Finite Group Databasebeta

← C2×#19147064 #25975159

Subgroups — C2×#19147064 #25975159

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×#14583552C211yesmaximal, characteristic, complemented
3#19147064C2116yesmaximal, direct product factor
4C2×#14583219C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583226C211yesmaximal, characteristic, complemented
7C2×#14583214C211yesmaximal, characteristic, complemented
8C2×#14583196C211yesmaximal, characteristic, complemented
9C2×#14583186C211yesmaximal, characteristic, complemented
10C2×#14583153C211yesmaximal, characteristic, complemented
11C2×#14583136C211yesmaximal, characteristic, complemented
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#106×D43C211yesmaximal, characteristic, complemented
16C2×C43×#501C211yesmaximal, characteristic, complemented
17C22×#10621902—21no—
18C22×D344C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583602—24no—
22#14583602C2218yescomplemented
23#14583552—24no—
24#14583552C2218yescomplemented
25C2×#13063320—21no—
26C2×#13063310—21no—
27C2×#13063310—21no—
28C2×#13063310—21no—
29C2×#13063301—21no—
30C2×#13063300—21no—
31C2×#13063300C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063300C2211yescharacteristic
34C2×#13063300C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×#13063287—21no—
39C2×#13063283C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583226C2218yescomplemented
44#14583219C2218yescomplemented
45#14583219C2218yescomplemented
46#14583214C2218yescomplemented
47#14583196C2218yescomplemented
48#14583186C2218yescomplemented
49#14583153C2218yescomplemented
50#14583136C2218yescomplemented
51#14583012C2218yescomplemented
52#14582972C2218yescomplemented
53#14582940C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#106×D43C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×#125×C43C2211yescharacteristic
71C43×#501C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#106×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621902—28no—
78C2×#10621902—48no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172D411yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C22×C4×D43C2311yescharacteristic
93C2×D344—24no—
94C2×D344C2314yes—
95C2×#10621872—24no—
96C2×#10621872C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—24no—
100C2×C8×D43C2314yes—
101#13063320—28no—
102#13063310—28no—
103#13063310—28no—
104#13063310—28no—
105#13063301—28no—
106#13063300—28no—
107#13063300—22no—
108#13063300—22no—
109#13063300—22no—
110#13063300—22no—
111#13063300C2314yes—
112#13063300C2314yes—
113#13063300C2314yes—
114#13063300C2314yes—
115C4×D172—22no—
116C4×D172—22no—
117C4×D172D414yes—
118C4×D172C2314yes—
119C4×D172C2314yes—
120C4×D172C2314yes—
121#13063287—28no—
122#13063283—22no—
123#13063283C2314yes—
124C2×C4⋊Dic43D411yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C4⋊C4×D43C2314yes—
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—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146#13063258C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149#13063256C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152#13063247C2314yes—
153#13063247C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063245C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160C22×Q8×C43—21no—
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C4⋊Q8×C43—22no—
164C4⋊Q8×C43C2314yes—
165#125×C43—22no—
166#125×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C42×C43C2311yescharacteristic
175#107×C43C2314yes—
176#107×C43C2314yes—
177#106×C43C2314yes—
178#106×C43C2314yes—
179#97×C43C2314yes—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43C2×D411yescharacteristic
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—24no—
185C2×Q8×C43—44no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197#10621902—432no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—24no—
201C2×D172—24no—
202C2×D172—24no—
203C2×D172—24no—
204C2×D172—24no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—44no—
210C2×D172—44no—
211C2×D172—44no—
212C2×D172—82no—
213C2×D172C2×D414yes—
214C2×D172C2412yes—
215C2×D172C2412yes—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43—82no—
229C2×C4×D43—82no—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2412yes—
233C2×C4×D43C2412yes—
234C2×C8×C43—22no—
235C2×C8×C43#4114yescomplemented
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C2412yes—
246C4⋊C4×C43C2412yes—
247C4⋊C4×C43C2412yes—
248C4⋊C4×C43C2412yes—
249C42×C43C2×D412yes—
250C42×C43C2412yes—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4C2×D414yes—
259(C2×D43)⋊C4C2×D414yes—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C2×D414yes—
263C4⋊Dic43C2412yes—
264C4⋊Dic43C2412yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268C4×Dic43—24no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273D344—28no—
274#10621872—28no—
275C8×D43—28no—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43AGL(1,ℤ/8)14yes—
291C22×D43C22×D412yes—
292C22×D43C22×D412yes—
293Q8×C43—48no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4112yes—
308C2×C4×C432−1+412yes—
309C2×C4×C43C2511yescharacteristic
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318D172—28no—
319D172—22no—
320D172—22no—
321D172—22no—
322D172—22no—
323D172—48no—
324D172—48no—
325D172—48no—
326D172—42no—
327D172—42no—
328D172—84no—
329C4×D43—24no—
330C4×D43—24no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—48no—
336C4×D43—48no—
337C4×D43—48no—
338C4×D43—84no—
339C4×D43—84no—
340C8×C43—22no—
341C8×C43C2×#4114yescomplemented
342C43⋊C8—22no—
343C43⋊C8—22no—
344C2×#3345—431nomaximal, Sylow
345C22×C43#54712yes—
346C22×C43C2×AGL(1,ℤ/8)12yes—
347C22×C43#57712yes—
348C22×C43C23×D411yescharacteristic
349C2×D43—28no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—44no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C2×D43—84no—
364C2×D43C2×AGL(1,ℤ/8)14yes—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43#54712yes—
372C4×C43C22×#4111yescharacteristic
373C4×C43C2×2−1+411yescharacteristic
374Dic43—22no—
375Dic43—22no—
376Dic43—42no—
377Dic43—42no—
378C2×#553—431no—
379C2×#547—431no—
380#3345—4316no—
381C2×#501D4311yescharacteristic, complemented
382C2×#481—431no—
383C2×#481—431no—
384C2×#482—431no—
385C2×#480—431no—
386C2×#478—431no—
387C2×#476—431no—
388C2×#469—431no—
389C2×#466—431no—
390C2×#442—431no—
391C2×#435—431no—
392C2×#428—431no—
393C22×#106—431no—
394C2×C43#334514yescomplemented
395C2×C43C2×#54711yescharacteristic
396C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C43C2×#57711yescharacteristic
398D43—24no—
399D43—42no—
400D43—82no—
401D43—82no—
402C22×#41—861no—
403C22×D8—431no—
404C22×M16—431no—
405C23×C8—431no—
406#553—438no—
407#553—864no—
408#547—438no—
409#547—864no—
410C2×C4⋊Q8C2×D4311yescharacteristic
411C2×#126—861no—
412C2×#125C2×D4311yescharacteristic
413C2×#123—861no—
414C2×#123—861no—
415C2×#123—861no—
416C2×C22⋊Q8—861no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×C4×D4—431no—
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×C4×D4—861no—
426C2×#117—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430#501C2×D4318yescomplemented
431#482—438no—
432#481—438no—
433#481—438no—
434#480—438no—
435#478—438no—
436#476—438no—
437#469—438no—
438#466—438no—
439#442—438no—
440#435—438no—
441#428—438no—
442C2×#107—431no—
443C2×#107C2×D4311yescharacteristic
444C2×#107C2×D4311yescharacteristic
445C2×#106—431no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×#106—438no—
450C2×#106C2×D4311yescharacteristic
451C2×#106C2×D4311yescharacteristic
452C2×C4⋊C8—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×#97C2×D4311yescharacteristic
462C43C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—868no—
464C2×#41—1728no—
465C22×Q8—21no—
466C22×D4—431no—
467C22×D4—431no—
468C22×D4—431no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—861no—
479C23×C4—861no—
480C2×D8—434no—
481C2×D8—864no—
482C2×M16—434no—
483C2×M16—864no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—434no—
487C22×C8—864no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D4314yes—
492#126—868no—
493#125—22no—
494#125C22×D4314yes—
495#123—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—868no—
499#121—434no—
500#121—434no—
501#121—434no—
502#121—434no—
503#121—862no—
504#121—862no—
505#121—862no—
506#121—862no—
507#121—868no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—434no—
511C4×D4—434no—
512C4×D4—868no—
513C4×D4—862no—
514C4×D4—862no—
515#117—434no—
516#117—862no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—862no—
528C2×C4⋊C4—862no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—861no—
546C2×C42C22×D4311yescharacteristic
547#107—434no—
548#107C22×D4314yes—
549#107C22×D4314yes—
550#106—434no—
551#106—434no—
552#106—434no—
553#106—434no—
554#106C22×D4314yes—
555#106C22×D4314yes—
556C4⋊C8—434no—
557#102—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562#102—434no—
563C22⋊C8—434no—
564C22⋊C8—434no—
565#97C22×D4314yes—
566C24—431no—
567C24—431no—
568C24—861no—
569C24—861no—
570#41—17232no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—434no—
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—3442no—
588C2×D4—1724no—
589C2×D4—1724no—
590C2×D4—1724no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—864no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—864no—
611C22×C4—864no—
612C22×C4—3442no—
613C22×C4—3442no—
614C22×C4—1724no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620D8—868no—
621M16—868no—
622C2×C8—22no—
623C2×C8—432no—
624C2×C8—432no—
625C2×C8—862no—
626C2×C8—862no—
627C2×C8—868no—
628C2×C8#1062190214yescomplemented
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—434no—
639C4⋊C4—432no—
640C4⋊C4—432no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4C23×D4312yes—
647C4⋊C4C23×D4312yes—
648C4⋊C4C23×D4312yes—
649C4⋊C4C23×D4312yes—
650C22⋊C4—434no—
651C22⋊C4—434no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C42—864no—
660C42D4×D4312yes—
661C42C23×D4312yes—
662C23—434no—
663C23—432no—
664C23—432no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—862no—
671C23—862no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23—1722no—
678C23C2×D4×D4311yescharacteristic
679Q8—48no—
680D4—868no—
681D4—862no—
682D4—862no—
683D4—862no—
684D4—862no—
685D4—3444no—
686D4—1728no—
687D4—1728no—
688D4—1728no—
689D4—1722no—
690D4—1722no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—864no—
706C2×C4—864no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—3444no—
714C2×C4—3444no—
715C2×C4—1728no—
716C2×C4—1728no—
717C2×C4—1728no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4C2×D4×D4312yes—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C2×#1062190212yes—
724C2×C4#1306337312yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—862no—
728C8—862no—
729C8C2×#1062190214yescomplemented
730C22—434no—
731C22—862no—
732C22—862no—
733C22—868no—
734C22—862no—
735C22—862no—
736C22—862no—
737C22—3444no—
738C22—3444no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—1724no—
746C22#1458355212yes—
747C22AGL(1,ℤ/8)×D4312yes—
748C22#1458370812yes—
749C22C22×D4×D4311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—862no—
757C4—862no—
758C4—1722no—
759C4—1722no—
760C4#1458355212yes—
761C4C22×#1062190211yescharacteristic
762C4C2×#1306337311yescharacteristic
763C2—864no—
764C2—3442no—
765C2—3442no—
766C2—1722no—
767C2#1914706414yesdirect product factor
768C2C2×#1458355211yescharacteristic
769C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
770C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#501C2
socleC23×C43C22×D4
hypercenterC2×#501D43
hypocenterC43C2×#3345
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#14583602C2semidirect
2. C2×#14583552C2semidirect
3. #19147064C2direct (N × H)
4. C2×#14583219C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583226C2semidirect
7. C2×#14583214C2semidirect
8. C2×#14583196C2semidirect
9. C2×#14583186C2semidirect
10. C2×#14583153C2semidirect
11. C2×#14583136C2semidirect
12. C2×#14583012C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582940C2semidirect
15. C2×#106×D43C2semidirect
16. C2×C43×#501C2semidirect
22. #14583602C22semidirect
24. #14583552C22semidirect
43. #14583226C22semidirect
44. #14583219C22semidirect
45. #14583219C22semidirect
46. #14583214C22semidirect
47. #14583196C22semidirect
48. #14583186C22semidirect
49. #14583153C22semidirect
50. #14583136C22semidirect
51. #14583012C22semidirect
52. #14582972C22semidirect
53. #14582940C22semidirect
59. #106×D43C22semidirect
71. C43×#501C22semidirect
235. C2×C8×C43#41semidirect
341. C8×C43C2×#41semidirect
381. C2×#501D43semidirect
394. C2×C43#3345semidirect
430. #501C2×D43semidirect
462. C43C2×#3345semidirect
628. C2×C8#10621902semidirect
729. C8C2×#10621902semidirect
767. C2#19147064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836022
C2×#145835522
#191470642
C2×#145832192
C2×#145832262
C2×#145832142
C2×#145831962
C2×#145831862
C2×#145831532
C2×#145831362
C2×#145830122
C2×#145829722
C2×#145829402
C2×#106×D432
C2×C43×#5012
C2×#334543