Finite Group Databasebeta

← C2×#14541384 #17913046

Subgroups — C2×#14541384 #17913046

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763505C211yesmaximal, characteristic, complemented
2#14541384C2116yesmaximal, direct product factor
3C2×#11763208C211yesmaximal, characteristic, complemented
4C2×#11763133C211yesmaximal, characteristic, complemented
5C2×#11763130C211yesmaximal, characteristic, complemented
6C2×#11763122C211yesmaximal, characteristic, complemented
7C2×#11763120C211yesmaximal, characteristic, complemented
8C2×#11763109C211yesmaximal, characteristic, complemented
9C2×#11763106C211yesmaximal, characteristic, complemented
10C2×#11763060C211yesmaximal, characteristic, complemented
11C2×#11763060C211yesmaximal, characteristic, complemented
12C2×C4×#63228C211yesmaximal, characteristic, complemented
13C2×#11762887C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C2×#11762849C211yesmaximal, characteristic, complemented
16C2×C17×#553C211yesmaximal, characteristic, complemented
17C22×#63228C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20#11763505—24no—
21#11763505C2218yescomplemented
22C2×#10587584—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587569—21no—
25C2×#10587616C2211yescharacteristic
26C2×#10587616C2211yescharacteristic
27C2×#10587625—21no—
28C2×C4×D68C2211yescharacteristic
29C2×#10587567—21no—
30C2×#10587612C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763208C2218yescomplemented
33#11763133C2218yescomplemented
34#11763130C2218yescomplemented
35#11763122C2218yescomplemented
36#11763120C2218yescomplemented
37#11763109C2218yescomplemented
38#11763106C2218yescomplemented
39#11763060C2218yescomplemented
40#11763060C2218yescomplemented
41C4×#63228C2218yescomplemented
42#11762887C2218yescomplemented
43#11762852C2218yescomplemented
44#11762849C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587478C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
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—
88C22×D68C2311yescharacteristic
89C22×C4×D17—21no—
90C17×#126—28no—
91C17×#125—22no—
92C17×#125C2314yes—
93C17×#123—28no—
94C17×#121—28no—
95C17×#121—22no—
96C17×#121—22no—
97C17×#121C2314yes—
98C17×#121C2314yes—
99C4×D4×C17—28no—
100C4×D4×C17—22no—
101C4×D4×C17D414yes—
102C4×D4×C17C2314yes—
103C4×D4×C17C2314yes—
104C17×#117—22no—
105C17×#117C2314yes—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—22no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C4⋊C4×C17C2314yes—
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124#10587625—28no—
125C2×#63228—24no—
126C2×#63228C2314yes—
127#10587616—22no—
128#10587616—22no—
129#10587616C2314yes—
130#10587616C2314yes—
131C2×#63227—21no—
132C2×#63227—21no—
133C2×#63227—21no—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142C2×#63225—21no—
143C2×#63225—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223—24no—
147C2×#63223C2314yes—
148C2×#63223C2314yes—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153#10587584—28no—
154#10587569—28no—
155#10587567—28no—
156C4×D68—22no—
157C4×D68C2314yes—
158#10587556—22no—
159#10587556C2314yes—
160#10587503C2314yes—
161#10587503C2314yes—
162#10587503C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587480C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587478C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178C4×#3622C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C24×C17C2×D411yescharacteristic
182C23×D17—21no—
183C2×D4×C17—24no—
184C2×D4×C17—24no—
185C2×D4×C17—21no—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—42no—
189C2×D4×C17—44no—
190C2×D4×C17—82no—
191C2×D4×C17C2×D414yes—
192C2×D4×C17C2412yes—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—22no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—24no—
201C22×C4×C17—24no—
202C22×C4×C17—82no—
203C22×C4×C17—82no—
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×D412yes—
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2412yes—
211C22×C4×C17C2412yes—
212C22×C4×C17C2411yescharacteristic
213C2×C22⋊D17—24no—
214C2×C22⋊D17—24no—
215C2×C22⋊D17—44no—
216C2×C22⋊D17—82no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—24no—
221C22×Dic17—82no—
222C2×D68—22no—
223C2×D68—22no—
224C2×D68—21no—
225C2×D68C2412yes—
226C2×C4×D17—24no—
227C2×C4×D17—82no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17C2×D414yes—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊C4×C17—24no—
242C22⋊C4×C17C2×D414yes—
243C22⋊C4×C17C2×D414yes—
244C42×C17—24no—
245C42×C17C2×D412yes—
246C42×C17C2412yes—
247C22⋊Dic17—24no—
248#63228—28no—
249#63227—24no—
250#63227—24no—
251#63227—24no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—21no—
255C4⋊Dic17—24no—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259#63225—24no—
260#63225—24no—
261C4×Dic17—24no—
262#63223—28no—
263#63223—28no—
264C2×#3622—22no—
265C2×#3622—22no—
266C2×#3622—22no—
267C2×#3622#4114yes—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272C2×#3355—171nomaximal, Sylow
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—42no—
281C23×C17—42no—
282C23×C17—42no—
283C23×C17C22×D412yes—
284C23×C17C22×D412yes—
285C23×C17C22×D411yescharacteristic
286C22×D17—22no—
287C22×D17—42no—
288C22×D17—42no—
289C22×D17—42no—
290D4×C17—22no—
291D4×C17—22no—
292D4×C17—44no—
293D4×C17—48no—
294D4×C17—42no—
295D4×C17—84no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—84no—
313C2×C4×C17—84no—
314C2×C4×C17C22×D412yes—
315C2×C4×C17C22×D412yes—
316C2×C4×C17C22×D412yes—
317C2×C4×C17C22×D412yes—
318C2×C4×C17C22×D411yescharacteristic
319C2×C4×C17C2×#4112yes—
320C2×C4×C172−1+412yes—
321C2×C4×C17C2511yescharacteristic
322C22⋊D17—48no—
323C22⋊D17—84no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—84no—
331D68—22no—
332D68—22no—
333D68—42no—
334C4×D17—84no—
335#3622—22no—
336#3622—22no—
337#3622—22no—
338#3622C2×#4114yes—
339C2×#553—171no—
340C2×#553D1711yescharacteristic, complemented
341#3355—1716no—
342C2×#499—171no—
343C2×#482—171no—
344C2×#482—171no—
345C2×#480—171no—
346C2×#480—171no—
347C2×#478—171no—
348C2×#478—171no—
349C2×#469—171no—
350C2×#469—171no—
351C2×C4×D8—171no—
352C2×#436—171no—
353C2×#428—171no—
354C2×#428—171no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—44no—
362C22×C17—44no—
363C22×C17—42no—
364C22×C17—42no—
365C22×C17—42no—
366C22×C17—84no—
367C22×C17#54712yes—
368C22×C17#57512yes—
369C22×C17#57612yes—
370C22×C17C23×D411yescharacteristic
371C2×D17—42no—
372C2×D17—42no—
373C2×D17—42no—
374C2×D17—84no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17—42no—
380C4×C17—42no—
381C4×C17—42no—
382C4×C17#54712yes—
383C4×C17C22×#4111yescharacteristic
384C4×C17C2×2−1+411yescharacteristic
385Dic17—42no—
386Dic17—42no—
387Dic17—42no—
388C22×D8—171no—
389C22×M16—171no—
390C22×M16—171no—
391#553—24no—
392#553—178no—
393#553—344no—
394#553C2×D1718yescomplemented
395C2×#126—21no—
396C2×#126—341no—
397C2×#125—171no—
398C2×#125C2×D1711yescharacteristic
399C2×#123—21no—
400C2×#123—341no—
401C2×#121—21no—
402C2×#121—171no—
403C2×#121—171no—
404C2×#121—341no—
405C2×#121C2×D1711yescharacteristic
406C2×#121C2×D1711yescharacteristic
407C2×C4×D4—21no—
408C2×C4×D4—171no—
409C2×C4×D4—341no—
410C2×C4×D4C2×D1711yescharacteristic
411C2×C4×D4C2×D1711yescharacteristic
412C2×#117—171no—
413C2×#117C2×D1711yescharacteristic
414C22×C4⋊C4—171no—
415C22×C4⋊C4C2×D1711yescharacteristic
416#499—178no—
417#482—178no—
418#482—178no—
419#480—178no—
420#480—178no—
421#478—178no—
422#478—178no—
423#469—178no—
424#469—178no—
425C4×D8—178no—
426#436—178no—
427#428—178no—
428#428—178no—
429C2×#107—171no—
430C2×#107—171no—
431C2×#107—171no—
432C2×#107—171no—
433C2×#107—171no—
434C2×#106—171no—
435C2×#106—171no—
436C2×#106—171no—
437C2×#106—171no—
438C2×C4⋊C8—171no—
439C2×#102—171no—
440C2×#102—171no—
441C2×#102—171no—
442C2×#102—171no—
443C2×#102—171no—
444C2×#102—171no—
445C2×C22⋊C8—171no—
446C2×C22⋊C8—171no—
447C2×C4×C8—171no—
448C2×C17—42no—
449C2×C17—42no—
450C2×C17—82no—
451C2×C17#335514yescomplemented
452C2×C17C2×#54711yescharacteristic
453C2×C17C2×#57511yescharacteristic
454C2×C17C2×#57611yescharacteristic
455D17—82no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—171no—
459C22×D4—341no—
460C22×D4—341no—
461C22×D4C22⋊D1711yescharacteristic
462C22×D4C22×D1711yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—341no—
466C23×C4—341no—
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469C2×D8—174no—
470C2×D8—344no—
471C2×M16—174no—
472C2×M16—174no—
473C2×M16—344no—
474C2×M16—344no—
475C22×C8—171no—
476C22×C8—171no—
477C22×C8—171no—
478C22×C8—171no—
479#126—28no—
480#126—348no—
481#125—22no—
482#125—174no—
483#125—342no—
484#125C22×D1714yes—
485#123—28no—
486#123—348no—
487#121—28no—
488#121—22no—
489#121—22no—
490#121—174no—
491#121—174no—
492#121—348no—
493#121—342no—
494#121—342no—
495#121C22×D1714yes—
496#121C22×D1714yes—
497C4×D4—28no—
498C4×D4—22no—
499C4×D4—174no—
500C4×D4—348no—
501C4×D4—342no—
502C4×D4C22⋊D1714yes—
503C4×D4C22×D1714yes—
504C4×D4C22×D1714yes—
505#117—22no—
506#117—174no—
507#117—342no—
508#117C22×D1714yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—174no—
516C2×C4⋊C4—171no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—342no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4—341no—
521C2×C4⋊C4C22⋊D1711yescharacteristic
522C2×C4⋊C4C22×D1711yescharacteristic
523C2×C4⋊C4C22×D1711yescharacteristic
524C2×C4⋊C4C22×D1714yes—
525C2×C4⋊C4C22×D1711yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—341no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4C22⋊D1711yescharacteristic
535C2×C22⋊C4C22⋊D1711yescharacteristic
536C2×C42—21no—
537C2×C42—341no—
538C2×C42C22×D1711yescharacteristic
539#107—174no—
540#107—174no—
541#107—174no—
542#107—174no—
543#107—174no—
544#106—174no—
545#106—174no—
546#106—174no—
547#106—174no—
548C4⋊C8—174no—
549#102—174no—
550#102—174no—
551#102—174no—
552#102—174no—
553#102—174no—
554#102—174no—
555C22⋊C8—174no—
556C22⋊C8—174no—
557C4×C8—174no—
558C17C2×#335511yescharacteristic, complemented, Sylow
559C24—21no—
560C24—341no—
561C24C2×C22⋊D1711yescharacteristic
562C24C2×C22⋊D1711yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—82no—
571C2×D4—172no—
572C2×D4—344no—
573C2×D4—344no—
574C2×D4—342no—
575C2×D4—342no—
576C2×D4—341no—
577C2×D4—684no—
578C2×D4—1362no—
579C2×D4C2×C22⋊D1714yes—
580C2×D4C23×D1712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—344no—
596C22×C4—344no—
597C22×C4—1362no—
598C22×C4—1362no—
599C22×C4C2×C22⋊D1712yes—
600C22×C4C2×C22⋊D1712yes—
601C22×C4C2×C22⋊D1711yescharacteristic
602C22×C4C2×C22⋊D1711yescharacteristic
603C22×C4C2×C22⋊D1711yescharacteristic
604C22×C4C2×C22⋊D1711yescharacteristic
605C22×C4C23×D1712yes—
606C22×C4C23×D1712yes—
607C22×C4C23×D1711yescharacteristic
608D8—348no—
609M16—348no—
610M16—348no—
611C2×C8—174no—
612C2×C8—172no—
613C2×C8—172no—
614C2×C8—172no—
615C2×C8—172no—
616C2×C8—342no—
617C2×C8—342no—
618C2×C8—342no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—172no—
626C4⋊C4—172no—
627C4⋊C4—172no—
628C4⋊C4—341no—
629C4⋊C4—341no—
630C4⋊C4—344no—
631C4⋊C4—341no—
632C4⋊C4—344no—
633C4⋊C4—344no—
634C4⋊C4C2×C22⋊D1714yes—
635C4⋊C4C23×D1712yes—
636C4⋊C4C23×D1712yes—
637C4⋊C4C23×D1712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—344no—
643C22⋊C4—344no—
644C22⋊C4—344no—
645C22⋊C4—344no—
646C22⋊C4C2×C22⋊D1714yes—
647C22⋊C4C2×C22⋊D1714yes—
648C42—24no—
649C42—344no—
650C42C2×C22⋊D1712yes—
651C42C23×D1712yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—342no—
663C23—682no—
664C23—682no—
665C23—682no—
666C23C22×C22⋊D1712yes—
667C23C22×C22⋊D1712yes—
668C23C22×C22⋊D1711yescharacteristic
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—342no—
676D4—342no—
677D4—688no—
678D4—682no—
679D4—1364no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—682no—
702C2×C4—682no—
703C2×C4—682no—
704C2×C4—1364no—
705C2×C4—1364no—
706C2×C4#41×D1712yes—
707C2×C4#1058769712yes—
708C2×C4C22×C22⋊D1712yes—
709C2×C4C22×C22⋊D1712yes—
710C2×C4C22×C22⋊D1712yes—
711C2×C4C22×C22⋊D1712yes—
712C2×C4C22×C22⋊D1711yescharacteristic
713C2×C4C24×D1711yescharacteristic
714C8—174no—
715C8—342no—
716C8—342no—
717C8—342no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—682no—
731C22—682no—
732C22—682no—
733C22—1364no—
734C22#1176345812yes—
735C22#1176360712yes—
736C22#1176361212yes—
737C22C23×C22⋊D1711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—682no—
746C4—682no—
747C4—682no—
748C4#1176345812yes—
749C4C2×#41×D1711yescharacteristic
750C4C2×#1058769711yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—1362no—
755C2#1454138414yesdirect product factor
756C2C2×#1176345811yescharacteristic
757C2C2×#1176360711yescharacteristic
758C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#553C2
socleC23×C17C22×D4
hypercenterC2×#553D17
hypocenterC17C2×#3355
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×#11763505C2semidirect
2. #14541384C2direct (N × H)
3. C2×#11763208C2semidirect
4. C2×#11763133C2semidirect
5. C2×#11763130C2semidirect
6. C2×#11763122C2semidirect
7. C2×#11763120C2semidirect
8. C2×#11763109C2semidirect
9. C2×#11763106C2semidirect
10. C2×#11763060C2semidirect
11. C2×#11763060C2semidirect
12. C2×C4×#63228C2semidirect
13. C2×#11762887C2semidirect
14. C2×#11762852C2semidirect
15. C2×#11762849C2semidirect
16. C2×C17×#553C2semidirect
21. #11763505C22semidirect
32. #11763208C22semidirect
33. #11763133C22semidirect
34. #11763130C22semidirect
35. #11763122C22semidirect
36. #11763120C22semidirect
37. #11763109C22semidirect
38. #11763106C22semidirect
39. #11763060C22semidirect
40. #11763060C22semidirect
41. C4×#63228C22semidirect
42. #11762887C22semidirect
43. #11762852C22semidirect
44. #11762849C22semidirect
65. C17×#553C22semidirect
340. C2×#553D17semidirect
394. #553C2×D17semidirect
451. C2×C17#3355semidirect
558. C17C2×#3355semidirect
755. C2#14541384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635052
#145413842
C2×#117632082
C2×#117631332
C2×#117631302
C2×#117631222
C2×#117631202
C2×#117631092
C2×#117631062
C2×#117630602
C2×C4×#632282
C2×#117628872
C2×#117628522
C2×#117628492
C2×C17×#5532
C2×#335517