Finite Group Databasebeta

← D17⋊#1511 #17965325

Subgroups — D17⋊#1511 #17965325

Order 4352.

1446 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17⋊#407C211yesmaximal, characteristic
2C2×#11763752C211yesmaximal, characteristic
3#14544194C212yesmaximal, complemented
4#14544193C214yesmaximal, complemented
5#14544192C212yesmaximal, complemented
6D17⋊#328C214yesmaximal, complemented
7C2×C22⋊Q8×D17C211yesmaximal, characteristic
8C2×D17⋊M16—21no—
9C22×C22⋊#595—21no—
10#11763781C2212yes—
11#11763780—21no—
12#11763780C2212yes—
13#11763779—21no—
14#11763777—21no—
15#11763777C2212yes—
16#11763752—21no—
17#11763752—21no—
18#11763752C2212yes—
19#11763752C2212yes—
20C2×(C2×#595)⋊C4—21no—
21C2×(C2×#595)⋊C4C2212yes—
22#11763663C2218yescomplemented
23#11763662C2218yescomplemented
24C22×Q8×D17C411yescharacteristic, complemented
25C23×C4×D17C2211yescharacteristic
26C2×#10587583C2211yescharacteristic
27C2×#10587610C411yescharacteristic, complemented
28C2×#10587582—21no—
29C2×#10587564—21no—
30C2×#10587632C2211yescharacteristic
31C22⋊Q8×D17—21no—
32C22⋊Q8×D17—21no—
33C22⋊Q8×D17—21no—
34C22⋊Q8×D17—21no—
35C22⋊Q8×D17C412yescomplemented
36C22⋊Q8×D17C412yescomplemented
37C22⋊Q8×D17C2212yes—
38C22⋊Q8×D17C2212yes—
39C2×C4⋊C4×D17—21no—
40C2×C4⋊C4×D17C411yescharacteristic, complemented
41C2×C22⋊C4×D17—21no—
42C2×C17×C22⋊Q8C411yescharacteristic, complemented
43C24×D17D411yescharacteristic
44C23×#595—22no—
45C22×Q8×C17C2×C411yescharacteristic, complemented
46C23×C4×C17C2×C411yescharacteristic
47C23×Dic17D411yescharacteristic
48C2×Q8×D17—21no—
49C2×Q8×D17—21no—
50C2×Q8×D17—44no—
51C2×Q8×D17C2×C412yes—
52C2×Q8×D17C2×C412yescomplemented
53C22×C4×D17—21no—
54C22×C4×D17—21no—
55C22×C4×D17—44no—
56C22×C4×D17C2×C411yescharacteristic
57C22×C4×D17C2×C411yescharacteristic
58C22×C4×D17C2×C411yescharacteristic
59C22×C4×D17D411yescharacteristic
60C22×C4×D17D411yescharacteristic
61C22×C4×D17D411yescharacteristic
62C22×C4×D17D411yescharacteristic
63C22×C4×D17D411yescharacteristic
64C22×C4×D17D411yescharacteristic
65C22×C4×D17C2311yescharacteristic
66C22×C4×D17C2311yescharacteristic
67C22×C4×D17C2311yescharacteristic
68C22×Dic34—21no—
69C22×Dic34C2×C411yescharacteristic, complemented
70C2×C22⋊#595—22no—
71C2×C22⋊#595—22no—
72C2×C22⋊#595—44no—
73C2×#63247—22no—
74D17⋊M16—44no—
75C2×#63243—22no—
76C2×#63242—22no—
77C17×C22⋊Q8—21no—
78C17×C22⋊Q8—21no—
79C17×C22⋊Q8C2×C412yes—
80C17×C22⋊Q8C2×C412yescomplemented
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
83C2×C22⋊C4×C17—21no—
84C2×C22⋊Dic17—21no—
85#10587632—21no—
86#10587632—21no—
87#10587632C2×C412yescomplemented
88#10587632C2312yes—
89C2×#63227—21no—
90C2×#63227—21no—
91C2×C4⋊Dic17—21no—
92C2×C4⋊Dic17C2×C411yescharacteristic, complemented
93#10587610—21no—
94#10587610—21no—
95#10587610C2×C412yes—
96#10587610C2×C412yescomplemented
97C2×#63225—21no—
98C2×#63225—21no—
99C2×#63225—21no—
100#10587583—21no—
101#10587583—21no—
102#10587583C2×C412yescomplemented
103#10587583C2312yes—
104#10587582—22no—
105#10587582—22no—
106#10587582—22no—
107#10587582—22no—
108C4⋊C4×D17—22no—
109C4⋊C4×D17—22no—
110C4⋊C4×D17—21no—
111C4⋊C4×D17—21no—
112C4⋊C4×D17—22no—
113C4⋊C4×D17—22no—
114C4⋊C4×D17C2×C412yes—
115C4⋊C4×D17C2×C412yescomplemented
116C22⋊C4×D17—22no—
117C22⋊C4×D17—22no—
118C22⋊C4×D17—22no—
119C22⋊C4×D17—22no—
120#10587564—22no—
121#10587564—22no—
122#10587564—22no—
123#10587564—22no—
124C22⋊#3624—22no—
125C22⋊#3624—22no—
126(C2×#595)⋊C4—22no—
127(C2×#595)⋊C4—22no—
128(C2×#595)⋊C4—22no—
129(C2×#595)⋊C4C2314yes—
130#10587543—22no—
131#10587543C2314yes—
132C24×C17C22⋊C411yescharacteristic
133C23×D17—24no—
134C23×D17—24no—
135C23×D17—42no—
136C23×D17C22⋊C411yescharacteristic
137C23×D17C22⋊C411yescharacteristic
138C23×D17C22⋊C411yescharacteristic
139C23×D17C2×D411yescharacteristic
140C23×D17C2×D411yescharacteristic
141C23×D17C2×D411yescharacteristic
142C22×#595—24no—
143C22×#595—44no—
144C22×#595—44no—
145C22×#595—44no—
146C2×Q8×C17—21no—
147C2×Q8×C17—42no—
148C2×Q8×C17C22×C412yes—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—42no—
152C22×C4×C17C22⋊C411yescharacteristic
153C22×C4×C17C22⋊C411yescharacteristic
154C22×C4×C17C22⋊C411yescharacteristic
155C22×C4×C17C22×C411yescharacteristic
156C22×C4×C17C22×C411yescharacteristic
157C22×C4×C17C22×C411yescharacteristic
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—42no—
161C22×Dic17C22⋊C411yescharacteristic
162C22×Dic17C22⋊C411yescharacteristic
163C22×Dic17C22⋊C411yescharacteristic
164C22×Dic17C2×D411yescharacteristic
165C22×Dic17C2×D411yescharacteristic
166C22×Dic17C2×D411yescharacteristic
167Q8×D17—44no—
168Q8×D17—44no—
169Q8×D17—44no—
170Q8×D17—44no—
171C2×C4×D17—24no—
172C2×C4×D17—24no—
173C2×C4×D17—22no—
174C2×C4×D17—22no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—42no—
178C2×C4×D17—42no—
179C2×C4×D17—42no—
180C2×C4×D17—42no—
181C2×C4×D17—42no—
182C2×C4×D17—42no—
183C2×C4×D17—42no—
184C2×C4×D17—42no—
185C2×C4×D17—42no—
186C2×C4×D17—42no—
187C2×C4×D17—44no—
188C2×C4×D17—44no—
189C2×C4×D17C22⋊C411yescharacteristic
190C2×C4×D17C22⋊C411yescharacteristic
191C2×C4×D17C22⋊C411yescharacteristic
192C2×C4×D17C22⋊C411yescharacteristic
193C2×C4×D17C22⋊C411yescharacteristic
194C2×C4×D17C22⋊C411yescharacteristic
195C2×C4×D17C22×C411yescharacteristic
196C2×C4×D17C22×C411yescharacteristic
197C2×C4×D17C22×C411yescharacteristic
198C2×C4×D17C2×D411yescharacteristic
199C2×C4×D17C2×D411yescharacteristic
200C2×C4×D17C2×D411yescharacteristic
201C2×C4×D17C2×D411yescharacteristic
202C2×C4×D17C2×D411yescharacteristic
203C2×C4×D17C2×D411yescharacteristic
204C2×C4×D17C2411yescharacteristic
205C2×Dic34—21no—
206C2×Dic34—22no—
207C2×Dic34—22no—
208C2×Dic34—44no—
209C2×Dic34—42no—
210C2×Dic34C22×C412yes—
211C22⋊#595—44no—
212C22⋊#595—44no—
213#63247—44no—
214C2×#3624—24no—
215#63243—44no—
216#63242—44no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17—22no—
219C4⋊C4×C17—22no—
220C4⋊C4×C17C22×C412yes—
221C22⋊C4×C17—22no—
222C22⋊C4×C17—22no—
223C22⋊Dic17—22no—
224C22⋊Dic17—22no—
225#63227—22no—
226#63227—22no—
227#63227—22no—
228#63227—22no—
229C4⋊Dic17—21no—
230C4⋊Dic17—22no—
231C4⋊Dic17—22no—
232C4⋊Dic17C22×C412yes—
233#63225—22no—
234#63225—22no—
235#63225—22no—
236#63225—22no—
237#63225—22no—
238#63225—22no—
239C2×#1511—171nomaximal, Sylow
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—41no—
243C23×C17C2×C22⋊C411yescharacteristic
244C23×C17C2×C22⋊C411yescharacteristic
245C23×C17C2×C22⋊C411yescharacteristic
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17—22no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—416no—
263C22×D17#9914yes—
264C22×D17C2×C22⋊C411yescharacteristic
265C22×D17C2×C22⋊C411yescharacteristic
266C22×D17C2×C22⋊C411yescharacteristic
267C22×D17#13714yes—
268C22×D17C22×D411yescharacteristic
269C2×#595—44no—
270C2×#595—44no—
271C2×#595—44no—
272C2×#595—88no—
273Q8×C17—42no—
274Q8×C17—42no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—42no—
284C2×C4×C17—42no—
285C2×C4×C17C2×C22⋊C411yescharacteristic
286C2×C4×C17C2×C22⋊C411yescharacteristic
287C2×C4×C17C2×C22⋊C411yescharacteristic
288C2×C4×C17C23×C411yescharacteristic
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—41no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—42no—
298C2×Dic17—42no—
299C2×Dic17C2×C22⋊C411yescharacteristic
300C2×Dic17C2×C22⋊C411yescharacteristic
301C2×Dic17C2×C22⋊C411yescharacteristic
302C2×Dic17C22×D411yescharacteristic
303C4×D17—22no—
304C4×D17—22no—
305C4×D17—22no—
306C4×D17—22no—
307C4×D17—22no—
308C4×D17—22no—
309C4×D17—22no—
310C4×D17—22no—
311C4×D17—41no—
312C4×D17—41no—
313C4×D17—41no—
314C4×D17—41no—
315C4×D17—41no—
316C4×D17—41no—
317C4×D17—41no—
318C4×D17—41no—
319C4×D17—44no—
320C4×D17—44no—
321C4×D17—44no—
322C4×D17—44no—
323Dic34—44no—
324Dic34—44no—
325Dic34—42no—
326Dic34—42no—
327#3624—44no—
328C22×C22⋊Q8—171no—
329C2×#407—171no—
330C2×#381—171no—
331#1511—172no—
332#1511—174no—
333#1511—172no—
334C2×#328—174no—
335C22×C17—21no—
336C22×C17—21no—
337C22×C17—21no—
338C22×C17—21no—
339C22×C17—21no—
340C22×C17—21no—
341C22×C17—21no—
342C22×C17—44no—
343C22×C17C2×#9912yes—
344C22×C17#41912yes—
345C22×C17C22×C22⋊C411yescharacteristic
346C2×D17—21no—
347C2×D17—21no—
348C2×D17—21no—
349C2×D17—21no—
350C2×D17—28no—
351C2×D17—28no—
352C2×D17—21no—
353C2×D17—21no—
354C2×D17—21no—
355C2×D17—44no—
356C2×D17—44no—
357C2×D17—44no—
358C2×D17—44no—
359C2×D17C2×#9912yes—
360C2×D17C2×#9912yes—
361C2×D17#41912yes—
362C2×D17#42112yes—
363C2×D17C2×#13712yes—
364#595—84no—
365C4×C17—21no—
366C4×C17—21no—
367C4×C17—21no—
368C4×C17—21no—
369C4×C17—42no—
370C4×C17—42no—
371Dic17—21no—
372Dic17—21no—
373Dic17—21no—
374Dic17—21no—
375Dic17—42no—
376Dic17—42no—
377C23×Q8—171no—
378C24×C4—171no—
379C22×M16—341no—
380C2×C22⋊Q8—171no—
381C2×C22⋊Q8—171no—
382C2×C22⋊Q8—172no—
383C2×C22⋊Q8—172no—
384C2×C22⋊Q8—172no—
385C2×C22⋊Q8—172no—
386C2×C22⋊Q8—171no—
387C2×C22⋊Q8—341no—
388C2×C22⋊Q8—341no—
389C2×C22⋊Q8—341no—
390C2×C22⋊Q8—341no—
391C2×C22⋊Q8—341no—
392C2×C22⋊Q8—341no—
393C2×C22⋊Q8#59511yescharacteristic, complemented
394C22×C4⋊C4—171no—
395C22×C4⋊C4—341no—
396C22×C22⋊C4—341no—
397C22×C22⋊C4—341no—
398#407—172no—
399#407—172no—
400#407—341no—
401#407—341no—
402C2×C22⋊C8—172no—
403C2×C22⋊C8—341no—
404#381—172no—
405#381—172no—
406#381—341no—
407#381—341no—
408C2×#95—172no—
409C2×#95—341no—
410#328—178no—
411#328—178no—
412C2×C17—22no—
413C2×C17—22no—
414C2×C17—41no—
415C2×C17C22×#9911yescharacteristic
416C2×C17C2×#41911yescharacteristic
417C2×C17C2×#42111yescharacteristic
418D17—22no—
419D17—22no—
420D17—41no—
421D17#151114yescomplemented
422C25—171no—
423C22×Q8—172no—
424C22×Q8—172no—
425C22×Q8—171no—
426C22×Q8—341no—
427C22×Q8—341no—
428C22×Q8—341no—
429C22×Q8—684no—
430C22×Q8C2×#59511yescharacteristic, complemented
431C23×C4—171no—
432C23×C4—171no—
433C23×C4—171no—
434C23×C4—171no—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—171no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4—171no—
444C23×C4—341no—
445C23×C4—341no—
446C23×C4—342no—
447C23×C4—684no—
448C23×C4C2×#59511yescharacteristic
449C2×M16—342no—
450C2×M16—342no—
451C2×M16—684no—
452C22×C8—342no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—172no—
456C22⋊Q8—172no—
457C22⋊Q8—172no—
458C22⋊Q8—172no—
459C22⋊Q8—172no—
460C22⋊Q8—172no—
461C22⋊Q8—342no—
462C22⋊Q8—342no—
463C22⋊Q8—342no—
464C22⋊Q8—342no—
465C22⋊Q8—342no—
466C22⋊Q8—342no—
467C22⋊Q8—342no—
468C22⋊Q8—342no—
469C22⋊Q8—341no—
470C22⋊Q8—341no—
471C22⋊Q8—341no—
472C22⋊Q8—341no—
473C22⋊Q8—341no—
474C22⋊Q8—341no—
475C22⋊Q8C2×#59512yes—
476C22⋊Q8C2×#59512yescomplemented
477C2×C4⋊C4—21no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—172no—
480C2×C4⋊C4—172no—
481C2×C4⋊C4—341no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—342no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—342no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4C2×#59511yescharacteristic, complemented
492C2×C22⋊C4—21no—
493C2×C22⋊C4—342no—
494C2×C22⋊C4—342no—
495C2×C22⋊C4—342no—
496C2×C22⋊C4—342no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—341no—
500C2×C22⋊C4—342no—
501C2×C22⋊C4—342no—
502C2×C22⋊C4—684no—
503C22⋊C8—174no—
504C22⋊C8—342no—
505C22⋊C8—342no—
506C22⋊C8—342no—
507#95—174no—
508#95—342no—
509#95—342no—
510#95—342no—
511C17C2×#151111yescharacteristic, complemented, Sylow
512C24—171no—
513C24—171no—
514C24—171no—
515C24—171no—
516C24—171no—
517C24—171no—
518C24—344no—
519C24—344no—
520C24—682no—
521C24C22⋊#59511yescharacteristic
522C2×Q8—21no—
523C2×Q8—42no—
524C2×Q8—172no—
525C2×Q8—342no—
526C2×Q8—342no—
527C2×Q8—341no—
528C2×Q8—682no—
529C2×Q8—684no—
530C2×Q8—684no—
531C2×Q8—684no—
532C2×Q8—684no—
533C2×Q8—684no—
534C2×Q8C22×#59512yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—171no—
539C22×C4—171no—
540C22×C4—171no—
541C22×C4—171no—
542C22×C4—171no—
543C22×C4—171no—
544C22×C4—171no—
545C22×C4—171no—
546C22×C4—171no—
547C22×C4—171no—
548C22×C4—171no—
549C22×C4—171no—
550C22×C4—171no—
551C22×C4—171no—
552C22×C4—171no—
553C22×C4—171no—
554C22×C4—171no—
555C22×C4—171no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—344no—
561C22×C4—344no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—344no—
569C22×C4—682no—
570C22×C4—682no—
571C22×C4—682no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—682no—
579C22×C4—684no—
580C22×C4—684no—
581C22×C4—682no—
582C22×C4—684no—
583C22×C4—684no—
584C22×C4—684no—
585C22×C4C22⋊#59511yescharacteristic
586C22×C4C22⋊#59511yescharacteristic
587C22×C4C22⋊#59511yescharacteristic
588C22×C4C22×#59511yescharacteristic
589C22×C4C22×#59511yescharacteristic
590C22×C4C22×#59511yescharacteristic
591M16—684no—
592M16—684no—
593C2×C8—344no—
594C2×C8—684no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—172no—
599C4⋊C4—342no—
600C4⋊C4—342no—
601C4⋊C4—342no—
602C4⋊C4—342no—
603C4⋊C4—342no—
604C4⋊C4—342no—
605C4⋊C4—341no—
606C4⋊C4—342no—
607C4⋊C4—342no—
608C4⋊C4C22×#59512yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—342no—
612C22⋊C4—342no—
613C22⋊C4—342no—
614C22⋊C4—342no—
615C22⋊C4—342no—
616C22⋊C4—342no—
617C22⋊C4—684no—
618C22⋊C4—684no—
619C23—22no—
620C23—22no—
621C23—41no—
622C23—171no—
623C23—174no—
624C23—174no—
625C23—171no—
626C23—171no—
627C23—171no—
628C23—342no—
629C23—342no—
630C23—342no—
631C23—342no—
632C23—342no—
633C23—342no—
634C23—342no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—681no—
642C23—681no—
643C23—681no—
644C23—6816no—
645C23C2×C22⋊#59511yescharacteristic
646C23C2×C22⋊#59511yescharacteristic
647C23C2×C22⋊#59511yescharacteristic
648Q8—42no—
649Q8—42no—
650Q8—682no—
651Q8—682no—
652Q8—684no—
653Q8—684no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—171no—
665C2×C4—171no—
666C2×C4—171no—
667C2×C4—171no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—684no—
689C2×C4—684no—
690C2×C4—684no—
691C2×C4—684no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—682no—
697C2×C4—682no—
698C2×C4—684no—
699C2×C4—684no—
700C2×C4—684no—
701C2×C4—1368no—
702C2×C4C2×C22⋊#59511yescharacteristic
703C2×C4C2×C22⋊#59511yescharacteristic
704C2×C4C2×C22⋊#59511yescharacteristic
705C2×C4C23×#59511yescharacteristic
706C8—684no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—44no—
715C22—172no—
716C22—172no—
717C22—172no—
718C22—172no—
719C22—172no—
720C22—348no—
721C22—348no—
722C22—341no—
723C22—341no—
724C22—341no—
725C22—341no—
726C22—341no—
727C22—341no—
728C22—341no—
729C22—684no—
730C22—684no—
731C22—684no—
732C22—684no—
733C22D17⋊#9912yes—
734C22#1176380212yes—
735C22C22×C22⋊#59511yescharacteristic
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—42no—
741C4—42no—
742C4—341no—
743C4—341no—
744C4—341no—
745C4—341no—
746C4—682no—
747C4—682no—
748C4—1364no—
749C2—22no—
750C2—22no—
751C2—41no—
752C2—174no—
753C2—342no—
754C2—342no—
755C2—681no—
756C2C2×D17⋊#9911yescharacteristic
757C2C2×#1176380211yescharacteristic
758C2D17⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×C22⋊Q8C4
socleC22×C17C22×C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC2×C22⋊Q8#595
hypocenterC17C2×#1511
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14544194C2semidirect
4. #14544193C2semidirect
5. #14544192C2semidirect
6. D17⋊#328C2semidirect
22. #11763663C22semidirect
23. #11763662C22semidirect
24. C22×Q8×D17C4semidirect
27. C2×#10587610C4semidirect
35. C22⋊Q8×D17C4semidirect
36. C22⋊Q8×D17C4semidirect
40. C2×C4⋊C4×D17C4semidirect
42. C2×C17×C22⋊Q8C4semidirect
45. C22×Q8×C17C2×C4semidirect
52. C2×Q8×D17C2×C4semidirect
69. C22×Dic34C2×C4semidirect
80. C17×C22⋊Q8C2×C4semidirect
82. C2×C4⋊C4×C17C2×C4semidirect
87. #10587632C2×C4semidirect
92. C2×C4⋊Dic17C2×C4semidirect
96. #10587610C2×C4semidirect
102. #10587583C2×C4semidirect
115. C4⋊C4×D17C2×C4semidirect
393. C2×C22⋊Q8#595semidirect
421. D17#1511semidirect
430. C22×Q8C2×#595semidirect
476. C22⋊Q8C2×#595semidirect
491. C2×C4⋊C4C2×#595semidirect
511. C17C2×#1511semidirect

Maximal subgroups

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

subgroupindex
D17⋊#4072
C2×#117637522
#145441942
#145441932
#145441922
D17⋊#3282
C2×C22⋊Q8×D172
C2×#151117