Finite Group Databasebeta

← C17×#14488 #16872232

Subgroups — C17×#14488 #16872232

Order 4352.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#388C211yesmaximal, characteristic
2C2×C17×#388C211yesmaximal, characteristic
3C2×C17×#385C211yesmaximal, characteristic
4C17×#1444C211yesmaximal, characteristic, complemented
5C17×#1442C211yesmaximal, characteristic, complemented
6C17×#1442C211yesmaximal, characteristic, complemented
7C17×#1441C211yesmaximal, characteristic, complemented
8C17×#1439C211yesmaximal, characteristic
9C17×#1439C211yesmaximal, characteristic
10C17×#1436C211yesmaximal, characteristic, complemented
11C17×C4⋊#95C211yesmaximal, characteristic, complemented
12C17×C4⋊#95C211yesmaximal, characteristic, complemented
13C17×#1434C211yesmaximal, characteristic, complemented
14C17×C22⋊#95C211yesmaximal, characteristic
15C17×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C17C2211yescharacteristic
17C22×C4⋊C4×C17C2211yescharacteristic
18C22×C4⋊C4×C17C2211yescharacteristic
19C22×C4⋊C4×C17C2211yescharacteristic
20C22×C4⋊C4×C17C2211yescharacteristic
21C22×C4⋊C4×C17C2211yescharacteristic
22C22×C4⋊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×C42×C17C2211yescharacteristic
30C22×C42×C17C2211yescharacteristic
31C17×#388—24no—
32C17×#388C418yescomplemented
33C17×#385—24no—
34C2×C17×#95C2211yescharacteristic
35C2×C17×#95C2211yescharacteristic
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C2×C17×#95C2211yescharacteristic
42C2×C17×#95C2211yescharacteristic
43C2×C17×#95C2211yescharacteristic
44C2×C17×#95C2211yescharacteristic
45C2×C17×#95C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C23×C4×C17—22no—
56C23×C4×C17—22no—
57C23×C4×C17—22no—
58C23×C4×C17—41no—
59C23×C4×C17—41no—
60C23×C4×C17—41no—
61C23×C4×C17—41no—
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—41no—
84C2×C4⋊C4×C17—41no—
85C2×C4⋊C4×C17—41no—
86C2×C4⋊C4×C17—41no—
87C2×C4⋊C4×C17—41no—
88C2×C4⋊C4×C17—41no—
89C2×C4⋊C4×C17—41no—
90C2×C4⋊C4×C17—41no—
91C2×C4⋊C4×C17—41no—
92C2×C4⋊C4×C17—41no—
93C2×C4⋊C4×C17C2×C414yescomplemented
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—41no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17—41no—
102C2×C22⋊C4×C17—41no—
103C2×C22⋊C4×C17—41no—
104C2×C22⋊C4×C17—41no—
105C2×C22⋊C4×C17—41no—
106C2×C22⋊C4×C17—41no—
107C2×C22⋊C4×C17C2×C414yes—
108C2×C22⋊C4×C17C2×C414yes—
109C2×C22⋊C4×C17C2×C414yes—
110C2×C22⋊C4×C17D414yes—
111C2×C22⋊C4×C17Q814yes—
112C2×C42×C17—22no—
113C2×C42×C17—22no—
114C2×C42×C17—41no—
115C2×C42×C17—41no—
116C2×C42×C17—41no—
117C2×C42×C17C2×C414yescomplemented
118C17×#95—22no—
119C17×#95—22no—
120C17×#95—22no—
121C17×#95—22no—
122C17×#95—22no—
123C17×#95—22no—
124C17×#95—22no—
125C17×#95—41no—
126C17×#95—41no—
127C17×#95—41no—
128C17×#95—41no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132C17×#95—41no—
133C17×#95—41no—
134C17×#95—41no—
135C17×#95—41no—
136C17×#95C2×C414yescomplemented
137C17×#95C2×C414yescomplemented
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17C22×C412yes—
151C24×C17C2×D412yes—
152C24×C17C2×Q812yes—
153C24×C17C2411yescharacteristic
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
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×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—21no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
240C22×C4×C17—44no—
241C22×C4×C17—44no—
242C22×C4×C17—44no—
243C22×C4×C17—44no—
244C22×C4×C17—44no—
245C22×C4×C17C22×C412yes—
246C22×C4×C17C22×C412yes—
247C22×C4×C17C22×C412yes—
248C22×C4×C17C22×C412yes—
249C22×C4×C17C22×C412yes—
250C22×C4×C17C22×C412yes—
251C22×C4×C17C2×D412yes—
252C22×C4×C17C2×D412yes—
253C22×C4×C17C2×Q812yes—
254C22×C4×C17C2×Q812yes—
255C22×C4×C17#4112yes—
256C22×C4×C17#4112yes—
257C22×C4×C17#4112yes—
258C22×C4×C17#4112yes—
259C4⋊C4×C17—44no—
260C4⋊C4×C17—44no—
261C4⋊C4×C17—44no—
262C4⋊C4×C17—44no—
263C4⋊C4×C17—44no—
264C4⋊C4×C17—44no—
265C22⋊C4×C17—44no—
266C22⋊C4×C17—44no—
267C22⋊C4×C17—44no—
268C22⋊C4×C17—44no—
269C22⋊C4×C17—44no—
270C22⋊C4×C17C4⋊C4116yescomplemented
271C42×C17—44no—
272C42×C17—44no—
273#14488C1711yesmaximal, characteristic, direct product factor, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17C2×C4⋊C414yes—
309C23×C17C23×C411yescharacteristic
310C23×C17C22×D411yescharacteristic
311C23×C17C22×Q811yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C172−1+411yescharacteristic
323C23×C172−1+411yescharacteristic
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—416no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17C2×C4⋊C414yes—
422C2×C4×C17C2×C4⋊C414yes—
423C2×#388C2×C1711yescharacteristic
424C2×#388C2×C1711yescharacteristic
425C2×#385C2×C1711yescharacteristic
426#1444C2×C1711yescharacteristic, complemented
427#1442C2×C1711yescharacteristic, complemented
428#1442C2×C1711yescharacteristic, complemented
429#1441C2×C1711yescharacteristic, complemented
430#1439C2×C1711yescharacteristic
431#1439C2×C1711yescharacteristic
432#1436C2×C1711yescharacteristic, complemented
433C4⋊#95C2×C1711yescharacteristic, complemented
434C4⋊#95C2×C1711yescharacteristic, complemented
435#1434C2×C1711yescharacteristic, complemented
436C22⋊#95C2×C1711yescharacteristic
437C22⋊#95C2×C1711yescharacteristic
438C22×C17—24no—
439C22×C17—24no—
440C22×C17—24no—
441C22×C17—42no—
442C22×C17—42no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17C22×C4⋊C411yescharacteristic
454C22×C17C4×#4111yescharacteristic
455C22×C17C4×#4111yescharacteristic
456C22×C17#51811yescharacteristic
457C22×C17#51811yescharacteristic
458C22×C17#52011yescharacteristic
459C22×C17#52011yescharacteristic
460C22×C17#53511yescharacteristic
461C22×C17#53611yescharacteristic
462C22×C17#53811yescharacteristic
463C22×C17#53811yescharacteristic
464C22×C17#53811yescharacteristic
465C22×C17#53911yescharacteristic
466C22×C17#54011yescharacteristic
467C22×C17#54211yescharacteristic
468C22×C17#54211yescharacteristic
469C22×C17#54211yescharacteristic
470C22×C17#54411yescharacteristic
471C22×C17#54411yescharacteristic
472C22×C17#54611yescharacteristic
473C22×C17#54611yescharacteristic
474C22×C17#54611yescharacteristic
475C22×C17#54611yescharacteristic
476C22×C17#55111yescharacteristic
477C22×C17#55211yescharacteristic
478C22×C17#55311yescharacteristic
479C22×C17#55411yescharacteristic
480C22×C17#55411yescharacteristic
481C22×C17#55411yescharacteristic
482C22×C17#55411yescharacteristic
483C22×C17#55611yescharacteristic
484C22×C17#56011yescharacteristic
485C22×C17#56011yescharacteristic
486C22×C17#56211yescharacteristic
487C22×C17#56211yescharacteristic
488C4×C17—24no—
489C4×C17—24no—
490C4×C17—42no—
491C4×C17—42no—
492C4×C17—42no—
493C4×C17—42no—
494C4×C17—42no—
495C4×C17—42no—
496C4×C17—42no—
497C4×C17—42no—
498C4×C17—81no—
499C4×C17—81no—
500C4×C17—81no—
501C4×C17—81no—
502C24×C4C22×C1711yescharacteristic
503C22×C4⋊C4C22×C1711yescharacteristic
504C22×C4⋊C4C22×C1711yescharacteristic
505C22×C4⋊C4C22×C1711yescharacteristic
506C22×C4⋊C4C22×C1711yescharacteristic
507C22×C4⋊C4C22×C1711yescharacteristic
508C22×C4⋊C4C22×C1711yescharacteristic
509C22×C22⋊C4C22×C1711yescharacteristic
510C22×C22⋊C4C22×C1711yescharacteristic
511C22×C22⋊C4C22×C1711yescharacteristic
512C22×C22⋊C4C22×C1711yescharacteristic
513C22×C22⋊C4C22×C1711yescharacteristic
514C22×C22⋊C4C22×C1711yescharacteristic
515C22×C42C22×C1711yescharacteristic
516C22×C42C22×C1711yescharacteristic
517#388—24no—
518#388C4×C1718yescomplemented
519#385—24no—
520C2×#95C22×C1711yescharacteristic
521C2×#95C22×C1711yescharacteristic
522C2×#95C22×C1711yescharacteristic
523C2×#95C22×C1711yescharacteristic
524C2×#95C22×C1711yescharacteristic
525C2×#95C22×C1711yescharacteristic
526C2×#95C22×C1711yescharacteristic
527C2×#95C22×C1711yescharacteristic
528C2×#95C22×C1711yescharacteristic
529C2×#95C22×C1711yescharacteristic
530C2×#95C22×C1711yescharacteristic
531C2×#95C22×C1711yescharacteristic
532C2×#95C22×C1711yescharacteristic
533C2×#95C22×C1711yescharacteristic
534C2×#95C22×C1711yescharacteristic
535C2×#95C22×C1711yescharacteristic
536C2×#95C22×C1711yescharacteristic
537C2×#95C22×C1711yescharacteristic
538C2×#95C22×C1711yescharacteristic
539C2×#95C22×C1711yescharacteristic
540C2×C17—44no—
541C2×C17#231711yescharacteristic
542C2×C17#233511yescharacteristic
543C2×C17#233711yescharacteristic
544C2×C17#234911yescharacteristic
545C2×C17#234911yescharacteristic
546C2×C17#237311yescharacteristic
547C2×C17#237711yescharacteristic
548C2×C17#268511yescharacteristic
549C2×C17#268711yescharacteristic
550C2×C17#270011yescharacteristic
551C2×C17#270311yescharacteristic
552C2×C17#274211yescharacteristic
553C2×C17#276811yescharacteristic
554C2×C17#278811yescharacteristic
555C2×C17#279011yescharacteristic
556C25C23×C1711yescharacteristic
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4C23×C1711yescharacteristic
565C23×C4C23×C1711yescharacteristic
566C23×C4C23×C1711yescharacteristic
567C23×C4C23×C1711yescharacteristic
568C23×C4C23×C1711yescharacteristic
569C23×C4C23×C1711yescharacteristic
570C23×C4C23×C1711yescharacteristic
571C23×C4C23×C1711yescharacteristic
572C23×C4C23×C1711yescharacteristic
573C23×C4C23×C1711yescharacteristic
574C23×C4C23×C1711yescharacteristic
575C23×C4C23×C1711yescharacteristic
576C23×C4C23×C1711yescharacteristic
577C23×C4C23×C1711yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4C2×C4×C1714yescomplemented
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4C2×C4×C1714yes—
610C2×C22⋊C4C2×C4×C1714yes—
611C2×C22⋊C4C2×C4×C1714yes—
612C2×C22⋊C4D4×C1714yes—
613C2×C22⋊C4Q8×C1714yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42C2×C4×C1714yescomplemented
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95C2×C4×C1714yescomplemented
639#95C2×C4×C1714yescomplemented
640C17#1448811yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C1712yes—
654C24C2×D4×C1712yes—
655C24C2×Q8×C1712yes—
656C24C24×C1711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C1712yes—
749C22×C4C22×C4×C1712yes—
750C22×C4C22×C4×C1712yes—
751C22×C4C22×C4×C1712yes—
752C22×C4C22×C4×C1712yes—
753C22×C4C22×C4×C1712yes—
754C22×C4C2×D4×C1712yes—
755C22×C4C2×D4×C1712yes—
756C22×C4C2×Q8×C1712yes—
757C22×C4C2×Q8×C1712yes—
758C22×C4#41×C1712yes—
759C22×C4#41×C1712yes—
760C22×C4#41×C1712yes—
761C22×C4#41×C1712yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C17116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C1714yes—
811C23C23×C4×C1711yescharacteristic
812C23C22×D4×C1711yescharacteristic
813C23C22×Q8×C1711yescharacteristic
814C23C2×#41×C1711yescharacteristic
815C23C2×#41×C1711yescharacteristic
816C23C2×#41×C1711yescharacteristic
817C23C2×#41×C1711yescharacteristic
818C23C17×H(5,𝔽2)11yescharacteristic
819C23C17×H(5,𝔽2)11yescharacteristic
820C23C17×H(5,𝔽2)11yescharacteristic
821C23C17×H(5,𝔽2)11yescharacteristic
822C23C17×H(5,𝔽2)11yescharacteristic
823C23C17×H(5,𝔽2)11yescharacteristic
824C23C17×2−1+411yescharacteristic
825C23C17×2−1+411yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4C2×C4⋊C4×C1714yes—
924C2×C4C2×C4⋊C4×C1714yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C1711yescharacteristic
941C22C4×#41×C1711yescharacteristic
942C22C4×#41×C1711yescharacteristic
943C22C17×#51811yescharacteristic
944C22C17×#51811yescharacteristic
945C22C17×#52011yescharacteristic
946C22C17×#52011yescharacteristic
947C22C17×#53511yescharacteristic
948C22C17×#53611yescharacteristic
949C22C17×#53811yescharacteristic
950C22C17×#53811yescharacteristic
951C22C17×#53811yescharacteristic
952C22C17×#53911yescharacteristic
953C22C17×#54011yescharacteristic
954C22C17×#54211yescharacteristic
955C22C17×#54211yescharacteristic
956C22C17×#54211yescharacteristic
957C22C17×#54411yescharacteristic
958C22C17×#54411yescharacteristic
959C22C17×#54611yescharacteristic
960C22C17×#54611yescharacteristic
961C22C17×#54611yescharacteristic
962C22C17×#54611yescharacteristic
963C22C17×#55111yescharacteristic
964C22C17×#55211yescharacteristic
965C22C17×#55311yescharacteristic
966C22C17×#55411yescharacteristic
967C22C17×#55411yescharacteristic
968C22C17×#55411yescharacteristic
969C22C17×#55411yescharacteristic
970C22C17×#55611yescharacteristic
971C22C17×#56011yescharacteristic
972C22C17×#56011yescharacteristic
973C22C17×#56211yescharacteristic
974C22C17×#56211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C17×#231711yescharacteristic
991C2C17×#233511yescharacteristic
992C2C17×#233711yescharacteristic
993C2C17×#234911yescharacteristic
994C2C17×#234911yescharacteristic
995C2C17×#237311yescharacteristic
996C2C17×#237711yescharacteristic
997C2C17×#268511yescharacteristic
998C2C17×#268711yescharacteristic
999C2C17×#270011yescharacteristic
1000C2C17×#270311yescharacteristic
1001C2C17×#274211yescharacteristic
1002C2C17×#276811yescharacteristic
1003C2C17×#278811yescharacteristic
1004C2C17×#279011yescharacteristic
subgroupG/H
center, socleC24×C17C24
commutatorC23C23×C4×C17
Frattini, cosocleC24C24×C17
prime radicalC25×C17C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

Complements

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

NH ≅ G/Ntype
4. C17×#1444C2semidirect
5. C17×#1442C2semidirect
6. C17×#1442C2semidirect
7. C17×#1441C2semidirect
10. C17×#1436C2semidirect
11. C17×C4⋊#95C2semidirect
12. C17×C4⋊#95C2semidirect
13. C17×#1434C2semidirect
32. C17×#388C4semidirect
93. C2×C4⋊C4×C17C2×C4semidirect
117. C2×C42×C17C2×C4semidirect
136. C17×#95C2×C4semidirect
137. C17×#95C2×C4semidirect
270. C22⋊C4×C17C4⋊C4semidirect
273. #14488C17direct (N × H)
426. #1444C2×C17semidirect
427. #1442C2×C17semidirect
428. #1442C2×C17semidirect
429. #1441C2×C17semidirect
432. #1436C2×C17semidirect
433. C4⋊#95C2×C17semidirect
434. C4⋊#95C2×C17semidirect
435. #1434C2×C17semidirect
518. #388C4×C17semidirect
595. C2×C4⋊C4C2×C4×C17semidirect
619. C2×C42C2×C4×C17semidirect
638. #95C2×C4×C17semidirect
639. #95C2×C4×C17semidirect
640. C17#14488direct (N × H)
773. C22⋊C4C4⋊C4×C17semidirect

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×#3852
C17×#14442
C17×#14422
C17×#14412
C17×#14392
C17×#14362
C17×C4⋊#952
C17×#14342
C17×C22⋊#952
#1448817