Finite Group Databasebeta

← C2×#14541405 #17913069

Subgroups — C2×#14541405 #17913069

Order 4352.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763523C211yesmaximal, characteristic
2C2×#11763517C211yesmaximal, characteristic, complemented
3#14541405C2116yesmaximal, direct product factor
4C2×#11763213C211yesmaximal, characteristic, complemented
5C2×#11763148C211yesmaximal, characteristic, complemented
6C2×#11763147C211yesmaximal, characteristic, complemented
7C2×#11763121C211yesmaximal, characteristic, complemented
8C2×#11763120C211yesmaximal, characteristic, complemented
9C2×#11763102C211yesmaximal, characteristic, complemented
10C2×#11763097C211yesmaximal, characteristic, complemented
11C2×#11763052C211yesmaximal, characteristic, complemented
12C2×SD16×Dic17C211yesmaximal, characteristic, complemented
13C2×#11762885C211yesmaximal, characteristic, complemented
14C2×#11762851C211yesmaximal, characteristic, complemented
15C2×#11762850C211yesmaximal, characteristic, complemented
16C2×C17×#468C211yesmaximal, characteristic, complemented
17C22×#63218C2211yescharacteristic
18#11763523—24no—
19#11763523C2218yes—
20#11763517—24no—
21#11763517C2218yescomplemented
22C2×#10587574C2211yescharacteristic
23C2×#10587574C2211yescharacteristic
24C2×#10587575—21no—
25C2×#10587622—21no—
26C2×#10587571—21no—
27C2×#10587583—21no—
28C2×#10587564—21no—
29C2×#10587632C2211yescharacteristic
30C2×#10587625—21no—
31C2×#10587624C2211yescharacteristic
32C2×Q8×Dic17C2211yescharacteristic
33C2×D4×Dic17C2211yescharacteristic
34C2×C4×C22⋊D17C2211yescharacteristic
35C2×#10587567—21no—
36C2×#10587612C2211yescharacteristic
37C2×#10587578C2211yescharacteristic
38C2×#10587563—21no—
39C22×C4⋊Dic17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41#11763213C2218yescomplemented
42#11763148C2218yescomplemented
43#11763147C2218yescomplemented
44#11763121C2218yescomplemented
45#11763120C2218yescomplemented
46#11763102C2218yescomplemented
47#11763097C2218yescomplemented
48#11763052C2218yescomplemented
49SD16×Dic17C2218yescomplemented
50#11762885C2218yescomplemented
51#11762851C2218yescomplemented
52#11762850C2218yescomplemented
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587485C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C22×M16×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121C2211yescharacteristic
73C17×#468C2218yescomplemented
74C2×C17×#107C2211yescharacteristic
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—
85C22×C4×D17—21no—
86C22×C4×D17C2311yescharacteristic
87C22×Dic34—21no—
88C22×Dic34—21no—
89C2×SD16×C17—24no—
90C2×SD16×C17C2314yes—
91C2×M16×C17—24no—
92C2×M16×C17C2314yes—
93C22×C8×C17C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C17×C22⋊Q8—22no—
96C17×C22⋊Q8C2314yes—
97C17×#121—22no—
98C17×#121C2314yes—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C22⋊C4×C17—21no—
103C2×C22⋊C4×C17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17D411yescharacteristic
108#10587632—22no—
109#10587632C2314yes—
110Q8×Dic17—22no—
111Q8×Dic17C2314yes—
112#10587625—28no—
113#10587624—22no—
114#10587624C2314yes—
115#10587622—28no—
116D4×Dic17—22no—
117D4×Dic17C2314yes—
118C4×C22⋊D17D414yes—
119C4×C22⋊D17C2314yes—
120C2×#63227—21no—
121C2×#63227—21no—
122C2×#63227D411yescharacteristic
123#10587612—22no—
124#10587612C2314yes—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225D411yescharacteristic
138C2×C4×Dic17—21no—
139C2×C4×Dic17—21no—
140C2×C4×Dic17—21no—
141C2×C4×Dic17C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C2×#63218—24no—
145C2×#63218C2314yes—
146#10587583—28no—
147#10587578—22no—
148#10587578C2314yes—
149C4⋊C4×D17—22no—
150C4⋊C4×D17C2314yes—
151#10587575—28no—
152#10587574—22no—
153#10587574—22no—
154#10587574C2314yes—
155#10587574C2314yes—
156#10587571—28no—
157#10587567—28no—
158#10587564—28no—
159#10587563—28no—
160C17×#107C2314yes—
161C17×#103C2314yes—
162C17×#102C2314yes—
163#10587506C2314yes—
164#10587506C2314yes—
165#10587503C2314yes—
166#10587503C2314yes—
167C22⋊#3622C2314yes—
168#10587491C2314yes—
169#10587489C2314yes—
170#10587489C2314yes—
171#10587488C2314yes—
172#10587488C2314yes—
173#10587485C2314yes—
174C8×Dic17C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C23×D17C2×D411yescharacteristic
182C2×Q8×C17—21no—
183C2×Q8×C17—22no—
184C2×Q8×C17—22no—
185C2×Q8×C17C2412yes—
186C2×D4×C17—24no—
187C2×D4×C17—21no—
188C2×D4×C17—22no—
189C2×D4×C17—22no—
190C2×D4×C17—82no—
191C2×D4×C17C2412yes—
192C22×C4×C17—22no—
193C22×C4×C17—22no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2412yes—
200C22×C4×C17C2411yescharacteristic
201C2×C22⋊D17—24no—
202C2×C22⋊D17—24no—
203C2×C22⋊D17—82no—
204C2×C22⋊D17C2×D414yes—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—24no—
210C22×Dic17—24no—
211C22×Dic17—44no—
212C22×Dic17—82no—
213C22×Dic17C2×D411yescharacteristic
214C22×Dic17C2×D411yescharacteristic
215C22×Dic17C2×D411yescharacteristic
216C2×C4×D17—22no—
217C2×C4×D17—22no—
218C2×C4×D17—24no—
219C2×C4×D17—82no—
220C2×C4×D17C2×D412yes—
221C2×C4×D17C2412yes—
222C2×Dic34—24no—
223C2×Dic34—24no—
224C2×Dic34—82no—
225C2×Dic34—82no—
226SD16×C17—28no—
227M16×C17—28no—
228C2×C8×C17—22no—
229C2×C8×C17#4114yes—
230C2×C8×C17C2412yes—
231C2×C8×C17C2412yes—
232C4⋊C4×C17—21no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C22⋊C4×C17—24no—
238C22⋊C4×C17—24no—
239C22⋊Dic17—24no—
240C22⋊Dic17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17C2×D414yes—
243#63227—24no—
244#63227—24no—
245#63227C2×D414yes—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—24no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—24no—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225C2×D414yes—
261C4×Dic17—24no—
262C4×Dic17—24no—
263C4×Dic17—24no—
264C4×Dic17C2×D412yes—
265C4×Dic17C2412yes—
266C2×#3622—22no—
267C2×#3622—22no—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270#63218—28no—
271C2×#3357—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—42no—
277C23×C17—42no—
278C23×C17—42no—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17C22×D412yes—
285Q8×C17—22no—
286Q8×C17—22no—
287Q8×C17—42no—
288D4×C17—22no—
289D4×C17—22no—
290D4×C17—42no—
291D4×C17—84no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17C22×D412yes—
303C2×C4×C17C22×D411yescharacteristic
304C2×C4×C17C2×#4112yes—
305C2×C4×C172−1+412yes—
306C2×C4×C17C2511yescharacteristic
307C22⋊D17—28no—
308C22⋊D17—84no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—48no—
320C2×Dic17—84no—
321C2×Dic17#13714yes—
322C2×Dic17C22×D412yes—
323C2×Dic17C22×D412yes—
324C2×Dic17C22×D412yes—
325C4×D17—24no—
326C4×D17—22no—
327C4×D17—22no—
328C4×D17—84no—
329Dic34—84no—
330Dic34—84no—
331C8×C17—22no—
332C8×C17C2×#4114yes—
333#3622—22no—
334#3622—22no—
335C2×#555—171no—
336C2×#554—171no—
337#3357—1716no—
338C2×#500—171no—
339C2×#485—171no—
340C2×#485—171no—
341C2×#480—171no—
342C2×#480—171no—
343C2×#477—171no—
344C2×#476—171no—
345C2×#468—171no—
346C2×#468D1711yescharacteristic, complemented
347C2×C4×SD16—171no—
348C2×#436—171no—
349C2×#428—171no—
350C2×#428—171no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—44no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—84no—
359C22×C17#54712yes—
360C22×C17C2×#13712yes—
361C22×C17#57612yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—22no—
364C2×D17—22no—
365C2×D17—22no—
366C2×D17—44no—
367C4×C17—22no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17#54712yes—
372C4×C17C22×#4111yescharacteristic
373C4×C17C2×2−1+411yescharacteristic
374Dic17—22no—
375Dic17—22no—
376Dic17—42no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17C2×#13714yes—
381C22×SD16C2×D1711yescharacteristic
382C22×M16—171no—
383C22×M16C2×D1711yescharacteristic
384#555—178no—
385#555—344no—
386#554—178no—
387#554—344no—
388C2×C4⋊Q8—171no—
389C2×C4⋊Q8—171no—
390C2×#125—341no—
391C2×#124—341no—
392C2×#124—341no—
393C2×C22⋊Q8—171no—
394C2×C22⋊Q8—341no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8C2×D1711yescharacteristic
397C2×#121—171no—
398C2×#121—341no—
399C2×#121C2×D1711yescharacteristic
400C2×C4×Q8—171no—
401C2×C4×D4—171no—
402C2×C4×D4—171no—
403C2×C4×D4—341no—
404C2×#117—171no—
405C2×#117—171no—
406C2×#117—341no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409#500—178no—
410#485—178no—
411#485—178no—
412#480—178no—
413#480—178no—
414#477—178no—
415#476—178no—
416#468—178no—
417#468C2×D1718yescomplemented
418C4×SD16—178no—
419#436—178no—
420#428—178no—
421#428—178no—
422C2×#107—171no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#107—171no—
427C2×#107C2×D1711yescharacteristic
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×C4⋊C8—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103C2×D1711yescharacteristic
435C2×#102—171no—
436C2×#102—171no—
437C2×#102C2×D1711yescharacteristic
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×C4×C8—171no—
441C2×C17—42no—
442C2×C17—82no—
443C2×C17#335714yescomplemented
444C2×C17C2×#54711yescharacteristic
445C2×C17C22×#13711yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—42no—
448C22×Q8—341no—
449C22×Q8—341no—
450C22×Q8C22×D1711yescharacteristic
451C22×D4—21no—
452C22×D4—171no—
453C22×D4—341no—
454C22×D4C22×D1711yescharacteristic
455C23×C4—171no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×SD16—24no—
461C2×SD16C22×D1714yes—
462C2×M16—24no—
463C2×M16—174no—
464C2×M16—344no—
465C2×M16C22×D1714yes—
466C22×C8—171no—
467C22×C8—171no—
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—174no—
472C4⋊Q8—342no—
473C4⋊Q8—342no—
474#125—348no—
475#124—348no—
476#124—348no—
477C22⋊Q8—22no—
478C22⋊Q8—174no—
479C22⋊Q8—348no—
480C22⋊Q8—348no—
481C22⋊Q8—342no—
482C22⋊Q8C22×D1714yes—
483#121—22no—
484#121—174no—
485#121—342no—
486#121—348no—
487#121C22×D1714yes—
488C4×Q8—174no—
489C4×Q8—342no—
490C4×D4—174no—
491C4×D4—174no—
492C4×D4—174no—
493C4×D4—342no—
494C4×D4—348no—
495#117—174no—
496#117—174no—
497#117—348no—
498#117—342no—
499#117—342no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—174no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—174no—
508C2×C4⋊C4—342no—
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—342no—
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—171no—
521C2×C22⋊C4—171no—
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—341no—
529C2×C42—341no—
530C2×C42—341no—
531#107—174no—
532#107—174no—
533#107—174no—
534#107—174no—
535#107—174no—
536#107C22×D1714yes—
537#106—174no—
538#106—174no—
539#106—174no—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103C22×D1714yes—
544#102—174no—
545#102—174no—
546#102C22×D1714yes—
547C22⋊C8—174no—
548C22⋊C8—174no—
549C4×C8—174no—
550C17C2×#335711yescharacteristic, complemented, Sylow
551C24—21no—
552C24—171no—
553C24D4×D1711yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—344no—
558C2×Q8—344no—
559C2×Q8—1362no—
560C2×Q8—1362no—
561C2×Q8C23×D1712yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—174no—
568C2×D4—344no—
569C2×D4—344no—
570C2×D4—1362no—
571C2×D4C23×D1712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—171no—
578C22×C4—171no—
579C22×C4—171no—
580C22×C4—172no—
581C22×C4—172no—
582C22×C4—344no—
583C22×C4—344no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—344no—
591C22×C4—684no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4D4×D1712yes—
595C22×C4D4×D1711yescharacteristic
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—28no—
599M16—28no—
600M16—348no—
601C2×C8—22no—
602C2×C8—172no—
603C2×C8—172no—
604C2×C8—342no—
605C2×C8—342no—
606C2×C8#6325414yes—
607C2×C8C23×D1712yes—
608C2×C8C23×D1712yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—174no—
613C4⋊C4—172no—
614C4⋊C4—172no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—341no—
625C4⋊C4—341no—
626C4⋊C4—341no—
627C4⋊C4C23×D1712yes—
628C4⋊C4C23×D1712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—174no—
632C22⋊C4—174no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C42—172no—
639C42—172no—
640C42—344no—
641C42—344no—
642C42—344no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—172no—
651C23—342no—
652C23—342no—
653C23—342no—
654C23C2×D4×D1712yes—
655C23C2×D4×D1711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1364no—
660Q8—1364no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—348no—
666D4—1364no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—174no—
678C2×C4—172no—
679C2×C4—172no—
680C2×C4—172no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—344no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—688no—
691C2×C4—682no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—682no—
695C2×C4—1364no—
696C2×C4—1364no—
697C2×C4C2×D4×D1712yes—
698C2×C4C2×D4×D1711yescharacteristic
699C2×C4C2×#6325412yes—
700C2×C4#1058769712yes—
701C2×C4C24×D1711yescharacteristic
702C8—22no—
703C8—342no—
704C8—342no—
705C8C2×#6325414yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—342no—
715C22—342no—
716C22—342no—
717C22—684no—
718C22#1176345912yes—
719C22#137×D1712yes—
720C22#1176361312yes—
721C22C22×D4×D1711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—174no—
727C4—342no—
728C4—342no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176345912yes—
734C4C22×#6325411yescharacteristic
735C4C2×#1058769711yescharacteristic
736C2—42no—
737C2—82no—
738C2—682no—
739C2#1454140514yesdirect product factor
740C2C2×#1176345911yescharacteristic
741C2C2×#137×D1711yescharacteristic
742C2C2×#1176361311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#468C2
socleC23×C17C22×D4
prime radicalC2×#11763523C2
hypercenterC2×#468D17
hypocenterC17C2×#3357
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#11763517C2semidirect
3. #14541405C2direct (N × H)
4. C2×#11763213C2semidirect
5. C2×#11763148C2semidirect
6. C2×#11763147C2semidirect
7. C2×#11763121C2semidirect
8. C2×#11763120C2semidirect
9. C2×#11763102C2semidirect
10. C2×#11763097C2semidirect
11. C2×#11763052C2semidirect
12. C2×SD16×Dic17C2semidirect
13. C2×#11762885C2semidirect
14. C2×#11762851C2semidirect
15. C2×#11762850C2semidirect
16. C2×C17×#468C2semidirect
21. #11763517C22semidirect
41. #11763213C22semidirect
42. #11763148C22semidirect
43. #11763147C22semidirect
44. #11763121C22semidirect
45. #11763120C22semidirect
46. #11763102C22semidirect
47. #11763097C22semidirect
48. #11763052C22semidirect
49. SD16×Dic17C22semidirect
50. #11762885C22semidirect
51. #11762851C22semidirect
52. #11762850C22semidirect
73. C17×#468C22semidirect
346. C2×#468D17semidirect
417. #468C2×D17semidirect
443. C2×C17#3357semidirect
550. C17C2×#3357semidirect
739. C2#14541405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635232
C2×#117635172
#145414052
C2×#117632132
C2×#117631482
C2×#117631472
C2×#117631212
C2×#117631202
C2×#117631022
C2×#117630972
C2×#117630522
C2×SD16×Dic172
C2×#117628852
C2×#117628512
C2×#117628502
C2×C17×#4682
C2×#335717