Finite Group Databasebeta

← C2×#14541539 #17914075

Subgroups — C2×#14541539 #17914075

Order 4352.

1950 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×#11763544C211yesmaximal, characteristic, complemented
2C2×#11763519C211yesmaximal, characteristic, complemented
3#14541539C2116yesmaximal, direct product factor
4C2×#11763174C211yesmaximal, characteristic, complemented
5C2×#11763169C211yesmaximal, characteristic, complemented
6C2×#11763164C211yesmaximal, characteristic, complemented
7C2×#11763117C211yesmaximal, characteristic, complemented
8C2×#11763110C211yesmaximal, characteristic, complemented
9C2×#11763090C211yesmaximal, characteristic, complemented
10C2×#11763025C211yesmaximal, characteristic, complemented
11C2×#11763025C211yesmaximal, characteristic, complemented
12C2×#11763005C211yesmaximal, characteristic
13C2×#11762922C211yesmaximal, characteristic, complemented
14C2×#11762911C211yesmaximal, characteristic, complemented
15C2×C4×D136C211yesmaximal, characteristic, complemented
16C2×C17×#446C211yesmaximal, characteristic, complemented
17C22×#63219C2211yescharacteristic
18C22×D136C2211yescharacteristic
19C22×D136C2211yescharacteristic
20#11763544—24no—
21#11763544C2218yescomplemented
22#11763519—24no—
23#11763519C2218yescomplemented
24C2×#10587555C2211yescharacteristic
25C2×#10587560C2211yescharacteristic
26C2×#10587556C2211yescharacteristic
27C2×#10587556C2211yescharacteristic
28C2×#10587633—21no—
29C2×#10587561C2211yescharacteristic
30C2×#10587561C2211yescharacteristic
31C2×#10587580—21no—
32C2×#10587580—21no—
33C2×#10587582—21no—
34C2×#10587582—21no—
35C2×#10587632—21no—
36C2×C4×Dic34C2211yescharacteristic
37C2×C4×D68C2211yescharacteristic
38C2×C4×D68C2211yescharacteristic
39C2×C4×D68C2211yescharacteristic
40C2×C4×D68C2211yescharacteristic
41C2×C4×D68C2211yescharacteristic
42C2×#10587579—21no—
43C2×C4⋊C4×D17—21no—
44#11763174C2218yescomplemented
45#11763169C2218yescomplemented
46#11763164C2218yescomplemented
47#11763117C2218yescomplemented
48#11763110C2218yescomplemented
49#11763090C2218yescomplemented
50#11763025C2218yescomplemented
51#11763025C2218yescomplemented
52#11763005C2218yes—
53#11762922C2218yescomplemented
54#11762911C2218yescomplemented
55C4×D136C2218yescomplemented
56C2×#10587489C2211yescharacteristic
57C2×#10587489C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587487C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587492C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587492C2211yescharacteristic
65C2×#10587492C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C2×C4×Q8×C17C2211yescharacteristic
70C17×#446C2218yescomplemented
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×#97C2211yescharacteristic
75C2×C17×#97C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic
77C22×Q8×C17D411yescharacteristic
78C22×D68—21no—
79C22×D68—21no—
80C22×D68C2311yescharacteristic
81C22×D68C2311yescharacteristic
82C22×D68C2311yescharacteristic
83C22×C4×D17—21no—
84C22×C4×D17—21no—
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×Dic34—21no—
89C22×Dic34C2311yescharacteristic
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C4×Q8×C17D414yes—
95C4×Q8×C17C2314yes—
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C4⋊C4×C17D411yescharacteristic
98C2×C4⋊C4×C17D411yescharacteristic
99C2×C42×C17C2311yescharacteristic
100C2×C42×C17C2311yescharacteristic
101C2×C42×C17C2311yescharacteristic
102#10587633—28no—
103#10587632—28no—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×#63227—21no—
108C2×#63227—21no—
109C2×#63227—21no—
110C2×#63227—21no—
111C2×#63227—21no—
112C2×#63227—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×#63225—21no—
119C2×#63225—21no—
120C2×#63225—21no—
121C2×#63225—21no—
122C2×#63225—21no—
123C2×C4×Dic17—21no—
124C2×D136—24no—
125C2×D136—24no—
126C2×D136C2314yes—
127C2×D136C2314yes—
128C2×#63219—24no—
129C2×#63219C2314yes—
130#10587582—28no—
131#10587582—28no—
132#10587580—28no—
133#10587580—28no—
134#10587579—28no—
135C4⋊C4×D17—28no—
136#10587561—22no—
137#10587561—22no—
138#10587561C2314yes—
139#10587561C2314yes—
140#10587560—22no—
141#10587560C2314yes—
142C4×D68—22no—
143C4×D68—22no—
144C4×D68—22no—
145C4×D68—22no—
146C4×D68—22no—
147C4×D68C2314yes—
148C4×D68C2314yes—
149C4×D68C2314yes—
150C4×D68C2314yes—
151C4×D68C2314yes—
152#10587556—22no—
153#10587556—22no—
154#10587556C2314yes—
155#10587556C2314yes—
156#10587555—22no—
157#10587555C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160C17×C4⋊C8C2314yes—
161C17×C4⋊C8C2314yes—
162C17×C4⋊C8C2314yes—
163C17×#97C2314yes—
164C17×#97C2314yes—
165C4×C8×C17C2314yes—
166#10587492C2314yes—
167#10587492C2314yes—
168#10587492C2314yes—
169#10587492C2314yes—
170#10587492C2314yes—
171#10587492C2314yes—
172#10587492C2314yes—
173#10587489C2314yes—
174#10587489C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C2×Q8×C17—42no—
183C2×Q8×C17C2×D414yes—
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2411yescharacteristic
191C22×Dic17—21no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C2×D68—21no—
197C2×D68—22no—
198C2×D68—22no—
199C2×D68—22no—
200C2×D68—22no—
201C2×D68—22no—
202C2×D68—24no—
203C2×D68—21no—
204C2×D68—21no—
205C2×D68—24no—
206C2×D68—44no—
207C2×D68—82no—
208C2×D68#4114yes—
209C2×D68C2412yes—
210C2×D68C2412yes—
211C2×D68C2412yes—
212C2×C4×D17—24no—
213C2×C4×D17—24no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—24no—
217C2×C4×D17—44no—
218C2×C4×D17—82no—
219C2×C4×D17—82no—
220C2×C4×D17—82no—
221C2×C4×D17—82no—
222C2×Dic34—22no—
223C2×Dic34—22no—
224C2×Dic34—21no—
225C2×Dic34—24no—
226C2×Dic34—82no—
227C2×Dic34C2412yes—
228C2×C8×C17—22no—
229C2×C8×C17—22no—
230C2×C8×C17—22no—
231C2×C8×C17—22no—
232C2×C8×C17C2412yes—
233C2×C8×C17C2412yes—
234C2×C8×C17C2412yes—
235C2×C8×C17C2412yes—
236C4⋊C4×C17C2×D414yes—
237C4⋊C4×C17C2×D414yes—
238C4⋊C4×C17C2×D414yes—
239C42×C17C2×D412yes—
240C42×C17C2×D412yes—
241C42×C17C2×D412yes—
242C42×C17C2412yes—
243C42×C17C2412yes—
244C42×C17C2412yes—
245#63227—24no—
246#63227—24no—
247#63227—24no—
248#63227—24no—
249#63227—24no—
250#63227—24no—
251#63227—24no—
252#63227—24no—
253#63227—24no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—24no—
258C4⋊Dic17—21no—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261C4⋊Dic17C2412yes—
262C4⋊Dic17C2412yes—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225—24no—
267#63225—24no—
268C4×Dic17—24no—
269D136—28no—
270D136—28no—
271#63219—28no—
272C2×#3370—171nomaximal, Sylow
273C23×C17C22×D411yescharacteristic
274C22×D17—24no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—22no—
278C22×D17—42no—
279C22×D17—42no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17—42no—
285C22×D17—42no—
286Q8×C17—44no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17C22×D412yes—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D411yescharacteristic
300C2×C4×C17C2×#4112yes—
301C2×C4×C172−1+412yes—
302C2×C4×C17C2511yescharacteristic
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313D68—24no—
314D68—22no—
315D68—22no—
316D68—22no—
317D68—22no—
318D68—22no—
319D68—48no—
320D68—42no—
321D68—42no—
322D68—84no—
323D68C2×#4114yes—
324C4×D17—48no—
325C4×D17—84no—
326C4×D17—84no—
327C4×D17—84no—
328C4×D17—84no—
329Dic34—22no—
330Dic34—22no—
331Dic34—42no—
332Dic34—84no—
333C8×C17—22no—
334C8×C17—22no—
335C8×C17—22no—
336C8×C17—22no—
337C2×#559—171no—
338C2×#554—171no—
339#3370—1716no—
340C2×#490—171no—
341C2×#489—171no—
342C2×#488—171no—
343C2×#479—171no—
344C2×#478—171no—
345C2×#474—171no—
346C2×#463—171no—
347C2×#463—171no—
348C2×#459—171no—
349C2×#446D1711yescharacteristic, complemented
350C2×#442—171no—
351C2×#440—171no—
352C2×C4×D8—171no—
353C22×C17#54812yes—
354C22×C17#57512yes—
355C22×C17#57612yes—
356C22×C17C23×D411yescharacteristic
357C2×D17—24no—
358C2×D17—48no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—42no—
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17—42no—
367C2×D17—84no—
368C2×D17—84no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—22no—
372C4×C17—22no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17#54812yes—
376C4×C17C22×#4111yescharacteristic
377C4×C17C2×2−1+411yescharacteristic
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382Dic17—42no—
383C22×SD16—171no—
384C22×D8—171no—
385C22×D8—171no—
386#559—178no—
387#559—344no—
388#554—178no—
389#554—344no—
390C2×C4⋊Q8—171no—
391C2×#127—171no—
392C2×#125—171no—
393C2×#125—171no—
394C2×#124—171no—
395C2×#124—171no—
396C2×#124—341no—
397C2×#123—341no—
398C2×#123—341no—
399C2×C22⋊Q8—341no—
400C2×C22⋊Q8—341no—
401C2×C22⋊Q8—341no—
402C2×C4×Q8—171no—
403C2×C4×Q8C2×D1711yescharacteristic
404C2×C4×D4—171no—
405C2×C4×D4—171no—
406C2×C4×D4—171no—
407C2×C4×D4—171no—
408C2×C4×D4—171no—
409C2×C4×D4—341no—
410C22×C4⋊C4—341no—
411#490—178no—
412#489—178no—
413#488—178no—
414#479—178no—
415#478—178no—
416#474—178no—
417#463—178no—
418#463—178no—
419#459—178no—
420#446C2×D1718yescomplemented
421#442—178no—
422#440—178no—
423C4×D8—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×C4⋊C8C2×D1711yescharacteristic
428C2×C4⋊C8C2×D1711yescharacteristic
429C2×C4⋊C8C2×D1711yescharacteristic
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#102—171no—
434C2×#102—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×#102—171no—
439C2×#102—171no—
440C2×#97C2×D1711yescharacteristic
441C2×#97C2×D1711yescharacteristic
442C2×C4×C8C2×D1711yescharacteristic
443C2×C17#337014yescomplemented
444C2×C17C2×#54811yescharacteristic
445C2×C17C2×#57511yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—44no—
448D17—82no—
449D17—82no—
450C22×Q8—171no—
451C22×Q8—341no—
452C22×Q8D6811yescharacteristic
453C22×D4—171no—
454C22×D4—171no—
455C22×D4—171no—
456C22×D4—341no—
457C22×D4—341no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C2×SD16—174no—
464C2×SD16—344no—
465C2×D8—174no—
466C2×D8—174no—
467C2×D8—344no—
468C2×D8—344no—
469C22×C8C22×D1711yescharacteristic
470C22×C8C22×D1711yescharacteristic
471C22×C8C22×D1711yescharacteristic
472C22×C8C22×D1711yescharacteristic
473C4⋊Q8—174no—
474C4⋊Q8—342no—
475#127—174no—
476#127—342no—
477#125—174no—
478#125—174no—
479#125—342no—
480#125—342no—
481#124—174no—
482#124—174no—
483#124—348no—
484#124—342no—
485#124—342no—
486#123—348no—
487#123—348no—
488C22⋊Q8—348no—
489C22⋊Q8—348no—
490C22⋊Q8—348no—
491C4×Q8—174no—
492C4×Q8—342no—
493C4×Q8D6814yes—
494C4×Q8C22×D1714yes—
495C4×D4—174no—
496C4×D4—174no—
497C4×D4—174no—
498C4×D4—174no—
499C4×D4—174no—
500C4×D4—348no—
501C4×D4—342no—
502C4×D4—342no—
503C4×D4—342no—
504C4×D4—342no—
505C4×D4—342no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
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—348no—
517C2×C4⋊C4D6811yescharacteristic
518C2×C4⋊C4D6811yescharacteristic
519C2×C4⋊C4D6811yescharacteristic
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531C2×C42C22×D1711yescharacteristic
532C2×C42C22×D1711yescharacteristic
533#107—174no—
534#107—174no—
535#106—174no—
536C4⋊C8C22×D1714yes—
537C4⋊C8C22×D1714yes—
538C4⋊C8C22×D1714yes—
539#103—174no—
540#103—174no—
541#103—174no—
542#102—174no—
543#102—174no—
544#102—174no—
545#102—174no—
546#102—174no—
547#102—174no—
548#102—174no—
549#97C22×D1714yes—
550#97C22×D1714yes—
551C4×C8C22×D1714yes—
552C17C2×#337011yescharacteristic, complemented, Sylow
553C24—341no—
554C24—341no—
555C24—341no—
556C2×Q8—42no—
557C2×Q8—172no—
558C2×Q8—341no—
559C2×Q8—344no—
560C2×Q8—342no—
561C2×Q8—342no—
562C2×Q8—1362no—
563C2×Q8C2×D6814yes—
564C2×D4—174no—
565C2×D4—172no—
566C2×D4—172no—
567C2×D4—172no—
568C2×D4—341no—
569C2×D4—344no—
570C2×D4—341no—
571C2×D4—341no—
572C2×D4—344no—
573C2×D4—342no—
574C2×D4—342no—
575C2×D4—342no—
576C2×D4—342no—
577C2×D4—342no—
578C2×D4—684no—
579C2×D4—1362no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—344no—
586C22×C4—344no—
587C22×C4—344no—
588C22×C4—344no—
589C22×C4—344no—
590C22×C4—684no—
591C22×C4—1362no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4—1362no—
595C22×C4C2×D6811yescharacteristic
596C22×C4C2×D6811yescharacteristic
597C22×C4C2×D6811yescharacteristic
598C22×C4C2×D6811yescharacteristic
599C22×C4C2×D6811yescharacteristic
600C22×C4C2×D6811yescharacteristic
601C22×C4C23×D1711yescharacteristic
602SD16—348no—
603D8—348no—
604D8—348no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D1712yes—
610C2×C8C23×D1712yes—
611C2×C8C23×D1712yes—
612C2×C8C23×D1712yes—
613C4⋊C4—172no—
614C4⋊C4—172no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—341no—
618C4⋊C4—341no—
619C4⋊C4—341no—
620C4⋊C4—341no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4C2×D6814yes—
628C4⋊C4C2×D6814yes—
629C4⋊C4C2×D6814yes—
630C22⋊C4—344no—
631C22⋊C4—344no—
632C22⋊C4—344no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C42—344no—
640C42C2×D6812yes—
641C42C2×D6812yes—
642C42C2×D6812yes—
643C42C23×D1712yes—
644C42C23×D1712yes—
645C42C23×D1712yes—
646C23—344no—
647C23—342no—
648C23—342no—
649C23—342no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23C22×D6811yescharacteristic
659Q8—44no—
660Q8—342no—
661Q8—342no—
662Q8—682no—
663Q8—1364no—
664D4—174no—
665D4—344no—
666D4—342no—
667D4—342no—
668D4—342no—
669D4—342no—
670D4—342no—
671D4—688no—
672D4—682no—
673D4—682no—
674D4—1364no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—688no—
687C2×C4—682no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—1364no—
693C2×C4—1364no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4C22×D6812yes—
697C2×C4C22×D6812yes—
698C2×C4C22×D6812yes—
699C2×C4C22×D6812yes—
700C2×C4C22×D6812yes—
701C2×C4C22×D6812yes—
702C2×C4C22×D6811yescharacteristic
703C2×C4#1058769412yes—
704C2×C4#41×D1712yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—344no—
711C22—682no—
712C22—682no—
713C22—688no—
714C22—682no—
715C22—682no—
716C22—682no—
717C22—682no—
718C22—682no—
719C22—682no—
720C22—1364no—
721C22—1364no—
722C22#1176347112yes—
723C22#1176360912yes—
724C22#1176361412yes—
725C22C23×D6811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—682no—
733C4—682no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4#1176347112yes—
738C4C2×#41×D1711yescharacteristic
739C4C2×#1058769411yescharacteristic
740C2—684no—
741C2—1362no—
742C2—1362no—
743C2#1454153914yesdirect product factor
744C2C2×#1176347111yescharacteristic
745C2C2×#1176360911yescharacteristic
746C2C2×#1176361411yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#446C2
socleC23×C17C22×D4
prime radicalC2×#11763005C2
hypercenterC2×#446D17
hypocenterC17C2×#3370
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#11763544C2semidirect
2. C2×#11763519C2semidirect
3. #14541539C2direct (N × H)
4. C2×#11763174C2semidirect
5. C2×#11763169C2semidirect
6. C2×#11763164C2semidirect
7. C2×#11763117C2semidirect
8. C2×#11763110C2semidirect
9. C2×#11763090C2semidirect
10. C2×#11763025C2semidirect
11. C2×#11763025C2semidirect
13. C2×#11762922C2semidirect
14. C2×#11762911C2semidirect
15. C2×C4×D136C2semidirect
16. C2×C17×#446C2semidirect
21. #11763544C22semidirect
23. #11763519C22semidirect
44. #11763174C22semidirect
45. #11763169C22semidirect
46. #11763164C22semidirect
47. #11763117C22semidirect
48. #11763110C22semidirect
49. #11763090C22semidirect
50. #11763025C22semidirect
51. #11763025C22semidirect
53. #11762922C22semidirect
54. #11762911C22semidirect
55. C4×D136C22semidirect
70. C17×#446C22semidirect
349. C2×#446D17semidirect
420. #446C2×D17semidirect
443. C2×C17#3370semidirect
552. C17C2×#3370semidirect
743. C2#14541539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
C2×#117635192
#145415392
C2×#117631742
C2×#117631692
C2×#117631642
C2×#117631172
C2×#117631102
C2×#117630902
C2×#117630252
C2×#117630052
C2×#117629222
C2×#117629112
C2×C4×D1362
C2×C17×#4462
C2×#337017