Finite Group Databasebeta

← #17049804

Subgroups — #17049804

Order 4352.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 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×#10587503C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic17C211yesmaximal, characteristic, complemented
5#14529717C211yesmaximal, characteristic, complemented
6#14529601C211yesmaximal, characteristic, complemented
7#14529223C211yesmaximal, characteristic, complemented
8#14529208C211yesmaximal, characteristic, complemented
9#14529102C211yesmaximal, characteristic, complemented
10#14529092C211yesmaximal, characteristic, complemented
11#14528784C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528715C211yesmaximal, characteristic, complemented
14#14528609C211yesmaximal, characteristic, complemented
15C2×C17×#546C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic, complemented
17C23×#3622C2211yescharacteristic
18C2×D4×Dic17—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic, complemented
21#11762881—24no—
22C2×C4⋊#3622C2211yescharacteristic, complemented
23#11762810—24no—
24C2×#10587506C2211yescharacteristic, complemented
25C2×#10587506C2211yescharacteristic, complemented
26C2×#10587506C2211yescharacteristic, complemented
27C2×#10587506C2211yescharacteristic, complemented
28C2×#10587503—24no—
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×#10587503C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×C22⋊#3622C2211yescharacteristic, complemented
39C2×#10587474C2211yescharacteristic, complemented
40#11762708—21no—
41#11762684—21no—
42#11762684—21no—
43#11762679C2211yescharacteristic, complemented
44#11762669C2211yescharacteristic
45#11762669C2211yescharacteristic, complemented
46C4×C4⋊Dic17C2211yescharacteristic, complemented
47#11762571C2211yescharacteristic, complemented
48#11762571C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51C22×#41×C17C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C17×#546—24no—
54C17×#546C418yescomplemented
55C2×C17×#124C2211yescharacteristic
56C2×C17×#123—21no—
57C2×C17×C22⋊Q8C2211yescharacteristic
58C2×C17×#121—21no—
59C2×C17×#121C2211yescharacteristic
60C2×C17×#120—21no—
61C2×C4×D4×C17C2211yescharacteristic
62C2×C4×D4×C17C2211yescharacteristic
63C22×C22⋊C4×C17—21no—
64C25×C17—21no—
65C2×#41×C17—22no—
66C2×#41×C17—22no—
67C2×#41×C17—22no—
68C2×#41×C17—41no—
69C2×#41×C17—41no—
70C2×#41×C17C2×C414yescomplemented
71C22×Q8×C17C2311yescharacteristic
72C22×D4×C17—22no—
73C22×D4×C17—22no—
74C22×D4×C17—21no—
75C22×D4×C17—21no—
76C22×D4×C17—21no—
77C22×D4×C17—22no—
78C22×D4×C17—41no—
79C22×D4×C17—41no—
80C22×D4×C17C2×C414yescomplemented
81C22×D4×C17D411yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×Dic17—21no—
89C23×Dic17—21no—
90C17×#124—22no—
91C17×#124C2×C414yescomplemented
92C17×#123—28no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8C2×C414yescomplemented
95C17×#121—22no—
96C17×#121—28no—
97C17×#121C2×C414yescomplemented
98C17×#120—28no—
99C4×D4×C17—22no—
100C4×D4×C17C2×C414yes—
101C4×D4×C17C2×C414yescomplemented
102C4×D4×C17D414yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17D411yescharacteristic
105C2×C4⋊C4×C17C2311yescharacteristic
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17—21no—
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17—28no—
112C2×C22⋊C4×C17D411yescharacteristic
113C2×C22⋊C4×C17D411yescharacteristic
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—41no—
144#10587506—41no—
145#10587503—22no—
146#10587503—22no—
147#10587503—22no—
148#10587503—22no—
149#10587503—22no—
150#10587503—41no—
151#10587503—41no—
152#10587503D414yescomplemented
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×C17—21no—
162C24×C17—24no—
163C24×C17—42no—
164C24×C17—42no—
165C24×C17—42no—
166C24×C17—42no—
167C24×C17—81no—
168C24×C17—81no—
169C24×C17C2×D411yescharacteristic
170C24×C17C2×D411yescharacteristic
171#41×C17—28no—
172#41×C17—44no—
173#41×C17—44no—
174#41×C17—44no—
175C2×Q8×C17—21no—
176C2×Q8×C17—21no—
177C2×Q8×C17—21no—
178C2×Q8×C17—21no—
179C2×Q8×C17—21no—
180C2×Q8×C17C22×C412yes—
181C2×D4×C17—22no—
182C2×D4×C17—22no—
183C2×D4×C17—28no—
184C2×D4×C17—24no—
185C2×D4×C17—24no—
186C2×D4×C17—24no—
187C2×D4×C17—21no—
188C2×D4×C17—21no—
189C2×D4×C17—21no—
190C2×D4×C17—21no—
191C2×D4×C17—21no—
192C2×D4×C17—21no—
193C2×D4×C17—21no—
194C2×D4×C17—21no—
195C2×D4×C17—44no—
196C2×D4×C17—44no—
197C2×D4×C17—44no—
198C2×D4×C17—42no—
199C2×D4×C17—42no—
200C2×D4×C17—42no—
201C2×D4×C17—42no—
202C2×D4×C17—81no—
203C2×D4×C17—81no—
204C2×D4×C17C22⋊C414yes—
205C2×D4×C17C22×C412yes—
206C2×D4×C17C22×C412yes—
207C2×D4×C17C2×D412yes—
208C2×D4×C17#4112yes—
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×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—24no—
220C22×C4×C17—24no—
221C22×C4×C17—42no—
222C22×C4×C17—42no—
223C22×C4×C17—81no—
224C22×C4×C17—81no—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2×D411yescharacteristic
230C22×C4×C17C2×D411yescharacteristic
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2411yescharacteristic
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—42no—
239C22×Dic17—42no—
240C22×Dic17—42no—
241C22×Dic17—42no—
242C22×Dic17—81no—
243C22×Dic17—81no—
244C4⋊C4×C17—24no—
245C4⋊C4×C17—21no—
246C4⋊C4×C17C22⋊C414yes—
247C4⋊C4×C17C22×C412yes—
248C22⋊C4×C17—24no—
249C22⋊C4×C17—24no—
250C22⋊C4×C17—24no—
251C22⋊C4×C17—24no—
252C22⋊C4×C17—24no—
253C22⋊C4×C17C22⋊C414yes—
254C22⋊C4×C17C22⋊C414yes—
255C42×C17C22×C412yes—
256C42×C17C2×D412yes—
257C22⋊Dic17—42no—
258C22⋊Dic17—42no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—21no—
262C4⋊Dic17—21no—
263C4⋊Dic17—21no—
264C4⋊Dic17—21no—
265C4⋊Dic17—21no—
266C4⋊Dic17—42no—
267C4⋊Dic17—42no—
268C4⋊Dic17—42no—
269C4⋊Dic17—81no—
270C4⋊Dic17C2×D412yes—
271C4×Dic17—42no—
272#63223—44no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—21no—
279C2×#3622—21no—
280C2×#3622—21no—
281C2×#3622—21no—
282C2×#3622—21no—
283C2×#3622—21no—
284C2×#3622—44no—
285C2×#3622C2×D412yes—
286#22419—171nomaximal, Sylow
287C23×C17—21no—
288C23×C17—21no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17—22no—
292C23×C17—21no—
293C23×C17—22no—
294C23×C17—21no—
295C23×C17—22no—
296C23×C17—21no—
297C23×C17—21no—
298C23×C17—21no—
299C23×C17—21no—
300C23×C17—22no—
301C23×C17—48no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—48no—
313C23×C17—84no—
314C23×C17—84no—
315C23×C17—84no—
316C23×C17—84no—
317C23×C17—84no—
318C23×C17C2×C22⋊C412yes—
319C23×C17C2×C22⋊C412yes—
320C23×C17AGL(1,ℤ/8)12yes—
321C23×C17#13712yes—
322C23×C17C22×D411yescharacteristic
323Q8×C17—22no—
324Q8×C17—22no—
325Q8×C17—41no—
326Q8×C17—41no—
327D4×C17—28no—
328D4×C17—22no—
329D4×C17—22no—
330D4×C17—22no—
331D4×C17—22no—
332D4×C17—22no—
333D4×C17—48no—
334D4×C17—48no—
335D4×C17—41no—
336D4×C17—41no—
337D4×C17—84no—
338D4×C17C4×D414yescomplemented
339C2×C4×C17—21no—
340C2×C4×C17—21no—
341C2×C4×C17—21no—
342C2×C4×C17—21no—
343C2×C4×C17—21no—
344C2×C4×C17—21no—
345C2×C4×C17—21no—
346C2×C4×C17—21no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—48no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—84no—
363C2×C4×C17C2×C22⋊C412yes—
364C2×C4×C17C2×C22⋊C412yes—
365C2×C4×C17C2×C22⋊C412yes—
366C2×C4×C17C2×C22⋊C412yes—
367C2×C4×C17C23×C411yescharacteristic
368C2×C4×C17C22×D411yescharacteristic
369C2×C4×C17C22×D411yescharacteristic
370C2×C4×C17C2×#4111yescharacteristic
371C2×C4×C17H(5,𝔽2)11yescharacteristic
372C2×C4×C17H(5,𝔽2)11yescharacteristic
373C2×Dic17—22no—
374C2×Dic17—41no—
375C2×Dic17—41no—
376C2×Dic17—41no—
377C2×Dic17—41no—
378C2×Dic17—41no—
379C2×Dic17—41no—
380C2×Dic17—41no—
381C2×Dic17—41no—
382C2×Dic17—41no—
383C2×Dic17—41no—
384C2×Dic17—41no—
385C2×Dic17—84no—
386C2×Dic17—84no—
387#3622—22no—
388#3622—41no—
389#3622—41no—
390#3622—41no—
391C2×#546D1711yescharacteristic
392C2×#435—171no—
393C2×#417—171no—
394C22×#102—171no—
395D4×C4⋊C4—171no—
396#1983—171no—
397#1959—171no—
398#1895—171no—
399#1892—171no—
400#1874—171no—
401#1872—171no—
402#1802—171no—
403#1788—171no—
404#1786—171no—
405#1762—171no—
406C22×C17—22no—
407C22×C17—22no—
408C22×C17—22no—
409C22×C17—22no—
410C22×C17—22no—
411C22×C17—22no—
412C22×C17—22no—
413C22×C17—24no—
414C22×C17—22no—
415C22×C17—22no—
416C22×C17—42no—
417C22×C17—42no—
418C22×C17—41no—
419C22×C17—42no—
420C22×C17—41no—
421C22×C17—42no—
422C22×C17—41no—
423C22×C17—42no—
424C22×C17—41no—
425C22×C17—42no—
426C22×C17—42no—
427C22×C17—42no—
428C22×C17—42no—
429C22×C17—816no—
430C22×C17—81no—
431C22×C17—81no—
432C22×C17—81no—
433C22×C17—81no—
434C22×C17#41714yescomplemented
435C22×C17C22×C22⋊C411yescharacteristic
436C22×C17D4211yescharacteristic
437C22×C17#54611yescharacteristic
438C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
439C22×C17C2×#13711yescharacteristic
440C22×C17#57611yescharacteristic
441C22×C17#57711yescharacteristic
442C4×C17—22no—
443C4×C17—22no—
444C4×C17—22no—
445C4×C17—22no—
446C4×C17—42no—
447C4×C17—42no—
448C4×C17C2×C4×D411yescharacteristic
449C4×C17#51811yescharacteristic
450C4×C17D4211yescharacteristic
451C4×C17#54611yescharacteristic
452Dic17—42no—
453Dic17—81no—
454Dic17—81no—
455Dic17—81no—
456C22×#41C2×D1711yescharacteristic
457C23×D4C2×D1711yescharacteristic
458C22×M16—171no—
459C23×C8—171no—
460#546—24no—
461#546Dic1718yescomplemented
462C2×#124C2×D1711yescharacteristic
463C2×#123—21no—
464C2×C22⋊Q8C2×D1711yescharacteristic
465C2×#121—21no—
466C2×#121C2×D1711yescharacteristic
467C2×#120—21no—
468C2×C4×D4—341no—
469C2×C4×D4C2×D1711yescharacteristic
470C2×C4×D4C2×D1711yescharacteristic
471C22×C4⋊C4—171no—
472C22×C4⋊C4—171no—
473C22×C22⋊C4—21no—
474#435—344no—
475C2×C4⋊C8—171no—
476#417—344no—
477C2×#103—171no—
478C2×#103—171no—
479C2×#103—171no—
480C2×#103—171no—
481C2×#102—171no—
482C2×#102—171no—
483C2×#102—171no—
484C2×#102—171no—
485C2×#102—171no—
486C2×#102—171no—
487C2×#102—171no—
488C2×#102—171no—
489C2×#102—344no—
490C2×C22⋊C8—171no—
491C2×C22⋊C8—171no—
492C2×#97—171no—
493#389—341no—
494#385—341no—
495#385—341no—
496#384—171no—
497#380—171no—
498#380—171no—
499C4×C4⋊C4—171no—
500#340—171no—
501#340—171no—
502#340—171no—
503#340—171no—
504C2×C17—24no—
505C2×C17—42no—
506C2×C17—44no—
507C2×C17—82no—
508C2×C17D4×C22⋊C411yescharacteristic
509C2×C17C2×#41711yescharacteristic
510C2×C17#289711yescharacteristic
511C2×C17#326411yescharacteristic
512C2×C17#326611yescharacteristic
513C2×C17#330611yescharacteristic
514C2×C17#331411yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41C2×Dic1714yescomplemented
522C22×Q8C22×D1711yescharacteristic
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×Dic1714yescomplemented
532C22×D4C22⋊D1711yescharacteristic
533C22×D4C22×D1711yescharacteristic
534C22×D4C22×D1711yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—341no—
538C23×C4—341no—
539C23×C4C22×D1711yescharacteristic
540C23×C4C22×D1711yescharacteristic
541C2×M16—342no—
542C2×M16—342no—
543C2×M16—681no—
544C22×C8—171no—
545C22×C8—171no—
546C22×C8—171no—
547C22×C8—171no—
548C22×C8—342no—
549C22×C8—342no—
550C22×C8—681no—
551#124—22no—
552#124C2×Dic1714yescomplemented
553#123—28no—
554C22⋊Q8—22no—
555C22⋊Q8C2×Dic1714yescomplemented
556#121—22no—
557#121—28no—
558#121C2×Dic1714yescomplemented
559#120—28no—
560C4×D4—22no—
561C4×D4—684no—
562C4×D4C2×Dic1714yes—
563C4×D4C2×Dic1714yescomplemented
564C4×D4C22⋊D1714yes—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—171no—
567C2×C4⋊C4—171no—
568C2×C4⋊C4—171no—
569C2×C4⋊C4—171no—
570C2×C4⋊C4—342no—
571C2×C4⋊C4—342no—
572C2×C4⋊C4—341no—
573C2×C4⋊C4—341no—
574C2×C4⋊C4—341no—
575C2×C4⋊C4—341no—
576C2×C4⋊C4—681no—
577C2×C4⋊C4—681no—
578C2×C4⋊C4C22⋊D1711yescharacteristic
579C2×C4⋊C4C22×D1711yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—28no—
586C2×C22⋊C4—341no—
587C2×C22⋊C4—341no—
588C2×C22⋊C4C22⋊D1711yescharacteristic
589C2×C22⋊C4C22⋊D1711yescharacteristic
590C2×C42—341no—
591C2×C42C22×D1711yescharacteristic
592C4⋊C8—342no—
593#103—342no—
594#103—342no—
595#103—681no—
596#103—681no—
597#102—174no—
598#102—342no—
599#102—342no—
600#102—342no—
601#102—342no—
602#102—342no—
603#102—681no—
604#102—681no—
605C22⋊C8—342no—
606C22⋊C8—342no—
607#97—342no—
608#95—341no—
609#95—341no—
610#95—341no—
611C17#2241911yescharacteristic, complemented, Sylow
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D1711yescharacteristic
622C24C2×C22⋊D1711yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×Dic1712yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—24no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic1714yes—
657C2×D4D4×D1712yes—
658C2×D4#6325412yes—
659C2×D4C22×Dic1712yes—
660C2×D4C22×Dic1712yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—341no—
678C22×C4—341no—
679C22×C4—341no—
680C22×C4—341no—
681C22×C4—682no—
682C22×C4—682no—
683C22×C4—682no—
684C22×C4—682no—
685C22×C4—1361no—
686C22×C4—1361no—
687C22×C4C22×Dic1712yes—
688C22×C4C22×Dic1712yes—
689C22×C4C2×C22⋊D1712yes—
690C22×C4C2×C22⋊D1712yes—
691C22×C4C2×C22⋊D1711yescharacteristic
692C22×C4C2×C22⋊D1711yescharacteristic
693C22×C4C2×C22⋊D1711yescharacteristic
694C22×C4C2×C22⋊D1711yescharacteristic
695C22×C4C23×D1711yescharacteristic
696M16—684no—
697C2×C8—172no—
698C2×C8—341no—
699C2×C8—341no—
700C2×C8—341no—
701C2×C8—341no—
702C2×C8—341no—
703C2×C8—341no—
704C2×C8—341no—
705C2×C8—341no—
706C2×C8—341no—
707C2×C8—341no—
708C2×C8—341no—
709C2×C8—684no—
710C4⋊C4—21no—
711C4⋊C4—24no—
712C4⋊C4—172no—
713C4⋊C4—341no—
714C4⋊C4—341no—
715C4⋊C4—341no—
716C4⋊C4—341no—
717C4⋊C4—341no—
718C4⋊C4—341no—
719C4⋊C4—341no—
720C4⋊C4—682no—
721C4⋊C4—682no—
722C4⋊C4—682no—
723C4⋊C4—1361no—
724C4⋊C4C22⋊Dic1714yes—
725C4⋊C4C22×Dic1712yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—682no—
732C22⋊C4—682no—
733C22⋊C4C22⋊Dic1714yes—
734C22⋊C4C22⋊Dic1714yes—
735C42—682no—
736C42C22×Dic1712yes—
737C42C2×C22⋊D1712yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23#1058763512yes—
770C23#1058763712yes—
771C23C2×C22⋊Dic1712yes—
772C23C2×C22⋊Dic1712yes—
773C23C22×C22⋊D1711yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic1714yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—342no—
815C2×C4—681no—
816C2×C4—681no—
817C2×C4—681no—
818C2×C4—681no—
819C2×C4—681no—
820C2×C4—681no—
821C2×C4—681no—
822C2×C4—681no—
823C2×C4—681no—
824C2×C4—681no—
825C2×C4—681no—
826C2×C4—1364no—
827C2×C4—1364no—
828C2×C4C2×C22⋊Dic1712yes—
829C2×C4C2×C22⋊Dic1712yes—
830C2×C4C2×C22⋊Dic1712yes—
831C2×C4C2×C22⋊Dic1712yes—
832C2×C4C2×D4×D1711yescharacteristic
833C2×C4C2×#6325411yescharacteristic
834C2×C4#1058769111yescharacteristic
835C2×C4#1058769111yescharacteristic
836C2×C4C23×Dic1711yescharacteristic
837C2×C4C22×C22⋊D1711yescharacteristic
838C8—342no—
839C8—681no—
840C8—681no—
841C8—681no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1176281014yescomplemented
871C22C22×C22⋊Dic1711yescharacteristic
872C22D4×C22⋊D1711yescharacteristic
873C22#1176345311yescharacteristic
874C22C2×#1058763511yescharacteristic
875C22C2×#1058763711yescharacteristic
876C22#1176361211yescharacteristic
877C22#1176362011yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—682no—
885C4—1361no—
886C4—1361no—
887C4—1361no—
888C4C2×D4×Dic1711yescharacteristic
889C4#1176328411yescharacteristic
890C4D4×C22⋊D1711yescharacteristic
891C4#1176345311yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic1711yescharacteristic
897C2C2×#1176281011yescharacteristic
898C2#1453731011yescharacteristic
899C2#1454026511yescharacteristic
900C2#1454029011yescharacteristic
901C2#1454074511yescharacteristic
902C2#1454086511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#546C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#546D17
hypocenterC17#22419
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. C2×#11762810C2semidirect
3. C22×#10587503C2semidirect
4. D4×C4⋊Dic17C2semidirect
5. #14529717C2semidirect
6. #14529601C2semidirect
7. #14529223C2semidirect
8. #14529208C2semidirect
9. #14529102C2semidirect
10. #14529092C2semidirect
11. #14528784C2semidirect
12. #14528724C2semidirect
13. #14528715C2semidirect
14. #14528609C2semidirect
16. C22×#63223C22semidirect
20. C22×C4⋊Dic17C22semidirect
22. C2×C4⋊#3622C22semidirect
24. C2×#10587506C22semidirect
25. C2×#10587506C22semidirect
26. C2×#10587506C22semidirect
27. C2×#10587506C22semidirect
38. C2×C22⋊#3622C22semidirect
39. C2×#10587474C22semidirect
43. #11762679C22semidirect
45. #11762669C22semidirect
46. C4×C4⋊Dic17C22semidirect
47. #11762571C22semidirect
48. #11762571C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
54. C17×#546C4semidirect
70. C2×#41×C17C2×C4semidirect
80. C22×D4×C17C2×C4semidirect
91. C17×#124C2×C4semidirect
94. C17×C22⋊Q8C2×C4semidirect
97. C17×#121C2×C4semidirect
101. C4×D4×C17C2×C4semidirect
152. #10587503D4semidirect
338. D4×C17C4×D4semidirect
434. C22×C17#417semidirect
461. #546Dic17semidirect
521. C2×#41C2×Dic17semidirect
531. C22×D4C2×Dic17semidirect
552. #124C2×Dic17semidirect
555. C22⋊Q8C2×Dic17semidirect
558. #121C2×Dic17semidirect
563. C4×D4C2×Dic17semidirect
611. C17#22419semidirect
789. D4D4×Dic17semidirect
870. 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×#105875032
D4×C4⋊Dic172
#145297172
#145296012
#145292232
#145292082
#145291022
#145290922
#145287842
#145287242
#145287152
#145286092
C2×C17×#5462
#2241917