Finite Group Databasebeta

← #17049834

Subgroups — #17049834

Order 4352.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2C2×#11762810C211yesmaximal, characteristic, complemented
3C22×#10587506C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic17C211yesmaximal, characteristic, complemented
5#14529717C211yesmaximal, characteristic, complemented
6#14529601C211yesmaximal, characteristic, complemented
7#14529218C211yesmaximal, characteristic, complemented
8#14529213C211yesmaximal, characteristic, complemented
9#14529102C211yesmaximal, characteristic, complemented
10#14529092C211yesmaximal, characteristic, complemented
11#14528789C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528719C211yesmaximal, characteristic, complemented
14#14528614C211yesmaximal, characteristic, complemented
15C2×C17×#548C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×D4×Dic17—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21#11762881—24no—
22C2×C4⋊#3622C2211yescharacteristic
23#11762810—24no—
24C2×#10587506—24no—
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587506C2211yescharacteristic
30C2×#10587506C2211yescharacteristic
31C2×#10587506C2211yescharacteristic
32C2×#10587506C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×#10587503C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×C22⋊#3622C2211yescharacteristic
39C2×#10587474C2211yescharacteristic
40#11762708—21no—
41#11762684—21no—
42#11762684—21no—
43#11762679C2211yescharacteristic
44#11762669C2211yescharacteristic
45#11762669C2211yescharacteristic
46C4×C4⋊Dic17C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C22×#41×C17C2211yescharacteristic
52C23×Q8×C17C2211yescharacteristic
53C17×#548—24no—
54C17×#548C418yescomplemented
55C2×C17×#124—21no—
56C2×C17×#124C2211yescharacteristic
57C2×C17×C22⋊Q8—21no—
58C2×C17×C22⋊Q8C2211yescharacteristic
59C2×C17×#121—21no—
60C2×C17×#121C2211yescharacteristic
61C2×C4×Q8×C17C2211yescharacteristic
62C2×C4×D4×C17—21no—
63C2×C4×D4×C17C2211yescharacteristic
64C2×#41×C17—22no—
65C2×#41×C17—22no—
66C2×#41×C17—22no—
67C2×#41×C17—41no—
68C2×#41×C17—41no—
69C2×#41×C17C2×C414yescomplemented
70C22×Q8×C17—21no—
71C22×Q8×C17—22no—
72C22×Q8×C17—22no—
73C22×Q8×C17—22no—
74C22×Q8×C17—41no—
75C22×Q8×C17—41no—
76C22×Q8×C17C2×C414yescomplemented
77C22×Q8×C17C2311yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17D411yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×Dic17—21no—
88C23×Dic17—21no—
89C17×#124—28no—
90C17×#124—22no—
91C17×#124C2×C414yescomplemented
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8—28no—
94C17×C22⋊Q8C2×C414yescomplemented
95C17×#121—28no—
96C17×#121—22no—
97C17×#121C2×C414yescomplemented
98C4×Q8×C17—22no—
99C4×Q8×C17C2×C414yescomplemented
100C4×D4×C17—28no—
101C4×D4×C17C2×C414yes—
102C4×D4×C17D414yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17D411yescharacteristic
106C2×C4⋊C4×C17C2311yescharacteristic
107C2×C22⋊C4×C17—21no—
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17D411yescharacteristic
112C2×C22⋊C4×C17D411yescharacteristic
113C2×C42×C17—21no—
114C2×C42×C17C2311yescharacteristic
115C2×C22⋊Dic17—21no—
116C2×C22⋊Dic17—21no—
117D4×Dic17—44no—
118C2×C4⋊Dic17—21no—
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17—41no—
126C2×C4⋊Dic17C2311yescharacteristic
127C2×C4⋊Dic17C2311yescharacteristic
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×C4×Dic17—21no—
131C2×#63223—22no—
132C2×#63223—22no—
133C2×#63223—41no—
134C22×#3622—22no—
135C22×#3622—22no—
136C22×#3622—41no—
137C22×#3622C2311yescharacteristic
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141#10587506—22no—
142#10587506—22no—
143#10587506—22no—
144#10587506—22no—
145#10587506—22no—
146#10587506—41no—
147#10587506—41no—
148#10587506D414yescomplemented
149#10587503—22no—
150#10587503—22no—
151#10587503—41no—
152#10587503—41no—
153#10587502—21no—
154#10587502—21no—
155#10587502—21no—
156C22⋊#3622—22no—
157C22⋊#3622—22no—
158C4⋊#3622—22no—
159#10587474—22no—
160C24×C17—21no—
161C24×C17C2×D411yescharacteristic
162C24×C17C2×D411yescharacteristic
163#41×C17—28no—
164#41×C17—44no—
165#41×C17—44no—
166#41×C17—44no—
167C2×Q8×C17—24no—
168C2×Q8×C17—21no—
169C2×Q8×C17—21no—
170C2×Q8×C17—21no—
171C2×Q8×C17—21no—
172C2×Q8×C17—28no—
173C2×Q8×C17—21no—
174C2×Q8×C17—21no—
175C2×Q8×C17—21no—
176C2×Q8×C17—21no—
177C2×Q8×C17—42no—
178C2×Q8×C17—42no—
179C2×Q8×C17—44no—
180C2×Q8×C17—44no—
181C2×Q8×C17—44no—
182C2×Q8×C17C22×C412yes—
183C2×Q8×C17C22×C412yes—
184C2×Q8×C17C2×D412yes—
185C2×Q8×C17#4112yes—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—24no—
189C2×D4×C17—24no—
190C2×D4×C17—21no—
191C2×D4×C17—21no—
192C2×D4×C17—21no—
193C2×D4×C17—21no—
194C2×D4×C17—21no—
195C2×D4×C17—42no—
196C2×D4×C17—42no—
197C2×D4×C17—42no—
198C2×D4×C17—42no—
199C2×D4×C17C22⋊C414yes—
200C2×D4×C17C22×C412yes—
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—24no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—24no—
214C22×C4×C17—42no—
215C22×C4×C17—42no—
216C22×C4×C17—42no—
217C22×C4×C17—42no—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C22×C412yes—
220C22×C4×C17C2×D411yescharacteristic
221C22×C4×C17C2×D411yescharacteristic
222C22×C4×C17C2×D411yescharacteristic
223C22×C4×C17C2×D411yescharacteristic
224C22×C4×C17C2×D412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2411yescharacteristic
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—42no—
232C22×Dic17—42no—
233C22×Dic17—42no—
234C22×Dic17—42no—
235C22×Dic17—81no—
236C22×Dic17—81no—
237C4⋊C4×C17—24no—
238C4⋊C4×C17—24no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17C22⋊C414yes—
241C4⋊C4×C17C22×C412yes—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17C22⋊C414yes—
247C22⋊C4×C17C22⋊C414yes—
248C42×C17—24no—
249C42×C17C22×C412yes—
250C42×C17C2×D412yes—
251C22⋊Dic17—42no—
252C22⋊Dic17—42no—
253C4⋊Dic17—21no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17—21no—
259C4⋊Dic17—21no—
260C4⋊Dic17—42no—
261C4⋊Dic17—42no—
262C4⋊Dic17—42no—
263C4⋊Dic17—81no—
264C4⋊Dic17C2×D412yes—
265C4×Dic17—42no—
266#63223—44no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—44no—
279C2×#3622C2×D412yes—
280#22421—171nomaximal, Sylow
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17—21no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17—22no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17C2×C22⋊C412yes—
299C23×C17C2×C22⋊C412yes—
300C23×C17AGL(1,ℤ/8)12yes—
301C23×C17#13712yes—
302C23×C17C22×D411yescharacteristic
303Q8×C17—22no—
304Q8×C17—22no—
305Q8×C17—22no—
306Q8×C17—22no—
307Q8×C17—22no—
308Q8×C17—48no—
309Q8×C17—41no—
310Q8×C17—41no—
311Q8×C17C4×D414yescomplemented
312D4×C17—28no—
313D4×C17—22no—
314D4×C17—22no—
315D4×C17—48no—
316D4×C17—48no—
317D4×C17—41no—
318D4×C17—41no—
319C2×C4×C17—22no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—22no—
323C2×C4×C17—21no—
324C2×C4×C17—21no—
325C2×C4×C17—22no—
326C2×C4×C17—21no—
327C2×C4×C17—21no—
328C2×C4×C17—21no—
329C2×C4×C17—21no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—48no—
341C2×C4×C17—48no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17C2×C22⋊C412yes—
347C2×C4×C17C2×C22⋊C412yes—
348C2×C4×C17C2×C22⋊C412yes—
349C2×C4×C17C2×C22⋊C412yes—
350C2×C4×C17C23×C411yescharacteristic
351C2×C4×C17C22×D411yescharacteristic
352C2×C4×C17C22×D411yescharacteristic
353C2×C4×C17C2×#4111yescharacteristic
354C2×C4×C17H(5,𝔽2)11yescharacteristic
355C2×C4×C17H(5,𝔽2)11yescharacteristic
356C2×Dic17—22no—
357C2×Dic17—41no—
358C2×Dic17—41no—
359C2×Dic17—41no—
360C2×Dic17—41no—
361C2×Dic17—41no—
362C2×Dic17—41no—
363C2×Dic17—41no—
364C2×Dic17—41no—
365C2×Dic17—41no—
366C2×Dic17—41no—
367C2×Dic17—41no—
368C2×Dic17—84no—
369C2×Dic17—84no—
370#3622—22no—
371#3622—41no—
372#3622—41no—
373#3622—41no—
374C2×#548D1711yescharacteristic
375C2×#435—171no—
376C2×#417—171no—
377C22×#103—171no—
378D4×C4⋊C4—171no—
379#1983—171no—
380#1959—171no—
381#1894—171no—
382#1893—171no—
383#1874—171no—
384#1872—171no—
385#1803—171no—
386#1788—171no—
387#1787—171no—
388#1763—171no—
389C22×C17—22no—
390C22×C17—22no—
391C22×C17—22no—
392C22×C17—22no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—22no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—41no—
399C22×C17—41no—
400C22×C17—41no—
401C22×C17—41no—
402C22×C17—42no—
403C22×C17—42no—
404C22×C17—42no—
405C22×C17—81no—
406C22×C17—81no—
407C22×C17—81no—
408C22×C17—81no—
409C22×C17#41714yescomplemented
410C22×C17C22×C22⋊C411yescharacteristic
411C22×C17D4211yescharacteristic
412C22×C17#54611yescharacteristic
413C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
414C22×C17C2×#13711yescharacteristic
415C22×C17#57711yescharacteristic
416C22×C17#57811yescharacteristic
417C4×C17—22no—
418C4×C17—22no—
419C4×C17—24no—
420C4×C17—22no—
421C4×C17—22no—
422C4×C17—42no—
423C4×C17—42no—
424C4×C17C2×C4×D411yescharacteristic
425C4×C17#51811yescharacteristic
426C4×C17D4211yescharacteristic
427C4×C17#54611yescharacteristic
428Dic17—42no—
429Dic17—81no—
430Dic17—81no—
431Dic17—81no—
432C22×#41C2×D1711yescharacteristic
433C23×Q8C2×D1711yescharacteristic
434C22×M16—171no—
435C23×C8—171no—
436#548—24no—
437#548Dic1718yescomplemented
438C2×#124—21no—
439C2×#124C2×D1711yescharacteristic
440C2×C22⋊Q8—21no—
441C2×C22⋊Q8C2×D1711yescharacteristic
442C2×#121—21no—
443C2×#121C2×D1711yescharacteristic
444C2×C4×Q8C2×D1711yescharacteristic
445C2×C4×D4—21no—
446C2×C4×D4—341no—
447C2×C4×D4C2×D1711yescharacteristic
448C22×C4⋊C4—171no—
449C22×C4⋊C4—171no—
450#435—344no—
451C2×C4⋊C8—171no—
452#417—344no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#103—171no—
458C2×#103—171no—
459C2×#103—171no—
460C2×#103—171no—
461C2×#103—344no—
462C2×#102—171no—
463C2×#102—171no—
464C2×#102—171no—
465C2×#102—171no—
466C2×C22⋊C8—171no—
467C2×C22⋊C8—171no—
468C2×#97—171no—
469#389—341no—
470#385—341no—
471#385—341no—
472#384—171no—
473#380—171no—
474#380—171no—
475C4×C4⋊C4—171no—
476#340—171no—
477#340—171no—
478#340—171no—
479#340—171no—
480C2×C17—24no—
481C2×C17—42no—
482C2×C17—82no—
483C2×C17D4×C22⋊C411yescharacteristic
484C2×C17C2×#41711yescharacteristic
485C2×C17#289811yescharacteristic
486C2×C17#326511yescharacteristic
487C2×C17#327011yescharacteristic
488C2×C17#330811yescharacteristic
489C2×C17#331611yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×Dic1714yescomplemented
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8C2×Dic1714yescomplemented
503C22×Q8C22×D1711yescharacteristic
504C22×Q8C22×D1711yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C22⋊D1711yescharacteristic
508C22×D4C22×D1711yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—341no—
512C23×C4—341no—
513C23×C4C22×D1711yescharacteristic
514C23×C4C22×D1711yescharacteristic
515C2×M16—342no—
516C2×M16—342no—
517C2×M16—681no—
518C22×C8—171no—
519C22×C8—171no—
520C22×C8—171no—
521C22×C8—171no—
522C22×C8—342no—
523C22×C8—342no—
524C22×C8—681no—
525#124—28no—
526#124—22no—
527#124C2×Dic1714yescomplemented
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C2×Dic1714yescomplemented
531#121—28no—
532#121—22no—
533#121C2×Dic1714yescomplemented
534C4×Q8—22no—
535C4×Q8C2×Dic1714yescomplemented
536C4×D4—28no—
537C4×D4—684no—
538C4×D4C2×Dic1714yes—
539C4×D4C22⋊D1714yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—171no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—171no—
545C2×C4⋊C4—171no—
546C2×C4⋊C4—342no—
547C2×C4⋊C4—342no—
548C2×C4⋊C4—341no—
549C2×C4⋊C4—341no—
550C2×C4⋊C4—341no—
551C2×C4⋊C4—341no—
552C2×C4⋊C4—681no—
553C2×C4⋊C4—681no—
554C2×C4⋊C4C22⋊D1711yescharacteristic
555C2×C4⋊C4C22×D1711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—341no—
561C2×C22⋊C4—341no—
562C2×C22⋊C4C22⋊D1711yescharacteristic
563C2×C22⋊C4C22⋊D1711yescharacteristic
564C2×C42—21no—
565C2×C42—341no—
566C2×C42C22×D1711yescharacteristic
567C4⋊C8—342no—
568#103—174no—
569#103—342no—
570#103—342no—
571#103—342no—
572#103—342no—
573#103—342no—
574#103—681no—
575#103—681no—
576#102—342no—
577#102—342no—
578#102—681no—
579#102—681no—
580C22⋊C8—342no—
581C22⋊C8—342no—
582#97—342no—
583#95—341no—
584#95—341no—
585#95—341no—
586C17#2242111yescharacteristic, complemented, Sylow
587C24—21no—
588C24C2×C22⋊D1711yescharacteristic
589C24C2×C22⋊D1711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—24no—
599C2×Q8—28no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8D4×D1712yes—
610C2×Q8#6325412yes—
611C2×Q8C22×Dic1712yes—
612C2×Q8C22×Dic1712yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4C22⋊Dic1714yes—
627C2×D4C22×Dic1712yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—341no—
646C22×C4—341no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4—682no—
650C22×C4—682no—
651C22×C4—682no—
652C22×C4—682no—
653C22×C4—1361no—
654C22×C4—1361no—
655C22×C4C22×Dic1712yes—
656C22×C4C22×Dic1712yes—
657C22×C4C2×C22⋊D1712yes—
658C22×C4C2×C22⋊D1712yes—
659C22×C4C2×C22⋊D1711yescharacteristic
660C22×C4C2×C22⋊D1711yescharacteristic
661C22×C4C2×C22⋊D1711yescharacteristic
662C22×C4C2×C22⋊D1711yescharacteristic
663C22×C4C23×D1711yescharacteristic
664M16—684no—
665C2×C8—172no—
666C2×C8—341no—
667C2×C8—341no—
668C2×C8—341no—
669C2×C8—341no—
670C2×C8—341no—
671C2×C8—341no—
672C2×C8—341no—
673C2×C8—341no—
674C2×C8—341no—
675C2×C8—341no—
676C2×C8—341no—
677C2×C8—684no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—172no—
682C4⋊C4—341no—
683C4⋊C4—341no—
684C4⋊C4—341no—
685C4⋊C4—341no—
686C4⋊C4—341no—
687C4⋊C4—341no—
688C4⋊C4—341no—
689C4⋊C4—682no—
690C4⋊C4—682no—
691C4⋊C4—682no—
692C4⋊C4—1361no—
693C4⋊C4C22⋊Dic1714yes—
694C4⋊C4C22×Dic1712yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—682no—
700C22⋊C4—682no—
701C22⋊C4C22⋊Dic1714yes—
702C22⋊C4C22⋊Dic1714yes—
703C42—24no—
704C42—682no—
705C42C22×Dic1712yes—
706C42C2×C22⋊D1712yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23#1058763512yes—
725C23#1058763712yes—
726C23C2×C22⋊Dic1712yes—
727C23C2×C22⋊Dic1712yes—
728C23C22×C22⋊D1711yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8D4×Dic1714yescomplemented
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—342no—
773C2×C4—681no—
774C2×C4—681no—
775C2×C4—681no—
776C2×C4—681no—
777C2×C4—681no—
778C2×C4—681no—
779C2×C4—681no—
780C2×C4—681no—
781C2×C4—681no—
782C2×C4—681no—
783C2×C4—681no—
784C2×C4—1364no—
785C2×C4—1364no—
786C2×C4C2×C22⋊Dic1712yes—
787C2×C4C2×C22⋊Dic1712yes—
788C2×C4C2×C22⋊Dic1712yes—
789C2×C4C2×C22⋊Dic1712yes—
790C2×C4C2×D4×D1711yescharacteristic
791C2×C4C2×#6325411yescharacteristic
792C2×C4#1058769111yescharacteristic
793C2×C4#1058769111yescharacteristic
794C2×C4C23×Dic1711yescharacteristic
795C2×C4C22×C22⋊D1711yescharacteristic
796C8—342no—
797C8—681no—
798C8—681no—
799C8—681no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22#1176281014yescomplemented
821C22C22×C22⋊Dic1711yescharacteristic
822C22D4×C22⋊D1711yescharacteristic
823C22#1176345311yescharacteristic
824C22C2×#1058763511yescharacteristic
825C22C2×#1058763711yescharacteristic
826C22#1176361711yescharacteristic
827C22#1176362411yescharacteristic
828C4—22no—
829C4—22no—
830C4—24no—
831C4—22no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—682no—
836C4—1361no—
837C4—1361no—
838C4—1361no—
839C4C2×D4×Dic1711yescharacteristic
840C4#1176328411yescharacteristic
841C4D4×C22⋊D1711yescharacteristic
842C4#1176345311yescharacteristic
843C2—24no—
844C2—42no—
845C2—82no—
846C2D4×C22⋊Dic1711yescharacteristic
847C2C2×#1176281011yescharacteristic
848C2#1453731711yescharacteristic
849C2#1454028011yescharacteristic
850C2#1454035011yescharacteristic
851C2#1454077511yescharacteristic
852C2#1454089511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#548C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#548D17
hypocenterC17#22421
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. C2×#11762810C2semidirect
3. C22×#10587506C2semidirect
4. D4×C4⋊Dic17C2semidirect
5. #14529717C2semidirect
6. #14529601C2semidirect
7. #14529218C2semidirect
8. #14529213C2semidirect
9. #14529102C2semidirect
10. #14529092C2semidirect
11. #14528789C2semidirect
12. #14528724C2semidirect
13. #14528719C2semidirect
14. #14528614C2semidirect
54. C17×#548C4semidirect
69. C2×#41×C17C2×C4semidirect
76. C22×Q8×C17C2×C4semidirect
91. C17×#124C2×C4semidirect
94. C17×C22⋊Q8C2×C4semidirect
97. C17×#121C2×C4semidirect
99. C4×Q8×C17C2×C4semidirect
148. #10587506D4semidirect
311. Q8×C17C4×D4semidirect
409. C22×C17#417semidirect
437. #548Dic17semidirect
495. C2×#41C2×Dic17semidirect
502. C22×Q8C2×Dic17semidirect
527. #124C2×Dic17semidirect
530. C22⋊Q8C2×Dic17semidirect
533. #121C2×Dic17semidirect
535. C4×Q8C2×Dic17semidirect
586. C17#22421semidirect
737. Q8D4×Dic17semidirect
820. C22#11762810semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
C2×#117628102
C22×#105875062
D4×C4⋊Dic172
#145297172
#145296012
#145292182
#145292132
#145291022
#145290922
#145287892
#145287242
#145287192
#145286142
C2×C17×#5482
#2242117