Finite Group Databasebeta

← C17×#14518 #16872262

Subgroups — C17×#14518 #16872262

Order 4352.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#394C211yesmaximal, characteristic
2C2×C17×#390C211yesmaximal, characteristic
3C2×C17×#389C211yesmaximal, characteristic, complemented
4C2×C17×#388C211yesmaximal, characteristic, complemented
5C2×C17×#386C211yesmaximal, characteristic
6C2×C17×#385C211yesmaximal, characteristic, complemented
7C2×C17×#385C211yesmaximal, characteristic, complemented
8C17×#1444C211yesmaximal, characteristic, complemented
9C17×#1440C211yesmaximal, characteristic, complemented
10C17×#1439C211yesmaximal, characteristic, complemented
11C17×#1439C211yesmaximal, characteristic, complemented
12C17×#1439C211yesmaximal, characteristic, complemented
13C17×#1437C211yesmaximal, characteristic, complemented
14C17×#1436C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C17C2211yescharacteristic
17C24×C4×C17C2211yescharacteristic
18C22×C4⋊C4×C17C2211yescharacteristic
19C22×C4⋊C4×C17C2211yescharacteristic
20C22×C4⋊C4×C17C2211yescharacteristic
21C22×C4⋊C4×C17C2211yescharacteristic
22C22×C4⋊C4×C17C2211yescharacteristic
23C22×C4⋊C4×C17C2211yescharacteristic
24C22×C22⋊C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17C2211yescharacteristic
26C22×C22⋊C4×C17C2211yescharacteristic
27C22×C22⋊C4×C17C2211yescharacteristic
28C22×C22⋊C4×C17C2211yescharacteristic
29C22×C22⋊C4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C22×C22⋊C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C17×#394C418yescomplemented
38C17×#390—24no—
39C17×#389—24no—
40C17×#388—24no—
41C17×#386—24no—
42C17×#385—24no—
43C17×#385—24no—
44C2×C17×#95C2211yescharacteristic
45C2×C17×#95C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C25×C17C2311yescharacteristic
60C22×D4×C17—22no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—41no—
65C22×D4×C17—41no—
66C22×D4×C17C2×C414yes—
67C23×C4×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—22no—
70C23×C4×C17—41no—
71C23×C4×C17—41no—
72C23×C4×C17—41no—
73C23×C4×C17—41no—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17—22no—
90C2×C4⋊C4×C17—22no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—41no—
99C2×C4⋊C4×C17—41no—
100C2×C4⋊C4×C17—41no—
101C2×C4⋊C4×C17—41no—
102C2×C4⋊C4×C17—41no—
103C2×C4⋊C4×C17—41no—
104C2×C4⋊C4×C17C2×C414yescomplemented
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—22no—
107C2×C22⋊C4×C17—22no—
108C2×C22⋊C4×C17—22no—
109C2×C22⋊C4×C17—22no—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—22no—
115C2×C22⋊C4×C17—22no—
116C2×C22⋊C4×C17—22no—
117C2×C22⋊C4×C17—22no—
118C2×C22⋊C4×C17—22no—
119C2×C22⋊C4×C17—22no—
120C2×C22⋊C4×C17—22no—
121C2×C22⋊C4×C17—41no—
122C2×C22⋊C4×C17—41no—
123C2×C22⋊C4×C17—41no—
124C2×C22⋊C4×C17—41no—
125C2×C22⋊C4×C17—41no—
126C2×C22⋊C4×C17—41no—
127C2×C22⋊C4×C17—41no—
128C2×C22⋊C4×C17—41no—
129C2×C22⋊C4×C17—41no—
130C2×C22⋊C4×C17—41no—
131C2×C22⋊C4×C17—41no—
132C2×C22⋊C4×C17—41no—
133C2×C22⋊C4×C17C2×C414yes—
134C2×C22⋊C4×C17C2×C414yes—
135C2×C22⋊C4×C17C2×C414yescomplemented
136C2×C22⋊C4×C17C2×C414yescomplemented
137C2×C22⋊C4×C17D414yes—
138C2×C42×C17—22no—
139C2×C42×C17—22no—
140C2×C42×C17—22no—
141C2×C42×C17—22no—
142C2×C42×C17—41no—
143C2×C42×C17—41no—
144C17×#95—22no—
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—22no—
148C17×#95—22no—
149C17×#95—22no—
150C17×#95—22no—
151C17×#95—41no—
152C17×#95—41no—
153C17×#95—41no—
154C17×#95—41no—
155C17×#95C2×C414yescomplemented
156C17×#95D414yes—
157C17×#95D414yescomplemented
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17C22×C412yes—
185C24×C17C22×C412yes—
186C24×C17C2×D412yes—
187C24×C17#4112yes—
188C24×C17C2411yescharacteristic
189C2×D4×C17—28no—
190C2×D4×C17—28no—
191C2×D4×C17—44no—
192C2×D4×C17—44no—
193C2×D4×C17—44no—
194C2×D4×C17—44no—
195C2×D4×C17—44no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17—21no—
242C22×C4×C17—21no—
243C22×C4×C17—21no—
244C22×C4×C17—21no—
245C22×C4×C17—21no—
246C22×C4×C17—21no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—21no—
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—21no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—21no—
263C22×C4×C17—21no—
264C22×C4×C17—21no—
265C22×C4×C17—21no—
266C22×C4×C17—21no—
267C22×C4×C17—21no—
268C22×C4×C17—21no—
269C22×C4×C17—21no—
270C22×C4×C17—21no—
271C22×C4×C17—21no—
272C22×C4×C17—44no—
273C22×C4×C17—44no—
274C22×C4×C17—44no—
275C22×C4×C17—44no—
276C22×C4×C17—44no—
277C22×C4×C17—44no—
278C22×C4×C17—44no—
279C22×C4×C17C22×C412yes—
280C22×C4×C17C22×C412yes—
281C22×C4×C17C22×C412yes—
282C22×C4×C17C22×C412yes—
283C22×C4×C17C22×C412yes—
284C22×C4×C17C2×D412yes—
285C22×C4×C17C2×D412yes—
286C22×C4×C17C2×D412yes—
287C22×C4×C17C2×D412yes—
288C22×C4×C17C2×D412yes—
289C22×C4×C17C2×D412yes—
290C22×C4×C17C2×D412yes—
291C22×C4×C17C2×D412yes—
292C22×C4×C17#4112yes—
293C22×C4×C17#4112yes—
294C4⋊C4×C17—28no—
295C4⋊C4×C17—44no—
296C4⋊C4×C17—44no—
297C4⋊C4×C17—44no—
298C4⋊C4×C17—44no—
299C4⋊C4×C17—44no—
300C22⋊C4×C17—28no—
301C22⋊C4×C17—28no—
302C22⋊C4×C17—28no—
303C22⋊C4×C17—44no—
304C22⋊C4×C17—44no—
305C22⋊C4×C17—44no—
306C22⋊C4×C17—44no—
307C22⋊C4×C17—44no—
308C22⋊C4×C17—44no—
309C22⋊C4×C17—44no—
310C22⋊C4×C17—44no—
311C42×C17—44no—
312C42×C17—44no—
313#14518C1711yesmaximal, characteristic, direct product factor, Sylow
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17C4×D414yes—
384C23×C17C23×C411yescharacteristic
385C23×C17C22×D411yescharacteristic
386C23×C17C22×D411yescharacteristic
387C23×C17C22×D411yescharacteristic
388C23×C17C2×#4111yescharacteristic
389C23×C17C2×#4111yescharacteristic
390C23×C17C2×#4111yescharacteristic
391C23×C17H(5,𝔽2)11yescharacteristic
392C23×C17H(5,𝔽2)11yescharacteristic
393C23×C17H(5,𝔽2)11yescharacteristic
394C23×C17H(5,𝔽2)11yescharacteristic
395C23×C17H(5,𝔽2)11yescharacteristic
396C23×C172−1+411yescharacteristic
397C23×C172−1+411yescharacteristic
398C23×C172−1+411yescharacteristic
399D4×C17—416no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—416no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
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—41no—
474C2×C4×C17—41no—
475C2×C4×C17—41no—
476C2×C4×C17—41no—
477C2×C4×C17—41no—
478C2×C4×C17—41no—
479C2×C4×C17—41no—
480C2×C4×C17—41no—
481C2×C4×C17—41no—
482C2×C4×C17—41no—
483C2×C4×C17—41no—
484C2×C4×C17—41no—
485C2×C4×C17—41no—
486C2×C4×C17—41no—
487C2×C4×C17—41no—
488C2×C4×C17—41no—
489C2×C4×C17—41no—
490C2×C4×C17C4×D414yes—
491C2×C4×C17C4×D414yes—
492C2×#394C2×C1711yescharacteristic
493C2×#390C2×C1711yescharacteristic
494C2×#389C2×C1711yescharacteristic, complemented
495C2×#388C2×C1711yescharacteristic, complemented
496C2×#386C2×C1711yescharacteristic
497C2×#385C2×C1711yescharacteristic, complemented
498C2×#385C2×C1711yescharacteristic, complemented
499#1444C2×C1711yescharacteristic, complemented
500#1440C2×C1711yescharacteristic, complemented
501#1439C2×C1711yescharacteristic, complemented
502#1439C2×C1711yescharacteristic, complemented
503#1439C2×C1711yescharacteristic, complemented
504#1437C2×C1711yescharacteristic, complemented
505#1436C2×C1711yescharacteristic, complemented
506#1434C2×C1711yescharacteristic, complemented
507C22×C17—24no—
508C22×C17—24no—
509C22×C17—24no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—81no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17—81no—
533C22×C17—81no—
534C22×C17—81no—
535C22×C17—81no—
536C22×C17—81no—
537C22×C17C2×C4×D411yescharacteristic
538C22×C17C2×C4×D411yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17#51811yescharacteristic
541C22×C17#52011yescharacteristic
542C22×C17#52011yescharacteristic
543C22×C17#52011yescharacteristic
544C22×C17#53411yescharacteristic
545C22×C17#53511yescharacteristic
546C22×C17#53511yescharacteristic
547C22×C17#53611yescharacteristic
548C22×C17#53611yescharacteristic
549C22×C17#53711yescharacteristic
550C22×C17#53911yescharacteristic
551C22×C17#53911yescharacteristic
552C22×C17#54011yescharacteristic
553C22×C17#54211yescharacteristic
554C22×C17#54211yescharacteristic
555C22×C17#54211yescharacteristic
556C22×C17D4211yescharacteristic
557C22×C17D4211yescharacteristic
558C22×C17D4211yescharacteristic
559C22×C17#54611yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54711yescharacteristic
562C22×C17#54711yescharacteristic
563C22×C17#54811yescharacteristic
564C22×C17#54811yescharacteristic
565C22×C17#55111yescharacteristic
566C22×C17#55311yescharacteristic
567C22×C17#55311yescharacteristic
568C22×C17#56011yescharacteristic
569C22×C17#56211yescharacteristic
570C22×C17#56211yescharacteristic
571C22×C17#56311yescharacteristic
572C4×C17—24no—
573C4×C17—24no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—42no—
578C4×C17—42no—
579C4×C17—42no—
580C4×C17—42no—
581C4×C17—42no—
582C4×C17—42no—
583C4×C17—81no—
584C4×C17—81no—
585C23×D4C22×C1711yescharacteristic
586C24×C4C22×C1711yescharacteristic
587C22×C4⋊C4C22×C1711yescharacteristic
588C22×C4⋊C4C22×C1711yescharacteristic
589C22×C4⋊C4C22×C1711yescharacteristic
590C22×C4⋊C4C22×C1711yescharacteristic
591C22×C4⋊C4C22×C1711yescharacteristic
592C22×C4⋊C4C22×C1711yescharacteristic
593C22×C22⋊C4C22×C1711yescharacteristic
594C22×C22⋊C4C22×C1711yescharacteristic
595C22×C22⋊C4C22×C1711yescharacteristic
596C22×C22⋊C4C22×C1711yescharacteristic
597C22×C22⋊C4C22×C1711yescharacteristic
598C22×C22⋊C4C22×C1711yescharacteristic
599C22×C22⋊C4C22×C1711yescharacteristic
600C22×C22⋊C4C22×C1711yescharacteristic
601C22×C22⋊C4C22×C1711yescharacteristic
602C22×C22⋊C4C22×C1711yescharacteristic
603C22×C22⋊C4C22×C1711yescharacteristic
604C22×C42C22×C1711yescharacteristic
605C22×C42C22×C1711yescharacteristic
606#394C4×C1718yescomplemented
607#390—24no—
608#389—24no—
609#388—24no—
610#386—24no—
611#385—24no—
612#385—24no—
613C2×#95C22×C1711yescharacteristic
614C2×#95C22×C1711yescharacteristic
615C2×#95C22×C1711yescharacteristic
616C2×#95C22×C1711yescharacteristic
617C2×#95C22×C1711yescharacteristic
618C2×#95C22×C1711yescharacteristic
619C2×#95C22×C1711yescharacteristic
620C2×#95C22×C1711yescharacteristic
621C2×#95C22×C1711yescharacteristic
622C2×#95C22×C1711yescharacteristic
623C2×#95C22×C1711yescharacteristic
624C2×#95C22×C1711yescharacteristic
625C2×#95C22×C1711yescharacteristic
626C2×#95C22×C1711yescharacteristic
627C2×C17—44no—
628C2×C17—82no—
629C2×C17#232211yescharacteristic
630C2×C17#232411yescharacteristic
631C2×C17#232611yescharacteristic
632C2×C17#235811yescharacteristic
633C2×C17#236111yescharacteristic
634C2×C17#236111yescharacteristic
635C2×C17#237611yescharacteristic
636C2×C17#266911yescharacteristic
637C2×C17#267211yescharacteristic
638C2×C17#267411yescharacteristic
639C2×C17#268111yescharacteristic
640C2×C17#270111yescharacteristic
641C2×C17#271111yescharacteristic
642C2×C17#272311yescharacteristic
643C2×C17#275711yescharacteristic
644C25C23×C1711yescharacteristic
645C25C23×C1711yescharacteristic
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4C2×C4×C1714yes—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4C23×C1711yescharacteristic
661C23×C4C23×C1711yescharacteristic
662C23×C4C23×C1711yescharacteristic
663C23×C4C23×C1711yescharacteristic
664C23×C4C23×C1711yescharacteristic
665C23×C4C23×C1711yescharacteristic
666C23×C4C23×C1711yescharacteristic
667C23×C4C23×C1711yescharacteristic
668C23×C4C23×C1711yescharacteristic
669C23×C4C23×C1711yescharacteristic
670C23×C4C23×C1711yescharacteristic
671C23×C4C23×C1711yescharacteristic
672C23×C4C23×C1711yescharacteristic
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4C2×C4×C1714yescomplemented
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4C2×C4×C1714yes—
720C2×C22⋊C4C2×C4×C1714yes—
721C2×C22⋊C4C2×C4×C1714yescomplemented
722C2×C22⋊C4C2×C4×C1714yescomplemented
723C2×C22⋊C4D4×C1714yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—41no—
729C2×C42—41no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—41no—
738#95—41no—
739#95—41no—
740#95—41no—
741#95C2×C4×C1714yescomplemented
742#95D4×C1714yes—
743#95D4×C1714yescomplemented
744C17#1451811yescharacteristic, direct product factor, Sylow
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24C22×C4×C1712yes—
772C24C22×C4×C1712yes—
773C24C2×D4×C1712yes—
774C24#41×C1712yes—
775C24C24×C1711yescharacteristic
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4C22×C4×C1712yes—
867C22×C4C22×C4×C1712yes—
868C22×C4C22×C4×C1712yes—
869C22×C4C22×C4×C1712yes—
870C22×C4C22×C4×C1712yes—
871C22×C4C2×D4×C1712yes—
872C22×C4C2×D4×C1712yes—
873C22×C4C2×D4×C1712yes—
874C22×C4C2×D4×C1712yes—
875C22×C4C2×D4×C1712yes—
876C22×C4C2×D4×C1712yes—
877C22×C4C2×D4×C1712yes—
878C22×C4C2×D4×C1712yes—
879C22×C4#41×C1712yes—
880C22×C4#41×C1712yes—
881C4⋊C4—28no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—44no—
899C42—44no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23C4×D4×C1714yes—
970C23C23×C4×C1711yescharacteristic
971C23C22×D4×C1711yescharacteristic
972C23C22×D4×C1711yescharacteristic
973C23C22×D4×C1711yescharacteristic
974C23C2×#41×C1711yescharacteristic
975C23C2×#41×C1711yescharacteristic
976C23C2×#41×C1711yescharacteristic
977C23C17×H(5,𝔽2)11yescharacteristic
978C23C17×H(5,𝔽2)11yescharacteristic
979C23C17×H(5,𝔽2)11yescharacteristic
980C23C17×H(5,𝔽2)11yescharacteristic
981C23C17×H(5,𝔽2)11yescharacteristic
982C23C17×2−1+411yescharacteristic
983C23C17×2−1+411yescharacteristic
984C23C17×2−1+411yescharacteristic
985D4—416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—416no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C4×D4×C1714yes—
1077C2×C4C4×D4×C1714yes—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×C4×D4×C1711yescharacteristic
1109C22C2×C4×D4×C1711yescharacteristic
1110C22C2×C4×D4×C1711yescharacteristic
1111C22C17×#51811yescharacteristic
1112C22C17×#52011yescharacteristic
1113C22C17×#52011yescharacteristic
1114C22C17×#52011yescharacteristic
1115C22C17×#53411yescharacteristic
1116C22C17×#53511yescharacteristic
1117C22C17×#53511yescharacteristic
1118C22C17×#53611yescharacteristic
1119C22C17×#53611yescharacteristic
1120C22C17×#53711yescharacteristic
1121C22C17×#53911yescharacteristic
1122C22C17×#53911yescharacteristic
1123C22C17×#54011yescharacteristic
1124C22C17×#54211yescharacteristic
1125C22C17×#54211yescharacteristic
1126C22C17×#54211yescharacteristic
1127C22D42×C1711yescharacteristic
1128C22D42×C1711yescharacteristic
1129C22D42×C1711yescharacteristic
1130C22C17×#54611yescharacteristic
1131C22C17×#54611yescharacteristic
1132C22C17×#54711yescharacteristic
1133C22C17×#54711yescharacteristic
1134C22C17×#54811yescharacteristic
1135C22C17×#54811yescharacteristic
1136C22C17×#55111yescharacteristic
1137C22C17×#55311yescharacteristic
1138C22C17×#55311yescharacteristic
1139C22C17×#56011yescharacteristic
1140C22C17×#56211yescharacteristic
1141C22C17×#56211yescharacteristic
1142C22C17×#56311yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C2—44no—
1157C2—82no—
1158C2C17×#232211yescharacteristic
1159C2C17×#232411yescharacteristic
1160C2C17×#232611yescharacteristic
1161C2C17×#235811yescharacteristic
1162C2C17×#236111yescharacteristic
1163C2C17×#236111yescharacteristic
1164C2C17×#237611yescharacteristic
1165C2C17×#266911yescharacteristic
1166C2C17×#267211yescharacteristic
1167C2C17×#267411yescharacteristic
1168C2C17×#268111yescharacteristic
1169C2C17×#270111yescharacteristic
1170C2C17×#271111yescharacteristic
1171C2C17×#272311yescharacteristic
1172C2C17×#275711yescharacteristic
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
3. C2×C17×#389C2semidirect
4. C2×C17×#388C2semidirect
6. C2×C17×#385C2semidirect
7. C2×C17×#385C2semidirect
8. C17×#1444C2semidirect
9. C17×#1440C2semidirect
10. C17×#1439C2semidirect
11. C17×#1439C2semidirect
12. C17×#1439C2semidirect
13. C17×#1437C2semidirect
14. C17×#1436C2semidirect
15. C17×#1434C2semidirect
37. C17×#394C4semidirect
104. C2×C4⋊C4×C17C2×C4semidirect
135. C2×C22⋊C4×C17C2×C4semidirect
136. C2×C22⋊C4×C17C2×C4semidirect
155. C17×#95C2×C4semidirect
157. C17×#95D4semidirect
313. #14518C17direct (N × H)
494. C2×#389C2×C17semidirect
495. C2×#388C2×C17semidirect
497. C2×#385C2×C17semidirect
498. C2×#385C2×C17semidirect
499. #1444C2×C17semidirect
500. #1440C2×C17semidirect
501. #1439C2×C17semidirect
502. #1439C2×C17semidirect
503. #1439C2×C17semidirect
504. #1437C2×C17semidirect
505. #1436C2×C17semidirect
506. #1434C2×C17semidirect
606. #394C4×C17semidirect
690. C2×C4⋊C4C2×C4×C17semidirect
721. C2×C22⋊C4C2×C4×C17semidirect
722. C2×C22⋊C4C2×C4×C17semidirect
741. #95C2×C4×C17semidirect
743. #95D4×C17semidirect
744. C17#14518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3942
C2×C17×#3902
C2×C17×#3892
C2×C17×#3882
C2×C17×#3862
C2×C17×#3852
C17×#14442
C17×#14402
C17×#14392
C17×#14372
C17×#14362
C17×#14342
#1451817