Finite Group Databasebeta

← C17×#61634 #16919378

Subgroups — C17×#61634 #16919378

Order 4352.

2018 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3538C211yesmaximal, characteristic, complemented
2C17×#3486C211yesmaximal, characteristic
3C17×#3312C214yesmaximal, complemented
4C17×#3300C214yesmaximal, complemented
5D4×Q16×C17C214yesmaximal, complemented
6C17×#3270C214yesmaximal, complemented
7C17×#3223C212yesmaximal, complemented
8C17×#3202C212yesmaximal, complemented
9C17×#3190C212yesmaximal, complemented
10C17×#3127C212yesmaximal, complemented
11C17×#3011C212yesmaximal, complemented
12C2×C17×#451C212yesmaximal, complemented
13C17×#2977C211yesmaximal, characteristic, complemented
14C2×C17×2−1+4C2211yescharacteristic
15C23×Q8×C17C2211yescharacteristic
16C2×C17×#137C2212yescomplemented
17C22×Q16×C17C2214yes—
18C22×Q16×C17C2212yescomplemented
19C17×#563—22no—
20C17×#552C2214yes—
21C17×#551—22no—
22D4×Q8×C17—22no—
23D4×Q8×C17C2214yes—
24D4×Q8×C17C2214yes—
25C17×#548—22no—
26C17×#548C2214yes—
27C17×#544—22no—
28C17×#541C2212yes—
29C17×#539—22no—
30C17×#536—22no—
31C17×#536C2211yescharacteristic
32C17×#536C2211yescharacteristic
33C17×#536C2212yes—
34C17×#525—22no—
35C17×#525C2211yescharacteristic
36C17×#525C2211yescharacteristic
37C2×C17×C22⋊Q8C2212yes—
38C17×#519C2211yescharacteristic
39C17×#497C2212yescomplemented
40C17×#494C2212yescomplemented
41C17×#491C2212yescomplemented
42C17×#488C2212yescomplemented
43C17×#485C2214yes—
44C17×#485C2214yescomplemented
45C17×#483C2212yes—
46C17×#480C2212yes—
47C17×#479C2214yescomplemented
48C17×#470C2214yescomplemented
49C17×#467C2214yes—
50C17×#467C2214yescomplemented
51C17×#465C2214yes—
52C17×#464C2214yescomplemented
53C17×#462C2214yescomplemented
54C17×#462C2214yescomplemented
55C17×#452C2214yes—
56C17×#452C2214yescomplemented
57C17×#451C2214yes—
58C17×#451C2214yes—
59C17×#451C2214yes—
60C17×#451C2214yes—
61C17×#451C2212yes—
62C17×#451C2214yescomplemented
63C17×#451C2214yescomplemented
64C17×#448C2212yes—
65C17×#441C2214yescomplemented
66C4×Q16×C17C2214yescomplemented
67C17×#435C2214yes—
68C8×D4×C17C2214yes—
69C17×#433C2212yes—
70C17×#419C2212yescomplemented
71C17×#416C2212yescomplemented
72C2×C17×#103C2214yes—
73C17×#408C2212yes—
74C2×C17×C22⋊C8C2212yes—
75C17×2−1+4—44no—
76C2×#41×C17—22no—
77C2×#41×C17—21no—
78C2×#41×C17C2312yes—
79C2×#41×C17C2311yescharacteristic
80C2×#41×C17C2311yescharacteristic
81C22×Q8×C17—21no—
82C22×Q8×C17—21no—
83C22×Q8×C17—22no—
84C22×Q8×C17—44no—
85C22×Q8×C17C2311yescharacteristic
86C22×Q8×C17C2314yes—
87C22×Q8×C17C2312yes—
88C22×Q8×C17C2312yes—
89C22×Q8×C17C2311yescharacteristic
90C22×Q8×C17C2312yes—
91C23×C4×C17—21no—
92C23×C4×C17C2311yescharacteristic
93C17×#137—44no—
94C2×Q16×C17—48no—
95C2×Q16×C17—44no—
96C2×Q16×C17C2314yes—
97C2×Q16×C17C2314yes—
98C2×Q16×C17C2314yes—
99C2×Q16×C17C2314yes—
100C2×Q16×C17C2314yes—
101C2×SD16×C17C2314yes—
102C2×M16×C17C2312yes—
103C22×C8×C17C2314yes—
104C22×C8×C17C2312yes—
105C17×C4⋊Q8—22no—
106C17×C4⋊Q8—21no—
107C17×C4⋊Q8—24no—
108C17×C4⋊Q8—24no—
109C17×C4⋊Q8C2312yes—
110C17×C4⋊Q8C2312yes—
111C17×#126—24no—
112C17×#126—24no—
113C17×#125—24no—
114C17×#125—24no—
115C17×#125C2312yes—
116C17×#124—21no—
117C17×#124—22no—
118C17×#124—24no—
119C17×#124C2312yes—
120C17×#123—22no—
121C17×#123—22no—
122C17×#123—22no—
123C17×#123—24no—
124C17×#123—21no—
125C17×#123—22no—
126C17×#123D412yes—
127C17×C22⋊Q8—22no—
128C17×C22⋊Q8—22no—
129C17×C22⋊Q8—24no—
130C17×C22⋊Q8—22no—
131C17×C22⋊Q8—24no—
132C17×C22⋊Q8—24no—
133C17×C22⋊Q8—24no—
134C17×C22⋊Q8—24no—
135C17×C22⋊Q8D412yes—
136C17×C22⋊Q8C2314yes—
137C17×C22⋊Q8C2314yes—
138C17×C22⋊Q8C2312yes—
139C17×C22⋊Q8C2314yes—
140C17×C22⋊Q8C2314yes—
141C17×#121—24no—
142C17×#121D412yes—
143C17×#121C2312yes—
144C17×#120—21no—
145C17×#120D412yes—
146C4×Q8×C17—22no—
147C4×Q8×C17C2314yes—
148C4×Q8×C17C2314yes—
149C4×D4×C17—24no—
150C4×D4×C17—24no—
151C4×D4×C17—22no—
152C4×D4×C17—24no—
153C4×D4×C17C2314yes—
154C17×#117—22no—
155C17×#117—24no—
156C17×#117C2311yescharacteristic
157C17×#117C2312yes—
158C17×#117C2311yescharacteristic
159C2×C4⋊C4×C17—22no—
160C2×C4⋊C4×C17C2312yes—
161C2×C22⋊C4×C17—22no—
162C17×#107C2314yes—
163C17×#106C2314yes—
164C17×C4⋊C8C2314yes—
165C17×#103C2314yes—
166C17×#103C2314yes—
167C17×#103C2314yes—
168C17×#103C2314yes—
169C17×#103C2314yes—
170C17×#103C2314yes—
171C17×#103C2314yes—
172C17×#102C2314yes—
173C17×C22⋊C8C2314yes—
174C17×C22⋊C8C2312yes—
175C17×C22⋊C8C2312yes—
176C17×C22⋊C8C2314yes—
177C17×#97C2312yes—
178C4×C8×C17C2312yes—
179C24×C17C2×D411yescharacteristic
180#41×C17—24no—
181#41×C17—42no—
182#41×C17—42no—
183#41×C17—42no—
184#41×C17—48no—
185#41×C17—44no—
186C2×Q8×C17—24no—
187C2×Q8×C17—21no—
188C2×Q8×C17—24no—
189C2×Q8×C17—21no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17—22no—
193C2×Q8×C17—28no—
194C2×Q8×C17—24no—
195C2×Q8×C17—44no—
196C2×Q8×C17—42no—
197C2×Q8×C17—42no—
198C2×Q8×C17—44no—
199C2×Q8×C17—44no—
200C2×Q8×C17—42no—
201C2×Q8×C17—42no—
202C2×Q8×C17—48no—
203C2×Q8×C17—44no—
204C2×Q8×C17C2×D411yescharacteristic
205C2×Q8×C17C2414yes—
206C2×Q8×C17C2412yes—
207C2×Q8×C17C2411yescharacteristic
208C2×Q8×C17C2412yes—
209C2×D4×C17—21no—
210C2×D4×C17—22no—
211C2×D4×C17—22no—
212C2×D4×C17C2×D414yes—
213C2×D4×C17C2×D412yes—
214C2×D4×C17C2×D411yescharacteristic
215C2×D4×C17C2411yescharacteristic
216C22×C4×C17—21no—
217C22×C4×C17—22no—
218C22×C4×C17—24no—
219C22×C4×C17—21no—
220C22×C4×C17—22no—
221C22×C4×C17—22no—
222C22×C4×C17—22no—
223C22×C4×C17—22no—
224C22×C4×C17—21no—
225C22×C4×C17—42no—
226C22×C4×C17—44no—
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2412yes—
230C22×C4×C17C2411yescharacteristic
231C22×C4×C17C2412yes—
232Q16×C17—28no—
233Q16×C17—28no—
234Q16×C17—44no—
235Q16×C17—44no—
236Q16×C17—44no—
237SD16×C17—44no—
238M16×C17—42no—
239C2×C8×C17—42no—
240C2×C8×C17—44no—
241C2×C8×C17C2414yes—
242C2×C8×C17C2414yes—
243C4⋊C4×C17—24no—
244C4⋊C4×C17—24no—
245C4⋊C4×C17—24no—
246C4⋊C4×C17—22no—
247C4⋊C4×C17—24no—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—22no—
250C4⋊C4×C17—24no—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—24no—
254C4⋊C4×C17C2×D414yes—
255C4⋊C4×C17C2×D412yes—
256C4⋊C4×C17C2414yes—
257C4⋊C4×C17C2412yes—
258C22⋊C4×C17—24no—
259C22⋊C4×C17—22no—
260C22⋊C4×C17—24no—
261C22⋊C4×C17—24no—
262C22⋊C4×C17—24no—
263C22⋊C4×C17—22no—
264C22⋊C4×C17—21no—
265C22⋊C4×C17—22no—
266C22⋊C4×C17—24no—
267C22⋊C4×C17C2×D414yes—
268C22⋊C4×C17C2×D414yes—
269C22⋊C4×C17C2×D412yes—
270C42×C17—22no—
271C42×C17—24no—
272C42×C17—21no—
273C42×C17—24no—
274C42×C17C2412yes—
275#61634C1711yesmaximal, characteristic, direct product factor, Sylow
276C23×C17—24no—
277C23×C17—21no—
278C23×C17—41no—
279C23×C17C22×D411yescharacteristic
280C23×C17C22×D412yes—
281C23×C17C22×D412yes—
282Q8×C17—24no—
283Q8×C17—22no—
284Q8×C17—24no—
285Q8×C17—24no—
286Q8×C17—24no—
287Q8×C17—22no—
288Q8×C17—41no—
289Q8×C17—48no—
290Q8×C17—44no—
291Q8×C17—42no—
292Q8×C17—82no—
293Q8×C17—82no—
294Q8×C17H(5,𝔽2)14yes—
295D4×C17—28no—
296D4×C17—22no—
297D4×C17—41no—
298D4×C17—42no—
299D4×C17—44no—
300D4×C17—42no—
301D4×C17—44no—
302C2×C4×C17—24no—
303C2×C4×C17—22no—
304C2×C4×C17—24no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—24no—
310C2×C4×C17—24no—
311C2×C4×C17—22no—
312C2×C4×C17—21no—
313C2×C4×C17—42no—
314C2×C4×C17—41no—
315C2×C4×C17—44no—
316C2×C4×C17—48no—
317C2×C4×C17—44no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17—44no—
321C2×C4×C17—82no—
322C2×C4×C17—82no—
323C2×C4×C17C22×D414yes—
324C2×C4×C17C22×D412yes—
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C22×D412yes—
327C2×C4×C17C2511yescharacteristic
328C8×C17—24no—
329C8×C17—24no—
330#3538C2×C1711yescharacteristic, complemented
331#3486C2×C1711yescharacteristic
332#3312C2×C1714yescomplemented
333#3300C2×C1714yescomplemented
334D4×Q16C2×C1714yescomplemented
335#3270C2×C1714yescomplemented
336#3223C2×C1712yescomplemented
337#3202C2×C1712yescomplemented
338#3190C2×C1712yescomplemented
339#3127C2×C1712yescomplemented
340#3011C2×C1712yescomplemented
341C2×#451C2×C1712yescomplemented
342#2977C2×C1711yescharacteristic, complemented
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—21no—
346C22×C17—22no—
347C22×C17—24no—
348C22×C17—22no—
349C22×C17—44no—
350C22×C17—41no—
351C22×C17—42no—
352C22×C17#57814yes—
353C22×C17C23×D411yescharacteristic
354C4×C17—24no—
355C4×C17—21no—
356C4×C17—22no—
357C4×C17—22no—
358C4×C17—24no—
359C4×C17—41no—
360C4×C17—42no—
361C4×C17—44no—
362C4×C17—44no—
363C4×C17—42no—
364C4×C17C2×H(5,𝔽2)12yes—
365C2×2−1+4C22×C1711yescharacteristic
366C23×Q8C22×C1711yescharacteristic
367C2×#137C22×C1712yescomplemented
368C22×Q16C22×C1714yes—
369C22×Q16C22×C1712yescomplemented
370#563—22no—
371#552C22×C1714yes—
372#551—22no—
373D4×Q8—22no—
374D4×Q8C22×C1714yes—
375D4×Q8C22×C1714yes—
376#548—22no—
377#548C22×C1714yes—
378#544—22no—
379#541C22×C1712yes—
380#539—22no—
381#536—22no—
382#536C22×C1711yescharacteristic
383#536C22×C1711yescharacteristic
384#536C22×C1712yes—
385#525—22no—
386#525C22×C1711yescharacteristic
387#525C22×C1711yescharacteristic
388C2×C22⋊Q8C22×C1712yes—
389#519C22×C1711yescharacteristic
390#497C22×C1712yescomplemented
391#494C22×C1712yescomplemented
392#491C22×C1712yescomplemented
393#488C22×C1712yescomplemented
394#485C22×C1714yes—
395#485C22×C1714yescomplemented
396#483C22×C1712yes—
397#480C22×C1712yes—
398#479C22×C1714yescomplemented
399#470C22×C1714yescomplemented
400#467C22×C1714yes—
401#467C22×C1714yescomplemented
402#465C22×C1714yes—
403#464C22×C1714yescomplemented
404#462C22×C1714yescomplemented
405#462C22×C1714yescomplemented
406#452C22×C1714yes—
407#452C22×C1714yescomplemented
408#451C22×C1714yes—
409#451C22×C1712yes—
410#451C22×C1714yes—
411#451C22×C1714yes—
412#451C22×C1714yes—
413#451C22×C1714yescomplemented
414#451C22×C1714yescomplemented
415#448C22×C1712yes—
416#441C22×C1714yescomplemented
417C4×Q16C22×C1714yescomplemented
418#435C22×C1714yes—
419C8×D4C22×C1714yes—
420#433C22×C1712yes—
421#419C22×C1712yescomplemented
422#416C22×C1712yescomplemented
423C2×#103C22×C1714yes—
424#408C22×C1712yes—
425C2×C22⋊C8C22×C1712yes—
426C2×C17—24no—
427C2×C17—42no—
428C2×C17—41no—
429C2×C17—81no—
430C2×C17#348411yescharacteristic
431C2×C17C2×#57812yes—
4322−1+4—44no—
433C2×#41—22no—
434C2×#41—21no—
435C2×#41C23×C1712yes—
436C2×#41C23×C1711yescharacteristic
437C2×#41C23×C1711yescharacteristic
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—22no—
441C22×Q8—44no—
442C22×Q8C23×C1711yescharacteristic
443C22×Q8C23×C1714yes—
444C22×Q8C23×C1712yes—
445C22×Q8C23×C1712yes—
446C22×Q8C23×C1711yescharacteristic
447C22×Q8C23×C1712yes—
448C23×C4—21no—
449C23×C4C23×C1711yescharacteristic
450#137—44no—
451C2×Q16—48no—
452C2×Q16—44no—
453C2×Q16C23×C1714yes—
454C2×Q16C23×C1714yes—
455C2×Q16C23×C1714yes—
456C2×Q16C23×C1714yes—
457C2×Q16C23×C1714yes—
458C2×SD16C23×C1714yes—
459C2×M16C23×C1712yes—
460C22×C8C23×C1714yes—
461C22×C8C23×C1712yes—
462C4⋊Q8—22no—
463C4⋊Q8—21no—
464C4⋊Q8—24no—
465C4⋊Q8—24no—
466C4⋊Q8C23×C1712yes—
467C4⋊Q8C23×C1712yes—
468#126—24no—
469#126—24no—
470#125—24no—
471#125—24no—
472#125C23×C1712yes—
473#124—21no—
474#124—22no—
475#124—24no—
476#124C23×C1712yes—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—24no—
481#123—21no—
482#123—22no—
483#123D4×C1712yes—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8—22no—
488C22⋊Q8—24no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8D4×C1712yes—
493C22⋊Q8C23×C1714yes—
494C22⋊Q8C23×C1714yes—
495C22⋊Q8C23×C1712yes—
496C22⋊Q8C23×C1714yes—
497C22⋊Q8C23×C1714yes—
498#121—24no—
499#121D4×C1712yes—
500#121C23×C1712yes—
501#120—21no—
502#120D4×C1712yes—
503C4×Q8—22no—
504C4×Q8C23×C1714yes—
505C4×Q8C23×C1714yes—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—22no—
509C4×D4—24no—
510C4×D4C23×C1714yes—
511#117—22no—
512#117—24no—
513#117C23×C1711yescharacteristic
514#117C23×C1712yes—
515#117C23×C1711yescharacteristic
516C2×C4⋊C4—22no—
517C2×C4⋊C4C23×C1712yes—
518C2×C22⋊C4—22no—
519#107C23×C1714yes—
520#106C23×C1714yes—
521C4⋊C8C23×C1714yes—
522#103C23×C1714yes—
523#103C23×C1714yes—
524#103C23×C1714yes—
525#103C23×C1714yes—
526#103C23×C1714yes—
527#103C23×C1714yes—
528#103C23×C1714yes—
529#102C23×C1714yes—
530C22⋊C8C23×C1714yes—
531C22⋊C8C23×C1712yes—
532C22⋊C8C23×C1712yes—
533C22⋊C8C23×C1714yes—
534#97C23×C1712yes—
535C4×C8C23×C1712yes—
536C17#6163411yescharacteristic, direct product factor, Sylow
537C24C2×D4×C1711yescharacteristic
538#41—24no—
539#41—42no—
540#41—42no—
541#41—42no—
542#41—48no—
543#41—44no—
544C2×Q8—24no—
545C2×Q8—21no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—28no—
552C2×Q8—24no—
553C2×Q8—44no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—48no—
561C2×Q8—44no—
562C2×Q8C2×D4×C1711yescharacteristic
563C2×Q8C24×C1712yes—
564C2×Q8C24×C1711yescharacteristic
565C2×Q8C24×C1714yes—
566C2×Q8C24×C1712yes—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4C2×D4×C1714yes—
571C2×D4C2×D4×C1712yes—
572C2×D4C2×D4×C1711yescharacteristic
573C2×D4C24×C1711yescharacteristic
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4C2×D4×C1712yes—
586C22×C4C2×D4×C1711yescharacteristic
587C22×C4C24×C1711yescharacteristic
588C22×C4C24×C1712yes—
589C22×C4C24×C1712yes—
590Q16—28no—
591Q16—28no—
592Q16—44no—
593Q16—44no—
594Q16—44no—
595SD16—44no—
596M16—42no—
597C2×C8—42no—
598C2×C8—44no—
599C2×C8C24×C1714yes—
600C2×C8C24×C1714yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4C2×D4×C1712yes—
613C4⋊C4C2×D4×C1714yes—
614C4⋊C4C24×C1714yes—
615C4⋊C4C24×C1712yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4C2×D4×C1712yes—
626C22⋊C4C2×D4×C1714yes—
627C22⋊C4C2×D4×C1714yes—
628C42—22no—
629C42—24no—
630C42—24no—
631C42—21no—
632C42C24×C1712yes—
633C23—24no—
634C23—21no—
635C23—41no—
636C23C22×D4×C1711yescharacteristic
637C23C22×D4×C1712yes—
638C23C22×D4×C1712yes—
639Q8—24no—
640Q8—22no—
641Q8—24no—
642Q8—24no—
643Q8—24no—
644Q8—22no—
645Q8—41no—
646Q8—48no—
647Q8—44no—
648Q8—42no—
649Q8—82no—
650Q8—82no—
651Q8C17×H(5,𝔽2)14yes—
652D4—28no—
653D4—22no—
654D4—41no—
655D4—42no—
656D4—44no—
657D4—42no—
658D4—44no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—44no—
673C2×C4—48no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C22×D4×C1714yes—
681C2×C4C22×D4×C1712yes—
682C2×C4C22×D4×C1711yescharacteristic
683C2×C4C22×D4×C1712yes—
684C2×C4C25×C1711yescharacteristic
685C8—24no—
686C8—24no—
687C22—22no—
688C22—22no—
689C22—21no—
690C22—22no—
691C22—24no—
692C22—22no—
693C22—44no—
694C22—41no—
695C22—42no—
696C22C17×#57814yes—
697C22C23×D4×C1711yescharacteristic
698C4—24no—
699C4—21no—
700C4—22no—
701C4—22no—
702C4—24no—
703C4—41no—
704C4—42no—
705C4—44no—
706C4—44no—
707C4—42no—
708C4C2×C17×H(5,𝔽2)12yes—
709C2—24no—
710C2—41no—
711C2—42no—
712C2—81no—
713C2C17×#348411yescharacteristic
714C2C2×C17×#57812yes—
subgroupG/H
center, socleC22×C17C23×D4
commutator, Frattini, cosocleC2×C4C25×C17
prime radicalC17×#3486C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C17×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3538C2semidirect
3. C17×#3312C2semidirect
4. C17×#3300C2semidirect
5. D4×Q16×C17C2semidirect
6. C17×#3270C2semidirect
7. C17×#3223C2semidirect
8. C17×#3202C2semidirect
9. C17×#3190C2semidirect
10. C17×#3127C2semidirect
11. C17×#3011C2semidirect
12. C2×C17×#451C2semidirect
13. C17×#2977C2semidirect
16. C2×C17×#137C22semidirect
18. C22×Q16×C17C22semidirect
39. C17×#497C22semidirect
40. C17×#494C22semidirect
41. C17×#491C22semidirect
42. C17×#488C22semidirect
44. C17×#485C22semidirect
47. C17×#479C22semidirect
48. C17×#470C22semidirect
50. C17×#467C22semidirect
52. C17×#464C22semidirect
53. C17×#462C22semidirect
54. C17×#462C22semidirect
56. C17×#452C22semidirect
62. C17×#451C22semidirect
63. C17×#451C22semidirect
65. C17×#441C22semidirect
66. C4×Q16×C17C22semidirect
70. C17×#419C22semidirect
71. C17×#416C22semidirect
275. #61634C17direct (N × H)
330. #3538C2×C17semidirect
332. #3312C2×C17semidirect
333. #3300C2×C17semidirect
334. D4×Q16C2×C17semidirect
335. #3270C2×C17semidirect
336. #3223C2×C17semidirect
337. #3202C2×C17semidirect
338. #3190C2×C17semidirect
339. #3127C2×C17semidirect
340. #3011C2×C17semidirect
341. C2×#451C2×C17semidirect
342. #2977C2×C17semidirect
367. C2×#137C22×C17semidirect
369. C22×Q16C22×C17semidirect
390. #497C22×C17semidirect
391. #494C22×C17semidirect
392. #491C22×C17semidirect
393. #488C22×C17semidirect
395. #485C22×C17semidirect
398. #479C22×C17semidirect
399. #470C22×C17semidirect
401. #467C22×C17semidirect
403. #464C22×C17semidirect
404. #462C22×C17semidirect
405. #462C22×C17semidirect
407. #452C22×C17semidirect
413. #451C22×C17semidirect
414. #451C22×C17semidirect
416. #441C22×C17semidirect
417. C4×Q16C22×C17semidirect
421. #419C22×C17semidirect
422. #416C22×C17semidirect
536. C17#61634direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35382
C17×#34862
C17×#33122
C17×#33002
D4×Q16×C172
C17×#32702
C17×#32232
C17×#32022
C17×#31902
C17×#31272
C17×#30112
C2×C17×#4512
C17×#29772
#6163417