Finite Group Databasebeta

← C17×#62862 #16920606

Subgroups — C17×#62862 #16920606

Order 4352.

7498 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3545C214yesmaximal, complemented
2C17×#3543C214yesmaximal, complemented
3C17×#3542C2116yesmaximal, complemented
4C17×#3534C218yesmaximal, complemented
5C17×#3533C218yesmaximal, complemented
6C17×#3532C218yesmaximal, complemented
7C17×#3491C212yesmaximal, complemented
8C17×#3490C214yesmaximal, complemented
9C17×#3485C212yesmaximal, complemented
10C17×#3484C214yesmaximal, complemented
11C2×C17×#535C211yesmaximal, characteristic, complemented
12C2×C17×#534C212yesmaximal, complemented
13C2×C17×H(5,𝔽2)C2212yescomplemented
14C22×#41×C17C2211yescharacteristic, complemented
15C23×D4×C17C2211yescharacteristic, complemented
16C23×D4×C17C2212yescomplemented
17C17×#563C2214yescomplemented
18C17×#562C22116yescomplemented
19C17×#562C2218yescomplemented
20C17×H(3,𝔽4)C2214yescomplemented
21C17×#560C2218yescomplemented
22C17×#560C22116yescomplemented
23C17×#560C2218yescomplemented
24C17×#559C2214yescomplemented
25C17×#555C2218yescomplemented
26C17×#553C22116yescomplemented
27C17×#552C22116yescomplemented
28C17×#551C2218yescomplemented
29C17×#551C22116yescomplemented
30C17×#551C22116yescomplemented
31C17×#551C22116yescomplemented
32C17×#550C2218yescomplemented
33C17×#547C22116yescomplemented
34C17×#546C22116yescomplemented
35C17×#546C22116yescomplemented
36C17×#546C22116yescomplemented
37C17×#546C22116yescomplemented
38C17×#546C22116yescomplemented
39C17×#546C22116yescomplemented
40D42×C17C2214yescomplemented
41D42×C17C22116yescomplemented
42D42×C17C22116yescomplemented
43C17×#543C2212yescomplemented
44C17×#542C22116yescomplemented
45C17×#540C22116yescomplemented
46C17×#540C22116yescomplemented
47C17×#539C2218yescomplemented
48C17×#539C2218yescomplemented
49C17×#538C22116yescomplemented
50C17×#538C22116yescomplemented
51C17×#538C22116yescomplemented
52C17×#538C2218yescomplemented
53C17×#537C2218yescomplemented
54C17×#536C2214yescomplemented
55C17×#535C2218yescomplemented
56C17×#535C2218yescomplemented
57C17×#535C2218yescomplemented
58C17×#535C22116yescomplemented
59C17×#534C2212yes—
60C17×#534C2218yescomplemented
61C17×#534C2218yescomplemented
62C17×#534C2218yescomplemented
63C17×#534C2218yescomplemented
64C17×#534C2218yescomplemented
65C17×#534C2214yescomplemented
66C17×#534C2214yescomplemented
67C17×#534C2218yescomplemented
68C2×C17×#127C2212yescomplemented
69C17×#529C2218yescomplemented
70C2×C17×#124C2212yescomplemented
71C17×#525C2218yescomplemented
72C17×#525C2214yescomplemented
73C17×#525C22116yescomplemented
74C2×C17×#123C2214yescomplemented
75C2×C17×#123C2214yescomplemented
76C2×C17×#123C2214yescomplemented
77C2×C17×#121C2218yescomplemented
78C2×C17×#121C2214yescomplemented
79C2×C17×#120C2214yescomplemented
80C2×C17×#120C2214yescomplemented
81C2×C17×#120C2214yescomplemented
82C2×C17×#120C2218yescomplemented
83C17×#518C2214yescomplemented
84C17×#518C2212yescomplemented
85C2×C17×#117C2211yescharacteristic, complemented
86C22×C22⋊C4×C17C2212yescomplemented
87C25×C17C2312yes—
88C25×C17C2312yescomplemented
89C17×H(5,𝔽2)—48no—
90C2×#41×C17—44no—
91C2×#41×C17C2318yes—
92C2×#41×C17C2314yes—
93C2×#41×C17C2318yescomplemented
94C2×#41×C17C23116yescomplemented
95C22×Q8×C17C2311yescharacteristic, complemented
96C22×D4×C17—44no—
97C22×D4×C17—48no—
98C22×D4×C17C2312yes—
99C22×D4×C17C2314yes—
100C22×D4×C17C2314yes—
101C22×D4×C17C2318yes—
102C22×D4×C17C2312yes—
103C22×D4×C17C2314yes—
104C22×D4×C17C2314yes—
105C22×D4×C17C2312yes—
106C22×D4×C17C2318yes—
107C22×D4×C17C2318yes—
108C22×D4×C17C2314yescomplemented
109C22×D4×C17C2311yescharacteristic, complemented
110C22×D4×C17C2318yescomplemented
111C22×D4×C17C2318yescomplemented
112C22×D4×C17C23116yescomplemented
113C23×C4×C17C2311yescharacteristic
114C23×C4×C17C2312yescomplemented
115C23×C4×C17C2312yescomplemented
116C23×C4×C17C2314yescomplemented
117C17×C4⋊Q8C2318yescomplemented
118C17×#127C2314yes—
119C17×#127C2318yescomplemented
120C17×#127C2314yescomplemented
121C17×#127C23116yescomplemented
122C17×#126C23116yescomplemented
123C17×#126C23116yescomplemented
124C17×#126C23116yescomplemented
125C17×#126C23116yescomplemented
126C17×#125C2318yescomplemented
127C17×#125C23116yescomplemented
128C17×#124C2314yes—
129C17×#124C2318yescomplemented
130C17×#124C2314yescomplemented
131C17×#124C2318yescomplemented
132C17×#124C23116yescomplemented
133C17×#124C23116yescomplemented
134C17×#124C2318yescomplemented
135C17×#124C23116yescomplemented
136C17×#123C2318yes—
137C17×#123C23116yes—
138C17×#123C2318yes—
139C17×#123C2318yes—
140C17×#123C2318yescomplemented
141C17×#123C2318yescomplemented
142C17×#123C2318yescomplemented
143C17×#123C2318yescomplemented
144C17×#123C2318yescomplemented
145C17×#123C23116yescomplemented
146C17×#123C2318yescomplemented
147C17×#123C23116yescomplemented
148C17×#123C23116yescomplemented
149C17×#123C23116yescomplemented
150C17×#123C23116yescomplemented
151C17×#123C2318yescomplemented
152C17×#123C23116yescomplemented
153C17×#123C23116yescomplemented
154C17×C22⋊Q8C23116yescomplemented
155C17×C22⋊Q8C2318yescomplemented
156C17×C22⋊Q8C23116yescomplemented
157C17×C22⋊Q8C23116yescomplemented
158C17×C22⋊Q8C2318yescomplemented
159C17×C22⋊Q8C23116yescomplemented
160C17×C22⋊Q8C23116yescomplemented
161C17×#121C23116yes—
162C17×#121C23116yes—
163C17×#121C2318yes—
164C17×#121C23116yes—
165C17×#121C2318yes—
166C17×#121C23116yescomplemented
167C17×#121C23116yescomplemented
168C17×#121C2318yescomplemented
169C17×#121C23116yescomplemented
170C17×#121C2318yescomplemented
171C17×#121C23116yescomplemented
172C17×#121C23116yescomplemented
173C17×#121C23116yescomplemented
174C17×#121C23116yescomplemented
175C17×#121C23116yescomplemented
176C17×#121C23116yescomplemented
177C17×#121C23116yescomplemented
178C17×#121C23116yescomplemented
179C17×#121C23116yescomplemented
180C17×#120C2318yes—
181C17×#120C2318yes—
182C17×#120C2318yes—
183C17×#120C2318yes—
184C17×#120C23116yes—
185C17×#120C2318yes—
186C17×#120C23116yes—
187C17×#120C2318yescomplemented
188C17×#120C2318yescomplemented
189C17×#120C2318yescomplemented
190C17×#120C2318yescomplemented
191C17×#120C2318yescomplemented
192C17×#120C23116yescomplemented
193C17×#120C23116yescomplemented
194C17×#120C2318yescomplemented
195C17×#120C2318yescomplemented
196C17×#120C23116yescomplemented
197C4×Q8×C17C2318yescomplemented
198C4×D4×C17C23116yes—
199C4×D4×C17C23116yescomplemented
200C4×D4×C17C23116yescomplemented
201C4×D4×C17C23116yescomplemented
202C4×D4×C17C23116yescomplemented
203C4×D4×C17C23116yescomplemented
204C4×D4×C17C23116yescomplemented
205C4×D4×C17C23116yescomplemented
206C4×D4×C17C2318yescomplemented
207C17×#117C2318yescomplemented
208C17×#117C2318yescomplemented
209C17×#117C2314yescomplemented
210C17×#117C23116yescomplemented
211C17×#117C23116yescomplemented
212C2×C4⋊C4×C17C2312yescomplemented
213C2×C4⋊C4×C17C2318yescomplemented
214C2×C4⋊C4×C17C2318yescomplemented
215C2×C22⋊C4×C17C2314yes—
216C2×C22⋊C4×C17C2318yes—
217C2×C22⋊C4×C17C2312yes—
218C2×C22⋊C4×C17C2318yes—
219C2×C22⋊C4×C17C2314yescomplemented
220C2×C22⋊C4×C17C2318yescomplemented
221C2×C22⋊C4×C17C2318yescomplemented
222C2×C22⋊C4×C17C2314yescomplemented
223C2×C22⋊C4×C17C2318yescomplemented
224C2×C22⋊C4×C17C2318yescomplemented
225C2×C22⋊C4×C17C23116yescomplemented
226C2×C22⋊C4×C17C2318yescomplemented
227C2×C42×C17C2312yescomplemented
228C24×C17—28no—
229C24×C17—44no—
230C24×C17—84no—
231C24×C17—84no—
232C24×C17C2412yes—
233C24×C17C2412yes—
234C24×C17C2412yes—
235C24×C17C2414yes—
236C24×C17C2414yes—
237C24×C17C2414yes—
238C24×C17C2414yes—
239C24×C17C2418yes—
240C24×C17C2411yescharacteristic
241#41×C17—416no—
242#41×C17—416no—
243#41×C17—48no—
244#41×C17—816no—
245C2×Q8×C17—42no—
246C2×Q8×C17C2418yes—
247C2×Q8×C17C2414yes—
248C2×Q8×C17C2414yes—
249C2×D4×C17—216no—
250C2×D4×C17—28no—
251C2×D4×C17—44no—
252C2×D4×C17—44no—
253C2×D4×C17—48no—
254C2×D4×C17—48no—
255C2×D4×C17—48no—
256C2×D4×C17—42no—
257C2×D4×C17—416no—
258C2×D4×C17—416no—
259C2×D4×C17—48no—
260C2×D4×C17—416no—
261C2×D4×C17—88no—
262C2×D4×C17—88no—
263C2×D4×C17—816no—
264C2×D4×C17C2418yes—
265C2×D4×C17C2418yes—
266C2×D4×C17C2418yes—
267C2×D4×C17C2412yes—
268C2×D4×C17C2412yes—
269C2×D4×C17C2414yes—
270C2×D4×C17C2418yes—
271C2×D4×C17C2414yes—
272C2×D4×C17C2418yes—
273C2×D4×C17C2414yes—
274C2×D4×C17C24116yes—
275C2×D4×C17C24116yes—
276C2×D4×C17C24116yes—
277C2×D4×C17C24116yes—
278C2×D4×C17C24116yes—
279C2×D4×C17C2412yes—
280C2×D4×C17C2414yes—
281C2×D4×C17C24116yes—
282C2×D4×C17C2412yes—
283C22×C4×C17—24no—
284C22×C4×C17—44no—
285C22×C4×C17—44no—
286C22×C4×C17—84no—
287C22×C4×C17C2414yes—
288C22×C4×C17C2414yes—
289C22×C4×C17C2411yescharacteristic
290C22×C4×C17C2411yescharacteristic
291C22×C4×C17C2412yes—
292C22×C4×C17C2418yes—
293C22×C4×C17C2418yes—
294C22×C4×C17C2418yes—
295C22×C4×C17C2414yes—
296C22×C4×C17C2418yes—
297C22×C4×C17C24116yes—
298C22×C4×C17C24116yes—
299C22×C4×C17C2414yes—
300C22×C4×C17C2418yes—
301C4⋊C4×C17C2418yes—
302C4⋊C4×C17C24116yes—
303C4⋊C4×C17C24116yes—
304C4⋊C4×C17C24116yes—
305C4⋊C4×C17C2418yes—
306C4⋊C4×C17C24116yes—
307C4⋊C4×C17C2418yes—
308C4⋊C4×C17C2418yes—
309C4⋊C4×C17C24116yes—
310C22⋊C4×C17C2418yes—
311C22⋊C4×C17C2418yes—
312C22⋊C4×C17C2418yes—
313C22⋊C4×C17C24116yes—
314C22⋊C4×C17C24116yes—
315C22⋊C4×C17C24116yes—
316C22⋊C4×C17C24116yes—
317C22⋊C4×C17C24116yes—
318C22⋊C4×C17C24116yes—
319C22⋊C4×C17C24116yes—
320C22⋊C4×C17C24116yes—
321C22⋊C4×C17C24116yes—
322C22⋊C4×C17C2418yes—
323C22⋊C4×C17C2418yes—
324C22⋊C4×C17C2418yes—
325C22⋊C4×C17C24116yes—
326C42×C17C2414yes—
327C42×C17C2418yes—
328C42×C17C24116yes—
329C42×C17C2414yes—
330#62862C1711yesmaximal, characteristic, direct product factor, Sylow
331C23×C17—24no—
332C23×C17—24no—
333C23×C17—24no—
334C23×C17—28no—
335C23×C17—28no—
336C23×C17—28no—
337C23×C17—44no—
338C23×C17—42no—
339C23×C17—44no—
340C23×C17—48no—
341C23×C17—44no—
342C23×C17—48no—
343C23×C17—48no—
344C23×C17—48no—
345C23×C17—416no—
346C23×C17—44no—
347C23×C17—48no—
348C23×C17—816no—
349C23×C17—816no—
350C23×C17H(5,𝔽2)14yes—
351C23×C17C2514yes—
352C23×C17C2518yes—
353C23×C17C2514yes—
354C23×C17C2514yes—
355C23×C17C2512yes—
356C23×C17C2511yescharacteristic
357Q8×C17—44no—
358Q8×C17—44no—
359Q8×C17—48no—
360D4×C17—216no—
361D4×C17—216no—
362D4×C17—216no—
363D4×C17—42no—
364D4×C17—44no—
365D4×C17—42no—
366D4×C17—42no—
367D4×C17—44no—
368D4×C17—42no—
369D4×C17—416no—
370D4×C17—48no—
371D4×C17—44no—
372D4×C17—44no—
373D4×C17—416no—
374D4×C17—416no—
375D4×C17—48no—
376D4×C17—416no—
377D4×C17—416no—
378D4×C17—416no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—28no—
382C2×C4×C17—28no—
383C2×C4×C17—24no—
384C2×C4×C17—48no—
385C2×C4×C17—48no—
386C2×C4×C17—48no—
387C2×C4×C17—416no—
388C2×C4×C17—44no—
389C2×C4×C17—48no—
390C2×C4×C17—44no—
391C2×C4×C17—416no—
392C2×C4×C17—48no—
393C2×C4×C17C2518yes—
394C2×C4×C17C2512yes—
395C2×C4×C17C25116yes—
396C2×C4×C17C2514yes—
397C2×C4×C17C2518yes—
398C2×C4×C17C2512yes—
399#3545C2×C1714yescomplemented
400#3543C2×C1714yescomplemented
401#3542C2×C17116yescomplemented
402#3534C2×C1718yescomplemented
403#3533C2×C1718yescomplemented
404#3532C2×C1718yescomplemented
405#3491C2×C1712yescomplemented
406#3490C2×C1714yescomplemented
407#3485C2×C1712yescomplemented
408#3484C2×C1714yescomplemented
409C2×#535C2×C1711yescharacteristic, complemented
410C2×#534C2×C1712yescomplemented
411C22×C17—24no—
412C22×C17—22no—
413C22×C17—24no—
414C22×C17—24no—
415C22×C17—28no—
416C22×C17—24no—
417C22×C17—28no—
418C22×C17—28no—
419C22×C17—216no—
420C22×C17—28no—
421C22×C17—44no—
422C22×C17—48no—
423C22×C17—48no—
424C22×C17—84no—
425C22×C17—88no—
426C22×C17—88no—
427C22×C17—88no—
428C22×C17—816no—
429C22×C17—164no—
430C22×C17C2×H(5,𝔽2)14yes—
431C22×C17C2×H(5,𝔽2)12yes—
432C22×C17C2611yescharacteristic
433C4×C17—22no—
434C4×C17—22no—
435C4×C17—28no—
436C4×C17—24no—
437C4×C17—216no—
438C4×C17—28no—
439C2×H(5,𝔽2)C22×C1712yescomplemented
440C22×#41C22×C1711yescharacteristic, complemented
441C23×D4C22×C1711yescharacteristic, complemented
442C23×D4C22×C1712yescomplemented
443#563C22×C1714yescomplemented
444#562C22×C17116yescomplemented
445#562C22×C1718yescomplemented
446H(3,𝔽4)C22×C1714yescomplemented
447#560C22×C1718yescomplemented
448#560C22×C17116yescomplemented
449#560C22×C1718yescomplemented
450#559C22×C1714yescomplemented
451#555C22×C1718yescomplemented
452#553C22×C17116yescomplemented
453#552C22×C17116yescomplemented
454#551C22×C17116yescomplemented
455#551C22×C17116yescomplemented
456#551C22×C1718yescomplemented
457#551C22×C17116yescomplemented
458#550C22×C1718yescomplemented
459#547C22×C17116yescomplemented
460#546C22×C17116yescomplemented
461#546C22×C17116yescomplemented
462#546C22×C17116yescomplemented
463#546C22×C17116yescomplemented
464#546C22×C17116yescomplemented
465#546C22×C17116yescomplemented
466D42C22×C17116yescomplemented
467D42C22×C1714yescomplemented
468D42C22×C17116yescomplemented
469#543C22×C1712yescomplemented
470#542C22×C17116yescomplemented
471#540C22×C17116yescomplemented
472#540C22×C17116yescomplemented
473#539C22×C1718yescomplemented
474#539C22×C1718yescomplemented
475#538C22×C17116yescomplemented
476#538C22×C17116yescomplemented
477#538C22×C17116yescomplemented
478#538C22×C1718yescomplemented
479#537C22×C1718yescomplemented
480#536C22×C1714yescomplemented
481#535C22×C1718yescomplemented
482#535C22×C1718yescomplemented
483#535C22×C1718yescomplemented
484#535C22×C17116yescomplemented
485#534C22×C1712yes—
486#534C22×C1718yescomplemented
487#534C22×C1718yescomplemented
488#534C22×C1714yescomplemented
489#534C22×C1718yescomplemented
490#534C22×C1718yescomplemented
491#534C22×C1718yescomplemented
492#534C22×C1718yescomplemented
493#534C22×C1714yescomplemented
494C2×#127C22×C1712yescomplemented
495#529C22×C1718yescomplemented
496C2×#124C22×C1712yescomplemented
497#525C22×C17116yescomplemented
498#525C22×C1718yescomplemented
499#525C22×C1714yescomplemented
500C2×#123C22×C1714yescomplemented
501C2×#123C22×C1714yescomplemented
502C2×#123C22×C1714yescomplemented
503C2×#121C22×C1718yescomplemented
504C2×#121C22×C1714yescomplemented
505C2×#120C22×C1714yescomplemented
506C2×#120C22×C1714yescomplemented
507C2×#120C22×C1714yescomplemented
508C2×#120C22×C1718yescomplemented
509#518C22×C1714yescomplemented
510#518C22×C1712yescomplemented
511C2×#117C22×C1711yescharacteristic, complemented
512C22×C22⋊C4C22×C1712yescomplemented
513C2×C17—24no—
514C2×C17—22no—
515C2×C17—44no—
516C2×C17—44no—
517C2×C17—48no—
518C2×C17—44no—
519C2×C17C22×H(5,𝔽2)11yescharacteristic
520C2×C17H(7,𝔽2)12yes—
521C25C23×C1712yes—
522C25C23×C1712yescomplemented
523H(5,𝔽2)—48no—
524C2×#41—44no—
525C2×#41C23×C1718yes—
526C2×#41C23×C1714yes—
527C2×#41C23×C1718yescomplemented
528C2×#41C23×C17116yescomplemented
529C22×Q8C23×C1711yescharacteristic, complemented
530C22×D4—44no—
531C22×D4—48no—
532C22×D4C23×C1712yes—
533C22×D4C23×C1714yes—
534C22×D4C23×C1714yes—
535C22×D4C23×C1718yes—
536C22×D4C23×C1712yes—
537C22×D4C23×C1714yes—
538C22×D4C23×C1714yes—
539C22×D4C23×C1712yes—
540C22×D4C23×C1718yes—
541C22×D4C23×C1718yes—
542C22×D4C23×C1714yescomplemented
543C22×D4C23×C1711yescharacteristic, complemented
544C22×D4C23×C1718yescomplemented
545C22×D4C23×C1718yescomplemented
546C22×D4C23×C17116yescomplemented
547C23×C4C23×C1711yescharacteristic
548C23×C4C23×C1712yescomplemented
549C23×C4C23×C1712yescomplemented
550C23×C4C23×C1714yescomplemented
551C4⋊Q8C23×C1718yescomplemented
552#127C23×C1714yes—
553#127C23×C1718yescomplemented
554#127C23×C1714yescomplemented
555#127C23×C17116yescomplemented
556#126C23×C17116yescomplemented
557#126C23×C17116yescomplemented
558#126C23×C17116yescomplemented
559#126C23×C17116yescomplemented
560#125C23×C1718yescomplemented
561#125C23×C17116yescomplemented
562#124C23×C1714yes—
563#124C23×C1718yescomplemented
564#124C23×C1714yescomplemented
565#124C23×C1718yescomplemented
566#124C23×C17116yescomplemented
567#124C23×C17116yescomplemented
568#124C23×C1718yescomplemented
569#124C23×C17116yescomplemented
570#123C23×C1718yes—
571#123C23×C17116yes—
572#123C23×C1718yes—
573#123C23×C1718yes—
574#123C23×C1718yescomplemented
575#123C23×C1718yescomplemented
576#123C23×C1718yescomplemented
577#123C23×C1718yescomplemented
578#123C23×C1718yescomplemented
579#123C23×C17116yescomplemented
580#123C23×C1718yescomplemented
581#123C23×C17116yescomplemented
582#123C23×C17116yescomplemented
583#123C23×C17116yescomplemented
584#123C23×C17116yescomplemented
585#123C23×C1718yescomplemented
586#123C23×C17116yescomplemented
587#123C23×C17116yescomplemented
588C22⋊Q8C23×C17116yescomplemented
589C22⋊Q8C23×C1718yescomplemented
590C22⋊Q8C23×C17116yescomplemented
591C22⋊Q8C23×C17116yescomplemented
592C22⋊Q8C23×C1718yescomplemented
593C22⋊Q8C23×C17116yescomplemented
594C22⋊Q8C23×C17116yescomplemented
595#121C23×C17116yes—
596#121C23×C17116yes—
597#121C23×C1718yes—
598#121C23×C17116yes—
599#121C23×C1718yes—
600#121C23×C17116yescomplemented
601#121C23×C17116yescomplemented
602#121C23×C1718yescomplemented
603#121C23×C17116yescomplemented
604#121C23×C1718yescomplemented
605#121C23×C17116yescomplemented
606#121C23×C17116yescomplemented
607#121C23×C17116yescomplemented
608#121C23×C17116yescomplemented
609#121C23×C17116yescomplemented
610#121C23×C17116yescomplemented
611#121C23×C17116yescomplemented
612#121C23×C17116yescomplemented
613#121C23×C17116yescomplemented
614#120C23×C1718yes—
615#120C23×C1718yes—
616#120C23×C1718yes—
617#120C23×C1718yes—
618#120C23×C17116yes—
619#120C23×C1718yes—
620#120C23×C17116yes—
621#120C23×C1718yescomplemented
622#120C23×C1718yescomplemented
623#120C23×C1718yescomplemented
624#120C23×C1718yescomplemented
625#120C23×C1718yescomplemented
626#120C23×C17116yescomplemented
627#120C23×C17116yescomplemented
628#120C23×C1718yescomplemented
629#120C23×C1718yescomplemented
630#120C23×C17116yescomplemented
631C4×Q8C23×C1718yescomplemented
632C4×D4C23×C17116yes—
633C4×D4C23×C17116yescomplemented
634C4×D4C23×C17116yescomplemented
635C4×D4C23×C17116yescomplemented
636C4×D4C23×C17116yescomplemented
637C4×D4C23×C17116yescomplemented
638C4×D4C23×C17116yescomplemented
639C4×D4C23×C17116yescomplemented
640C4×D4C23×C1718yescomplemented
641#117C23×C1718yescomplemented
642#117C23×C1718yescomplemented
643#117C23×C1714yescomplemented
644#117C23×C17116yescomplemented
645#117C23×C17116yescomplemented
646C2×C4⋊C4C23×C1712yescomplemented
647C2×C4⋊C4C23×C1718yescomplemented
648C2×C4⋊C4C23×C1718yescomplemented
649C2×C22⋊C4C23×C1714yes—
650C2×C22⋊C4C23×C1718yes—
651C2×C22⋊C4C23×C1712yes—
652C2×C22⋊C4C23×C1718yes—
653C2×C22⋊C4C23×C1714yescomplemented
654C2×C22⋊C4C23×C1718yescomplemented
655C2×C22⋊C4C23×C1718yescomplemented
656C2×C22⋊C4C23×C1714yescomplemented
657C2×C22⋊C4C23×C1718yescomplemented
658C2×C22⋊C4C23×C1718yescomplemented
659C2×C22⋊C4C23×C17116yescomplemented
660C2×C22⋊C4C23×C1718yescomplemented
661C2×C42C23×C1712yescomplemented
662C17#6286211yescharacteristic, direct product factor, Sylow
663C24—28no—
664C24—44no—
665C24—84no—
666C24—84no—
667C24C24×C1714yes—
668C24C24×C1714yes—
669C24C24×C1714yes—
670C24C24×C1712yes—
671C24C24×C1712yes—
672C24C24×C1712yes—
673C24C24×C1718yes—
674C24C24×C1714yes—
675C24C24×C1711yescharacteristic
676#41—416no—
677#41—416no—
678#41—48no—
679#41—816no—
680C2×Q8—42no—
681C2×Q8C24×C1718yes—
682C2×Q8C24×C1714yes—
683C2×Q8C24×C1714yes—
684C2×D4—216no—
685C2×D4—28no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—42no—
692C2×D4—416no—
693C2×D4—416no—
694C2×D4—48no—
695C2×D4—416no—
696C2×D4—88no—
697C2×D4—88no—
698C2×D4—816no—
699C2×D4C24×C1718yes—
700C2×D4C24×C1718yes—
701C2×D4C24×C1718yes—
702C2×D4C24×C17116yes—
703C2×D4C24×C17116yes—
704C2×D4C24×C1718yes—
705C2×D4C24×C17116yes—
706C2×D4C24×C17116yes—
707C2×D4C24×C17116yes—
708C2×D4C24×C1712yes—
709C2×D4C24×C1712yes—
710C2×D4C24×C1714yes—
711C2×D4C24×C1714yes—
712C2×D4C24×C1714yes—
713C2×D4C24×C1718yes—
714C2×D4C24×C1714yes—
715C2×D4C24×C17116yes—
716C2×D4C24×C1712yes—
717C2×D4C24×C1712yes—
718C22×C4—24no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—84no—
722C22×C4C24×C1711yescharacteristic
723C22×C4C24×C1714yes—
724C22×C4C24×C1712yes—
725C22×C4C24×C1714yes—
726C22×C4C24×C1711yescharacteristic
727C22×C4C24×C1714yes—
728C22×C4C24×C1718yes—
729C22×C4C24×C17116yes—
730C22×C4C24×C1718yes—
731C22×C4C24×C17116yes—
732C22×C4C24×C1718yes—
733C22×C4C24×C1718yes—
734C22×C4C24×C1714yes—
735C22×C4C24×C1718yes—
736C4⋊C4C24×C17116yes—
737C4⋊C4C24×C1718yes—
738C4⋊C4C24×C17116yes—
739C4⋊C4C24×C17116yes—
740C4⋊C4C24×C17116yes—
741C4⋊C4C24×C17116yes—
742C4⋊C4C24×C1718yes—
743C4⋊C4C24×C1718yes—
744C4⋊C4C24×C1718yes—
745C22⋊C4C24×C1718yes—
746C22⋊C4C24×C1718yes—
747C22⋊C4C24×C1718yes—
748C22⋊C4C24×C1718yes—
749C22⋊C4C24×C1718yes—
750C22⋊C4C24×C17116yes—
751C22⋊C4C24×C17116yes—
752C22⋊C4C24×C17116yes—
753C22⋊C4C24×C17116yes—
754C22⋊C4C24×C17116yes—
755C22⋊C4C24×C17116yes—
756C22⋊C4C24×C17116yes—
757C22⋊C4C24×C17116yes—
758C22⋊C4C24×C17116yes—
759C22⋊C4C24×C1718yes—
760C22⋊C4C24×C17116yes—
761C42C24×C1714yes—
762C42C24×C1714yes—
763C42C24×C17116yes—
764C42C24×C1718yes—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—28no—
769C23—28no—
770C23—28no—
771C23—44no—
772C23—42no—
773C23—44no—
774C23—48no—
775C23—44no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—416no—
780C23—44no—
781C23—48no—
782C23—816no—
783C23—816no—
784C23C17×H(5,𝔽2)14yes—
785C23C25×C1714yes—
786C23C25×C1718yes—
787C23C25×C1714yes—
788C23C25×C1714yes—
789C23C25×C1712yes—
790C23C25×C1711yescharacteristic
791Q8—44no—
792Q8—44no—
793Q8—48no—
794D4—216no—
795D4—216no—
796D4—216no—
797D4—42no—
798D4—44no—
799D4—42no—
800D4—42no—
801D4—44no—
802D4—42no—
803D4—416no—
804D4—48no—
805D4—44no—
806D4—44no—
807D4—416no—
808D4—416no—
809D4—48no—
810D4—416no—
811D4—416no—
812D4—416no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—48no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—416no—
822C2×C4—44no—
823C2×C4—48no—
824C2×C4—44no—
825C2×C4—416no—
826C2×C4—48no—
827C2×C4C25×C1718yes—
828C2×C4C25×C1712yes—
829C2×C4C25×C17116yes—
830C2×C4C25×C1714yes—
831C2×C4C25×C1718yes—
832C2×C4C25×C1712yes—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—24no—
839C22—28no—
840C22—28no—
841C22—216no—
842C22—28no—
843C22—44no—
844C22—48no—
845C22—48no—
846C22—88no—
847C22—88no—
848C22—88no—
849C22—84no—
850C22—816no—
851C22—164no—
852C22C2×C17×H(5,𝔽2)14yes—
853C22C2×C17×H(5,𝔽2)12yes—
854C22C26×C1711yescharacteristic
855C4—22no—
856C4—22no—
857C4—28no—
858C4—24no—
859C4—216no—
860C4—28no—
861C2—24no—
862C2—22no—
863C2—44no—
864C2—44no—
865C2—48no—
866C2—44no—
867C2C22×C17×H(5,𝔽2)11yescharacteristic
868C2C17×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×#3545C2semidirect
2. C17×#3543C2semidirect
3. C17×#3542C2semidirect
4. C17×#3534C2semidirect
5. C17×#3533C2semidirect
6. C17×#3532C2semidirect
7. C17×#3491C2semidirect
8. C17×#3490C2semidirect
9. C17×#3485C2semidirect
10. C17×#3484C2semidirect
11. C2×C17×#535C2semidirect
12. C2×C17×#534C2semidirect
13. C2×C17×H(5,𝔽2)C22semidirect
14. C22×#41×C17C22semidirect
15. C23×D4×C17C22semidirect
16. C23×D4×C17C22semidirect
17. C17×#563C22semidirect
18. C17×#562C22semidirect
19. C17×#562C22semidirect
20. C17×H(3,𝔽4)C22semidirect
21. C17×#560C22semidirect
22. C17×#560C22semidirect
23. C17×#560C22semidirect
24. C17×#559C22semidirect
25. C17×#555C22semidirect
26. C17×#553C22semidirect
27. C17×#552C22semidirect
28. C17×#551C22semidirect
29. C17×#551C22semidirect
30. C17×#551C22semidirect
31. C17×#551C22semidirect
32. C17×#550C22semidirect
33. C17×#547C22semidirect
34. C17×#546C22semidirect
35. C17×#546C22semidirect
36. C17×#546C22semidirect
37. C17×#546C22semidirect
38. C17×#546C22semidirect
39. C17×#546C22semidirect
40. D42×C17C22semidirect
41. D42×C17C22semidirect
42. D42×C17C22semidirect
43. C17×#543C22semidirect
44. C17×#542C22semidirect
45. C17×#540C22semidirect
46. C17×#540C22semidirect
47. C17×#539C22semidirect
48. C17×#539C22semidirect
49. C17×#538C22semidirect
50. C17×#538C22semidirect
51. C17×#538C22semidirect
52. C17×#538C22semidirect
53. C17×#537C22semidirect
54. C17×#536C22semidirect
55. C17×#535C22semidirect
56. C17×#535C22semidirect
57. C17×#535C22semidirect
58. C17×#535C22semidirect
60. C17×#534C22semidirect
61. C17×#534C22semidirect
62. C17×#534C22semidirect
63. C17×#534C22semidirect
64. C17×#534C22semidirect
65. C17×#534C22semidirect
66. C17×#534C22semidirect
67. C17×#534C22semidirect
68. C2×C17×#127C22semidirect
69. C17×#529C22semidirect
70. C2×C17×#124C22semidirect
71. C17×#525C22semidirect
72. C17×#525C22semidirect
73. C17×#525C22semidirect
74. C2×C17×#123C22semidirect
75. C2×C17×#123C22semidirect
76. C2×C17×#123C22semidirect
77. C2×C17×#121C22semidirect
78. C2×C17×#121C22semidirect
79. C2×C17×#120C22semidirect
80. C2×C17×#120C22semidirect
81. C2×C17×#120C22semidirect
82. C2×C17×#120C22semidirect
83. C17×#518C22semidirect
84. C17×#518C22semidirect
85. C2×C17×#117C22semidirect
86. C22×C22⋊C4×C17C22semidirect
88. C25×C17C23semidirect
93. C2×#41×C17C23semidirect
94. C2×#41×C17C23semidirect
95. C22×Q8×C17C23semidirect
108. C22×D4×C17C23semidirect
109. C22×D4×C17C23semidirect
110. C22×D4×C17C23semidirect
111. C22×D4×C17C23semidirect
112. C22×D4×C17C23semidirect
114. C23×C4×C17C23semidirect
115. C23×C4×C17C23semidirect
116. C23×C4×C17C23semidirect
117. C17×C4⋊Q8C23semidirect
119. C17×#127C23semidirect
120. C17×#127C23semidirect
121. C17×#127C23semidirect
122. C17×#126C23semidirect
123. C17×#126C23semidirect
124. C17×#126C23semidirect
125. C17×#126C23semidirect
126. C17×#125C23semidirect
127. C17×#125C23semidirect
129. C17×#124C23semidirect
130. C17×#124C23semidirect
131. C17×#124C23semidirect
132. C17×#124C23semidirect
133. C17×#124C23semidirect
134. C17×#124C23semidirect
135. C17×#124C23semidirect
140. C17×#123C23semidirect
141. C17×#123C23semidirect
142. C17×#123C23semidirect
143. C17×#123C23semidirect
144. C17×#123C23semidirect
145. C17×#123C23semidirect
146. C17×#123C23semidirect
147. C17×#123C23semidirect
148. C17×#123C23semidirect
149. C17×#123C23semidirect
150. C17×#123C23semidirect
151. C17×#123C23semidirect
152. C17×#123C23semidirect
153. C17×#123C23semidirect
154. C17×C22⋊Q8C23semidirect
155. C17×C22⋊Q8C23semidirect
156. C17×C22⋊Q8C23semidirect
157. C17×C22⋊Q8C23semidirect
158. C17×C22⋊Q8C23semidirect
159. C17×C22⋊Q8C23semidirect
160. C17×C22⋊Q8C23semidirect
166. C17×#121C23semidirect
167. C17×#121C23semidirect
168. C17×#121C23semidirect
169. C17×#121C23semidirect
170. C17×#121C23semidirect
171. C17×#121C23semidirect
172. C17×#121C23semidirect
173. C17×#121C23semidirect
174. C17×#121C23semidirect
175. C17×#121C23semidirect
176. C17×#121C23semidirect
177. C17×#121C23semidirect
178. C17×#121C23semidirect
179. C17×#121C23semidirect
187. C17×#120C23semidirect
188. C17×#120C23semidirect
189. C17×#120C23semidirect
190. C17×#120C23semidirect
191. C17×#120C23semidirect
192. C17×#120C23semidirect
193. C17×#120C23semidirect
194. C17×#120C23semidirect
195. C17×#120C23semidirect
196. C17×#120C23semidirect
197. C4×Q8×C17C23semidirect
199. C4×D4×C17C23semidirect
200. C4×D4×C17C23semidirect
201. C4×D4×C17C23semidirect
202. C4×D4×C17C23semidirect
203. C4×D4×C17C23semidirect
204. C4×D4×C17C23semidirect
205. C4×D4×C17C23semidirect
206. C4×D4×C17C23semidirect
207. C17×#117C23semidirect
208. C17×#117C23semidirect
209. C17×#117C23semidirect
210. C17×#117C23semidirect
211. C17×#117C23semidirect
212. C2×C4⋊C4×C17C23semidirect
213. C2×C4⋊C4×C17C23semidirect
214. C2×C4⋊C4×C17C23semidirect
219. C2×C22⋊C4×C17C23semidirect
220. C2×C22⋊C4×C17C23semidirect
221. C2×C22⋊C4×C17C23semidirect
222. C2×C22⋊C4×C17C23semidirect
223. C2×C22⋊C4×C17C23semidirect
224. C2×C22⋊C4×C17C23semidirect
225. C2×C22⋊C4×C17C23semidirect
226. C2×C22⋊C4×C17C23semidirect
227. C2×C42×C17C23semidirect
330. #62862C17direct (N × H)
399. #3545C2×C17semidirect
400. #3543C2×C17semidirect
401. #3542C2×C17semidirect
402. #3534C2×C17semidirect
403. #3533C2×C17semidirect
404. #3532C2×C17semidirect
405. #3491C2×C17semidirect
406. #3490C2×C17semidirect
407. #3485C2×C17semidirect
408. #3484C2×C17semidirect
409. C2×#535C2×C17semidirect
410. C2×#534C2×C17semidirect
439. C2×H(5,𝔽2)C22×C17semidirect
440. C22×#41C22×C17semidirect
441. C23×D4C22×C17semidirect
442. C23×D4C22×C17semidirect
443. #563C22×C17semidirect
444. #562C22×C17semidirect
445. #562C22×C17semidirect
446. H(3,𝔽4)C22×C17semidirect
447. #560C22×C17semidirect
448. #560C22×C17semidirect
449. #560C22×C17semidirect
450. #559C22×C17semidirect
451. #555C22×C17semidirect
452. #553C22×C17semidirect
453. #552C22×C17semidirect
454. #551C22×C17semidirect
455. #551C22×C17semidirect
456. #551C22×C17semidirect
457. #551C22×C17semidirect
458. #550C22×C17semidirect
459. #547C22×C17semidirect
460. #546C22×C17semidirect
461. #546C22×C17semidirect
462. #546C22×C17semidirect
463. #546C22×C17semidirect
464. #546C22×C17semidirect
465. #546C22×C17semidirect
466. D42C22×C17semidirect
467. D42C22×C17semidirect
468. D42C22×C17semidirect
469. #543C22×C17semidirect
470. #542C22×C17semidirect
471. #540C22×C17semidirect
472. #540C22×C17semidirect
473. #539C22×C17semidirect
474. #539C22×C17semidirect
475. #538C22×C17semidirect
476. #538C22×C17semidirect
477. #538C22×C17semidirect
478. #538C22×C17semidirect
479. #537C22×C17semidirect
480. #536C22×C17semidirect
481. #535C22×C17semidirect
482. #535C22×C17semidirect
483. #535C22×C17semidirect
484. #535C22×C17semidirect
486. #534C22×C17semidirect
487. #534C22×C17semidirect
488. #534C22×C17semidirect
489. #534C22×C17semidirect
490. #534C22×C17semidirect
491. #534C22×C17semidirect
492. #534C22×C17semidirect
493. #534C22×C17semidirect
494. C2×#127C22×C17semidirect
495. #529C22×C17semidirect
496. C2×#124C22×C17semidirect
497. #525C22×C17semidirect
498. #525C22×C17semidirect
499. #525C22×C17semidirect
500. C2×#123C22×C17semidirect
501. C2×#123C22×C17semidirect
502. C2×#123C22×C17semidirect
503. C2×#121C22×C17semidirect
504. C2×#121C22×C17semidirect
505. C2×#120C22×C17semidirect
506. C2×#120C22×C17semidirect
507. C2×#120C22×C17semidirect
508. C2×#120C22×C17semidirect
509. #518C22×C17semidirect
510. #518C22×C17semidirect
511. C2×#117C22×C17semidirect
512. C22×C22⋊C4C22×C17semidirect
522. C25C23×C17semidirect
527. C2×#41C23×C17semidirect
528. C2×#41C23×C17semidirect
529. C22×Q8C23×C17semidirect
542. C22×D4C23×C17semidirect
543. C22×D4C23×C17semidirect
544. C22×D4C23×C17semidirect
545. C22×D4C23×C17semidirect
546. C22×D4C23×C17semidirect
548. C23×C4C23×C17semidirect
549. C23×C4C23×C17semidirect
550. C23×C4C23×C17semidirect
551. C4⋊Q8C23×C17semidirect
553. #127C23×C17semidirect
554. #127C23×C17semidirect
555. #127C23×C17semidirect
556. #126C23×C17semidirect
557. #126C23×C17semidirect
558. #126C23×C17semidirect
559. #126C23×C17semidirect
560. #125C23×C17semidirect
561. #125C23×C17semidirect
563. #124C23×C17semidirect
564. #124C23×C17semidirect
565. #124C23×C17semidirect
566. #124C23×C17semidirect
567. #124C23×C17semidirect
568. #124C23×C17semidirect
569. #124C23×C17semidirect
574. #123C23×C17semidirect
575. #123C23×C17semidirect
576. #123C23×C17semidirect
577. #123C23×C17semidirect
578. #123C23×C17semidirect
579. #123C23×C17semidirect
580. #123C23×C17semidirect
581. #123C23×C17semidirect
582. #123C23×C17semidirect
583. #123C23×C17semidirect
584. #123C23×C17semidirect
585. #123C23×C17semidirect
586. #123C23×C17semidirect
587. #123C23×C17semidirect
588. C22⋊Q8C23×C17semidirect
589. C22⋊Q8C23×C17semidirect
590. C22⋊Q8C23×C17semidirect
591. C22⋊Q8C23×C17semidirect
592. C22⋊Q8C23×C17semidirect
593. C22⋊Q8C23×C17semidirect
594. C22⋊Q8C23×C17semidirect
600. #121C23×C17semidirect
601. #121C23×C17semidirect
602. #121C23×C17semidirect
603. #121C23×C17semidirect
604. #121C23×C17semidirect
605. #121C23×C17semidirect
606. #121C23×C17semidirect
607. #121C23×C17semidirect
608. #121C23×C17semidirect
609. #121C23×C17semidirect
610. #121C23×C17semidirect
611. #121C23×C17semidirect
612. #121C23×C17semidirect
613. #121C23×C17semidirect
621. #120C23×C17semidirect
622. #120C23×C17semidirect
623. #120C23×C17semidirect
624. #120C23×C17semidirect
625. #120C23×C17semidirect
626. #120C23×C17semidirect
627. #120C23×C17semidirect
628. #120C23×C17semidirect
629. #120C23×C17semidirect
630. #120C23×C17semidirect
631. C4×Q8C23×C17semidirect
633. C4×D4C23×C17semidirect
634. C4×D4C23×C17semidirect
635. C4×D4C23×C17semidirect
636. C4×D4C23×C17semidirect
637. C4×D4C23×C17semidirect
638. C4×D4C23×C17semidirect
639. C4×D4C23×C17semidirect
640. C4×D4C23×C17semidirect
641. #117C23×C17semidirect
642. #117C23×C17semidirect
643. #117C23×C17semidirect
644. #117C23×C17semidirect
645. #117C23×C17semidirect
646. C2×C4⋊C4C23×C17semidirect
647. C2×C4⋊C4C23×C17semidirect
648. C2×C4⋊C4C23×C17semidirect
653. C2×C22⋊C4C23×C17semidirect
654. C2×C22⋊C4C23×C17semidirect
655. C2×C22⋊C4C23×C17semidirect
656. C2×C22⋊C4C23×C17semidirect
657. C2×C22⋊C4C23×C17semidirect
658. C2×C22⋊C4C23×C17semidirect
659. C2×C22⋊C4C23×C17semidirect
660. C2×C22⋊C4C23×C17semidirect
661. C2×C42C23×C17semidirect
662. C17#62862direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35452
C17×#35432
C17×#35422
C17×#35342
C17×#35332
C17×#35322
C17×#34912
C17×#34902
C17×#34852
C17×#34842
C2×C17×#5352
C2×C17×#5342
#6286217