Finite Group Databasebeta

← C2×#14541248 #17912881

Subgroups — C2×#14541248 #17912881

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763463C211yesmaximal, characteristic, complemented
2#14541248C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763127C211yesmaximal, characteristic, complemented
5C2×#11763125C211yesmaximal, characteristic, complemented
6C2×#11763133C211yesmaximal, characteristic, complemented
7C2×#11763120C211yesmaximal, characteristic, complemented
8C2×#11763106C211yesmaximal, characteristic, complemented
9C2×#11763099C211yesmaximal, characteristic, complemented
10C2×#11763060C211yesmaximal, characteristic, complemented
11C2×#11763043C211yesmaximal, characteristic, complemented
12C2×#11762919C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C22×#10587479C211yesmaximal, characteristic, complemented
16C2×C17×#553C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×#63228C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20C23×#3622C2211yescharacteristic
21#11763463—24no—
22#11763463C2218yescomplemented
23C2×#10587555C2211yescharacteristic
24C2×#10587572—21no—
25C2×#10587572—21no—
26C2×#10587583—21no—
27C2×#10587616C2211yescharacteristic
28C2×#10587616C2211yescharacteristic
29C2×C4×D68C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763219C2218yescomplemented
33#11763133C2218yescomplemented
34#11763127C2218yescomplemented
35#11763125C2218yescomplemented
36#11763120C2218yescomplemented
37#11763106C2218yescomplemented
38#11763099C2218yescomplemented
39#11763060C2218yescomplemented
40#11763043C2218yescomplemented
41#11762919C2218yescomplemented
42#11762881C2218yescomplemented
43#11762852C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2218yescomplemented
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#553—24no—
65C17×#553C2218yescomplemented
66C2×C17×#126—21no—
67C2×C17×#125C2211yescharacteristic
68C2×C17×#123—21no—
69C2×C17×#121—21no—
70C2×C17×#121C2211yescharacteristic
71C2×C17×#121C2211yescharacteristic
72C2×C4×D4×C17—21no—
73C2×C4×D4×C17C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17D411yescharacteristic
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C22×C22⋊D17—21no—
86C22×C22⋊D17—21no—
87C23×Dic17—21no—
88C23×Dic17—21no—
89C2×#63254—28no—
90C2×#63254—48no—
91C22×D68C2311yescharacteristic
92C22×C4×D17—21no—
93C22×Dic34—21no—
94C17×#126—28no—
95C17×#125—22no—
96C17×#125C2314yes—
97C17×#123—28no—
98C17×#121—28no—
99C17×#121—22no—
100C17×#121—22no—
101C17×#121C2314yes—
102C17×#121C2314yes—
103C4×D4×C17—28no—
104C4×D4×C17—22no—
105C4×D4×C17D414yes—
106C4×D4×C17C2314yes—
107C4×D4×C17C2314yes—
108C17×#117—22no—
109C17×#117C2314yes—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17—22no—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17D411yescharacteristic
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2314yes—
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17—21no—
121C2×C22⋊C4×C17—21no—
122C2×C22⋊C4×C17—21no—
123C2×C22⋊C4×C17D411yescharacteristic
124C2×C22⋊C4×C17D411yescharacteristic
125C2×C42×C17—21no—
126C2×C42×C17C2311yescharacteristic
127C2×#63228—24no—
128C2×#63228C2314yes—
129#10587616—22no—
130#10587616—22no—
131#10587616C2314yes—
132#10587616C2314yes—
133C2×#63227—21no—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—22no—
138C2×C4⋊Dic17—21no—
139C2×C4⋊Dic17—21no—
140C2×C4⋊Dic17—21no—
141C2×C4⋊Dic17C2314yes—
142C2×C4⋊Dic17C2314yes—
143C2×C4⋊Dic17C2311yescharacteristic
144C2×C4⋊Dic17C2311yescharacteristic
145C2×C4⋊Dic17C2311yescharacteristic
146C2×#63223—24no—
147C2×#63223C2314yes—
148C22×#3622—24no—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2314yes—
153C22×#3622C2311yescharacteristic
154#10587583—28no—
155#10587572—28no—
156#10587572—28no—
157C4×D68—22no—
158C4×D68C2314yes—
159#10587555—22no—
160#10587555C2314yes—
161#10587503C2314yes—
162#10587503C2314yes—
163#10587503C2314yes—
164C22⋊#3622C2314yes—
165C22⋊#3622C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587480C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587479C2314yes—
173#10587479C2314yes—
174#10587479C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179#10587474C2314yes—
180C24×C17—21no—
181C24×C17C2×D411yescharacteristic
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C2×D4×C17—24no—
185C2×D4×C17—24no—
186C2×D4×C17—24no—
187C2×D4×C17—21no—
188C2×D4×C17—22no—
189C2×D4×C17—22no—
190C2×D4×C17—44no—
191C2×D4×C17—82no—
192C2×D4×C17C2×D414yes—
193C2×D4×C17C2412yes—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—22no—
197C22×C4×C17—22no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—24no—
202C22×C4×C17—24no—
203C22×C4×C17—82no—
204C22×C4×C17—82no—
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2412yes—
212C22×C4×C17C2412yes—
213C22×C4×C17C2411yescharacteristic
214C2×C22⋊D17—24no—
215C2×C22⋊D17—24no—
216C2×C22⋊D17—44no—
217C2×C22⋊D17—44no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—24no—
222C22×Dic17—24no—
223C22×Dic17—44no—
224C22×Dic17—44no—
225#63254—432no—
226C2×D68—22no—
227C2×D68—22no—
228C2×D68—21no—
229C2×D68C2412yes—
230C2×C4×D17—24no—
231C2×C4×D17—44no—
232C2×Dic34—24no—
233C2×Dic34—44no—
234C4⋊C4×C17—24no—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—24no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17C2×D414yes—
241C4⋊C4×C17C2412yes—
242C4⋊C4×C17C2412yes—
243C4⋊C4×C17C2412yes—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C22⋊C4×C17C2×D414yes—
249C22⋊C4×C17C2×D414yes—
250C42×C17—24no—
251C42×C17C2×D412yes—
252C42×C17C2412yes—
253#63228—28no—
254#63227—24no—
255#63227—24no—
256#63227—24no—
257C4⋊Dic17—21no—
258C4⋊Dic17—21no—
259C4⋊Dic17—24no—
260C4⋊Dic17—21no—
261C4⋊Dic17—24no—
262C4⋊Dic17—24no—
263C4⋊Dic17C2412yes—
264C4⋊Dic17C2412yes—
265C4⋊Dic17C2412yes—
266#63223—28no—
267C2×#3622—22no—
268C2×#3622—22no—
269C2×#3622—22no—
270C2×#3622—28no—
271C2×#3622#4114yescomplemented
272C2×#3622C2412yes—
273C2×#3622C2412yes—
274C2×#3622C2412yes—
275C2×#3622C2412yes—
276C2×#3345—171nomaximal, Sylow
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—42no—
284C23×C17—42no—
285C23×C17—42no—
286C23×C17AGL(1,ℤ/8)14yes—
287C23×C17C22×D412yes—
288C23×C17C22×D412yes—
289C23×C17C22×D411yescharacteristic
290C22×D17—22no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294D4×C17—28no—
295D4×C17—22no—
296D4×C17—22no—
297D4×C17—48no—
298D4×C17—42no—
299D4×C17—84no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—24no—
305C2×C4×C17—24no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—42no—
314C2×C4×C17—42no—
315C2×C4×C17—42no—
316C2×C4×C17—84no—
317C2×C4×C17—84no—
318C2×C4×C17C22×D412yes—
319C2×C4×C17C22×D412yes—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D412yes—
322C2×C4×C17C22×D411yescharacteristic
323C2×C4×C17C2×#4112yes—
324C2×C4×C172−1+412yes—
325C2×C4×C17C2511yescharacteristic
326C22⋊D17—48no—
327C22⋊D17—48no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—48no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—48no—
336D68—22no—
337D68—22no—
338D68—42no—
339C4×D17—48no—
340Dic34—48no—
341#3622—22no—
342#3622—22no—
343#3622—22no—
344#3622C2×#4114yescomplemented
345C2×#553D1711yescharacteristic, complemented
346C2×#547—171no—
347#3345—1716no—
348C2×#501—171no—
349C2×#481—171no—
350C2×#481—171no—
351C2×#482—171no—
352C2×#480—171no—
353C2×#478—171no—
354C2×#476—171no—
355C2×#469—171no—
356C2×#466—171no—
357C2×#442—171no—
358C2×#435—171no—
359C2×#428—171no—
360C22×#106—171no—
361C22×C17—28no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—22no—
367C22×C17—44no—
368C22×C17—42no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—84no—
372C22×C17#54712yes—
373C22×C17C2×AGL(1,ℤ/8)14yes—
374C22×C17C2×AGL(1,ℤ/8)12yes—
375C22×C17#57712yes—
376C22×C17C23×D411yescharacteristic
377C2×D17—42no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—84no—
381C4×C17—22no—
382C4×C17—22no—
383C4×C17—22no—
384C4×C17—22no—
385C4×C17—42no—
386C4×C17—42no—
387C4×C17—42no—
388C4×C17#54712yes—
389C4×C17C22×#4111yescharacteristic
390C4×C17C2×2−1+411yescharacteristic
391Dic17—42no—
392Dic17—42no—
393Dic17—42no—
394C22×#41—341no—
395C22×D8—171no—
396C22×M16—171no—
397C23×C8—171no—
398#553—24no—
399#553C2×D1718yescomplemented
400#547—178no—
401#547—344no—
402C2×C4⋊Q8—171no—
403C2×#126—21no—
404C2×#125C2×D1711yescharacteristic
405C2×#123—21no—
406C2×#123—341no—
407C2×#123—341no—
408C2×C22⋊Q8—341no—
409C2×#121—21no—
410C2×#121—171no—
411C2×#121—171no—
412C2×#121C2×D1711yescharacteristic
413C2×#121C2×D1711yescharacteristic
414C2×C4×D4—21no—
415C2×C4×D4—171no—
416C2×C4×D4C2×D1711yescharacteristic
417C2×C4×D4C2×D1711yescharacteristic
418C2×#117C2×D1711yescharacteristic
419C22×C4⋊C4—171no—
420C22×C4⋊C4—171no—
421C22×C4⋊C4C2×D1711yescharacteristic
422#501—178no—
423#482—178no—
424#481—178no—
425#481—178no—
426#480—178no—
427#478—178no—
428#476—178no—
429#469—178no—
430#466—178no—
431#442—178no—
432#435—178no—
433#428—178no—
434C2×#107—171no—
435C2×#107—171no—
436C2×#107—171no—
437C2×#106—171no—
438C2×#106—171no—
439C2×#106—171no—
440C2×#106—171no—
441C2×#106—178no—
442C2×#106—171no—
443C2×#106—171no—
444C2×C4⋊C8—171no—
445C2×#102—171no—
446C2×#102—171no—
447C2×#102—171no—
448C2×#102—171no—
449C2×#102—171no—
450C2×#102—171no—
451C2×C22⋊C8—171no—
452C2×C22⋊C8—171no—
453C2×#97—171no—
454C2×C17—24no—
455C2×C17—42no—
456C2×C17—82no—
457C2×C17#334514yescomplemented
458C2×C17C2×#54711yescharacteristic
459C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
460C2×C17C2×#57711yescharacteristic
461D17—82no—
462C2×#41—348no—
463C2×#41—688no—
464C22×Q8—341no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—171no—
468C22×D4—341no—
469C22×D4—341no—
470C22×D4C22⋊D1711yescharacteristic
471C22×D4C22×D1711yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—341no—
475C23×C4—341no—
476C23×C4—341no—
477C23×C4C22×D1711yescharacteristic
478C23×C4C22×D1711yescharacteristic
479C2×D8—174no—
480C2×D8—344no—
481C2×M16—174no—
482C2×M16—344no—
483C22×C8—171no—
484C22×C8—171no—
485C22×C8—174no—
486C22×C8—171no—
487C22×C8—171no—
488C22×C8—344no—
489C4⋊Q8—174no—
490C4⋊Q8—342no—
491#126—28no—
492#125—22no—
493#125C22×D1714yes—
494#123—28no—
495#123—348no—
496#123—348no—
497C22⋊Q8—348no—
498#121—28no—
499#121—22no—
500#121—22no—
501#121—174no—
502#121—174no—
503#121—342no—
504#121—342no—
505#121C22×D1714yes—
506#121C22×D1714yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—174no—
510C4×D4—342no—
511C4×D4C22⋊D1714yes—
512C4×D4C22×D1714yes—
513C4×D4C22×D1714yes—
514#117—22no—
515#117C22×D1714yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4—171no—
523C2×C4⋊C4—174no—
524C2×C4⋊C4—174no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—342no—
528C2×C4⋊C4—342no—
529C2×C4⋊C4—341no—
530C2×C4⋊C4C22⋊D1711yescharacteristic
531C2×C4⋊C4C22×D1711yescharacteristic
532C2×C4⋊C4C22×D1711yescharacteristic
533C2×C4⋊C4C22×D1714yes—
534C2×C4⋊C4C22×D1711yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—341no—
540C2×C22⋊C4—341no—
541C2×C22⋊C4—341no—
542C2×C22⋊C4C22⋊D1711yescharacteristic
543C2×C22⋊C4C22⋊D1711yescharacteristic
544C2×C42—21no—
545C2×C42C22×D1711yescharacteristic
546#107—174no—
547#107—174no—
548#107—174no—
549#106—174no—
550#106—174no—
551#106—174no—
552#106—174no—
553#106—174no—
554#106—174no—
555C4⋊C8—174no—
556#102—174no—
557#102—174no—
558#102—174no—
559#102—174no—
560#102—174no—
561#102—174no—
562C22⋊C8—174no—
563C22⋊C8—174no—
564#97—174no—
565C17C2×#334511yescharacteristic, complemented, Sylow
566C24—21no—
567C24—341no—
568C24C2×C22⋊D1711yescharacteristic
569C24C2×C22⋊D1711yescharacteristic
570#41—6832no—
571C2×Q8—344no—
572C2×Q8—684no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—172no—
582C2×D4—344no—
583C2×D4—344no—
584C2×D4—342no—
585C2×D4—342no—
586C2×D4—341no—
587C2×D4—684no—
588C2×D4—684no—
589C2×D4C2×C22⋊D1714yes—
590C2×D4C23×D1712yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—344no—
603C22×C4—344no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—341no—
607C22×C4—344no—
608C22×C4—684no—
609C22×C4—684no—
610C22×C4—684no—
611C22×C4C2×C22⋊D1712yes—
612C22×C4C2×C22⋊D1712yes—
613C22×C4C2×C22⋊D1711yescharacteristic
614C22×C4C2×C22⋊D1711yescharacteristic
615C22×C4C2×C22⋊D1711yescharacteristic
616C22×C4C2×C22⋊D1711yescharacteristic
617C22×C4C23×D1712yes—
618C22×C4C23×D1712yes—
619C22×C4C23×D1711yescharacteristic
620D8—348no—
621M16—348no—
622C2×C8—174no—
623C2×C8—172no—
624C2×C8—172no—
625C2×C8—172no—
626C2×C8—172no—
627C2×C8—348no—
628C2×C8—342no—
629C2×C8—342no—
630C2×C8—342no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—172no—
638C4⋊C4—172no—
639C4⋊C4—172no—
640C4⋊C4—341no—
641C4⋊C4—341no—
642C4⋊C4—341no—
643C4⋊C4—344no—
644C4⋊C4—344no—
645C4⋊C4—344no—
646C4⋊C4C2×C22⋊D1714yes—
647C4⋊C4C23×D1712yes—
648C4⋊C4C23×D1712yes—
649C4⋊C4C23×D1712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—344no—
655C22⋊C4—344no—
656C22⋊C4—344no—
657C22⋊C4C2×C22⋊D1714yes—
658C22⋊C4C2×C22⋊D1714yes—
659C42—24no—
660C42C2×C22⋊D1712yes—
661C42C23×D1712yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—342no—
672C23—682no—
673C23—682no—
674C23—682no—
675C23#1058763514yes—
676C23C22×C22⋊D1712yes—
677C23C22×C22⋊D1712yes—
678C23C22×C22⋊D1711yescharacteristic
679Q8—688no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—342no—
687D4—342no—
688D4—688no—
689D4—688no—
690D4—682no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—688no—
713C2×C4—688no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—688no—
718C2×C4#41×D1712yes—
719C2×C4#1058769712yes—
720C2×C4C22×C22⋊D1712yes—
721C2×C4C22×C22⋊D1712yes—
722C2×C4C22×C22⋊D1712yes—
723C2×C4C22×C22⋊D1712yes—
724C2×C4C22×C22⋊D1711yescharacteristic
725C2×C4C24×D1711yescharacteristic
726C8—174no—
727C8—342no—
728C8—342no—
729C8—342no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—682no—
742C22—682no—
743C22—682no—
744C22—1364no—
745C22#1176345812yes—
746C22C2×#1058763514yes—
747C22C2×#1058763512yes—
748C22#1176362012yes—
749C22C23×C22⋊D1711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—682no—
758C4—682no—
759C4—682no—
760C4#1176345812yes—
761C4C2×#41×D1711yescharacteristic
762C4C2×#1058769711yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—1362no—
767C2#1454124814yesdirect product factor
768C2C2×#1176345811yescharacteristic
769C2C22×#1058763511yescharacteristic
770C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#553C2
socleC23×C17C22×D4
hypercenterC2×#553D17
hypocenterC17C2×#3345
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11763463C2semidirect
2. #14541248C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763127C2semidirect
5. C2×#11763125C2semidirect
6. C2×#11763133C2semidirect
7. C2×#11763120C2semidirect
8. C2×#11763106C2semidirect
9. C2×#11763099C2semidirect
10. C2×#11763060C2semidirect
11. C2×#11763043C2semidirect
12. C2×#11762919C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762852C2semidirect
15. C22×#10587479C2semidirect
16. C2×C17×#553C2semidirect
22. #11763463C22semidirect
32. #11763219C22semidirect
33. #11763133C22semidirect
34. #11763127C22semidirect
35. #11763125C22semidirect
36. #11763120C22semidirect
37. #11763106C22semidirect
38. #11763099C22semidirect
39. #11763060C22semidirect
40. #11763043C22semidirect
41. #11762919C22semidirect
42. #11762881C22semidirect
43. #11762852C22semidirect
53. C2×#10587479C22semidirect
65. C17×#553C22semidirect
271. C2×#3622#41semidirect
344. #3622C2×#41semidirect
345. C2×#553D17semidirect
399. #553C2×D17semidirect
457. C2×C17#3345semidirect
565. C17C2×#3345semidirect
767. C2#14541248direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634632
#145412482
C2×#117632192
C2×#117631272
C2×#117631252
C2×#117631332
C2×#117631202
C2×#117631062
C2×#117630992
C2×#117630602
C2×#117630432
C2×#117629192
C2×#117628812
C2×#117628522
C22×#105874792
C2×C17×#5532
C2×#334517