Finite Group Databasebeta

← #16962439

Subgroups — #16962439

Order 4352.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762703C211yesmaximal, characteristic, complemented
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762668C211yesmaximal, characteristic, complemented
4#14527045C211yesmaximal, characteristic, complemented
5#14527039C211yesmaximal, characteristic, complemented
6#14527027C211yesmaximal, characteristic, complemented
7#14527023C211yesmaximal, characteristic
8#14527023C211yesmaximal, characteristic
9#14527021C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527008C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762703—24no—
31#11762685C418yescomplemented
32#11762668—24no—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—22no—
63C22×C22⋊D17—22no—
64C22×C22⋊D17—41no—
65C22×C22⋊D17—41no—
66C22×C22⋊D17—41no—
67C22×C22⋊D17—41no—
68C22×C22⋊D17C2×C414yes—
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17C2×C414yes—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17—41no—
90C2×C22⋊C4×C17—41no—
91C2×C22⋊C4×C17C2×C414yes—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17C2×C414yes—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227C2×C414yes—
116C2×#63225—22no—
117C2×#63225—41no—
118C2×#63225—41no—
119C2×#63225—41no—
120C2×#63225—41no—
121C2×#63225D414yescomplemented
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—41no—
125C2×C4×Dic17—41no—
126C2×C4×Dic17—41no—
127C2×C4×Dic17—41no—
128C17×#95—22no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502C2×C414yes—
145#10587502C2×C414yes—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17C22×C412yes—
161C24×C17C2411yescharacteristic
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17C22×C412yes—
175C23×D17#4112yes—
176C23×D17#4112yes—
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×C17C22×C412yes—
217C22×C4×C17C22×C412yes—
218C22×C4×C17C2×D412yes—
219C2×C22⋊D17—28no—
220C2×C22⋊D17—44no—
221C2×C22⋊D17—44no—
222C2×C22⋊D17—44no—
223C2×C22⋊D17—44no—
224C2×C22⋊D17—44no—
225C2×C22⋊D17—44no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17C22×C412yes—
268C22×Dic17C22×C412yes—
269C22×Dic17C22×C412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C22×Dic17#4112yes—
275C2×C4×D17—28no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C22⋊C4×C17—44no—
283C22⋊C4×C17—44no—
284C22⋊C4×C17—44no—
285C22⋊Dic17—28no—
286C22⋊Dic17—44no—
287C22⋊Dic17—44no—
288#63227—44no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63225—44no—
294#63225—44no—
295C4×Dic17—44no—
296C4×Dic17—44no—
297#14415—171nomaximal, Sylow
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17C23×C411yescharacteristic
334C23×C17C22×D411yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17C2×#4111yescharacteristic
337C23×C17C2×#4111yescharacteristic
338C23×C17C2×#4111yescharacteristic
339C23×C17C2×#4111yescharacteristic
340C23×C17H(5,𝔽2)11yescharacteristic
341C23×C17H(5,𝔽2)11yescharacteristic
342C23×C17H(5,𝔽2)11yescharacteristic
343C23×C17H(5,𝔽2)11yescharacteristic
344C23×C17H(5,𝔽2)11yescharacteristic
345C23×C17H(5,𝔽2)11yescharacteristic
346C23×C17H(5,𝔽2)11yescharacteristic
347C23×C172−1+411yescharacteristic
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17#11714yes—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
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×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C22⋊D17—416no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17C4×D414yes—
475C4×D17—416no—
476C2×#388—171no—
477C2×#386—171no—
478C2×#380—171no—
479#1443—171no—
480#1442—171no—
481#1440D1711yescharacteristic, complemented
482#1439—171no—
483#1438—171no—
484#1438—171no—
485#1437—171no—
486#1437—171no—
487#1437—171no—
488#1436—171no—
489#1434—171no—
490C22⋊#95—171no—
491C22×C17—42no—
492C22×C17—42no—
493C22×C17—42no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
498C22×C17—81no—
499C22×C17—81no—
500C22×C17—81no—
501C22×C17—81no—
502C22×C17—81no—
503C22×C17—81no—
504C22×C17—81no—
505C22×C17—81no—
506C22×C17C2×#11711yescharacteristic
507C22×C17C2×C4×D411yescharacteristic
508C22×C17C4×#4111yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#51811yescharacteristic
511C22×C17#51811yescharacteristic
512C22×C17#52011yescharacteristic
513C22×C17#53411yescharacteristic
514C22×C17#53511yescharacteristic
515C22×C17#53811yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#53811yescharacteristic
519C22×C17#53811yescharacteristic
520C22×C17#53811yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53911yescharacteristic
523C22×C17#54011yescharacteristic
524C22×C17#54211yescharacteristic
525C22×C17#54611yescharacteristic
526C22×C17#54611yescharacteristic
527C22×C17#54811yescharacteristic
528C22×C17#55011yescharacteristic
529C22×C17#55111yescharacteristic
530C22×C17#55111yescharacteristic
531C22×C17#55211yescharacteristic
532C22×C17#55311yescharacteristic
533C22×C17#55311yescharacteristic
534C22×C17#55311yescharacteristic
535C22×C17#55311yescharacteristic
536C22×C17#55511yescharacteristic
537C22×C17#56011yescharacteristic
538C22×C17#56011yescharacteristic
539C22×C17#56211yescharacteristic
540C22×C17#56211yescharacteristic
541C2×D17—24no—
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C4×C17—42no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—81no—
560C4×C17—81no—
561C4×C17—81no—
562Dic17—24no—
563Dic17—42no—
564Dic17—42no—
565Dic17—42no—
566Dic17—42no—
567Dic17—42no—
568Dic17—81no—
569C23×D4—171no—
570C24×C4—171no—
571C22×C4⋊C4—171no—
572C22×C4⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4C2×D1711yescharacteristic
582C22×C22⋊C4C2×D1711yescharacteristic
583C22×C22⋊C4C2×D1711yescharacteristic
584C22×C42—171no—
585C22×C42—171no—
586#388—344no—
587#386—178no—
588#380—344no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95C2×D1711yescharacteristic
604C2×#95C2×D1711yescharacteristic
605C2×#95C2×D1711yescharacteristic
606C2×#95C2×D1711yescharacteristic
607C2×C17—82no—
608C2×C17#231211yescharacteristic
609C2×C17#232111yescharacteristic
610C2×C17#233511yescharacteristic
611C2×C17#235211yescharacteristic
612C2×C17#235311yescharacteristic
613C2×C17#236311yescharacteristic
614C2×C17#237711yescharacteristic
615C2×C17#268811yescharacteristic
616C2×C17#269611yescharacteristic
617C2×C17#271411yescharacteristic
618C2×C17#273011yescharacteristic
619C2×C17#275611yescharacteristic
620C2×C17#277811yescharacteristic
621C2×C17#277911yescharacteristic
622C2×C17#278111yescharacteristic
623D17—44no—
624C25—171no—
625C25C22×D1711yescharacteristic
626C22×D4—174no—
627C22×D4—342no—
628C22×D4—342no—
629C22×D4—681no—
630C22×D4—681no—
631C22×D4—681no—
632C22×D4—681no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—171no—
637C23×C4—171no—
638C23×C4—171no—
639C23×C4—174no—
640C23×C4—171no—
641C23×C4—342no—
642C23×C4—342no—
643C23×C4—681no—
644C23×C4—681no—
645C23×C4—681no—
646C23×C4—681no—
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C23×C4C22×D1711yescharacteristic
652C23×C4C22×D1711yescharacteristic
653C2×C4⋊C4—174no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—681no—
656C2×C4⋊C4—681no—
657C2×C4⋊C4—681no—
658C2×C4⋊C4—681no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—174no—
668C2×C22⋊C4—174no—
669C2×C22⋊C4—342no—
670C2×C22⋊C4—342no—
671C2×C22⋊C4—342no—
672C2×C22⋊C4—342no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4—681no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4C4×D1714yes—
692C2×C42—342no—
693C2×C42—342no—
694C2×C42—681no—
695C2×C42—681no—
696C2×C42—681no—
697C2×C42—681no—
698#95—22no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—174no—
703#95—174no—
704#95—342no—
705#95—342no—
706#95—342no—
707#95—342no—
708#95—342no—
709#95—681no—
710#95—681no—
711#95—681no—
712#95—681no—
713#95—681no—
714#95—681no—
715#95—681no—
716C17#1441511yescharacteristic, complemented, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—172no—
732C24—172no—
733C24—172no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24C2×C4×D1712yes—
747C24C23×D1711yescharacteristic
748C2×D4—348no—
749C2×D4—684no—
750C2×D4—684no—
751C2×D4—684no—
752C2×D4—684no—
753C2×D4—684no—
754C2×D4—684no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—172no—
795C22×C4—172no—
796C22×C4—172no—
797C22×C4—172no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—172no—
802C22×C4—348no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—684no—
845C22×C4—684no—
846C22×C4—684no—
847C22×C4—684no—
848C22×C4—684no—
849C22×C4—684no—
850C22×C4C2×C4×D1712yes—
851C22×C4C2×C4×D1712yes—
852C22×C4D4×D1712yes—
853C4⋊C4—684no—
854C4⋊C4—684no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—348no—
859C22⋊C4—684no—
860C22⋊C4—684no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C42—684no—
867C42—684no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—174no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23C22×C4×D1711yescharacteristic
939C23C2×D4×D1711yescharacteristic
940C23#1058769111yescharacteristic
941C23#1058769111yescharacteristic
942C23#1058769111yescharacteristic
943C23#1058769111yescharacteristic
944C23#1058769111yescharacteristic
945C23#41×D1711yescharacteristic
946C23#41×D1711yescharacteristic
947C23#41×D1711yescharacteristic
948C23#41×D1711yescharacteristic
949C23#41×D1711yescharacteristic
950C23#1058769611yescharacteristic
951C23#1058769611yescharacteristic
952C23#1058769711yescharacteristic
953D4—6816no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—174no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—6816no—
1019C2×C4—681no—
1020C2×C4—681no—
1021C2×C4—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—344no—
1062C22—344no—
1063C22—344no—
1064C22—682no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22#117×D1711yescharacteristic
1077C22C4×D4×D1711yescharacteristic
1078C22#1176327711yescharacteristic
1079C22#1176328111yescharacteristic
1080C22#1176328111yescharacteristic
1081C22#1176328211yescharacteristic
1082C22#1176328811yescharacteristic
1083C22#1176336911yescharacteristic
1084C22#1176337511yescharacteristic
1085C22#1176339111yescharacteristic
1086C22#1176339111yescharacteristic
1087C22#1176339311yescharacteristic
1088C22#1176339311yescharacteristic
1089C22#1176339511yescharacteristic
1090C22#1176339511yescharacteristic
1091C22#1176339811yescharacteristic
1092C22#1176340011yescharacteristic
1093C22#1176340911yescharacteristic
1094C22#1176342711yescharacteristic
1095C22#1176344811yescharacteristic
1096C22#1176345111yescharacteristic
1097C22#1176346711yescharacteristic
1098C22#1176347711yescharacteristic
1099C22#1176348711yescharacteristic
1100C22#1176348711yescharacteristic
1101C22#1176349511yescharacteristic
1102C22#1176350411yescharacteristic
1103C22#1176350411yescharacteristic
1104C22#1176350411yescharacteristic
1105C22#1176351011yescharacteristic
1106C22#1176352111yescharacteristic
1107C22#1176354711yescharacteristic
1108C22#1176354811yescharacteristic
1109C22#1176355411yescharacteristic
1110C22#1176355611yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—344no—
1118C4—682no—
1119C4—682no—
1120C4—682no—
1121C4—682no—
1122C4—682no—
1123C4—1361no—
1124C2—82no—
1125C2—684no—
1126C2#1453137811yescharacteristic
1127C2#1453144011yescharacteristic
1128C2#1453157211yescharacteristic
1129C2#1453171211yescharacteristic
1130C2#1453172111yescharacteristic
1131C2#1453181711yescharacteristic
1132C2#1453193611yescharacteristic
1133C2#1453522211yescharacteristic
1134C2#1453533611yescharacteristic
1135C2#1453558611yescharacteristic
1136C2#1453578711yescharacteristic
1137C2#1453611111yescharacteristic
1138C2#1453640111yescharacteristic
1139C2#1453641611yescharacteristic
1140C2#1453645211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1440C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1440D17
hypocenterC17#14415
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. C2×#11762703C2semidirect
3. C2×#11762668C2semidirect
4. #14527045C2semidirect
5. #14527039C2semidirect
6. #14527027C2semidirect
9. #14527021C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527015C2semidirect
13. #14527008C2semidirect
14. #14527005C2semidirect
15. C17×#1440C2semidirect
31. #11762685C4semidirect
121. C2×#63225D4semidirect
481. #1440D17semidirect
716. C17#14415semidirect

Maximal subgroups

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

subgroupindex
C2×#117627032
C2×#117626852
C2×#117626682
#145270452
#145270392
#145270272
#145270232
#145270212
#145270202
#145270152
#145270082
#145270052
C17×#14402
#1441517