×C8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#465C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C2×#10621900—28no—
83C2×#10621900—48no—
84C22×Dic86—21no—
85C22×D172—24no—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—22no—
89C22×D172—21no—
90C22×D172—42no—
91C22×D172C2311yescharacteristic
92C22×D172C2314yes—
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C23×Dic43—21no—
97C23×Dic43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43C2311yescharacteristic
102C2×#10621882—24no—
103C2×#10621882—42no—
104C2×#10621882C2314yes—
105C2×#10621882C2314yes—
106C2×#10621872—42no—
107C2×#10621872C2314yescomplemented
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110#13063324—22no—
111#13063324C2314yescomplemented
112#13063314—22no—
113#13063314C2314yes—
114#13063310—28no—
115#13063307—28no—
116#13063306—28no—
117#13063302—28no—
118#13063300—22no—
119#13063300—28no—
120#13063300C2314yes—
121#13063296—22no—
122#13063296C2314yescomplemented
123#13063295—28no—
124D4×Dic43—22no—
125D4×Dic43C2314yescomplemented
126#13063287—22no—
127#13063287C2314yes—
128C4×C22⋊D43D414yes—
129C4×C22⋊D43C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—22no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2314yes—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yescomplemented
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43D411yescharacteristic
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C22⋊C4×D43—28no—
149C2×C4×Dic43C2311yescharacteristic
150#13063256C2314yescomplemented
151#13063256C2314yescomplemented
152Dic43⋊C8C2314yescomplemented
153#13063249C2314yescomplemented
154#13063249C2314yescomplemented
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063245C2314yes—
160#13063245C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162(C2×D43)⋊C8C2314yescomplemented
163#13063235C2314yescomplemented
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43—21no—
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C2×SD16×C43—42no—
169C2×SD16×C43C2314yescomplemented
170C22×C8×C43—42no—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2314yes—
174C22⋊Q8×C43—22no—
175C22⋊Q8×C43C2314yes—
176#121×C43—22no—
177#121×C43C2314yes—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183#106×C43C2314yescomplemented
184#103×C43C2314yescomplemented
185#102×C43C2314yescomplemented
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—24no—
191C23×D43—44no—
192C23×D43—44no—
193C23×D43—82no—
194C23×D43C2×D411yescharacteristic
195C2×Q8×C43—21no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43C2412yes—
199C2×D4×C43—21no—
200C2×D4×C43—24no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43—44no—
204C2×D4×C43C2412yes—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—24no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—24no—
222C22×Dic43—44no—
223C22×Dic43—44no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227#10621902—28no—
228#10621902—44no—
229#10621902—48no—
230#10621900—432no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—24no—
234C2×D172—21no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—28no—
240C2×D172—44no—
241C2×D172—44no—
242C2×D172—44no—
243C2×D172—48no—
244C2×D172—82no—
245C2×D172#4114yescomplemented
246C2×D172C2412yes—
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—82no—
256C2×C4×D43C2×D412yes—
257C2×C4×D43C2412yes—
258C2×Dic86—24no—
259C2×Dic86—44no—
260SD16×C43—44no—
261C2×C8×C43—22no—
262C2×C8×C43—22no—
263C2×C8×C43—44no—
264C2×C8×C43C2412yes—
265C2×C8×C43C2412yes—
266C4⋊C4×C43—24no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C2412yes—
270C4⋊C4×C43C2412yes—
271C22⋊C4×C43—24no—
272C22⋊C4×C43—24no—
273C22⋊Dic43—24no—
274C22⋊Dic43—24no—
275C22⋊Dic43C2×D414yes—
276#10621882—28no—
277#10621882—44no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4C2×D414yes—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—24no—
286C4⋊Dic43C2412yes—
287C4⋊Dic43C2412yes—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290Dic43⋊C4C2×D414yes—
291C4×Dic43C2×D412yes—
292C4×Dic43C2412yes—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297#10621872—44no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43AGL(1,ℤ/8)14yes—
305C23×C43C22×D412yes—
306C23×C43C22×D411yescharacteristic
307C22×D43—22no—
308C22×D43—24no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—48no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—48no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—84no—
321C22×D43—816no—
322C22×D43C22×D412yes—
323Q8×C43—22no—
324Q8×C43—22no—
325Q8×C43—42no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—48no—
329D4×C43—42no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43C22×D412yes—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4112yes—
343C2×C4×C43H(5,𝔽2)12yes—
344C2×C4×C43C2511yescharacteristic
345C22⋊D43—28no—
346C22⋊D43—48no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—48no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—48no—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—24no—
360D172—22no—
361D172—22no—
362D172—22no—
363D172—48no—
364D172—48no—
365D172—42no—
366D172—84no—
367D172C2×#4114yescomplemented
368C4×D43—24no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—48no—
372C4×D43—48no—
373C4×D43—84no—
374Dic86—48no—
375C8×C43—22no—
376C8×C43—22no—
377C43⋊C8—22no—
378C43⋊C8—22no—
379C2×#3306—431nomaximal, Sylow
380C22×C43—22no—
381C22×C43—28no—
382C22×C43—22no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—84no—
387C22×C43#54612yes—
388C22×C43C2×AGL(1,ℤ/8)14yes—
389C22×C43C2×AGL(1,ℤ/8)12yes—
390C22×C43#57712yes—
391C22×C43C23×D411yescharacteristic
392C2×D43—24no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—44no—
397C2×D43—48no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—816no—
404C2×D43—84no—
405C4×C43—22no—
406C4×C43—42no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43#54612yes—
410C4×C43C22×#4111yescharacteristic
411C4×C43C2×H(5,𝔽2)11yescharacteristic
412Dic43—22no—
413Dic43—22no—
414Dic43—22no—
415Dic43—42no—
416Dic43—42no—
417C2×#547—431no—
418C2×#546—431no—
419#3306—4316no—
420C2×#489—431no—
421C2×#481—431no—
422C2×#483—431no—
423C2×#476—431no—
424C2×#469—431no—
425C2×#465D4311yescharacteristic, complemented
426C2×#463—431no—
427C2×#449—431no—
428C2×#447—431no—
429C2×#442—431no—
430C2×#435—431no—
431C2×#417—431no—
432C22×#102—431no—
433C2×C43—24no—
434C2×C43—82no—
435C2×C43#330614yescomplemented
436C2×C43C2×#54611yescharacteristic
437C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C43C2×#57711yescharacteristic
439D43—42no—
440D43—44no—
441D43—82no—
442C22×#41—431no—
443C22×#41—861no—
444C23×D4—431no—
445C22×SD16C2×D4311yescharacteristic, complemented
446C22×D8—431no—
447C22×D8—431no—
448C22×M16—431no—
449C23×C8C2×D4311yescharacteristic
450#547—438no—
451#547—864no—
452#546—438no—
453#546—864no—
454C2×C4⋊Q8—431no—
455C2×#124—431no—
456C2×#123—861no—
457C2×#123—861no—
458C2×#123—861no—
459C2×C22⋊Q8—861no—
460C2×C22⋊Q8C2×D4311yescharacteristic
461C2×#121—431no—
462C2×#121—431no—
463C2×#121—861no—
464C2×#121C2×D4311yescharacteristic
465C2×#120—861no—
466C2×C4×D4—431no—
467C2×C4×D4—431no—
468C2×C4×D4—431no—
469C22×C4⋊C4—431no—
470C22×C4⋊C4—431no—
471C22×C22⋊C4—861no—
472#489—438no—
473#483—438no—
474#481—438no—
475#476—438no—
476#469—438no—
477#465C2×D4318yescomplemented
478#463—438no—
479#449—438no—
480#447—438no—
481#442—438no—
482#435—438no—
483C2×#106—431no—
484C2×#106—431no—
485C2×#106C2×D4311yescharacteristic, complemented
486C2×C4⋊C8—431no—
487#417—438no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103C2×D4311yescharacteristic, complemented
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—438no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102C2×D4311yescharacteristic, complemented
499C2×C22⋊C8—431no—
500C2×C22⋊C8—431no—
501C2×#97—431no—
502C43C2×#330611yescharacteristic, complemented, Sylow
503C25—861no—
504C2×#41—434no—
505C2×#41—862no—
506C2×#41—868no—
507C2×#41—864no—
508C2×#41—1722no—
509C2×#41—1728no—
510C22×Q8—861no—
511C22×Q8C22×D4311yescharacteristic
512C22×D4—21no—
513C22×D4—431no—
514C22×D4—431no—
515C22×D4—431no—
516C22×D4—434no—
517C22×D4—864no—
518C22×D4—861no—
519C22×D4—861no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—862no—
523C22×D4—1722no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—431no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C2×SD16—42no—
533C2×SD16C22×D4314yescomplemented
534C2×D8—434no—
535C2×D8—434no—
536C2×D8—864no—
537C2×D8—1722no—
538C2×M16—434no—
539C2×M16—1722no—
540C22×C8—42no—
541C22×C8—431no—
542C22×C8—431no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545C22×C8C22×D4314yes—
546C4⋊Q8—434no—
547C4⋊Q8—862no—
548#124—434no—
549#124—862no—
550#123—868no—
551#123—868no—
552#123—868no—
553C22⋊Q8—22no—
554C22⋊Q8—868no—
555C22⋊Q8C22×D4314yes—
556#121—22no—
557#121—434no—
558#121—434no—
559#121—868no—
560#121—862no—
561#121—862no—
562#121C22×D4314yes—
563#120—868no—
564C4×D4—434no—
565C4×D4—434no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—862no—
569C4×D4—862no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—431no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—434no—
576C2×C4⋊C4—862no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—862no—
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—431no—
586C2×C22⋊C4—431no—
587C2×C22⋊C4—868no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C42—431no—
595#106—434no—
596#106—434no—
597#106C22×D4314yescomplemented
598C4⋊C8—434no—
599#103—434no—
600#103—434no—
601#103C22×D4314yescomplemented
602#102—434no—
603#102—434no—
604#102—434no—
605#102—434no—
606#102—434no—
607#102—434no—
608#102C22×D4314yescomplemented
609C22⋊C8—434no—
610C22⋊C8—434no—
611#97—434no—
612C24—21no—
613C24—431no—
614C24—861no—
615C24—864no—
616C24—861no—
617C24—3442no—
618C24—1724no—
619C24—1724no—
620C24D4×D4311yescharacteristic
621#41—868no—
622#41—1724no—
623#41—1728no—
624#41—17232no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—864no—
629C2×Q8—1724no—
630C2×Q8C23×D4312yes—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—44no—
636C2×D4—434no—
637C2×D4—434no—
638C2×D4—432no—
639C2×D4—432no—
640C2×D4—868no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—864no—
644C2×D4—864no—
645C2×D4—861no—
646C2×D4—864no—
647C2×D4—861no—
648C2×D4—862no—
649C2×D4—862no—
650C2×D4—862no—
651C2×D4—3442no—
652C2×D4—1724no—
653C2×D4—1728no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1724no—
657C2×D4C23×D4312yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—864no—
669C22×C4—864no—
670C22×C4—864no—
671C22×C4—864no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—864no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—3442no—
678C22×C4—1724no—
679C22×C4—1724no—
680C22×C4—1724no—
681C22×C4—1724no—
682C22×C4D4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4C23×D4312yes—
685C22×C4C23×D4311yescharacteristic
686SD16—44no—
687D8—868no—
688D8—1724no—
689M16—1724no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—44no—
693C2×C8—432no—
694C2×C8—432no—
695C2×C8—862no—
696C2×C8—862no—
697C2×C8C23×D4312yes—
698C2×C8C23×D4312yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—434no—
703C4⋊C4—432no—
704C4⋊C4—432no—
705C4⋊C4—864no—
706C4⋊C4—864no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—864no—
710C4⋊C4C23×D4312yes—
711C4⋊C4C23×D4312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—864no—
722C42—432no—
723C42—432no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—432no—
731C23—862no—
732C23—862no—
733C23—862no—
734C23—862no—
735C23—864no—
736C23—862no—
737C23—34416no—
738C23—3444no—
739C23—1728no—
740C23—1728no—
741C23—1722no—
742C23—1722no—
743C23—1722no—
744C23—1722no—
745C23—1722no—
746C23#1306335214yes—
747C23C2×D4×D4312yes—
748C23C2×D4×D4311yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—1728no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—42no—
757D4—434no—
758D4—868no—
759D4—862no—
760D4—862no—
761D4—862no—
762D4—864no—
763D4—3444no—
764D4—1728no—
765D4—1728no—
766D4—1728no—
767D4—1722no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—432no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—864no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—3444no—
790C2×C4—1728no—
791C2×C4—1728no—
792C2×C4—1728no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1728no—
796C2×C4C2×D4×D4312yes—
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4#41×D4312yes—
799C2×C4#1306337012yes—
800C2×C4C24×D4311yescharacteristic
801C8—22no—
802C8—22no—
803C8—862no—
804C8—862no—
805C22—22no—
806C22—22no—
807C22—28no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—84no—
812C22—862no—
813C22—864no—
814C22—862no—
815C22—862no—
816C22—34416no—
817C22—3444no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1724no—
824C22—1728no—
825C22#1458353812yes—
826C22C2×#1306335214yes—
827C22C2×#1306335212yes—
828C22#1458370612yes—
829C22C22×D4×D4311yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—862no—
835C4—862no—
836C4—862no—
837C4—1722no—
838C4—1722no—
839C4#1458353812yes—
840C4C2×#41×D4311yescharacteristic
841C4C2×#1306337011yescharacteristic
842C2—24no—
843C2—82no—
844C2—3442no—
845C2—1722no—
846C2—1724no—
847C2#1914656214yesdirect product factor
848C2C2×#1458353811yescharacteristic
849C2C22×#1306335211yescharacteristic
850C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#465C2
socleC23×C43C22×D4
hypercenterC2×#465D43
hypocenterC43C2×#3306
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. C2×#14583549C2semidirect
2. C2×#14583540C2semidirect
3. #19146562C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583227C2semidirect
7. C2×#14583188C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583116C2semidirect
10. C2×#14583043C2semidirect
11. C2×#14583032C2semidirect
12. C2×#14583008C2semidirect
13. C2×#14582970C2semidirect
14. C2×#14582899C2semidirect
15. C22×#13063247C2semidirect
16. C2×C43×#465C2semidirect
22. C22×#10621872C22semidirect
24. #14583549C22semidirect
26. #14583540C22semidirect
27. C2×#13063324C22semidirect
35. C2×#13063296C22semidirect
37. C2×D4×Dic43C22semidirect
41. C2×C4⋊C4×D43C22semidirect
43. #14583260C22semidirect
44. #14583227C22semidirect
45. #14583219C22semidirect
46. #14583188C22semidirect
47. #14583151C22semidirect
48. #14583116C22semidirect
49. #14583043C22semidirect
50. #14583032C22semidirect
51. #14583008C22semidirect
52. #14582970C22semidirect
53. C2×#13063256C22semidirect
54. C2×#13063256C22semidirect
55. C2×Dic43⋊C8C22semidirect
56. #14582899C22semidirect
57. C2×#13063249C22semidirect
58. C2×#13063249C22semidirect
63. C2×#13063247C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063235C22semidirect
69. C22×SD16×C43C22semidirect
73. C43×#465C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
76. C2×#102×C43C22semidirect
107. C2×#10621872C23semidirect
111. #13063324C23semidirect
122. #13063296C23semidirect
125. D4×Dic43C23semidirect
139. C4⋊C4×D43C23semidirect
150. #13063256C23semidirect
151. #13063256C23semidirect
152. Dic43⋊C8C23semidirect
153. #13063249C23semidirect
154. #13063249C23semidirect
162. (C2×D43)⋊C8C23semidirect
163. #13063235C23semidirect
169. C2×SD16×C43C23semidirect
183. #106×C43C23semidirect
184. #103×C43C23semidirect
185. #102×C43C23semidirect
245. C2×D172#41semidirect
367. D172C2×#41semidirect
425. C2×#465D43semidirect
435. C2×C43#3306semidirect
445. C22×SD16C2×D43semidirect
477. #465C2×D43semidirect
485. C2×#106C2×D43semidirect
490. C2×#103C2×D43semidirect
498. C2×#102C2×D43semidirect
502. C43C2×#3306semidirect
533. C2×SD16C22×D43semidirect
597. #106C22×D43semidirect
601. #103C22×D43semidirect
608. #102C22×D43semidirect
847. C2#19146562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835492
C2×#145835402
#191465622
C2×#145832602
C2×#145832192
C2×#145832272
C2×#145831882
C2×#145831512
C2×#145831162
C2×#145830432
C2×#145830322
C2×#145830082
C2×#145829702
C2×#145828992
C22×#130632472
C2×C43×#4652
C2×#330643