Finite Group Databasebeta

← C2×#14541366 #17913026

Subgroups — C2×#14541366 #17913026

Order 4352.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763527C211yesmaximal, characteristic, complemented
2C2×#11763459C211yesmaximal, characteristic
3#14541366C2116yesmaximal, direct product factor
4C2×#11763213C211yesmaximal, characteristic, complemented
5C2×#11763146C211yesmaximal, characteristic, complemented
6C2×#11763145C211yesmaximal, characteristic, complemented
7C2×#11763131C211yesmaximal, characteristic, complemented
8C2×#11763093C211yesmaximal, characteristic, complemented
9C2×#11763087C211yesmaximal, characteristic, complemented
10C2×#11763054C211yesmaximal, characteristic, complemented
11C2×#11763053C211yesmaximal, characteristic, complemented
12C2×#11762900C211yesmaximal, characteristic, complemented
13C2×#11762884C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C2×#11762848C211yesmaximal, characteristic, complemented
16C2×C17×#482C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×#63229C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20C22×#63218C2211yescharacteristic
21#11763527—24no—
22#11763527C2218yescomplemented
23#11763459—24no—
24#11763459C2218yes—
25C2×#10587574C2211yescharacteristic
26C2×#10587574C2211yescharacteristic
27C2×#10587562—21no—
28C2×#10587565—21no—
29C2×#10587571—21no—
30C2×#10587569—21no—
31C2×#10587621—21no—
32C2×#10587583C2211yescharacteristic
33C2×#10587610C2211yescharacteristic
34C2×#10587564—21no—
35C2×#10587624C2211yescharacteristic
36C2×C4×Dic34—21no—
37C2×#10587573C2211yescharacteristic
38C2×D4×Dic17C2211yescharacteristic
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×#10587578C2211yescharacteristic
41C22×C4⋊Dic17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43#11763213C2218yescomplemented
44#11763146C2218yescomplemented
45#11763145C2218yescomplemented
46#11763131C2218yescomplemented
47#11763093C2218yescomplemented
48#11763087C2218yescomplemented
49#11763054C2218yescomplemented
50#11763053C2218yescomplemented
51#11762900C2218yescomplemented
52#11762884C2218yescomplemented
53#11762852C2218yescomplemented
54#11762848C2218yescomplemented
55C2×#10587489C2211yescharacteristic
56C2×#10587489C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58C2×#10587478C2211yescharacteristic
59C2×#10587478C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587479C2211yescharacteristic
62C2×#10587485C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×#10587503C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C2×C17×#121C2211yescharacteristic
70C2×C17×#117C2211yescharacteristic
71C17×#482C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×#102C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17D411yescharacteristic
82C23×Dic17—21no—
83C23×Dic17—21no—
84C2×#63254—28no—
85C2×#63254—48no—
86C22×C4×D17—21no—
87C22×C4×D17C2311yescharacteristic
88C22×Dic34—21no—
89C22×Dic34—21no—
90C22×Dic34C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C17×#121—22no—
94C17×#121C2314yes—
95C17×#117—22no—
96C17×#117C2314yes—
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C42×C17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17D411yescharacteristic
107#10587624—22no—
108#10587624C2314yes—
109#10587621—28no—
110D4×Dic17—22no—
111D4×Dic17C2314yes—
112C2×#63229—24no—
113C2×#63229C2314yes—
114C4×C22⋊D17D414yes—
115C4×C22⋊D17C2314yes—
116C2×#63227—21no—
117C2×#63227—21no—
118C2×#63227D411yescharacteristic
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17C2314yes—
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126#10587610—22no—
127#10587610C2314yes—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225D411yescharacteristic
134C2×C4×Dic17—21no—
135C2×C4×Dic17—21no—
136C2×C4×Dic17C2311yescharacteristic
137C2×#63223—24no—
138C2×#63223C2314yes—
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C2×#63218—24no—
142C2×#63218C2314yes—
143#10587583—22no—
144#10587583C2314yes—
145#10587578—22no—
146#10587578C2314yes—
147C4⋊C4×D17—22no—
148C4⋊C4×D17C2314yes—
149#10587574—22no—
150#10587574—22no—
151#10587574C2314yes—
152#10587574C2314yes—
153#10587573—22no—
154#10587573C2314yes—
155#10587571—28no—
156#10587569—28no—
157#10587565—28no—
158#10587564—28no—
159#10587562—28no—
160C4×Dic34—28no—
161C17×#107C2314yes—
162C17×#106C2314yes—
163C17×#102C2314yes—
164C17×#102C2314yes—
165C17×C22⋊C8C2314yes—
166#10587503C2314yes—
167#10587491C2314yes—
168#10587489C2314yes—
169#10587489C2314yes—
170#10587487C2314yes—
171#10587487C2314yes—
172#10587485C2314yes—
173C8×Dic17C2314yes—
174#10587481C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179#10587478C2314yes—
180C24×C17—21no—
181C24×C17C2×D411yescharacteristic
182C23×D17C2×D411yescharacteristic
183C2×D4×C17—24no—
184C2×D4×C17—21no—
185C2×D4×C17—22no—
186C2×D4×C17—22no—
187C2×D4×C17—44no—
188C2×D4×C17C2412yes—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D412yes—
196C22×C4×C17C2412yes—
197C22×C4×C17C2411yescharacteristic
198C2×C22⋊D17—24no—
199C2×C22⋊D17—24no—
200C2×C22⋊D17—44no—
201C2×C22⋊D17C2×D414yes—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—24no—
207C22×Dic17—24no—
208C22×Dic17—44no—
209C22×Dic17—44no—
210C22×Dic17C2×D411yescharacteristic
211C22×Dic17C2×D411yescharacteristic
212C22×Dic17C2×D411yescharacteristic
213#63254—432no—
214C2×C4×D17—22no—
215C2×C4×D17—22no—
216C2×C4×D17—24no—
217C2×C4×D17—44no—
218C2×C4×D17C2×D412yes—
219C2×C4×D17C2412yes—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—24no—
225C2×Dic34—44no—
226C2×Dic34—44no—
227C2×Dic34C2412yes—
228C2×C8×C17—22no—
229C2×C8×C17—22no—
230C2×C8×C17C2412yes—
231C2×C8×C17C2412yes—
232C4⋊C4×C17—21no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C22⋊C4×C17—24no—
240C42×C17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244C22⋊Dic17C2×D414yes—
245#63229—28no—
246#63227—24no—
247#63227—24no—
248#63227C2×D414yes—
249C4⋊Dic17—24no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—24no—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225C2×D414yes—
263C4×Dic17—24no—
264C4×Dic17—24no—
265C4×Dic17C2×D412yes—
266C4×Dic17C2412yes—
267#63223—28no—
268C2×#3622—22no—
269C2×#3622#4114yescomplemented
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272#63218—28no—
273C2×#3353—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17—42no—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17C22×D412yes—
287D4×C17—22no—
288D4×C17—22no—
289D4×C17—48no—
290D4×C17—42no—
291C2×C4×C17—22no—
292C2×C4×C17—24no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17C22×D412yes—
302C2×C4×C17C22×D411yescharacteristic
303C2×C4×C17C2×#4112yes—
304C2×C4×C172−1+412yes—
305C2×C4×C17C2511yescharacteristic
306C22⋊D17—28no—
307C22⋊D17—48no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—48no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—48no—
320C2×Dic17AGL(1,ℤ/8)14yes—
321C2×Dic17C22×D412yes—
322C2×Dic17C22×D412yes—
323C2×Dic17C22×D412yes—
324C4×D17—24no—
325C4×D17—22no—
326C4×D17—22no—
327C4×D17—48no—
328Dic34—22no—
329Dic34—22no—
330Dic34—42no—
331Dic34—48no—
332Dic34—48no—
333C8×C17—22no—
334C8×C17—22no—
335#3622—22no—
336#3622C2×#4114yescomplemented
337C2×#556—171no—
338C2×#547—171no—
339#3353—1716no—
340C2×#500—171no—
341C2×#484—171no—
342C2×#484—171no—
343C2×#482—171no—
344C2×#482D1711yescharacteristic, complemented
345C2×#475—171no—
346C2×#474—171no—
347C2×#468—171no—
348C2×#468—171no—
349C2×C4×SD16—171no—
350C2×#436—171no—
351C2×#428—171no—
352C2×#428—171no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—44no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—84no—
361C22×C17#54712yes—
362C22×C17C2×AGL(1,ℤ/8)12yes—
363C22×C17#57812yes—
364C22×C17C23×D411yescharacteristic
365C2×D17—22no—
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—44no—
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17#54712yes—
374C4×C17C22×#4111yescharacteristic
375C4×C17C2×2−1+411yescharacteristic
376Dic17—22no—
377Dic17—22no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382Dic17C2×AGL(1,ℤ/8)14yes—
383C22×#41—341no—
384C22×SD16—171no—
385C22×M16—171no—
386C22×M16—171no—
387#556—178no—
388#556—344no—
389#547—178no—
390#547—344no—
391C2×C4⋊Q8—171no—
392C2×C4⋊Q8—171no—
393C2×#126—341no—
394C2×#126—341no—
395C2×#124—341no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—171no—
400C2×C22⋊Q8—341no—
401C2×#121—171no—
402C2×#121C2×D1711yescharacteristic
403C2×C4×Q8—171no—
404C2×C4×Q8—341no—
405C2×C4×D4—171no—
406C2×C4×D4—171no—
407C2×#117—171no—
408C2×#117C2×D1711yescharacteristic
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411#500—178no—
412#484—178no—
413#484—178no—
414#482—178no—
415#482C2×D1718yescomplemented
416#475—178no—
417#474—178no—
418#468—178no—
419#468—178no—
420C4×SD16—178no—
421#436—178no—
422#428—178no—
423#428—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#107—171no—
429C2×#107C2×D1711yescharacteristic
430C2×#106—171no—
431C2×#106—171no—
432C2×#106C2×D1711yescharacteristic
433C2×C4⋊C8—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#102—171no—
438C2×#102C2×D1711yescharacteristic
439C2×#102C2×D1711yescharacteristic
440C2×C22⋊C8—171no—
441C2×C22⋊C8C2×D1711yescharacteristic
442C2×C4×C8—171no—
443C2×C17—42no—
444C2×C17—82no—
445C2×C17#335314yescomplemented
446C2×C17C2×#54711yescharacteristic
447C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C17C2×#57811yescharacteristic
449D17—42no—
450C2×#41—348no—
451C2×#41—688no—
452C22×Q8—171no—
453C22×Q8—341no—
454C22×Q8—341no—
455C22×D4—21no—
456C22×D4—171no—
457C22×D4—341no—
458C22×D4C22×D1711yescharacteristic
459C23×C4—171no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4C22×D1711yescharacteristic
464C2×SD16—174no—
465C2×SD16—344no—
466C2×M16—174no—
467C2×M16—174no—
468C2×M16—344no—
469C2×M16—344no—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C4⋊Q8—174no—
475C4⋊Q8—174no—
476C4⋊Q8—342no—
477C4⋊Q8—342no—
478#126—348no—
479#126—348no—
480#124—348no—
481#123—348no—
482#123—348no—
483C22⋊Q8—174no—
484C22⋊Q8—174no—
485C22⋊Q8—348no—
486C22⋊Q8—342no—
487C22⋊Q8—342no—
488#121—22no—
489#121—174no—
490#121—342no—
491#121C22×D1714yes—
492C4×Q8—174no—
493C4×Q8—348no—
494C4×Q8—342no—
495C4×D4—174no—
496C4×D4—174no—
497C4×D4—174no—
498C4×D4—342no—
499#117—22no—
500#117—174no—
501#117—342no—
502#117C22×D1714yes—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—174no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—174no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—342no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4C22×D1711yescharacteristic
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C42—21no—
531C2×C42—171no—
532C2×C42—341no—
533C2×C42—341no—
534#107—174no—
535#107—174no—
536#107—174no—
537#107—174no—
538#107—174no—
539#107C22×D1714yes—
540#106—174no—
541#106—174no—
542#106C22×D1714yes—
543C4⋊C8—174no—
544#103—174no—
545#103—174no—
546#103—174no—
547#102—174no—
548#102C22×D1714yes—
549#102C22×D1714yes—
550C22⋊C8—174no—
551C22⋊C8C22×D1714yes—
552C4×C8—174no—
553C17C2×#335311yescharacteristic, complemented, Sylow
554C24—21no—
555C24—171no—
556C24D4×D1711yescharacteristic
557#41—6832no—
558C2×Q8—172no—
559C2×Q8—344no—
560C2×Q8—344no—
561C2×Q8—341no—
562C2×Q8—342no—
563C2×Q8—342no—
564C2×Q8—684no—
565C2×Q8—684no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—174no—
572C2×D4—344no—
573C2×D4—344no—
574C2×D4—684no—
575C2×D4C23×D1712yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—171no—
582C22×C4—171no—
583C22×C4—171no—
584C22×C4—172no—
585C22×C4—172no—
586C22×C4—344no—
587C22×C4—344no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—344no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—684no—
598C22×C4D4×D1712yes—
599C22×C4D4×D1711yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602SD16—348no—
603M16—348no—
604M16—348no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—174no—
608C2×C8—172no—
609C2×C8—172no—
610C2×C8—342no—
611C2×C8C23×D1712yes—
612C2×C8C23×D1712yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—174no—
617C4⋊C4—172no—
618C4⋊C4—172no—
619C4⋊C4—172no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—341no—
626C4⋊C4—341no—
627C4⋊C4—344no—
628C4⋊C4—341no—
629C4⋊C4—344no—
630C4⋊C4C23×D1712yes—
631C4⋊C4C23×D1712yes—
632C4⋊C4C23×D1712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—174no—
636C22⋊C4—174no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C22⋊C4—344no—
640C22⋊C4—344no—
641C22⋊C4—344no—
642C42—24no—
643C42—172no—
644C42—172no—
645C42—344no—
646C42—344no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—172no—
655C23—342no—
656C23—342no—
657C23—342no—
658C23C2×D4×D1712yes—
659C23C2×D4×D1711yescharacteristic
660Q8—342no—
661Q8—342no—
662Q8—688no—
663Q8—688no—
664Q8—682no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—348no—
670D4—688no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—174no—
682C2×C4—172no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—344no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—688no—
695C2×C4—688no—
696C2×C4—688no—
697C2×C4—682no—
698C2×C4—682no—
699C2×C4—682no—
700C2×C4—682no—
701C2×C4C2×D4×D1712yes—
702C2×C4C2×D4×D1711yescharacteristic
703C2×C4#41×D1712yes—
704C2×C4#1058769712yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—22no—
708C8—174no—
709C8—342no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—342no—
719C22—342no—
720C22—342no—
721C22—684no—
722C22#1176345712yes—
723C22AGL(1,ℤ/8)×D1712yes—
724C22#1176362312yes—
725C22C22×D4×D1711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—174no—
731C4—342no—
732C4—342no—
733C4—682no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4#1176345712yes—
738C4C2×#41×D1711yescharacteristic
739C4C2×#1058769711yescharacteristic
740C2—42no—
741C2—82no—
742C2—682no—
743C2#1454136614yesdirect product factor
744C2C2×#1176345711yescharacteristic
745C2C2×AGL(1,ℤ/8)×D1711yescharacteristic
746C2C2×#1176362311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#482C2
socleC23×C17C22×D4
prime radicalC2×#11763459C2
hypercenterC2×#482D17
hypocenterC17C2×#3353
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#11763527C2semidirect
3. #14541366C2direct (N × H)
4. C2×#11763213C2semidirect
5. C2×#11763146C2semidirect
6. C2×#11763145C2semidirect
7. C2×#11763131C2semidirect
8. C2×#11763093C2semidirect
9. C2×#11763087C2semidirect
10. C2×#11763054C2semidirect
11. C2×#11763053C2semidirect
12. C2×#11762900C2semidirect
13. C2×#11762884C2semidirect
14. C2×#11762852C2semidirect
15. C2×#11762848C2semidirect
16. C2×C17×#482C2semidirect
22. #11763527C22semidirect
43. #11763213C22semidirect
44. #11763146C22semidirect
45. #11763145C22semidirect
46. #11763131C22semidirect
47. #11763093C22semidirect
48. #11763087C22semidirect
49. #11763054C22semidirect
50. #11763053C22semidirect
51. #11762900C22semidirect
52. #11762884C22semidirect
53. #11762852C22semidirect
54. #11762848C22semidirect
71. C17×#482C22semidirect
269. C2×#3622#41semidirect
336. #3622C2×#41semidirect
344. C2×#482D17semidirect
415. #482C2×D17semidirect
445. C2×C17#3353semidirect
553. C17C2×#3353semidirect
743. C2#14541366direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635272
C2×#117634592
#145413662
C2×#117632132
C2×#117631462
C2×#117631452
C2×#117631312
C2×#117630932
C2×#117630872
C2×#117630542
C2×#117630532
C2×#117629002
C2×#117628842
C2×#117628522
C2×#117628482
C2×C17×#4822
C2×#335317