Finite Group Databasebeta

← C2×#14541678 #17914796

Subgroups — C2×#14541678 #17914796

Order 4352.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763518C211yesmaximal, characteristic, complemented
2C2×#11763474C211yesmaximal, characteristic, complemented
3#14541678C2116yesmaximal, direct product factor
4C2×#11763216C211yesmaximal, characteristic, complemented
5C2×#11763215C211yesmaximal, characteristic, complemented
6C2×#11763206C211yesmaximal, characteristic, complemented
7C2×#11763110C211yesmaximal, characteristic, complemented
8C2×#11763108C211yesmaximal, characteristic, complemented
9C2×#11763098C211yesmaximal, characteristic, complemented
10C2×#11763097C211yesmaximal, characteristic, complemented
11C2×#11763087C211yesmaximal, characteristic, complemented
12C2×#11762938C211yesmaximal, characteristic, complemented
13C2×#11762919C211yesmaximal, characteristic
14C2×#11762918C211yesmaximal, characteristic
15C2×#11762889C211yesmaximal, characteristic
16C2×C17×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D17—21no—
18C22×#63228C2211yescharacteristic
19#11763518—24no—
20#11763518C2218yescomplemented
21#11763474—24no—
22#11763474C2218yescomplemented
23C2×#10587574C2211yescharacteristic
24C2×#10587574C2211yescharacteristic
25C2×#10587574C2211yescharacteristic
26C2×#10587556C2211yescharacteristic
27C2×#10587576C2211yescharacteristic
28C2×#10587610—21no—
29C2×#10587582—21no—
30C2×#10587582—21no—
31C2×#10587564—21no—
32C2×#10587564—21no—
33C2×#10587632—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×D4×Dic17C2211yescharacteristic
37C2×D4×Dic17C2211yescharacteristic
38C2×#10587579C2211yescharacteristic
39C2×#10587579C2211yescharacteristic
40C22×#63225—21no—
41#11763216C2218yescomplemented
42#11763215C2218yescomplemented
43#11763206C2218yescomplemented
44#11763110C2218yescomplemented
45#11763108C2218yescomplemented
46#11763098C2218yescomplemented
47#11763097C2218yescomplemented
48#11763087C2218yescomplemented
49#11762938C2218yescomplemented
50#11762919C2218yes—
51#11762918C2218yes—
52#11762889C2218yes—
53C2×#10587489C2211yescharacteristic
54C2×#10587478C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587479C2211yescharacteristic
60C2×#10587485C2211yescharacteristic
61C2×#10587485C2211yescharacteristic
62C2×#10587492C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66C2×#10587474C2211yescharacteristic
67C2×#10587486C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C2×C17×C4⋊Q8C2211yescharacteristic
70C2×C4×D4×C17C2211yescharacteristic
71C17×#476C2218yescomplemented
72C2×C17×#106C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×C4⋊C8C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17—21no—
80C23×Dic17—21no—
81C23×Dic17—21no—
82C2×Q8×D17—28no—
83C2×Q8×D17—48no—
84C22×D68C2311yescharacteristic
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×Dic34—21no—
89C22×Dic34—21no—
90C22×Dic34—21no—
91C22×Dic34D411yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C17×C4⋊Q8—22no—
95C17×C4⋊Q8C2314yes—
96C4×D4×C17—22no—
97C4×D4×C17C2314yes—
98C2×C4⋊C4×C17—21no—
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C22⋊C4×C17—21no—
103C2×C42×C17C2311yescharacteristic
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106#10587632—28no—
107D4×Dic17—22no—
108D4×Dic17—22no—
109D4×Dic17C2314yes—
110D4×Dic17C2314yes—
111C2×#63228Q818yescomplemented
112C2×#63228C2314yes—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×C4⋊Dic17—21no—
117C2×C4⋊Dic17D411yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2311yescharacteristic
121#10587610—28no—
122C2×#63225—28no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225D411yescharacteristic
130C2×#63225D411yescharacteristic
131C2×C4×Dic17C2311yescharacteristic
132C2×C4×Dic17C2311yescharacteristic
133C22×#3622C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135#10587582—28no—
136#10587582—28no—
137#10587579—22no—
138#10587579—22no—
139#10587579C2314yes—
140#10587579C2314yes—
141#10587576—22no—
142#10587576C2314yes—
143#10587574—22no—
144#10587574—22no—
145#10587574—22no—
146#10587574C2314yes—
147#10587574C2314yes—
148#10587574C2314yes—
149#10587564—28no—
150#10587564—28no—
151C4×D68—22no—
152C4×D68C2314yes—
153#10587556—22no—
154#10587556C2314yes—
155C4×Dic34D414yes—
156C4×Dic34C2314yes—
157C17×#106C2314yes—
158C17×#106C2314yes—
159C17×C4⋊C8C2314yes—
160C17×#102C2314yes—
161C17×#102C2314yes—
162#10587503C2314yes—
163#10587492C2314yes—
164#10587492C2314yes—
165#10587489C2314yes—
166#10587488C2314yes—
167#10587486C2314yes—
168#10587485C2314yes—
169#10587485C2314yes—
170C8×Dic17C2314yes—
171#10587480C2314yes—
172#10587479C2314yes—
173#10587479C2314yes—
174#10587479C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177#10587474C2314yes—
178C24×C17—21no—
179C23×D17—21no—
180C2×Q8×C17—24no—
181C2×Q8×C17—44no—
182C2×D4×C17—21no—
183C2×D4×C17—22no—
184C2×D4×C17C2×Q814yescomplemented
185C2×D4×C17C2412yes—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—24no—
190C22×C4×C17—82no—
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2411yescharacteristic
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—24no—
198C22×Dic17—24no—
199C22×Dic17—44no—
200C22×Dic17—82no—
201C22×Dic17C2×D411yescharacteristic
202C22×Dic17C2×D411yescharacteristic
203C22×Dic17C2×D411yescharacteristic
204C22×Dic17C2×D411yescharacteristic
205Q8×D17—432no—
206C2×D68—21no—
207C2×D68—22no—
208C2×D68C2×Q814yes—
209C2×D68C2412yes—
210C2×C4×D17—24no—
211C2×C4×D17—24no—
212C2×C4×D17—24no—
213C2×C4×D17—44no—
214C2×C4×D17—44no—
215C2×C4×D17—44no—
216C2×Dic34—24no—
217C2×Dic34—24no—
218C2×Dic34—24no—
219C2×Dic34—24no—
220C2×Dic34—44no—
221C2×Dic34—44no—
222C2×Dic34—82no—
223C2×Dic34C2×D414yes—
224C2×C8×C17—22no—
225C2×C8×C17—22no—
226C2×C8×C17C2412yes—
227C2×C8×C17C2412yes—
228C4⋊C4×C17—21no—
229C4⋊C4×C17—21no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17C2412yes—
233C4⋊C4×C17C2412yes—
234C4⋊C4×C17C2412yes—
235C22⋊C4×C17—24no—
236C42×C17C2×D412yes—
237C42×C17C2412yes—
238C22⋊Dic17—24no—
239C22⋊Dic17—24no—
240#63228C2×Q8116yescomplemented
241#63227—24no—
242#63227—24no—
243#63227—24no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17C2×D414yes—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225C2×D414yes—
259#63225C2×D414yes—
260C4×Dic17C2×D412yes—
261C4×Dic17C2×D412yes—
262C4×Dic17C2412yes—
263C4×Dic17C2412yes—
264C2×#3622—22no—
265C2×#3622C2×Q814yescomplemented
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C2×#3384—171nomaximal, Sylow
269C23×C17—24no—
270C23×C17—22no—
271C23×C17—42no—
272C23×C17—42no—
273C23×C17C22×D411yescharacteristic
274C22×D17—24no—
275C22×D17—22no—
276C22×D17—42no—
277C22×D17—42no—
278Q8×C17—48no—
279D4×C17—24no—
280D4×C17—22no—
281D4×C17C22×Q814yescomplemented
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—84no—
291C2×C4×C17C22×D412yes—
292C2×C4×C17C22×D412yes—
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17C22×Q812yes—
295C2×C4×C172−1+412yes—
296C2×C4×C17C2511yescharacteristic
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—42no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306C2×Dic17—48no—
307C2×Dic17—84no—
308C2×Dic17AGL(1,ℤ/8)14yes—
309C2×Dic17C22×D412yes—
310C2×Dic17C22×D412yes—
311C2×Dic17C22×D412yes—
312C2×Dic17C22×D412yes—
313D68—24no—
314D68—22no—
315D68C22×Q814yes—
316C4×D17—48no—
317C4×D17—48no—
318C4×D17—48no—
319Dic34—28no—
320Dic34—48no—
321Dic34—48no—
322Dic34—84no—
323C8×C17—22no—
324C8×C17—22no—
325#3622—22no—
326#3622C22×Q814yescomplemented
327C2×#554—171no—
328C2×D4×Q8—171no—
329#3384—1716no—
330C2×#501—171no—
331C2×#501—171no—
332C2×#498—171no—
333C2×#478—171no—
334C2×#478—171no—
335C2×#476—171no—
336C2×#476—171no—
337C2×#476D1711yescharacteristic, complemented
338C2×#474—171no—
339C2×#446—171no—
340C2×#442—171no—
341C2×#442—171no—
342C2×C4×D8—171no—
343C22×C17—24no—
344C22×C17—48no—
345C22×C17—42no—
346C22×C17—42no—
347C22×C17D4×Q812yes—
348C22×C17C2×AGL(1,ℤ/8)12yes—
349C22×C17#57712yes—
350C22×C17C23×D411yescharacteristic
351C2×D17—24no—
352C2×D17—48no—
353C2×D17—42no—
354C2×D17—42no—
355C4×C17—22no—
356C4×C17—22no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17D4×Q812yes—
361C4×C17C23×Q811yescharacteristic
362C4×C17C2×2−1+411yescharacteristic
363Dic17—22no—
364Dic17—22no—
365Dic17—22no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17C2×AGL(1,ℤ/8)14yes—
370C23×Q8—341no—
371C22×D8—171no—
372#554—178no—
373#554—344no—
374D4×Q8—178no—
375D4×Q8—344no—
376C2×C4⋊Q8—171no—
377C2×C4⋊Q8—171no—
378C2×C4⋊Q8—171no—
379C2×C4⋊Q8C2×D1711yescharacteristic
380C2×#125—171no—
381C2×#125—171no—
382C2×C22⋊Q8—341no—
383C2×C22⋊Q8—341no—
384C2×C22⋊Q8—341no—
385C2×C22⋊Q8—341no—
386C2×C22⋊Q8—341no—
387C2×C22⋊Q8—341no—
388C2×C4×Q8—171no—
389C2×C4×D4—171no—
390C2×C4×D4—171no—
391C2×C4×D4—171no—
392C2×C4×D4—171no—
393C2×C4×D4—171no—
394C2×C4×D4C2×D1711yescharacteristic
395C22×C4⋊C4—341no—
396#501—178no—
397#501—178no—
398#498—178no—
399#478—178no—
400#478—178no—
401#476—178no—
402#476—178no—
403#476C2×D1718yescomplemented
404#474—178no—
405#446—178no—
406#442—178no—
407#442—178no—
408C4×D8—178no—
409C2×#107—171no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#106—171no—
413C2×#106—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×#106C2×D1711yescharacteristic
417C2×#106C2×D1711yescharacteristic
418C2×C4⋊C8—171no—
419C2×C4⋊C8—171no—
420C2×C4⋊C8C2×D1711yescharacteristic
421C2×#102—171no—
422C2×#102—171no—
423C2×#102—171no—
424C2×#102—171no—
425C2×#102C2×D1711yescharacteristic
426C2×#102C2×D1711yescharacteristic
427C2×#97—171no—
428C2×#97—171no—
429C2×C4×C8—171no—
430C2×C17—44no—
431C2×C17#338414yescomplemented
432C2×C17C2×D4×Q811yescharacteristic
433C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
434C2×C17C2×#57711yescharacteristic
435D17—44no—
436C22×Q8—21no—
437C22×Q8—171no—
438C22×Q8—341no—
439C22×Q8—341no—
440C22×Q8—341no—
441C22×Q8—348no—
442C22×Q8—688no—
443C22×D4—171no—
444C22×D4C22×D1711yescharacteristic
445C23×C4—21no—
446C23×C4—341no—
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4—341no—
451C2×D8—178no—
452C2×D8—174no—
453C22×C8—171no—
454C22×C8—171no—
455C22×C8C22×D1711yescharacteristic
456C22×C8C22×D1711yescharacteristic
457C4⋊Q8—22no—
458C4⋊Q8—174no—
459C4⋊Q8—174no—
460C4⋊Q8—174no—
461C4⋊Q8—342no—
462C4⋊Q8—342no—
463C4⋊Q8—342no—
464C4⋊Q8C22×D1714yes—
465#125—174no—
466#125—174no—
467#125—342no—
468#125—342no—
469C22⋊Q8—348no—
470C22⋊Q8—348no—
471C22⋊Q8—348no—
472C22⋊Q8—348no—
473C22⋊Q8—348no—
474C22⋊Q8—348no—
475C4×Q8—174no—
476C4×Q8—174no—
477C4×D4—22no—
478C4×D4—174no—
479C4×D4—174no—
480C4×D4—174no—
481C4×D4—174no—
482C4×D4—174no—
483C4×D4—342no—
484C4×D4—342no—
485C4×D4—342no—
486C4×D4—342no—
487C4×D4—342no—
488C4×D4C22×D1714yes—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—348no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4—341no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4C22×D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C4⋊C4C22×D1711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C42—171no—
514C2×C42—171no—
515C2×C42C22×D1711yescharacteristic
516#107—174no—
517#107—174no—
518#107—174no—
519#106—174no—
520#106—174no—
521#106—174no—
522#106—174no—
523#106C22×D1714yes—
524#106C22×D1714yes—
525C4⋊C8—174no—
526C4⋊C8—174no—
527C4⋊C8C22×D1714yes—
528#102—174no—
529#102—174no—
530#102—174no—
531#102—174no—
532#102C22×D1714yes—
533#102C22×D1714yes—
534#97—174no—
535#97—174no—
536C4×C8—174no—
537C17C2×#338411yescharacteristic, complemented, Sylow
538C24—21no—
539C24—341no—
540C2×Q8—24no—
541C2×Q8—44no—
542C2×Q8—174no—
543C2×Q8—344no—
544C2×Q8—344no—
545C2×Q8—344no—
546C2×Q8—344no—
547C2×Q8—684no—
548C2×Q8—684no—
549C2×Q8—6832no—
550C2×Q8—1362no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—174no—
554C2×D4—172no—
555C2×D4—341no—
556C2×D4—342no—
557C2×D4Q8×D1714yescomplemented
558C2×D4C23×D1712yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—171no—
565C22×C4—171no—
566C22×C4—171no—
567C22×C4—171no—
568C22×C4—344no—
569C22×C4—344no—
570C22×C4—344no—
571C22×C4—344no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—344no—
576C22×C4—684no—
577C22×C4—684no—
578C22×C4—684no—
579C22×C4—684no—
580C22×C4—1362no—
581C22×C4D4×D1711yescharacteristic
582C22×C4D4×D1711yescharacteristic
583C22×C4C23×D1711yescharacteristic
584D8—1716no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—174no—
588C2×C8—172no—
589C2×C8—172no—
590C2×C8—342no—
591C2×C8C23×D1712yes—
592C2×C8C23×D1712yes—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—174no—
598C4⋊C4—174no—
599C4⋊C4—174no—
600C4⋊C4—172no—
601C4⋊C4—172no—
602C4⋊C4—172no—
603C4⋊C4—344no—
604C4⋊C4—344no—
605C4⋊C4—344no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C4⋊C4C23×D1712yes—
616C22⋊C4—24no—
617C22⋊C4—344no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C22⋊C4—344no—
622C42—172no—
623C42—172no—
624C42—172no—
625C42—172no—
626C42D4×D1712yes—
627C42C23×D1712yes—
628C23—24no—
629C23—22no—
630C23—42no—
631C23—42no—
632C23—344no—
633C23—342no—
634C23—682no—
635C23—682no—
636C23C2×D4×D1711yescharacteristic
637Q8—48no—
638Q8—348no—
639Q8—688no—
640Q8—688no—
641Q8—1364no—
642D4—24no—
643D4—22no—
644D4—174no—
645D4—344no—
646D4—342no—
647D4C2×Q8×D1714yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—84no—
657C2×C4—174no—
658C2×C4—172no—
659C2×C4—172no—
660C2×C4—172no—
661C2×C4—172no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—688no—
669C2×C4—688no—
670C2×C4—688no—
671C2×C4—688no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—682no—
675C2×C4—1364no—
676C2×C4C2×D4×D1712yes—
677C2×C4C2×D4×D1712yes—
678C2×C4C2×D4×D1711yescharacteristic
679C2×C4C2×Q8×D1712yes—
680C2×C4#1058769712yes—
681C2×C4C24×D1711yescharacteristic
682C8—22no—
683C8—22no—
684C8—174no—
685C8—342no—
686C22—24no—
687C22—48no—
688C22—42no—
689C22—42no—
690C22—344no—
691C22—688no—
692C22—682no—
693C22—682no—
694C22#1176347212yes—
695C22AGL(1,ℤ/8)×D1712yes—
696C22#1176361512yes—
697C22C22×D4×D1711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—174no—
704C4—342no—
705C4—342no—
706C4—342no—
707C4—682no—
708C4—682no—
709C4—682no—
710C4#1176347212yes—
711C4C22×Q8×D1711yescharacteristic
712C4C2×#1058769711yescharacteristic
713C2—44no—
714C2—684no—
715C2#1454167814yesdirect product factor
716C2C2×#1176347211yescharacteristic
717C2C2×AGL(1,ℤ/8)×D1711yescharacteristic
718C2C2×#1176361511yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#476C2
socleC23×C17C22×D4
prime radicalC22×#63228C22
hypercenterC2×#476D17
hypocenterC17C2×#3384
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#11763518C2semidirect
2. C2×#11763474C2semidirect
3. #14541678C2direct (N × H)
4. C2×#11763216C2semidirect
5. C2×#11763215C2semidirect
6. C2×#11763206C2semidirect
7. C2×#11763110C2semidirect
8. C2×#11763108C2semidirect
9. C2×#11763098C2semidirect
10. C2×#11763097C2semidirect
11. C2×#11763087C2semidirect
12. C2×#11762938C2semidirect
16. C2×C17×#476C2semidirect
20. #11763518C22semidirect
22. #11763474C22semidirect
41. #11763216C22semidirect
42. #11763215C22semidirect
43. #11763206C22semidirect
44. #11763110C22semidirect
45. #11763108C22semidirect
46. #11763098C22semidirect
47. #11763097C22semidirect
48. #11763087C22semidirect
49. #11762938C22semidirect
71. C17×#476C22semidirect
111. C2×#63228Q8semidirect
184. C2×D4×C17C2×Q8semidirect
240. #63228C2×Q8semidirect
265. C2×#3622C2×Q8semidirect
281. D4×C17C22×Q8semidirect
326. #3622C22×Q8semidirect
337. C2×#476D17semidirect
403. #476C2×D17semidirect
431. C2×C17#3384semidirect
537. C17C2×#3384semidirect
557. C2×D4Q8×D17semidirect
647. D4C2×Q8×D17semidirect
715. C2#14541678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635182
C2×#117634742
#145416782
C2×#117632162
C2×#117632152
C2×#117632062
C2×#117631102
C2×#117631082
C2×#117630982
C2×#117630972
C2×#117630872
C2×#117629382
C2×#117629192
C2×#117629182
C2×#117628892
C2×C17×#4762
C2×#338417