Finite Group Databasebeta

← C2×#14538862 #17902405

Subgroups — C2×#14538862 #17902405

Order 4352.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763341C211yesmaximal, characteristic
2C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
3#14538862C2116yesmaximal, direct product factor
4C2×#11763141C211yesmaximal, characteristic, complemented
5C2×#11763121C211yesmaximal, characteristic
6C2×#11763119C211yesmaximal, characteristic, complemented
7C2×#11763118C211yesmaximal, characteristic, complemented
8C2×#11763030C211yesmaximal, characteristic, complemented
9C2×#11763029C211yesmaximal, characteristic, complemented
10C2×#11762966C211yesmaximal, characteristic, complemented
11C2×#11762946C211yesmaximal, characteristic
12C2×C4×Dic68C211yesmaximal, characteristic, complemented
13C2×C4×#63231C211yesmaximal, characteristic, complemented
14C2×C4×#63229C211yesmaximal, characteristic, complemented
15C2×#11762860C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C17C211yesmaximal, characteristic, complemented
17C22×Q8×D17C2211yescharacteristic
18C22×Dic68C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63229C2211yescharacteristic
21#11763341—24no—
22#11763341C2218yes—
23C2×#10587565—21no—
24C2×#10587576C2211yescharacteristic
25C2×#10587622C2211yescharacteristic
26C2×#10587569—21no—
27C2×#10587583C2211yescharacteristic
28C2×#10587624C2211yescharacteristic
29C2×Q8×Dic17C2211yescharacteristic
30C2×C4×Dic34—21no—
31C2×C4×Dic34C2211yescharacteristic
32C2×C4×Dic34C2211yescharacteristic
33C2×#10587573—21no—
34C2×#10587573C2211yescharacteristic
35C4×Q8×D17—24no—
36C4×Q8×D17C2218yescomplemented
37C2×C4×C22⋊D17—21no—
38C2×#10587612—21no—
39C2×C4⋊C4×D17—21no—
40C2×C4⋊C4×D17C2211yescharacteristic
41C2×C42×D17—21no—
42C2×C42×D17C2211yescharacteristic
43#11763141C2218yescomplemented
44#11763121C2218yes—
45#11763119C2218yescomplemented
46#11763118C2218yescomplemented
47#11763030C2218yescomplemented
48#11763029C2218yescomplemented
49#11762966C2218yescomplemented
50#11762946C2218yes—
51C4×Dic68C2218yescomplemented
52C4×#63231C2218yescomplemented
53C4×#63229C2218yescomplemented
54#11762860C2218yescomplemented
55C2×#10587489C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587485C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587481C2211yescharacteristic
64C2×#10587481C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×#10587491C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C4×#3622C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C2×C4×Q8×C17C2211yescharacteristic
71C2×C4×D4×C17C2211yescharacteristic
72C4×SD16×C17C2218yescomplemented
73C2×C17×#106C2211yescharacteristic
74C2×C17×#103C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17—21no—
80C22×C22⋊D17—21no—
81C2×Q8×D17—24no—
82C2×Q8×D17—22no—
83C2×Q8×D17—24no—
84C2×Q8×D17C2314yes—
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×C4×D17D411yescharacteristic
88C22×C4×D17D411yescharacteristic
89C22×C4×D17C2311yescharacteristic
90C22×Dic34—21no—
91C22×Dic34C2311yescharacteristic
92C22×Dic34C2311yescharacteristic
93C2×SD16×C17—24no—
94C2×SD16×C17C2314yes—
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C4×Q8×C17—22no—
98C4×Q8×C17C2314yes—
99C4×D4×C17—22no—
100C4×D4×C17C2314yes—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C22⋊C4×C17—21no—
105C2×C42×C17—21no—
106C2×C42×C17C2311yescharacteristic
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17—21no—
109C2×C22⋊Dic17—21no—
110Q8×Dic17—22no—
111Q8×Dic17C2314yes—
112C2×#63231—24no—
113C2×#63231C2314yes—
114#10587624—22no—
115#10587624C2314yes—
116#10587622—22no—
117#10587622C2314yes—
118C2×#63229—24no—
119C2×#63229C2314yes—
120C4×C22⋊D17—28no—
121C2×#63227—21no—
122#10587612—28no—
123C2×C4⋊Dic17—21no—
124C2×C4⋊Dic17—21no—
125C2×C4⋊Dic17—21no—
126C2×C4⋊Dic17C2311yescharacteristic
127C2×C4⋊Dic17C2311yescharacteristic
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×C4×Dic17—21no—
134C2×C4×Dic17—21no—
135C2×C4×Dic17—21no—
136C2×C4×Dic17—21no—
137C2×C4×Dic17D411yescharacteristic
138C2×C4×Dic17D411yescharacteristic
139C2×C4×Dic17C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142C2×Dic68—24no—
143C2×Dic68C2314yes—
144#10587583—22no—
145#10587583C2314yes—
146C4⋊C4×D17—28no—
147C4⋊C4×D17—22no—
148C4⋊C4×D17C2314yes—
149#10587576—22no—
150#10587576C2314yes—
151#10587573—22no—
152#10587573—28no—
153#10587573C2314yes—
154#10587569—28no—
155#10587565—28no—
156C42×D17—28no—
157C42×D17D414yes—
158C42×D17C2314yes—
159C4×Dic34—28no—
160C4×Dic34—22no—
161C4×Dic34—22no—
162C4×Dic34C2314yes—
163C4×Dic34C2314yes—
164C17×#106C2314yes—
165C17×#103C2314yes—
166C17×#102C2314yes—
167C4×C8×C17C2314yes—
168#10587506C2314yes—
169#10587503C2314yes—
170#10587491C2314yes—
171#10587491C2314yes—
172#10587489C2314yes—
173#10587487C2314yes—
174#10587487C2314yes—
175#10587485C2314yes—
176#10587485C2314yes—
177#10587481C2314yes—
178#10587481C2314yes—
179#10587479C2314yes—
180#10587478C2314yes—
181C4×#3622C2314yes—
182C24×C17—21no—
183C23×D17C2×D411yescharacteristic
184C2×Q8×C17—21no—
185C2×Q8×C17—22no—
186C2×Q8×C17#4114yes—
187C2×Q8×C17C2412yes—
188C2×D4×C17—21no—
189C2×D4×C17—22no—
190C2×D4×C17—22no—
191C2×D4×C17C2412yes—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—24no—
196C22×C4×C17—44no—
197C22×C4×C17C2×D411yescharacteristic
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2411yescharacteristic
200C2×C22⋊D17—24no—
201C2×C22⋊D17—44no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17C2×D411yescharacteristic
207C22×Dic17C2×D411yescharacteristic
208C22×Dic17C2×D411yescharacteristic
209Q8×D17—216no—
210Q8×D17—28no—
211Q8×D17—28no—
212C2×C4×D17—28no—
213C2×C4×D17—24no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—22no—
217C2×C4×D17—22no—
218C2×C4×D17—24no—
219C2×C4×D17—44no—
220C2×C4×D17C2×D414yes—
221C2×C4×D17C2×D414yes—
222C2×C4×D17C2×D412yes—
223C2×C4×D17C2412yes—
224C2×Dic34—28no—
225C2×Dic34—21no—
226C2×Dic34—22no—
227C2×Dic34—24no—
228C2×Dic34—22no—
229C2×Dic34—22no—
230C2×Dic34—21no—
231C2×Dic34#4114yes—
232C2×Dic34C2412yes—
233C2×Dic34C2412yes—
234SD16×C17—28no—
235C2×C8×C17—22no—
236C2×C8×C17—22no—
237C2×C8×C17C2412yes—
238C2×C8×C17C2412yes—
239C4⋊C4×C17—24no—
240C4⋊C4×C17—21no—
241C4⋊C4×C17—21no—
242C4⋊C4×C17C2412yes—
243C4⋊C4×C17C2412yes—
244C22⋊C4×C17—24no—
245C42×C17—24no—
246C42×C17C2×D412yes—
247C42×C17C2412yes—
248C22⋊Dic17—24no—
249C22⋊Dic17—24no—
250C22⋊Dic17—24no—
251#63231—28no—
252#63229—28no—
253#63227—24no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—24no—
257C4⋊Dic17—24no—
258C4⋊Dic17—24no—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266C4×Dic17—24no—
267C4×Dic17—24no—
268C4×Dic17—24no—
269C4×Dic17—24no—
270C4×Dic17C2×D414yes—
271C4×Dic17C2×D412yes—
272C4×Dic17C2×D414yes—
273C4×Dic17C2412yes—
274C2×#3622—22no—
275C2×#3622—22no—
276C2×#3622C2412yes—
277C2×#3622C2412yes—
278Dic68—28no—
279C2×#3108—171nomaximal, Sylow
280C23×C17—22no—
281C23×C17—42no—
282C23×C17—42no—
283C23×C17—42no—
284C23×C17C22×D411yescharacteristic
285C22×D17—22no—
286C22×D17—22no—
287C22×D17#13514yes—
288C22×D17C22×D412yes—
289Q8×C17—24no—
290Q8×C17—22no—
291Q8×C17C2×#4114yes—
292D4×C17—22no—
293D4×C17—22no—
294D4×C17—42no—
295C2×C4×C17—24no—
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—48no—
303C2×C4×C17#13714yes—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D411yescharacteristic
306C2×C4×C17C22×D412yes—
307C2×C4×C17C2×#4112yes—
308C2×C4×C17C2×#4112yes—
309C2×C4×C17C2511yescharacteristic
310C22⋊D17—48no—
311C2×Dic17—22no—
312C2×Dic17—24no—
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—42no—
322C2×Dic17C22×D412yes—
323C2×Dic17C22×D412yes—
324C2×Dic17C22×D412yes—
325C4×D17—216no—
326C4×D17—28no—
327C4×D17—24no—
328C4×D17—28no—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—48no—
332Dic34—216no—
333Dic34—24no—
334Dic34—22no—
335Dic34—22no—
336Dic34—22no—
337Dic34—42no—
338Dic34C2×#4114yes—
339C8×C17—22no—
340C8×C17—22no—
341#3622—22no—
342#3622—22no—
343C2×#529—171no—
344C22×C4×Q8—171no—
345#3108—1716no—
346C2×#483—171no—
347C2×#480—171no—
348C2×#479—171no—
349C2×#479—171no—
350C2×#464—171no—
351C2×#464—171no—
352C2×#451—171no—
353C2×#448—171no—
354C2×C4×Q16—171no—
355C2×C4×Q16—171no—
356C2×C4×SD16—171no—
357C2×C4×SD16D1711yescharacteristic, complemented
358C2×#431—171no—
359C22×C17—42no—
360C22×C17—42no—
361C22×C17—42no—
362C22×C17—84no—
363C22×C17#52512yes—
364C22×C17C2×#13512yes—
365C22×C17C2×#13712yes—
366C22×C17C23×D411yescharacteristic
367C2×D17—28no—
368C2×D17—22no—
369C2×D17—22no—
370C2×D17C2×#13514yes—
371C4×C17—24no—
372C4×C17—22no—
373C4×C17—42no—
374C4×C17—42no—
375C4×C17#52512yes—
376C4×C17C2×#13714yes—
377C4×C17C22×#4111yescharacteristic
378C4×C17C22×#4111yescharacteristic
379Dic17—22no—
380Dic17—24no—
381Dic17—22no—
382Dic17—22no—
383Dic17—42no—
384Dic17—42no—
385Dic17—42no—
386C23×Q8—171no—
387C22×Q16—171no—
388C22×Q16—171no—
389C22×SD16—171no—
390C22×SD16C2×D1711yescharacteristic
391#529—178no—
392#529—344no—
393C2×#126—341no—
394C2×#125—171no—
395C2×#124—171no—
396C2×#123—341no—
397C2×C22⋊Q8—171no—
398C2×#121—171no—
399C2×C4×Q8—171no—
400C2×C4×Q8—178no—
401C2×C4×Q8—171no—
402C2×C4×Q8—171no—
403C2×C4×Q8—171no—
404C2×C4×Q8—341no—
405C2×C4×Q8—341no—
406C2×C4×Q8—344no—
407C2×C4×Q8C2×D1711yescharacteristic
408C2×C4×D4—341no—
409C2×C4×D4C2×D1711yescharacteristic
410C2×#117—341no—
411C22×C4⋊C4—171no—
412C22×C4⋊C4—341no—
413C22×C42—171no—
414C22×C42—341no—
415#483—178no—
416#480—178no—
417#479—178no—
418#479—178no—
419#464—178no—
420#464—178no—
421#451—178no—
422#448—178no—
423C4×Q16—178no—
424C4×Q16—178no—
425C4×SD16—178no—
426C4×SD16C2×D1718yescomplemented
427#431—178no—
428C2×#107—171no—
429C2×#107—171no—
430C2×#106—171no—
431C2×#106C2×D1711yescharacteristic
432C2×C4⋊C8—171no—
433C2×C4⋊C8—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#103—171no—
438C2×#103—171no—
439C2×#103C2×D1711yescharacteristic
440C2×#102—171no—
441C2×#102C2×D1711yescharacteristic
442C2×C22⋊C8—171no—
443C2×C22⋊C8—171no—
444C2×C4×C8—171no—
445C2×C4×C8C2×D1711yescharacteristic
446C2×C17—82no—
447C2×C17#310814yescomplemented
448C2×C17C2×#52511yescharacteristic
449C2×C17C22×#13511yescharacteristic
450C2×C17C22×#13711yescharacteristic
451D17—24no—
452C22×Q8—174no—
453C22×Q8—171no—
454C22×Q8—171no—
455C22×Q8—341no—
456C22×Q8—342no—
457C22×Q8—344no—
458C22×Q8—344no—
459C22×Q8C22×D1711yescharacteristic
460C22×D4—341no—
461C22×D4C22×D1711yescharacteristic
462C23×C4—21no—
463C23×C4—171no—
464C23×C4—171no—
465C23×C4—171no—
466C23×C4—341no—
467C23×C4—341no—
468C2×Q16—174no—
469C2×Q16—174no—
470C2×Q16—344no—
471C2×Q16—344no—
472C2×SD16—24no—
473C2×SD16—174no—
474C2×SD16—344no—
475C2×SD16C22×D1714yes—
476C22×C8—171no—
477C22×C8—171no—
478C22×C8C22×D1711yescharacteristic
479C22×C8C22×D1711yescharacteristic
480#126—348no—
481#125—174no—
482#125—342no—
483#124—174no—
484#124—342no—
485#123—348no—
486C22⋊Q8—174no—
487C22⋊Q8—342no—
488#121—174no—
489#121—342no—
490C4×Q8—22no—
491C4×Q8—174no—
492C4×Q8—174no—
493C4×Q8—174no—
494C4×Q8—174no—
495C4×Q8—348no—
496C4×Q8—342no—
497C4×Q8—348no—
498C4×Q8—342no—
499C4×Q8—342no—
500C4×Q8—342no—
501C4×Q8C22×D1714yes—
502C4×D4—22no—
503C4×D4—348no—
504C4×D4C22×D1714yes—
505#117—348no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—174no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—348no—
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⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C4⋊C4C22×D1711yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C42—21no—
528C2×C42—171no—
529C2×C42—171no—
530C2×C42—171no—
531C2×C42—174no—
532C2×C42—174no—
533C2×C42—348no—
534C2×C42—341no—
535C2×C42—341no—
536C2×C42—341no—
537C2×C42—341no—
538C2×C42C22×D1711yescharacteristic
539#107—174no—
540#107—174no—
541#106—174no—
542#106C22×D1714yes—
543C4⋊C8—174no—
544C4⋊C8—174no—
545#103—174no—
546#103—174no—
547#103—174no—
548#103—174no—
549#103—174no—
550#103C22×D1714yes—
551#102—174no—
552#102C22×D1714yes—
553C22⋊C8—174no—
554C22⋊C8—174no—
555C4×C8—174no—
556C4×C8C22×D1714yes—
557C17C2×#310811yescharacteristic, complemented, Sylow
558C24—21no—
559C24—171no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—174no—
563C2×Q8—172no—
564C2×Q8—172no—
565C2×Q8—344no—
566C2×Q8—348no—
567C2×Q8—348no—
568C2×Q8—3416no—
569C2×Q8—348no—
570C2×Q8—342no—
571C2×Q8—341no—
572C2×Q8—341no—
573C2×Q8—342no—
574C2×Q8—342no—
575C2×Q8#6325214yes—
576C2×Q8C23×D1712yes—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—344no—
581C2×D4—684no—
582C2×D4C23×D1712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—171no—
589C22×C4—171no—
590C22×C4—171no—
591C22×C4—174no—
592C22×C4—174no—
593C22×C4—172no—
594C22×C4—172no—
595C22×C4—344no—
596C22×C4—344no—
597C22×C4—348no—
598C22×C4—344no—
599C22×C4—341no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—344no—
603C22×C4—341no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—684no—
607C22×C4D4×D1711yescharacteristic
608C22×C4D4×D1711yescharacteristic
609C22×C4C23×D1711yescharacteristic
610Q16—348no—
611Q16—348no—
612SD16—28no—
613SD16—348no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—172no—
617C2×C8—172no—
618C2×C8—342no—
619C2×C8—342no—
620C2×C8C23×D1712yes—
621C2×C8C23×D1712yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—172no—
626C4⋊C4—172no—
627C4⋊C4—344no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4—344no—
632C4⋊C4—344no—
633C4⋊C4—341no—
634C4⋊C4—341no—
635C4⋊C4—344no—
636C4⋊C4—344no—
637C4⋊C4C23×D1712yes—
638C4⋊C4C23×D1712yes—
639C22⋊C4—24no—
640C22⋊C4—344no—
641C22⋊C4—344no—
642C22⋊C4—344no—
643C22⋊C4—344no—
644C42—24no—
645C42—174no—
646C42—172no—
647C42—174no—
648C42—172no—
649C42—344no—
650C42—344no—
651C42—344no—
652C42—344no—
653C42D4×D1712yes—
654C42C23×D1712yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—174no—
660C23—172no—
661C23—342no—
662C23—342no—
663C23C2×D4×D1711yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—174no—
667Q8—3416no—
668Q8—344no—
669Q8—342no—
670Q8—342no—
671Q8—342no—
672Q8—682no—
673Q8C2×#6325214yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—688no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—172no—
687C2×C4—172no—
688C2×C4—172no—
689C2×C4—348no—
690C2×C4—3416no—
691C2×C4—342no—
692C2×C4—344no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—344no—
697C2×C4—348no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—688no—
704C2×C4—682no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4#1058760114yes—
708C2×C4C2×#6325212yes—
709C2×C4C2×D4×D1712yes—
710C2×C4C2×D4×D1711yescharacteristic
711C2×C4C2×D4×D1712yes—
712C2×C4#41×D1712yes—
713C2×C4C24×D1711yescharacteristic
714C8—22no—
715C8—22no—
716C8—342no—
717C8—342no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—174no—
723C22—348no—
724C22—342no—
725C22—342no—
726C22#1176331812yes—
727C22#135×D1712yes—
728C22C2×#1058760112yes—
729C22C22×D4×D1711yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—342no—
735C4—342no—
736C4—342no—
737C4—344no—
738C4—682no—
739C4—682no—
740C4—682no—
741C4#1176331812yes—
742C4C2×#1058760114yes—
743C4C2×#41×D1711yescharacteristic
744C4C22×#6325211yescharacteristic
745C2—82no—
746C2—344no—
747C2#1453886214yesdirect product factor
748C2C2×#1176331811yescharacteristic
749C2C2×#135×D1711yescharacteristic
750C2C22×#1058760111yescharacteristic
subgroupG/H
centerC22×C4D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C4×SD16×C17C2
socleC23×C17C22×D4
prime radicalC2×#10587624C22
hypercenterC2×C4×SD16D17
hypocenterC17C2×#3108
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D17C2semidirect
3. #14538862C2direct (N × H)
4. C2×#11763141C2semidirect
6. C2×#11763119C2semidirect
7. C2×#11763118C2semidirect
8. C2×#11763030C2semidirect
9. C2×#11763029C2semidirect
10. C2×#11762966C2semidirect
12. C2×C4×Dic68C2semidirect
13. C2×C4×#63231C2semidirect
14. C2×C4×#63229C2semidirect
15. C2×#11762860C2semidirect
16. C2×C4×SD16×C17C2semidirect
36. C4×Q8×D17C22semidirect
43. #11763141C22semidirect
45. #11763119C22semidirect
46. #11763118C22semidirect
47. #11763030C22semidirect
48. #11763029C22semidirect
49. #11762966C22semidirect
51. C4×Dic68C22semidirect
52. C4×#63231C22semidirect
53. C4×#63229C22semidirect
54. #11762860C22semidirect
72. C4×SD16×C17C22semidirect
357. C2×C4×SD16D17semidirect
426. C4×SD16C2×D17semidirect
447. C2×C17#3108semidirect
557. C17C2×#3108semidirect
747. C2#14538862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633412
C2×C4×Q8×D172
#145388622
C2×#117631412
C2×#117631212
C2×#117631192
C2×#117631182
C2×#117630302
C2×#117630292
C2×#117629662
C2×#117629462
C2×C4×Dic682
C2×C4×#632312
C2×C4×#632292
C2×#117628602
C2×C4×SD16×C172
C2×#310817