Finite Group Databasebeta

← C2×#19146032 #25969535

Subgroups — C2×#19146032 #25969535

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583503C211yesmaximal, characteristic, complemented
2C2×#14583500C211yesmaximal, characteristic, complemented
3#19146032C2116yesmaximal, direct product factor
4C2×#14583201C211yesmaximal, characteristic, complemented
5C2×#14583200C211yesmaximal, characteristic, complemented
6C2×#14583199C211yesmaximal, characteristic, complemented
7C2×#14583197C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583149C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583132C211yesmaximal, characteristic, complemented
12C2×#14583092C211yesmaximal, characteristic, complemented
13C2×#14583092C211yesmaximal, characteristic, complemented
14C2×#14583091C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#459C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583503—24no—
22#14583503C2218yescomplemented
23#14583500—24no—
24#14583500C2218yescomplemented
25C2×#13063321C2211yescharacteristic
26C2×#13063317C2211yescharacteristic
27C2×#13063316C2211yescharacteristic
28C2×#13063308—21no—
29C2×#13063307—21no—
30C2×#13063306—21no—
31C2×#13063306—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063299—21no—
34C2×#13063298—21no—
35C2×#13063297—21no—
36C2×#13063297—21no—
37C2×#13063296C2211yescharacteristic
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×D4×Dic43C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×#13063282C2211yescharacteristic
44#14583201C2218yescomplemented
45#14583200C2218yescomplemented
46#14583199C2218yescomplemented
47#14583197C2218yescomplemented
48#14583151C2218yescomplemented
49#14583149C2218yescomplemented
50#14583134C2218yescomplemented
51#14583132C2218yescomplemented
52#14583092C2218yescomplemented
53#14583092C2218yescomplemented
54#14583091C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#459C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172C2311yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×#10621882—42no—
89C2×#10621882—42no—
90C2×#10621882C2314yes—
91C2×#10621882C2314yes—
92C2×#10621872—42no—
93C2×#10621872C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—42no—
97C2×C8×D43C2314yes—
98#13063321—22no—
99#13063321C2314yes—
100#13063317—22no—
101#13063317C2314yes—
102#13063316—22no—
103#13063316C2314yes—
104#13063308—28no—
105#13063307—28no—
106#13063306—28no—
107#13063306—28no—
108#13063300—22no—
109#13063300C2314yes—
110#13063299—28no—
111#13063298—28no—
112#13063297—28no—
113#13063297—28no—
114#13063296—22no—
115#13063296—22no—
116#13063296—22no—
117#13063296C2314yes—
118#13063296C2314yes—
119#13063296C2314yes—
120C4×D172—22no—
121C4×D172C2314yes—
122D4×Dic43—22no—
123D4×Dic43—22no—
124D4×Dic43C2314yes—
125D4×Dic43C2314yes—
126#13063282D414yes—
127#13063282C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160C22×D4×C43—21no—
161C22×D4×C43—21no—
162C22×D4×C43C2311yescharacteristic
163C22×D4×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C23×C4×C43—21no—
166C2×D8×C43—42no—
167C2×D8×C43—42no—
168C2×D8×C43C2314yes—
169C2×D8×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#127×C43—22no—
173#127×C43C2314yes—
174C4×D4×C43—22no—
175C4×D4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C23×D43—21no—
186C23×D43C2×D411yescharacteristic
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—82no—
199C2×D4×C43—82no—
200C2×D4×C43C2412yes—
201C2×D4×C43C2412yes—
202C2×D4×C43C2412yes—
203C22×C4×C43—24no—
204C22×C4×C43—21no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—82no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43—82no—
217C2×C22⋊D43—82no—
218C2×C22⋊D43—82no—
219C22×Dic43—24no—
220C22×Dic43—24no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—82no—
225C22×Dic43—82no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—82no—
234C2×D172C2412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—24no—
238C2×C4×D43—82no—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2412yes—
241D8×C43—44no—
242D8×C43—44no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C2412yes—
249C22⋊C4×C43—24no—
250C42×C43C2×D412yes—
251C42×C43C2412yes—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257#10621882—44no—
258#10621882—44no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4C2×D414yes—
262(C2×D43)⋊C4C2×D414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—24no—
267C4⋊Dic43C2412yes—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4C2×D414yes—
274Dic43⋊C4C2×D414yes—
275C4×Dic43C2×D412yes—
276C4×Dic43C2412yes—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8C2412yes—
280C2×C43⋊C8C2412yes—
281#10621872—44no—
282C8×D43—44no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43C22×D412yes—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—42no—
311D4×C43—42no—
312D4×C43—42no—
313D4×C43—84no—
314D4×C43—84no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—42no—
319C2×C4×C43—84no—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43H(5,𝔽2)12yes—
324C2×C4×C432−1+412yes—
325C2×C4×C43C2511yescharacteristic
326C22⋊D43—84no—
327C22⋊D43—84no—
328C22⋊D43—84no—
329C22⋊D43—84no—
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—84no—
341C2×Dic43—84no—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—22no—
346D172—22no—
347D172—42no—
348D172—84no—
349C4×D43—24no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—84no—
353C8×C43—22no—
354C8×C43—22no—
355C43⋊C8—22no—
356C43⋊C8—22no—
357C2×#3259—431nomaximal, Sylow
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—84no—
368C22×C43—84no—
369C22×C43—84no—
370C22×C43#53712yes—
371C22×C43#57612yes—
372C22×C43#57612yes—
373C22×C43C23×D411yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—44no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—84no—
382C4×C43—22no—
383C4×C43—22no—
384C4×C43—42no—
385C4×C43#53712yes—
386C4×C43C2×H(5,𝔽2)11yescharacteristic
387C4×C43C2×2−1+411yescharacteristic
388Dic43—22no—
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394C2×#540—431no—
395C2×#540—431no—
396#3259—4316no—
397C2×#478—431no—
398C2×#478—431no—
399C2×#478—431no—
400C2×#478—431no—
401C2×#469—431no—
402C2×#469—431no—
403C2×#466—431no—
404C2×#466—431no—
405C2×#459—431no—
406C2×#459—431no—
407C2×#459—431no—
408C2×#459D4311yescharacteristic, complemented
409C2×#424—431no—
410C2×C43—82no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#325914yescomplemented
414C2×C43C2×#53711yescharacteristic
415C2×C43C2×#57611yescharacteristic
416C2×C43C2×#57611yescharacteristic
417D43—42no—
418D43—82no—
419C22×D8—431no—
420C22×D8—431no—
421C22×D8C2×D4311yescharacteristic
422C22×D8C2×D4311yescharacteristic
423C22×M16—431no—
424C23×C8—431no—
425#540—438no—
426#540—438no—
427#540—864no—
428#540—864no—
429C2×#127—431no—
430C2×#127C2×D4311yescharacteristic
431C2×#125—431no—
432C2×#125—431no—
433C2×#123—861no—
434C2×#123—861no—
435C2×#123—861no—
436C2×#123—861no—
437C2×#121—431no—
438C2×#121—431no—
439C2×#121—431no—
440C2×#121—431no—
441C2×#121—861no—
442C2×#121—861no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4C2×D4311yescharacteristic
449C2×#117—431no—
450#478—438no—
451#478—438no—
452#478—438no—
453#478—438no—
454#469—438no—
455#469—438no—
456#466—438no—
457#466—438no—
458#459—438no—
459#459—438no—
460#459—438no—
461#459C2×D4318yescomplemented
462C2×#107—431no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466#424—438no—
467C2×C4⋊C8—431no—
468C2×C4⋊C8—431no—
469C2×C4⋊C8—431no—
470C2×C4⋊C8C2×D4311yescharacteristic
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C43C2×#325911yescharacteristic, complemented, Sylow
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—431no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4—861no—
488C22×D4—861no—
489C22×D4C22×D4311yescharacteristic
490C22×D4C22×D4311yescharacteristic
491C22×D4C22×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C2×D8—42no—
498C2×D8—42no—
499C2×D8—434no—
500C2×D8—434no—
501C2×D8—1722no—
502C2×D8—1722no—
503C2×D8C22×D4314yes—
504C2×D8C22×D4314yes—
505C2×M16—434no—
506C2×M16—1722no—
507C22×C8—431no—
508C22×C8—431no—
509C22×C8—434no—
510C22×C8—1722no—
511C22×C8C22×D4311yescharacteristic
512C22×C8C22×D4311yescharacteristic
513#127—22no—
514#127—434no—
515#127—862no—
516#127C22×D4314yes—
517#125—434no—
518#125—434no—
519#125—862no—
520#125—862no—
521#123—868no—
522#123—868no—
523#123—868no—
524#123—868no—
525#121—434no—
526#121—434no—
527#121—434no—
528#121—434no—
529#121—868no—
530#121—868no—
531#121—868no—
532#121—868no—
533#121—862no—
534#121—862no—
535#121—862no—
536#121—862no—
537C4×D4—22no—
538C4×D4—434no—
539C4×D4—434no—
540C4×D4—434no—
541C4×D4—862no—
542C4×D4—862no—
543C4×D4—862no—
544C4×D4C22×D4314yes—
545#117—434no—
546#117—434no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C42—431no—
568C2×C42C22×D4311yescharacteristic
569#107—434no—
570#107—434no—
571#106—434no—
572#106—434no—
573C4⋊C8—434no—
574C4⋊C8—434no—
575C4⋊C8—434no—
576C4⋊C8C22×D4314yes—
577#102—434no—
578#102—434no—
579#102—434no—
580#102—434no—
581#102—434no—
582#102—434no—
583#102C22×D4314yes—
584#102C22×D4314yes—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—431no—
589C24—861no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—432no—
604C2×D4—864no—
605C2×D4—864no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—861no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—3442no—
614C2×D4—3442no—
615C2×D4—3442no—
616C2×D4—3442no—
617C2×D4—3442no—
618C2×D4—3442no—
619C2×D4C23×D4312yes—
620C2×D4C23×D4312yes—
621C2×D4C23×D4312yes—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—82no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—432no—
629C22×C4—432no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—864no—
638C22×C4—3442no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4C23×D4311yescharacteristic
644D8—44no—
645D8—44no—
646D8—1724no—
647D8—1724no—
648M16—1724no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—432no—
652C2×C8—432no—
653C2×C8—862no—
654C2×C8—862no—
655C2×C8—1724no—
656C2×C8C23×D4312yes—
657C2×C8C23×D4312yes—
658C4⋊C4—21no—
659C4⋊C4—434no—
660C4⋊C4—434no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—432no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4C23×D4312yes—
672C22⋊C4—24no—
673C22⋊C4—434no—
674C22⋊C4—434no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C42—432no—
683C42—432no—
684C42D4×D4312yes—
685C42C23×D4312yes—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—432no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—862no—
703C23—1722no—
704C23—1722no—
705C23—1722no—
706C23C2×D4×D4311yescharacteristic
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—84no—
717D4—84no—
718D4—862no—
719D4—862no—
720D4—3444no—
721D4—3444no—
722D4—3444no—
723D4—3444no—
724D4—3444no—
725D4—3444no—
726D4—1722no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—864no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—3444no—
745C2×C4—3444no—
746C2×C4—3444no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C2×D4×D4312yes—
751C2×C4C2×D4×D4312yes—
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4#1306337012yes—
754C2×C4#1306337212yes—
755C2×C4C24×D4311yescharacteristic
756C8—22no—
757C8—22no—
758C8—862no—
759C8—862no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—84no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—3444no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1724no—
780C22#1458347812yes—
781C22#1458370012yes—
782C22#1458370312yes—
783C22C22×D4×D4311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—862no—
788C4—862no—
789C4—862no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C4#1458347812yes—
794C4C2×#1306337011yescharacteristic
795C4C2×#1306337211yescharacteristic
796C2—82no—
797C2—82no—
798C2—82no—
799C2—3442no—
800C2—1722no—
801C2#1914603214yesdirect product factor
802C2C2×#1458347811yescharacteristic
803C2C2×#1458370011yescharacteristic
804C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#459C2
socleC23×C43C22×D4
hypercenterC2×#459D43
hypocenterC43C2×#3259
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#14583503C2semidirect
2. C2×#14583500C2semidirect
3. #19146032C2direct (N × H)
4. C2×#14583201C2semidirect
5. C2×#14583200C2semidirect
6. C2×#14583199C2semidirect
7. C2×#14583197C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583149C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583132C2semidirect
12. C2×#14583092C2semidirect
13. C2×#14583092C2semidirect
14. C2×#14583091C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#459C2semidirect
22. #14583503C22semidirect
24. #14583500C22semidirect
44. #14583201C22semidirect
45. #14583200C22semidirect
46. #14583199C22semidirect
47. #14583197C22semidirect
48. #14583151C22semidirect
49. #14583149C22semidirect
50. #14583134C22semidirect
51. #14583132C22semidirect
52. #14583092C22semidirect
53. #14583092C22semidirect
54. #14583091C22semidirect
59. #14582924C22semidirect
73. C43×#459C22semidirect
408. C2×#459D43semidirect
413. C2×C43#3259semidirect
461. #459C2×D43semidirect
479. C43C2×#3259semidirect
801. C2#19146032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835032
C2×#145835002
#191460322
C2×#145832012
C2×#145832002
C2×#145831992
C2×#145831972
C2×#145831512
C2×#145831492
C2×#145831342
C2×#145831322
C2×#145830922
C2×#145830912
C2×#145829242
C2×C43×#4592
C2×#325943