Finite Group Databasebeta

← C17×#22062 #16879806

Subgroups — C17×#22062 #16879806

Order 4352.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3002C211yesmaximal, characteristic
2C17×#2930C211yesmaximal, characteristic, complemented
3C17×#2879C211yesmaximal, characteristic, complemented
4C17×#1975C211yesmaximal, characteristic, complemented
5C17×#1974C211yesmaximal, characteristic, complemented
6C17×#1938C211yesmaximal, characteristic, complemented
7C17×#1937C211yesmaximal, characteristic, complemented
8C17×#1929C211yesmaximal, characteristic, complemented
9C17×#1929C211yesmaximal, characteristic, complemented
10C17×#1876C211yesmaximal, characteristic, complemented
11C17×#1876C211yesmaximal, characteristic, complemented
12C17×#1871C211yesmaximal, characteristic, complemented
13C17×#1855C211yesmaximal, characteristic, complemented
14C17×#1789C211yesmaximal, characteristic, complemented
15C17×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C17C2211yescharacteristic
17C2×C17×#135C2211yescharacteristic
18C2×C17×#135C2211yescharacteristic
19C2×C17×#131C2211yescharacteristic, complemented
20C22×M16×C17C2211yescharacteristic
21C22×M16×C17C2211yescharacteristic
22C17×#525C2211yescharacteristic
23C17×#452C411yescharacteristic, complemented
24C17×#452C411yescharacteristic, complemented
25C17×#451C411yescharacteristic, complemented
26C17×#450C411yescharacteristic, complemented
27C17×#449C411yescharacteristic, complemented
28C17×#449C411yescharacteristic, complemented
29C17×#448C411yescharacteristic, complemented
30C17×#447C411yescharacteristic, complemented
31C17×#436—21no—
32C17×#436—21no—
33C17×#435—21no—
34C17×#435—21no—
35C2×C17×#108C2211yescharacteristic, complemented
36C2×C17×#108C2211yescharacteristic, complemented
37C17×#424C2211yescharacteristic, complemented
38C2×C17×#104C2211yescharacteristic
39C2×C17×#104C2211yescharacteristic
40C2×C17×#104C2211yescharacteristic
41C2×C17×#104C2211yescharacteristic
42C2×C17×#104C2211yescharacteristic, complemented
43C2×C17×#104C2211yescharacteristic, complemented
44C17×#416C2211yescharacteristic
45C17×#416C2211yescharacteristic
46C17×#408—21no—
47C17×#408—21no—
48C17×#408C2211yescharacteristic
49C17×#408C2211yescharacteristic
50C17×#408C2211yescharacteristic
51C17×#408C2211yescharacteristic
52C17×#408C2211yescharacteristic, complemented
53C17×#407—21no—
54C17×#407—21no—
55C17×#407C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C17×#405C2211yescharacteristic, complemented
58C2×C17×#97C2211yescharacteristic, complemented
59C2×C4×C8×C17C2211yescharacteristic, complemented
60C4×C22⋊C4×C17C2211yescharacteristic
61C17×#341C2211yescharacteristic, complemented
62C17×#341C2211yescharacteristic, complemented
63C17×#339C2211yescharacteristic, complemented
64C17×#339C2211yescharacteristic, complemented
65C17×#336C2211yescharacteristic, complemented
66C17×#336C2211yescharacteristic, complemented
67C2×#41×C17—21no—
68C2×#41×C17—21no—
69C2×#41×C17—41no—
70C2×#41×C17—41no—
71C2×#41×C17—41no—
72C2×#41×C17—41no—
73C2×#41×C17C2×C411yescharacteristic
74C2×#41×C17C2×C411yescharacteristic
75C2×#41×C17C2311yescharacteristic
76C2×#41×C17C2311yescharacteristic
77C2×#41×C17C2311yescharacteristic
78C22×Q8×C17C2×C411yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17C2×C411yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C17×#135—41no—
84C17×#135—41no—
85C17×#135—41no—
86C17×#135—41no—
87C2×Q16×C17C2×C411yescharacteristic
88C2×Q16×C17C2×C411yescharacteristic
89C2×SD16×C17C2×C411yescharacteristic
90C2×SD16×C17C2×C411yescharacteristic
91C2×SD16×C17C2×C411yescharacteristic
92C2×SD16×C17C2×C411yescharacteristic
93C2×D8×C17C2×C411yescharacteristic
94C2×D8×C17C2×C411yescharacteristic
95C17×#131—41no—
96C17×#131—41no—
97C2×M16×C17—21no—
98C2×M16×C17—21no—
99C2×M16×C17—41no—
100C2×M16×C17—41no—
101C2×M16×C17—41no—
102C2×M16×C17—41no—
103C2×M16×C17D411yescharacteristic
104C2×M16×C17D411yescharacteristic
105C2×M16×C17D411yescharacteristic
106C2×M16×C17D411yescharacteristic
107C2×M16×C17C2311yescharacteristic
108C2×M16×C17C2311yescharacteristic
109C2×M16×C17C2311yescharacteristic
110C2×M16×C17C2311yescharacteristic
111C22×C8×C17—21no—
112C22×C8×C17—21no—
113C22×C8×C17C2311yescharacteristic
114C22×C8×C17C2311yescharacteristic
115C22×C8×C17C2311yescharacteristic
116C22×C8×C17C2311yescharacteristic
117C17×#123—21no—
118C17×C22⋊Q8C2×C411yescharacteristic
119C17×C22⋊Q8C2×C411yescharacteristic
120C17×#121C2×C411yescharacteristic
121C17×#121C2×C411yescharacteristic
122C17×#120—21no—
123C4×D4×C17—21no—
124C4×D4×C17—21no—
125C17×#117C2311yescharacteristic
126C2×C22⋊C4×C17—21no—
127C2×C42×C17C2311yescharacteristic
128C2×C42×C17C2311yescharacteristic
129C17×#108—41no—
130C17×#108—41no—
131C17×C4⋊C8—21no—
132C17×C4⋊C8—21no—
133C17×#104—41no—
134C17×#104—41no—
135C17×#104—41no—
136C17×#104—41no—
137C17×#104—41no—
138C17×#104—41no—
139C17×#103C2×C411yescharacteristic
140C17×#103C2×C411yescharacteristic
141C17×#103C2×C411yescharacteristic
142C17×#103C2×C411yescharacteristic
143C17×#102C2×C411yescharacteristic
144C17×#102C2×C411yescharacteristic
145C17×#102C2×C411yescharacteristic
146C17×#102C2×C411yescharacteristic
147C17×C22⋊C8—21no—
148C17×C22⋊C8—21no—
149C17×C22⋊C8—21no—
150C17×C22⋊C8—21no—
151C17×C22⋊C8—21no—
152C17×C22⋊C8—21no—
153C17×C22⋊C8—21no—
154C17×C22⋊C8—21no—
155C17×C22⋊C8—21no—
156C17×C22⋊C8—21no—
157C17×C22⋊C8—21no—
158C17×C22⋊C8—21no—
159C17×C22⋊C8C2×C411yescharacteristic
160C17×C22⋊C8C2×C411yescharacteristic
161C17×C22⋊C8C2×C411yescharacteristic
162C17×C22⋊C8C2×C411yescharacteristic
163C17×#97—21no—
164C17×#97—41no—
165C4×C8×C17—21no—
166C4×C8×C17—41no—
167C17×#95—21no—
168C24×C17—21no—
169C24×C17#4111yescharacteristic
170#41×C17—21no—
171#41×C17—21no—
172#41×C17—21no—
173#41×C17—21no—
174#41×C17—21no—
175#41×C17—21no—
176#41×C17—21no—
177#41×C17—21no—
178#41×C17—21no—
179#41×C17—21no—
180#41×C17—21no—
181#41×C17—21no—
182#41×C17—41no—
183#41×C17—41no—
184#41×C17—41no—
185#41×C17—41no—
186#41×C17—42no—
187#41×C17—42no—
188#41×C17—42no—
189#41×C17—42no—
190C2×Q8×C17—21no—
191C2×Q8×C17—41no—
192C2×Q8×C17—41no—
193C2×Q8×C17C22×C411yescharacteristic
194C2×Q8×C17C22×C411yescharacteristic
195C2×Q8×C17C22×C411yescharacteristic
196C2×D4×C17—21no—
197C2×D4×C17—21no—
198C2×D4×C17—21no—
199C2×D4×C17—21no—
200C2×D4×C17—21no—
201C2×D4×C17—21no—
202C2×D4×C17—21no—
203C2×D4×C17—21no—
204C2×D4×C17—41no—
205C2×D4×C17—41no—
206C2×D4×C17—42no—
207C2×D4×C17—42no—
208C2×D4×C17C22×C411yescharacteristic
209C2×D4×C17C22×C411yescharacteristic
210C2×D4×C17C22×C411yescharacteristic
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—42no—
224C22×C4×C17—42no—
225C22×C4×C17C22×C411yescharacteristic
226C22×C4×C17C22×C411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17#4111yescharacteristic
230C22×C4×C17C2411yescharacteristic
231Q16×C17—41no—
232Q16×C17—41no—
233SD16×C17—41no—
234SD16×C17—41no—
235SD16×C17—41no—
236SD16×C17—41no—
237D8×C17—41no—
238D8×C17—41no—
239M16×C17—21no—
240M16×C17—21no—
241M16×C17—21no—
242M16×C17—21no—
243M16×C17—21no—
244M16×C17—21no—
245M16×C17—21no—
246M16×C17—21no—
247M16×C17—41no—
248M16×C17—41no—
249M16×C17—41no—
250M16×C17—41no—
251M16×C17—42no—
252M16×C17—42no—
253C2×C8×C17—21no—
254C2×C8×C17—21no—
255C2×C8×C17—21no—
256C2×C8×C17—21no—
257C2×C8×C17—21no—
258C2×C8×C17—21no—
259C2×C8×C17—21no—
260C2×C8×C17—21no—
261C2×C8×C17—21no—
262C2×C8×C17—21no—
263C2×C8×C17—21no—
264C2×C8×C17—21no—
265C2×C8×C17—42no—
266C2×C8×C17—42no—
267C2×C8×C17C22×C411yescharacteristic
268C2×C8×C17C22×C411yescharacteristic
269C2×C8×C17C22×C411yescharacteristic
270C2×C8×C17C22×C411yescharacteristic
271C2×C8×C17C2×D411yescharacteristic
272C2×C8×C17C2×D411yescharacteristic
273C2×C8×C17C2×D411yescharacteristic
274C2×C8×C17C2×D411yescharacteristic
275C4⋊C4×C17—21no—
276C4⋊C4×C17—21no—
277C4⋊C4×C17C22×C411yescharacteristic
278C4⋊C4×C17C22×C411yescharacteristic
279C22⋊C4×C17—21no—
280C22⋊C4×C17—21no—
281C22⋊C4×C17—21no—
282C22⋊C4×C17—21no—
283C22⋊C4×C17—21no—
284C22⋊C4×C17—42no—
285C42×C17—21no—
286C42×C17—21no—
287C42×C17—21no—
288C42×C17—21no—
289C42×C17—21no—
290#22062C1711yesmaximal, characteristic, direct product factor, Sylow
291C23×C17—21no—
292C23×C17—21no—
293C23×C17—21no—
294C23×C17—21no—
295C23×C17—21no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—42no—
299C23×C17—81no—
300C23×C17—81no—
301C23×C17C4×D411yescharacteristic
302C23×C17C4×D411yescharacteristic
303C23×C17C2×#4111yescharacteristic
304Q8×C17—21no—
305Q8×C17—21no—
306Q8×C17—21no—
307Q8×C17—21no—
308Q8×C17—21no—
309Q8×C17—21no—
310Q8×C17—42no—
311D4×C17—21no—
312D4×C17—21no—
313D4×C17—21no—
314D4×C17—21no—
315D4×C17—21no—
316D4×C17—21no—
317D4×C17—42no—
318D4×C17—42no—
319D4×C17—42no—
320D4×C17—41no—
321D4×C17—41no—
322D4×C17—41no—
323D4×C17—41no—
324D4×C17—41no—
325D4×C17—41no—
326D4×C17—81no—
327D4×C17—81no—
328C2×C4×C17—21no—
329C2×C4×C17—21no—
330C2×C4×C17—21no—
331C2×C4×C17—21no—
332C2×C4×C17—21no—
333C2×C4×C17—21no—
334C2×C4×C17—21no—
335C2×C4×C17—21no—
336C2×C4×C17—21no—
337C2×C4×C17—21no—
338C2×C4×C17—22no—
339C2×C4×C17—21no—
340C2×C4×C17—21no—
341C2×C4×C17—21no—
342C2×C4×C17—21no—
343C2×C4×C17—21no—
344C2×C4×C17—42no—
345C2×C4×C17—42no—
346C2×C4×C17—41no—
347C2×C4×C17—42no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17C4×D411yescharacteristic
359C2×C4×C17C4×D411yescharacteristic
360C2×C4×C17C23×C411yescharacteristic
361C2×C4×C17C22×D411yescharacteristic
362C2×C4×C17H(5,𝔽2)11yescharacteristic
363C2×C4×C17H(5,𝔽2)11yescharacteristic
364C2×C4×C17H(5,𝔽2)11yescharacteristic
365C2×C4×C17H(5,𝔽2)11yescharacteristic
366C8×C17—21no—
367C8×C17—21no—
368C8×C17—21no—
369C8×C17—21no—
370C8×C17—21no—
371C8×C17—21no—
372C8×C17—21no—
373C8×C17—21no—
374C8×C17—41no—
375C8×C17—41no—
376C8×C17—41no—
377C8×C17—41no—
378#3002C2×C1711yescharacteristic
379#2930C2×C1711yescharacteristic, complemented
380#2879C2×C1711yescharacteristic, complemented
381#1975C2×C1711yescharacteristic, complemented
382#1974C2×C1711yescharacteristic, complemented
383#1938C2×C1711yescharacteristic, complemented
384#1937C2×C1711yescharacteristic, complemented
385#1929C2×C1711yescharacteristic, complemented
386#1929C2×C1711yescharacteristic, complemented
387#1876C2×C1711yescharacteristic, complemented
388#1876C2×C1711yescharacteristic, complemented
389#1871C2×C1711yescharacteristic, complemented
390#1855C2×C1711yescharacteristic, complemented
391#1789C2×C1711yescharacteristic, complemented
392#1753C2×C1711yescharacteristic, complemented
393C22×C17—21no—
394C22×C17—21no—
395C22×C17—21no—
396C22×C17—21no—
397C22×C17—21no—
398C22×C17—21no—
399C22×C17—21no—
400C22×C17—21no—
401C22×C17—41no—
402C22×C17—41no—
403C22×C17—41no—
404C22×C17—41no—
405C22×C17—41no—
406C22×C17—41no—
407C22×C17—41no—
408C22×C17—41no—
409C22×C17—41no—
410C22×C17—81no—
411C22×C17—81no—
412C22×C17—84no—
413C22×C17C2×C4×D411yescharacteristic
414C22×C17#53811yescharacteristic
415C22×C17#53811yescharacteristic
416C4×C17—21no—
417C4×C17—21no—
418C4×C17—42no—
419C4×C17—41no—
420C4×C17—41no—
421C4×C17—41no—
422C4×C17—41no—
423C4×C17—41no—
424C4×C17—81no—
425C4×C17#51811yescharacteristic
426C4×C17#51811yescharacteristic
427C4×C17#53411yescharacteristic
428C4×C17#53511yescharacteristic
429C22×#41C22×C1711yescharacteristic
430C2×#135C22×C1711yescharacteristic
431C2×#135C22×C1711yescharacteristic
432C2×#131C22×C1711yescharacteristic, complemented
433C22×M16C22×C1711yescharacteristic
434C22×M16C22×C1711yescharacteristic
435#525C22×C1711yescharacteristic
436#452C4×C1711yescharacteristic, complemented
437#452C4×C1711yescharacteristic, complemented
438#451C4×C1711yescharacteristic, complemented
439#450C4×C1711yescharacteristic, complemented
440#449C4×C1711yescharacteristic, complemented
441#449C4×C1711yescharacteristic, complemented
442#448C4×C1711yescharacteristic, complemented
443#447C4×C1711yescharacteristic, complemented
444#436—21no—
445#436—21no—
446#435—21no—
447#435—21no—
448C2×#108C22×C1711yescharacteristic, complemented
449C2×#108C22×C1711yescharacteristic, complemented
450#424C22×C1711yescharacteristic, complemented
451C2×#104C22×C1711yescharacteristic
452C2×#104C22×C1711yescharacteristic
453C2×#104C22×C1711yescharacteristic
454C2×#104C22×C1711yescharacteristic
455C2×#104C22×C1711yescharacteristic, complemented
456C2×#104C22×C1711yescharacteristic, complemented
457#416C22×C1711yescharacteristic
458#416C22×C1711yescharacteristic
459#408—21no—
460#408—21no—
461#408C22×C1711yescharacteristic
462#408C22×C1711yescharacteristic
463#408C22×C1711yescharacteristic
464#408C22×C1711yescharacteristic
465#408C22×C1711yescharacteristic, complemented
466#407—21no—
467#407—21no—
468#407C22×C1711yescharacteristic
469C2×C22⋊C8C22×C1711yescharacteristic
470#405C22×C1711yescharacteristic, complemented
471C2×#97C22×C1711yescharacteristic, complemented
472C2×C4×C8C22×C1711yescharacteristic, complemented
473C4×C22⋊C4C22×C1711yescharacteristic
474#341C22×C1711yescharacteristic, complemented
475#341C22×C1711yescharacteristic, complemented
476#339C22×C1711yescharacteristic, complemented
477#339C22×C1711yescharacteristic, complemented
478#336C22×C1711yescharacteristic, complemented
479#336C22×C1711yescharacteristic, complemented
480C2×C17—21no—
481C2×C17—21no—
482C2×C17—41no—
483C2×C17—41no—
484C2×C17—81no—
485C2×C17—81no—
486C2×C17—81no—
487C2×C17#232111yescharacteristic
488C2×C17#295611yescharacteristic
489C2×C17#295711yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×C4×C1711yescharacteristic
497C2×#41C2×C4×C1711yescharacteristic
498C2×#41C23×C1711yescharacteristic
499C2×#41C23×C1711yescharacteristic
500C2×#41C23×C1711yescharacteristic
501C22×Q8C2×C4×C1711yescharacteristic
502C22×D4—21no—
503C22×D4C2×C4×C1711yescharacteristic
504C23×C4—21no—
505C23×C4C23×C1711yescharacteristic
506#135—41no—
507#135—41no—
508#135—41no—
509#135—41no—
510C2×Q16C2×C4×C1711yescharacteristic
511C2×Q16C2×C4×C1711yescharacteristic
512C2×SD16C2×C4×C1711yescharacteristic
513C2×SD16C2×C4×C1711yescharacteristic
514C2×SD16C2×C4×C1711yescharacteristic
515C2×SD16C2×C4×C1711yescharacteristic
516C2×D8C2×C4×C1711yescharacteristic
517C2×D8C2×C4×C1711yescharacteristic
518#131—41no—
519#131—41no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16D4×C1711yescharacteristic
527C2×M16D4×C1711yescharacteristic
528C2×M16D4×C1711yescharacteristic
529C2×M16D4×C1711yescharacteristic
530C2×M16C23×C1711yescharacteristic
531C2×M16C23×C1711yescharacteristic
532C2×M16C23×C1711yescharacteristic
533C2×M16C23×C1711yescharacteristic
534C22×C8—21no—
535C22×C8—21no—
536C22×C8C23×C1711yescharacteristic
537C22×C8C23×C1711yescharacteristic
538C22×C8C23×C1711yescharacteristic
539C22×C8C23×C1711yescharacteristic
540#123—21no—
541C22⋊Q8C2×C4×C1711yescharacteristic
542C22⋊Q8C2×C4×C1711yescharacteristic
543#121C2×C4×C1711yescharacteristic
544#121C2×C4×C1711yescharacteristic
545#120—21no—
546C4×D4—21no—
547C4×D4—21no—
548#117C23×C1711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C42C23×C1711yescharacteristic
551C2×C42C23×C1711yescharacteristic
552#108—41no—
553#108—41no—
554C4⋊C8—21no—
555C4⋊C8—21no—
556#104—41no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#103C2×C4×C1711yescharacteristic
563#103C2×C4×C1711yescharacteristic
564#103C2×C4×C1711yescharacteristic
565#103C2×C4×C1711yescharacteristic
566#102C2×C4×C1711yescharacteristic
567#102C2×C4×C1711yescharacteristic
568#102C2×C4×C1711yescharacteristic
569#102C2×C4×C1711yescharacteristic
570C22⋊C8—21no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8C2×C4×C1711yescharacteristic
583C22⋊C8C2×C4×C1711yescharacteristic
584C22⋊C8C2×C4×C1711yescharacteristic
585C22⋊C8C2×C4×C1711yescharacteristic
586#97—21no—
587#97—41no—
588C4×C8—21no—
589C4×C8—41no—
590#95—21no—
591C17#2206211yescharacteristic, direct product factor, Sylow
592C24—21no—
593C24#41×C1711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C1711yescharacteristic
618C2×Q8C22×C4×C1711yescharacteristic
619C2×Q8C22×C4×C1711yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C1711yescharacteristic
633C2×D4C22×C4×C1711yescharacteristic
634C2×D4C22×C4×C1711yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C1711yescharacteristic
650C22×C4C22×C4×C1711yescharacteristic
651C22×C4C2×D4×C1711yescharacteristic
652C22×C4C2×D4×C1711yescharacteristic
653C22×C4#41×C1711yescharacteristic
654C22×C4C24×C1711yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C1711yescharacteristic
692C2×C8C22×C4×C1711yescharacteristic
693C2×C8C22×C4×C1711yescharacteristic
694C2×C8C22×C4×C1711yescharacteristic
695C2×C8C2×D4×C1711yescharacteristic
696C2×C8C2×D4×C1711yescharacteristic
697C2×C8C2×D4×C1711yescharacteristic
698C2×C8C2×D4×C1711yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C1711yescharacteristic
702C4⋊C4C22×C4×C1711yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C1711yescharacteristic
725C23C4×D4×C1711yescharacteristic
726C23C2×#41×C1711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C1711yescharacteristic
782C2×C4C4×D4×C1711yescharacteristic
783C2×C4C23×C4×C1711yescharacteristic
784C2×C4C22×D4×C1711yescharacteristic
785C2×C4C17×H(5,𝔽2)11yescharacteristic
786C2×C4C17×H(5,𝔽2)11yescharacteristic
787C2×C4C17×H(5,𝔽2)11yescharacteristic
788C2×C4C17×H(5,𝔽2)11yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C1711yescharacteristic
822C22C17×#53811yescharacteristic
823C22C17×#53811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4C17×#51811yescharacteristic
834C4C17×#51811yescharacteristic
835C4C17×#53411yescharacteristic
836C4C17×#53511yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C17×#232111yescharacteristic
845C2C17×#295611yescharacteristic
846C2C17×#295711yescharacteristic
subgroupG/H
centerC2×C4×C17C22×D4
commutatorC2×C4C23×C4×C17
Frattini, cosocleC22×C4C24×C17
socleC22×C17C2×C4×D4
prime radicalC17×#3002C2
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
2. C17×#2930C2semidirect
3. C17×#2879C2semidirect
4. C17×#1975C2semidirect
5. C17×#1974C2semidirect
6. C17×#1938C2semidirect
7. C17×#1937C2semidirect
8. C17×#1929C2semidirect
9. C17×#1929C2semidirect
10. C17×#1876C2semidirect
11. C17×#1876C2semidirect
12. C17×#1871C2semidirect
13. C17×#1855C2semidirect
14. C17×#1789C2semidirect
15. C17×#1753C2semidirect
19. C2×C17×#131C22semidirect
23. C17×#452C4semidirect
24. C17×#452C4semidirect
25. C17×#451C4semidirect
26. C17×#450C4semidirect
27. C17×#449C4semidirect
28. C17×#449C4semidirect
29. C17×#448C4semidirect
30. C17×#447C4semidirect
35. C2×C17×#108C22semidirect
36. C2×C17×#108C22semidirect
37. C17×#424C22semidirect
42. C2×C17×#104C22semidirect
43. C2×C17×#104C22semidirect
52. C17×#408C22semidirect
57. C17×#405C22semidirect
58. C2×C17×#97C22semidirect
59. C2×C4×C8×C17C22semidirect
61. C17×#341C22semidirect
62. C17×#341C22semidirect
63. C17×#339C22semidirect
64. C17×#339C22semidirect
65. C17×#336C22semidirect
66. C17×#336C22semidirect
290. #22062C17direct (N × H)
379. #2930C2×C17semidirect
380. #2879C2×C17semidirect
381. #1975C2×C17semidirect
382. #1974C2×C17semidirect
383. #1938C2×C17semidirect
384. #1937C2×C17semidirect
385. #1929C2×C17semidirect
386. #1929C2×C17semidirect
387. #1876C2×C17semidirect
388. #1876C2×C17semidirect
389. #1871C2×C17semidirect
390. #1855C2×C17semidirect
391. #1789C2×C17semidirect
392. #1753C2×C17semidirect
432. C2×#131C22×C17semidirect
436. #452C4×C17semidirect
437. #452C4×C17semidirect
438. #451C4×C17semidirect
439. #450C4×C17semidirect
440. #449C4×C17semidirect
441. #449C4×C17semidirect
442. #448C4×C17semidirect
443. #447C4×C17semidirect
448. C2×#108C22×C17semidirect
449. C2×#108C22×C17semidirect
450. #424C22×C17semidirect
455. C2×#104C22×C17semidirect
456. C2×#104C22×C17semidirect
465. #408C22×C17semidirect
470. #405C22×C17semidirect
471. C2×#97C22×C17semidirect
472. C2×C4×C8C22×C17semidirect
474. #341C22×C17semidirect
475. #341C22×C17semidirect
476. #339C22×C17semidirect
477. #339C22×C17semidirect
478. #336C22×C17semidirect
479. #336C22×C17semidirect
591. C17#22062direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30022
C17×#29302
C17×#28792
C17×#19752
C17×#19742
C17×#19382
C17×#19372
C17×#19292
C17×#18762
C17×#18712
C17×#18552
C17×#17892
C17×#17532
#2206217