Finite Group Databasebeta

← C2×#14540114 #17907122

Subgroups — C2×#14540114 #17907122

Order 4352.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763361C211yesmaximal, characteristic, complemented
2C2×#11763340C211yesmaximal, characteristic
3#14540114C2116yesmaximal, direct product factor
4C2×#11763119C211yesmaximal, characteristic, complemented
5C2×#11763118C211yesmaximal, characteristic, complemented
6C2×#11763093C211yesmaximal, characteristic, complemented
7C2×#11763087C211yesmaximal, characteristic, complemented
8C2×#11763050C211yesmaximal, characteristic, complemented
9C2×#11763048C211yesmaximal, characteristic, complemented
10C2×#11763036C211yesmaximal, characteristic
11C2×#11763030C211yesmaximal, characteristic, complemented
12C2×#11763029C211yesmaximal, characteristic, complemented
13C2×#11763018C211yesmaximal, characteristic, complemented
14C2×#11763012C211yesmaximal, characteristic, complemented
15C22×#10587485C211yesmaximal, characteristic, complemented
16C2×C17×#465C211yesmaximal, characteristic
17C22×Dic68C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C23×#3622C2211yescharacteristic
21#11763361—24no—
22#11763361C2218yescomplemented
23C2×#10587574C2211yescharacteristic
24C2×#10587630C2211yescharacteristic
25#11763340—24no—
26#11763340C2218yes—
27C2×#10587565—21no—
28C2×#10587576C2211yescharacteristic
29C2×#10587575—21no—
30C2×#10587622C2211yescharacteristic
31C2×#10587621—21no—
32C2×#10587610C2211yescharacteristic
33C2×#10587610C2211yescharacteristic
34C2×#10587564—21no—
35C2×Q8×Dic17C2211yescharacteristic
36C2×#10587573—21no—
37C2×#10587573C2211yescharacteristic
38C2×#10587573C2211yescharacteristic
39C2×D4×Dic17—21no—
40C2×D4×Dic17C2211yescharacteristic
41C2×#10587563—21no—
42C2×#10587563—21no—
43C22×C4×Dic17C2211yescharacteristic
44#11763119C2218yescomplemented
45#11763118C2218yescomplemented
46#11763093C2218yescomplemented
47#11763087C2218yescomplemented
48#11763050C2218yescomplemented
49#11763048C2218yescomplemented
50#11763036C2218yes—
51#11763030C2218yescomplemented
52#11763029C2218yescomplemented
53#11763018C2218yescomplemented
54#11763012C2218yescomplemented
55C2×#10587489C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587485C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587485C2211yescharacteristic
61C2×#10587485C2211yescharacteristic
62C2×#10587485C2218yescomplemented
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587506C2211yescharacteristic
66C2×#10587481C2211yescharacteristic
67C2×#10587481C2211yescharacteristic
68C2×#10587503C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121C2211yescharacteristic
73C17×#465C2218yes—
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17—21no—
82C23×Dic17D411yescharacteristic
83C23×Dic17D411yescharacteristic
84C22×Dic34—21no—
85C22×Dic34C2311yescharacteristic
86C22×Dic34C2311yescharacteristic
87C2×SD16×C17—42no—
88C2×SD16×C17C2314yes—
89C22×C8×C17—42no—
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2314yes—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8C2314yes—
95C17×#121—22no—
96C17×#121C2314yes—
97C2×C4⋊C4×C17—21no—
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107Q8×Dic17—22no—
108Q8×Dic17C2314yes—
109#10587630—22no—
110#10587630C2314yes—
111C2×#63231—42no—
112C2×#63231C2314yes—
113#10587622—22no—
114#10587622C2314yes—
115#10587621—28no—
116D4×Dic17—22no—
117D4×Dic17—28no—
118D4×Dic17C2314yes—
119C2×#63229—42no—
120C2×#63229C2314yes—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—21no—
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125#10587610—22no—
126#10587610—22no—
127#10587610C2314yes—
128#10587610C2314yes—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×C4×Dic17—21no—
138C2×C4×Dic17—21no—
139C2×C4×Dic17—21no—
140C2×C4×Dic17D411yescharacteristic
141C2×C4×Dic17D411yescharacteristic
142C2×C4×Dic17D414yes—
143C2×C4×Dic17C2311yescharacteristic
144C2×C4×Dic17C2311yescharacteristic
145C2×C4×Dic17C2314yes—
146C22×#3622—42no—
147C22×#3622C2311yescharacteristic
148C22×#3622C2311yescharacteristic
149C22×#3622C2314yes—
150C2×Dic68—42no—
151C2×Dic68C2314yes—
152#10587576—22no—
153#10587576C2314yes—
154#10587575—28no—
155#10587574—22no—
156#10587574C2314yes—
157#10587573—28no—
158#10587573—22no—
159#10587573—22no—
160#10587573C2314yes—
161#10587573C2314yes—
162#10587565—28no—
163#10587564—28no—
164#10587563—28no—
165#10587563—28no—
166C17×#106C2314yes—
167C17×#103C2314yes—
168C17×#102C2314yes—
169#10587506C2314yes—
170#10587503C2314yes—
171#10587489C2314yes—
172#10587487C2314yes—
173#10587487C2314yes—
174#10587485C2314yes—
175#10587485C2314yes—
176#10587485C2314yes—
177#10587485C2314yes—
178#10587481C2314yes—
179#10587481C2314yes—
180#10587479C2314yes—
181#10587478C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184C2×Q8×C17—21no—
185C2×Q8×C17—22no—
186C2×Q8×C17—22no—
187C2×Q8×C17C2412yes—
188C2×D4×C17—24no—
189C2×D4×C17—21no—
190C2×D4×C17—22no—
191C2×D4×C17—22no—
192C2×D4×C17—44no—
193C2×D4×C17C2412yes—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17C2×D412yes—
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2412yes—
202C22×C4×C17C2411yescharacteristic
203C22×Dic17—24no—
204C22×Dic17—24no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—24no—
210C22×Dic17—44no—
211C22×Dic17C2×D414yes—
212C22×Dic17C2×D414yes—
213C22×Dic17C2×D411yescharacteristic
214C22×Dic17C2×D411yescharacteristic
215C22×Dic17C2×D411yescharacteristic
216C22×Dic17C2×D411yescharacteristic
217C2×Dic34—22no—
218C2×Dic34—22no—
219C2×Dic34—22no—
220C2×Dic34—22no—
221C2×Dic34—21no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—44no—
225C2×Dic34C2412yes—
226C2×Dic34C2412yes—
227SD16×C17—44no—
228C2×C8×C17—22no—
229C2×C8×C17—22no—
230C2×C8×C17—44no—
231C2×C8×C17C2412yes—
232C2×C8×C17C2412yes—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—24no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C22⋊C4×C17—24no—
240C22⋊Dic17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244C22⋊Dic17—24no—
245#63231—44no—
246#63229—44no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—24no—
250C4⋊Dic17—24no—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225—24no—
261C4×Dic17—24no—
262C4×Dic17—24no—
263C4×Dic17—24no—
264C4×Dic17C2×D414yes—
265C4×Dic17C2×D414yes—
266C4×Dic17C2×D412yes—
267C4×Dic17C2×D412yes—
268C4×Dic17C2412yes—
269C4×Dic17C2412yes—
270C2×#3622—22no—
271C2×#3622—22no—
272C2×#3622—44no—
273C2×#3622C2412yes—
274C2×#3622C2412yes—
275Dic68—44no—
276C2×#3248—171nomaximal, Sylow
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—42no—
281C23×C17—42no—
282C23×C17—42no—
283C23×C17#13714yes—
284C23×C17C22×D412yes—
285C23×C17C22×D411yescharacteristic
286Q8×C17—22no—
287Q8×C17—22no—
288Q8×C17—42no—
289D4×C17—22no—
290D4×C17—22no—
291D4×C17—48no—
292D4×C17—42no—
293C2×C4×C17—22no—
294C2×C4×C17—24no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D411yescharacteristic
305C2×C4×C17H(5,𝔽2)12yes—
306C2×C4×C172−1+412yes—
307C2×C4×C17C2511yescharacteristic
308C2×Dic17—22no—
309C2×Dic17—28no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—28no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—48no—
322C2×Dic17#13514yes—
323C2×Dic17C22×D412yes—
324C2×Dic17C22×D412yes—
325C2×Dic17C22×D412yes—
326C2×Dic17C22×D412yes—
327Dic34—22no—
328Dic34—22no—
329Dic34—22no—
330Dic34—22no—
331Dic34—42no—
332Dic34—42no—
333Dic34—48no—
334C8×C17—22no—
335C8×C17—22no—
336#3622—22no—
337#3622—22no—
338C2×#533—171no—
339C2×#529—171no—
340#3248—1716no—
341C2×#479—171no—
342C2×#479—171no—
343C2×#475—171no—
344C2×#474—171no—
345C2×#467—171no—
346C2×#467—171no—
347C2×#465—171no—
348C2×#465D1711yescharacteristic
349C2×#464—171no—
350C2×#464—171no—
351C2×#462—171no—
352C2×#461—171no—
353C22×C4⋊C8—171no—
354C22×C17—22no—
355C22×C17—28no—
356C22×C17—22no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—84no—
361C22×C17#53712yes—
362C22×C17C2×#13512yes—
363C22×C17C2×#13714yes—
364C22×C17C2×#13712yes—
365C22×C17C23×D411yescharacteristic
366C4×C17—22no—
367C4×C17—42no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17#53712yes—
371C4×C17C2×H(5,𝔽2)11yescharacteristic
372C4×C17C2×2−1+411yescharacteristic
373Dic17—22no—
374Dic17—22no—
375Dic17—22no—
376Dic17—42no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17C2×#13514yes—
381C22×Q16—171no—
382C22×Q16—171no—
383C22×SD16—171no—
384C22×SD16C2×D1711yescharacteristic
385C23×C8—171no—
386C23×C8C2×D1711yescharacteristic
387#533—178no—
388#533—344no—
389C2×C4⋊Q8—171no—
390C2×C4⋊Q8—171no—
391#529—178no—
392#529—344no—
393C2×#126—341no—
394C2×#125—171no—
395C2×#125—341no—
396C2×#124—171no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—171no—
400C2×C22⋊Q8—341no—
401C2×C22⋊Q8C2×D1711yescharacteristic
402C2×#121C2×D1711yescharacteristic
403C2×C4×Q8—171no—
404C2×C4×Q8—171no—
405C2×C4×Q8—171no—
406C2×C4×Q8—341no—
407C2×C4×D4—171no—
408C2×C4×D4—341no—
409C2×#117—341no—
410C2×#117—341no—
411C22×C42—171no—
412#479—178no—
413#479—178no—
414#475—178no—
415#474—178no—
416#467—178no—
417#467—178no—
418#465—178no—
419#465C2×D1718yes—
420#464—178no—
421#464—178no—
422#462—178no—
423#461—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×#106C2×D1711yescharacteristic
428C2×C4⋊C8—171no—
429C2×C4⋊C8—171no—
430C2×C4⋊C8—171no—
431C2×C4⋊C8—171no—
432C2×C4⋊C8—178no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#103—171no—
438C2×#103C2×D1711yescharacteristic
439C2×#102—171no—
440C2×#102C2×D1711yescharacteristic
441C2×C17—24no—
442C2×C17—82no—
443C2×C17#324814yescomplemented
444C2×C17C2×#53711yescharacteristic
445C2×C17C22×#13511yescharacteristic
446C2×C17C22×#13711yescharacteristic
447C22×Q8—171no—
448C22×Q8—171no—
449C22×Q8—341no—
450C22×Q8C22×D1711yescharacteristic
451C22×D4—21no—
452C22×D4C22×D1711yescharacteristic
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—341no—
456C23×C4C22×D1711yescharacteristic
457C2×Q16—174no—
458C2×Q16—174no—
459C2×Q16—682no—
460C2×Q16—682no—
461C2×SD16—42no—
462C2×SD16—174no—
463C2×SD16—682no—
464C2×SD16C22×D1714yes—
465C22×C8—42no—
466C22×C8—171no—
467C22×C8—171no—
468C22×C8—174no—
469C22×C8—682no—
470C22×C8C22×D1711yescharacteristic
471C22×C8C22×D1711yescharacteristic
472C22×C8C22×D1714yes—
473C4⋊Q8—174no—
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476C4⋊Q8—342no—
477#126—348no—
478#125—174no—
479#125—342no—
480#125—348no—
481#124—174no—
482#124—342no—
483#123—348no—
484C22⋊Q8—22no—
485C22⋊Q8—174no—
486C22⋊Q8—174no—
487C22⋊Q8—348no—
488C22⋊Q8—342no—
489C22⋊Q8—342no—
490C22⋊Q8C22×D1714yes—
491#121—22no—
492#121C22×D1714yes—
493C4×Q8—174no—
494C4×Q8—174no—
495C4×Q8—174no—
496C4×Q8—342no—
497C4×Q8—342no—
498C4×Q8—348no—
499C4×Q8—342no—
500C4×D4—174no—
501C4×D4—342no—
502C4×D4—348no—
503#117—348no—
504#117—348no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
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—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4C22×D1711yescharacteristic
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C42—171no—
528C2×C42—171no—
529C2×C42—174no—
530C2×C42—171no—
531C2×C42—171no—
532C2×C42—174no—
533C2×C42—341no—
534C2×C42—341no—
535C2×C42—341no—
536#107—174no—
537#107—174no—
538#106—174no—
539#106C22×D1714yes—
540C4⋊C8—174no—
541C4⋊C8—174no—
542C4⋊C8—174no—
543C4⋊C8—174no—
544#103—174no—
545#103—174no—
546#103—174no—
547#103—174no—
548#103—174no—
549#103C22×D1714yes—
550#102—174no—
551#102C22×D1714yes—
552C17C2×#324811yescharacteristic, complemented, Sylow
553C24—21no—
554C24D4×D1711yescharacteristic
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—172no—
559C2×Q8—172no—
560C2×Q8—344no—
561C2×Q8—341no—
562C2×Q8—341no—
563C2×Q8—342no—
564C2×Q8—342no—
565C2×Q8—342no—
566C2×Q8—342no—
567C2×Q8—684no—
568C2×Q8C23×D1712yes—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4C23×D1712yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—171no—
581C22×C4—174no—
582C22×C4—174no—
583C22×C4—171no—
584C22×C4—171no—
585C22×C4—171no—
586C22×C4—344no—
587C22×C4—344no—
588C22×C4—344no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—684no—
594C22×C4D4×D1712yes—
595C22×C4D4×D1711yescharacteristic
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598Q16—684no—
599Q16—684no—
600SD16—44no—
601SD16—684no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—44no—
605C2×C8—172no—
606C2×C8—172no—
607C2×C8—342no—
608C2×C8—342no—
609C2×C8—684no—
610C2×C8C23×D1712yes—
611C2×C8C23×D1712yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4—344no—
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—344no—
629C4⋊C4C23×D1712yes—
630C4⋊C4C23×D1712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C42—174no—
639C42—172no—
640C42—172no—
641C42—174no—
642C42—172no—
643C42—172no—
644C42—344no—
645C42—344no—
646C42—344no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23#1058760114yes—
654C23C2×D4×D1712yes—
655C23C2×D4×D1711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—342no—
660Q8—342no—
661Q8—342no—
662Q8—342no—
663Q8—688no—
664Q8—682no—
665Q8—682no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—174no—
681C2×C4—172no—
682C2×C4—172no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—348no—
686C2×C4—342no—
687C2×C4—348no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—688no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4—682no—
698C2×C4—682no—
699C2×C4C2×D4×D1712yes—
700C2×C4C2×D4×D1711yescharacteristic
701C2×C4#1058769112yes—
702C2×C4#1058769712yes—
703C2×C4C24×D1711yescharacteristic
704C8—22no—
705C8—22no—
706C8—342no—
707C8—342no—
708C22—22no—
709C22—28no—
710C22—22no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—84no—
715C22#1176338612yes—
716C22#135×D1712yes—
717C22C2×#1058760114yes—
718C22C2×#1058760112yes—
719C22C22×D4×D1711yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—174no—
725C4—342no—
726C4—342no—
727C4—342no—
728C4—682no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4#1176338612yes—
733C4C2×#1058769111yescharacteristic
734C4C2×#1058769711yescharacteristic
735C2—24no—
736C2—82no—
737C2#1454011414yesdirect product factor
738C2C2×#1176338611yescharacteristic
739C2C2×#135×D1711yescharacteristic
740C2C22×#1058760111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#465C2
socleC23×C17C22×D4
prime radicalC2×C17×#121C22
hypercenterC2×#465D17
hypocenterC17C2×#3248
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#11763361C2semidirect
3. #14540114C2direct (N × H)
4. C2×#11763119C2semidirect
5. C2×#11763118C2semidirect
6. C2×#11763093C2semidirect
7. C2×#11763087C2semidirect
8. C2×#11763050C2semidirect
9. C2×#11763048C2semidirect
11. C2×#11763030C2semidirect
12. C2×#11763029C2semidirect
13. C2×#11763018C2semidirect
14. C2×#11763012C2semidirect
15. C22×#10587485C2semidirect
22. #11763361C22semidirect
44. #11763119C22semidirect
45. #11763118C22semidirect
46. #11763093C22semidirect
47. #11763087C22semidirect
48. #11763050C22semidirect
49. #11763048C22semidirect
51. #11763030C22semidirect
52. #11763029C22semidirect
53. #11763018C22semidirect
54. #11763012C22semidirect
62. C2×#10587485C22semidirect
443. C2×C17#3248semidirect
552. C17C2×#3248semidirect
737. C2#14540114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633612
C2×#117633402
#145401142
C2×#117631192
C2×#117631182
C2×#117630932
C2×#117630872
C2×#117630502
C2×#117630482
C2×#117630362
C2×#117630302
C2×#117630292
C2×#117630182
C2×#117630122
C22×#105874852
C2×C17×#4652
C2×#324817