Finite Group Databasebeta

← C17×#24464 #16882208

Subgroups — C17×#24464 #16882208

Order 4352.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3488C211yesmaximal, characteristic, complemented
2C17×#3055C211yesmaximal, characteristic, complemented
3C2×C17×#453C211yesmaximal, characteristic, complemented
4C17×#3006C211yesmaximal, characteristic, complemented
5C22×C17×#104C211yesmaximal, characteristic, complemented
6C17×#2856C211yesmaximal, characteristic, complemented
7C17×#2039C211yesmaximal, characteristic, complemented
8C17×#2037C211yesmaximal, characteristic, complemented
9C17×#2006C211yesmaximal, characteristic, complemented
10C17×#2002C211yesmaximal, characteristic, complemented
11C17×#1900C211yesmaximal, characteristic, complemented
12C17×#1896C211yesmaximal, characteristic, complemented
13C17×#1883C211yesmaximal, characteristic, complemented
14C17×#1859C211yesmaximal, characteristic, complemented
15C17×#1792C211yesmaximal, characteristic, complemented
16C2×C17×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C17C2211yescharacteristic
18C2×C17×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C17×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C17×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×M16×C17C2211yescharacteristic, complemented
22C17×#550—21no—
23C17×#548—21no—
24C17×#546—22no—
25C17×#546—21no—
26D42×C17—22no—
27D42×C17—21no—
28C17×#537—21no—
29C17×#537C2211yescharacteristic
30C17×#535—21no—
31C17×#535C2211yescharacteristic
32C2×C17×#127C2211yescharacteristic, complemented
33C17×#525—21no—
34C17×#525C2211yescharacteristic
35C2×C17×#121—21no—
36C2×C17×#121—22no—
37C2×C17×#121C2211yescharacteristic
38C2×C17×#121C2211yescharacteristic, complemented
39C17×#520C2211yescharacteristic
40C22×C42×C17C2211yescharacteristic, complemented
41C17×#469—21no—
42C17×#468—21no—
43C17×#466—21no—
44C17×#465—21no—
45C17×#453—24no—
46C17×#449—21no—
47C17×#449—21no—
48C17×#448—21no—
49C17×#447—21no—
50C17×#428C2211yescharacteristic, complemented
51C2×C17×#104—24no—
52C2×C17×#104C2211yescharacteristic
53C2×C17×#104C2211yescharacteristic
54C2×C17×#104C2211yescharacteristic, complemented
55C2×C17×#104C2211yescharacteristic, complemented
56C2×C17×#104C2211yescharacteristic, complemented
57C2×C17×#104C2211yescharacteristic, complemented
58C17×#418C2211yescharacteristic, complemented
59C17×#417C2211yescharacteristic
60C17×#417C2211yescharacteristic, complemented
61C17×#417C2211yescharacteristic, complemented
62C2×C17×#100C2211yescharacteristic, complemented
63C2×C17×#100C2211yescharacteristic, complemented
64C17×#407C2211yescharacteristic, complemented
65C17×#390—22no—
66C17×#390C2211yescharacteristic, complemented
67C17×#390C2211yescharacteristic, complemented
68C17×#384C2211yescharacteristic, complemented
69C17×#343C2211yescharacteristic, complemented
70C17×#343C2211yescharacteristic, complemented
71C17×#339C2211yescharacteristic, complemented
72C17×#339C2211yescharacteristic, complemented
73C17×H(5,𝔽2)—22no—
74C17×H(5,𝔽2)—22no—
75C17×H(5,𝔽2)—41no—
76C17×H(5,𝔽2)—41no—
77C2×#41×C17—21no—
78C2×#41×C17—21no—
79C2×#41×C17—21no—
80C2×#41×C17—21no—
81C2×#41×C17—22no—
82C2×#41×C17—22no—
83C2×#41×C17—41no—
84C2×#41×C17—41no—
85C2×#41×C17D411yescharacteristic, complemented
86C2×#41×C17D411yescharacteristic, complemented
87C2×#41×C17C2311yescharacteristic
88C2×#41×C17C2311yescharacteristic
89C2×#41×C17C2311yescharacteristic
90C22×Q8×C17D411yescharacteristic, complemented
91C22×D4×C17—21no—
92C22×D4×C17—22no—
93C22×D4×C17—22no—
94C22×D4×C17—21no—
95C22×D4×C17—21no—
96C22×D4×C17—21no—
97C22×D4×C17—22no—
98C22×D4×C17D412yes—
99C22×D4×C17D411yescharacteristic, complemented
100C22×D4×C17C2311yescharacteristic
101C22×D4×C17C2311yescharacteristic
102C23×C4×C17—21no—
103C23×C4×C17—21no—
104C23×C4×C17C2311yescharacteristic
105C17×AGL(1,ℤ/8)—22no—
106C17×AGL(1,ℤ/8)—22no—
107C17×AGL(1,ℤ/8)—22no—
108C17×AGL(1,ℤ/8)—41no—
109C17×AGL(1,ℤ/8)—41no—
110C17×AGL(1,ℤ/8)—41no—
111C2×SD16×C17—21no—
112C2×SD16×C17—21no—
113C2×SD16×C17—21no—
114C2×D8×C17—21no—
115C2×D8×C17—21no—
116C2×D8×C17—21no—
117C2×M16×C17—21no—
118C2×M16×C17—22no—
119C2×M16×C17—41no—
120C2×M16×C17C2311yescharacteristic
121C2×M16×C17C2311yescharacteristic
122C2×M16×C17C2311yescharacteristic
123C2×M16×C17C2311yescharacteristic
124C22×C8×C17—21no—
125C17×#127—22no—
126C17×#127—21no—
127C17×#127—22no—
128C17×#127—41no—
129C17×#124—22no—
130C17×#124—21no—
131C17×#123—22no—
132C17×#123—21no—
133C17×C22⋊Q8—22no—
134C17×C22⋊Q8—21no—
135C17×C22⋊Q8—21no—
136C17×C22⋊Q8D411yescharacteristic, complemented
137C17×C22⋊Q8D411yescharacteristic, complemented
138C17×#121—22no—
139C17×#121—22no—
140C17×#121—22no—
141C17×#121—22no—
142C17×#121—22no—
143C17×#121—21no—
144C17×#121—21no—
145C17×#121—21no—
146C17×#121—21no—
147C17×#121—21no—
148C17×#121—21no—
149C17×#121—22no—
150C17×#121—21no—
151C17×#121—21no—
152C17×#121—21no—
153C17×#121—21no—
154C17×#121—21no—
155C17×#121—21no—
156C17×#121—48no—
157C17×#121D411yescharacteristic, complemented
158C17×#121D411yescharacteristic, complemented
159C17×#120—22no—
160C17×#120—22no—
161C17×#120—22no—
162C17×#120—21no—
163C17×#120—22no—
164C4×Q8×C17—21no—
165C4×D4×C17—22no—
166C4×D4×C17—22no—
167C4×D4×C17—21no—
168C4×D4×C17—22no—
169C4×D4×C17—21no—
170C4×D4×C17—21no—
171C17×#117—21no—
172C17×#117C2311yescharacteristic
173C2×C4⋊C4×C17—21no—
174C2×C4⋊C4×C17—22no—
175C2×C4⋊C4×C17C2311yescharacteristic
176C2×C4⋊C4×C17C2311yescharacteristic
177C2×C22⋊C4×C17—22no—
178C2×C22⋊C4×C17—22no—
179C2×C22⋊C4×C17—22no—
180C2×C22⋊C4×C17—21no—
181C2×C22⋊C4×C17D412yes—
182C2×C42×C17—22no—
183C2×C42×C17—21no—
184C2×C42×C17—41no—
185C2×C42×C17C2311yescharacteristic
186C2×C42×C17C2311yescharacteristic
187C17×#107—21no—
188C17×#106—21no—
189C17×#104—22no—
190C17×#104—22no—
191C17×#104—22no—
192C17×#104—22no—
193C17×#104—41no—
194C17×#104D414yescomplemented
195C17×#103—21no—
196C17×#103—21no—
197C17×#103—21no—
198C17×#102—21no—
199C17×#102—21no—
200C17×#102—21no—
201C17×#102—21no—
202C17×#102—21no—
203C17×#100—22no—
204C17×#100—41no—
205C17×C22⋊C8—21no—
206C17×C22⋊C8—21no—
207C24×C17—22no—
208C24×C17—21no—
209C24×C17—21no—
210C24×C17C2×D411yescharacteristic
211C24×C17C2×D412yes—
212#41×C17—21no—
213#41×C17—21no—
214#41×C17—22no—
215#41×C17—22no—
216#41×C17—21no—
217#41×C17—21no—
218#41×C17—21no—
219#41×C17—21no—
220#41×C17—21no—
221#41×C17—21no—
222#41×C17—21no—
223#41×C17—21no—
224#41×C17—42no—
225#41×C17—42no—
226#41×C17—41no—
227#41×C17—41no—
228#41×C17—42no—
229#41×C17—42no—
230#41×C17—42no—
231#41×C17—42no—
232#41×C17—42no—
233#41×C17—42no—
234#41×C17C2×D412yes—
235#41×C17#4112yes—
236C2×Q8×C17—21no—
237C2×Q8×C17—22no—
238C2×Q8×C17—41no—
239C2×Q8×C17C2×D411yescharacteristic
240C2×Q8×C17C2×D411yescharacteristic
241C2×Q8×C17C2×D411yescharacteristic
242C2×D4×C17—21no—
243C2×D4×C17—22no—
244C2×D4×C17—22no—
245C2×D4×C17—22no—
246C2×D4×C17—21no—
247C2×D4×C17—21no—
248C2×D4×C17—22no—
249C2×D4×C17—21no—
250C2×D4×C17—21no—
251C2×D4×C17—21no—
252C2×D4×C17—22no—
253C2×D4×C17—22no—
254C2×D4×C17—22no—
255C2×D4×C17—21no—
256C2×D4×C17—22no—
257C2×D4×C17—21no—
258C2×D4×C17—21no—
259C2×D4×C17—21no—
260C2×D4×C17—21no—
261C2×D4×C17—21no—
262C2×D4×C17—21no—
263C2×D4×C17—21no—
264C2×D4×C17—21no—
265C2×D4×C17—21no—
266C2×D4×C17—21no—
267C2×D4×C17—21no—
268C2×D4×C17—21no—
269C2×D4×C17—21no—
270C2×D4×C17—41no—
271C2×D4×C17—42no—
272C2×D4×C17—42no—
273C2×D4×C17—44no—
274C2×D4×C17—44no—
275C2×D4×C17—44no—
276C2×D4×C17—42no—
277C2×D4×C17—42no—
278C2×D4×C17—44no—
279C2×D4×C17—44no—
280C2×D4×C17—42no—
281C2×D4×C17—42no—
282C2×D4×C17—44no—
283C2×D4×C17—44no—
284C2×D4×C17—41no—
285C2×D4×C17—41no—
286C2×D4×C17—84no—
287C2×D4×C17C2×D411yescharacteristic
288C2×D4×C17C2×D411yescharacteristic
289C2×D4×C17C2×D411yescharacteristic
290C22×C4×C17—21no—
291C22×C4×C17—21no—
292C22×C4×C17—21no—
293C22×C4×C17—21no—
294C22×C4×C17—21no—
295C22×C4×C17—21no—
296C22×C4×C17—22no—
297C22×C4×C17—24no—
298C22×C4×C17—21no—
299C22×C4×C17—21no—
300C22×C4×C17—22no—
301C22×C4×C17—21no—
302C22×C4×C17—21no—
303C22×C4×C17—21no—
304C22×C4×C17—21no—
305C22×C4×C17—21no—
306C22×C4×C17—42no—
307C22×C4×C17—42no—
308C22×C4×C17—42no—
309C22×C4×C17—42no—
310C22×C4×C17C2×D411yescharacteristic
311C22×C4×C17C2×D411yescharacteristic
312C22×C4×C17C2×D411yescharacteristic
313C22×C4×C17C2×D411yescharacteristic
314C22×C4×C17C2×D411yescharacteristic
315C22×C4×C17C2×D412yes—
316C22×C4×C17C2411yescharacteristic
317SD16×C17—42no—
318SD16×C17—42no—
319SD16×C17—42no—
320D8×C17—42no—
321D8×C17—42no—
322D8×C17—42no—
323M16×C17—21no—
324M16×C17—21no—
325M16×C17—21no—
326M16×C17—21no—
327M16×C17—21no—
328M16×C17—21no—
329M16×C17—21no—
330M16×C17—42no—
331M16×C17C2×D412yescomplemented
332C2×C8×C17—21no—
333C2×C8×C17—21no—
334C2×C8×C17—21no—
335C2×C8×C17—21no—
336C2×C8×C17—42no—
337C4⋊C4×C17—22no—
338C4⋊C4×C17—22no—
339C4⋊C4×C17—21no—
340C4⋊C4×C17—21no—
341C4⋊C4×C17—21no—
342C4⋊C4×C17—21no—
343C4⋊C4×C17—21no—
344C4⋊C4×C17—21no—
345C4⋊C4×C17—44no—
346C4⋊C4×C17C2×D411yescharacteristic
347C4⋊C4×C17C2×D411yescharacteristic
348C22⋊C4×C17—22no—
349C22⋊C4×C17—22no—
350C22⋊C4×C17—22no—
351C22⋊C4×C17—22no—
352C22⋊C4×C17—22no—
353C22⋊C4×C17—21no—
354C22⋊C4×C17—21no—
355C22⋊C4×C17—21no—
356C22⋊C4×C17—22no—
357C22⋊C4×C17—21no—
358C22⋊C4×C17—21no—
359C22⋊C4×C17—22no—
360C22⋊C4×C17—44no—
361C22⋊C4×C17—44no—
362C22⋊C4×C17—41no—
363C22⋊C4×C17—41no—
364C42×C17—22no—
365C42×C17—21no—
366C42×C17—21no—
367C42×C17—21no—
368C42×C17—21no—
369C42×C17—42no—
370C42×C17C2×D412yescomplemented
371#24464C1711yesmaximal, characteristic, direct product factor, Sylow
372C23×C17—21no—
373C23×C17—21no—
374C23×C17—21no—
375C23×C17—22no—
376C23×C17—22no—
377C23×C17—21no—
378C23×C17—21no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—41no—
382C23×C17—42no—
383C23×C17—44no—
384C23×C17—42no—
385C23×C17—42no—
386C23×C17—42no—
387C23×C17—42no—
388C23×C17—42no—
389C23×C17—41no—
390C23×C17—41no—
391C23×C17—41no—
392C23×C17—81no—
393C23×C17—82no—
394C23×C17—82no—
395C23×C17#12011yescharacteristic
396C23×C17#12011yescharacteristic
397C23×C17C22×D411yescharacteristic
398Q8×C17—21no—
399Q8×C17—21no—
400Q8×C17—21no—
401Q8×C17—21no—
402Q8×C17—21no—
403Q8×C17—42no—
404Q8×C17#12112yescomplemented
405D4×C17—22no—
406D4×C17—22no—
407D4×C17—21no—
408D4×C17—21no—
409D4×C17—21no—
410D4×C17—21no—
411D4×C17—21no—
412D4×C17—42no—
413D4×C17—42no—
414D4×C17—44no—
415D4×C17—42no—
416D4×C17—44no—
417D4×C17—41no—
418D4×C17—41no—
419D4×C17—41no—
420D4×C17—41no—
421D4×C17—44no—
422D4×C17—42no—
423D4×C17—41no—
424D4×C17—41no—
425D4×C17—41no—
426D4×C17—41no—
427D4×C17—41no—
428D4×C17—41no—
429D4×C17—41no—
430D4×C17—41no—
431D4×C17—88no—
432D4×C17—81no—
433D4×C17—82no—
434D4×C17—82no—
435D4×C17—82no—
436D4×C17—82no—
437D4×C17—82no—
438D4×C17—82no—
439D4×C17#12112yescomplemented
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—21no—
443C2×C4×C17—22no—
444C2×C4×C17—21no—
445C2×C4×C17—21no—
446C2×C4×C17—21no—
447C2×C4×C17—21no—
448C2×C4×C17—21no—
449C2×C4×C17—21no—
450C2×C4×C17—21no—
451C2×C4×C17—21no—
452C2×C4×C17—22no—
453C2×C4×C17—21no—
454C2×C4×C17—21no—
455C2×C4×C17—22no—
456C2×C4×C17—22no—
457C2×C4×C17—21no—
458C2×C4×C17—22no—
459C2×C4×C17—21no—
460C2×C4×C17—21no—
461C2×C4×C17—21no—
462C2×C4×C17—42no—
463C2×C4×C17—42no—
464C2×C4×C17—42no—
465C2×C4×C17—48no—
466C2×C4×C17—44no—
467C2×C4×C17—41no—
468C2×C4×C17—41no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—41no—
472C2×C4×C17—41no—
473C2×C4×C17—42no—
474C2×C4×C17—42no—
475C2×C4×C17—41no—
476C2×C4×C17—82no—
477C2×C4×C17#12011yescharacteristic
478C2×C4×C17#12011yescharacteristic
479C2×C4×C17C22×D411yescharacteristic
480C2×C4×C17C22×D411yescharacteristic
481C2×C4×C17C22×D411yescharacteristic
482C2×C4×C17C2×#4111yescharacteristic
483C2×C4×C17H(5,𝔽2)11yescharacteristic
484C2×C4×C17H(5,𝔽2)11yescharacteristic
485C8×C17—22no—
486C8×C17—41no—
487C8×C17—41no—
488C8×C17—41no—
489#3488C2×C1711yescharacteristic, complemented
490#3055C2×C1711yescharacteristic, complemented
491C2×#453C2×C1711yescharacteristic, complemented
492#3006C2×C1711yescharacteristic, complemented
493C22×#104C2×C1711yescharacteristic, complemented
494#2856C2×C1711yescharacteristic, complemented
495#2039C2×C1711yescharacteristic, complemented
496#2037C2×C1711yescharacteristic, complemented
497#2006C2×C1711yescharacteristic, complemented
498#2002C2×C1711yescharacteristic, complemented
499#1900C2×C1711yescharacteristic, complemented
500#1896C2×C1711yescharacteristic, complemented
501#1883C2×C1711yescharacteristic, complemented
502#1859C2×C1711yescharacteristic, complemented
503#1792C2×C1711yescharacteristic, complemented
504C22×C17—21no—
505C22×C17—21no—
506C22×C17—21no—
507C22×C17—21no—
508C22×C17—21no—
509C22×C17—22no—
510C22×C17—21no—
511C22×C17—21no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—41no—
515C22×C17—41no—
516C22×C17—41no—
517C22×C17—41no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—41no—
521C22×C17—41no—
522C22×C17—41no—
523C22×C17—42no—
524C22×C17—41no—
525C22×C17—84no—
526C22×C17—82no—
527C22×C17—82no—
528C22×C17—82no—
529C22×C17—82no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17—81no—
533C22×C17—164no—
534C22×C17#45312yescomplemented
535C22×C17C2×#12011yescharacteristic
536C22×C17D4211yescharacteristic
537C22×C17#54611yescharacteristic
538C4×C17—24no—
539C4×C17—21no—
540C4×C17—21no—
541C4×C17—22no—
542C4×C17—42no—
543C4×C17—41no—
544C4×C17—41no—
545C4×C17—42no—
546C4×C17—41no—
547C4×C17—41no—
548C4×C17—81no—
549C4×C17C2×#12111yescharacteristic
550C4×C17#53411yescharacteristic
551C4×C17D4211yescharacteristic
552C4×C17#54611yescharacteristic
553C2×H(5,𝔽2)C22×C1711yescharacteristic
554C22×#41C22×C1711yescharacteristic
555C2×AGL(1,ℤ/8)C22×C1711yescharacteristic
556C2×AGL(1,ℤ/8)C22×C1711yescharacteristic, complemented
557C2×AGL(1,ℤ/8)C22×C1711yescharacteristic, complemented
558C22×M16C22×C1711yescharacteristic, complemented
559#550—21no—
560#548—21no—
561#546—21no—
562#546—22no—
563D42—22no—
564D42—21no—
565#537—21no—
566#537C22×C1711yescharacteristic
567#535—21no—
568#535C22×C1711yescharacteristic
569C2×#127C22×C1711yescharacteristic, complemented
570#525—21no—
571#525C22×C1711yescharacteristic
572C2×#121—21no—
573C2×#121—22no—
574C2×#121C22×C1711yescharacteristic
575C2×#121C22×C1711yescharacteristic, complemented
576#520C22×C1711yescharacteristic
577C22×C42C22×C1711yescharacteristic, complemented
578#469—21no—
579#468—21no—
580#466—21no—
581#465—21no—
582#453—24no—
583#449—21no—
584#449—21no—
585#448—21no—
586#447—21no—
587#428C22×C1711yescharacteristic, complemented
588C2×#104—24no—
589C2×#104C22×C1711yescharacteristic
590C2×#104C22×C1711yescharacteristic
591C2×#104C22×C1711yescharacteristic, complemented
592C2×#104C22×C1711yescharacteristic, complemented
593C2×#104C22×C1711yescharacteristic, complemented
594C2×#104C22×C1711yescharacteristic, complemented
595#418C22×C1711yescharacteristic, complemented
596#417C22×C1711yescharacteristic
597#417C22×C1711yescharacteristic, complemented
598#417C22×C1711yescharacteristic, complemented
599C2×#100C22×C1711yescharacteristic, complemented
600C2×#100C22×C1711yescharacteristic, complemented
601#407C22×C1711yescharacteristic, complemented
602#390—22no—
603#390C22×C1711yescharacteristic, complemented
604#390C22×C1711yescharacteristic, complemented
605#384C22×C1711yescharacteristic, complemented
606#343C22×C1711yescharacteristic, complemented
607#343C22×C1711yescharacteristic, complemented
608#339C22×C1711yescharacteristic, complemented
609#339C22×C1711yescharacteristic, complemented
610C2×C17—21no—
611C2×C17—21no—
612C2×C17—22no—
613C2×C17—41no—
614C2×C17—42no—
615C2×C17—81no—
616C2×C17—82no—
617C2×C17—81no—
618C2×C17—161no—
619C2×C17#241011yescharacteristic
620C2×C17C2×#45311yescharacteristic
621C2×C17#301811yescharacteristic
622H(5,𝔽2)—22no—
623H(5,𝔽2)—22no—
624H(5,𝔽2)—41no—
625H(5,𝔽2)—41no—
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—22no—
631C2×#41—22no—
632C2×#41—41no—
633C2×#41—41no—
634C2×#41D4×C1711yescharacteristic, complemented
635C2×#41D4×C1711yescharacteristic, complemented
636C2×#41C23×C1711yescharacteristic
637C2×#41C23×C1711yescharacteristic
638C2×#41C23×C1711yescharacteristic
639C22×Q8D4×C1711yescharacteristic, complemented
640C22×D4—21no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—21no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—22no—
647C22×D4D4×C1712yes—
648C22×D4D4×C1711yescharacteristic, complemented
649C22×D4C23×C1711yescharacteristic
650C22×D4C23×C1711yescharacteristic
651C23×C4—21no—
652C23×C4—21no—
653C23×C4C23×C1711yescharacteristic
654AGL(1,ℤ/8)—22no—
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—41no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×D8—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×M16—21no—
667C2×M16—22no—
668C2×M16—41no—
669C2×M16C23×C1711yescharacteristic
670C2×M16C23×C1711yescharacteristic
671C2×M16C23×C1711yescharacteristic
672C2×M16C23×C1711yescharacteristic
673C22×C8—21no—
674#127—22no—
675#127—21no—
676#127—22no—
677#127—41no—
678#124—22no—
679#124—21no—
680#123—22no—
681#123—21no—
682C22⋊Q8—22no—
683C22⋊Q8—21no—
684C22⋊Q8—21no—
685C22⋊Q8D4×C1711yescharacteristic, complemented
686C22⋊Q8D4×C1711yescharacteristic, complemented
687#121—22no—
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—21no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—22no—
699#121—21no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—48no—
706#121D4×C1711yescharacteristic, complemented
707#121D4×C1711yescharacteristic, complemented
708#120—22no—
709#120—22no—
710#120—22no—
711#120—21no—
712#120—22no—
713C4×Q8—21no—
714C4×D4—22no—
715C4×D4—22no—
716C4×D4—21no—
717C4×D4—22no—
718C4×D4—21no—
719C4×D4—21no—
720#117—21no—
721#117C23×C1711yescharacteristic
722C2×C4⋊C4—21no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4C23×C1711yescharacteristic
725C2×C4⋊C4C23×C1711yescharacteristic
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4D4×C1712yes—
731C2×C42—22no—
732C2×C42—21no—
733C2×C42—41no—
734C2×C42C23×C1711yescharacteristic
735C2×C42C23×C1711yescharacteristic
736#107—21no—
737#106—21no—
738#104—22no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—41no—
743#104D4×C1714yescomplemented
744#103—21no—
745#103—21no—
746#103—21no—
747#102—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#100—22no—
753#100—41no—
754C22⋊C8—21no—
755C22⋊C8—21no—
756C17#2446411yescharacteristic, direct product factor, Sylow
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C1711yescharacteristic
761C24C2×D4×C1712yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C1712yes—
785#41#41×C1712yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C1711yescharacteristic
790C2×Q8C2×D4×C1711yescharacteristic
791C2×Q8C2×D4×C1711yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C1711yescharacteristic
838C2×D4C2×D4×C1711yescharacteristic
839C2×D4C2×D4×C1711yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C1711yescharacteristic
861C22×C4C2×D4×C1711yescharacteristic
862C22×C4C2×D4×C1711yescharacteristic
863C22×C4C2×D4×C1711yescharacteristic
864C22×C4C2×D4×C1711yescharacteristic
865C22×C4C2×D4×C1712yes—
866C22×C4C24×C1711yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C1712yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C1711yescharacteristic
897C4⋊C4C2×D4×C1711yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C1712yescomplemented
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23C17×#12011yescharacteristic
945C23C17×#12011yescharacteristic
946C23C22×D4×C1711yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8C17×#12112yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—82no—
982D4—81no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4C17×#12112yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4C17×#12011yescharacteristic
1027C2×C4C17×#12011yescharacteristic
1028C2×C4C22×D4×C1711yescharacteristic
1029C2×C4C22×D4×C1711yescharacteristic
1030C2×C4C22×D4×C1711yescharacteristic
1031C2×C4C2×#41×C1711yescharacteristic
1032C2×C4C17×H(5,𝔽2)11yescharacteristic
1033C2×C4C17×H(5,𝔽2)11yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—42no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—42no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C17×#45312yescomplemented
1069C22C2×C17×#12011yescharacteristic
1070C22D42×C1711yescharacteristic
1071C22C17×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×C17×#12111yescharacteristic
1084C4C17×#53411yescharacteristic
1085C4D42×C1711yescharacteristic
1086C4C17×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C17×#241011yescharacteristic
1097C2C2×C17×#45311yescharacteristic
1098C2C17×#301811yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3488C2semidirect
2. C17×#3055C2semidirect
3. C2×C17×#453C2semidirect
4. C17×#3006C2semidirect
5. C22×C17×#104C2semidirect
6. C17×#2856C2semidirect
7. C17×#2039C2semidirect
8. C17×#2037C2semidirect
9. C17×#2006C2semidirect
10. C17×#2002C2semidirect
11. C17×#1900C2semidirect
12. C17×#1896C2semidirect
13. C17×#1883C2semidirect
14. C17×#1859C2semidirect
15. C17×#1792C2semidirect
19. C2×C17×AGL(1,ℤ/8)C22semidirect
20. C2×C17×AGL(1,ℤ/8)C22semidirect
21. C22×M16×C17C22semidirect
32. C2×C17×#127C22semidirect
38. C2×C17×#121C22semidirect
40. C22×C42×C17C22semidirect
50. C17×#428C22semidirect
54. C2×C17×#104C22semidirect
55. C2×C17×#104C22semidirect
56. C2×C17×#104C22semidirect
57. C2×C17×#104C22semidirect
58. C17×#418C22semidirect
60. C17×#417C22semidirect
61. C17×#417C22semidirect
62. C2×C17×#100C22semidirect
63. C2×C17×#100C22semidirect
64. C17×#407C22semidirect
66. C17×#390C22semidirect
67. C17×#390C22semidirect
68. C17×#384C22semidirect
69. C17×#343C22semidirect
70. C17×#343C22semidirect
71. C17×#339C22semidirect
72. C17×#339C22semidirect
85. C2×#41×C17D4semidirect
86. C2×#41×C17D4semidirect
90. C22×Q8×C17D4semidirect
99. C22×D4×C17D4semidirect
136. C17×C22⋊Q8D4semidirect
137. C17×C22⋊Q8D4semidirect
157. C17×#121D4semidirect
158. C17×#121D4semidirect
194. C17×#104D4semidirect
331. M16×C17C2×D4semidirect
370. C42×C17C2×D4semidirect
371. #24464C17direct (N × H)
404. Q8×C17#121semidirect
439. D4×C17#121semidirect
489. #3488C2×C17semidirect
490. #3055C2×C17semidirect
491. C2×#453C2×C17semidirect
492. #3006C2×C17semidirect
493. C22×#104C2×C17semidirect
494. #2856C2×C17semidirect
495. #2039C2×C17semidirect
496. #2037C2×C17semidirect
497. #2006C2×C17semidirect
498. #2002C2×C17semidirect
499. #1900C2×C17semidirect
500. #1896C2×C17semidirect
501. #1883C2×C17semidirect
502. #1859C2×C17semidirect
503. #1792C2×C17semidirect
534. C22×C17#453semidirect
556. C2×AGL(1,ℤ/8)C22×C17semidirect
557. C2×AGL(1,ℤ/8)C22×C17semidirect
558. C22×M16C22×C17semidirect
569. C2×#127C22×C17semidirect
575. C2×#121C22×C17semidirect
577. C22×C42C22×C17semidirect
587. #428C22×C17semidirect
591. C2×#104C22×C17semidirect
592. C2×#104C22×C17semidirect
593. C2×#104C22×C17semidirect
594. C2×#104C22×C17semidirect
595. #418C22×C17semidirect
597. #417C22×C17semidirect
598. #417C22×C17semidirect
599. C2×#100C22×C17semidirect
600. C2×#100C22×C17semidirect
601. #407C22×C17semidirect
603. #390C22×C17semidirect
604. #390C22×C17semidirect
605. #384C22×C17semidirect
606. #343C22×C17semidirect
607. #343C22×C17semidirect
608. #339C22×C17semidirect
609. #339C22×C17semidirect
634. C2×#41D4×C17semidirect
635. C2×#41D4×C17semidirect
639. C22×Q8D4×C17semidirect
648. C22×D4D4×C17semidirect
685. C22⋊Q8D4×C17semidirect
686. C22⋊Q8D4×C17semidirect
706. #121D4×C17semidirect
707. #121D4×C17semidirect
743. #104D4×C17semidirect
756. C17#24464direct (N × H)
881. M16C2×D4×C17semidirect
920. C42C2×D4×C17semidirect
953. Q8C17×#121semidirect
988. D4C17×#121semidirect
1068. C22C17×#453semidirect

Maximal subgroups

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

subgroupindex
C17×#34882
C17×#30552
C2×C17×#4532
C17×#30062
C22×C17×#1042
C17×#28562
C17×#20392
C17×#20372
C17×#20062
C17×#20022
C17×#19002
C17×#18962
C17×#18832
C17×#18592
C17×#17922
#2446417