Finite Group Databasebeta

← C17×#16513 #16874257

Subgroups — C17×#16513 #16874257

Order 4352.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#397C211yesmaximal, characteristic, complemented
2C2×C17×#396C211yesmaximal, characteristic, complemented
3C2×C17×#394C211yesmaximal, characteristic
4C2×C17×#386C211yesmaximal, characteristic
5C2×C17×#385C211yesmaximal, characteristic, complemented
6C2×C17×#380C211yesmaximal, characteristic, complemented
7C17×#1442C211yesmaximal, characteristic, complemented
8C17×#1441C211yesmaximal, characteristic, complemented
9C17×#1441C211yesmaximal, characteristic, complemented
10C17×#1441C211yesmaximal, characteristic, complemented
11C17×#1440C211yesmaximal, characteristic, complemented
12C17×#1440C211yesmaximal, characteristic, complemented
13C17×#1439C211yesmaximal, characteristic, complemented
14C17×#1439C211yesmaximal, characteristic, complemented
15C17×#1438C211yesmaximal, characteristic
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
35C17×#397—24no—
36C17×#396—24no—
37C17×#394—24no—
38C17×#386—24no—
39C17×#385—24no—
40C17×#380—24no—
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
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C25×C17C2311yescharacteristic
58C25×C17C2311yescharacteristic
59C22×D4×C17—22no—
60C22×D4×C17—22no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—41no—
65C22×D4×C17—41no—
66C23×C4×C17—22no—
67C23×C4×C17—22no—
68C23×C4×C17—41no—
69C23×C4×C17—41no—
70C23×C4×C17—41no—
71C23×C4×C17—41no—
72C23×C4×C17D414yes—
73C23×C4×C17C2311yescharacteristic
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
86C2×C4⋊C4×C17—22no—
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—41no—
96C2×C4⋊C4×C17—41no—
97C2×C4⋊C4×C17—41no—
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×C17D414yescomplemented
104C2×C22⋊C4×C17—22no—
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—22no—
122C2×C22⋊C4×C17—22no—
123C2×C22⋊C4×C17—22no—
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×C17—41no—
134C2×C22⋊C4×C17—41no—
135C2×C22⋊C4×C17—41no—
136C2×C22⋊C4×C17D414yes—
137C17×#95—22no—
138C17×#95—22no—
139C17×#95—22no—
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—22no—
143C17×#95—22no—
144C17×#95—22no—
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—22no—
148C17×#95—22no—
149C17×#95—41no—
150C17×#95—41no—
151C17×#95—41no—
152C17×#95—41no—
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×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×C17C2×D412yes—
180C24×C17C2×D412yes—
181C24×C17#4112yes—
182C24×C17#4112yes—
183C24×C17C2411yescharacteristic
184C2×D4×C17—28no—
185C2×D4×C17—44no—
186C2×D4×C17—44no—
187C2×D4×C17—44no—
188C2×D4×C17—44no—
189C2×D4×C17—44no—
190C2×D4×C17—44no—
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—28no—
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—21no—
273C22×C4×C17—21no—
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×C17C2×D412yes—
281C22×C4×C17C2×D412yes—
282C22×C4×C17C2×D412yes—
283C22×C4×C17C2×D412yes—
284C22×C4×C17C2×D412yes—
285C22×C4×C17C2×D412yes—
286C22×C4×C17C2×D412yes—
287C22×C4×C17#4112yes—
288C22×C4×C17#4112yes—
289C4⋊C4×C17—44no—
290C4⋊C4×C17—44no—
291C4⋊C4×C17—44no—
292C4⋊C4×C17—44no—
293C4⋊C4×C17—44no—
294C4⋊C4×C17—44no—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C22⋊C4×C17—44no—
299C22⋊C4×C17—44no—
300C22⋊C4×C17—44no—
301C22⋊C4×C17—44no—
302C22⋊C4×C17—44no—
303C22⋊C4×C17—44no—
304C22⋊C4×C17—44no—
305C22⋊C4×C17—44no—
306#16513C1711yesmaximal, characteristic, direct product factor, Sylow
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
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—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×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#12114yes—
377C23×C17C22×D411yescharacteristic
378C23×C17C22×D411yescharacteristic
379C23×C17C22×D411yescharacteristic
380C23×C17C2×#4111yescharacteristic
381C23×C17C2×#4111yescharacteristic
382C23×C17C2×#4111yescharacteristic
383C23×C17C2×#4111yescharacteristic
384C23×C17H(5,𝔽2)11yescharacteristic
385C23×C17H(5,𝔽2)11yescharacteristic
386C23×C17H(5,𝔽2)11yescharacteristic
387C23×C17H(5,𝔽2)11yescharacteristic
388C23×C17H(5,𝔽2)11yescharacteristic
389C23×C172−1+411yescharacteristic
390C23×C172−1+411yescharacteristic
391C23×C172−1+411yescharacteristic
392D4×C17—416no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
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—416no—
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×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#12114yes—
485C2×#397C2×C1711yescharacteristic, complemented
486C2×#396C2×C1711yescharacteristic, complemented
487C2×#394C2×C1711yescharacteristic
488C2×#386C2×C1711yescharacteristic
489C2×#385C2×C1711yescharacteristic, complemented
490C2×#380C2×C1711yescharacteristic, complemented
491#1442C2×C1711yescharacteristic, complemented
492#1441C2×C1711yescharacteristic, complemented
493#1441C2×C1711yescharacteristic, complemented
494#1441C2×C1711yescharacteristic, complemented
495#1440C2×C1711yescharacteristic, complemented
496#1440C2×C1711yescharacteristic, complemented
497#1439C2×C1711yescharacteristic, complemented
498#1439C2×C1711yescharacteristic, complemented
499#1438C2×C1711yescharacteristic
500C22×C17—24no—
501C22×C17—24no—
502C22×C17—24no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—42no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
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—81no—
523C22×C17—81no—
524C22×C17—81no—
525C22×C17—81no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17—81no—
530C22×C17C2×#12111yescharacteristic
531C22×C17C2×#12111yescharacteristic
532C22×C17#52511yescharacteristic
533C22×C17#53411yescharacteristic
534C22×C17#53411yescharacteristic
535C22×C17#53411yescharacteristic
536C22×C17#53511yescharacteristic
537C22×C17#53611yescharacteristic
538C22×C17#53711yescharacteristic
539C22×C17#53711yescharacteristic
540C22×C17#53711yescharacteristic
541C22×C17#53811yescharacteristic
542C22×C17#53811yescharacteristic
543C22×C17#53811yescharacteristic
544C22×C17#53911yescharacteristic
545C22×C17#53911yescharacteristic
546C22×C17#53911yescharacteristic
547C22×C17#54011yescharacteristic
548C22×C17#54211yescharacteristic
549C22×C17D4211yescharacteristic
550C22×C17#54611yescharacteristic
551C22×C17#54611yescharacteristic
552C22×C17#54711yescharacteristic
553C22×C17#54711yescharacteristic
554C22×C17#54811yescharacteristic
555C22×C17#54811yescharacteristic
556C22×C17#55111yescharacteristic
557C22×C17#55111yescharacteristic
558C22×C17#55211yescharacteristic
559C22×C17#55311yescharacteristic
560C22×C17#55611yescharacteristic
561C22×C17#56211yescharacteristic
562C22×C17#56211yescharacteristic
563C22×C17#56311yescharacteristic
564C22×C17#56311yescharacteristic
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—81no—
573C4×C17—81no—
574C4×C17—81no—
575C4×C17—81no—
576C4×C17—81no—
577C4×C17—81no—
578C23×D4C22×C1711yescharacteristic
579C24×C4C22×C1711yescharacteristic
580C22×C4⋊C4C22×C1711yescharacteristic
581C22×C4⋊C4C22×C1711yescharacteristic
582C22×C4⋊C4C22×C1711yescharacteristic
583C22×C4⋊C4C22×C1711yescharacteristic
584C22×C4⋊C4C22×C1711yescharacteristic
585C22×C4⋊C4C22×C1711yescharacteristic
586C22×C22⋊C4C22×C1711yescharacteristic
587C22×C22⋊C4C22×C1711yescharacteristic
588C22×C22⋊C4C22×C1711yescharacteristic
589C22×C22⋊C4C22×C1711yescharacteristic
590C22×C22⋊C4C22×C1711yescharacteristic
591C22×C22⋊C4C22×C1711yescharacteristic
592C22×C22⋊C4C22×C1711yescharacteristic
593C22×C22⋊C4C22×C1711yescharacteristic
594C22×C22⋊C4C22×C1711yescharacteristic
595C22×C22⋊C4C22×C1711yescharacteristic
596C22×C22⋊C4C22×C1711yescharacteristic
597#397—24no—
598#396—24no—
599#394—24no—
600#386—24no—
601#385—24no—
602#380—24no—
603C2×#95C22×C1711yescharacteristic
604C2×#95C22×C1711yescharacteristic
605C2×#95C22×C1711yescharacteristic
606C2×#95C22×C1711yescharacteristic
607C2×#95C22×C1711yescharacteristic
608C2×#95C22×C1711yescharacteristic
609C2×#95C22×C1711yescharacteristic
610C2×#95C22×C1711yescharacteristic
611C2×#95C22×C1711yescharacteristic
612C2×#95C22×C1711yescharacteristic
613C2×#95C22×C1711yescharacteristic
614C2×#95C22×C1711yescharacteristic
615C2×#95C22×C1711yescharacteristic
616C2×#95C22×C1711yescharacteristic
617C2×#95C22×C1711yescharacteristic
618C2×#95C22×C1711yescharacteristic
619C2×C17—44no—
620C2×C17—82no—
621C2×C17#241511yescharacteristic
622C2×C17#241611yescharacteristic
623C2×C17#253411yescharacteristic
624C2×C17#261711yescharacteristic
625C2×C17#261811yescharacteristic
626C2×C17#263011yescharacteristic
627C2×C17#267111yescharacteristic
628C2×C17#267611yescharacteristic
629C2×C17#269511yescharacteristic
630C2×C17#271511yescharacteristic
631C2×C17#272311yescharacteristic
632C2×C17#272811yescharacteristic
633C2×C17#275011yescharacteristic
634C2×C17#278611yescharacteristic
635C2×C17#281411yescharacteristic
636C25C23×C1711yescharacteristic
637C25C23×C1711yescharacteristic
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—41no—
644C22×D4—41no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4D4×C1714yes—
652C23×C4C23×C1711yescharacteristic
653C23×C4C23×C1711yescharacteristic
654C23×C4C23×C1711yescharacteristic
655C23×C4C23×C1711yescharacteristic
656C23×C4C23×C1711yescharacteristic
657C23×C4C23×C1711yescharacteristic
658C23×C4C23×C1711yescharacteristic
659C23×C4C23×C1711yescharacteristic
660C23×C4C23×C1711yescharacteristic
661C23×C4C23×C1711yescharacteristic
662C23×C4C23×C1711yescharacteristic
663C23×C4C23×C1711yescharacteristic
664C23×C4C23×C1711yescharacteristic
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4—41no—
682C2×C4⋊C4D4×C1714yescomplemented
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
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—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
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⋊C4D4×C1714yes—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732C17#1651311yescharacteristic, direct product factor, Sylow
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
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—
759C24C2×D4×C1712yes—
760C24C2×D4×C1712yes—
761C24#41×C1712yes—
762C24#41×C1712yes—
763C24C24×C1711yescharacteristic
764C2×D4—28no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
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—28no—
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—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4C2×D4×C1712yes—
861C22×C4C2×D4×C1712yes—
862C22×C4C2×D4×C1712yes—
863C22×C4C2×D4×C1712yes—
864C22×C4C2×D4×C1712yes—
865C22×C4C2×D4×C1712yes—
866C22×C4C2×D4×C1712yes—
867C22×C4#41×C1712yes—
868C22×C4#41×C1712yes—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C22⋊C4—28no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
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—
955C23C17×#12114yes—
956C23C22×D4×C1711yescharacteristic
957C23C22×D4×C1711yescharacteristic
958C23C22×D4×C1711yescharacteristic
959C23C2×#41×C1711yescharacteristic
960C23C2×#41×C1711yescharacteristic
961C23C2×#41×C1711yescharacteristic
962C23C2×#41×C1711yescharacteristic
963C23C17×H(5,𝔽2)11yescharacteristic
964C23C17×H(5,𝔽2)11yescharacteristic
965C23C17×H(5,𝔽2)11yescharacteristic
966C23C17×H(5,𝔽2)11yescharacteristic
967C23C17×H(5,𝔽2)11yescharacteristic
968C23C17×2−1+411yescharacteristic
969C23C17×2−1+411yescharacteristic
970C23C17×2−1+411yescharacteristic
971D4—416no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
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—416no—
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—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
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×C4C17×#12114yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×C17×#12111yescharacteristic
1095C22C2×C17×#12111yescharacteristic
1096C22C17×#52511yescharacteristic
1097C22C17×#53411yescharacteristic
1098C22C17×#53411yescharacteristic
1099C22C17×#53411yescharacteristic
1100C22C17×#53511yescharacteristic
1101C22C17×#53611yescharacteristic
1102C22C17×#53711yescharacteristic
1103C22C17×#53711yescharacteristic
1104C22C17×#53711yescharacteristic
1105C22C17×#53811yescharacteristic
1106C22C17×#53811yescharacteristic
1107C22C17×#53811yescharacteristic
1108C22C17×#53911yescharacteristic
1109C22C17×#53911yescharacteristic
1110C22C17×#53911yescharacteristic
1111C22C17×#54011yescharacteristic
1112C22C17×#54211yescharacteristic
1113C22D42×C1711yescharacteristic
1114C22C17×#54611yescharacteristic
1115C22C17×#54611yescharacteristic
1116C22C17×#54711yescharacteristic
1117C22C17×#54711yescharacteristic
1118C22C17×#54811yescharacteristic
1119C22C17×#54811yescharacteristic
1120C22C17×#55111yescharacteristic
1121C22C17×#55111yescharacteristic
1122C22C17×#55211yescharacteristic
1123C22C17×#55311yescharacteristic
1124C22C17×#55611yescharacteristic
1125C22C17×#56211yescharacteristic
1126C22C17×#56211yescharacteristic
1127C22C17×#56311yescharacteristic
1128C22C17×#56311yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—44no—
1143C2—82no—
1144C2C17×#241511yescharacteristic
1145C2C17×#241611yescharacteristic
1146C2C17×#253411yescharacteristic
1147C2C17×#261711yescharacteristic
1148C2C17×#261811yescharacteristic
1149C2C17×#263011yescharacteristic
1150C2C17×#267111yescharacteristic
1151C2C17×#267611yescharacteristic
1152C2C17×#269511yescharacteristic
1153C2C17×#271511yescharacteristic
1154C2C17×#272311yescharacteristic
1155C2C17×#272811yescharacteristic
1156C2C17×#275011yescharacteristic
1157C2C17×#278611yescharacteristic
1158C2C17×#281411yescharacteristic
subgroupG/H
center, socleC24×C17C24
commutator, Frattini, cosocleC24C24×C17
prime radicalC23×D4×C17C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C17×#397C2semidirect
2. C2×C17×#396C2semidirect
5. C2×C17×#385C2semidirect
6. C2×C17×#380C2semidirect
7. C17×#1442C2semidirect
8. C17×#1441C2semidirect
9. C17×#1441C2semidirect
10. C17×#1441C2semidirect
11. C17×#1440C2semidirect
12. C17×#1440C2semidirect
13. C17×#1439C2semidirect
14. C17×#1439C2semidirect
103. C2×C4⋊C4×C17D4semidirect
306. #16513C17direct (N × H)
485. C2×#397C2×C17semidirect
486. C2×#396C2×C17semidirect
489. C2×#385C2×C17semidirect
490. C2×#380C2×C17semidirect
491. #1442C2×C17semidirect
492. #1441C2×C17semidirect
493. #1441C2×C17semidirect
494. #1441C2×C17semidirect
495. #1440C2×C17semidirect
496. #1440C2×C17semidirect
497. #1439C2×C17semidirect
498. #1439C2×C17semidirect
682. C2×C4⋊C4D4×C17semidirect
732. C17#16513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3972
C2×C17×#3962
C2×C17×#3942
C2×C17×#3862
C2×C17×#3852
C2×C17×#3802
C17×#14422
C17×#14412
C17×#14402
C17×#14392
C17×#14382
#1651317