Finite Group Databasebeta

← C2×#19146730 #25973149

Subgroups — C2×#19146730 #25973149

Order 11008.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D172C211yesmaximal, characteristic, complemented
2#19146730C2116yesmaximal, direct product factor
3C2×#14583265C211yesmaximal, characteristic, complemented
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583150C211yesmaximal, characteristic, complemented
8C2×#14583133C211yesmaximal, characteristic, complemented
9C2×#14583094C211yesmaximal, characteristic, complemented
10C2×#14583032C211yesmaximal, characteristic, complemented
11C2×#14583032C211yesmaximal, characteristic, complemented
12C2×#14583009C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582903C211yesmaximal, characteristic, complemented
15C22×#13063245C211yesmaximal, characteristic, complemented
16C2×C43×#553C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×D4×D43—21no—
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic, complemented
22C22×#10621882C2211yescharacteristic, complemented
23C22×#10621877C2211yescharacteristic, complemented
24C23×C43⋊C8C2211yescharacteristic, complemented
25D4×D172—24no—
26D4×D172C2218yescomplemented
27C2×#13063322C2211yescharacteristic
28C2×#13063300—21no—
29C2×#13063299C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×#13063295—21no—
32C2×#13063295—21no—
33C2×C4×D172C2211yescharacteristic
34#14583265C2218yescomplemented
35#14583223C2218yescomplemented
36#14583217C2218yescomplemented
37#14583196C2218yescomplemented
38#14583150C2218yescomplemented
39#14583133C2218yescomplemented
40#14583094C2218yescomplemented
41#14583032C2218yescomplemented
42#14583032C2218yescomplemented
43#14583009C2218yescomplemented
44#14582971C2218yescomplemented
45C2×#13063258C2211yescharacteristic, complemented
46C2×#13063256C2211yescharacteristic, complemented
47C2×#13063256C2211yescharacteristic, complemented
48C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
49#14582903C2218yescomplemented
50C2×#13063246C2211yescharacteristic, complemented
51C2×#13063245C2211yescharacteristic
52C2×#13063245C2211yescharacteristic
53C2×#13063245C2211yescharacteristic
54C2×#13063245C2211yescharacteristic, complemented
55C2×#13063245C2211yescharacteristic, complemented
56C2×#13063245C2211yescharacteristic, complemented
57C2×#13063245C2211yescharacteristic, complemented
58C2×#13063245C2211yescharacteristic, complemented
59C2×#13063245C2211yescharacteristic, complemented
60C2×#13063245C2218yescomplemented
61C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
62C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
63C2×#13063236C2211yescharacteristic, complemented
64C43×#553—24no—
65C43×#553C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43C2211yescharacteristic, complemented
68C2×#123×C43—21no—
69C2×#121×C43—21no—
70C2×#121×C43C2211yescharacteristic, complemented
71C2×#121×C43C2211yescharacteristic, complemented
72C2×C4×D4×C43—21no—
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic, complemented
75C2×#117×C43C2211yescharacteristic, complemented
76C22×C4⋊C4×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C24×D43—21no—
79C22×D172—24no—
80C22×D172—24no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172—22no—
85C22×D172—22no—
86C22×D172—21no—
87C22×D172—42no—
88C22×D172—42no—
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×D172C2314yes—
92C22×D172C2314yes—
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C2×D4×D43—28no—
97C2×D4×D43—48no—
98C22×C4×D43—21no—
99C2×#10621882—24no—
100C2×#10621882—42no—
101C2×#10621882—42no—
102C2×#10621882C2314yes—
103C2×#10621882C2314yescomplemented
104C2×#10621882C2314yescomplemented
105C2×#10621877—42no—
106C2×#10621877C2314yescomplemented
107C22×C43⋊C8—42no—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2314yescomplemented
113#13063322—22no—
114#13063322C2314yes—
115#13063300—28no—
116#13063299—22no—
117#13063299—22no—
118#13063299C2314yes—
119#13063299C2314yes—
120#13063295—28no—
121#13063295—28no—
122C4×D172—22no—
123C4×D172C2314yes—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4—21no—
127C2×(C2×D43)⋊C4—21no—
128#13063258C2314yescomplemented
129#13063256C2314yescomplemented
130#13063256C2314yescomplemented
131C4⋊(C43⋊C8)C2314yescomplemented
132#13063246C2314yescomplemented
133#13063245C2314yes—
134#13063245C2314yes—
135#13063245C2314yes—
136#13063245C2314yescomplemented
137#13063245C2314yescomplemented
138#13063245C2314yescomplemented
139#13063245C2314yescomplemented
140#13063245C2314yescomplemented
141#13063245C2314yescomplemented
142C22⋊(C43⋊C8)C2314yescomplemented
143C22⋊(C43⋊C8)C2314yescomplemented
144#13063236C2314yescomplemented
145C22×D4×C43—21no—
146C22×D4×C43—21no—
147C22×D4×C43D411yescharacteristic
148C22×D4×C43C2311yescharacteristic
149C23×C4×C43—21no—
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153#126×C43—28no—
154#125×C43—22no—
155#125×C43C2314yescomplemented
156#123×C43—28no—
157#121×C43—28no—
158#121×C43—22no—
159#121×C43—22no—
160#121×C43C2314yescomplemented
161#121×C43C2314yescomplemented
162C4×D4×C43—28no—
163C4×D4×C43—22no—
164C4×D4×C43D414yes—
165C4×D4×C43C2314yes—
166C4×D4×C43C2314yescomplemented
167#117×C43—22no—
168#117×C43C2314yescomplemented
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2314yescomplemented
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C22⋊C4×C43D411yescharacteristic
184C2×C42×C43—21no—
185C2×C42×C43C2311yescharacteristic
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C24×C43C2×D411yescharacteristic
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—24no—
194C23×D43—44no—
195C23×D43—44no—
196C23×D43—44no—
197C23×D43—44no—
198C23×D43—82no—
199C23×D43—82no—
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—24no—
203C2×D4×C43—24no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—44no—
207C2×D4×C43—82no—
208C2×D4×C43C2×D414yes—
209C2×D4×C43C2412yes—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—24no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—24no—
219C22×C4×C43—82no—
220C22×C4×C43—82no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2412yes—
228C22×C4×C43C2412yes—
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—24no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—44no—
233C2×C22⋊D43—44no—
234C22×Dic43—21no—
235D4×D43—432no—
236C2×D172—21no—
237C2×D172—22no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—22no—
245C2×D172—22no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—28no—
249C2×D172—28no—
250C2×D172—44no—
251C2×D172—44no—
252C2×D172—44no—
253C2×D172—44no—
254C2×D172—48no—
255C2×D172—48no—
256C2×D172—44no—
257C2×D172—82no—
258C2×D172#4114yes—
259C2×D172C2412yes—
260C2×D172C2412yes—
261C2×D172C2412yes—
262C2×C4×D43—24no—
263C2×C4×D43—44no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—24no—
267C4⋊C4×C43—24no—
268C4⋊C4×C43—24no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C2×D414yes—
271C4⋊C4×C43C2412yes—
272C4⋊C4×C43C2412yes—
273C4⋊C4×C43C2412yes—
274C22⋊C4×C43—24no—
275C22⋊C4×C43—24no—
276C22⋊C4×C43—24no—
277C22⋊C4×C43—24no—
278C22⋊C4×C43C2×D414yes—
279C22⋊C4×C43C2×D414yes—
280C42×C43—24no—
281C42×C43C2×D412yes—
282C42×C43C2412yes—
283#10621882—28no—
284#10621882—44no—
285#10621882—44no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289C4⋊Dic43—21no—
290C4⋊Dic43C2412yes—
291#10621877—44no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—22no—
296C2×C43⋊C8—44no—
297C2×C43⋊C8C2412yes—
298C2×C43⋊C8C2412yes—
299C2×C43⋊C8C2412yes—
300C2×C43⋊C8C2412yes—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43AGL(1,ℤ/8)14yes—
311C23×C43C22×D412yes—
312C23×C43C22×D412yes—
313C23×C43C22×D411yescharacteristic
314C22×D43—24no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—48no—
319C22×D43—48no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43—48no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—48no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—84no—
331C22×D43—84no—
332C22×D43—816no—
333C22×D43—816no—
334D4×C43—28no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—48no—
338D4×C43—42no—
339D4×C43—84no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—42no—
354C2×C4×C43—42no—
355C2×C4×C43—42no—
356C2×C4×C43—84no—
357C2×C4×C43—84no—
358C2×C4×C43C22×D412yes—
359C2×C4×C43C22×D412yes—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C2×#4112yes—
364C2×C4×C43H(5,𝔽2)12yes—
365C2×C4×C43C2511yescharacteristic
366C22⋊D43—48no—
367C22⋊D43—48no—
368C2×Dic43—22no—
369C2×Dic43—42no—
370D172—24no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—48no—
377D172—48no—
378D172—48no—
379D172—42no—
380D172—42no—
381D172—84no—
382D172C2×#4114yes—
383C4×D43—48no—
384C43⋊C8—22no—
385C43⋊C8—22no—
386C43⋊C8—22no—
387C43⋊C8—22no—
388C2×#3318—431nomaximal, Sylow
389C22×C43—22no—
390C22×C43—28no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—44no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—84no—
400C22×C43#54612yes—
401C22×C43C2×AGL(1,ℤ/8)14yes—
402C22×C43C2×AGL(1,ℤ/8)12yes—
403C22×C43#57612yes—
404C22×C43C23×D411yescharacteristic
405C2×D43—24no—
406C2×D43—48no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—816no—
417C2×D43—84no—
418C2×D43—84no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43#54612yes—
427C4×C43C22×#4111yescharacteristic
428C4×C43C2×H(5,𝔽2)11yescharacteristic
429Dic43—42no—
430C2×#553D4311yescharacteristic, complemented
431C2×D42—431no—
432#3318—4316no—
433C2×#490—431no—
434C2×#481—431no—
435C2×#482—431no—
436C2×#478—431no—
437C2×#469—431no—
438C2×#466—431no—
439C2×#459—431no—
440C2×#447—431no—
441C2×#447—431no—
442C2×#442—431no—
443C2×#435—431no—
444C2×#418—431no—
445C22×#102—431no—
446C2×C43—24no—
447C2×C43—42no—
448C2×C43—82no—
449C2×C43#331814yescomplemented
450C2×C43C2×#54611yescharacteristic
451C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C43C2×#57611yescharacteristic
453D43—44no—
454D43—82no—
455D43—82no—
456C23×D4—431no—
457C23×D4—431no—
458C23×D4—861no—
459C22×D8—431no—
460C22×D8—431no—
461C22×D8—431no—
462C22×M16—431no—
463C23×C8—431no—
464#553—24no—
465#553C2×D4318yescomplemented
466D42—438no—
467D42—864no—
468C2×#127—431no—
469C2×#126—21no—
470C2×#125C2×D4311yescharacteristic, complemented
471C2×#123—21no—
472C2×#121—21no—
473C2×#121—431no—
474C2×#121—431no—
475C2×#121—861no—
476C2×#121C2×D4311yescharacteristic, complemented
477C2×#121C2×D4311yescharacteristic, complemented
478C2×#120—861no—
479C2×#120—861no—
480C2×C4×D4—21no—
481C2×C4×D4—431no—
482C2×C4×D4C2×D4311yescharacteristic
483C2×C4×D4C2×D4311yescharacteristic, complemented
484C2×#117C2×D4311yescharacteristic, complemented
485C22×C4⋊C4C2×D4311yescharacteristic, complemented
486#490—438no—
487#482—438no—
488#481—438no—
489#478—438no—
490#469—438no—
491#466—438no—
492#459—438no—
493#447—438no—
494#447—438no—
495#442—438no—
496#435—438no—
497C2×#107—431no—
498C2×#106—431no—
499C2×#106—431no—
500C2×C4⋊C8—431no—
501#418—438no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—438no—
513C2×C22⋊C8—431no—
514C2×C22⋊C8—431no—
515C2×#97—431no—
516C43C2×#331811yescharacteristic, complemented, Sylow
517C25—861no—
518C25—861no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—431no—
522C22×D4—431no—
523C22×D4—431no—
524C22×D4—434no—
525C22×D4—434no—
526C22×D4—864no—
527C22×D4—864no—
528C22×D4—861no—
529C22×D4—861no—
530C22×D4—868no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4—862no—
536C22×D4—862no—
537C22×D4—1722no—
538C22×D4—1722no—
539C22×D4—1728no—
540C22×D4C22⋊D4311yescharacteristic
541C22×D4C22×D4311yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—861no—
545C23×C4C22×D4311yescharacteristic
546C23×C4C22×D4311yescharacteristic
547C2×D8—434no—
548C2×D8—434no—
549C2×D8—434no—
550C2×D8—864no—
551C2×D8—1722no—
552C2×D8—1722no—
553C2×M16—434no—
554C2×M16—1722no—
555C22×C8—431no—
556C22×C8—431no—
557C22×C8—431no—
558C22×C8—431no—
559C22×C8—434no—
560C22×C8—1722no—
561#127—434no—
562#127—862no—
563#126—28no—
564#125—22no—
565#125C22×D4314yescomplemented
566#123—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—434no—
571#121—434no—
572#121—862no—
573#121—862no—
574#121—868no—
575#121C22×D4314yescomplemented
576#121C22×D4314yescomplemented
577#120—868no—
578#120—868no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—434no—
582C4×D4—862no—
583C4×D4C22⋊D4314yes—
584C4×D4C22×D4314yes—
585C4×D4C22×D4314yescomplemented
586#117—22no—
587#117C22×D4314yescomplemented
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4C22⋊D4311yescharacteristic
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C4⋊C4C22×D4314yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4C22⋊D4311yescharacteristic
606C2×C22⋊C4C22⋊D4311yescharacteristic
607C2×C42—21no—
608C2×C42C22×D4311yescharacteristic
609#107—434no—
610#106—434no—
611#106—434no—
612C4⋊C8—434no—
613#102—434no—
614#102—434no—
615#102—434no—
616#102—434no—
617#102—434no—
618#102—434no—
619#102—434no—
620#102—434no—
621#102—434no—
622#102—434no—
623C22⋊C8—434no—
624C22⋊C8—434no—
625#97—434no—
626C24—21no—
627C24—861no—
628C24—864no—
629C24—864no—
630C24—861no—
631C24—861no—
632C24—3442no—
633C24—3442no—
634C24—1724no—
635C24—1724no—
636C24—1724no—
637C24—1724no—
638C24C2×C22⋊D4311yescharacteristic
639C24C2×C22⋊D4311yescharacteristic
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—434no—
649C2×D4—432no—
650C2×D4—432no—
651C2×D4—432no—
652C2×D4—868no—
653C2×D4—868no—
654C2×D4—864no—
655C2×D4—864no—
656C2×D4—861no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—862no—
668C2×D4—3442no—
669C2×D4—1724no—
670C2×D4—1724no—
671C2×D4—1728no—
672C2×D4—1728no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4—17232no—
677C2×D4—1724no—
678C2×D4—1724no—
679C2×D4C2×C22⋊D4314yes—
680C2×D4C23×D4312yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—82no—
691C22×C4—82no—
692C22×C4—861no—
693C22×C4—864no—
694C22×C4—1724no—
695C22×C4C2×C22⋊D4312yes—
696C22×C4C2×C22⋊D4312yes—
697C22×C4C2×C22⋊D4311yescharacteristic
698C22×C4C2×C22⋊D4311yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4311yescharacteristic
701C22×C4C23×D4312yes—
702C22×C4C23×D4312yes—
703C22×C4C23×D4311yescharacteristic
704D8—868no—
705D8—1724no—
706D8—1724no—
707M16—1724no—
708C2×C8—432no—
709C2×C8—432no—
710C2×C8—432no—
711C2×C8—432no—
712C2×C8—862no—
713C2×C8—862no—
714C2×C8—862no—
715C2×C8—862no—
716C2×C8—1724no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—432no—
724C4⋊C4—861no—
725C4⋊C4C2×C22⋊D4314yes—
726C4⋊C4C23×D4312yes—
727C4⋊C4C23×D4312yes—
728C4⋊C4C23×D4312yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4C2×C22⋊D4314yes—
737C22⋊C4C2×C22⋊D4314yes—
738C42—24no—
739C42C2×C22⋊D4312yes—
740C42C23×D4312yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—862no—
751C23—864no—
752C23—862no—
753C23—862no—
754C23—34416no—
755C23—3444no—
756C23—3444no—
757C23—34416no—
758C23—1728no—
759C23—1728no—
760C23—1728no—
761C23—1728no—
762C23—1722no—
763C23—1722no—
764C23—1722no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23#1306335014yes—
771C23C22×C22⋊D4312yes—
772C23C22×C22⋊D4312yes—
773C23C22×C22⋊D4311yescharacteristic
774D4—28no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—84no—
780D4—434no—
781D4—862no—
782D4—862no—
783D4—862no—
784D4—862no—
785D4—862no—
786D4—864no—
787D4—3444no—
788D4—1728no—
789D4—1728no—
790D4—1728no—
791D4—1728no—
792D4—1728no—
793D4—1722no—
794D4—1722no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—862no—
814C2×C4—1728no—
815C2×C4—1722no—
816C2×C4C22×C22⋊D4312yes—
817C2×C4C22×C22⋊D4312yes—
818C2×C4C22×C22⋊D4312yes—
819C2×C4C22×C22⋊D4312yes—
820C2×C4C22×C22⋊D4311yescharacteristic
821C2×C4#41×D4312yes—
822C2×C4#1306337112yes—
823C2×C4C24×D4311yescharacteristic
824C8—862no—
825C8—862no—
826C8—862no—
827C8—862no—
828C22—22no—
829C22—22no—
830C22—28no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22—864no—
840C22—34416no—
841C22—34416no—
842C22—3444no—
843C22—3444no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1728no—
853C22#1458353712yes—
854C22C2×#1306335014yes—
855C22C2×#1306335012yes—
856C22#1458370212yes—
857C22C23×C22⋊D4311yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—1722no—
866C4#1458353712yes—
867C4C2×#41×D4311yescharacteristic
868C4C2×#1306337111yescharacteristic
869C2—24no—
870C2—42no—
871C2—82no—
872C2—3442no—
873C2—3442no—
874C2—1724no—
875C2#1914673014yesdirect product factor
876C2C2×#1458353711yescharacteristic
877C2C22×#1306335011yescharacteristic
878C2C2×#1458370211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43C2×#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×D172C2semidirect
2. #19146730C2direct (N × H)
3. C2×#14583265C2semidirect
4. C2×#14583217C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583150C2semidirect
8. C2×#14583133C2semidirect
9. C2×#14583094C2semidirect
10. C2×#14583032C2semidirect
11. C2×#14583032C2semidirect
12. C2×#14583009C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582903C2semidirect
15. C22×#13063245C2semidirect
16. C2×C43×#553C2semidirect
21. C22×#10621882C22semidirect
22. C22×#10621882C22semidirect
23. C22×#10621877C22semidirect
24. C23×C43⋊C8C22semidirect
26. D4×D172C22semidirect
34. #14583265C22semidirect
35. #14583223C22semidirect
36. #14583217C22semidirect
37. #14583196C22semidirect
38. #14583150C22semidirect
39. #14583133C22semidirect
40. #14583094C22semidirect
41. #14583032C22semidirect
42. #14583032C22semidirect
43. #14583009C22semidirect
44. #14582971C22semidirect
45. C2×#13063258C22semidirect
46. C2×#13063256C22semidirect
47. C2×#13063256C22semidirect
48. C2×C4⋊(C43⋊C8)C22semidirect
49. #14582903C22semidirect
50. C2×#13063246C22semidirect
54. C2×#13063245C22semidirect
55. C2×#13063245C22semidirect
56. C2×#13063245C22semidirect
57. C2×#13063245C22semidirect
58. C2×#13063245C22semidirect
59. C2×#13063245C22semidirect
60. C2×#13063245C22semidirect
61. C2×C22⋊(C43⋊C8)C22semidirect
62. C2×C22⋊(C43⋊C8)C22semidirect
63. C2×#13063236C22semidirect
65. C43×#553C22semidirect
67. C2×#125×C43C22semidirect
70. C2×#121×C43C22semidirect
71. C2×#121×C43C22semidirect
74. C2×C4×D4×C43C22semidirect
75. C2×#117×C43C22semidirect
76. C22×C4⋊C4×C43C22semidirect
103. C2×#10621882C23semidirect
104. C2×#10621882C23semidirect
106. C2×#10621877C23semidirect
112. C22×C43⋊C8C23semidirect
128. #13063258C23semidirect
129. #13063256C23semidirect
130. #13063256C23semidirect
131. C4⋊(C43⋊C8)C23semidirect
132. #13063246C23semidirect
136. #13063245C23semidirect
137. #13063245C23semidirect
138. #13063245C23semidirect
139. #13063245C23semidirect
140. #13063245C23semidirect
141. #13063245C23semidirect
142. C22⋊(C43⋊C8)C23semidirect
143. C22⋊(C43⋊C8)C23semidirect
144. #13063236C23semidirect
155. #125×C43C23semidirect
160. #121×C43C23semidirect
161. #121×C43C23semidirect
166. C4×D4×C43C23semidirect
168. #117×C43C23semidirect
177. C2×C4⋊C4×C43C23semidirect
430. C2×#553D43semidirect
449. C2×C43#3318semidirect
465. #553C2×D43semidirect
470. C2×#125C2×D43semidirect
476. C2×#121C2×D43semidirect
477. C2×#121C2×D43semidirect
483. C2×C4×D4C2×D43semidirect
484. C2×#117C2×D43semidirect
485. C22×C4⋊C4C2×D43semidirect
516. C43C2×#3318semidirect
565. #125C22×D43semidirect
575. #121C22×D43semidirect
576. #121C22×D43semidirect
585. C4×D4C22×D43semidirect
587. #117C22×D43semidirect
597. C2×C4⋊C4C22×D43semidirect
875. C2#19146730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D1722
#191467302
C2×#145832652
C2×#145832172
C2×#145832232
C2×#145831962
C2×#145831502
C2×#145831332
C2×#145830942
C2×#145830322
C2×#145830092
C2×#145829712
C2×#145829032
C22×#130632452
C2×C43×#5532
C2×#331843