Finite Group Databasebeta

← C2×#14541269 #17912903

Subgroups — C2×#14541269 #17912903

Order 4352.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763516C211yesmaximal, characteristic, complemented
2#14541269C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763144C211yesmaximal, characteristic, complemented
5C2×#11763125C211yesmaximal, characteristic, complemented
6C2×#11763150C211yesmaximal, characteristic, complemented
7C2×#11763120C211yesmaximal, characteristic, complemented
8C2×#11763113C211yesmaximal, characteristic, complemented
9C2×#11763089C211yesmaximal, characteristic, complemented
10C2×#11763053C211yesmaximal, characteristic, complemented
11C2×#11763036C211yesmaximal, characteristic, complemented
12C2×#11762909C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C22×#10587478C211yesmaximal, characteristic, complemented
16C2×C17×#553C211yesmaximal, characteristic
17C22×#63229C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763516—24no—
21#11763516C2218yescomplemented
22C2×#10587555C2211yescharacteristic
23C2×#10587576—21no—
24C2×#10587610C2211yescharacteristic
25C2×#10587610C2211yescharacteristic
26C2×#10587564—21no—
27C2×#10587564—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×D4×Dic17—21no—
30C22×C4⋊Dic17C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763219C2218yescomplemented
33#11763150C2218yescomplemented
34#11763144C2218yescomplemented
35#11763125C2218yescomplemented
36#11763120C2218yescomplemented
37#11763113C2218yescomplemented
38#11763089C2218yescomplemented
39#11763053C2218yescomplemented
40#11763036C2218yescomplemented
41#11762909C2218yescomplemented
42#11762881C2218yescomplemented
43#11762852C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587478C2211yescharacteristic
50C2×#10587478C2218yescomplemented
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#553—24no—
65C17×#553C2218yes—
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
85C23×Dic17—21no—
86C23×Dic17—21no—
87C22×Dic34—21no—
88C22×Dic34C2311yescharacteristic
89C17×#126—28no—
90C17×#125—22no—
91C17×#125C2314yes—
92C17×#123—28no—
93C17×#121—28no—
94C17×#121—22no—
95C17×#121—22no—
96C17×#121C2314yes—
97C17×#121C2314yes—
98C4×D4×C17—28no—
99C4×D4×C17—22no—
100C4×D4×C17D414yes—
101C4×D4×C17C2314yes—
102C4×D4×C17C2314yes—
103C17×#117—22no—
104C17×#117C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—22no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2314yes—
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C42×C17—21no—
121C2×C42×C17C2311yescharacteristic
122C2×C22⋊Dic17—21no—
123C2×C22⋊Dic17—21no—
124D4×Dic17—28no—
125C2×#63229—24no—
126C2×#63229C2314yes—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17—21no—
131C2×C4⋊Dic17—21no—
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2314yes—
134C2×C4⋊Dic17C2314yes—
135C2×C4⋊Dic17C2311yescharacteristic
136C2×C4⋊Dic17C2311yescharacteristic
137#10587610—22no—
138#10587610—22no—
139#10587610C2314yes—
140#10587610C2314yes—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×#63225—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223C2314yes—
147C22×#3622—24no—
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2314yes—
152C22×#3622C2311yescharacteristic
153#10587576—28no—
154#10587564—28no—
155#10587564—28no—
156#10587555—22no—
157#10587555C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587503C2314yes—
161#10587503C2314yes—
162#10587503C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587481C2314yes—
166#10587481C2314yes—
167#10587481C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587478C2314yes—
172#10587478C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178#10587474C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C24×C17C2×D411yescharacteristic
182C2×D4×C17—24no—
183C2×D4×C17—24no—
184C2×D4×C17—24no—
185C2×D4×C17—21no—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—44no—
189C2×D4×C17—82no—
190C2×D4×C17C2×D414yes—
191C2×D4×C17C2412yes—
192C22×C4×C17—22no—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—24no—
200C22×C4×C17—24no—
201C22×C4×C17—82no—
202C22×C4×C17—82no—
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D412yes—
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2412yes—
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—24no—
217C22×Dic17—24no—
218C22×Dic17—82no—
219C22×Dic17—82no—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—82no—
225C2×Dic34C2412yes—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—21no—
229C4⋊C4×C17—21no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17C2×D414yes—
233C4⋊C4×C17C2412yes—
234C4⋊C4×C17C2412yes—
235C4⋊C4×C17C2412yes—
236C22⋊C4×C17—24no—
237C22⋊C4×C17—24no—
238C22⋊C4×C17—24no—
239C22⋊C4×C17—24no—
240C22⋊C4×C17C2×D414yes—
241C22⋊C4×C17C2×D414yes—
242C42×C17—24no—
243C42×C17C2×D412yes—
244C42×C17C2412yes—
245C22⋊Dic17—24no—
246C22⋊Dic17—24no—
247#63229—28no—
248C4⋊Dic17—21no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—24no—
252C4⋊Dic17—24no—
253C4⋊Dic17—24no—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260C4×Dic17—24no—
261#63223—28no—
262C2×#3622—22no—
263C2×#3622—22no—
264C2×#3622—22no—
265C2×#3622—28no—
266C2×#3622#4114yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270C2×#3622C2412yes—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17—42no—
281C23×C17#13714yes—
282C23×C17C22×D412yes—
283C23×C17C22×D412yes—
284C23×C17C22×D411yescharacteristic
285D4×C17—28no—
286D4×C17—22no—
287D4×C17—22no—
288D4×C17—48no—
289D4×C17—42no—
290D4×C17—84no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—24no—
296C2×C4×C17—24no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—84no—
308C2×C4×C17—84no—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D412yes—
312C2×C4×C17C22×D412yes—
313C2×C4×C17C22×D411yescharacteristic
314C2×C4×C17C2×#4112yes—
315C2×C4×C172−1+412yes—
316C2×C4×C17C2511yescharacteristic
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—84no—
326C2×Dic17—84no—
327Dic34—22no—
328Dic34—22no—
329Dic34—42no—
330Dic34—84no—
331#3622—22no—
332#3622—22no—
333#3622—22no—
334#3622C2×#4114yes—
335C2×#554—171no—
336C2×#553D1711yescharacteristic
337#3346—1716no—
338C2×#501—171no—
339C2×#484—171no—
340C2×#481—171no—
341C2×#485—171no—
342C2×#480—171no—
343C2×#479—171no—
344C2×#474—171no—
345C2×#468—171no—
346C2×#465—171no—
347C2×#440—171no—
348C2×#435—171no—
349C2×#428—171no—
350C22×#107—171no—
351C22×C17—28no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—44no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—42no—
361C22×C17—84no—
362C22×C17#54712yes—
363C22×C17C2×#13714yes—
364C22×C17C2×#13712yes—
365C22×C17#57612yes—
366C22×C17C23×D411yescharacteristic
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17—42no—
374C4×C17#54712yes—
375C4×C17C22×#4111yescharacteristic
376C4×C17C2×2−1+411yescharacteristic
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×SD16—171no—
382C22×M16—171no—
383C23×C8—171no—
384#554—178no—
385#554—344no—
386#553—24no—
387#553C2×D1718yes—
388C2×C4⋊Q8—171no—
389C2×#126—21no—
390C2×#125—341no—
391C2×#125C2×D1711yescharacteristic
392C2×#123—21no—
393C2×C22⋊Q8—171no—
394C2×C22⋊Q8—171no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8—341no—
397C2×#121—21no—
398C2×#121C2×D1711yescharacteristic
399C2×#121C2×D1711yescharacteristic
400C2×C4×Q8—171no—
401C2×C4×D4—21no—
402C2×C4×D4—341no—
403C2×C4×D4C2×D1711yescharacteristic
404C2×C4×D4C2×D1711yescharacteristic
405C2×#117C2×D1711yescharacteristic
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4C2×D1711yescharacteristic
409#501—178no—
410#485—178no—
411#484—178no—
412#481—178no—
413#480—178no—
414#479—178no—
415#474—178no—
416#468—178no—
417#465—178no—
418#440—178no—
419#435—178no—
420#428—178no—
421C2×#107—171no—
422C2×#107—171no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—178no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×C4⋊C8—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×#97—171no—
441C2×C17—24no—
442C2×C17—42no—
443C2×C17—82no—
444C2×C17#334614yescomplemented
445C2×C17C2×#54711yescharacteristic
446C2×C17C22×#13711yescharacteristic
447C2×C17C2×#57611yescharacteristic
448C22×Q8—171no—
449C22×Q8—341no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22⋊D1711yescharacteristic
453C22×D4C22×D1711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—344no—
462C2×M16—174no—
463C2×M16—344no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—174no—
467C22×C8—171no—
468C22×C8—171no—
469C22×C8—344no—
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#126—28no—
473#125—22no—
474#125—348no—
475#125C22×D1714yes—
476#123—28no—
477C22⋊Q8—174no—
478C22⋊Q8—174no—
479C22⋊Q8—342no—
480C22⋊Q8—342no—
481C22⋊Q8—348no—
482C22⋊Q8—348no—
483#121—28no—
484#121—22no—
485#121—22no—
486#121C22×D1714yes—
487#121C22×D1714yes—
488C4×Q8—174no—
489C4×Q8—342no—
490C4×D4—28no—
491C4×D4—22no—
492C4×D4—348no—
493C4×D4C22⋊D1714yes—
494C4×D4C22×D1714yes—
495C4×D4C22×D1714yes—
496#117—22no—
497#117C22×D1714yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—174no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4C22⋊D1711yescharacteristic
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1714yes—
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4C22⋊D1711yescharacteristic
527C2×C22⋊C4C22⋊D1711yescharacteristic
528C2×C42—21no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531#107—174no—
532#107—174no—
533#107—174no—
534#107—174no—
535#107—174no—
536#107—174no—
537#106—174no—
538#106—174no—
539#106—174no—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#102—174no—
545#102—174no—
546#102—174no—
547C22⋊C8—174no—
548C22⋊C8—174no—
549#97—174no—
550C17C2×#334611yescharacteristic, complemented, Sylow
551C24—21no—
552C24C2×C22⋊D1711yescharacteristic
553C24C2×C22⋊D1711yescharacteristic
554C2×Q8—172no—
555C2×Q8—341no—
556C2×Q8—344no—
557C2×Q8—342no—
558C2×Q8—342no—
559C2×Q8—1362no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×C22⋊D1714yes—
569C2×D4C23×D1712yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—344no—
586C22×C4—344no—
587C22×C4—1362no—
588C22×C4—1362no—
589C22×C4C2×C22⋊D1712yes—
590C22×C4C2×C22⋊D1712yes—
591C22×C4C2×C22⋊D1711yescharacteristic
592C22×C4C2×C22⋊D1711yescharacteristic
593C22×C4C2×C22⋊D1711yescharacteristic
594C22×C4C2×C22⋊D1711yescharacteristic
595C22×C4C23×D1712yes—
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—348no—
599M16—348no—
600C2×C8—174no—
601C2×C8—172no—
602C2×C8—172no—
603C2×C8—172no—
604C2×C8—172no—
605C2×C8—348no—
606C2×C8—342no—
607C2×C8—342no—
608C2×C8—342no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—172no—
618C4⋊C4—341no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4C2×C22⋊D1714yes—
628C4⋊C4C23×D1712yes—
629C4⋊C4C23×D1712yes—
630C4⋊C4C23×D1712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4C2×C22⋊D1714yes—
638C22⋊C4C2×C22⋊D1714yes—
639C42—24no—
640C42—344no—
641C42C2×C22⋊D1712yes—
642C42C23×D1712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#1058763714yes—
653C23C22×C22⋊D1712yes—
654C23C22×C22⋊D1712yes—
655C23C22×C22⋊D1711yescharacteristic
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—1364no—
693C2×C4—1364no—
694C2×C4#41×D1712yes—
695C2×C4#1058769712yes—
696C2×C4C22×C22⋊D1712yes—
697C2×C4C22×C22⋊D1712yes—
698C2×C4C22×C22⋊D1712yes—
699C2×C4C22×C22⋊D1712yes—
700C2×C4C22×C22⋊D1711yescharacteristic
701C2×C4C24×D1711yescharacteristic
702C8—174no—
703C8—342no—
704C8—342no—
705C8—342no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22#1176345812yes—
718C22C2×#1058763714yes—
719C22C2×#1058763712yes—
720C22#1176361212yes—
721C22C23×C22⋊D1711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176345812yes—
734C4C2×#41×D1711yescharacteristic
735C4C2×#1058769711yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#1454126914yesdirect product factor
740C2C2×#1176345811yescharacteristic
741C2C22×#1058763711yescharacteristic
742C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#553C2
socleC23×C17C22×D4
hypercenterC2×#553D17
hypocenterC17C2×#3346
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×#11763516C2semidirect
2. #14541269C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763144C2semidirect
5. C2×#11763125C2semidirect
6. C2×#11763150C2semidirect
7. C2×#11763120C2semidirect
8. C2×#11763113C2semidirect
9. C2×#11763089C2semidirect
10. C2×#11763053C2semidirect
11. C2×#11763036C2semidirect
12. C2×#11762909C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762852C2semidirect
15. C22×#10587478C2semidirect
21. #11763516C22semidirect
32. #11763219C22semidirect
33. #11763150C22semidirect
34. #11763144C22semidirect
35. #11763125C22semidirect
36. #11763120C22semidirect
37. #11763113C22semidirect
38. #11763089C22semidirect
39. #11763053C22semidirect
40. #11763036C22semidirect
41. #11762909C22semidirect
42. #11762881C22semidirect
43. #11762852C22semidirect
50. C2×#10587478C22semidirect
444. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541269direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635162
#145412692
C2×#117632192
C2×#117631442
C2×#117631252
C2×#117631502
C2×#117631202
C2×#117631132
C2×#117630892
C2×#117630532
C2×#117630362
C2×#117629092
C2×#117628812
C2×#117628522
C22×#105874782
C2×C17×#5532
C2×#334617