Finite Group Databasebeta

← #17054615

Subgroups — #17054615

Order 4352.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762910C211yesmaximal, characteristic, complemented
2C2×#11762805C211yesmaximal, characteristic
3#14531815C211yesmaximal, characteristic, complemented
4#14531614C211yesmaximal, characteristic
5#14529656C211yesmaximal, characteristic, complemented
6#14529476C211yesmaximal, characteristic, complemented
7#14529427C211yesmaximal, characteristic, complemented
8#14529208C211yesmaximal, characteristic, complemented
9#14529127C211yesmaximal, characteristic, complemented
10#14529120C211yesmaximal, characteristic, complemented
11#14529047C211yesmaximal, characteristic, complemented
12#14528985C211yesmaximal, characteristic, complemented
13#14528611C211yesmaximal, characteristic, complemented
14#14528563C211yesmaximal, characteristic, complemented
15C2×C17×#452C211yesmaximal, characteristic
16C23×#3622C2211yescharacteristic
17C2×Q8×Dic17C2211yescharacteristic
18C2×D4×Dic17C2211yescharacteristic
19C2×D4×Dic17C2211yescharacteristic
20C2×#10587612C2211yescharacteristic
21#11762910—24no—
22C2×#10587489C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24#11762805—24no—
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587486C2211yescharacteristic
32C2×#10587486C2211yescharacteristic
33#11762716C2211yescharacteristic
34#11762716C2211yescharacteristic
35#11762716C2211yescharacteristic
36#11762708C2211yescharacteristic
37#11762702—21no—
38#11762702—21no—
39#11762695—21no—
40#11762689—21no—
41#11762689—21no—
42#11762672—21no—
43#11762669C2211yescharacteristic
44C4⋊C4×Dic17—21no—
45C4⋊C4×Dic17C2211yescharacteristic
46C4×C22⋊Dic17C2211yescharacteristic
47C2×#10587502—21no—
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C22×#41×C17C2211yescharacteristic
55C22×Q16×C17C2211yescharacteristic
56C22×SD16×C17C2211yescharacteristic
57C2×C17×C22⋊Q8C2211yescharacteristic
58C17×#452C418yescomplemented
59C2×C17×#103C2211yescharacteristic
60C2×C17×#102C2211yescharacteristic
61C2×C17×C22⋊C8C2211yescharacteristic
62C2×#41×C17—22no—
63C2×#41×C17—22no—
64C2×#41×C17—22no—
65C2×#41×C17—41no—
66C2×#41×C17—41no—
67C2×#41×C17C2×C414yes—
68C22×Q8×C17C2311yescharacteristic
69C22×Q8×C17C2311yescharacteristic
70C22×D4×C17—21no—
71C22×D4×C17C2311yescharacteristic
72C23×C4×C17—21no—
73C23×C4×C17C2311yescharacteristic
74C23×Dic17—21no—
75C23×Dic17—21no—
76C2×Q16×C17—41no—
77C2×Q16×C17—41no—
78C2×Q16×C17C2×C414yescomplemented
79C2×SD16×C17—22no—
80C2×SD16×C17—22no—
81C2×SD16×C17C2×C414yes—
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C17×C22⋊Q8—22no—
85C17×C22⋊Q8C2×C414yescomplemented
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17C2311yescharacteristic
88C2×C22⋊C4×C17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17D411yescharacteristic
94C2×C22⋊Dic17D411yescharacteristic
95Q8×Dic17—22no—
96Q8×Dic17—41no—
97D4×Dic17—22no—
98D4×Dic17—22no—
99D4×Dic17—41no—
100D4×Dic17—41no—
101#10587612—22no—
102#10587612—41no—
103C2×C4⋊Dic17—21no—
104C2×C4⋊Dic17—21no—
105C2×C4⋊Dic17C2311yescharacteristic
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4×Dic17—21no—
110C2×C4×Dic17—21no—
111C2×C4×Dic17—21no—
112C2×C4×Dic17C2311yescharacteristic
113C2×C4×Dic17C2311yescharacteristic
114C22×#3622—22no—
115C22×#3622—22no—
116C22×#3622—41no—
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C17×#103C2×C414yescomplemented
120C17×#102C2×C414yes—
121C17×C22⋊C8C2×C414yescomplemented
122#10587506—22no—
123#10587506—22no—
124#10587506—22no—
125#10587506—41no—
126#10587503—22no—
127#10587503D414yes—
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587502D411yescharacteristic
138#10587502D411yescharacteristic
139#10587489—22no—
140#10587488—41no—
141#10587486—22no—
142#10587486—41no—
143C24×C17—21no—
144C24×C17C2×D411yescharacteristic
145#41×C17—28no—
146#41×C17—44no—
147#41×C17—44no—
148#41×C17—44no—
149C2×Q8×C17—21no—
150C2×Q8×C17—21no—
151C2×Q8×C17—21no—
152C2×Q8×C17—21no—
153C2×Q8×C17—21no—
154C2×Q8×C17—21no—
155C2×Q8×C17—21no—
156C2×Q8×C17—21no—
157C2×Q8×C17—21no—
158C2×Q8×C17—21no—
159C2×Q8×C17C22×C412yes—
160C2×Q8×C17C22×C412yes—
161C2×D4×C17—24no—
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—21no—
165C2×D4×C17—42no—
166C2×D4×C17—42no—
167C2×D4×C17C22×C412yes—
168C2×D4×C17C2×D412yes—
169C2×D4×C17#4112yes—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—24no—
178C22×C4×C17—42no—
179C22×C4×C17—42no—
180C22×C4×C17C22×C412yes—
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17#4112yes—
183C22×C4×C17C2411yescharacteristic
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—42no—
189C22×Dic17—42no—
190C22×Dic17—42no—
191C22×Dic17—42no—
192C22×Dic17—81no—
193C22×Dic17—81no—
194C22×Dic17C2×D411yescharacteristic
195C22×Dic17C2×D411yescharacteristic
196C22×Dic17C2×D411yescharacteristic
197C22×Dic17C2×D411yescharacteristic
198Q16×C17—44no—
199SD16×C17—28no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17C22×C412yes—
205C2×C8×C17C22×C412yes—
206C4⋊C4×C17—24no—
207C4⋊C4×C17—21no—
208C4⋊C4×C17C22×C412yes—
209C22⋊C4×C17—24no—
210C22⋊Dic17—41no—
211C22⋊Dic17—41no—
212C22⋊Dic17—42no—
213C22⋊Dic17—42no—
214C22⋊Dic17—42no—
215C22⋊Dic17—81no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—42no—
224C4⋊Dic17—42no—
225C4⋊Dic17C2×D412yes—
226C4×Dic17—21no—
227C4×Dic17—21no—
228C4×Dic17—21no—
229C4×Dic17—21no—
230C4×Dic17—42no—
231C4×Dic17—42no—
232C4×Dic17—42no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—44no—
239C2×#3622C2×D412yes—
240#22856—171nomaximal, Sylow
241C23×C17—22no—
242C23×C17—21no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17C4×D412yes—
255C23×C17C22×D411yescharacteristic
256Q8×C17—22no—
257Q8×C17—22no—
258Q8×C17—22no—
259Q8×C17—22no—
260Q8×C17—41no—
261Q8×C17—41no—
262Q8×C17—41no—
263Q8×C17—41no—
264D4×C17—22no—
265D4×C17—22no—
266D4×C17—22no—
267D4×C17—48no—
268D4×C17C4×D414yes—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—48no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17C4×D412yes—
286C2×C4×C17C23×C411yescharacteristic
287C2×C4×C17C22×D411yescharacteristic
288C2×C4×C17C2×#4111yescharacteristic
289C2×C4×C17C2×#4111yescharacteristic
290C2×C4×C17H(5,𝔽2)11yescharacteristic
291C2×C4×C17H(5,𝔽2)11yescharacteristic
292C2×Dic17—21no—
293C2×Dic17—22no—
294C2×Dic17—21no—
295C2×Dic17—21no—
296C2×Dic17—21no—
297C2×Dic17—21no—
298C2×Dic17—21no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—84no—
317C2×Dic17—84no—
318C8×C17—22no—
319C8×C17—22no—
320#3622—22no—
321#3622—41no—
322C2×#452D1711yescharacteristic
323C2×#440—171no—
324C2×#416—171no—
325#2362—171no—
326#2339—171no—
327#1971—171no—
328#1935—171no—
329#1928—171no—
330#1892—171no—
331#1878—171no—
332#1877—171no—
333#1864—171no—
334#1854—171no—
335#1762—171no—
336#1752—171no—
337C22×C17—22no—
338C22×C17—24no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—42no—
342C22×C17—42no—
343C22×C17—42no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—42no—
351C22×C17C2×C4×D411yescharacteristic
352C22×C17D4211yescharacteristic
353C22×C17#54611yescharacteristic
354C22×C17#57511yescharacteristic
355C22×C17#57511yescharacteristic
356C22×C17#57711yescharacteristic
357C22×C17#57811yescharacteristic
358C4×C17—22no—
359C4×C17—42no—
360C4×C17—42no—
361C4×C17—42no—
362C4×C17C2×C4×D411yescharacteristic
363C4×C17#51811yescharacteristic
364C4×C17#54611yescharacteristic
365C4×C17#55111yescharacteristic
366Dic17—41no—
367Dic17—42no—
368Dic17—41no—
369Dic17—41no—
370Dic17—41no—
371Dic17—81no—
372Dic17—81no—
373Dic17—81no—
374C22×#41C2×D1711yescharacteristic
375C22×Q16C2×D1711yescharacteristic
376C22×SD16C2×D1711yescharacteristic
377C23×C8—171no—
378C2×C22⋊Q8C2×D1711yescharacteristic
379C2×C4×Q8—171no—
380C2×C4×D4—171no—
381C2×C4×D4—171no—
382C2×#117—171no—
383#452Dic1718yescomplemented
384#440—344no—
385C2×#107—171no—
386C2×#106—171no—
387#416—344no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#103—171no—
391C2×#103—171no—
392C2×#103C2×D1711yescharacteristic
393C2×#102—171no—
394C2×#102—171no—
395C2×#102C2×D1711yescharacteristic
396C2×C22⋊C8C2×D1711yescharacteristic
397C2×#97—171no—
398C2×#97—171no—
399#391—171no—
400#391—171no—
401#391—171no—
402#389—171no—
403#388—341no—
404#388—341no—
405#387—341no—
406#386—341no—
407#386—341no—
408#381—341no—
409#380—171no—
410C4×C4⋊C4—171no—
411C4×C4⋊C4—341no—
412C4×C22⋊C4—171no—
413C2×#95—341no—
414#340—171no—
415#340—171no—
416#340—171no—
417#340—171no—
418#336—171no—
419#336—171no—
420C2×C17—42no—
421C2×C17—44no—
422C2×C17#235811yescharacteristic
423C2×C17#294311yescharacteristic
424C2×C17#294711yescharacteristic
425C2×C17#326711yescharacteristic
426C2×C17#326911yescharacteristic
427C2×C17#331111yescharacteristic
428C2×C17#331511yescharacteristic
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—41no—
433C2×#41—41no—
434C2×#41C2×Dic1714yes—
435C22×Q8C22×D1711yescharacteristic
436C22×Q8C22×D1711yescharacteristic
437C22×D4—21no—
438C22×D4C22×D1711yescharacteristic
439C23×C4—21no—
440C23×C4—341no—
441C23×C4—341no—
442C23×C4C22×D1711yescharacteristic
443C2×Q16—41no—
444C2×Q16—41no—
445C2×Q16C2×Dic1714yescomplemented
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16C2×Dic1714yes—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8—342no—
452C22×C8—342no—
453C22×C8—681no—
454C22×C8C22×D1711yescharacteristic
455C22×C8C22×D1711yescharacteristic
456C22⋊Q8—22no—
457C22⋊Q8C2×Dic1714yescomplemented
458C4×Q8—342no—
459C4×Q8—681no—
460C4×D4—342no—
461C4×D4—342no—
462C4×D4—681no—
463C4×D4—681no—
464#117—342no—
465#117—681no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—171no—
468C2×C4⋊C4—171no—
469C2×C4⋊C4—171no—
470C2×C4⋊C4—171no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4C22×D1711yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—171no—
476C2×C22⋊C4—171no—
477C2×C22⋊C4—341no—
478C2×C22⋊C4—341no—
479C2×C22⋊C4—341no—
480C2×C22⋊C4—341no—
481C2×C42—171no—
482C2×C42—171no—
483C2×C42—341no—
484C2×C42—341no—
485C2×C42—341no—
486#107—342no—
487#106—681no—
488#103—342no—
489#103—342no—
490#103—342no—
491#103—681no—
492#103C2×Dic1714yescomplemented
493#102—174no—
494#102—342no—
495#102C2×Dic1714yes—
496C22⋊C8C2×Dic1714yescomplemented
497#97—342no—
498#97—681no—
499#95—171no—
500#95—171no—
501#95—341no—
502#95—341no—
503#95—341no—
504#95—341no—
505#95—341no—
506#95—341no—
507#95—341no—
508#95—341no—
509#95—341no—
510C17#2285611yescharacteristic, complemented, Sylow
511C24—21no—
512C24D4×D1711yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C22×Dic1712yes—
528C2×Q8C22×Dic1712yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4D4×D1712yes—
536C2×D4#6325412yes—
537C2×D4C22×Dic1712yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—171no—
549C22×C4—171no—
550C22×C4—171no—
551C22×C4—171no—
552C22×C4—341no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—682no—
557C22×C4—682no—
558C22×C4—682no—
559C22×C4—682no—
560C22×C4—1361no—
561C22×C4—1361no—
562C22×C4D4×D1711yescharacteristic
563C22×C4#6325412yes—
564C22×C4C22×Dic1712yes—
565C22×C4C23×D1711yescharacteristic
566Q16—44no—
567SD16—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—172no—
573C2×C8—341no—
574C2×C8—341no—
575C2×C8—341no—
576C2×C8—341no—
577C2×C8—341no—
578C2×C8—684no—
579C2×C8C22×Dic1712yes—
580C2×C8C22×Dic1712yes—
581C4⋊C4—21no—
582C4⋊C4—24no—
583C4⋊C4—172no—
584C4⋊C4—341no—
585C4⋊C4—341no—
586C4⋊C4—341no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—682no—
592C4⋊C4—682no—
593C4⋊C4C22×Dic1712yes—
594C22⋊C4—24no—
595C22⋊C4—681no—
596C22⋊C4—681no—
597C22⋊C4—682no—
598C22⋊C4—682no—
599C22⋊C4—682no—
600C22⋊C4—1361no—
601C42—341no—
602C42—341no—
603C42—341no—
604C42—341no—
605C42—682no—
606C42—682no—
607C42—682no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—22no—
615C23—22no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23D4×Dic1712yes—
622C23C2×D4×D1711yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4D4×Dic1714yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—341no—
653C2×C4—341no—
654C2×C4—341no—
655C2×C4—341no—
656C2×C4—341no—
657C2×C4—341no—
658C2×C4—341no—
659C2×C4—341no—
660C2×C4—341no—
661C2×C4—341no—
662C2×C4—342no—
663C2×C4—341no—
664C2×C4—341no—
665C2×C4—681no—
666C2×C4—681no—
667C2×C4—681no—
668C2×C4—681no—
669C2×C4—681no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—1364no—
677C2×C4—1364no—
678C2×C4D4×Dic1712yes—
679C2×C4C2×D4×D1711yescharacteristic
680C2×C4C2×#6325411yescharacteristic
681C2×C4C2×#6325411yescharacteristic
682C2×C4#1058769111yescharacteristic
683C2×C4#1058769111yescharacteristic
684C2×C4C23×Dic1711yescharacteristic
685C8—22no—
686C8—22no—
687C8—342no—
688C8—681no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×D4×Dic1711yescharacteristic
704C22#1176344111yescharacteristic
705C22#1176344611yescharacteristic
706C22#1176360611yescharacteristic
707C22#1176360611yescharacteristic
708C22#1176361811yescharacteristic
709C22#1176362511yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—681no—
715C4—681no—
716C4—682no—
717C4—681no—
718C4—681no—
719C4—1361no—
720C4—1361no—
721C4—1361no—
722C4C2×D4×Dic1711yescharacteristic
723C4#1176328411yescharacteristic
724C4#1176344611yescharacteristic
725C4#1176349011yescharacteristic
726C2—42no—
727C2—44no—
728C2#1453176811yescharacteristic
729C2#1453758511yescharacteristic
730C2#1453762811yescharacteristic
731C2#1454031311yescharacteristic
732C2#1454034311yescharacteristic
733C2#1454082411yescharacteristic
734C2#1454088411yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#452C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
cosocleC22×C4×C17C24
hypercenterC2×#452D17
hypocenterC17#22856
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#11762910C2semidirect
3. #14531815C2semidirect
5. #14529656C2semidirect
6. #14529476C2semidirect
7. #14529427C2semidirect
8. #14529208C2semidirect
9. #14529127C2semidirect
10. #14529120C2semidirect
11. #14529047C2semidirect
12. #14528985C2semidirect
13. #14528611C2semidirect
14. #14528563C2semidirect
58. C17×#452C4semidirect
78. C2×Q16×C17C2×C4semidirect
85. C17×C22⋊Q8C2×C4semidirect
119. C17×#103C2×C4semidirect
121. C17×C22⋊C8C2×C4semidirect
383. #452Dic17semidirect
445. C2×Q16C2×Dic17semidirect
457. C22⋊Q8C2×Dic17semidirect
492. #103C2×Dic17semidirect
496. C22⋊C8C2×Dic17semidirect
510. C17#22856semidirect

Maximal subgroups

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

subgroupindex
C2×#117629102
C2×#117628052
#145318152
#145316142
#145296562
#145294762
#145294272
#145292082
#145291272
#145291202
#145290472
#145289852
#145286112
#145285632
C2×C17×#4522
#2285617