Finite Group Databasebeta

← C2×#14541136 #17912742

Subgroups — C2×#14541136 #17912742

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763517C211yesmaximal, characteristic, complemented
2C2×#11763459C211yesmaximal, characteristic
3#14541136C2116yesmaximal, direct product factor
4C2×#11763206C211yesmaximal, characteristic, complemented
5C2×#11763126C211yesmaximal, characteristic, complemented
6C2×#11763125C211yesmaximal, characteristic, complemented
7C2×#11763138C211yesmaximal, characteristic, complemented
8C2×#11763137C211yesmaximal, characteristic, complemented
9C2×#11763092C211yesmaximal, characteristic, complemented
10C2×#11763097C211yesmaximal, characteristic, complemented
11C2×#11763035C211yesmaximal, characteristic, complemented
12C2×SD16×Dic17C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D17C211yesmaximal, characteristic, complemented
14C22×#10587488C211yesmaximal, characteristic, complemented
15C2×#106×D17C211yesmaximal, characteristic, complemented
16C2×C17×#465C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×C8×D17C2211yescharacteristic
19#11763517—24no—
20#11763517C2218yescomplemented
21#11763459—24no—
22#11763459C2218yes—
23C2×#10587574C2211yescharacteristic
24C2×#10587574C2211yescharacteristic
25C2×#10587575—21no—
26C2×#10587569—21no—
27C2×#10587621—21no—
28C2×#10587583—21no—
29C2×#10587564—21no—
30C2×#10587564—21no—
31C2×#10587632C2211yescharacteristic
32C2×#10587624C2211yescharacteristic
33C2×Q8×Dic17C2211yescharacteristic
34C2×D4×Dic17C2211yescharacteristic
35C2×C4×C22⋊D17C2211yescharacteristic
36C2×#10587567—21no—
37C22×C4⋊Dic17C2211yescharacteristic
38C22×C4⋊Dic17C2211yescharacteristic
39C2×C4⋊C4×D17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41#11763206C2218yescomplemented
42#11763138C2218yescomplemented
43#11763137C2218yescomplemented
44#11763126C2218yescomplemented
45#11763125C2218yescomplemented
46#11763097C2218yescomplemented
47#11763092C2218yescomplemented
48#11763035C2218yescomplemented
49SD16×Dic17C2218yescomplemented
50C8×C22⋊D17C2218yescomplemented
51C2×#10587488C2211yescharacteristic
52C2×#10587488C2211yescharacteristic
53C2×#10587488C2211yescharacteristic
54C2×#10587488C2211yescharacteristic
55C2×#10587488C2218yescomplemented
56C2×#10587479C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587479C2211yescharacteristic
60#106×D17C2218yescomplemented
61C2×#10587485C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121C2211yescharacteristic
73C17×#465C2218yescomplemented
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17D411yescharacteristic
83C23×Dic17—21no—
84C23×Dic17—21no—
85C23×Dic17—21no—
86C2×#63254—28no—
87C2×#63254—48no—
88C22×C4×D17—21no—
89C22×C4×D17—21no—
90C22×C4×D17C2311yescharacteristic
91C22×Dic34—21no—
92C22×Dic34—21no—
93C2×SD16×C17—24no—
94C2×SD16×C17C2314yes—
95C22×C8×C17—24no—
96C22×C8×C17C2311yescharacteristic
97C22×C8×C17C2314yes—
98C22×C8×C17C2311yescharacteristic
99C17×C22⋊Q8—22no—
100C17×C22⋊Q8C2314yes—
101C17×#121—22no—
102C17×#121C2314yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17C2311yescharacteristic
105C2×C4⋊C4×C17C2311yescharacteristic
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17—21no—
108C2×C22⋊Dic17—21no—
109C2×C22⋊Dic17—21no—
110C2×C22⋊Dic17D411yescharacteristic
111#10587632—22no—
112#10587632C2314yes—
113Q8×Dic17—22no—
114Q8×Dic17C2314yes—
115#10587624—22no—
116#10587624C2314yes—
117#10587621—28no—
118D4×Dic17—22no—
119D4×Dic17C2314yes—
120C4×C22⋊D17D414yes—
121C4×C22⋊D17C2314yes—
122C2×#63227—21no—
123C2×#63227D411yescharacteristic
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17—21no—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2314yes—
133C2×C4⋊Dic17C2311yescharacteristic
134C2×C4⋊Dic17C2311yescharacteristic
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225D411yescharacteristic
141C2×C4×Dic17—21no—
142C2×C4×Dic17C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145C2×C8×D17—24no—
146C2×C8×D17C2314yes—
147#10587583—28no—
148C4⋊C4×D17—22no—
149C4⋊C4×D17—22no—
150C4⋊C4×D17C2314yes—
151C4⋊C4×D17C2314yes—
152#10587575—28no—
153#10587574—22no—
154#10587574—22no—
155#10587574C2314yes—
156#10587574C2314yes—
157#10587569—28no—
158#10587567—28no—
159#10587564—28no—
160#10587564—28no—
161C17×#106C2314yes—
162C17×#103C2314yes—
163C17×#102C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169#10587491C2314yes—
170#10587488C2314yes—
171#10587488C2314yes—
172#10587488C2314yes—
173#10587488C2314yes—
174#10587485C2314yes—
175C8×Dic17C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178#10587479C2314yes—
179#10587479C2314yes—
180C24×C17—21no—
181C24×C17C2×D411yescharacteristic
182C23×D17C2×D411yescharacteristic
183C2×Q8×C17—21no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17C2412yes—
187C2×D4×C17—24no—
188C2×D4×C17—21no—
189C2×D4×C17—22no—
190C2×D4×C17—22no—
191C2×D4×C17—44no—
192C2×D4×C17C2412yes—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2412yes—
201C22×C4×C17C2411yescharacteristic
202C2×C22⋊D17—24no—
203C2×C22⋊D17—44no—
204C2×C22⋊D17SD1618yescomplemented
205C2×C22⋊D17C2×D414yes—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—24no—
211C22×Dic17—24no—
212C22×Dic17—24no—
213C22×Dic17—44no—
214C22×Dic17—44no—
215C22×Dic17—82no—
216C22×Dic17C2×D411yescharacteristic
217C22×Dic17C2×D411yescharacteristic
218C22×Dic17C2×D411yescharacteristic
219#63254—432no—
220C2×C4×D17—22no—
221C2×C4×D17—22no—
222C2×C4×D17—24no—
223C2×C4×D17—24no—
224C2×C4×D17—44no—
225C2×C4×D17—82no—
226C2×C4×D17C2×D412yes—
227C2×C4×D17C2412yes—
228C2×Dic34—24no—
229C2×Dic34—24no—
230C2×Dic34—44no—
231C2×Dic34—82no—
232SD16×C17—28no—
233C2×C8×C17—22no—
234C2×C8×C17—28no—
235C2×C8×C17#4114yescomplemented
236C2×C8×C17C2412yes—
237C2×C8×C17C2412yes—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—24no—
240C4⋊C4×C17—21no—
241C4⋊C4×C17C2412yes—
242C4⋊C4×C17C2412yes—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C22⋊Dic17—24no—
246C22⋊Dic17—24no—
247C22⋊Dic17C2×D414yes—
248#63227—24no—
249#63227C2×D414yes—
250C4⋊Dic17—24no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—24no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—24no—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225C2×D414yes—
267C4×Dic17—24no—
268C4×Dic17C2×D412yes—
269C4×Dic17C2412yes—
270C2×#3622—22no—
271C2×#3622—22no—
272C2×#3622C2412yes—
273C2×#3622C2412yes—
274C8×D17—28no—
275C2×#3335—171nomaximal, Sylow
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—42no—
280C23×C17—42no—
281C23×C17—42no—
282C23×C17C2×SD1614yes—
283C23×C17C22×D412yes—
284C23×C17C22×D411yescharacteristic
285C22×D17—22no—
286C22×D17—22no—
287C22×D17C2×SD1614yes—
288C22×D17C22×D412yes—
289Q8×C17—22no—
290Q8×C17—22no—
291Q8×C17—42no—
292D4×C17—22no—
293D4×C17—22no—
294D4×C17—48no—
295D4×C17—42no—
296C2×C4×C17—22no—
297C2×C4×C17—24no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C2×#4112yes—
309C2×C4×C172−1+412yes—
310C2×C4×C17C2511yescharacteristic
311C22⋊D17—48no—
312C22⋊D17C2×SD16116yescomplemented
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—48no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—48no—
325C2×Dic17—84no—
326C2×Dic17C2×SD1614yes—
327C2×Dic17C22×D412yes—
328C2×Dic17C22×D412yes—
329C2×Dic17C22×D412yes—
330C4×D17—24no—
331C4×D17—22no—
332C4×D17—22no—
333C4×D17—48no—
334C4×D17—84no—
335Dic34—48no—
336Dic34—84no—
337C8×C17—22no—
338C8×C17C2×#4114yescomplemented
339#3622—22no—
340#3622—22no—
341C2×#554—171no—
342C2×#547—171no—
343#3335—1716no—
344C2×#498—171no—
345C2×#481—171no—
346C2×#481—171no—
347C2×#483—171no—
348C2×#483—171no—
349C2×#475—171no—
350C2×#476—171no—
351C2×#465—171no—
352C2×#465D1711yescharacteristic, complemented
353C2×C4×SD16—171no—
354C2×C8×D4—171no—
355C22×#106—171no—
356C22×#106—171no—
357C22×C17—28no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—42no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17—84no—
364C22×C17#54712yes—
365C22×C17C22×SD1614yes—
366C22×C17C22×SD1612yes—
367C22×C17#57712yes—
368C22×C17C23×D411yescharacteristic
369C2×D17—28no—
370C2×D17—22no—
371C2×D17—22no—
372C2×D17C22×SD1614yes—
373C4×C17—22no—
374C4×C17—42no—
375C4×C17—42no—
376C4×C17—42no—
377C4×C17#54712yes—
378C4×C17C22×#4111yescharacteristic
379C4×C17C2×2−1+411yescharacteristic
380Dic17—22no—
381Dic17—22no—
382Dic17—42no—
383Dic17—42no—
384Dic17—42no—
385Dic17—42no—
386Dic17C22×SD1614yes—
387C22×#41—341no—
388C22×SD16C2×D1711yescharacteristic
389C23×C8—171no—
390C23×C8C2×D1711yescharacteristic
391#554—178no—
392#554—344no—
393#547—178no—
394#547—344no—
395C2×C4⋊Q8—171no—
396C2×C4⋊Q8—171no—
397C2×#125—341no—
398C2×#123—341no—
399C2×#123—341no—
400C2×C22⋊Q8—171no—
401C2×C22⋊Q8—341no—
402C2×C22⋊Q8—341no—
403C2×C22⋊Q8—341no—
404C2×C22⋊Q8C2×D1711yescharacteristic
405C2×#121—171no—
406C2×#121C2×D1711yescharacteristic
407C2×C4×Q8—171no—
408C2×C4×D4—171no—
409C2×C4×D4—171no—
410C2×C4×D4—341no—
411C22×C4⋊C4—171no—
412C22×C4⋊C4—171no—
413C22×C4⋊C4—171no—
414C22×C4⋊C4—171no—
415#498—178no—
416#483—178no—
417#483—178no—
418#481—178no—
419#481—178no—
420#476—178no—
421#475—178no—
422#465—178no—
423#465C2×D1718yescomplemented
424C4×SD16—178no—
425C8×D4—178no—
426C2×#106—171no—
427C2×#106—178no—
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×#106—171no—
432C2×#106—171no—
433C2×#106—171no—
434C2×#106—171no—
435C2×#106—178no—
436C2×#106C2×D1711yescharacteristic
437C2×C4⋊C8—171no—
438C2×#103—171no—
439C2×#103—171no—
440C2×#103C2×D1711yescharacteristic
441C2×#102—171no—
442C2×#102—171no—
443C2×#102C2×D1711yescharacteristic
444C2×C22⋊C8—171no—
445C2×C22⋊C8—171no—
446C2×C4×C8—171no—
447C2×C17—24no—
448C2×C17—82no—
449C2×C17#333514yescomplemented
450C2×C17C2×#54711yescharacteristic
451C2×C17C23×SD1611yescharacteristic
452C2×C17C2×#57711yescharacteristic
453D17—24no—
454C2×#41—348no—
455C2×#41—688no—
456C22×Q8—341no—
457C22×Q8—341no—
458C22×Q8C22×D1711yescharacteristic
459C22×D4—21no—
460C22×D4—171no—
461C22×D4—341no—
462C22×D4C22×D1711yescharacteristic
463C23×C4—171no—
464C23×C4—341no—
465C23×C4—341no—
466C23×C4—341no—
467C23×C4—341no—
468C23×C4—341no—
469C23×C4C22×D1711yescharacteristic
470C2×SD16—24no—
471C2×SD16C22×D1714yes—
472C22×C8—24no—
473C22×C8—171no—
474C22×C8—171no—
475C22×C8—174no—
476C22×C8—344no—
477C22×C8C22×D1711yescharacteristic
478C22×C8C22×D1714yes—
479C22×C8C22×D1711yescharacteristic
480C4⋊Q8—174no—
481C4⋊Q8—174no—
482C4⋊Q8—342no—
483C4⋊Q8—342no—
484#125—348no—
485#123—348no—
486#123—348no—
487C22⋊Q8—22no—
488C22⋊Q8—174no—
489C22⋊Q8—348no—
490C22⋊Q8—348no—
491C22⋊Q8—348no—
492C22⋊Q8—342no—
493C22⋊Q8C22×D1714yes—
494#121—22no—
495#121—174no—
496#121—342no—
497#121C22×D1714yes—
498C4×Q8—174no—
499C4×Q8—342no—
500C4×D4—174no—
501C4×D4—174no—
502C4×D4—174no—
503C4×D4—342no—
504C4×D4—348no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—174no—
512C2×C4⋊C4—174no—
513C2×C4⋊C4—174no—
514C2×C4⋊C4—174no—
515C2×C4⋊C4—342no—
516C2×C4⋊C4—342no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4—341no—
521C2×C4⋊C4—341no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—342no—
526C2×C4⋊C4—342no—
527C2×C4⋊C4C22×D1711yescharacteristic
528C2×C4⋊C4C22×D1711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—171no—
532C2×C22⋊C4—171no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C42—171no—
537C2×C42—341no—
538#106—174no—
539#106—174no—
540#106—174no—
541#106—174no—
542#106—174no—
543#106—174no—
544#106—174no—
545#106—174no—
546#106C22×D1714yes—
547C4⋊C8—174no—
548#103—174no—
549#103—174no—
550#103C22×D1714yes—
551#102—174no—
552#102—174no—
553#102C22×D1714yes—
554C22⋊C8—174no—
555C22⋊C8—174no—
556C4×C8—174no—
557C17C2×#333511yescharacteristic, complemented, Sylow
558C24—21no—
559C24—171no—
560C24D4×D1711yescharacteristic
561#41—6832no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—344no—
566C2×Q8—344no—
567C2×Q8—684no—
568C2×Q8—1362no—
569C2×Q8C23×D1712yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—174no—
576C2×D4—178no—
577C2×D4—344no—
578C2×D4—684no—
579C2×D4C23×D1712yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—171no—
586C22×C4—171no—
587C22×C4—171no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—344no—
591C22×C4—344no—
592C22×C4—344no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—344no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—344no—
601C22×C4—684no—
602C22×C4—684no—
603C22×C4—684no—
604C22×C4—1362no—
605C22×C4—1362no—
606C22×C4D4×D1712yes—
607C22×C4D4×D1711yescharacteristic
608C22×C4C23×D1712yes—
609C22×C4C23×D1711yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—172no—
614C2×C8—172no—
615C2×C8—342no—
616C2×C8—342no—
617C2×C8—348no—
618C2×C8#6325414yescomplemented
619C2×C8C23×D1712yes—
620C2×C8C23×D1712yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—174no—
625C4⋊C4—172no—
626C4⋊C4—172no—
627C4⋊C4—172no—
628C4⋊C4—172no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4—344no—
632C4⋊C4—344no—
633C4⋊C4—344no—
634C4⋊C4—344no—
635C4⋊C4—341no—
636C4⋊C4—341no—
637C4⋊C4—341no—
638C4⋊C4—344no—
639C4⋊C4—344no—
640C4⋊C4—341no—
641C4⋊C4C23×D1712yes—
642C4⋊C4C23×D1712yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—174no—
646C22⋊C4—174no—
647C22⋊C4—344no—
648C22⋊C4—344no—
649C22⋊C4—344no—
650C42—172no—
651C42—172no—
652C42—344no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—174no—
660C23—172no—
661C23—342no—
662C23—342no—
663C23SD16×D1714yes—
664C23C2×D4×D1712yes—
665C23C2×D4×D1711yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—688no—
670Q8—1364no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—1716no—
676D4—688no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—174no—
688C2×C4—172no—
689C2×C4—172no—
690C2×C4—172no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—344no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—688no—
701C2×C4—688no—
702C2×C4—682no—
703C2×C4—682no—
704C2×C4—688no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4—1364no—
708C2×C4—1364no—
709C2×C4C2×D4×D1712yes—
710C2×C4C2×D4×D1711yescharacteristic
711C2×C4C2×#6325412yes—
712C2×C4#1058769712yes—
713C2×C4C24×D1711yescharacteristic
714C8—22no—
715C8—342no—
716C8—342no—
717C8C2×#6325414yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—174no—
726C22—348no—
727C22—342no—
728C22—342no—
729C22#1176345912yes—
730C22C2×SD16×D1714yes—
731C22C2×SD16×D1712yes—
732C22#1176361612yes—
733C22C22×D4×D1711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—174no—
739C4—342no—
740C4—342no—
741C4—682no—
742C4—682no—
743C4—682no—
744C4—682no—
745C4#1176345912yes—
746C4C22×#6325411yescharacteristic
747C4C2×#1058769711yescharacteristic
748C2—24no—
749C2—82no—
750C2—344no—
751C2#1454113614yesdirect product factor
752C2C2×#1176345911yescharacteristic
753C2C22×SD16×D1711yescharacteristic
754C2C2×#1176361611yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#465C2
socleC23×C17C22×D4
prime radicalC2×#11763459C2
hypercenterC2×#465D17
hypocenterC17C2×#3335
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×#11763517C2semidirect
3. #14541136C2direct (N × H)
4. C2×#11763206C2semidirect
5. C2×#11763126C2semidirect
6. C2×#11763125C2semidirect
7. C2×#11763138C2semidirect
8. C2×#11763137C2semidirect
9. C2×#11763092C2semidirect
10. C2×#11763097C2semidirect
11. C2×#11763035C2semidirect
12. C2×SD16×Dic17C2semidirect
13. C2×C8×C22⋊D17C2semidirect
14. C22×#10587488C2semidirect
15. C2×#106×D17C2semidirect
16. C2×C17×#465C2semidirect
20. #11763517C22semidirect
41. #11763206C22semidirect
42. #11763138C22semidirect
43. #11763137C22semidirect
44. #11763126C22semidirect
45. #11763125C22semidirect
46. #11763097C22semidirect
47. #11763092C22semidirect
48. #11763035C22semidirect
49. SD16×Dic17C22semidirect
50. C8×C22⋊D17C22semidirect
55. C2×#10587488C22semidirect
60. #106×D17C22semidirect
73. C17×#465C22semidirect
204. C2×C22⋊D17SD16semidirect
235. C2×C8×C17#41semidirect
312. C22⋊D17C2×SD16semidirect
338. C8×C17C2×#41semidirect
352. C2×#465D17semidirect
423. #465C2×D17semidirect
449. C2×C17#3335semidirect
557. C17C2×#3335semidirect
618. C2×C8#63254semidirect
717. C8C2×#63254semidirect
751. C2#14541136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635172
C2×#117634592
#145411362
C2×#117632062
C2×#117631262
C2×#117631252
C2×#117631382
C2×#117631372
C2×#117630922
C2×#117630972
C2×#117630352
C2×SD16×Dic172
C2×C8×C22⋊D172
C22×#105874882
C2×#106×D172
C2×C17×#4652
C2×#333517