Finite Group Databasebeta

← C17×#14259 #16872003

Subgroups — C17×#14259 #16872003

Order 4352.

2098 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#386C211yesmaximal, characteristic
2C2×C17×#386C211yesmaximal, characteristic
3C2×C17×#386C211yesmaximal, characteristic
4C2×C17×#385C211yesmaximal, characteristic, complemented
5C22×C17×#95C211yesmaximal, characteristic, complemented
6C17×#1443C212yesmaximal, complemented
7C17×#1442C212yesmaximal, complemented
8C17×#1440C212yesmaximal, complemented
9C17×#1439C212yesmaximal, complemented
10C17×C22⋊#95C211yesmaximal, characteristic, complemented
11C17×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C17C2211yescharacteristic
13C24×C4×C17C2211yescharacteristic
14C24×C4×C17C2211yescharacteristic
15C24×C4×C17C2211yescharacteristic
16C22×C4⋊C4×C17C2212yes—
17C22×C22⋊C4×C17C2211yescharacteristic
18C22×C22⋊C4×C17C2211yescharacteristic
19C22×C22⋊C4×C17C2211yescharacteristic
20C22×C22⋊C4×C17C2211yescharacteristic
21C22×C22⋊C4×C17C2212yes—
22C22×C22⋊C4×C17C2211yescharacteristic
23C22×C22⋊C4×C17C2212yes—
24C17×#386—24no—
25C17×#386—24no—
26C17×#386C418yescomplemented
27C17×#385—24no—
28C2×C17×#95—24no—
29C2×C17×#95C2212yes—
30C2×C17×#95C2212yes—
31C2×C17×#95C2212yes—
32C2×C17×#95C2211yescharacteristic
33C2×C17×#95C2212yes—
34C2×C17×#95C2211yescharacteristic
35C2×C17×#95C2212yes—
36C2×C17×#95C2212yes—
37C2×C17×#95C2212yes—
38C2×C17×#95C2212yes—
39C2×C17×#95C2212yes—
40C25×C17C2311yescharacteristic
41C25×C17C2311yescharacteristic
42C22×D4×C17—22no—
43C22×D4×C17—22no—
44C22×D4×C17—22no—
45C22×D4×C17—22no—
46C22×D4×C17—22no—
47C22×D4×C17—22no—
48C22×D4×C17C2×C414yes—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—42no—
56C23×C4×C17—42no—
57C23×C4×C17—42no—
58C23×C4×C17—42no—
59C23×C4×C17—42no—
60C23×C4×C17—42no—
61C23×C4×C17C2×C414yes—
62C23×C4×C17D414yes—
63C23×C4×C17D414yes—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2312yes—
67C23×C4×C17C2312yes—
68C23×C4×C17C2312yes—
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2312yes—
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17—24no—
74C2×C4⋊C4×C17—42no—
75C2×C4⋊C4×C17—42no—
76C2×C22⋊C4×C17—22no—
77C2×C22⋊C4×C17—22no—
78C2×C22⋊C4×C17—22no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—24no—
87C2×C22⋊C4×C17—42no—
88C2×C22⋊C4×C17—42no—
89C2×C22⋊C4×C17—42no—
90C2×C22⋊C4×C17—42no—
91C2×C22⋊C4×C17—42no—
92C2×C22⋊C4×C17—42no—
93C2×C22⋊C4×C17C2×C414yes—
94C2×C22⋊C4×C17C2×C418yescomplemented
95C17×#95—24no—
96C17×#95—24no—
97C17×#95—24no—
98C17×#95—22no—
99C17×#95—22no—
100C17×#95—24no—
101C17×#95—42no—
102C17×#95—42no—
103C17×#95—42no—
104C17×#95—42no—
105C17×#95C2×C418yescomplemented
106C24×C17—22no—
107C24×C17—22no—
108C24×C17—22no—
109C24×C17—22no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—21no—
114C24×C17—21no—
115C24×C17—21no—
116C24×C17—22no—
117C24×C17—22no—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17C22×C412yes—
121C24×C17C22×C412yes—
122C24×C17C2×D412yes—
123C24×C17C2×D412yes—
124C24×C17#4112yes—
125C24×C17#4112yes—
126C24×C17#4112yes—
127C24×C17#4112yes—
128C24×C17C2411yescharacteristic
129C2×D4×C17—28no—
130C2×D4×C17—28no—
131C2×D4×C17—28no—
132C2×D4×C17—44no—
133C2×D4×C17—44no—
134C2×D4×C17—44no—
135C2×D4×C17—44no—
136C22×C4×C17—28no—
137C22×C4×C17—28no—
138C22×C4×C17—28no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—22no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—48no—
189C22×C4×C17—48no—
190C22×C4×C17—44no—
191C22×C4×C17—44no—
192C22×C4×C17—44no—
193C22×C4×C17—44no—
194C22×C4×C17—44no—
195C22×C4×C17—44no—
196C22×C4×C17—48no—
197C22×C4×C17—48no—
198C22×C4×C17—48no—
199C22×C4×C17—48no—
200C22×C4×C17C22×C414yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C22×C414yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D414yes—
206C4⋊C4×C17—48no—
207C22⋊C4×C17—28no—
208C22⋊C4×C17—48no—
209C22⋊C4×C17—48no—
210C22⋊C4×C17—44no—
211C22⋊C4×C17—44no—
212C22⋊C4×C17—44no—
213C22⋊C4×C17—44no—
214#14259C1711yesmaximal, characteristic, direct product factor, Sylow
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—24no—
220C23×C17—22no—
221C23×C17—22no—
222C23×C17—24no—
223C23×C17—24no—
224C23×C17—24no—
225C23×C17—24no—
226C23×C17—24no—
227C23×C17—24no—
228C23×C17—24no—
229C23×C17—24no—
230C23×C17—24no—
231C23×C17—22no—
232C23×C17—22no—
233C23×C17—22no—
234C23×C17—24no—
235C23×C17—24no—
236C23×C17—41no—
237C23×C17—41no—
238C23×C17—41no—
239C23×C17—41no—
240C23×C17—41no—
241C23×C17—41no—
242C23×C17—42no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—42no—
246C23×C17—42no—
247C23×C17—42no—
248C23×C17—42no—
249C23×C17—42no—
250C23×C17—42no—
251C23×C17—42no—
252C23×C17—42no—
253C23×C17—42no—
254C23×C17#11714yes—
255C23×C17C4×D414yes—
256C23×C17C4×D414yes—
257C23×C17#12114yes—
258C23×C17#12314yes—
259C23×C17#12414yes—
260C23×C17#12614yes—
261C23×C17C23×C411yescharacteristic
262C23×C17C22×D411yescharacteristic
263C23×C17C22×D411yescharacteristic
264C23×C17C2×#4111yescharacteristic
265C23×C17C2×#4111yescharacteristic
266C23×C17C2×#4111yescharacteristic
267C23×C17C2×#4111yescharacteristic
268C23×C17H(5,𝔽2)12yes—
269C23×C17H(5,𝔽2)12yes—
270C23×C17H(5,𝔽2)12yes—
271C23×C172−1+412yes—
272D4×C17—416no—
273C2×C4×C17—22no—
274C2×C4×C17—24no—
275C2×C4×C17—24no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—24no—
279C2×C4×C17—24no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—24no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—24no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—416no—
292C2×C4×C17—416no—
293C2×C4×C17—416no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—42no—
313C2×C4×C17—42no—
314C2×C4×C17—41no—
315C2×C4×C17—41no—
316C2×C4×C17—42no—
317C2×C4×C17—41no—
318C2×C4×C17—41no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—41no—
322C2×C4×C17—41no—
323C2×C4×C17—42no—
324C2×C4×C17—42no—
325C2×C4×C17—42no—
326C2×C4×C17—42no—
327C2×C4×C17—42no—
328C2×C4×C17—42no—
329C2×C4×C17—42no—
330C2×C4×C17—42no—
331C2×#386C2×C1711yescharacteristic
332C2×#386C2×C1711yescharacteristic
333C2×#386C2×C1711yescharacteristic
334C2×#385C2×C1711yescharacteristic, complemented
335C22×#95C2×C1711yescharacteristic, complemented
336#1443C2×C1712yescomplemented
337#1442C2×C1712yescomplemented
338#1440C2×C1712yescomplemented
339#1439C2×C1712yescomplemented
340C22⋊#95C2×C1711yescharacteristic, complemented
341C22⋊#95C2×C1711yescharacteristic, complemented
342C22×C17—28no—
343C22×C17—24no—
344C22×C17—24no—
345C22×C17—28no—
346C22×C17—24no—
347C22×C17—24no—
348C22×C17—24no—
349C22×C17—24no—
350C22×C17—28no—
351C22×C17—28no—
352C22×C17—44no—
353C22×C17—42no—
354C22×C17—42no—
355C22×C17—44no—
356C22×C17—42no—
357C22×C17—81no—
358C22×C17—81no—
359C22×C17—81no—
360C22×C17—81no—
361C22×C17—82no—
362C22×C17—82no—
363C22×C17#38818yes—
364C22×C17C2×#11711yescharacteristic
365C22×C17C2×C4×D411yescharacteristic
366C22×C17C2×C4×D411yescharacteristic
367C22×C17#51812yes—
368C22×C17#52012yes—
369C22×C17C2×#12111yescharacteristic
370C22×C17C2×#12311yescharacteristic
371C22×C17C2×#12411yescharacteristic
372C22×C17C2×#12611yescharacteristic
373C22×C17#53411yescharacteristic
374C22×C17#53411yescharacteristic
375C22×C17#53412yes—
376C22×C17#53511yescharacteristic
377C22×C17#53611yescharacteristic
378C22×C17#53712yes—
379C22×C17#53812yes—
380C22×C17#53812yes—
381C22×C17#53812yes—
382C22×C17#53812yes—
383C22×C17#53912yes—
384C22×C17#53912yes—
385C22×C17#53912yes—
386C22×C17#53912yes—
387C4×C17—44no—
388C4×C17—44no—
389C4×C17—44no—
390C4×C17—42no—
391C4×C17—42no—
392C4×C17—42no—
393C4×C17—81no—
394C4×C17—81no—
395C4×C17—82no—
396C23×D4C22×C1711yescharacteristic
397C24×C4C22×C1711yescharacteristic
398C24×C4C22×C1711yescharacteristic
399C24×C4C22×C1711yescharacteristic
400C22×C4⋊C4C22×C1712yes—
401C22×C22⋊C4C22×C1711yescharacteristic
402C22×C22⋊C4C22×C1711yescharacteristic
403C22×C22⋊C4C22×C1711yescharacteristic
404C22×C22⋊C4C22×C1711yescharacteristic
405C22×C22⋊C4C22×C1712yes—
406C22×C22⋊C4C22×C1711yescharacteristic
407C22×C22⋊C4C22×C1712yes—
408#386—24no—
409#386—24no—
410#386C4×C1718yescomplemented
411#385—24no—
412C2×#95—24no—
413C2×#95C22×C1712yes—
414C2×#95C22×C1712yes—
415C2×#95C22×C1712yes—
416C2×#95C22×C1711yescharacteristic
417C2×#95C22×C1712yes—
418C2×#95C22×C1711yescharacteristic
419C2×#95C22×C1712yes—
420C2×#95C22×C1712yes—
421C2×#95C22×C1712yes—
422C2×#95C22×C1712yes—
423C2×#95C22×C1712yes—
424C2×C17—28no—
425C2×C17—82no—
426C2×C17C2×#38811yescharacteristic
427C2×C17#231812yes—
428C2×C17#232111yescharacteristic
429C2×C17#232211yescharacteristic
430C2×C17#232512yes—
431C2×C17#261711yescharacteristic
432C2×C17#261811yescharacteristic
433C2×C17#262211yescharacteristic
434C2×C17#262311yescharacteristic
435C2×C17#263912yes—
436C2×C17#264312yes—
437C25C23×C1711yescharacteristic
438C25C23×C1711yescharacteristic
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4C2×C4×C1714yes—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4C2×C4×C1714yes—
459C23×C4D4×C1714yes—
460C23×C4D4×C1714yes—
461C23×C4C23×C1711yescharacteristic
462C23×C4C23×C1711yescharacteristic
463C23×C4C23×C1712yes—
464C23×C4C23×C1712yes—
465C23×C4C23×C1712yes—
466C23×C4C23×C1711yescharacteristic
467C23×C4C23×C1712yes—
468C23×C4C23×C1711yescharacteristic
469C23×C4C23×C1711yescharacteristic
470C2×C4⋊C4—24no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4C2×C4×C1714yes—
491C2×C22⋊C4C2×C4×C1718yescomplemented
492#95—24no—
493#95—24no—
494#95—24no—
495#95—22no—
496#95—22no—
497#95—24no—
498#95—42no—
499#95—42no—
500#95—42no—
501#95—42no—
502#95C2×C4×C1718yescomplemented
503C17#1425911yescharacteristic, direct product factor, Sylow
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24C22×C4×C1712yes—
519C24C22×C4×C1712yes—
520C24C2×D4×C1712yes—
521C24C2×D4×C1712yes—
522C24#41×C1712yes—
523C24#41×C1712yes—
524C24#41×C1712yes—
525C24#41×C1712yes—
526C24C24×C1711yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4C22×C4×C1712yes—
599C22×C4C22×C4×C1714yes—
600C22×C4C22×C4×C1714yes—
601C22×C4C2×D4×C1712yes—
602C22×C4C2×D4×C1712yes—
603C22×C4C2×D4×C1714yes—
604C4⋊C4—48no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23C17×#11714yes—
652C23C4×D4×C1714yes—
653C23C4×D4×C1714yes—
654C23C17×#12114yes—
655C23C17×#12314yes—
656C23C17×#12414yes—
657C23C17×#12614yes—
658C23C23×C4×C1711yescharacteristic
659C23C22×D4×C1711yescharacteristic
660C23C22×D4×C1711yescharacteristic
661C23C2×#41×C1711yescharacteristic
662C23C2×#41×C1711yescharacteristic
663C23C2×#41×C1711yescharacteristic
664C23C2×#41×C1711yescharacteristic
665C23C17×H(5,𝔽2)12yes—
666C23C17×H(5,𝔽2)12yes—
667C23C17×H(5,𝔽2)12yes—
668C23C17×2−1+412yes—
669D4—416no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—416no—
689C2×C4—416no—
690C2×C4—416no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—28no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—28no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—82no—
748C22—82no—
749C22C17×#38818yes—
750C22C2×C17×#11711yescharacteristic
751C22C2×C4×D4×C1711yescharacteristic
752C22C2×C4×D4×C1711yescharacteristic
753C22C17×#51812yes—
754C22C17×#52012yes—
755C22C2×C17×#12111yescharacteristic
756C22C2×C17×#12311yescharacteristic
757C22C2×C17×#12411yescharacteristic
758C22C2×C17×#12611yescharacteristic
759C22C17×#53411yescharacteristic
760C22C17×#53411yescharacteristic
761C22C17×#53412yes—
762C22C17×#53511yescharacteristic
763C22C17×#53611yescharacteristic
764C22C17×#53712yes—
765C22C17×#53812yes—
766C22C17×#53812yes—
767C22C17×#53812yes—
768C22C17×#53812yes—
769C22C17×#53912yes—
770C22C17×#53912yes—
771C22C17×#53912yes—
772C22C17×#53912yes—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—81no—
780C4—81no—
781C4—82no—
782C2—28no—
783C2—82no—
784C2C2×C17×#38811yescharacteristic
785C2C17×#231812yes—
786C2C17×#232111yescharacteristic
787C2C17×#232211yescharacteristic
788C2C17×#232512yes—
789C2C17×#261711yescharacteristic
790C2C17×#261811yescharacteristic
791C2C17×#262211yescharacteristic
792C2C17×#262311yescharacteristic
793C2C17×#263912yes—
794C2C17×#264312yes—
subgroupG/H
center, socleC24×C17C24
commutatorC23C23×C4×C17
Frattini, cosocleC24C24×C17
prime radicalC23×D4×C17C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C17×#385C2semidirect
5. C22×C17×#95C2semidirect
6. C17×#1443C2semidirect
7. C17×#1442C2semidirect
8. C17×#1440C2semidirect
9. C17×#1439C2semidirect
10. C17×C22⋊#95C2semidirect
11. C17×C22⋊#95C2semidirect
26. C17×#386C4semidirect
94. C2×C22⋊C4×C17C2×C4semidirect
105. C17×#95C2×C4semidirect
214. #14259C17direct (N × H)
334. C2×#385C2×C17semidirect
335. C22×#95C2×C17semidirect
336. #1443C2×C17semidirect
337. #1442C2×C17semidirect
338. #1440C2×C17semidirect
339. #1439C2×C17semidirect
340. C22⋊#95C2×C17semidirect
341. C22⋊#95C2×C17semidirect
410. #386C4×C17semidirect
491. C2×C22⋊C4C2×C4×C17semidirect
502. #95C2×C4×C17semidirect
503. C17#14259direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3862
C2×C17×#3852
C22×C17×#952
C17×#14432
C17×#14422
C17×#14402
C17×#14392
C17×C22⋊#952
#1425917