Finite Group Databasebeta

← C2×#14541137 #17912743

Subgroups — C2×#14541137 #17912743

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×#11763514C211yesmaximal, characteristic, complemented
2C2×#11763460C211yesmaximal, characteristic
3#14541137C2116yesmaximal, direct product factor
4C2×#11763206C211yesmaximal, characteristic, complemented
5C2×#11763129C211yesmaximal, characteristic, complemented
6C2×#11763127C211yesmaximal, characteristic, complemented
7C2×#11763141C211yesmaximal, characteristic, complemented
8C2×#11763139C211yesmaximal, characteristic, complemented
9C2×#11763093C211yesmaximal, characteristic, complemented
10C2×#11763098C211yesmaximal, characteristic, complemented
11C2×#11763039C211yesmaximal, characteristic, complemented
12C2×#11763038C211yesmaximal, characteristic, complemented
13C2×#11762896C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D17C211yesmaximal, characteristic, complemented
15C2×#106×D17C211yesmaximal, characteristic, complemented
16C22×C17×#106C211yesmaximal, characteristic, complemented
17C22×#63252—21no—
18C22×#63219C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763514—24no—
21#11763514C2218yescomplemented
22#11763460—24no—
23#11763460C2218yes—
24C2×#10587574C2211yescharacteristic
25C2×#10587574C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587580—21no—
28C2×#10587615—21no—
29C2×#10587583C2211yescharacteristic
30C2×#10587610—21no—
31C2×#10587610C2211yescharacteristic
32C2×#10587582—21no—
33C2×#10587582—21no—
34C2×#10587581C2211yescharacteristic
35C2×#10587616C2211yescharacteristic
36C2×#10587573C2211yescharacteristic
37C2×#10587579C2211yescharacteristic
38C2×C4×C22⋊D17—21no—
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763206C2218yescomplemented
43#11763141C2218yescomplemented
44#11763139C2218yescomplemented
45#11763129C2218yescomplemented
46#11763127C2218yescomplemented
47#11763098C2218yescomplemented
48#11763093C2218yescomplemented
49#11763039C2218yescomplemented
50#11763038C2218yescomplemented
51#11762896C2218yescomplemented
52C8×C22⋊D17C2218yescomplemented
53C2×#10587488C2211yescharacteristic
54C2×#10587479C2211yescharacteristic
55C2×#10587479C2211yescharacteristic
56C2×#10587479C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58#106×D17C2218yescomplemented
59C2×#10587485C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587481C2211yescharacteristic
62C2×#10587481C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587480C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C23×C8×C17C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C22×C4⋊C4×C17C2211yescharacteristic
72C2×C17×#106C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×#106C2211yescharacteristic
75C2×C17×#106C2211yescharacteristic
76C2×C17×#106C2218yescomplemented
77C23×C4×C17—21no—
78C23×C4×C17—21no—
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17D411yescharacteristic
82C2×#63252—28no—
83C2×#63252—48no—
84C22×D68—21no—
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C22×C4×D17C2311yescharacteristic
90C22×Dic34—21no—
91C22×Dic34—21no—
92C22×Dic34C2311yescharacteristic
93C22×C8×C17—24no—
94C22×C8×C17C2311yescharacteristic
95C22×C8×C17C2314yes—
96C22×C8×C17C2311yescharacteristic
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—22no—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17—21no—
101C2×C4⋊C4×C17C2314yes—
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C4⋊C4×C17C2314yes—
105C2×C4⋊C4×C17C2311yescharacteristic
106C2×C4⋊C4×C17C2311yescharacteristic
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17D411yescharacteristic
109#10587616—22no—
110#10587616C2314yes—
111#10587615—28no—
112C4×C22⋊D17—28no—
113C4×C22⋊D17D414yes—
114C4×C22⋊D17C2314yes—
115C2×#63227—21no—
116C2×#63227—21no—
117C2×#63227—21no—
118C2×#63227—21no—
119C2×#63227D411yescharacteristic
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17C2311yescharacteristic
122C2×C4⋊Dic17C2311yescharacteristic
123#10587610—22no—
124#10587610—28no—
125#10587610C2314yes—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225D411yescharacteristic
133C2×C4×Dic17—21no—
134C2×C4×Dic17C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C22×#3622C2311yescharacteristic
137C2×#63219—24no—
138C2×#63219C2314yes—
139C2×C8×D17—24no—
140C2×C8×D17C2314yes—
141#10587583—22no—
142#10587583C2314yes—
143#10587582—28no—
144#10587582—28no—
145#10587581—22no—
146#10587581C2314yes—
147#10587580—28no—
148#10587579—22no—
149#10587579C2314yes—
150C4⋊C4×D17—22no—
151C4⋊C4×D17—22no—
152C4⋊C4×D17C2314yes—
153C4⋊C4×D17C2314yes—
154#10587575—28no—
155#10587574—22no—
156#10587574—22no—
157#10587574C2314yes—
158#10587574C2314yes—
159#10587573—22no—
160#10587573C2314yes—
161C17×#106C2314yes—
162C17×#106C2314yes—
163C17×#106C2314yes—
164C17×#106C2314yes—
165C22⋊#3622C2314yes—
166#10587492C2314yes—
167#10587491C2314yes—
168#10587488C2314yes—
169#10587487C2314yes—
170#10587485C2314yes—
171C8×Dic17C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587480C2314yes—
175#10587480C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178#10587479C2314yes—
179#10587479C2314yes—
180C24×C17C2×D411yescharacteristic
181C23×D17—21no—
182C23×D17C2×D411yescharacteristic
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—24no—
190C22×C4×C17—24no—
191C22×C4×C17—44no—
192C22×C4×C17—82no—
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2×D412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2411yescharacteristic
197C2×C22⋊D17—24no—
198C2×C22⋊D17—44no—
199C2×C22⋊D17SD1618yescomplemented
200C2×C22⋊D17C2×D414yes—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17C2×D411yescharacteristic
205C22×Dic17C2×D411yescharacteristic
206C22×Dic17C2×D411yescharacteristic
207#63252—432no—
208C2×D68—22no—
209C2×D68—22no—
210C2×D68—24no—
211C2×D68—21no—
212C2×D68—44no—
213C2×D68C2412yes—
214C2×C4×D17—22no—
215C2×C4×D17—22no—
216C2×C4×D17—24no—
217C2×C4×D17—24no—
218C2×C4×D17—24no—
219C2×C4×D17—44no—
220C2×C4×D17—44no—
221C2×C4×D17—82no—
222C2×C4×D17C2×D412yes—
223C2×C4×D17C2412yes—
224C2×Dic34—22no—
225C2×Dic34—22no—
226C2×Dic34—21no—
227C2×Dic34—24no—
228C2×Dic34—24no—
229C2×Dic34—44no—
230C2×Dic34—82no—
231C2×Dic34C2412yes—
232C2×C8×C17—22no—
233C2×C8×C17—28no—
234C2×C8×C17#4114yescomplemented
235C2×C8×C17C2412yes—
236C2×C8×C17C2412yes—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17—24no—
241C4⋊C4×C17—21no—
242C4⋊C4×C17—24no—
243C4⋊C4×C17C2412yes—
244C4⋊C4×C17C2412yes—
245C4⋊C4×C17C2412yes—
246C4⋊C4×C17C2412yes—
247C22⋊Dic17—24no—
248C22⋊Dic17C2×D414yes—
249#63227—24no—
250#63227—24no—
251#63227—24no—
252#63227—24no—
253#63227C2×D414yes—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—24no—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225C2×D414yes—
266C4×Dic17—24no—
267C4×Dic17C2×D412yes—
268C4×Dic17C2412yes—
269C2×#3622—22no—
270C2×#3622—22no—
271C2×#3622C2412yes—
272C2×#3622C2412yes—
273#63219—28no—
274C8×D17—28no—
275C2×#3335—171nomaximal, Sylow
276C23×C17—22no—
277C23×C17—22no—
278C23×C17C2×SD1614yes—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—42no—
285C22×D17—42no—
286C22×D17—42no—
287C22×D17C2×SD1614yes—
288C22×D17C22×D412yes—
289C2×C4×C17—22no—
290C2×C4×C17—24no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—48no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—84no—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D411yescharacteristic
305C2×C4×C17C2×#4112yes—
306C2×C4×C172−1+412yes—
307C2×C4×C17C2511yescharacteristic
308C22⋊D17—48no—
309C22⋊D17C2×SD16116yescomplemented
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×Dic17C2×SD1614yes—
319C2×Dic17C22×D412yes—
320C2×Dic17C22×D412yes—
321C2×Dic17C22×D412yes—
322D68—22no—
323D68—22no—
324D68—48no—
325D68—42no—
326C4×D17—24no—
327C4×D17—22no—
328C4×D17—22no—
329C4×D17—48no—
330C4×D17—48no—
331C4×D17—84no—
332Dic34—22no—
333Dic34—22no—
334Dic34—42no—
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×#465—171no—
353C2×C4×SD16—171no—
354C2×C8×D4—171no—
355C22×#106—171no—
356C22×#106D1711yescharacteristic, complemented
357C22×C17—28no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17#54712yes—
361C22×C17C22×SD1614yes—
362C22×C17C22×SD1612yes—
363C22×C17#57712yes—
364C22×C17C23×D411yescharacteristic
365C2×D17—28no—
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—42no—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—84no—
372C2×D17C22×SD1614yes—
373C4×C17—22no—
374C4×C17—42no—
375C4×C17—42no—
376C4×C17—42no—
377C4×C17—42no—
378C4×C17#54712yes—
379C4×C17C22×#4111yescharacteristic
380C4×C17C2×2−1+411yescharacteristic
381Dic17—22no—
382Dic17—22no—
383Dic17—42no—
384Dic17—42no—
385Dic17—42no—
386Dic17C22×SD1614yes—
387C22×#41—341no—
388C22×SD16—171no—
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—171no—
402C2×C22⋊Q8—341no—
403C2×C22⋊Q8—341no—
404C2×C22⋊Q8—341no—
405C2×#121—171no—
406C2×#121—171no—
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⋊C4C2×D1711yescharacteristic
414C22×C4⋊C4C2×D1711yescharacteristic
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#465—178no—
424C4×SD16—178no—
425C8×D4—178no—
426C2×#106—171no—
427C2×#106—171no—
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×#106—178no—
432C2×#106C2×D1711yescharacteristic
433C2×#106C2×D1711yescharacteristic
434C2×#106C2×D1711yescharacteristic
435C2×#106C2×D1711yescharacteristic
436C2×#106C2×D1718yescomplemented
437C2×C4⋊C8—171no—
438C2×#103—171no—
439C2×#103—171no—
440C2×#103—171no—
441C2×#102—171no—
442C2×#102—171no—
443C2×#102—171no—
444C2×C22⋊C8—171no—
445C2×C22⋊C8—171no—
446C2×C4×C8—171no—
447C2×C17—24no—
448C2×C17#333514yescomplemented
449C2×C17C2×#54711yescharacteristic
450C2×C17C23×SD1611yescharacteristic
451C2×C17C2×#57711yescharacteristic
452D17—24no—
453D17—82no—
454C2×#41—348no—
455C2×#41—688no—
456C22×Q8—171no—
457C22×Q8—341no—
458C22×Q8—341no—
459C22×D4—171no—
460C22×D4—171no—
461C22×D4—341no—
462C22×D4—341no—
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—171no—
466C23×C4—341no—
467C23×C4—341no—
468C23×C4—341no—
469C23×C4C22×D1711yescharacteristic
470C2×SD16—174no—
471C2×SD16—344no—
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—174no—
488C22⋊Q8—174no—
489C22⋊Q8—348no—
490C22⋊Q8—348no—
491C22⋊Q8—348no—
492C22⋊Q8—342no—
493C22⋊Q8—342no—
494#121—174no—
495#121—174no—
496#121—342no—
497#121—342no—
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—21no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—174no—
513C2×C4⋊C4—174no—
514C2×C4⋊C4—342no—
515C2×C4⋊C4—342no—
516C2×C4⋊C4—341no—
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⋊C4C22×D1711yescharacteristic
524C2×C4⋊C4C22×D1711yescharacteristic
525C2×C4⋊C4C22×D1711yescharacteristic
526C2×C4⋊C4C22×D1711yescharacteristic
527C2×C4⋊C4C22×D1714yes—
528C2×C4⋊C4C22×D1714yes—
529C2×C22⋊C4—171no—
530C2×C22⋊C4—171no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
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#106C22×D1714yes—
544#106C22×D1714yes—
545#106C22×D1714yes—
546#106C22×D1714yes—
547C4⋊C8—174no—
548#103—174no—
549#103—174no—
550#103—174no—
551#102—174no—
552#102—174no—
553#102—174no—
554C22⋊C8—174no—
555C22⋊C8—174no—
556C4×C8—174no—
557C17C2×#333511yescharacteristic, complemented, Sylow
558C24—171no—
559C24—341no—
560C24D4×D1711yescharacteristic
561#41—6832no—
562C2×Q8—172no—
563C2×Q8—344no—
564C2×Q8—344no—
565C2×Q8—341no—
566C2×Q8—342no—
567C2×Q8—342no—
568C2×Q8—684no—
569C2×Q8—1362no—
570C2×D4—174no—
571C2×D4—178no—
572C2×D4—172no—
573C2×D4—344no—
574C2×D4—344no—
575C2×D4—342no—
576C2×D4—341no—
577C2×D4—342no—
578C2×D4—684no—
579C2×D4—684no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—171no—
591C22×C4—171no—
592C22×C4—171no—
593C22×C4—172no—
594C22×C4—172no—
595C22×C4—344no—
596C22×C4—344no—
597C22×C4—344no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—684no—
604C22×C4—684no—
605C22×C4—1362no—
606C22×C4D4×D1712yes—
607C22×C4D4×D1711yescharacteristic
608C22×C4C23×D1712yes—
609C22×C4C23×D1711yescharacteristic
610SD16—348no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—172no—
614C2×C8—172no—
615C2×C8—342no—
616C2×C8—342no—
617C2×C8—348no—
618C2×C8#6325214yescomplemented
619C2×C8C23×D1712yes—
620C2×C8C23×D1712yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—174no—
628C4⋊C4—172no—
629C4⋊C4—172no—
630C4⋊C4—344no—
631C4⋊C4—344no—
632C4⋊C4—344no—
633C4⋊C4—344no—
634C4⋊C4—344no—
635C4⋊C4—344no—
636C4⋊C4—341no—
637C4⋊C4—341no—
638C4⋊C4—344no—
639C4⋊C4C23×D1712yes—
640C4⋊C4C23×D1712yes—
641C4⋊C4C23×D1712yes—
642C4⋊C4C23×D1712yes—
643C22⋊C4—174no—
644C22⋊C4—174no—
645C22⋊C4—344no—
646C22⋊C4—344no—
647C22⋊C4—344no—
648C22⋊C4—344no—
649C22⋊C4—344no—
650C42—172no—
651C42—172no—
652C42—344no—
653C23—22no—
654C23—22no—
655C23—174no—
656C23—172no—
657C23—342no—
658C23—342no—
659C23—342no—
660C23—682no—
661C23—682no—
662C23—682no—
663C23SD16×D1714yes—
664C23C2×D4×D1712yes—
665C23C2×D4×D1711yescharacteristic
666Q8—342no—
667Q8—342no—
668Q8—688no—
669Q8—682no—
670Q8—1364no—
671D4—1716no—
672D4—342no—
673D4—342no—
674D4—688no—
675D4—688no—
676D4—682no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—174no—
692C2×C4—172no—
693C2×C4—172no—
694C2×C4—172no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—344no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—688no—
704C2×C4—688no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4—682no—
708C2×C4—1364no—
709C2×C4C2×#6325212yes—
710C2×C4C2×D4×D1712yes—
711C2×C4C2×D4×D1711yescharacteristic
712C2×C4#1058769412yes—
713C2×C4C24×D1711yescharacteristic
714C8—22no—
715C8—342no—
716C8—342no—
717C8C2×#6325214yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—174no—
722C22—348no—
723C22—342no—
724C22—342no—
725C22—682no—
726C22—682no—
727C22—682no—
728C22—1364no—
729C22#1176346012yes—
730C22C2×SD16×D1714yes—
731C22C2×SD16×D1712yes—
732C22#1176361512yes—
733C22C22×D4×D1711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—174no—
740C4—342no—
741C4—342no—
742C4—682no—
743C4—682no—
744C4—682no—
745C4#1176346012yes—
746C4C22×#6325211yescharacteristic
747C4C2×#1058769411yescharacteristic
748C2—24no—
749C2—344no—
750C2—1362no—
751C2#1454113714yesdirect product factor
752C2C2×#1176346011yescharacteristic
753C2C22×SD16×D1711yescharacteristic
754C2C2×#1176361511yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#106C2
socleC23×C17C22×D4
prime radicalC2×#11763460C2
hypercenterC22×#106D17
hypocenterC17C2×#3335
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#11763514C2semidirect
3. #14541137C2direct (N × H)
4. C2×#11763206C2semidirect
5. C2×#11763129C2semidirect
6. C2×#11763127C2semidirect
7. C2×#11763141C2semidirect
8. C2×#11763139C2semidirect
9. C2×#11763093C2semidirect
10. C2×#11763098C2semidirect
11. C2×#11763039C2semidirect
12. C2×#11763038C2semidirect
13. C2×#11762896C2semidirect
14. C2×C8×C22⋊D17C2semidirect
15. C2×#106×D17C2semidirect
16. C22×C17×#106C2semidirect
21. #11763514C22semidirect
42. #11763206C22semidirect
43. #11763141C22semidirect
44. #11763139C22semidirect
45. #11763129C22semidirect
46. #11763127C22semidirect
47. #11763098C22semidirect
48. #11763093C22semidirect
49. #11763039C22semidirect
50. #11763038C22semidirect
51. #11762896C22semidirect
52. C8×C22⋊D17C22semidirect
58. #106×D17C22semidirect
76. C2×C17×#106C22semidirect
199. C2×C22⋊D17SD16semidirect
234. C2×C8×C17#41semidirect
309. C22⋊D17C2×SD16semidirect
338. C8×C17C2×#41semidirect
356. C22×#106D17semidirect
436. C2×#106C2×D17semidirect
448. C2×C17#3335semidirect
557. C17C2×#3335semidirect
618. C2×C8#63252semidirect
717. C8C2×#63252semidirect
751. C2#14541137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635142
C2×#117634602
#145411372
C2×#117632062
C2×#117631292
C2×#117631272
C2×#117631412
C2×#117631392
C2×#117630932
C2×#117630982
C2×#117630392
C2×#117630382
C2×#117628962
C2×C8×C22⋊D172
C2×#106×D172
C22×C17×#1062
C2×#333517