Finite Group Databasebeta

← C17×#22097 #16879841

Subgroups — C17×#22097 #16879841

Order 4352.

712 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3091C211yesmaximal, characteristic
2C17×#2930C211yesmaximal, characteristic
3C17×#2905C211yesmaximal, characteristic, complemented
4C17×#1946C211yesmaximal, characteristic, complemented
5C17×#1945C211yesmaximal, characteristic, complemented
6C17×#1938C211yesmaximal, characteristic, complemented
7C17×#1937C211yesmaximal, characteristic, complemented
8C17×#1922C211yesmaximal, characteristic, complemented
9C17×#1922C211yesmaximal, characteristic, complemented
10C17×#1871C211yesmaximal, characteristic
11C17×#1866C211yesmaximal, characteristic, complemented
12C17×#1866C211yesmaximal, characteristic, complemented
13C17×#1855C211yesmaximal, characteristic, complemented
14C17×#1826C211yesmaximal, characteristic, complemented
15C17×#1753C211yesmaximal, characteristic, complemented
16C2×C17×#131C2211yescharacteristic
17C22×M16×C17C2211yescharacteristic
18C22×M16×C17C2211yescharacteristic
19C17×#525C2211yescharacteristic
20C2×C17×#117C2211yescharacteristic
21C17×#485C411yescharacteristic, complemented
22C17×#485C411yescharacteristic, complemented
23C17×#484C411yescharacteristic, complemented
24C17×#483C411yescharacteristic, complemented
25C17×#482C411yescharacteristic, complemented
26C17×#482C411yescharacteristic, complemented
27C17×#481C411yescharacteristic, complemented
28C17×#480C411yescharacteristic, complemented
29C17×#436—21no—
30C17×#436—21no—
31C17×#435—21no—
32C17×#435—21no—
33C2×C17×#108C2211yescharacteristic
34C2×C17×#108C2211yescharacteristic
35C17×#427C2211yescharacteristic
36C17×#427C2211yescharacteristic
37C17×#424—21no—
38C17×#424—21no—
39C17×#424C2211yescharacteristic
40C17×#424C2211yescharacteristic
41C17×#424C2211yescharacteristic
42C17×#424C2211yescharacteristic
43C17×#424C2211yescharacteristic
44C17×#423—21no—
45C17×#423—21no—
46C2×C17×#104C2211yescharacteristic
47C2×C17×#104C2211yescharacteristic
48C17×#416C2211yescharacteristic
49C17×#416C2211yescharacteristic
50C17×#408C2211yescharacteristic
51C17×#407C2211yescharacteristic
52C2×C17×C22⋊C8C2211yescharacteristic
53C17×#405C2211yescharacteristic
54C2×C17×#97C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#341C2211yescharacteristic
58C17×#341C2211yescharacteristic
59C17×#339C2211yescharacteristic
60C17×#339C2211yescharacteristic
61C17×#339C2211yescharacteristic
62C17×#339C2211yescharacteristic
63C17×#339C2211yescharacteristic
64C17×#339C2211yescharacteristic
65C17×#336C2211yescharacteristic
66C17×#336C2211yescharacteristic
67C2×#41×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C17×#131—41no—
70C17×#131—41no—
71C2×M16×C17—21no—
72C2×M16×C17—21no—
73C2×M16×C17—41no—
74C2×M16×C17—41no—
75C2×M16×C17—41no—
76C2×M16×C17—41no—
77C2×M16×C17D411yescharacteristic
78C2×M16×C17D411yescharacteristic
79C2×M16×C17D411yescharacteristic
80C2×M16×C17D411yescharacteristic
81C2×M16×C17C2311yescharacteristic
82C2×M16×C17C2311yescharacteristic
83C2×M16×C17C2311yescharacteristic
84C2×M16×C17C2311yescharacteristic
85C22×C8×C17—21no—
86C22×C8×C17—21no—
87C22×C8×C17C2311yescharacteristic
88C22×C8×C17C2311yescharacteristic
89C22×C8×C17C2311yescharacteristic
90C22×C8×C17C2311yescharacteristic
91C17×#123—21no—
92C17×C22⋊Q8C2×C411yescharacteristic
93C17×C22⋊Q8C2×C411yescharacteristic
94C17×#121C2×C411yescharacteristic
95C17×#121C2×C411yescharacteristic
96C17×#120—21no—
97C4×D4×C17—21no—
98C4×D4×C17—21no—
99C17×#117—21no—
100C17×#117—21no—
101C17×#117C2×C411yescharacteristic
102C17×#117C2×C411yescharacteristic
103C17×#117C2311yescharacteristic
104C17×#117C2311yescharacteristic
105C17×#117C2311yescharacteristic
106C2×C4⋊C4×C17C2×C411yescharacteristic
107C2×C4⋊C4×C17C2×C411yescharacteristic
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C42×C17—21no—
111C2×C42×C17C2311yescharacteristic
112C2×C42×C17C2311yescharacteristic
113C17×#108—41no—
114C17×#108—41no—
115C17×#107C2×C411yescharacteristic
116C17×#107C2×C411yescharacteristic
117C17×#107C2×C411yescharacteristic
118C17×#107C2×C411yescharacteristic
119C17×#106C2×C411yescharacteristic
120C17×#106C2×C411yescharacteristic
121C17×#106C2×C411yescharacteristic
122C17×#106C2×C411yescharacteristic
123C17×C4⋊C8—21no—
124C17×C4⋊C8—21no—
125C17×C4⋊C8—21no—
126C17×C4⋊C8—21no—
127C17×C4⋊C8—21no—
128C17×C4⋊C8—21no—
129C17×C4⋊C8—21no—
130C17×C4⋊C8—21no—
131C17×C4⋊C8—21no—
132C17×C4⋊C8—21no—
133C17×#104—41no—
134C17×#104—41no—
135C17×#103C2×C411yescharacteristic
136C17×#103C2×C411yescharacteristic
137C17×#103C2×C411yescharacteristic
138C17×#103C2×C411yescharacteristic
139C17×#102C2×C411yescharacteristic
140C17×#102C2×C411yescharacteristic
141C17×#102C2×C411yescharacteristic
142C17×#102C2×C411yescharacteristic
143C17×C22⋊C8—21no—
144C17×C22⋊C8—21no—
145C17×C22⋊C8—21no—
146C17×C22⋊C8—21no—
147C17×C22⋊C8C2×C411yescharacteristic
148C17×C22⋊C8C2×C411yescharacteristic
149C17×C22⋊C8C2×C411yescharacteristic
150C17×C22⋊C8C2×C411yescharacteristic
151C17×#97—21no—
152C17×#97—41no—
153C4×C8×C17—21no—
154C4×C8×C17—41no—
155C17×#95—21no—
156C24×C17#4111yescharacteristic
157#41×C17—21no—
158#41×C17—21no—
159#41×C17—21no—
160#41×C17—21no—
161C2×Q8×C17C22×C411yescharacteristic
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—21no—
165C2×D4×C17C22×C411yescharacteristic
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17C22×C411yescharacteristic
176C22×C4×C17C22×C411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17#4111yescharacteristic
180C22×C4×C17C2411yescharacteristic
181M16×C17—21no—
182M16×C17—21no—
183M16×C17—21no—
184M16×C17—21no—
185M16×C17—21no—
186M16×C17—21no—
187M16×C17—21no—
188M16×C17—21no—
189M16×C17—41no—
190M16×C17—41no—
191M16×C17—41no—
192M16×C17—41no—
193M16×C17—42no—
194M16×C17—42no—
195C2×C8×C17—21no—
196C2×C8×C17—21no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
205C2×C8×C17—21no—
206C2×C8×C17—21no—
207C2×C8×C17—42no—
208C2×C8×C17—42no—
209C2×C8×C17C22×C411yescharacteristic
210C2×C8×C17C22×C411yescharacteristic
211C2×C8×C17C22×C411yescharacteristic
212C2×C8×C17C22×C411yescharacteristic
213C2×C8×C17C2×D411yescharacteristic
214C2×C8×C17C2×D411yescharacteristic
215C2×C8×C17C2×D411yescharacteristic
216C2×C8×C17C2×D411yescharacteristic
217C4⋊C4×C17—21no—
218C4⋊C4×C17—21no—
219C4⋊C4×C17—21no—
220C4⋊C4×C17—21no—
221C4⋊C4×C17C22×C411yescharacteristic
222C4⋊C4×C17C22×C411yescharacteristic
223C4⋊C4×C17C22×C411yescharacteristic
224C4⋊C4×C17C22×C411yescharacteristic
225C4⋊C4×C17C22×C411yescharacteristic
226C4⋊C4×C17C22×C411yescharacteristic
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—42no—
237C42×C17—21no—
238C42×C17—21no—
239C42×C17—21no—
240C42×C17—21no—
241C42×C17—21no—
242C42×C17—21no—
243C42×C17—21no—
244C42×C17—21no—
245C42×C17—21no—
246#22097C1711yesmaximal, characteristic, direct product factor, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17C4×D411yescharacteristic
253C23×C17C4×D411yescharacteristic
254C23×C17C2×#4111yescharacteristic
255Q8×C17—21no—
256Q8×C17—21no—
257D4×C17—21no—
258D4×C17—21no—
259D4×C17—41no—
260D4×C17—41no—
261D4×C17—81no—
262D4×C17—81no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—22no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—21no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—81no—
289C2×C4×C17—81no—
290C2×C4×C17C4×D411yescharacteristic
291C2×C4×C17C4×D411yescharacteristic
292C2×C4×C17C23×C411yescharacteristic
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17H(5,𝔽2)11yescharacteristic
295C2×C4×C17H(5,𝔽2)11yescharacteristic
296C2×C4×C172−1+411yescharacteristic
297C2×C4×C172−1+411yescharacteristic
298C8×C17—21no—
299C8×C17—21no—
300C8×C17—21no—
301C8×C17—21no—
302C8×C17—21no—
303C8×C17—21no—
304C8×C17—21no—
305C8×C17—21no—
306C8×C17—41no—
307C8×C17—41no—
308C8×C17—41no—
309C8×C17—41no—
310#3091C2×C1711yescharacteristic
311#2930C2×C1711yescharacteristic
312#2905C2×C1711yescharacteristic, complemented
313#1946C2×C1711yescharacteristic, complemented
314#1945C2×C1711yescharacteristic, complemented
315#1938C2×C1711yescharacteristic, complemented
316#1937C2×C1711yescharacteristic, complemented
317#1922C2×C1711yescharacteristic, complemented
318#1922C2×C1711yescharacteristic, complemented
319#1871C2×C1711yescharacteristic
320#1866C2×C1711yescharacteristic, complemented
321#1866C2×C1711yescharacteristic, complemented
322#1855C2×C1711yescharacteristic, complemented
323#1826C2×C1711yescharacteristic, complemented
324#1753C2×C1711yescharacteristic, complemented
325C22×C17—21no—
326C22×C17—21no—
327C22×C17—21no—
328C22×C17—21no—
329C22×C17—21no—
330C22×C17—21no—
331C22×C17—21no—
332C22×C17—21no—
333C22×C17—41no—
334C22×C17—41no—
335C22×C17—41no—
336C22×C17—81no—
337C22×C17—81no—
338C22×C17C2×C4×D411yescharacteristic
339C22×C17#53911yescharacteristic
340C22×C17#53911yescharacteristic
341C4×C17—21no—
342C4×C17—21no—
343C4×C17—42no—
344C4×C17—41no—
345C4×C17—41no—
346C4×C17—41no—
347C4×C17—41no—
348C4×C17—41no—
349C4×C17—41no—
350C4×C17—41no—
351C4×C17—81no—
352C4×C17#52011yescharacteristic
353C4×C17#52011yescharacteristic
354C4×C17#53411yescharacteristic
355C4×C17#53611yescharacteristic
356C2×#131C22×C1711yescharacteristic
357C22×M16C22×C1711yescharacteristic
358C22×M16C22×C1711yescharacteristic
359#525C22×C1711yescharacteristic
360C2×#117C22×C1711yescharacteristic
361#485C4×C1711yescharacteristic, complemented
362#485C4×C1711yescharacteristic, complemented
363#484C4×C1711yescharacteristic, complemented
364#483C4×C1711yescharacteristic, complemented
365#482C4×C1711yescharacteristic, complemented
366#482C4×C1711yescharacteristic, complemented
367#481C4×C1711yescharacteristic, complemented
368#480C4×C1711yescharacteristic, complemented
369#436—21no—
370#436—21no—
371#435—21no—
372#435—21no—
373C2×#108C22×C1711yescharacteristic
374C2×#108C22×C1711yescharacteristic
375#427C22×C1711yescharacteristic
376#427C22×C1711yescharacteristic
377#424—21no—
378#424—21no—
379#424C22×C1711yescharacteristic
380#424C22×C1711yescharacteristic
381#424C22×C1711yescharacteristic
382#424C22×C1711yescharacteristic
383#424C22×C1711yescharacteristic
384#423—21no—
385#423—21no—
386C2×#104C22×C1711yescharacteristic
387C2×#104C22×C1711yescharacteristic
388#416C22×C1711yescharacteristic
389#416C22×C1711yescharacteristic
390#408C22×C1711yescharacteristic
391#407C22×C1711yescharacteristic
392C2×C22⋊C8C22×C1711yescharacteristic
393#405C22×C1711yescharacteristic
394C2×#97C22×C1711yescharacteristic
395C2×C4×C8C22×C1711yescharacteristic
396C4×C22⋊C4C22×C1711yescharacteristic
397#341C22×C1711yescharacteristic
398#341C22×C1711yescharacteristic
399#339C22×C1711yescharacteristic
400#339C22×C1711yescharacteristic
401#339C22×C1711yescharacteristic
402#339C22×C1711yescharacteristic
403#339C22×C1711yescharacteristic
404#339C22×C1711yescharacteristic
405#336C22×C1711yescharacteristic
406#336C22×C1711yescharacteristic
407C2×C17—21no—
408C2×C17—21no—
409C2×C17—41no—
410C2×C17—41no—
411C2×C17—81no—
412C2×C17#232211yescharacteristic
413C2×C17#295611yescharacteristic
414C2×C17#295711yescharacteristic
415C2×#41C23×C1711yescharacteristic
416C23×C4C23×C1711yescharacteristic
417#131—41no—
418#131—41no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—41no—
422C2×M16—41no—
423C2×M16—41no—
424C2×M16—41no—
425C2×M16D4×C1711yescharacteristic
426C2×M16D4×C1711yescharacteristic
427C2×M16D4×C1711yescharacteristic
428C2×M16D4×C1711yescharacteristic
429C2×M16C23×C1711yescharacteristic
430C2×M16C23×C1711yescharacteristic
431C2×M16C23×C1711yescharacteristic
432C2×M16C23×C1711yescharacteristic
433C22×C8—21no—
434C22×C8—21no—
435C22×C8C23×C1711yescharacteristic
436C22×C8C23×C1711yescharacteristic
437C22×C8C23×C1711yescharacteristic
438C22×C8C23×C1711yescharacteristic
439#123—21no—
440C22⋊Q8C2×C4×C1711yescharacteristic
441C22⋊Q8C2×C4×C1711yescharacteristic
442#121C2×C4×C1711yescharacteristic
443#121C2×C4×C1711yescharacteristic
444#120—21no—
445C4×D4—21no—
446C4×D4—21no—
447#117—21no—
448#117—21no—
449#117C2×C4×C1711yescharacteristic
450#117C2×C4×C1711yescharacteristic
451#117C23×C1711yescharacteristic
452#117C23×C1711yescharacteristic
453#117C23×C1711yescharacteristic
454C2×C4⋊C4C2×C4×C1711yescharacteristic
455C2×C4⋊C4C2×C4×C1711yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42C23×C1711yescharacteristic
460C2×C42C23×C1711yescharacteristic
461#108—41no—
462#108—41no—
463#107C2×C4×C1711yescharacteristic
464#107C2×C4×C1711yescharacteristic
465#107C2×C4×C1711yescharacteristic
466#107C2×C4×C1711yescharacteristic
467#106C2×C4×C1711yescharacteristic
468#106C2×C4×C1711yescharacteristic
469#106C2×C4×C1711yescharacteristic
470#106C2×C4×C1711yescharacteristic
471C4⋊C8—21no—
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8—21no—
475C4⋊C8—21no—
476C4⋊C8—21no—
477C4⋊C8—21no—
478C4⋊C8—21no—
479C4⋊C8—21no—
480C4⋊C8—21no—
481#104—41no—
482#104—41no—
483#103C2×C4×C1711yescharacteristic
484#103C2×C4×C1711yescharacteristic
485#103C2×C4×C1711yescharacteristic
486#103C2×C4×C1711yescharacteristic
487#102C2×C4×C1711yescharacteristic
488#102C2×C4×C1711yescharacteristic
489#102C2×C4×C1711yescharacteristic
490#102C2×C4×C1711yescharacteristic
491C22⋊C8—21no—
492C22⋊C8—21no—
493C22⋊C8—21no—
494C22⋊C8—21no—
495C22⋊C8C2×C4×C1711yescharacteristic
496C22⋊C8C2×C4×C1711yescharacteristic
497C22⋊C8C2×C4×C1711yescharacteristic
498C22⋊C8C2×C4×C1711yescharacteristic
499#97—21no—
500#97—41no—
501C4×C8—21no—
502C4×C8—41no—
503#95—21no—
504C17#2209711yescharacteristic, direct product factor, Sylow
505C24#41×C1711yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×C4×C1711yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×C4×C1711yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4C22×C4×C1711yescharacteristic
525C22×C4C22×C4×C1711yescharacteristic
526C22×C4C2×D4×C1711yescharacteristic
527C22×C4C2×D4×C1711yescharacteristic
528C22×C4#41×C1711yescharacteristic
529C22×C4C24×C1711yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—41no—
539M16—41no—
540M16—41no—
541M16—41no—
542M16—42no—
543M16—42no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—42no—
557C2×C8—42no—
558C2×C8C22×C4×C1711yescharacteristic
559C2×C8C22×C4×C1711yescharacteristic
560C2×C8C22×C4×C1711yescharacteristic
561C2×C8C22×C4×C1711yescharacteristic
562C2×C8C2×D4×C1711yescharacteristic
563C2×C8C2×D4×C1711yescharacteristic
564C2×C8C2×D4×C1711yescharacteristic
565C2×C8C2×D4×C1711yescharacteristic
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4C22×C4×C1711yescharacteristic
571C4⋊C4C22×C4×C1711yescharacteristic
572C4⋊C4C22×C4×C1711yescharacteristic
573C4⋊C4C22×C4×C1711yescharacteristic
574C4⋊C4C22×C4×C1711yescharacteristic
575C4⋊C4C22×C4×C1711yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—42no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23C4×D4×C1711yescharacteristic
601C23C4×D4×C1711yescharacteristic
602C23C2×#41×C1711yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4C4×D4×C1711yescharacteristic
639C2×C4C4×D4×C1711yescharacteristic
640C2×C4C23×C4×C1711yescharacteristic
641C2×C4C22×D4×C1711yescharacteristic
642C2×C4C17×H(5,𝔽2)11yescharacteristic
643C2×C4C17×H(5,𝔽2)11yescharacteristic
644C2×C4C17×2−1+411yescharacteristic
645C2×C4C17×2−1+411yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—21no—
653C8—21no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—41no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×C4×D4×C1711yescharacteristic
672C22C17×#53911yescharacteristic
673C22C17×#53911yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4C17×#52011yescharacteristic
686C4C17×#52011yescharacteristic
687C4C17×#53411yescharacteristic
688C4C17×#53611yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2C17×#232211yescharacteristic
695C2C17×#295611yescharacteristic
696C2C17×#295711yescharacteristic
subgroupG/H
centerC2×C4×C17C22×D4
commutatorC2×C4C23×C4×C17
Frattini, cosocleC22×C4C24×C17
socleC22×C17C2×C4×D4
prime radicalC17×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C22×M16×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#2905C2semidirect
4. C17×#1946C2semidirect
5. C17×#1945C2semidirect
6. C17×#1938C2semidirect
7. C17×#1937C2semidirect
8. C17×#1922C2semidirect
9. C17×#1922C2semidirect
11. C17×#1866C2semidirect
12. C17×#1866C2semidirect
13. C17×#1855C2semidirect
14. C17×#1826C2semidirect
15. C17×#1753C2semidirect
21. C17×#485C4semidirect
22. C17×#485C4semidirect
23. C17×#484C4semidirect
24. C17×#483C4semidirect
25. C17×#482C4semidirect
26. C17×#482C4semidirect
27. C17×#481C4semidirect
28. C17×#480C4semidirect
246. #22097C17direct (N × H)
312. #2905C2×C17semidirect
313. #1946C2×C17semidirect
314. #1945C2×C17semidirect
315. #1938C2×C17semidirect
316. #1937C2×C17semidirect
317. #1922C2×C17semidirect
318. #1922C2×C17semidirect
320. #1866C2×C17semidirect
321. #1866C2×C17semidirect
322. #1855C2×C17semidirect
323. #1826C2×C17semidirect
324. #1753C2×C17semidirect
361. #485C4×C17semidirect
362. #485C4×C17semidirect
363. #484C4×C17semidirect
364. #483C4×C17semidirect
365. #482C4×C17semidirect
366. #482C4×C17semidirect
367. #481C4×C17semidirect
368. #480C4×C17semidirect
504. C17#22097direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30912
C17×#29302
C17×#29052
C17×#19462
C17×#19452
C17×#19382
C17×#19372
C17×#19222
C17×#18712
C17×#18662
C17×#18552
C17×#18262
C17×#17532
#2209717