Finite Group Databasebeta

← C17×#14645 #16872389

Subgroups — C17×#14645 #16872389

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#394C211yesmaximal, characteristic
2C17×#1445C211yesmaximal, characteristic, complemented
3C17×#1443C211yesmaximal, characteristic, complemented
4C17×#1441C211yesmaximal, characteristic, complemented
5C17×#1440C211yesmaximal, characteristic, complemented
6C17×#1440C211yesmaximal, characteristic, complemented
7C17×#1439C211yesmaximal, characteristic, complemented
8C17×#1439C211yesmaximal, characteristic, complemented
9C17×#1439C211yesmaximal, characteristic, complemented
10C17×#1439C211yesmaximal, characteristic, complemented
11C17×#1438C211yesmaximal, characteristic
12C17×#1438C211yesmaximal, characteristic
13C17×#1437C211yesmaximal, characteristic, complemented
14C17×#1437C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C17C2211yescharacteristic
17C22×C4⋊C4×C17C2211yescharacteristic
18C22×C4⋊C4×C17C2211yescharacteristic
19C22×C4⋊C4×C17C2211yescharacteristic
20C22×C22⋊C4×C17C2211yescharacteristic
21C22×C22⋊C4×C17C2211yescharacteristic
22C22×C22⋊C4×C17C2211yescharacteristic
23C22×C22⋊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×C42×C17C2211yescharacteristic
33C17×#394C418yescomplemented
34C2×C17×#95C2211yescharacteristic
35C2×C17×#95C2211yescharacteristic
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C2×C17×#95C2211yescharacteristic
42C2×C17×#95C2211yescharacteristic
43C2×C17×#95C2211yescharacteristic
44C2×C17×#95C2211yescharacteristic
45C2×C17×#95C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C25×C17C2311yescharacteristic
53C25×C17C2311yescharacteristic
54C22×D4×C17—41no—
55C22×D4×C17—41no—
56C22×D4×C17—41no—
57C22×D4×C17—41no—
58C22×D4×C17—41no—
59C22×D4×C17—41no—
60C22×D4×C17C2×C414yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17—22no—
75C2×C4⋊C4×C17—41no—
76C2×C4⋊C4×C17—41no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17—41no—
79C2×C4⋊C4×C17—41no—
80C2×C4⋊C4×C17—41no—
81C2×C4⋊C4×C17—41no—
82C2×C4⋊C4×C17C2×C414yes—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17—41no—
90C2×C22⋊C4×C17—41no—
91C2×C22⋊C4×C17—41no—
92C2×C22⋊C4×C17—41no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17—41no—
95C2×C22⋊C4×C17—41no—
96C2×C22⋊C4×C17—41no—
97C2×C22⋊C4×C17—41no—
98C2×C22⋊C4×C17—41no—
99C2×C22⋊C4×C17—41no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17—41no—
102C2×C22⋊C4×C17—41no—
103C2×C22⋊C4×C17—41no—
104C2×C22⋊C4×C17—41no—
105C2×C22⋊C4×C17—41no—
106C2×C22⋊C4×C17—41no—
107C2×C22⋊C4×C17—41no—
108C2×C22⋊C4×C17—41no—
109C2×C22⋊C4×C17—41no—
110C2×C22⋊C4×C17—41no—
111C2×C22⋊C4×C17—41no—
112C2×C22⋊C4×C17—41no—
113C2×C22⋊C4×C17—41no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17C2×C414yes—
116C2×C22⋊C4×C17C2×C414yes—
117C2×C22⋊C4×C17C2×C414yes—
118C2×C22⋊C4×C17C2×C414yes—
119C2×C42×C17—41no—
120C2×C42×C17—41no—
121C2×C42×C17—41no—
122C17×#95—22no—
123C17×#95—41no—
124C17×#95—41no—
125C17×#95—41no—
126C17×#95—41no—
127C17×#95—41no—
128C17×#95—41no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132C17×#95—41no—
133C17×#95—41no—
134C17×#95—41no—
135C17×#95—41no—
136C17×#95—41no—
137C17×#95—41no—
138C17×#95—41no—
139C17×#95C2×C414yes—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
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×C17C22×C412yes—
169C24×C17C22×C412yes—
170C24×C17C2411yescharacteristic
171C2×D4×C17—44no—
172C2×D4×C17—44no—
173C2×D4×C17—44no—
174C2×D4×C17—44no—
175C2×D4×C17—44no—
176C2×D4×C17—44no—
177C2×D4×C17—44no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
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×C17C22×C412yes—
263C22×C4×C17C22×C412yes—
264C22×C4×C17C22×C412yes—
265C22×C4×C17C22×C412yes—
266C22×C4×C17C22×C412yes—
267C22×C4×C17#4112yes—
268C22×C4×C17#4112yes—
269C4⋊C4×C17—44no—
270C4⋊C4×C17—44no—
271C4⋊C4×C17—44no—
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×C17—44no—
280C22⋊C4×C17—44no—
281C22⋊C4×C17—44no—
282C22⋊C4×C17—44no—
283C22⋊C4×C17—44no—
284C42×C17—44no—
285#14645C1711yesmaximal, characteristic, direct product factor, Sylow
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
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×C17C23×C411yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17H(5,𝔽2)11yescharacteristic
360C23×C17H(5,𝔽2)11yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C17H(5,𝔽2)11yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C17H(5,𝔽2)11yescharacteristic
367C23×C17H(5,𝔽2)11yescharacteristic
368C23×C17H(5,𝔽2)11yescharacteristic
369C23×C172−1+411yescharacteristic
370C23×C172−1+411yescharacteristic
371D4×C17—416no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
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×#394C2×C1711yescharacteristic
464#1445C2×C1711yescharacteristic, complemented
465#1443C2×C1711yescharacteristic, complemented
466#1441C2×C1711yescharacteristic, complemented
467#1440C2×C1711yescharacteristic, complemented
468#1440C2×C1711yescharacteristic, complemented
469#1439C2×C1711yescharacteristic, complemented
470#1439C2×C1711yescharacteristic, complemented
471#1439C2×C1711yescharacteristic, complemented
472#1439C2×C1711yescharacteristic, complemented
473#1438C2×C1711yescharacteristic
474#1438C2×C1711yescharacteristic
475#1437C2×C1711yescharacteristic, complemented
476#1437C2×C1711yescharacteristic, complemented
477#1436C2×C1711yescharacteristic, complemented
478C22×C17—42no—
479C22×C17—42no—
480C22×C17—42no—
481C22×C17—42no—
482C22×C17—42no—
483C22×C17—42no—
484C22×C17—42no—
485C22×C17—42no—
486C22×C17—42no—
487C22×C17—42no—
488C22×C17—42no—
489C22×C17—42no—
490C22×C17—42no—
491C22×C17—42no—
492C22×C17—81no—
493C22×C17—81no—
494C22×C17—81no—
495C22×C17—81no—
496C22×C17—81no—
497C22×C17—81no—
498C22×C17—81no—
499C22×C17—81no—
500C22×C17—81no—
501C22×C17—81no—
502C22×C17—81no—
503C22×C17—81no—
504C22×C17—81no—
505C22×C17—81no—
506C22×C17—81no—
507C22×C17—81no—
508C22×C17C4×#4111yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#51811yescharacteristic
511C22×C17#51811yescharacteristic
512C22×C17#51811yescharacteristic
513C22×C17#52011yescharacteristic
514C22×C17#52011yescharacteristic
515C22×C17#53811yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#53811yescharacteristic
519C22×C17#53811yescharacteristic
520C22×C17#53911yescharacteristic
521C22×C17#54011yescharacteristic
522C22×C17#54011yescharacteristic
523C22×C17#54011yescharacteristic
524C22×C17#54211yescharacteristic
525C22×C17#54211yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17#56011yescharacteristic
528C22×C17#56011yescharacteristic
529C22×C17#56011yescharacteristic
530C22×C17#56011yescharacteristic
531C22×C17#56011yescharacteristic
532C22×C17#56011yescharacteristic
533C22×C17#56011yescharacteristic
534C22×C17#56011yescharacteristic
535C22×C17H(3,𝔽4)11yescharacteristic
536C22×C17#56211yescharacteristic
537C22×C17#56211yescharacteristic
538C22×C17#56211yescharacteristic
539C22×C17#56211yescharacteristic
540C22×C17#56211yescharacteristic
541C22×C17#56211yescharacteristic
542C22×C17#56311yescharacteristic
543C4×C17—42no—
544C4×C17—42no—
545C4×C17—42no—
546C4×C17—42no—
547C4×C17—42no—
548C4×C17—42no—
549C4×C17—42no—
550C4×C17—81no—
551C4×C17—81no—
552C4×C17—81no—
553C4×C17—81no—
554C4×C17—81no—
555C4×C17—81no—
556C23×D4C22×C1711yescharacteristic
557C22×C4⋊C4C22×C1711yescharacteristic
558C22×C4⋊C4C22×C1711yescharacteristic
559C22×C4⋊C4C22×C1711yescharacteristic
560C22×C22⋊C4C22×C1711yescharacteristic
561C22×C22⋊C4C22×C1711yescharacteristic
562C22×C22⋊C4C22×C1711yescharacteristic
563C22×C22⋊C4C22×C1711yescharacteristic
564C22×C22⋊C4C22×C1711yescharacteristic
565C22×C22⋊C4C22×C1711yescharacteristic
566C22×C22⋊C4C22×C1711yescharacteristic
567C22×C22⋊C4C22×C1711yescharacteristic
568C22×C22⋊C4C22×C1711yescharacteristic
569C22×C22⋊C4C22×C1711yescharacteristic
570C22×C22⋊C4C22×C1711yescharacteristic
571C22×C22⋊C4C22×C1711yescharacteristic
572C22×C42C22×C1711yescharacteristic
573#394C4×C1718yescomplemented
574C2×#95C22×C1711yescharacteristic
575C2×#95C22×C1711yescharacteristic
576C2×#95C22×C1711yescharacteristic
577C2×#95C22×C1711yescharacteristic
578C2×#95C22×C1711yescharacteristic
579C2×#95C22×C1711yescharacteristic
580C2×#95C22×C1711yescharacteristic
581C2×#95C22×C1711yescharacteristic
582C2×#95C22×C1711yescharacteristic
583C2×#95C22×C1711yescharacteristic
584C2×#95C22×C1711yescharacteristic
585C2×#95C22×C1711yescharacteristic
586C2×#95C22×C1711yescharacteristic
587C2×#95C22×C1711yescharacteristic
588C2×#95C22×C1711yescharacteristic
589C2×#95C22×C1711yescharacteristic
590C2×#95C22×C1711yescharacteristic
591C2×#95C22×C1711yescharacteristic
592C2×C17—82no—
593C2×C17—82no—
594C2×C17#233311yescharacteristic
595C2×C17#233511yescharacteristic
596C2×C17#233711yescharacteristic
597C2×C17#237511yescharacteristic
598C2×C17#237611yescharacteristic
599C2×C17#237711yescharacteristic
600C2×C17#237711yescharacteristic
601C2×C17#282511yescharacteristic
602C2×C17#282611yescharacteristic
603C2×C17#282811yescharacteristic
604C2×C17#282911yescharacteristic
605C2×C17#282911yescharacteristic
606C2×C17#282911yescharacteristic
607C2×C17#283211yescharacteristic
608C2×C17#283711yescharacteristic
609C25C23×C1711yescharacteristic
610C25C23×C1711yescharacteristic
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4C2×C4×C1714yes—
618C23×C4C23×C1711yescharacteristic
619C23×C4C23×C1711yescharacteristic
620C23×C4C23×C1711yescharacteristic
621C23×C4C23×C1711yescharacteristic
622C23×C4C23×C1711yescharacteristic
623C23×C4C23×C1711yescharacteristic
624C23×C4C23×C1711yescharacteristic
625C23×C4C23×C1711yescharacteristic
626C23×C4C23×C1711yescharacteristic
627C23×C4C23×C1711yescharacteristic
628C23×C4C23×C1711yescharacteristic
629C23×C4C23×C1711yescharacteristic
630C23×C4C23×C1711yescharacteristic
631C2×C4⋊C4—22no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4C2×C4×C1714yes—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4C2×C4×C1714yes—
673C2×C22⋊C4C2×C4×C1714yes—
674C2×C22⋊C4C2×C4×C1714yes—
675C2×C22⋊C4C2×C4×C1714yes—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42—41no—
679#95—22no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95C2×C4×C1714yes—
697C17#1464511yescharacteristic, direct product factor, Sylow
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24C22×C4×C1712yes—
727C24C22×C4×C1712yes—
728C24C24×C1711yescharacteristic
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
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×C4C22×C4×C1712yes—
821C22×C4C22×C4×C1712yes—
822C22×C4C22×C4×C1712yes—
823C22×C4C22×C4×C1712yes—
824C22×C4C22×C4×C1712yes—
825C22×C4#41×C1712yes—
826C22×C4#41×C1712yes—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C42—44no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23C23×C4×C1711yescharacteristic
914C23C2×#41×C1711yescharacteristic
915C23C2×#41×C1711yescharacteristic
916C23C17×H(5,𝔽2)11yescharacteristic
917C23C17×H(5,𝔽2)11yescharacteristic
918C23C17×H(5,𝔽2)11yescharacteristic
919C23C17×H(5,𝔽2)11yescharacteristic
920C23C17×H(5,𝔽2)11yescharacteristic
921C23C17×H(5,𝔽2)11yescharacteristic
922C23C17×H(5,𝔽2)11yescharacteristic
923C23C17×H(5,𝔽2)11yescharacteristic
924C23C17×H(5,𝔽2)11yescharacteristic
925C23C17×H(5,𝔽2)11yescharacteristic
926C23C17×2−1+411yescharacteristic
927C23C17×2−1+411yescharacteristic
928D4—416no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22C4×#41×C1711yescharacteristic
1051C22C17×#51811yescharacteristic
1052C22C17×#51811yescharacteristic
1053C22C17×#51811yescharacteristic
1054C22C17×#51811yescharacteristic
1055C22C17×#52011yescharacteristic
1056C22C17×#52011yescharacteristic
1057C22C17×#53811yescharacteristic
1058C22C17×#53811yescharacteristic
1059C22C17×#53811yescharacteristic
1060C22C17×#53811yescharacteristic
1061C22C17×#53811yescharacteristic
1062C22C17×#53911yescharacteristic
1063C22C17×#54011yescharacteristic
1064C22C17×#54011yescharacteristic
1065C22C17×#54011yescharacteristic
1066C22C17×#54211yescharacteristic
1067C22C17×#54211yescharacteristic
1068C22C17×#54211yescharacteristic
1069C22C17×#56011yescharacteristic
1070C22C17×#56011yescharacteristic
1071C22C17×#56011yescharacteristic
1072C22C17×#56011yescharacteristic
1073C22C17×#56011yescharacteristic
1074C22C17×#56011yescharacteristic
1075C22C17×#56011yescharacteristic
1076C22C17×#56011yescharacteristic
1077C22C17×H(3,𝔽4)11yescharacteristic
1078C22C17×#56211yescharacteristic
1079C22C17×#56211yescharacteristic
1080C22C17×#56211yescharacteristic
1081C22C17×#56211yescharacteristic
1082C22C17×#56211yescharacteristic
1083C22C17×#56211yescharacteristic
1084C22C17×#56311yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C2—82no—
1099C2—82no—
1100C2C17×#233311yescharacteristic
1101C2C17×#233511yescharacteristic
1102C2C17×#233711yescharacteristic
1103C2C17×#237511yescharacteristic
1104C2C17×#237611yescharacteristic
1105C2C17×#237711yescharacteristic
1106C2C17×#237711yescharacteristic
1107C2C17×#282511yescharacteristic
1108C2C17×#282611yescharacteristic
1109C2C17×#282811yescharacteristic
1110C2C17×#282911yescharacteristic
1111C2C17×#282911yescharacteristic
1112C2C17×#282911yescharacteristic
1113C2C17×#283211yescharacteristic
1114C2C17×#283711yescharacteristic
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
2. C17×#1445C2semidirect
3. C17×#1443C2semidirect
4. C17×#1441C2semidirect
5. C17×#1440C2semidirect
6. C17×#1440C2semidirect
7. C17×#1439C2semidirect
8. C17×#1439C2semidirect
9. C17×#1439C2semidirect
10. C17×#1439C2semidirect
13. C17×#1437C2semidirect
14. C17×#1437C2semidirect
15. C17×#1436C2semidirect
33. C17×#394C4semidirect
285. #14645C17direct (N × H)
464. #1445C2×C17semidirect
465. #1443C2×C17semidirect
466. #1441C2×C17semidirect
467. #1440C2×C17semidirect
468. #1440C2×C17semidirect
469. #1439C2×C17semidirect
470. #1439C2×C17semidirect
471. #1439C2×C17semidirect
472. #1439C2×C17semidirect
475. #1437C2×C17semidirect
476. #1437C2×C17semidirect
477. #1436C2×C17semidirect
573. #394C4×C17semidirect
697. C17#14645direct (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
C17×#14452
C17×#14432
C17×#14412
C17×#14402
C17×#14392
C17×#14382
C17×#14372
C17×#14362
#1464517