Finite Group Databasebeta

← C2×#19144837 #25964890

Subgroups — C2×#19144837 #25964890

Order 11008.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583500C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144837C2116yesmaximal, direct product factor
4C2×#14583225C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583201C211yesmaximal, characteristic, complemented
7C2×#14583198C211yesmaximal, characteristic, complemented
8C2×#14583093C211yesmaximal, characteristic, complemented
9C2×#14583092C211yesmaximal, characteristic, complemented
10C2×#14583034C211yesmaximal, characteristic, complemented
11C2×#14583031C211yesmaximal, characteristic, complemented
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×C4×#10621882C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582961C211yesmaximal, characteristic, complemented
16C2×C43×#442C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583500—24no—
22#14583500C2218yescomplemented
23C2×#13063321C2211yescharacteristic, complemented
24C2×#13063316C2211yescharacteristic, complemented
25C2×#13063308—21no—
26C2×#13063307—21no—
27C2×#13063300C2211yescharacteristic
28C2×#13063299—21no—
29C2×#13063298—21no—
30C2×#13063296C2211yescharacteristic
31#14583371—24no—
32#14583371C2218yescomplemented
33C2×C4×D172C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic, complemented
35C2×D4×Dic43C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×(C22⋊D43)⋊C4—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282C2211yescharacteristic
41C22×(C2×D43)⋊C4—21no—
42C2×C22⋊C4×D43—21no—
43#14583225C2218yescomplemented
44#14583222C2218yescomplemented
45#14583201C2218yescomplemented
46#14583198C2218yescomplemented
47#14583093C2218yescomplemented
48#14583092C2218yescomplemented
49#14583034C2218yescomplemented
50#14583031C2218yescomplemented
51#14583012C2218yescomplemented
52C4×#10621882C2218yescomplemented
53C4×#10621882C2218yescomplemented
54#14582961C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063257C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic, complemented
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic, complemented
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic, complemented
72C43×#442C2218yescomplemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic, complemented
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C2×D4×D43—24no—
86C2×D4×D43—24no—
87C2×D4×D43—22no—
88C2×D4×D43C2314yes—
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×D344—24no—
95C2×D344C2314yes—
96C2×#10621882—24no—
97C2×#10621882—24no—
98C2×#10621882C2314yes—
99C2×#10621882C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102#13063321—22no—
103#13063321C2314yescomplemented
104#13063316—22no—
105#13063316C2314yescomplemented
106#13063308—28no—
107#13063307—28no—
108#13063300—22no—
109#13063300C2314yes—
110#13063299—28no—
111#13063298—28no—
112#13063296—22no—
113#13063296C2314yes—
114C4×D172—22no—
115C4×D172—22no—
116C4×D172C2314yes—
117C4×D172C2314yescomplemented
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120#13063287—22no—
121#13063287C2314yes—
122C4×C22⋊D43—28no—
123(C22⋊D43)⋊C4—28no—
124#13063283—22no—
125#13063283C2314yes—
126#13063282D414yes—
127#13063282C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D411yescharacteristic
133C2×Dic43⋊C4D411yescharacteristic
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—28no—
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×(C2×D43)⋊C4D411yescharacteristic
144C22⋊C4×D43—28no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yescomplemented
148#13063258C2314yescomplemented
149#13063257C2314yescomplemented
150Dic43⋊C8C2314yescomplemented
151Dic43⋊C8C2314yescomplemented
152#13063247C2314yes—
153#13063247C2314yescomplemented
154#13063246C2314yes—
155#13063246C2314yescomplemented
156#13063245C2314yes—
157#13063245C2314yescomplemented
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160C4×C43⋊C8C2314yescomplemented
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43—21no—
165C2×D8×C43—24no—
166C2×D8×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43—22no—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C4×D4×C43C2314yescomplemented
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yescomplemented
179#102×C43C2314yes—
180#102×C43C2314yescomplemented
181#97×C43C2314yescomplemented
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43—28no—
186C23×D43—24no—
187C23×D43—21no—
188C23×D43—82no—
189C23×D43—82no—
190C23×D43C2×D411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43#4114yes—
197C2×D4×C43C2412yes—
198C2×D4×C43C2412yes—
199C22×C4×C43—24no—
200C22×C4×C43—24no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—82no—
204C22×C4×C43—82no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—28no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—82no—
214C2×C22⋊D43—82no—
215C2×C22⋊D43—82no—
216C22×Dic43—24no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—82no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223D4×D43—216no—
224D4×D43—28no—
225D4×D43—28no—
226C2×D172—21no—
227C2×D172—22no—
228C2×D172—21no—
229C2×D172—24no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172—82no—
233C2×D172#4114yes—
234C2×D172C2412yes—
235C2×D172C2412yes—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—82no—
242C2×C4×D43—82no—
243C2×C4×D43—82no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246D8×C43—28no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2412yes—
254C4⋊C4×C43C2412yes—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—24no—
257C42×C43C2×D412yes—
258C42×C43C2412yes—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261#10621882—28no—
262#10621882—28no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4C2×D414yes—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—24no—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4C2×D414yes—
277Dic43⋊C4C2×D414yes—
278C4×Dic43—24no—
279C4×Dic43C2×D412yes—
280C4×Dic43C2412yes—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285D344—28no—
286C23×C43—24no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—24no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—216no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—84no—
308C22×D43—84no—
309C22×D43—816no—
310C22×D43C22×D412yes—
311D4×C43—24no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—42no—
316D4×C43C2×#4114yes—
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×C43—84no—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4112yes—
329C2×C4×C43C2×#4112yes—
330C2×C4×C43C2511yescharacteristic
331C22⋊D43—216no—
332C22⋊D43—84no—
333C22⋊D43—84no—
334C22⋊D43—84no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—84no—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346D172—24no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—42no—
351D172—84no—
352D172C2×#4114yes—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—84no—
357C4×D43—84no—
358C4×D43—84no—
359C8×C43—22no—
360C8×C43—22no—
361C43⋊C8—22no—
362C43⋊C8—22no—
363C2×#3122—431nomaximal, Sylow
364C22×C43—24no—
365C22×C43—48no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—84no—
372C22×C43#52512yes—
373C22×C43#57612yes—
374C22×C43#57612yes—
375C22×C43C23×D411yescharacteristic
376C2×D43—22no—
377C2×D43—24no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—44no—
381C2×D43—48no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—816no—
388C2×D43—84no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#52512yes—
394C4×C43C22×#4111yescharacteristic
395C4×C43C22×#4111yescharacteristic
396Dic43—22no—
397Dic43—22no—
398Dic43—22no—
399Dic43—42no—
400Dic43—42no—
401C2×#540—431no—
402C2×#518—431no—
403#3122—4316no—
404C2×#482—431no—
405C2×#482—431no—
406C2×#478—431no—
407C2×#478—431no—
408C2×#459—431no—
409C2×#459—431no—
410C2×#447—431no—
411C2×#447—431no—
412C2×#442—431no—
413C2×#442D4311yescharacteristic, complemented
414C2×C4×D8—431no—
415C2×C4×D8—431no—
416C2×#433—431no—
417C2×C43—44no—
418C2×C43—82no—
419C2×C43#312214yescomplemented
420C2×C43C2×#52511yescharacteristic
421C2×C43C2×#57611yescharacteristic
422C2×C43C2×#57611yescharacteristic
423D43—42no—
424D43—44no—
425D43—82no—
426C23×D4—431no—
427C22×D8—431no—
428C22×D8—431no—
429C22×D8—431no—
430C22×D8C2×D4311yescharacteristic
431#540—438no—
432#540—864no—
433C2×#127—431no—
434C2×#125—431no—
435C2×#123—861no—
436C2×#123—861no—
437C2×#121—431no—
438C2×#121—431no—
439C2×#121—861no—
440C2×#121—861no—
441#518—438no—
442#518—864no—
443C2×C4×D4—431no—
444C2×C4×D4—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×C4×D4—861no—
449C2×C4×D4C2×D4311yescharacteristic
450C2×C4×D4C2×D4311yescharacteristic, complemented
451C2×#117—431no—
452C2×#117—431no—
453C22×C22⋊C4—861no—
454C22×C22⋊C4—861no—
455#482—438no—
456#482—438no—
457#478—438no—
458#478—438no—
459#459—438no—
460#459—438no—
461#447—438no—
462#447—438no—
463#442—438no—
464#442C2×D4318yescomplemented
465C4×D8—438no—
466C4×D8—438no—
467#433—438no—
468C2×#107—431no—
469C2×#107—431no—
470C2×#106—431no—
471C2×#106C2×D4311yescharacteristic, complemented
472C2×C4⋊C8—431no—
473C2×C4⋊C8—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×#102C2×D4311yescharacteristic, complemented
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×#97C2×D4311yescharacteristic, complemented
485C2×C4×C8—431no—
486C43C2×#312211yescharacteristic, complemented, Sylow
487C25—861no—
488C22×D4—434no—
489C22×D4—431no—
490C22×D4—431no—
491C22×D4—861no—
492C22×D4—862no—
493C22×D4—861no—
494C22×D4—861no—
495C22×D4—861no—
496C22×D4—864no—
497C22×D4—864no—
498C22×D4—861no—
499C22×D4C22×D4311yescharacteristic
500C22×D4C22×D4311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508C2×D8—24no—
509C2×D8—434no—
510C2×D8—434no—
511C2×D8—434no—
512C2×D8—864no—
513C2×D8—864no—
514C2×D8—864no—
515C2×D8C22×D4314yes—
516C22×C8—431no—
517C22×C8—431no—
518C22×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520#127—434no—
521#127—862no—
522#125—434no—
523#125—862no—
524#123—868no—
525#123—868no—
526#121—434no—
527#121—434no—
528#121—868no—
529#121—868no—
530#121—862no—
531#121—862no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—434no—
535C4×D4—434no—
536C4×D4—434no—
537C4×D4—434no—
538C4×D4—862no—
539C4×D4—862no—
540C4×D4—868no—
541C4×D4—868no—
542C4×D4—862no—
543C4×D4—862no—
544C4×D4C22×D4314yes—
545C4×D4C22×D4314yescomplemented
546#117—434no—
547#117—434no—
548#117—434no—
549#117—862no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—868no—
563C2×C22⋊C4—868no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—431no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#107—434no—
576#106—434no—
577#106C22×D4314yescomplemented
578C4⋊C8—434no—
579C4⋊C8—434no—
580#102—434no—
581#102—434no—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yescomplemented
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97C22×D4314yescomplemented
591C4×C8—434no—
592C24—21no—
593C24—21no—
594C24—431no—
595C24—864no—
596C24—868no—
597C24—861no—
598C24—861no—
599C24—3442no—
600C24—3442no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—434no—
607C2×D4—432no—
608C2×D4—432no—
609C2×D4—864no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—864no—
613C2×D4—868no—
614C2×D4—8616no—
615C2×D4—868no—
616C2×D4—868no—
617C2×D4—864no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—3442no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4#1062189814yes—
628C2×D4C23×D4312yes—
629C2×D4C23×D4312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—82no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—3442no—
650C22×C4—3442no—
651C22×C4—3442no—
652C22×C4—3442no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656D8—28no—
657D8—868no—
658D8—868no—
659D8—868no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8C23×D4312yes—
667C2×C8C23×D4312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—434no—
671C4⋊C4—434no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4C23×D4312yes—
679C4⋊C4C23×D4312yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—434no—
683C22⋊C4—434no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C42—432no—
692C42—432no—
693C42—864no—
694C42D4×D4312yes—
695C42C23×D4312yes—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—432no—
705C23—8616no—
706C23—862no—
707C23—864no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—3444no—
713C23—3444no—
714C23—34416no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23—1722no—
719C23—1722no—
720C23C2×D4×D4311yescharacteristic
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—434no—
727D4—8616no—
728D4—864no—
729D4—862no—
730D4—862no—
731D4—862no—
732D4—3444no—
733D4—3444no—
734D4—3444no—
735D4—3444no—
736D4—1722no—
737D4C2×#1062189814yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—864no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—3444no—
758C2×C4—3444no—
759C2×C4—3444no—
760C2×C4—3444no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4C2×D4×D4312yes—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4312yes—
767C2×C4C2×#1062189812yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—862no—
772C8—862no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—864no—
785C22—34416no—
786C22—3444no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22—1724no—
793C22—1728no—
794C22#1458340812yes—
795C22#1458370312yes—
796C22#1458370312yes—
797C22C22×D4×D4311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—862no—
803C4—862no—
804C4—862no—
805C4—1722no—
806C4—1722no—
807C4#1458340812yes—
808C4C2×#41×D4311yescharacteristic
809C4C22×#1062189811yescharacteristic
810C2—44no—
811C2—82no—
812C2—3442no—
813C2—1722no—
814C2—1724no—
815C2#1914483714yesdirect product factor
816C2C2×#1458340811yescharacteristic
817C2C2×#1458370311yescharacteristic
818C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
hypercenterC2×#442D43
hypocenterC43C2×#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583500C2semidirect
2. C2×#14583371C2semidirect
3. #19144837C2direct (N × H)
4. C2×#14583225C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583201C2semidirect
7. C2×#14583198C2semidirect
8. C2×#14583093C2semidirect
9. C2×#14583092C2semidirect
10. C2×#14583034C2semidirect
11. C2×#14583031C2semidirect
12. C2×#14583012C2semidirect
13. C2×C4×#10621882C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582961C2semidirect
16. C2×C43×#442C2semidirect
22. #14583500C22semidirect
23. C2×#13063321C22semidirect
24. C2×#13063316C22semidirect
32. #14583371C22semidirect
34. C2×C4×D172C22semidirect
43. #14583225C22semidirect
44. #14583222C22semidirect
45. #14583201C22semidirect
46. #14583198C22semidirect
47. #14583093C22semidirect
48. #14583092C22semidirect
49. #14583034C22semidirect
50. #14583031C22semidirect
51. #14583012C22semidirect
52. C4×#10621882C22semidirect
53. C4×#10621882C22semidirect
54. #14582961C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063257C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. C2×Dic43⋊C8C22semidirect
61. C2×#13063247C22semidirect
63. C2×#13063246C22semidirect
65. C2×#13063245C22semidirect
68. C2×C4×C43⋊C8C22semidirect
71. C2×C4×D4×C43C22semidirect
72. C43×#442C22semidirect
73. C2×#106×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×#97×C43C22semidirect
103. #13063321C23semidirect
105. #13063316C23semidirect
117. C4×D172C23semidirect
147. #13063258C23semidirect
148. #13063258C23semidirect
149. #13063257C23semidirect
150. Dic43⋊C8C23semidirect
151. Dic43⋊C8C23semidirect
153. #13063247C23semidirect
155. #13063246C23semidirect
157. #13063245C23semidirect
160. C4×C43⋊C8C23semidirect
172. C4×D4×C43C23semidirect
178. #106×C43C23semidirect
180. #102×C43C23semidirect
181. #97×C43C23semidirect
413. C2×#442D43semidirect
419. C2×C43#3122semidirect
450. C2×C4×D4C2×D43semidirect
464. #442C2×D43semidirect
471. C2×#106C2×D43semidirect
481. C2×#102C2×D43semidirect
484. C2×#97C2×D43semidirect
486. C43C2×#3122semidirect
545. C4×D4C22×D43semidirect
577. #106C22×D43semidirect
587. #102C22×D43semidirect
590. #97C22×D43semidirect
815. C2#19144837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835002
C2×#145833712
#191448372
C2×#145832252
C2×#145832222
C2×#145832012
C2×#145831982
C2×#145830932
C2×#145830922
C2×#145830342
C2×#145830312
C2×#145830122
C2×C4×#106218822
C2×#145829612
C2×C43×#4422
C2×#312243