Finite Group Databasebeta

← C17×#14267 #16872011

Subgroups — C17×#14267 #16872011

Order 4352.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#388C211yesmaximal, characteristic, complemented
2C2×C17×#386C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
4C17×#1443C211yesmaximal, characteristic, complemented
5C17×#1442C211yesmaximal, characteristic, complemented
6C17×#1440C211yesmaximal, characteristic, complemented
7C17×#1439C211yesmaximal, characteristic, complemented
8C17×#1439C211yesmaximal, characteristic, complemented
9C17×#1439C211yesmaximal, characteristic, complemented
10C17×#1438C211yesmaximal, characteristic
11C17×#1438C211yesmaximal, characteristic
12C17×#1437C211yesmaximal, characteristic, complemented
13C17×#1436C211yesmaximal, characteristic, complemented
14C17×#1434C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C17C2211yescharacteristic
17C24×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×C42×C17C2211yescharacteristic
32C22×C42×C17C2211yescharacteristic
33C17×#388—24no—
34C17×#386C418yescomplemented
35C4×C22⋊C4×C17—24no—
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
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C25×C17C2311yescharacteristic
56C22×D4×C17—22no—
57C22×D4×C17—22no—
58C22×D4×C17—41no—
59C22×D4×C17—41no—
60C22×D4×C17—41no—
61C22×D4×C17—41no—
62C22×D4×C17C2×C414yes—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—41no—
66C23×C4×C17—41no—
67C23×C4×C17—41no—
68C23×C4×C17—41no—
69C23×C4×C17C2×C414yes—
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
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
83C2×C4⋊C4×C17—22no—
84C2×C4⋊C4×C17—22no—
85C2×C4⋊C4×C17—41no—
86C2×C4⋊C4×C17—41no—
87C2×C4⋊C4×C17—41no—
88C2×C4⋊C4×C17—41no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
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×C17—41no—
116C2×C22⋊C4×C17—41no—
117C2×C22⋊C4×C17—41no—
118C2×C22⋊C4×C17—41no—
119C2×C22⋊C4×C17C2×C414yes—
120C2×C22⋊C4×C17C2×C414yes—
121C2×C22⋊C4×C17C2×C414yes—
122C2×C42×C17—22no—
123C2×C42×C17—41no—
124C2×C42×C17—41no—
125C2×C42×C17—41no—
126C2×C42×C17—41no—
127C2×C42×C17D414yescomplemented
128C17×#95—22no—
129C17×#95—22no—
130C17×#95—22no—
131C17×#95—22no—
132C17×#95—22no—
133C17×#95—22no—
134C17×#95—41no—
135C17×#95—41no—
136C17×#95—41no—
137C17×#95—41no—
138C17×#95—41no—
139C17×#95—41no—
140C17×#95—41no—
141C17×#95—41no—
142C17×#95—41no—
143C17×#95—41no—
144C17×#95C2×C414yes—
145C17×#95C2×C414yes—
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×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17C22×C412yes—
173C24×C17C22×C412yes—
174C24×C17#4112yes—
175C24×C17#4112yes—
176C24×C17C2411yescharacteristic
177C2×D4×C17—28no—
178C2×D4×C17—44no—
179C2×D4×C17—44no—
180C2×D4×C17—44no—
181C2×D4×C17—44no—
182C2×D4×C17—44no—
183C2×D4×C17—44no—
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—28no—
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—44no—
266C22×C4×C17—44no—
267C22×C4×C17—44no—
268C22×C4×C17—44no—
269C22×C4×C17—44no—
270C22×C4×C17—44no—
271C22×C4×C17C22×C412yes—
272C22×C4×C17C22×C412yes—
273C22×C4×C17C22×C412yes—
274C22×C4×C17C22×C412yes—
275C22×C4×C17C22×C412yes—
276C22×C4×C17C2×D412yes—
277C22×C4×C17C2×D412yes—
278C22×C4×C17C2×D412yes—
279C22×C4×C17#4112yes—
280C22×C4×C17#4112yes—
281C22×C4×C17#4112yes—
282C4⋊C4×C17—44no—
283C4⋊C4×C17—44no—
284C22⋊C4×C17—28no—
285C22⋊C4×C17—28no—
286C22⋊C4×C17—28no—
287C22⋊C4×C17—44no—
288C22⋊C4×C17—44no—
289C22⋊C4×C17—44no—
290C22⋊C4×C17—44no—
291C22⋊C4×C17—44no—
292C22⋊C4×C17—44no—
293C22⋊C4×C17—44no—
294C22⋊C4×C17—44no—
295C42×C17—44no—
296C42×C17—44no—
297#14267C1711yesmaximal, characteristic, direct product factor, Sylow
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
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—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×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#11714yes—
368C23×C17C23×C411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C2×#4111yescharacteristic
371C23×C17C2×#4111yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17C2×#4111yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17H(5,𝔽2)11yescharacteristic
376C23×C17H(5,𝔽2)11yescharacteristic
377C23×C17H(5,𝔽2)11yescharacteristic
378C23×C17H(5,𝔽2)11yescharacteristic
379C23×C17H(5,𝔽2)11yescharacteristic
380C23×C17H(5,𝔽2)11yescharacteristic
381C23×C17H(5,𝔽2)11yescharacteristic
382C23×C172−1+411yescharacteristic
383D4×C17—416no—
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—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—416no—
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×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×C17C4×D414yes—
476C2×#388C2×C1711yescharacteristic, complemented
477C2×#386C2×C1711yescharacteristic
478C2×C4×C22⋊C4C2×C1711yescharacteristic, complemented
479#1443C2×C1711yescharacteristic, complemented
480#1442C2×C1711yescharacteristic, complemented
481#1440C2×C1711yescharacteristic, complemented
482#1439C2×C1711yescharacteristic, complemented
483#1439C2×C1711yescharacteristic, complemented
484#1439C2×C1711yescharacteristic, complemented
485#1438C2×C1711yescharacteristic
486#1438C2×C1711yescharacteristic
487#1437C2×C1711yescharacteristic, complemented
488#1436C2×C1711yescharacteristic, complemented
489#1434C2×C1711yescharacteristic, complemented
490C22⋊#95C2×C1711yescharacteristic, complemented
491C22×C17—24no—
492C22×C17—24no—
493C22×C17—24no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
498C22×C17—42no—
499C22×C17—42no—
500C22×C17—42no—
501C22×C17—42no—
502C22×C17—42no—
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—81no—
514C22×C17—81no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17C2×#11711yescharacteristic
522C22×C17C2×C4×D411yescharacteristic
523C22×C17C4×#4111yescharacteristic
524C22×C17#51811yescharacteristic
525C22×C17#51811yescharacteristic
526C22×C17#51811yescharacteristic
527C22×C17#52011yescharacteristic
528C22×C17#52511yescharacteristic
529C22×C17#52511yescharacteristic
530C22×C17#52911yescharacteristic
531C22×C17#52911yescharacteristic
532C22×C17#53411yescharacteristic
533C22×C17#53511yescharacteristic
534C22×C17#53511yescharacteristic
535C22×C17#53711yescharacteristic
536C22×C17#53811yescharacteristic
537C22×C17#53811yescharacteristic
538C22×C17#53811yescharacteristic
539C22×C17#53811yescharacteristic
540C22×C17#53811yescharacteristic
541C22×C17#53811yescharacteristic
542C22×C17#53811yescharacteristic
543C22×C17#53811yescharacteristic
544C22×C17#53811yescharacteristic
545C22×C17#53811yescharacteristic
546C22×C17#53811yescharacteristic
547C22×C17#53911yescharacteristic
548C22×C17#53911yescharacteristic
549C22×C17#53911yescharacteristic
550C22×C17#54011yescharacteristic
551C22×C17#54011yescharacteristic
552C22×C17#54011yescharacteristic
553C22×C17#54011yescharacteristic
554C22×C17#54211yescharacteristic
555C22×C17#54211yescharacteristic
556C4×C17—24no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—42no—
560C4×C17—42no—
561C4×C17—42no—
562C4×C17—42no—
563C4×C17—42no—
564C4×C17—42no—
565C4×C17—81no—
566C4×C17—81no—
567C4×C17—81no—
568C4×C17—81no—
569C23×D4C22×C1711yescharacteristic
570C24×C4C22×C1711yescharacteristic
571C22×C4⋊C4C22×C1711yescharacteristic
572C22×C4⋊C4C22×C1711yescharacteristic
573C22×C22⋊C4C22×C1711yescharacteristic
574C22×C22⋊C4C22×C1711yescharacteristic
575C22×C22⋊C4C22×C1711yescharacteristic
576C22×C22⋊C4C22×C1711yescharacteristic
577C22×C22⋊C4C22×C1711yescharacteristic
578C22×C22⋊C4C22×C1711yescharacteristic
579C22×C22⋊C4C22×C1711yescharacteristic
580C22×C22⋊C4C22×C1711yescharacteristic
581C22×C22⋊C4C22×C1711yescharacteristic
582C22×C22⋊C4C22×C1711yescharacteristic
583C22×C22⋊C4C22×C1711yescharacteristic
584C22×C42C22×C1711yescharacteristic
585C22×C42C22×C1711yescharacteristic
586#388—24no—
587#386C4×C1718yescomplemented
588C4×C22⋊C4—24no—
589C2×#95C22×C1711yescharacteristic
590C2×#95C22×C1711yescharacteristic
591C2×#95C22×C1711yescharacteristic
592C2×#95C22×C1711yescharacteristic
593C2×#95C22×C1711yescharacteristic
594C2×#95C22×C1711yescharacteristic
595C2×#95C22×C1711yescharacteristic
596C2×#95C22×C1711yescharacteristic
597C2×#95C22×C1711yescharacteristic
598C2×#95C22×C1711yescharacteristic
599C2×#95C22×C1711yescharacteristic
600C2×#95C22×C1711yescharacteristic
601C2×#95C22×C1711yescharacteristic
602C2×#95C22×C1711yescharacteristic
603C2×#95C22×C1711yescharacteristic
604C2×#95C22×C1711yescharacteristic
605C2×#95C22×C1711yescharacteristic
606C2×#95C22×C1711yescharacteristic
607C2×C17—44no—
608C2×C17—82no—
609C2×C17#229011yescharacteristic
610C2×C17#231211yescharacteristic
611C2×C17#231811yescharacteristic
612C2×C17#232111yescharacteristic
613C2×C17#232411yescharacteristic
614C2×C17#233311yescharacteristic
615C2×C17#233511yescharacteristic
616C2×C17#263011yescharacteristic
617C2×C17#263111yescharacteristic
618C2×C17#263511yescharacteristic
619C2×C17#263611yescharacteristic
620C2×C17#264811yescharacteristic
621C2×C17#264811yescharacteristic
622C2×C17#264911yescharacteristic
623C2×C17#265311yescharacteristic
624C25C23×C1711yescharacteristic
625C25C23×C1711yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4C2×C4×C1714yes—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4C2×C4×C1714yes—
640C23×C4C23×C1711yescharacteristic
641C23×C4C23×C1711yescharacteristic
642C23×C4C23×C1711yescharacteristic
643C23×C4C23×C1711yescharacteristic
644C23×C4C23×C1711yescharacteristic
645C23×C4C23×C1711yescharacteristic
646C23×C4C23×C1711yescharacteristic
647C23×C4C23×C1711yescharacteristic
648C23×C4C23×C1711yescharacteristic
649C23×C4C23×C1711yescharacteristic
650C23×C4C23×C1711yescharacteristic
651C23×C4C23×C1711yescharacteristic
652C23×C4C23×C1711yescharacteristic
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4C2×C4×C1714yes—
690C2×C22⋊C4C2×C4×C1714yes—
691C2×C22⋊C4C2×C4×C1714yes—
692C2×C42—22no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42D4×C1714yescomplemented
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95C2×C4×C1714yes—
715#95C2×C4×C1714yes—
716C17#1426711yescharacteristic, direct product factor, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C22×C4×C1712yes—
744C24C22×C4×C1712yes—
745C24#41×C1712yes—
746C24#41×C1712yes—
747C24C24×C1711yescharacteristic
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
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—28no—
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—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4C22×C4×C1712yes—
843C22×C4C22×C4×C1712yes—
844C22×C4C22×C4×C1712yes—
845C22×C4C22×C4×C1712yes—
846C22×C4C22×C4×C1712yes—
847C22×C4C2×D4×C1712yes—
848C22×C4C2×D4×C1712yes—
849C22×C4C2×D4×C1712yes—
850C22×C4#41×C1712yes—
851C22×C4#41×C1712yes—
852C22×C4#41×C1712yes—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C42—44no—
867C42—44no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
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—
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—
937C23C17×#11714yes—
938C23C23×C4×C1711yescharacteristic
939C23C22×D4×C1711yescharacteristic
940C23C2×#41×C1711yescharacteristic
941C23C2×#41×C1711yescharacteristic
942C23C2×#41×C1711yescharacteristic
943C23C2×#41×C1711yescharacteristic
944C23C2×#41×C1711yescharacteristic
945C23C17×H(5,𝔽2)11yescharacteristic
946C23C17×H(5,𝔽2)11yescharacteristic
947C23C17×H(5,𝔽2)11yescharacteristic
948C23C17×H(5,𝔽2)11yescharacteristic
949C23C17×H(5,𝔽2)11yescharacteristic
950C23C17×H(5,𝔽2)11yescharacteristic
951C23C17×H(5,𝔽2)11yescharacteristic
952C23C17×2−1+411yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
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—416no—
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—
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×C4C4×D4×C1714yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×C17×#11711yescharacteristic
1077C22C2×C4×D4×C1711yescharacteristic
1078C22C4×#41×C1711yescharacteristic
1079C22C17×#51811yescharacteristic
1080C22C17×#51811yescharacteristic
1081C22C17×#51811yescharacteristic
1082C22C17×#52011yescharacteristic
1083C22C17×#52511yescharacteristic
1084C22C17×#52511yescharacteristic
1085C22C17×#52911yescharacteristic
1086C22C17×#52911yescharacteristic
1087C22C17×#53411yescharacteristic
1088C22C17×#53511yescharacteristic
1089C22C17×#53511yescharacteristic
1090C22C17×#53711yescharacteristic
1091C22C17×#53811yescharacteristic
1092C22C17×#53811yescharacteristic
1093C22C17×#53811yescharacteristic
1094C22C17×#53811yescharacteristic
1095C22C17×#53811yescharacteristic
1096C22C17×#53811yescharacteristic
1097C22C17×#53811yescharacteristic
1098C22C17×#53811yescharacteristic
1099C22C17×#53811yescharacteristic
1100C22C17×#53811yescharacteristic
1101C22C17×#53811yescharacteristic
1102C22C17×#53911yescharacteristic
1103C22C17×#53911yescharacteristic
1104C22C17×#53911yescharacteristic
1105C22C17×#54011yescharacteristic
1106C22C17×#54011yescharacteristic
1107C22C17×#54011yescharacteristic
1108C22C17×#54011yescharacteristic
1109C22C17×#54211yescharacteristic
1110C22C17×#54211yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C2—44no—
1125C2—82no—
1126C2C17×#229011yescharacteristic
1127C2C17×#231211yescharacteristic
1128C2C17×#231811yescharacteristic
1129C2C17×#232111yescharacteristic
1130C2C17×#232411yescharacteristic
1131C2C17×#233311yescharacteristic
1132C2C17×#233511yescharacteristic
1133C2C17×#263011yescharacteristic
1134C2C17×#263111yescharacteristic
1135C2C17×#263511yescharacteristic
1136C2C17×#263611yescharacteristic
1137C2C17×#264811yescharacteristic
1138C2C17×#264811yescharacteristic
1139C2C17×#264911yescharacteristic
1140C2C17×#265311yescharacteristic
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
1. C2×C17×#388C2semidirect
3. C2×C4×C22⋊C4×C17C2semidirect
4. C17×#1443C2semidirect
5. C17×#1442C2semidirect
6. C17×#1440C2semidirect
7. C17×#1439C2semidirect
8. C17×#1439C2semidirect
9. C17×#1439C2semidirect
12. C17×#1437C2semidirect
13. C17×#1436C2semidirect
14. C17×#1434C2semidirect
15. C17×C22⋊#95C2semidirect
34. C17×#386C4semidirect
127. C2×C42×C17D4semidirect
297. #14267C17direct (N × H)
476. C2×#388C2×C17semidirect
478. C2×C4×C22⋊C4C2×C17semidirect
479. #1443C2×C17semidirect
480. #1442C2×C17semidirect
481. #1440C2×C17semidirect
482. #1439C2×C17semidirect
483. #1439C2×C17semidirect
484. #1439C2×C17semidirect
487. #1437C2×C17semidirect
488. #1436C2×C17semidirect
489. #1434C2×C17semidirect
490. C22⋊#95C2×C17semidirect
587. #386C4×C17semidirect
697. C2×C42D4×C17semidirect
716. C17#14267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3882
C2×C17×#3862
C2×C4×C22⋊C4×C172
C17×#14432
C17×#14422
C17×#14402
C17×#14392
C17×#14382
C17×#14372
C17×#14362
C17×#14342
C17×C22⋊#952
#1426717