Finite Group Databasebeta

← C17×#62863 #16920607

Subgroups — C17×#62863 #16920607

Order 4352.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3560C218yesmaximal, complemented
2C17×#3558C218yesmaximal, complemented
3C17×#3537C218yesmaximal, complemented
4C17×#3534C218yesmaximal, complemented
5C17×#3533C218yesmaximal, complemented
6C17×#3532C218yesmaximal, complemented
7C17×#3505C214yesmaximal, complemented
8C17×#3496C214yesmaximal, complemented
9C17×#3484C214yesmaximal, complemented
10C2×C17×#538C212yesmaximal, complemented
11C2×C17×#534C211yesmaximal, characteristic, complemented
12C2×C17×H(5,𝔽2)C2214yescomplemented
13C23×D4×C17C2212yescomplemented
14C17×#563C2218yescomplemented
15C17×#562C22116yescomplemented
16C17×H(3,𝔽4)C2218yescomplemented
17C17×#560C2218yescomplemented
18C17×#560C2218yescomplemented
19C17×#560C22116yescomplemented
20C17×#559C2218yescomplemented
21C17×#553C22116yescomplemented
22C17×#553C2218yescomplemented
23C17×#553C22116yescomplemented
24C17×#552C2218yescomplemented
25C17×#551C22116yescomplemented
26C17×#551C2218yescomplemented
27C17×#551C2218yescomplemented
28C17×#548C2218yescomplemented
29C17×#547C2218yescomplemented
30C17×#547C2218yescomplemented
31C17×#546C2218yescomplemented
32C17×#546C22116yescomplemented
33C17×#546C22116yescomplemented
34C17×#546C22116yescomplemented
35C17×#546C22116yescomplemented
36C17×#546C22116yescomplemented
37D42×C17C22116yescomplemented
38D42×C17C22116yescomplemented
39D42×C17C2218yescomplemented
40D42×C17C2218yescomplemented
41D42×C17C2218yescomplemented
42C17×#542C22116yescomplemented
43C17×#540C22116yescomplemented
44C17×#539C22116yescomplemented
45C17×#539C2218yescomplemented
46C17×#538C22116yescomplemented
47C17×#538C22116yescomplemented
48C17×#538C22116yescomplemented
49C17×#538C22116yescomplemented
50C17×#538C2218yescomplemented
51C17×#538C2218yescomplemented
52C17×#538C2218yescomplemented
53C17×#537C2218yescomplemented
54C17×#535C2218yescomplemented
55C17×#535C22116yescomplemented
56C17×#534C2218yescomplemented
57C17×#534C2218yescomplemented
58C17×#534C2218yescomplemented
59C17×#534C2218yescomplemented
60C17×#534C22116yescomplemented
61C17×#534C2218yescomplemented
62C17×#532C2218yescomplemented
63C17×#529C2218yescomplemented
64C2×C17×#126C2214yescomplemented
65C2×C17×#124C2214yescomplemented
66C17×#525C2218yescomplemented
67C17×#525C2218yescomplemented
68C2×C17×#123C2214yescomplemented
69C2×C17×#123C2214yescomplemented
70C2×C17×C22⋊Q8C2212yescomplemented
71C2×C17×#121C2214yescomplemented
72C2×C17×#121C2212yescomplemented
73C2×C17×#121C2214yescomplemented
74C2×C17×#121C2218yescomplemented
75C2×C17×#120C2214yescomplemented
76C2×C17×#120C2214yescomplemented
77C2×C17×#120C2218yescomplemented
78C17×#518C2214yescomplemented
79C2×C4×D4×C17C2214yescomplemented
80C22×C22⋊C4×C17C2211yescharacteristic, complemented
81C25×C17C2311yescharacteristic
82C25×C17C2312yes—
83C17×H(5,𝔽2)—416no—
84C2×#41×C17C2318yes—
85C2×#41×C17C23116yescomplemented
86C2×#41×C17C2318yescomplemented
87C22×Q8×C17C2312yescomplemented
88C22×D4×C17—48no—
89C22×D4×C17C2314yes—
90C22×D4×C17C2314yes—
91C22×D4×C17C2314yes—
92C22×D4×C17C2318yes—
93C22×D4×C17C23116yes—
94C22×D4×C17C2314yes—
95C22×D4×C17C2314yes—
96C22×D4×C17C2314yes—
97C22×D4×C17C23116yescomplemented
98C22×D4×C17C23116yescomplemented
99C22×D4×C17C2312yescomplemented
100C22×D4×C17C2318yescomplemented
101C23×C4×C17C2312yes—
102C23×C4×C17C2312yes—
103C23×C4×C17C2314yescomplemented
104C17×C4⋊Q8C2318yescomplemented
105C17×#127C2318yes—
106C17×#127C2318yes—
107C17×#127C2318yescomplemented
108C17×#126C23116yescomplemented
109C17×#126C23116yescomplemented
110C17×#126C23116yescomplemented
111C17×#126C23116yescomplemented
112C17×#126C23116yescomplemented
113C17×#125C2318yescomplemented
114C17×#125C23116yescomplemented
115C17×#124C2318yes—
116C17×#124C2318yes—
117C17×#124C23116yescomplemented
118C17×#124C23116yescomplemented
119C17×#124C2318yescomplemented
120C17×#124C23116yescomplemented
121C17×#124C23116yescomplemented
122C17×#123C23116yes—
123C17×#123C2318yes—
124C17×#123C2318yes—
125C17×#123C23116yes—
126C17×#123C2318yes—
127C17×#123C2318yes—
128C17×#123C23116yescomplemented
129C17×#123C23116yescomplemented
130C17×#123C23116yescomplemented
131C17×#123C23116yescomplemented
132C17×#123C23116yescomplemented
133C17×#123C23116yescomplemented
134C17×#123C23116yescomplemented
135C17×#123C23116yescomplemented
136C17×C22⋊Q8C2318yes—
137C17×C22⋊Q8C2318yescomplemented
138C17×C22⋊Q8C2318yescomplemented
139C17×C22⋊Q8C23116yescomplemented
140C17×C22⋊Q8C23116yescomplemented
141C17×C22⋊Q8C23116yescomplemented
142C17×C22⋊Q8C23116yescomplemented
143C17×#121C2318yes—
144C17×#121C2318yes—
145C17×#121C2318yes—
146C17×#121C2318yes—
147C17×#121C2318yes—
148C17×#121C23116yes—
149C17×#121C23116yes—
150C17×#121C23116yes—
151C17×#121C23116yes—
152C17×#121C2318yescomplemented
153C17×#121C23116yescomplemented
154C17×#121C23116yescomplemented
155C17×#121C23116yescomplemented
156C17×#121C2318yescomplemented
157C17×#121C23116yescomplemented
158C17×#121C2318yescomplemented
159C17×#121C2318yescomplemented
160C17×#121C23116yescomplemented
161C17×#121C23116yescomplemented
162C17×#121C23116yescomplemented
163C17×#121C23116yescomplemented
164C17×#121C23116yescomplemented
165C17×#120C23116yes—
166C17×#120C23116yes—
167C17×#120C2318yes—
168C17×#120C2318yes—
169C17×#120C23116yes—
170C17×#120C23116yes—
171C17×#120C2318yes—
172C17×#120C2318yes—
173C17×#120C23116yescomplemented
174C17×#120C23116yescomplemented
175C17×#120C23116yescomplemented
176C17×#120C23116yescomplemented
177C17×#120C23116yescomplemented
178C4×Q8×C17C2318yescomplemented
179C4×D4×C17C2318yes—
180C4×D4×C17C2318yes—
181C4×D4×C17C2318yescomplemented
182C4×D4×C17C2318yescomplemented
183C4×D4×C17C23116yescomplemented
184C4×D4×C17C23116yescomplemented
185C4×D4×C17C23116yescomplemented
186C4×D4×C17C23116yescomplemented
187C4×D4×C17C23116yescomplemented
188C4×D4×C17C2318yescomplemented
189C4×D4×C17C2318yescomplemented
190C4×D4×C17C2318yescomplemented
191C4×D4×C17C23116yescomplemented
192C17×#117C2318yes—
193C17×#117C2318yescomplemented
194C17×#117C23116yescomplemented
195C2×C4⋊C4×C17C2314yes—
196C2×C4⋊C4×C17C2314yescomplemented
197C2×C4⋊C4×C17C2314yescomplemented
198C2×C4⋊C4×C17C2312yescomplemented
199C2×C4⋊C4×C17C2318yescomplemented
200C2×C4⋊C4×C17C2312yescomplemented
201C2×C22⋊C4×C17C2314yes—
202C2×C22⋊C4×C17C2314yes—
203C2×C22⋊C4×C17C2314yes—
204C2×C22⋊C4×C17C2314yes—
205C2×C22⋊C4×C17C2318yes—
206C2×C22⋊C4×C17C2318yes—
207C2×C22⋊C4×C17C2314yes—
208C2×C22⋊C4×C17C2314yes—
209C2×C22⋊C4×C17C2314yescomplemented
210C2×C22⋊C4×C17C23116yescomplemented
211C2×C22⋊C4×C17C2314yescomplemented
212C2×C22⋊C4×C17C23116yescomplemented
213C2×C42×C17C2314yescomplemented
214C24×C17—24no—
215C24×C17—44no—
216C24×C17—82no—
217C24×C17—84no—
218C24×C17C2412yes—
219C24×C17C2414yes—
220C24×C17C2414yes—
221C24×C17C2414yes—
222C24×C17C2418yes—
223C24×C17C2418yes—
224C24×C17C2411yescharacteristic
225#41×C17—416no—
226#41×C17—432no—
227#41×C17—88no—
228C2×Q8×C17—82no—
229C2×Q8×C17C2418yes—
230C2×Q8×C17C2418yes—
231C2×D4×C17—216no—
232C2×D4×C17—216no—
233C2×D4×C17—48no—
234C2×D4×C17—432no—
235C2×D4×C17—416no—
236C2×D4×C17—432no—
237C2×D4×C17—84no—
238C2×D4×C17—84no—
239C2×D4×C17—84no—
240C2×D4×C17—82no—
241C2×D4×C17—88no—
242C2×D4×C17—816no—
243C2×D4×C17C2418yes—
244C2×D4×C17C24116yes—
245C2×D4×C17C2418yes—
246C2×D4×C17C2418yes—
247C2×D4×C17C2418yes—
248C2×D4×C17C2418yes—
249C2×D4×C17C24116yes—
250C2×D4×C17C2418yes—
251C2×D4×C17C24116yes—
252C2×D4×C17C24116yes—
253C2×D4×C17C24116yes—
254C2×D4×C17C24116yes—
255C2×D4×C17C2418yes—
256C2×D4×C17C2418yes—
257C22×C4×C17—44no—
258C22×C4×C17—82no—
259C22×C4×C17—84no—
260C22×C4×C17C2414yes—
261C22×C4×C17C2414yes—
262C22×C4×C17C2414yes—
263C22×C4×C17C2418yes—
264C22×C4×C17C2418yes—
265C22×C4×C17C2414yes—
266C22×C4×C17C2418yes—
267C22×C4×C17C24116yes—
268C22×C4×C17C24116yes—
269C22×C4×C17C2418yes—
270C22×C4×C17C2412yes—
271C22×C4×C17C2412yes—
272C22×C4×C17C2414yes—
273C22×C4×C17C2414yes—
274C4⋊C4×C17C2418yes—
275C4⋊C4×C17C24116yes—
276C4⋊C4×C17C2418yes—
277C4⋊C4×C17C2418yes—
278C4⋊C4×C17C24116yes—
279C4⋊C4×C17C24116yes—
280C4⋊C4×C17C24116yes—
281C4⋊C4×C17C2418yes—
282C4⋊C4×C17C2418yes—
283C4⋊C4×C17C2418yes—
284C22⋊C4×C17C2418yes—
285C22⋊C4×C17C2418yes—
286C22⋊C4×C17C24116yes—
287C22⋊C4×C17C24116yes—
288C22⋊C4×C17C24116yes—
289C22⋊C4×C17C24116yes—
290C22⋊C4×C17C24116yes—
291C22⋊C4×C17C24116yes—
292C22⋊C4×C17C24116yes—
293C22⋊C4×C17C24116yes—
294C22⋊C4×C17C24116yes—
295C22⋊C4×C17C2414yes—
296C22⋊C4×C17C2418yes—
297C22⋊C4×C17C2414yes—
298C22⋊C4×C17C2418yes—
299C22⋊C4×C17C2418yes—
300C22⋊C4×C17C2418yes—
301C22⋊C4×C17C2418yes—
302C42×C17C2418yes—
303C42×C17C2418yes—
304C42×C17C2418yes—
305C42×C17C2418yes—
306#62863C1711yesmaximal, characteristic, direct product factor, Sylow
307C23×C17—24no—
308C23×C17—28no—
309C23×C17—28no—
310C23×C17—28no—
311C23×C17—42no—
312C23×C17—44no—
313C23×C17—44no—
314C23×C17—48no—
315C23×C17—44no—
316C23×C17—44no—
317C23×C17—44no—
318C23×C17—48no—
319C23×C17—416no—
320C23×C17—48no—
321C23×C17—416no—
322C23×C17—88no—
323C23×C17—816no—
324C23×C17H(5,𝔽2)14yes—
325C23×C17C2514yes—
326C23×C17C2518yes—
327C23×C17C2518yes—
328C23×C17C2511yescharacteristic
329C23×C17C2512yes—
330Q8×C17—48no—
331Q8×C17—48no—
332D4×C17—232no—
333D4×C17—216no—
334D4×C17—216no—
335D4×C17—48no—
336D4×C17—48no—
337D4×C17—48no—
338D4×C17—416no—
339D4×C17—416no—
340D4×C17—48no—
341D4×C17—416no—
342D4×C17—48no—
343D4×C17—416no—
344D4×C17—48no—
345D4×C17—416no—
346C2×C4×C17—28no—
347C2×C4×C17—28no—
348C2×C4×C17—48no—
349C2×C4×C17—44no—
350C2×C4×C17—42no—
351C2×C4×C17—44no—
352C2×C4×C17—48no—
353C2×C4×C17—44no—
354C2×C4×C17—42no—
355C2×C4×C17—48no—
356C2×C4×C17—416no—
357C2×C4×C17—48no—
358C2×C4×C17—44no—
359C2×C4×C17—416no—
360C2×C4×C17C2518yes—
361C2×C4×C17C2514yes—
362C2×C4×C17C2518yes—
363C2×C4×C17C2514yes—
364C2×C4×C17C2518yes—
365C2×C4×C17C2518yes—
366#3560C2×C1718yescomplemented
367#3558C2×C1718yescomplemented
368#3537C2×C1718yescomplemented
369#3534C2×C1718yescomplemented
370#3533C2×C1718yescomplemented
371#3532C2×C1718yescomplemented
372#3505C2×C1714yescomplemented
373#3496C2×C1714yescomplemented
374#3484C2×C1714yescomplemented
375C2×#538C2×C1712yescomplemented
376C2×#534C2×C1711yescharacteristic, complemented
377C22×C17—22no—
378C22×C17—22no—
379C22×C17—22no—
380C22×C17—28no—
381C22×C17—24no—
382C22×C17—28no—
383C22×C17—28no—
384C22×C17—216no—
385C22×C17—28no—
386C22×C17—28no—
387C22×C17—44no—
388C22×C17—48no—
389C22×C17—88no—
390C22×C17—88no—
391C22×C17—88no—
392C22×C17—816no—
393C22×C17—168no—
394C22×C17C2×H(5,𝔽2)12yes—
395C22×C17C2×H(5,𝔽2)14yes—
396C22×C17C2611yescharacteristic
397C4×C17—28no—
398C4×C17—28no—
399C4×C17—24no—
400C4×C17—28no—
401C4×C17—24no—
402C4×C17—28no—
403C2×H(5,𝔽2)C22×C1714yescomplemented
404C23×D4C22×C1712yescomplemented
405#563C22×C1718yescomplemented
406#562C22×C17116yescomplemented
407H(3,𝔽4)C22×C1718yescomplemented
408#560C22×C17116yescomplemented
409#560C22×C1718yescomplemented
410#560C22×C1718yescomplemented
411#559C22×C1718yescomplemented
412#553C22×C17116yescomplemented
413#553C22×C1718yescomplemented
414#553C22×C17116yescomplemented
415#552C22×C1718yescomplemented
416#551C22×C17116yescomplemented
417#551C22×C1718yescomplemented
418#551C22×C1718yescomplemented
419#548C22×C1718yescomplemented
420#547C22×C1718yescomplemented
421#547C22×C1718yescomplemented
422#546C22×C1718yescomplemented
423#546C22×C17116yescomplemented
424#546C22×C17116yescomplemented
425#546C22×C17116yescomplemented
426#546C22×C17116yescomplemented
427#546C22×C17116yescomplemented
428D42C22×C1718yescomplemented
429D42C22×C17116yescomplemented
430D42C22×C17116yescomplemented
431D42C22×C1718yescomplemented
432D42C22×C1718yescomplemented
433#542C22×C17116yescomplemented
434#540C22×C17116yescomplemented
435#539C22×C17116yescomplemented
436#539C22×C1718yescomplemented
437#538C22×C17116yescomplemented
438#538C22×C1718yescomplemented
439#538C22×C1718yescomplemented
440#538C22×C17116yescomplemented
441#538C22×C17116yescomplemented
442#538C22×C17116yescomplemented
443#538C22×C1718yescomplemented
444#537C22×C1718yescomplemented
445#535C22×C1718yescomplemented
446#535C22×C17116yescomplemented
447#534C22×C1718yescomplemented
448#534C22×C1718yescomplemented
449#534C22×C1718yescomplemented
450#534C22×C1718yescomplemented
451#534C22×C17116yescomplemented
452#534C22×C1718yescomplemented
453#532C22×C1718yescomplemented
454#529C22×C1718yescomplemented
455C2×#126C22×C1714yescomplemented
456C2×#124C22×C1714yescomplemented
457#525C22×C1718yescomplemented
458#525C22×C1718yescomplemented
459C2×#123C22×C1714yescomplemented
460C2×#123C22×C1714yescomplemented
461C2×C22⋊Q8C22×C1712yescomplemented
462C2×#121C22×C1714yescomplemented
463C2×#121C22×C1714yescomplemented
464C2×#121C22×C1712yescomplemented
465C2×#121C22×C1718yescomplemented
466C2×#120C22×C1714yescomplemented
467C2×#120C22×C1714yescomplemented
468C2×#120C22×C1718yescomplemented
469#518C22×C1714yescomplemented
470C2×C4×D4C22×C1714yescomplemented
471C22×C22⋊C4C22×C1711yescharacteristic, complemented
472C2×C17—22no—
473C2×C17—24no—
474C2×C17—44no—
475C2×C17—48no—
476C2×C17—48no—
477C2×C17C22×H(5,𝔽2)11yescharacteristic
478C2×C17H(7,𝔽2)12yes—
479C25C23×C1711yescharacteristic
480C25C23×C1712yes—
481H(5,𝔽2)—416no—
482C2×#41C23×C1718yes—
483C2×#41C23×C17116yescomplemented
484C2×#41C23×C1718yescomplemented
485C22×Q8C23×C1712yescomplemented
486C22×D4—48no—
487C22×D4C23×C1714yes—
488C22×D4C23×C1714yes—
489C22×D4C23×C1714yes—
490C22×D4C23×C1718yes—
491C22×D4C23×C17116yes—
492C22×D4C23×C1714yes—
493C22×D4C23×C1714yes—
494C22×D4C23×C1714yes—
495C22×D4C23×C17116yescomplemented
496C22×D4C23×C17116yescomplemented
497C22×D4C23×C1712yescomplemented
498C22×D4C23×C1718yescomplemented
499C23×C4C23×C1712yes—
500C23×C4C23×C1712yes—
501C23×C4C23×C1714yescomplemented
502C4⋊Q8C23×C1718yescomplemented
503#127C23×C1718yes—
504#127C23×C1718yes—
505#127C23×C1718yescomplemented
506#126C23×C17116yescomplemented
507#126C23×C17116yescomplemented
508#126C23×C17116yescomplemented
509#126C23×C17116yescomplemented
510#126C23×C17116yescomplemented
511#125C23×C1718yescomplemented
512#125C23×C17116yescomplemented
513#124C23×C1718yes—
514#124C23×C1718yes—
515#124C23×C17116yescomplemented
516#124C23×C17116yescomplemented
517#124C23×C1718yescomplemented
518#124C23×C17116yescomplemented
519#124C23×C17116yescomplemented
520#123C23×C17116yes—
521#123C23×C1718yes—
522#123C23×C1718yes—
523#123C23×C17116yes—
524#123C23×C1718yes—
525#123C23×C1718yes—
526#123C23×C17116yescomplemented
527#123C23×C17116yescomplemented
528#123C23×C17116yescomplemented
529#123C23×C17116yescomplemented
530#123C23×C17116yescomplemented
531#123C23×C17116yescomplemented
532#123C23×C17116yescomplemented
533#123C23×C17116yescomplemented
534C22⋊Q8C23×C1718yes—
535C22⋊Q8C23×C1718yescomplemented
536C22⋊Q8C23×C1718yescomplemented
537C22⋊Q8C23×C17116yescomplemented
538C22⋊Q8C23×C17116yescomplemented
539C22⋊Q8C23×C17116yescomplemented
540C22⋊Q8C23×C17116yescomplemented
541#121C23×C1718yes—
542#121C23×C1718yes—
543#121C23×C1718yes—
544#121C23×C1718yes—
545#121C23×C1718yes—
546#121C23×C17116yes—
547#121C23×C17116yes—
548#121C23×C17116yes—
549#121C23×C17116yes—
550#121C23×C1718yescomplemented
551#121C23×C17116yescomplemented
552#121C23×C17116yescomplemented
553#121C23×C17116yescomplemented
554#121C23×C1718yescomplemented
555#121C23×C17116yescomplemented
556#121C23×C1718yescomplemented
557#121C23×C1718yescomplemented
558#121C23×C17116yescomplemented
559#121C23×C17116yescomplemented
560#121C23×C17116yescomplemented
561#121C23×C17116yescomplemented
562#121C23×C17116yescomplemented
563#120C23×C17116yes—
564#120C23×C17116yes—
565#120C23×C1718yes—
566#120C23×C1718yes—
567#120C23×C17116yes—
568#120C23×C17116yes—
569#120C23×C1718yes—
570#120C23×C1718yes—
571#120C23×C17116yescomplemented
572#120C23×C17116yescomplemented
573#120C23×C17116yescomplemented
574#120C23×C17116yescomplemented
575#120C23×C17116yescomplemented
576C4×Q8C23×C1718yescomplemented
577C4×D4C23×C1718yes—
578C4×D4C23×C1718yes—
579C4×D4C23×C1718yescomplemented
580C4×D4C23×C1718yescomplemented
581C4×D4C23×C17116yescomplemented
582C4×D4C23×C17116yescomplemented
583C4×D4C23×C17116yescomplemented
584C4×D4C23×C17116yescomplemented
585C4×D4C23×C17116yescomplemented
586C4×D4C23×C1718yescomplemented
587C4×D4C23×C1718yescomplemented
588C4×D4C23×C1718yescomplemented
589C4×D4C23×C17116yescomplemented
590#117C23×C1718yes—
591#117C23×C1718yescomplemented
592#117C23×C17116yescomplemented
593C2×C4⋊C4C23×C1714yes—
594C2×C4⋊C4C23×C1714yescomplemented
595C2×C4⋊C4C23×C1714yescomplemented
596C2×C4⋊C4C23×C1712yescomplemented
597C2×C4⋊C4C23×C1718yescomplemented
598C2×C4⋊C4C23×C1712yescomplemented
599C2×C22⋊C4C23×C1714yes—
600C2×C22⋊C4C23×C1714yes—
601C2×C22⋊C4C23×C1714yes—
602C2×C22⋊C4C23×C1714yes—
603C2×C22⋊C4C23×C1718yes—
604C2×C22⋊C4C23×C1718yes—
605C2×C22⋊C4C23×C1714yes—
606C2×C22⋊C4C23×C1714yes—
607C2×C22⋊C4C23×C1714yescomplemented
608C2×C22⋊C4C23×C17116yescomplemented
609C2×C22⋊C4C23×C1714yescomplemented
610C2×C22⋊C4C23×C17116yescomplemented
611C2×C42C23×C1714yescomplemented
612C17#6286311yescharacteristic, direct product factor, Sylow
613C24—24no—
614C24—44no—
615C24—82no—
616C24—84no—
617C24C24×C1714yes—
618C24C24×C1714yes—
619C24C24×C1712yes—
620C24C24×C1714yes—
621C24C24×C1718yes—
622C24C24×C1718yes—
623C24C24×C1711yescharacteristic
624#41—416no—
625#41—432no—
626#41—88no—
627C2×Q8—82no—
628C2×Q8C24×C1718yes—
629C2×Q8C24×C1718yes—
630C2×D4—216no—
631C2×D4—216no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—416no—
635C2×D4—432no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—84no—
639C2×D4—82no—
640C2×D4—88no—
641C2×D4—816no—
642C2×D4C24×C1718yes—
643C2×D4C24×C1718yes—
644C2×D4C24×C17116yes—
645C2×D4C24×C1718yes—
646C2×D4C24×C1718yes—
647C2×D4C24×C17116yes—
648C2×D4C24×C17116yes—
649C2×D4C24×C17116yes—
650C2×D4C24×C17116yes—
651C2×D4C24×C1718yes—
652C2×D4C24×C1718yes—
653C2×D4C24×C1718yes—
654C2×D4C24×C17116yes—
655C2×D4C24×C1718yes—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—84no—
659C22×C4C24×C1714yes—
660C22×C4C24×C1714yes—
661C22×C4C24×C1714yes—
662C22×C4C24×C1714yes—
663C22×C4C24×C1714yes—
664C22×C4C24×C1712yes—
665C22×C4C24×C1712yes—
666C22×C4C24×C1714yes—
667C22×C4C24×C17116yes—
668C22×C4C24×C1718yes—
669C22×C4C24×C1718yes—
670C22×C4C24×C17116yes—
671C22×C4C24×C1718yes—
672C22×C4C24×C1718yes—
673C4⋊C4C24×C1718yes—
674C4⋊C4C24×C1718yes—
675C4⋊C4C24×C1718yes—
676C4⋊C4C24×C17116yes—
677C4⋊C4C24×C17116yes—
678C4⋊C4C24×C1718yes—
679C4⋊C4C24×C1718yes—
680C4⋊C4C24×C1718yes—
681C4⋊C4C24×C17116yes—
682C4⋊C4C24×C17116yes—
683C22⋊C4C24×C1718yes—
684C22⋊C4C24×C1714yes—
685C22⋊C4C24×C1718yes—
686C22⋊C4C24×C1714yes—
687C22⋊C4C24×C17116yes—
688C22⋊C4C24×C17116yes—
689C22⋊C4C24×C17116yes—
690C22⋊C4C24×C17116yes—
691C22⋊C4C24×C1718yes—
692C22⋊C4C24×C1718yes—
693C22⋊C4C24×C1718yes—
694C22⋊C4C24×C17116yes—
695C22⋊C4C24×C17116yes—
696C22⋊C4C24×C17116yes—
697C22⋊C4C24×C17116yes—
698C22⋊C4C24×C1718yes—
699C22⋊C4C24×C1718yes—
700C22⋊C4C24×C17116yes—
701C42C24×C1718yes—
702C42C24×C1718yes—
703C42C24×C1718yes—
704C42C24×C1718yes—
705C23—24no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—48no—
717C23—416no—
718C23—48no—
719C23—416no—
720C23—88no—
721C23—816no—
722C23C17×H(5,𝔽2)14yes—
723C23C25×C1714yes—
724C23C25×C1718yes—
725C23C25×C1718yes—
726C23C25×C1711yescharacteristic
727C23C25×C1712yes—
728Q8—48no—
729Q8—48no—
730D4—232no—
731D4—216no—
732D4—216no—
733D4—48no—
734D4—48no—
735D4—48no—
736D4—416no—
737D4—416no—
738D4—48no—
739D4—416no—
740D4—48no—
741D4—416no—
742D4—48no—
743D4—416no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—416no—
758C2×C4C25×C1718yes—
759C2×C4C25×C1714yes—
760C2×C4C25×C1714yes—
761C2×C4C25×C1718yes—
762C2×C4C25×C1718yes—
763C2×C4C25×C1718yes—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×C17×H(5,𝔽2)12yes—
782C22C2×C17×H(5,𝔽2)14yes—
783C22C26×C1711yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×C17×H(5,𝔽2)11yescharacteristic
796C2C17×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C17C26
commutator, Frattini, cosocleC22C26×C17
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3560C2semidirect
2. C17×#3558C2semidirect
3. C17×#3537C2semidirect
4. C17×#3534C2semidirect
5. C17×#3533C2semidirect
6. C17×#3532C2semidirect
7. C17×#3505C2semidirect
8. C17×#3496C2semidirect
9. C17×#3484C2semidirect
10. C2×C17×#538C2semidirect
11. C2×C17×#534C2semidirect
12. C2×C17×H(5,𝔽2)C22semidirect
13. C23×D4×C17C22semidirect
14. C17×#563C22semidirect
15. C17×#562C22semidirect
16. C17×H(3,𝔽4)C22semidirect
17. C17×#560C22semidirect
18. C17×#560C22semidirect
19. C17×#560C22semidirect
20. C17×#559C22semidirect
21. C17×#553C22semidirect
22. C17×#553C22semidirect
23. C17×#553C22semidirect
24. C17×#552C22semidirect
25. C17×#551C22semidirect
26. C17×#551C22semidirect
27. C17×#551C22semidirect
28. C17×#548C22semidirect
29. C17×#547C22semidirect
30. C17×#547C22semidirect
31. C17×#546C22semidirect
32. C17×#546C22semidirect
33. C17×#546C22semidirect
34. C17×#546C22semidirect
35. C17×#546C22semidirect
36. C17×#546C22semidirect
37. D42×C17C22semidirect
38. D42×C17C22semidirect
39. D42×C17C22semidirect
40. D42×C17C22semidirect
41. D42×C17C22semidirect
42. C17×#542C22semidirect
43. C17×#540C22semidirect
44. C17×#539C22semidirect
45. C17×#539C22semidirect
46. C17×#538C22semidirect
47. C17×#538C22semidirect
48. C17×#538C22semidirect
49. C17×#538C22semidirect
50. C17×#538C22semidirect
51. C17×#538C22semidirect
52. C17×#538C22semidirect
53. C17×#537C22semidirect
54. C17×#535C22semidirect
55. C17×#535C22semidirect
56. C17×#534C22semidirect
57. C17×#534C22semidirect
58. C17×#534C22semidirect
59. C17×#534C22semidirect
60. C17×#534C22semidirect
61. C17×#534C22semidirect
62. C17×#532C22semidirect
63. C17×#529C22semidirect
64. C2×C17×#126C22semidirect
65. C2×C17×#124C22semidirect
66. C17×#525C22semidirect
67. C17×#525C22semidirect
68. C2×C17×#123C22semidirect
69. C2×C17×#123C22semidirect
70. C2×C17×C22⋊Q8C22semidirect
71. C2×C17×#121C22semidirect
72. C2×C17×#121C22semidirect
73. C2×C17×#121C22semidirect
74. C2×C17×#121C22semidirect
75. C2×C17×#120C22semidirect
76. C2×C17×#120C22semidirect
77. C2×C17×#120C22semidirect
78. C17×#518C22semidirect
79. C2×C4×D4×C17C22semidirect
80. C22×C22⋊C4×C17C22semidirect
85. C2×#41×C17C23semidirect
86. C2×#41×C17C23semidirect
87. C22×Q8×C17C23semidirect
97. C22×D4×C17C23semidirect
98. C22×D4×C17C23semidirect
99. C22×D4×C17C23semidirect
100. C22×D4×C17C23semidirect
103. C23×C4×C17C23semidirect
104. C17×C4⋊Q8C23semidirect
107. C17×#127C23semidirect
108. C17×#126C23semidirect
109. C17×#126C23semidirect
110. C17×#126C23semidirect
111. C17×#126C23semidirect
112. C17×#126C23semidirect
113. C17×#125C23semidirect
114. C17×#125C23semidirect
117. C17×#124C23semidirect
118. C17×#124C23semidirect
119. C17×#124C23semidirect
120. C17×#124C23semidirect
121. C17×#124C23semidirect
128. C17×#123C23semidirect
129. C17×#123C23semidirect
130. C17×#123C23semidirect
131. C17×#123C23semidirect
132. C17×#123C23semidirect
133. C17×#123C23semidirect
134. C17×#123C23semidirect
135. C17×#123C23semidirect
137. C17×C22⋊Q8C23semidirect
138. C17×C22⋊Q8C23semidirect
139. C17×C22⋊Q8C23semidirect
140. C17×C22⋊Q8C23semidirect
141. C17×C22⋊Q8C23semidirect
142. C17×C22⋊Q8C23semidirect
152. C17×#121C23semidirect
153. C17×#121C23semidirect
154. C17×#121C23semidirect
155. C17×#121C23semidirect
156. C17×#121C23semidirect
157. C17×#121C23semidirect
158. C17×#121C23semidirect
159. C17×#121C23semidirect
160. C17×#121C23semidirect
161. C17×#121C23semidirect
162. C17×#121C23semidirect
163. C17×#121C23semidirect
164. C17×#121C23semidirect
173. C17×#120C23semidirect
174. C17×#120C23semidirect
175. C17×#120C23semidirect
176. C17×#120C23semidirect
177. C17×#120C23semidirect
178. C4×Q8×C17C23semidirect
181. C4×D4×C17C23semidirect
182. C4×D4×C17C23semidirect
183. C4×D4×C17C23semidirect
184. C4×D4×C17C23semidirect
185. C4×D4×C17C23semidirect
186. C4×D4×C17C23semidirect
187. C4×D4×C17C23semidirect
188. C4×D4×C17C23semidirect
189. C4×D4×C17C23semidirect
190. C4×D4×C17C23semidirect
191. C4×D4×C17C23semidirect
193. C17×#117C23semidirect
194. C17×#117C23semidirect
196. C2×C4⋊C4×C17C23semidirect
197. C2×C4⋊C4×C17C23semidirect
198. C2×C4⋊C4×C17C23semidirect
199. C2×C4⋊C4×C17C23semidirect
200. C2×C4⋊C4×C17C23semidirect
209. C2×C22⋊C4×C17C23semidirect
210. C2×C22⋊C4×C17C23semidirect
211. C2×C22⋊C4×C17C23semidirect
212. C2×C22⋊C4×C17C23semidirect
213. C2×C42×C17C23semidirect
306. #62863C17direct (N × H)
366. #3560C2×C17semidirect
367. #3558C2×C17semidirect
368. #3537C2×C17semidirect
369. #3534C2×C17semidirect
370. #3533C2×C17semidirect
371. #3532C2×C17semidirect
372. #3505C2×C17semidirect
373. #3496C2×C17semidirect
374. #3484C2×C17semidirect
375. C2×#538C2×C17semidirect
376. C2×#534C2×C17semidirect
403. C2×H(5,𝔽2)C22×C17semidirect
404. C23×D4C22×C17semidirect
405. #563C22×C17semidirect
406. #562C22×C17semidirect
407. H(3,𝔽4)C22×C17semidirect
408. #560C22×C17semidirect
409. #560C22×C17semidirect
410. #560C22×C17semidirect
411. #559C22×C17semidirect
412. #553C22×C17semidirect
413. #553C22×C17semidirect
414. #553C22×C17semidirect
415. #552C22×C17semidirect
416. #551C22×C17semidirect
417. #551C22×C17semidirect
418. #551C22×C17semidirect
419. #548C22×C17semidirect
420. #547C22×C17semidirect
421. #547C22×C17semidirect
422. #546C22×C17semidirect
423. #546C22×C17semidirect
424. #546C22×C17semidirect
425. #546C22×C17semidirect
426. #546C22×C17semidirect
427. #546C22×C17semidirect
428. D42C22×C17semidirect
429. D42C22×C17semidirect
430. D42C22×C17semidirect
431. D42C22×C17semidirect
432. D42C22×C17semidirect
433. #542C22×C17semidirect
434. #540C22×C17semidirect
435. #539C22×C17semidirect
436. #539C22×C17semidirect
437. #538C22×C17semidirect
438. #538C22×C17semidirect
439. #538C22×C17semidirect
440. #538C22×C17semidirect
441. #538C22×C17semidirect
442. #538C22×C17semidirect
443. #538C22×C17semidirect
444. #537C22×C17semidirect
445. #535C22×C17semidirect
446. #535C22×C17semidirect
447. #534C22×C17semidirect
448. #534C22×C17semidirect
449. #534C22×C17semidirect
450. #534C22×C17semidirect
451. #534C22×C17semidirect
452. #534C22×C17semidirect
453. #532C22×C17semidirect
454. #529C22×C17semidirect
455. C2×#126C22×C17semidirect
456. C2×#124C22×C17semidirect
457. #525C22×C17semidirect
458. #525C22×C17semidirect
459. C2×#123C22×C17semidirect
460. C2×#123C22×C17semidirect
461. C2×C22⋊Q8C22×C17semidirect
462. C2×#121C22×C17semidirect
463. C2×#121C22×C17semidirect
464. C2×#121C22×C17semidirect
465. C2×#121C22×C17semidirect
466. C2×#120C22×C17semidirect
467. C2×#120C22×C17semidirect
468. C2×#120C22×C17semidirect
469. #518C22×C17semidirect
470. C2×C4×D4C22×C17semidirect
471. C22×C22⋊C4C22×C17semidirect
483. C2×#41C23×C17semidirect
484. C2×#41C23×C17semidirect
485. C22×Q8C23×C17semidirect
495. C22×D4C23×C17semidirect
496. C22×D4C23×C17semidirect
497. C22×D4C23×C17semidirect
498. C22×D4C23×C17semidirect
501. C23×C4C23×C17semidirect
502. C4⋊Q8C23×C17semidirect
505. #127C23×C17semidirect
506. #126C23×C17semidirect
507. #126C23×C17semidirect
508. #126C23×C17semidirect
509. #126C23×C17semidirect
510. #126C23×C17semidirect
511. #125C23×C17semidirect
512. #125C23×C17semidirect
515. #124C23×C17semidirect
516. #124C23×C17semidirect
517. #124C23×C17semidirect
518. #124C23×C17semidirect
519. #124C23×C17semidirect
526. #123C23×C17semidirect
527. #123C23×C17semidirect
528. #123C23×C17semidirect
529. #123C23×C17semidirect
530. #123C23×C17semidirect
531. #123C23×C17semidirect
532. #123C23×C17semidirect
533. #123C23×C17semidirect
535. C22⋊Q8C23×C17semidirect
536. C22⋊Q8C23×C17semidirect
537. C22⋊Q8C23×C17semidirect
538. C22⋊Q8C23×C17semidirect
539. C22⋊Q8C23×C17semidirect
540. C22⋊Q8C23×C17semidirect
550. #121C23×C17semidirect
551. #121C23×C17semidirect
552. #121C23×C17semidirect
553. #121C23×C17semidirect
554. #121C23×C17semidirect
555. #121C23×C17semidirect
556. #121C23×C17semidirect
557. #121C23×C17semidirect
558. #121C23×C17semidirect
559. #121C23×C17semidirect
560. #121C23×C17semidirect
561. #121C23×C17semidirect
562. #121C23×C17semidirect
571. #120C23×C17semidirect
572. #120C23×C17semidirect
573. #120C23×C17semidirect
574. #120C23×C17semidirect
575. #120C23×C17semidirect
576. C4×Q8C23×C17semidirect
579. C4×D4C23×C17semidirect
580. C4×D4C23×C17semidirect
581. C4×D4C23×C17semidirect
582. C4×D4C23×C17semidirect
583. C4×D4C23×C17semidirect
584. C4×D4C23×C17semidirect
585. C4×D4C23×C17semidirect
586. C4×D4C23×C17semidirect
587. C4×D4C23×C17semidirect
588. C4×D4C23×C17semidirect
589. C4×D4C23×C17semidirect
591. #117C23×C17semidirect
592. #117C23×C17semidirect
594. C2×C4⋊C4C23×C17semidirect
595. C2×C4⋊C4C23×C17semidirect
596. C2×C4⋊C4C23×C17semidirect
597. C2×C4⋊C4C23×C17semidirect
598. C2×C4⋊C4C23×C17semidirect
607. C2×C22⋊C4C23×C17semidirect
608. C2×C22⋊C4C23×C17semidirect
609. C2×C22⋊C4C23×C17semidirect
610. C2×C22⋊C4C23×C17semidirect
611. C2×C42C23×C17semidirect
612. C17#62863direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35602
C17×#35582
C17×#35372
C17×#35342
C17×#35332
C17×#35322
C17×#35052
C17×#34962
C17×#34842
C2×C17×#5382
C2×C17×#5342
#6286317