Finite Group Databasebeta

← #17049864

Subgroups — #17049864

Order 4352.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2C2×#11762814C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4#14531713C211yesmaximal, characteristic, complemented
5#14529712C211yesmaximal, characteristic, complemented
6#14529609C211yesmaximal, characteristic, complemented
7#14529223C211yesmaximal, characteristic, complemented
8#14529213C211yesmaximal, characteristic, complemented
9#14529107C211yesmaximal, characteristic, complemented
10#14529102C211yesmaximal, characteristic, complemented
11#14528794C211yesmaximal, characteristic, complemented
12#14528715C211yesmaximal, characteristic, complemented
13#14528715C211yesmaximal, characteristic, complemented
14#14528609C211yesmaximal, characteristic, complemented
15C2×D42×C17C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic, complemented
17C23×#3622C2211yescharacteristic, complemented
18C2×#10587612C2211yescharacteristic, complemented
19C22×C4⋊Dic17C2211yescharacteristic, complemented
20#11762881—24no—
21C2×C4⋊#3622C2211yescharacteristic, complemented
22#11762814—24no—
23C2×#10587503—24no—
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic, complemented
29C2×#10587503C2211yescharacteristic, complemented
30C2×#10587503C2211yescharacteristic, complemented
31C2×#10587503C2211yescharacteristic, complemented
32C2×#10587503C2211yescharacteristic, complemented
33C2×#10587503C2211yescharacteristic, complemented
34C2×#10587503C2211yescharacteristic, complemented
35C2×#10587503C2211yescharacteristic, complemented
36C2×C22⋊#3622C2211yescharacteristic, complemented
37C2×C22⋊#3622C2211yescharacteristic, complemented
38C2×#10587474C2211yescharacteristic, complemented
39#11762702—21no—
40#11762695—21no—
41#11762689—21no—
42#11762675C2211yescharacteristic, complemented
43#11762669C2211yescharacteristic, complemented
44#11762669C2211yescharacteristic, complemented
45C4×C4⋊Dic17C2211yescharacteristic, complemented
46C22⋊C4×Dic17—21no—
47#11762571C2211yescharacteristic, complemented
48#11762571C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51C23×D4×C17—21no—
52C23×D4×C17C2211yescharacteristic
53C23×D4×C17C2211yescharacteristic
54D42×C17—24no—
55D42×C17C418yescomplemented
56C2×C17×#127C2211yescharacteristic
57C2×C17×#121—21no—
58C2×C17×#121C2211yescharacteristic
59C2×C17×#121C2211yescharacteristic
60C2×C17×#120—21no—
61C2×C17×#120—21no—
62C2×C4×D4×C17C2211yescharacteristic
63C2×C4×D4×C17C2211yescharacteristic
64C25×C17—21no—
65C25×C17—21no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—21no—
71C22×D4×C17—21no—
72C22×D4×C17—28no—
73C22×D4×C17—21no—
74C22×D4×C17—21no—
75C22×D4×C17—21no—
76C22×D4×C17—22no—
77C22×D4×C17—22no—
78C22×D4×C17—21no—
79C22×D4×C17—41no—
80C22×D4×C17—41no—
81C22×D4×C17—41no—
82C22×D4×C17—41no—
83C22×D4×C17—44no—
84C22×D4×C17—44no—
85C22×D4×C17C2×C414yes—
86C22×D4×C17C2×C414yescomplemented
87C22×D4×C17D411yescharacteristic
88C22×D4×C17C2311yescharacteristic
89C22×D4×C17C2311yescharacteristic
90C22×D4×C17C2311yescharacteristic
91C23×C4×C17—21no—
92C23×C4×C17C2311yescharacteristic
93C23×C4×C17C2311yescharacteristic
94C23×Dic17—21no—
95C17×#127—22no—
96C17×#127C2×C414yescomplemented
97C17×#121—22no—
98C17×#121—22no—
99C17×#121—28no—
100C17×#121C2×C414yes—
101C17×#121C2×C414yescomplemented
102C17×#120—28no—
103C17×#120—28no—
104C4×D4×C17—22no—
105C4×D4×C17C2×C414yes—
106C4×D4×C17C2×C414yescomplemented
107C4×D4×C17D414yes—
108C2×C4⋊C4×C17D411yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17D411yescharacteristic
114C2×C22⋊C4×C17D411yescharacteristic
115C2×C42×C17C2311yescharacteristic
116C2×C22⋊Dic17—21no—
117C2×C22⋊Dic17—21no—
118C2×C22⋊Dic17—21no—
119#10587612—22no—
120#10587612—41no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—41no—
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2311yescharacteristic
127C2×C4⋊Dic17C2311yescharacteristic
128C2×C4×Dic17—21no—
129C2×C4×Dic17—21no—
130C2×#63223—22no—
131C2×#63223—22no—
132C2×#63223—41no—
133C22×#3622—22no—
134C22×#3622—22no—
135C22×#3622—41no—
136C22×#3622C2311yescharacteristic
137C22×#3622C2311yescharacteristic
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140#10587503—22no—
141#10587503—22no—
142#10587503—22no—
143#10587503—22no—
144#10587503—22no—
145#10587503—22no—
146#10587503—22no—
147#10587503—41no—
148#10587503—41no—
149#10587503—41no—
150#10587503—41no—
151#10587503D414yescomplemented
152#10587502—21no—
153#10587502—21no—
154#10587502—21no—
155#10587502—21no—
156#10587502—21no—
157C22⋊#3622—22no—
158C22⋊#3622—22no—
159C4⋊#3622—22no—
160#10587474—22no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—24no—
165C24×C17—24no—
166C24×C17—42no—
167C24×C17—42no—
168C24×C17—42no—
169C24×C17—42no—
170C24×C17—42no—
171C24×C17—42no—
172C24×C17—42no—
173C24×C17—42no—
174C24×C17—81no—
175C24×C17—81no—
176C24×C17—81no—
177C24×C17—81no—
178C24×C17C2×D411yescharacteristic
179C24×C17C2×D411yescharacteristic
180C2×D4×C17—22no—
181C2×D4×C17—22no—
182C2×D4×C17—28no—
183C2×D4×C17—28no—
184C2×D4×C17—24no—
185C2×D4×C17—24no—
186C2×D4×C17—24no—
187C2×D4×C17—24no—
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—21no—
196C2×D4×C17—21no—
197C2×D4×C17—21no—
198C2×D4×C17—21no—
199C2×D4×C17—21no—
200C2×D4×C17—21no—
201C2×D4×C17—21no—
202C2×D4×C17—21no—
203C2×D4×C17—44no—
204C2×D4×C17—44no—
205C2×D4×C17—44no—
206C2×D4×C17—44no—
207C2×D4×C17—44no—
208C2×D4×C17—44no—
209C2×D4×C17—42no—
210C2×D4×C17—42no—
211C2×D4×C17—42no—
212C2×D4×C17—42no—
213C2×D4×C17—42no—
214C2×D4×C17—42no—
215C2×D4×C17—432no—
216C2×D4×C17—42no—
217C2×D4×C17—42no—
218C2×D4×C17—42no—
219C2×D4×C17—42no—
220C2×D4×C17—81no—
221C2×D4×C17—81no—
222C2×D4×C17C22⋊C414yes—
223C2×D4×C17C22×C412yes—
224C2×D4×C17C22×C412yes—
225C2×D4×C17C22×C412yes—
226C2×D4×C17C2×D412yes—
227C2×D4×C17#4112yes—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—24no—
238C22×C4×C17—42no—
239C22×C4×C17—42no—
240C22×C4×C17C22×C412yes—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C2×D411yescharacteristic
243C22×C4×C17C2×D411yescharacteristic
244C22×C4×C17C2×D411yescharacteristic
245C22×C4×C17C2×D411yescharacteristic
246C22×C4×C17C2×D412yes—
247C22×C4×C17C2×D412yes—
248C22×C4×C17C2411yescharacteristic
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—42no—
254C22×Dic17—42no—
255C22×Dic17—81no—
256C4⋊C4×C17—21no—
257C4⋊C4×C17C22⋊C414yes—
258C4⋊C4×C17C22×C412yes—
259C22⋊C4×C17—24no—
260C22⋊C4×C17—24no—
261C22⋊C4×C17—24no—
262C22⋊C4×C17C22⋊C414yes—
263C22⋊C4×C17C22⋊C414yes—
264C42×C17C22×C412yes—
265C42×C17C2×D412yes—
266C22⋊Dic17—42no—
267C22⋊Dic17—42no—
268C22⋊Dic17—81no—
269C4⋊Dic17—21no—
270C4⋊Dic17—21no—
271C4⋊Dic17—21no—
272C4⋊Dic17—21no—
273C4⋊Dic17—21no—
274C4⋊Dic17—21no—
275C4⋊Dic17—21no—
276C4⋊Dic17—42no—
277C4⋊Dic17C2×D412yescomplemented
278C4×Dic17—42no—
279C4×Dic17—81no—
280#63223—44no—
281C2×#3622—21no—
282C2×#3622—21no—
283C2×#3622—21no—
284C2×#3622—21no—
285C2×#3622—21no—
286C2×#3622—21no—
287C2×#3622—21no—
288C2×#3622—21no—
289C2×#3622—21no—
290C2×#3622—21no—
291C2×#3622—21no—
292C2×#3622—44no—
293C2×#3622C2×D412yescomplemented
294#22423—171nomaximal, Sylow
295C23×C17—21no—
296C23×C17—21no—
297C23×C17—21no—
298C23×C17—21no—
299C23×C17—22no—
300C23×C17—21no—
301C23×C17—22no—
302C23×C17—21no—
303C23×C17—22no—
304C23×C17—21no—
305C23×C17—21no—
306C23×C17—21no—
307C23×C17—21no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—48no—
311C23×C17—48no—
312C23×C17—48no—
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—48no—
330C23×C17—84no—
331C23×C17—84no—
332C23×C17—84no—
333C23×C17—84no—
334C23×C17—84no—
335C23×C17—84no—
336C23×C17—84no—
337C23×C17—84no—
338C23×C17—84no—
339C23×C17—84no—
340C23×C17C2×C22⋊C412yes—
341C23×C17C2×C22⋊C412yes—
342C23×C17AGL(1,ℤ/8)12yes—
343C23×C17AGL(1,ℤ/8)12yes—
344C23×C17C22×D411yescharacteristic
345D4×C17—28no—
346D4×C17—22no—
347D4×C17—22no—
348D4×C17—22no—
349D4×C17—22no—
350D4×C17—22no—
351D4×C17—22no—
352D4×C17—22no—
353D4×C17—48no—
354D4×C17—48no—
355D4×C17—48no—
356D4×C17—48no—
357D4×C17—48no—
358D4×C17—41no—
359D4×C17—41no—
360D4×C17—41no—
361D4×C17—41no—
362D4×C17—84no—
363D4×C17C4×D414yes—
364C2×C4×C17—21no—
365C2×C4×C17—21no—
366C2×C4×C17—21no—
367C2×C4×C17—21no—
368C2×C4×C17—21no—
369C2×C4×C17—21no—
370C2×C4×C17—21no—
371C2×C4×C17—21no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—48no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17C2×C22⋊C412yes—
385C2×C4×C17C2×C22⋊C412yes—
386C2×C4×C17C2×C22⋊C412yes—
387C2×C4×C17C2×C22⋊C412yes—
388C2×C4×C17C23×C411yescharacteristic
389C2×C4×C17C22×D411yescharacteristic
390C2×C4×C17C22×D411yescharacteristic
391C2×C4×C17C2×#4111yescharacteristic
392C2×C4×C17H(5,𝔽2)11yescharacteristic
393C2×C4×C17H(5,𝔽2)11yescharacteristic
394C2×Dic17—22no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—84no—
407#3622—22no—
408#3622—41no—
409#3622—41no—
410#3622—41no—
411C2×D42D1711yescharacteristic
412C2×#435—171no—
413C2×#418—171no—
414C22×#102—171no—
415#2352—171no—
416#1982—171no—
417#1961—171no—
418#1895—171no—
419#1893—171no—
420#1875—171no—
421#1874—171no—
422#1804—171no—
423#1786—171no—
424#1786—171no—
425#1762—171no—
426C22×C17—22no—
427C22×C17—22no—
428C22×C17—22no—
429C22×C17—22no—
430C22×C17—22no—
431C22×C17—22no—
432C22×C17—22no—
433C22×C17—24no—
434C22×C17—22no—
435C22×C17—22no—
436C22×C17—42no—
437C22×C17—42no—
438C22×C17—41no—
439C22×C17—42no—
440C22×C17—41no—
441C22×C17—42no—
442C22×C17—41no—
443C22×C17—42no—
444C22×C17—41no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—816no—
453C22×C17—816no—
454C22×C17—81no—
455C22×C17—81no—
456C22×C17—81no—
457C22×C17—81no—
458C22×C17—81no—
459C22×C17—81no—
460C22×C17—81no—
461C22×C17—81no—
462C22×C17#41814yescomplemented
463C22×C17C22×C22⋊C411yescharacteristic
464C22×C17D4211yescharacteristic
465C22×C17#54611yescharacteristic
466C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C17#57611yescharacteristic
469C22×C17#57711yescharacteristic
470C4×C17—22no—
471C4×C17—22no—
472C4×C17—22no—
473C4×C17—22no—
474C4×C17—42no—
475C4×C17C2×C4×D411yescharacteristic
476C4×C17#51811yescharacteristic
477C4×C17D4211yescharacteristic
478C4×C17#54611yescharacteristic
479Dic17—42no—
480Dic17—81no—
481Dic17—81no—
482Dic17—81no—
483C23×D4—21no—
484C23×D4C2×D1711yescharacteristic
485C23×D4C2×D1711yescharacteristic
486C22×M16—171no—
487C23×C8—171no—
488D42—24no—
489D42Dic1718yescomplemented
490C2×#127C2×D1711yescharacteristic
491C2×#121—21no—
492C2×#121C2×D1711yescharacteristic
493C2×#121C2×D1711yescharacteristic
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×D4C2×D1711yescharacteristic
497C2×C4×D4C2×D1711yescharacteristic
498C2×#117—171no—
499C22×C4⋊C4—171no—
500#435—344no—
501C2×C4⋊C8—171no—
502#418—344no—
503C2×#102—171no—
504C2×#102—171no—
505C2×#102—171no—
506C2×#102—171no—
507C2×#102—171no—
508C2×#102—171no—
509C2×#102—171no—
510C2×#102—171no—
511C2×#102—171no—
512C2×#102—171no—
513C2×#102—171no—
514C2×#102—171no—
515C2×#102—344no—
516C2×C22⋊C8—171no—
517C2×C22⋊C8—171no—
518C2×#97—171no—
519#388—341no—
520#387—341no—
521#386—341no—
522#382—171no—
523#380—171no—
524#380—171no—
525C4×C4⋊C4—171no—
526C4×C22⋊C4—341no—
527#340—171no—
528#340—171no—
529#340—171no—
530#340—171no—
531C2×C17—24no—
532C2×C17—42no—
533C2×C17—44no—
534C2×C17—82no—
535C2×C17—82no—
536C2×C17D4×C22⋊C411yescharacteristic
537C2×C17C2×#41811yescharacteristic
538C2×C17#289711yescharacteristic
539C2×C17#326411yescharacteristic
540C2×C17#326511yescharacteristic
541C2×C17#331011yescharacteristic
542C2×C17#331811yescharacteristic
543C25—21no—
544C25—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—28no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—21no—
558C22×D4—41no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—44no—
563C22×D4—44no—
564C22×D4C2×Dic1714yes—
565C22×D4C2×Dic1714yescomplemented
566C22×D4C22⋊D1711yescharacteristic
567C22×D4C22×D1711yescharacteristic
568C22×D4C22×D1711yescharacteristic
569C22×D4C22×D1711yescharacteristic
570C23×C4—21no—
571C23×C4—341no—
572C23×C4C22×D1711yescharacteristic
573C23×C4C22×D1711yescharacteristic
574C2×M16—342no—
575C2×M16—342no—
576C2×M16—681no—
577C22×C8—171no—
578C22×C8—171no—
579C22×C8—171no—
580C22×C8—171no—
581C22×C8—342no—
582C22×C8—342no—
583C22×C8—681no—
584#127—22no—
585#127C2×Dic1714yescomplemented
586#121—22no—
587#121—22no—
588#121—28no—
589#121C2×Dic1714yes—
590#121C2×Dic1714yescomplemented
591#120—28no—
592#120—28no—
593C4×D4—22no—
594C4×D4C2×Dic1714yes—
595C4×D4C2×Dic1714yescomplemented
596C4×D4C22⋊D1714yes—
597#117—342no—
598#117—681no—
599C2×C4⋊C4—171no—
600C2×C4⋊C4—171no—
601C2×C4⋊C4—171no—
602C2×C4⋊C4—171no—
603C2×C4⋊C4—342no—
604C2×C4⋊C4—341no—
605C2×C4⋊C4—681no—
606C2×C4⋊C4C22⋊D1711yescharacteristic
607C2×C4⋊C4C22×D1711yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—341no—
612C2×C22⋊C4—341no—
613C2×C22⋊C4—341no—
614C2×C22⋊C4C22⋊D1711yescharacteristic
615C2×C22⋊C4C22⋊D1711yescharacteristic
616C2×C42—341no—
617C2×C42—341no—
618C2×C42C22×D1711yescharacteristic
619C4⋊C8—342no—
620#102—174no—
621#102—342no—
622#102—342no—
623#102—342no—
624#102—342no—
625#102—342no—
626#102—342no—
627#102—342no—
628#102—681no—
629#102—681no—
630#102—681no—
631#102—681no—
632C22⋊C8—342no—
633C22⋊C8—342no—
634#97—342no—
635#95—341no—
636#95—341no—
637#95—341no—
638#95—341no—
639#95—341no—
640C17#2242311yescharacteristic, complemented, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×C22⋊D1711yescharacteristic
659C24C2×C22⋊D1711yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊Dic1714yes—
703C2×D4D4×D1712yes—
704C2×D4#6325412yes—
705C2×D4C22×Dic1712yes—
706C2×D4C22×Dic1712yes—
707C2×D4C22×Dic1712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—682no—
725C22×C4—682no—
726C22×C4—1361no—
727C22×C4C22×Dic1712yes—
728C22×C4C22×Dic1712yes—
729C22×C4C2×C22⋊D1712yes—
730C22×C4C2×C22⋊D1712yes—
731C22×C4C2×C22⋊D1711yescharacteristic
732C22×C4C2×C22⋊D1711yescharacteristic
733C22×C4C2×C22⋊D1711yescharacteristic
734C22×C4C2×C22⋊D1711yescharacteristic
735C22×C4C23×D1711yescharacteristic
736M16—684no—
737C2×C8—172no—
738C2×C8—341no—
739C2×C8—341no—
740C2×C8—341no—
741C2×C8—341no—
742C2×C8—341no—
743C2×C8—341no—
744C2×C8—341no—
745C2×C8—341no—
746C2×C8—341no—
747C2×C8—341no—
748C2×C8—341no—
749C2×C8—684no—
750C4⋊C4—21no—
751C4⋊C4—172no—
752C4⋊C4—341no—
753C4⋊C4—341no—
754C4⋊C4—341no—
755C4⋊C4—341no—
756C4⋊C4—341no—
757C4⋊C4—341no—
758C4⋊C4—341no—
759C4⋊C4—682no—
760C4⋊C4C22⋊Dic1714yes—
761C4⋊C4C22×Dic1712yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—682no—
766C22⋊C4—682no—
767C22⋊C4—1361no—
768C22⋊C4C22⋊Dic1714yes—
769C22⋊C4C22⋊Dic1714yes—
770C42—682no—
771C42—1361no—
772C42C22×Dic1712yes—
773C42C2×C22⋊D1712yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#1058761812yes—
820C23#1058761812yes—
821C23C2×C22⋊Dic1712yes—
822C23C2×C22⋊Dic1712yes—
823C23C22×C22⋊D1711yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4D4×Dic1714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—48no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—342no—
864C2×C4—681no—
865C2×C4—681no—
866C2×C4—681no—
867C2×C4—681no—
868C2×C4—681no—
869C2×C4—681no—
870C2×C4—681no—
871C2×C4—681no—
872C2×C4—681no—
873C2×C4—681no—
874C2×C4—681no—
875C2×C4—1364no—
876C2×C4C2×C22⋊Dic1712yes—
877C2×C4C2×C22⋊Dic1712yes—
878C2×C4C2×C22⋊Dic1712yes—
879C2×C4C2×C22⋊Dic1712yes—
880C2×C4C2×D4×D1711yescharacteristic
881C2×C4C2×#6325411yescharacteristic
882C2×C4#1058769111yescharacteristic
883C2×C4#1058769111yescharacteristic
884C2×C4C23×Dic1711yescharacteristic
885C2×C4C22×C22⋊D1711yescharacteristic
886C8—342no—
887C8—681no—
888C8—681no—
889C8—681no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#1176281414yescomplemented
927C22C22×C22⋊Dic1711yescharacteristic
928C22D4×C22⋊D1711yescharacteristic
929C22#1176345311yescharacteristic
930C22C2×#1058761811yescharacteristic
931C22C2×#1058761811yescharacteristic
932C22#1176361211yescharacteristic
933C22#1176362011yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—682no—
940C4—1361no—
941C4—1361no—
942C4—1361no—
943C4C2×D4×Dic1711yescharacteristic
944C4#1176328411yescharacteristic
945C4D4×C22⋊D1711yescharacteristic
946C4#1176345311yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊Dic1711yescharacteristic
953C2C2×#1176281411yescharacteristic
954C2#1453731011yescharacteristic
955C2#1454026011yescharacteristic
956C2#1454027511yescharacteristic
957C2#1454080511yescharacteristic
958C2#1454092511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×D42×C17C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×D42D17
hypocenterC17#22423
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. C2×#11762814C2semidirect
3. C22×#10587503C2semidirect
4. #14531713C2semidirect
5. #14529712C2semidirect
6. #14529609C2semidirect
7. #14529223C2semidirect
8. #14529213C2semidirect
9. #14529107C2semidirect
10. #14529102C2semidirect
11. #14528794C2semidirect
12. #14528715C2semidirect
13. #14528715C2semidirect
14. #14528609C2semidirect
16. C22×#63223C22semidirect
17. C23×#3622C22semidirect
18. C2×#10587612C22semidirect
19. C22×C4⋊Dic17C22semidirect
21. C2×C4⋊#3622C22semidirect
28. C2×#10587503C22semidirect
29. C2×#10587503C22semidirect
30. C2×#10587503C22semidirect
31. C2×#10587503C22semidirect
32. C2×#10587503C22semidirect
33. C2×#10587503C22semidirect
34. C2×#10587503C22semidirect
35. C2×#10587503C22semidirect
36. C2×C22⋊#3622C22semidirect
37. C2×C22⋊#3622C22semidirect
38. C2×#10587474C22semidirect
42. #11762675C22semidirect
43. #11762669C22semidirect
44. #11762669C22semidirect
45. C4×C4⋊Dic17C22semidirect
47. #11762571C22semidirect
48. #11762571C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
55. D42×C17C4semidirect
86. C22×D4×C17C2×C4semidirect
96. C17×#127C2×C4semidirect
101. C17×#121C2×C4semidirect
106. C4×D4×C17C2×C4semidirect
151. #10587503D4semidirect
277. C4⋊Dic17C2×D4semidirect
293. C2×#3622C2×D4semidirect
462. C22×C17#418semidirect
489. D42Dic17semidirect
565. C22×D4C2×Dic17semidirect
585. #127C2×Dic17semidirect
590. #121C2×Dic17semidirect
595. C4×D4C2×Dic17semidirect
640. C17#22423semidirect
926. C22#11762814semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
C2×#117628142
C22×#105875032
#145317132
#145297122
#145296092
#145292232
#145292132
#145291072
#145291022
#145287942
#145287152
#145286092
C2×D42×C172
#2242317