Finite Group Databasebeta

← C2×#14539063 #17902657

Subgroups — C2×#14539063 #17902657

Order 4352.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic, complemented
2C2×#11763289C211yesmaximal, characteristic, complemented
3#14539063C2116yesmaximal, direct product factor
4C2×#11763128C211yesmaximal, characteristic, complemented
5C2×#11763140C211yesmaximal, characteristic, complemented
6C2×#11763095C211yesmaximal, characteristic, complemented
7C2×#11763100C211yesmaximal, characteristic, complemented
8C2×#11763032C211yesmaximal, characteristic, complemented
9C2×#11763025C211yesmaximal, characteristic, complemented
10C2×#11762973C211yesmaximal, characteristic, complemented
11C2×#11762956C211yesmaximal, characteristic
12C2×#11762922C211yesmaximal, characteristic, complemented
13C2×#11762917C211yesmaximal, characteristic, complemented
14C2×C4×#63219C211yesmaximal, characteristic, complemented
15C2×C4×#63219C211yesmaximal, characteristic, complemented
16C2×C17×#433C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C22×Dic68C2211yescharacteristic
19C22×#63219C2211yescharacteristic
20C22×#63219C2211yescharacteristic
21C22×D136C2211yescharacteristic
22#11763430—24no—
23#11763430C2218yescomplemented
24C2×#10587555C2211yescharacteristic
25C2×#10587584—21no—
26C2×#10587561C2211yescharacteristic
27C2×#10587571—21no—
28C2×#10587569—21no—
29C2×#10587610C2211yescharacteristic
30C2×#10587582—21no—
31C2×#10587616C2211yescharacteristic
32#11763289—24no—
33#11763289C2218yescomplemented
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×Dic34C2211yescharacteristic
37C2×C4×D68C2211yescharacteristic
38C2×C4×D68C2211yescharacteristic
39C2×C4×D68C2211yescharacteristic
40C2×#10587567—21no—
41C2×#10587567—21no—
42C2×#10587578—21no—
43C22×C4⋊Dic17C2211yescharacteristic
44C2×C4⋊C4×D17—21no—
45#11763140C2218yescomplemented
46#11763128C2218yescomplemented
47#11763100C2218yescomplemented
48#11763095C2218yescomplemented
49#11763032C2218yescomplemented
50#11763025C2218yescomplemented
51#11762973C2218yescomplemented
52#11762956C2218yes—
53#11762922C2218yescomplemented
54#11762917C2218yescomplemented
55C4×#63219C2218yescomplemented
56C4×#63219C2218yescomplemented
57C2×#10587488C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587487C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587492C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C2×C17×#117C2211yescharacteristic
70C17×#433C2218yescomplemented
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×#97C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C22×C22⋊D17—21no—
79C22×C22⋊D17—21no—
80C23×Dic17—21no—
81C2×#63252—22no—
82C2×#63252—24no—
83C2×#63252—24no—
84C2×#63252C2314yes—
85C22×D68C2311yescharacteristic
86C22×D68C2311yescharacteristic
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C22×C4×D17—21no—
90C22×C4×D17—21no—
91C22×Dic34—21no—
92C22×Dic34C2311yescharacteristic
93C22×Dic34C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C22×C8×C17C2311yescharacteristic
98C17×#117D414yes—
99C17×#117C2314yes—
100C2×C4⋊C4×C17D411yescharacteristic
101C2×C4⋊C4×C17D411yescharacteristic
102C2×C22⋊C4×C17D411yescharacteristic
103C2×C22⋊C4×C17D411yescharacteristic
104C2×C42×C17C2311yescharacteristic
105C2×C42×C17C2311yescharacteristic
106C2×C22⋊Dic17—21no—
107#10587616—22no—
108#10587616C2314yes—
109C2×#63227—21no—
110C2×#63227—21no—
111C2×#63227—21no—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×C4⋊Dic17—21no—
116C2×C4⋊Dic17—22no—
117C2×C4⋊Dic17—21no—
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2314yes—
121C2×C4⋊Dic17C2311yescharacteristic
122C2×C4⋊Dic17C2311yescharacteristic
123#10587610—22no—
124#10587610C2314yes—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×C4×Dic17—21no—
130C2×C4×Dic17—21no—
131C2×C4×Dic17—21no—
132C2×Dic68—24no—
133C2×Dic68C2314yes—
134C2×D136—24no—
135C2×D136C2314yes—
136C2×#63219—24no—
137C2×#63219—24no—
138C2×#63219C2314yes—
139C2×#63219C2314yes—
140#10587584—28no—
141#10587582—28no—
142#10587578—28no—
143C4⋊C4×D17—28no—
144#10587571—28no—
145#10587569—28no—
146#10587567—28no—
147#10587567—28no—
148#10587561—22no—
149#10587561C2314yes—
150C4×D68—22no—
151C4×D68—22no—
152C4×D68—22no—
153C4×D68C2314yes—
154C4×D68C2314yes—
155C4×D68C2314yes—
156#10587555—22no—
157#10587555C2314yes—
158C4×Dic34—22no—
159C4×Dic34—22no—
160C4×Dic34—22no—
161C4×Dic34C2314yes—
162C4×Dic34C2314yes—
163C4×Dic34C2314yes—
164C17×C4⋊C8C2314yes—
165C17×C4⋊C8C2314yes—
166C17×C22⋊C8C2314yes—
167C17×C22⋊C8C2314yes—
168C17×#97C2314yes—
169C4×C8×C17C2314yes—
170#10587492C2314yes—
171#10587492C2314yes—
172#10587492C2314yes—
173#10587492C2314yes—
174#10587488C2314yes—
175#10587488C2314yes—
176#10587488C2314yes—
177#10587488C2314yes—
178#10587487C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587487C2314yes—
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C23×D17—21no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2411yescharacteristic
195C2×C22⋊D17—28no—
196C2×C22⋊D17—24no—
197C2×C22⋊D17—24no—
198C2×C22⋊D17—82no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—24no—
206C22×Dic17—82no—
207#63252—216no—
208#63252—28no—
209#63252—28no—
210C2×D68—21no—
211C2×D68—22no—
212C2×D68—22no—
213C2×D68—22no—
214C2×D68—21no—
215C2×D68#4114yes—
216C2×D68C2412yes—
217C2×D68C2412yes—
218C2×C4×D17—28no—
219C2×C4×D17—24no—
220C2×C4×D17—24no—
221C2×C4×D17—24no—
222C2×C4×D17—24no—
223C2×C4×D17—82no—
224C2×C4×D17—82no—
225C2×C4×D17—82no—
226C2×Dic34—21no—
227C2×Dic34—22no—
228C2×Dic34—22no—
229C2×Dic34—22no—
230C2×Dic34—21no—
231C2×Dic34—24no—
232C2×Dic34—82no—
233C2×Dic34#4114yes—
234C2×Dic34C2412yes—
235C2×Dic34C2412yes—
236C2×C8×C17—22no—
237C2×C8×C17—22no—
238C2×C8×C17—22no—
239C2×C8×C17—22no—
240C2×C8×C17C2412yes—
241C2×C8×C17C2412yes—
242C2×C8×C17C2412yes—
243C2×C8×C17C2412yes—
244C4⋊C4×C17C2×D414yes—
245C4⋊C4×C17C2×D414yes—
246C22⋊C4×C17C2×D414yes—
247C22⋊C4×C17C2×D414yes—
248C42×C17C2×D412yes—
249C42×C17C2×D412yes—
250C42×C17C2412yes—
251C42×C17C2412yes—
252C22⋊Dic17—24no—
253#63227—24no—
254#63227—24no—
255#63227—24no—
256#63227—24no—
257#63227—24no—
258#63227—24no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—21no—
262C4⋊Dic17—21no—
263C4⋊Dic17—24no—
264C4⋊Dic17—24no—
265C4⋊Dic17C2412yes—
266C4⋊Dic17C2412yes—
267C4⋊Dic17C2412yes—
268C4⋊Dic17C2412yes—
269#63225—24no—
270#63225—24no—
271#63225—24no—
272#63225—24no—
273C4×Dic17—24no—
274C4×Dic17—24no—
275C4×Dic17—24no—
276Dic68—28no—
277D136—28no—
278#63219—28no—
279#63219—28no—
280C2×#3125—171nomaximal, Sylow
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17C22×D412yes—
285C23×C17C22×D411yescharacteristic
286C22×D17—24no—
287C22×D17—22no—
288C22×D17—22no—
289C22×D17—42no—
290C22×D17—42no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—24no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17C22×D412yes—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C2×#4112yes—
309C2×C4×C17C2×#4112yes—
310C2×C4×C17C2511yescharacteristic
311C22⋊D17—216no—
312C22⋊D17—84no—
313C2×Dic17—24no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—84no—
326D68—24no—
327D68—22no—
328D68—22no—
329D68—22no—
330D68—42no—
331D68C2×#4114yes—
332C4×D17—216no—
333C4×D17—84no—
334C4×D17—84no—
335C4×D17—84no—
336Dic34—24no—
337Dic34—22no—
338Dic34—22no—
339Dic34—22no—
340Dic34—42no—
341Dic34—84no—
342Dic34C2×#4114yes—
343C8×C17—22no—
344C8×C17—22no—
345C8×C17—22no—
346C8×C17—22no—
347C2×#542—171no—
348C2×#520—171no—
349#3125—1716no—
350C2×#481—171no—
351C2×#483—171no—
352C2×#475—171no—
353C2×#476—171no—
354C2×#464—171no—
355C2×#463—171no—
356C2×#452—171no—
357C2×#449—171no—
358C2×#442—171no—
359C2×#441—171no—
360C2×C4×SD16—171no—
361C2×C4×SD16—171no—
362C2×#433D1711yescharacteristic, complemented
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—44no—
367C22×C17#52512yes—
368C22×C17#57712yes—
369C22×C17#57712yes—
370C22×C17C23×D411yescharacteristic
371C2×D17—24no—
372C2×D17—48no—
373C2×D17—42no—
374C2×D17—42no—
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—42no—
378C2×D17—84no—
379C4×C17—22no—
380C4×C17—22no—
381C4×C17—22no—
382C4×C17—22no—
383C4×C17—22no—
384C4×C17#52512yes—
385C4×C17C22×#4111yescharacteristic
386C4×C17C22×#4111yescharacteristic
387Dic17—24no—
388Dic17—42no—
389Dic17—42no—
390Dic17—42no—
391Dic17—42no—
392Dic17—42no—
393C22×#41—171no—
394C22×Q16—171no—
395C22×SD16—171no—
396C22×SD16—171no—
397C22×D8—171no—
398#542—178no—
399#542—344no—
400C2×C4⋊Q8—171no—
401C2×#126—341no—
402C2×#124—171no—
403C2×#124—341no—
404C2×#123—341no—
405C2×C22⋊Q8—171no—
406C2×C22⋊Q8—341no—
407C2×#121—171no—
408#520—178no—
409#520—344no—
410C2×C4×Q8—171no—
411C2×C4×Q8—171no—
412C2×C4×Q8—171no—
413C2×C4×D4—171no—
414C2×C4×D4—171no—
415C2×C4×D4—171no—
416C2×C4×D4—341no—
417C2×C4×D4—341no—
418C2×#117—341no—
419C2×#117C2×D1711yescharacteristic
420C22×C4⋊C4—171no—
421C22×C4⋊C4—341no—
422#483—178no—
423#481—178no—
424#476—178no—
425#475—178no—
426#464—178no—
427#463—178no—
428#452—178no—
429#449—178no—
430#442—178no—
431#441—178no—
432C4×SD16—178no—
433C4×SD16—178no—
434#433C2×D1718yescomplemented
435C2×#106—171no—
436C2×#106—171no—
437C2×#106—171no—
438C2×#106—171no—
439C2×C4⋊C8C2×D1711yescharacteristic
440C2×C4⋊C8C2×D1711yescharacteristic
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#102—171no—
446C2×#102—171no—
447C2×#102—171no—
448C2×#102—171no—
449C2×C22⋊C8C2×D1711yescharacteristic
450C2×C22⋊C8C2×D1711yescharacteristic
451C2×#97C2×D1711yescharacteristic
452C2×C4×C8C2×D1711yescharacteristic
453C2×C17—42no—
454C2×C17#312514yescomplemented
455C2×C17C2×#52511yescharacteristic
456C2×C17C2×#57711yescharacteristic
457C2×C17C2×#57711yescharacteristic
458D17—44no—
459D17—82no—
460C2×#41—174no—
461C2×#41—344no—
462C2×#41—344no—
463C2×#41—342no—
464C22×Q8—171no—
465C22×Q8—171no—
466C22×Q8—341no—
467C22×D4—171no—
468C22×D4—171no—
469C22×D4—341no—
470C22×D4—341no—
471C23×C4—341no—
472C23×C4—341no—
473C23×C4—341no—
474C23×C4—341no—
475C23×C4—341no—
476C23×C4C22×D1711yescharacteristic
477C2×Q16—174no—
478C2×Q16—344no—
479C2×SD16—174no—
480C2×SD16—174no—
481C2×SD16—344no—
482C2×SD16—344no—
483C2×D8—174no—
484C2×D8—344no—
485C22×C8C22×D1711yescharacteristic
486C22×C8C22×D1711yescharacteristic
487C22×C8C22×D1711yescharacteristic
488C22×C8C22×D1711yescharacteristic
489C4⋊Q8—174no—
490C4⋊Q8—342no—
491#126—348no—
492#124—174no—
493#124—348no—
494#124—342no—
495#123—348no—
496C22⋊Q8—174no—
497C22⋊Q8—342no—
498C22⋊Q8—348no—
499#121—174no—
500#121—342no—
501C4×Q8—174no—
502C4×Q8—174no—
503C4×Q8—174no—
504C4×Q8—342no—
505C4×Q8—342no—
506C4×Q8—342no—
507C4×D4—174no—
508C4×D4—174no—
509C4×D4—174no—
510C4×D4—348no—
511C4×D4—348no—
512C4×D4—342no—
513C4×D4—342no—
514C4×D4—342no—
515#117—348no—
516#117D6814yes—
517#117C22×D1714yes—
518C2×C4⋊C4—171no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—174no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4—171no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—342no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C4⋊C4—341no—
529C2×C4⋊C4—341no—
530C2×C4⋊C4—348no—
531C2×C4⋊C4D6811yescharacteristic
532C2×C4⋊C4D6811yescharacteristic
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C22⋊C4—341no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4—341no—
539C2×C22⋊C4—341no—
540C2×C22⋊C4D6811yescharacteristic
541C2×C22⋊C4D6811yescharacteristic
542C2×C42—341no—
543C2×C42—341no—
544C2×C42—341no—
545C2×C42C22×D1711yescharacteristic
546C2×C42C22×D1711yescharacteristic
547#106—174no—
548#106—174no—
549#106—174no—
550#106—174no—
551C4⋊C8C22×D1714yes—
552C4⋊C8C22×D1714yes—
553#103—174no—
554#103—174no—
555#103—174no—
556#103—174no—
557#102—174no—
558#102—174no—
559#102—174no—
560#102—174no—
561C22⋊C8C22×D1714yes—
562C22⋊C8C22×D1714yes—
563#97C22×D1714yes—
564C4×C8C22×D1714yes—
565C17C2×#312511yescharacteristic, complemented, Sylow
566C24—341no—
567C24—341no—
568C24C2×D6811yescharacteristic
569#41—348no—
570#41—348no—
571#41—3416no—
572C2×Q8—174no—
573C2×Q8—172no—
574C2×Q8—172no—
575C2×Q8—341no—
576C2×Q8—341no—
577C2×Q8—344no—
578C2×Q8—342no—
579C2×Q8—342no—
580C2×Q8—342no—
581C2×Q8—1362no—
582C2×D4—174no—
583C2×D4—172no—
584C2×D4—172no—
585C2×D4—348no—
586C2×D4—344no—
587C2×D4—344no—
588C2×D4—341no—
589C2×D4—341no—
590C2×D4—342no—
591C2×D4—342no—
592C2×D4—342no—
593C2×D4—1362no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—348no—
597C22×C4—341no—
598C22×C4—344no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—344no—
605C22×C4—344no—
606C22×C4—344no—
607C22×C4—344no—
608C22×C4—1362no—
609C22×C4—1362no—
610C22×C4—1362no—
611C22×C4—1362no—
612C22×C4C2×D6812yes—
613C22×C4C2×D6811yescharacteristic
614C22×C4C2×D6811yescharacteristic
615C22×C4C2×D6811yescharacteristic
616C22×C4C2×D6811yescharacteristic
617C22×C4C2×D6811yescharacteristic
618C22×C4C23×D1712yes—
619C22×C4C23×D1711yescharacteristic
620Q16—348no—
621SD16—348no—
622SD16—348no—
623D8—348no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D1712yes—
629C2×C8C23×D1712yes—
630C2×C8C23×D1712yes—
631C2×C8C23×D1712yes—
632C4⋊C4—172no—
633C4⋊C4—172no—
634C4⋊C4—172no—
635C4⋊C4—172no—
636C4⋊C4—344no—
637C4⋊C4—341no—
638C4⋊C4—341no—
639C4⋊C4—341no—
640C4⋊C4—341no—
641C4⋊C4—344no—
642C4⋊C4—344no—
643C4⋊C4—344no—
644C4⋊C4—344no—
645C4⋊C4—344no—
646C4⋊C4C2×D6814yes—
647C4⋊C4C2×D6814yes—
648C22⋊C4—344no—
649C22⋊C4—344no—
650C22⋊C4—344no—
651C22⋊C4—344no—
652C22⋊C4—344no—
653C22⋊C4—344no—
654C22⋊C4—344no—
655C22⋊C4C2×D6814yes—
656C22⋊C4C2×D6814yes—
657C42—344no—
658C42—344no—
659C42—344no—
660C42C2×D6812yes—
661C42C2×D6812yes—
662C42C23×D1712yes—
663C42C23×D1712yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—344no—
668C23—342no—
669C23—342no—
670C23—682no—
671C23—682no—
672C23—682no—
673C23—682no—
674C23—682no—
675C23C22×D6812yes—
676C23C22×D6811yescharacteristic
677Q8—174no—
678Q8—344no—
679Q8—342no—
680Q8—342no—
681Q8—342no—
682Q8—682no—
683Q8—1364no—
684D4—174no—
685D4—3416no—
686D4—344no—
687D4—342no—
688D4—342no—
689D4—342no—
690D4—682no—
691D4—1364no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—3416no—
701C2×C4—344no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—682no—
709C2×C4—682no—
710C2×C4—682no—
711C2×C4—682no—
712C2×C4—682no—
713C2×C4—1364no—
714C2×C4—1364no—
715C2×C4—1364no—
716C2×C4—1364no—
717C2×C4C22×D6812yes—
718C2×C4C22×D6812yes—
719C2×C4C22×D6812yes—
720C2×C4C22×D6812yes—
721C2×C4C22×D6812yes—
722C2×C4C22×D6811yescharacteristic
723C2×C4#41×D1712yes—
724C2×C4#41×D1712yes—
725C2×C4C24×D1711yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—344no—
735C22—688no—
736C22—682no—
737C22—682no—
738C22—682no—
739C22—682no—
740C22—682no—
741C22—1364no—
742C22#1176332112yes—
743C22#1176362112yes—
744C22#1176362112yes—
745C22C23×D6811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—344no—
752C4—682no—
753C4—682no—
754C4—682no—
755C4—682no—
756C4—682no—
757C4#1176332112yes—
758C4C2×#41×D1711yescharacteristic
759C4C2×#41×D1711yescharacteristic
760C2—42no—
761C2—684no—
762C2—1362no—
763C2#1453906314yesdirect product factor
764C2C2×#1176332111yescharacteristic
765C2C2×#1176362111yescharacteristic
766C2C2×#1176362111yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC2×#11762956C2
hypercenterC2×#433D17
hypocenterC17C2×#3125
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#11763430C2semidirect
2. C2×#11763289C2semidirect
3. #14539063C2direct (N × H)
4. C2×#11763128C2semidirect
5. C2×#11763140C2semidirect
6. C2×#11763095C2semidirect
7. C2×#11763100C2semidirect
8. C2×#11763032C2semidirect
9. C2×#11763025C2semidirect
10. C2×#11762973C2semidirect
12. C2×#11762922C2semidirect
13. C2×#11762917C2semidirect
14. C2×C4×#63219C2semidirect
15. C2×C4×#63219C2semidirect
16. C2×C17×#433C2semidirect
23. #11763430C22semidirect
33. #11763289C22semidirect
45. #11763140C22semidirect
46. #11763128C22semidirect
47. #11763100C22semidirect
48. #11763095C22semidirect
49. #11763032C22semidirect
50. #11763025C22semidirect
51. #11762973C22semidirect
53. #11762922C22semidirect
54. #11762917C22semidirect
55. C4×#63219C22semidirect
56. C4×#63219C22semidirect
70. C17×#433C22semidirect
362. C2×#433D17semidirect
434. #433C2×D17semidirect
454. C2×C17#3125semidirect
565. C17C2×#3125semidirect
763. C2#14539063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
C2×#117632892
#145390632
C2×#117631282
C2×#117631402
C2×#117630952
C2×#117631002
C2×#117630322
C2×#117630252
C2×#117629732
C2×#117629562
C2×#117629222
C2×#117629172
C2×C4×#632192
C2×C17×#4332
C2×#312517