Finite Group Databasebeta

← #17197364

Subgroups — #17197364

Order 4352.

2318 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531976C214yesmaximal, complemented
2#14531804C212yesmaximal
3#14531793C212yesmaximal, complemented
4#14531741C211yesmaximal, characteristic, complemented
5#14531733C211yesmaximal, characteristic, complemented
6#14531713C212yesmaximal, complemented
7Q8×C4⋊Dic17C211yesmaximal, characteristic, complemented
8D4×C4⋊Dic17C212yesmaximal, complemented
9D4×C4⋊Dic17C211yesmaximal, characteristic, complemented
10#14531526C212yesmaximal, complemented
11#14531497C212yesmaximal, complemented
12#14531456C214yesmaximal, complemented
13#14531407C212yesmaximal, complemented
14#14531393C212yesmaximal, complemented
15C2×#11762679C211yesmaximal, characteristic, complemented
16#14531182C211yesmaximal, characteristic, complemented
17C2×C17×#529C211yesmaximal, characteristic
18C2×Q8×Dic17C2212yes—
19C2×D4×Dic17C2214yes—
20C2×D4×Dic17C2212yes—
21C2×#10587612C2212yes—
22C22×C4⋊Dic17C2212yes—
23C22×C4⋊Dic17C2212yes—
24C22×C4⋊Dic17C2212yes—
25C22×C4⋊Dic17C2212yes—
26#11762716C2212yes—
27#11762712C2212yes—
28#11762708C2214yes—
29#11762708C2214yes—
30#11762708C2214yes—
31#11762708C2212yes—
32#11762708C2214yes—
33#11762708C2212yes—
34#11762702C2214yes—
35#11762702C2214yes—
36#11762702C2214yes—
37#11762702C2214yes—
38#11762695C2214yes—
39#11762695C2214yes—
40#11762695C2214yes—
41#11762695C2214yes—
42#11762689C2214yes—
43#11762684C2214yes—
44#11762684C2214yes—
45#11762684C2214yes—
46#11762684C2214yes—
47#11762684C2214yes—
48#11762679C2212yes—
49#11762679C2212yes—
50#11762679C2211yescharacteristic
51#11762679C2211yescharacteristic
52#11762679C2212yes—
53#11762679C2212yes—
54#11762677C2212yes—
55#11762675C2211yescharacteristic
56#11762675C2211yescharacteristic
57#11762675C2212yes—
58#11762672C2212yes—
59#11762669C2212yes—
60#11762669C2212yes—
61#11762669C2211yescharacteristic
62#11762669C2211yescharacteristic
63C4⋊C4×Dic17C2212yes—
64C4⋊C4×Dic17C2212yes—
65C4×C4⋊Dic17C2212yes—
66C4×C4⋊Dic17C2212yes—
67C4×C4⋊Dic17C2211yescharacteristic
68C4×C4⋊Dic17C2211yescharacteristic
69C22⋊C4×Dic17C2214yes—
70C4×C22⋊Dic17C2212yes—
71#11762655C2212yes—
72C17×#529C4116yescomplemented
73C2×C17×#126C2212yes—
74C2×C17×#125C2211yescharacteristic
75C2×C17×#124C2211yescharacteristic
76C2×C17×#123C2212yes—
77C2×C17×C22⋊Q8C2211yescharacteristic
78C2×C17×#121C2211yescharacteristic
79C2×C4×Q8×C17C2211yescharacteristic
80C2×C4×D4×C17C2212yes—
81C2×C4×D4×C17C2211yescharacteristic
82C2×C17×#117C2212yes—
83C22×C42×C17C2211yescharacteristic
84C22×Q8×C17C2311yescharacteristic
85C22×D4×C17C2312yes—
86C22×D4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×C4×C17C2311yescharacteristic
89C23×C4×C17C2311yescharacteristic
90C23×C4×C17C2312yes—
91C23×Dic17C2314yes—
92C23×Dic17C2314yes—
93C17×#126C2×C4116yescomplemented
94C17×#125C2×C418yescomplemented
95C17×#124C2×C418yescomplemented
96C17×#123C2×C4116yescomplemented
97C17×C22⋊Q8C2×C418yescomplemented
98C17×#121C2×C418yes—
99C4×Q8×C17C2×C418yescomplemented
100C4×D4×C17C2×C418yescomplemented
101C4×D4×C17C2×C4116yescomplemented
102C17×#117C2×C4116yescomplemented
103C2×C4⋊C4×C17C2312yes—
104C2×C4⋊C4×C17C2312yes—
105C2×C4⋊C4×C17C2312yes—
106C2×C4⋊C4×C17C2312yes—
107C2×C4⋊C4×C17C2311yescharacteristic
108C2×C4⋊C4×C17C2311yescharacteristic
109C2×C22⋊C4×C17C2312yes—
110C2×C22⋊C4×C17C2312yes—
111C2×C22⋊C4×C17C2312yes—
112C2×C22⋊C4×C17C2312yes—
113C2×C22⋊C4×C17C2312yes—
114C2×C42×C17C2×C418yescomplemented
115C2×C42×C17C2311yescharacteristic
116C2×C42×C17C2311yescharacteristic
117C2×C42×C17C2311yescharacteristic
118C2×C42×C17C2311yescharacteristic
119C2×C42×C17C2312yes—
120C2×C22⋊Dic17C2312yes—
121C2×C22⋊Dic17C2312yes—
122C2×C22⋊Dic17C2314yes—
123C2×C22⋊Dic17C2314yes—
124C2×C22⋊Dic17C2314yes—
125Q8×Dic17—44no—
126D4×Dic17—48no—
127D4×Dic17—44no—
128#10587612—44no—
129C2×C4⋊Dic17—44no—
130C2×C4⋊Dic17—44no—
131C2×C4⋊Dic17—44no—
132C2×C4⋊Dic17—44no—
133C2×C4⋊Dic17C2312yes—
134C2×C4⋊Dic17C2312yes—
135C2×C4⋊Dic17C2311yescharacteristic
136C2×C4⋊Dic17C2312yes—
137C2×C4⋊Dic17C2312yes—
138C2×C4⋊Dic17C2311yescharacteristic
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2312yes—
142C2×C4⋊Dic17C2314yes—
143C2×C4⋊Dic17C2314yes—
144C2×C4⋊Dic17C2314yes—
145C2×C4⋊Dic17C2312yes—
146C2×C4⋊Dic17C2314yes—
147C2×C4⋊Dic17C2314yes—
148C2×C4⋊Dic17C2314yes—
149C2×C4×Dic17C2312yes—
150C2×C4×Dic17C2312yes—
151C2×C4×Dic17C2314yes—
152C2×C4×Dic17C2314yes—
153C2×C4×Dic17C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2312yes—
158#10587502C2312yes—
159#10587502C2312yes—
160#10587502C2312yes—
161#10587502C2314yes—
162#10587502C2314yes—
163#10587502C2314yes—
164#10587502C2312yes—
165#10587502C2312yes—
166#10587502C2312yes—
167#10587502C2312yes—
168C24×C17C2412yes—
169C24×C17C2411yescharacteristic
170C2×Q8×C17—22no—
171C2×Q8×C17—22no—
172C2×Q8×C17C22×C414yes—
173C2×D4×C17—24no—
174C2×D4×C17—24no—
175C2×D4×C17—22no—
176C2×D4×C17—22no—
177C2×D4×C17C22×C418yes—
178C2×D4×C17C22×C414yes—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—24no—
184C22×C4×C17—22no—
185C22×C4×C17—24no—
186C22×C4×C17—22no—
187C22×C4×C17C22×C414yes—
188C22×C4×C17C22×C414yes—
189C22×C4×C17C22×C414yes—
190C22×C4×C17C22×C418yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2411yescharacteristic
193C22×C4×C17C2411yescharacteristic
194C22×C4×C17C2411yescharacteristic
195C22×C4×C17C2411yescharacteristic
196C22×C4×C17C2412yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2411yescharacteristic
199C22×C4×C17C2411yescharacteristic
200C22×Dic17—28no—
201C22×Dic17—44no—
202C22×Dic17—44no—
203C22×Dic17—44no—
204C22×Dic17—44no—
205C22×Dic17—44no—
206C22×Dic17C2412yes—
207C22×Dic17C2414yes—
208C22×Dic17C2414yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C4⋊C4×C17C22×C414yes—
213C4⋊C4×C17C22×C418yes—
214C4⋊C4×C17C22×C418yes—
215C4⋊C4×C17C22×C418yes—
216C4⋊C4×C17C22×C418yes—
217C4⋊C4×C17C22×C414yes—
218C22⋊C4×C17C22×C418yes—
219C22⋊C4×C17C22×C418yes—
220C22⋊C4×C17C22×C418yes—
221C22⋊C4×C17C22×C418yes—
222C22⋊C4×C17C22×C418yes—
223C42×C17C22×C414yes—
224C42×C17C22×C414yes—
225C42×C17C22×C414yes—
226C42×C17C22×C414yes—
227C42×C17C22×C418yes—
228C22⋊Dic17—24no—
229C22⋊Dic17—24no—
230C22⋊Dic17—44no—
231C22⋊Dic17—44no—
232C22⋊Dic17—44no—
233C4⋊Dic17—24no—
234C4⋊Dic17—22no—
235C4⋊Dic17—24no—
236C4⋊Dic17—24no—
237C4⋊Dic17—24no—
238C4⋊Dic17—22no—
239C4⋊Dic17—22no—
240C4⋊Dic17—22no—
241C4⋊Dic17—42no—
242C4⋊Dic17—44no—
243C4⋊Dic17—44no—
244C4⋊Dic17—44no—
245C4⋊Dic17—42no—
246C4⋊Dic17—44no—
247C4⋊Dic17—44no—
248C4⋊Dic17—44no—
249C4×Dic17—24no—
250C4×Dic17—24no—
251C4×Dic17—44no—
252C4×Dic17—44no—
253C4×Dic17—44no—
254#34384—171nomaximal, Sylow
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—22no—
260C23×C17—22no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17C23×C414yes—
266C23×C17C23×C412yes—
267C23×C17H(5,𝔽2)12yes—
268C23×C172−1+412yes—
269C23×C17C2511yescharacteristic
270Q8×C17—28no—
271D4×C17—216no—
272D4×C17—28no—
273C2×C4×C17—28no—
274C2×C4×C17—22no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—28no—
289C2×C4×C17—216no—
290C2×C4×C17—28no—
291C2×C4×C17C23×C412yes—
292C2×C4×C17C23×C412yes—
293C2×C4×C17C23×C412yes—
294C2×C4×C17C23×C412yes—
295C2×C4×C17C23×C414yes—
296C2×C4×C17C23×C414yes—
297C2×C4×C17C23×C414yes—
298C2×C4×C17C23×C412yes—
299C2×C4×C17C23×C412yes—
300C2×C4×C17H(5,𝔽2)12yes—
301C2×C4×C17H(5,𝔽2)12yes—
302C2×C4×C172−1+412yes—
303C2×C4×C172−1+412yes—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—24no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—24no—
315C2×Dic17—24no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—88no—
323C2×Dic17—88no—
324C2×#529D1711yescharacteristic
325#2383—174no—
326#2361—172no—
327#2360—172no—
328#2355—171no—
329#2354—171no—
330#2352—172no—
331Q8×C4⋊C4—171no—
332D4×C4⋊C4—171no—
333D4×C4⋊C4—172no—
334#2330—172no—
335#2326—172no—
336#2322—174no—
337#2317—172no—
338#2314—172no—
339C2×#384—171no—
340#2283—171no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—24no—
348C22×C17—24no—
349C22×C17—24no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17#52014yes—
355C22×C17C24×C411yescharacteristic
356C22×C17C2×H(5,𝔽2)11yescharacteristic
357C22×C17C2×H(5,𝔽2)11yescharacteristic
358C22×C17C2×H(5,𝔽2)11yescharacteristic
359C22×C17C2×2−1+411yescharacteristic
360C22×C17C2×2−1+411yescharacteristic
361C22×C17C2×2−1+411yescharacteristic
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—24no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17—24no—
368C4×C17—24no—
369C4×C17#52014yes—
370C4×C17#52014yes—
371Dic17—44no—
372Dic17—42no—
373Dic17—44no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377#529Dic17116yescomplemented
378C2×#126C2×D1712yes—
379C2×#125C2×D1711yescharacteristic
380C2×#124C2×D1711yescharacteristic
381C2×#123C2×D1712yes—
382C2×C22⋊Q8C2×D1711yescharacteristic
383C2×#121C2×D1711yescharacteristic
384C2×C4×Q8—172no—
385C2×C4×Q8C2×D1711yescharacteristic
386C2×C4×D4—174no—
387C2×C4×D4—172no—
388C2×C4×D4C2×D1712yes—
389C2×C4×D4C2×D1711yescharacteristic
390C2×#117—172no—
391C2×#117C2×D1712yes—
392C22×C4⋊C4—172no—
393C22×C4⋊C4—172no—
394C22×C4⋊C4—172no—
395C22×C4⋊C4—172no—
396C22×C42C2×D1711yescharacteristic
397#391—172no—
398#390—172no—
399#389—174no—
400#389—174no—
401#389—174no—
402#389—172no—
403#389—174no—
404#389—172no—
405#388—174no—
406#388—174no—
407#388—174no—
408#388—174no—
409#387—174no—
410#387—174no—
411#387—174no—
412#387—174no—
413#386—174no—
414#385—174no—
415#385—174no—
416#385—174no—
417#385—174no—
418#385—174no—
419#384—172no—
420#384—172no—
421#384—172no—
422#384—171no—
423#384—171no—
424#384—172no—
425#383—172no—
426#382—171no—
427#382—171no—
428#382—172no—
429#381—172no—
430#380—172no—
431#380—172no—
432#380—171no—
433#380—171no—
434C4×C4⋊C4—172no—
435C4×C4⋊C4—172no—
436C4×C4⋊C4—172no—
437C4×C4⋊C4—172no—
438C4×C4⋊C4—171no—
439C4×C4⋊C4—171no—
440C4×C22⋊C4—172no—
441C4×C22⋊C4—174no—
442#376—172no—
443C2×C17—24no—
444C2×C17—44no—
445C2×C17C2×#52011yescharacteristic
446C2×C17C2×#52011yescharacteristic
447C2×C17C2×#52011yescharacteristic
448C2×C17#354311yescharacteristic
449C2×C17#354411yescharacteristic
450C2×C17#355211yescharacteristic
451C2×C17#355211yescharacteristic
452C22×Q8C22×D1711yescharacteristic
453C22×D4C22×D1712yes—
454C22×D4C22×D1711yescharacteristic
455C23×C4—174no—
456C23×C4—174no—
457C23×C4C22×D1711yescharacteristic
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C23×C4C22×D1712yes—
461#126C2×Dic17116yescomplemented
462#125C2×Dic1718yescomplemented
463#124C2×Dic1718yescomplemented
464#123C2×Dic17116yescomplemented
465C22⋊Q8C2×Dic1718yescomplemented
466#121C2×Dic1718yes—
467C4×Q8—684no—
468C4×Q8C2×Dic1718yescomplemented
469C4×D4—684no—
470C4×D4—688no—
471C4×D4C2×Dic1718yescomplemented
472C4×D4C2×Dic17116yescomplemented
473#117—684no—
474#117C2×Dic17116yescomplemented
475C2×C4⋊C4—171no—
476C2×C4⋊C4—172no—
477C2×C4⋊C4—172no—
478C2×C4⋊C4—172no—
479C2×C4⋊C4—172no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—171no—
483C2×C4⋊C4—172no—
484C2×C4⋊C4—174no—
485C2×C4⋊C4—174no—
486C2×C4⋊C4—174no—
487C2×C4⋊C4—172no—
488C2×C4⋊C4—174no—
489C2×C4⋊C4—174no—
490C2×C4⋊C4—174no—
491C2×C4⋊C4—684no—
492C2×C4⋊C4—684no—
493C2×C4⋊C4—684no—
494C2×C4⋊C4—684no—
495C2×C4⋊C4C22×D1712yes—
496C2×C4⋊C4C22×D1712yes—
497C2×C4⋊C4C22×D1711yescharacteristic
498C2×C4⋊C4C22×D1712yes—
499C2×C4⋊C4C22×D1711yescharacteristic
500C2×C4⋊C4C22×D1712yes—
501C2×C22⋊C4—172no—
502C2×C22⋊C4—172no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—174no—
505C2×C22⋊C4—174no—
506C2×C22⋊C4C22×D1712yes—
507C2×C22⋊C4C22×D1712yes—
508C2×C22⋊C4C22×D1712yes—
509C2×C22⋊C4C22×D1712yes—
510C2×C22⋊C4C22×D1712yes—
511C2×C42—172no—
512C2×C42—172no—
513C2×C42—174no—
514C2×C42—174no—
515C2×C42—174no—
516C2×C42C2×Dic1718yescomplemented
517C2×C42C22×D1711yescharacteristic
518C2×C42C22×D1712yes—
519C2×C42C22×D1711yescharacteristic
520C2×C42C22×D1711yescharacteristic
521C2×C42C22×D1711yescharacteristic
522#95—172no—
523#95—172no—
524#95—172no—
525#95—172no—
526#95—174no—
527#95—172no—
528#95—172no—
529#95—174no—
530#95—174no—
531#95—172no—
532#95—172no—
533#95—174no—
534#95—174no—
535#95—174no—
536C17#3438411yescharacteristic, complemented, Sylow
537C24C23×D1712yes—
538C24C23×D1711yescharacteristic
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8C22×Dic1714yes—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4C22×Dic1718yes—
547C2×D4C22×Dic1714yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—172no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—174no—
561C22×C4—174no—
562C22×C4—348no—
563C22×C4—684no—
564C22×C4—684no—
565C22×C4—684no—
566C22×C4—684no—
567C22×C4—684no—
568C22×C4C22×Dic1714yes—
569C22×C4C22×Dic1714yes—
570C22×C4C22×Dic1714yes—
571C22×C4C22×Dic1718yes—
572C22×C4C23×D1712yes—
573C22×C4C23×D1712yes—
574C22×C4C23×D1712yes—
575C22×C4C23×D1711yescharacteristic
576C22×C4C23×D1711yescharacteristic
577C22×C4C23×D1711yescharacteristic
578C22×C4C23×D1711yescharacteristic
579C22×C4C23×D1711yescharacteristic
580C22×C4C23×D1711yescharacteristic
581C4⋊C4—342no—
582C4⋊C4—344no—
583C4⋊C4—344no—
584C4⋊C4—344no—
585C4⋊C4—344no—
586C4⋊C4—342no—
587C4⋊C4—342no—
588C4⋊C4—342no—
589C4⋊C4—684no—
590C4⋊C4—684no—
591C4⋊C4—684no—
592C4⋊C4—682no—
593C4⋊C4—684no—
594C4⋊C4—682no—
595C4⋊C4—684no—
596C4⋊C4—684no—
597C4⋊C4C22×Dic1718yes—
598C4⋊C4C22×Dic1718yes—
599C4⋊C4C22×Dic1714yes—
600C4⋊C4C22×Dic1718yes—
601C4⋊C4C22×Dic1714yes—
602C4⋊C4C22×Dic1718yes—
603C22⋊C4—344no—
604C22⋊C4—344no—
605C22⋊C4—684no—
606C22⋊C4—684no—
607C22⋊C4—684no—
608C22⋊C4C22×Dic1718yes—
609C22⋊C4C22×Dic1718yes—
610C22⋊C4C22×Dic1718yes—
611C22⋊C4C22×Dic1718yes—
612C22⋊C4C22×Dic1718yes—
613C42—344no—
614C42—344no—
615C42—684no—
616C42—684no—
617C42—684no—
618C42C22×Dic1714yes—
619C42C22×Dic1714yes—
620C42C22×Dic1714yes—
621C42C22×Dic1714yes—
622C42C22×Dic1718yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1058769612yes—
634C23#1058769712yes—
635C23C23×Dic1714yes—
636C23C23×Dic1712yes—
637C23C24×D1711yescharacteristic
638Q8—28no—
639D4—216no—
640D4—28no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—28no—
657C2×C4—216no—
658C2×C4—28no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—344no—
664C2×C4—344no—
665C2×C4—344no—
666C2×C4—342no—
667C2×C4—344no—
668C2×C4—344no—
669C2×C4—342no—
670C2×C4—344no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—1368no—
678C2×C4—1368no—
679C2×C4#1058769612yes—
680C2×C4#1058769612yes—
681C2×C4#1058769712yes—
682C2×C4#1058769712yes—
683C2×C4C23×Dic1712yes—
684C2×C4C23×Dic1712yes—
685C2×C4C23×Dic1712yes—
686C2×C4C23×Dic1712yes—
687C2×C4C23×Dic1714yes—
688C2×C4C23×Dic1714yes—
689C2×C4C23×Dic1714yes—
690C2×C4C23×Dic1712yes—
691C2×C4C23×Dic1712yes—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22#1176329214yes—
706C22C24×Dic1711yescharacteristic
707C22C2×#1058769611yescharacteristic
708C22C2×#1058769611yescharacteristic
709C22C2×#1058769611yescharacteristic
710C22C2×#1058769711yescharacteristic
711C22C2×#1058769711yescharacteristic
712C22C2×#1058769711yescharacteristic
713C4—22no—
714C4—22no—
715C4—24no—
716C4—22no—
717C4—22no—
718C4—24no—
719C4—24no—
720C4—682no—
721C4—684no—
722C4—684no—
723C4—682no—
724C4—682no—
725C4—682no—
726C4#1176329214yes—
727C4#1176329214yes—
728C2—24no—
729C2—44no—
730C2C2×#1176329211yescharacteristic
731C2C2×#1176329211yescharacteristic
732C2C2×#1176329211yescharacteristic
733C2#1454311411yescharacteristic
734C2#1454312411yescharacteristic
735C2#1454322111yescharacteristic
736C2#1454322911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×C17×#529C2
socle, cosocleC23×C17C25
prime radicalC2×C17×#121C22
hypercenterC2×#529D17
hypocenterC17#34384
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #14531976C2semidirect
3. #14531793C2semidirect
4. #14531741C2semidirect
5. #14531733C2semidirect
6. #14531713C2semidirect
7. Q8×C4⋊Dic17C2semidirect
8. D4×C4⋊Dic17C2semidirect
9. D4×C4⋊Dic17C2semidirect
10. #14531526C2semidirect
11. #14531497C2semidirect
12. #14531456C2semidirect
13. #14531407C2semidirect
14. #14531393C2semidirect
15. C2×#11762679C2semidirect
16. #14531182C2semidirect
72. C17×#529C4semidirect
93. C17×#126C2×C4semidirect
94. C17×#125C2×C4semidirect
95. C17×#124C2×C4semidirect
96. C17×#123C2×C4semidirect
97. C17×C22⋊Q8C2×C4semidirect
99. C4×Q8×C17C2×C4semidirect
100. C4×D4×C17C2×C4semidirect
101. C4×D4×C17C2×C4semidirect
102. C17×#117C2×C4semidirect
114. C2×C42×C17C2×C4semidirect
377. #529Dic17semidirect
461. #126C2×Dic17semidirect
462. #125C2×Dic17semidirect
463. #124C2×Dic17semidirect
464. #123C2×Dic17semidirect
465. C22⋊Q8C2×Dic17semidirect
468. C4×Q8C2×Dic17semidirect
471. C4×D4C2×Dic17semidirect
472. C4×D4C2×Dic17semidirect
474. #117C2×Dic17semidirect
516. C2×C42C2×Dic17semidirect
536. C17#34384semidirect

Maximal subgroups

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

subgroupindex
#145319762
#145318042
#145317932
#145317412
#145317332
#145317132
Q8×C4⋊Dic172
D4×C4⋊Dic172
#145315262
#145314972
#145314562
#145314072
#145313932
C2×#117626792
#145311822
C2×C17×#5292
#3438417