Finite Group Databasebeta

← D17⋊#1508 #17965239

Subgroups — D17⋊#1508 #17965239

Order 4352.

1554 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14544184C212yesmaximal, complemented
4#14544183C212yesmaximal, complemented
5#14544182C214yesmaximal, complemented
6D17⋊#328C214yesmaximal, complemented
7C2×C22⋊Q8×D17C211yesmaximal, characteristic
8C2×D17⋊M16—21no—
9C22×C22⋊#595—21no—
10C22×C4×#595—21no—
11#11763781C2212yes—
12#11763780—21no—
13#11763780C2212yes—
14#11763779—21no—
15#11763777—21no—
16#11763777C2212yes—
17C4×C22⋊#595—21no—
18C4×C22⋊#595—21no—
19C4×C22⋊#595C2212yes—
20C4×C22⋊#595C2212yes—
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—28no—
71C2×C22⋊#595—22no—
72C2×C22⋊#595—22no—
73C2×#63247—22no—
74C2×C4×#595—22no—
75C2×C4×#595—22no—
76C2×C4×#595—44no—
77D17⋊M16—44no—
78C2×#63243—22no—
79C2×#63242—22no—
80C17×C22⋊Q8—21no—
81C17×C22⋊Q8—21no—
82C17×C22⋊Q8C2×C412yes—
83C17×C22⋊Q8C2×C412yescomplemented
84C2×C4⋊C4×C17—21no—
85C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
86C2×C22⋊C4×C17—21no—
87C2×C22⋊Dic17—21no—
88#10587632—21no—
89#10587632—21no—
90#10587632C2×C412yescomplemented
91#10587632C2312yes—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×C4⋊Dic17—21no—
95C2×C4⋊Dic17C2×C411yescharacteristic, complemented
96#10587610—21no—
97#10587610—21no—
98#10587610C2×C412yes—
99#10587610C2×C412yescomplemented
100C2×#63225—21no—
101C2×#63225—21no—
102C2×#63225—21no—
103#10587583—21no—
104#10587583—21no—
105#10587583C2×C412yescomplemented
106#10587583C2312yes—
107#10587582—22no—
108#10587582—22no—
109#10587582—22no—
110#10587582—22no—
111C4⋊C4×D17—22no—
112C4⋊C4×D17—22no—
113C4⋊C4×D17—21no—
114C4⋊C4×D17—21no—
115C4⋊C4×D17—22no—
116C4⋊C4×D17—22no—
117C4⋊C4×D17C2×C412yes—
118C4⋊C4×D17C2×C412yescomplemented
119C22⋊C4×D17—22no—
120C22⋊C4×D17—22no—
121C22⋊C4×D17—22no—
122C22⋊C4×D17—22no—
123#10587564—22no—
124#10587564—22no—
125#10587564—22no—
126#10587564—22no—
127C22⋊#3624—22no—
128C22⋊#3624—22no—
129(C2×#595)⋊C4—22no—
130(C2×#595)⋊C4C2314yes—
131#10587543—22no—
132#10587543C2314yes—
133C24×C17C22⋊C411yescharacteristic
134C23×D17—24no—
135C23×D17—24no—
136C23×D17—42no—
137C23×D17C22⋊C411yescharacteristic
138C23×D17C22⋊C411yescharacteristic
139C23×D17C22⋊C411yescharacteristic
140C23×D17C2×D411yescharacteristic
141C23×D17C2×D411yescharacteristic
142C23×D17C2×D411yescharacteristic
143C22×#595—28no—
144C22×#595—24no—
145C22×#595—44no—
146C22×#595—44no—
147C2×Q8×C17—21no—
148C2×Q8×C17—42no—
149C2×Q8×C17C22×C412yes—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—42no—
153C22×C4×C17C22⋊C411yescharacteristic
154C22×C4×C17C22⋊C411yescharacteristic
155C22×C4×C17C22⋊C411yescharacteristic
156C22×C4×C17C22×C411yescharacteristic
157C22×C4×C17C22×C411yescharacteristic
158C22×C4×C17C22×C411yescharacteristic
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—42no—
162C22×Dic17C22⋊C411yescharacteristic
163C22×Dic17C22⋊C411yescharacteristic
164C22×Dic17C22⋊C411yescharacteristic
165C22×Dic17C2×D411yescharacteristic
166C22×Dic17C2×D411yescharacteristic
167C22×Dic17C2×D411yescharacteristic
168Q8×D17—44no—
169Q8×D17—44no—
170Q8×D17—44no—
171Q8×D17—44no—
172C2×C4×D17—24no—
173C2×C4×D17—24no—
174C2×C4×D17—24no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
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—42no—
188C2×C4×D17—44no—
189C2×C4×D17—44no—
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×D17C22×C411yescharacteristic
199C2×C4×D17C2×D411yescharacteristic
200C2×C4×D17C2×D411yescharacteristic
201C2×C4×D17C2×D411yescharacteristic
202C2×C4×D17C2×D411yescharacteristic
203C2×C4×D17C2×D411yescharacteristic
204C2×C4×D17C2×D411yescharacteristic
205C2×C4×D17C2411yescharacteristic
206C2×Dic34—21no—
207C2×Dic34—22no—
208C2×Dic34—22no—
209C2×Dic34—44no—
210C2×Dic34—42no—
211C2×Dic34C22×C412yes—
212C22⋊#595—28no—
213C22⋊#595—28no—
214#63247—44no—
215C2×#3624—24no—
216C4×#595—44no—
217C4×#595—44no—
218#63243—44no—
219#63242—44no—
220C4⋊C4×C17—21no—
221C4⋊C4×C17—22no—
222C4⋊C4×C17—22no—
223C4⋊C4×C17C22×C412yes—
224C22⋊C4×C17—22no—
225C22⋊C4×C17—22no—
226C22⋊Dic17—22no—
227C22⋊Dic17—22no—
228#63227—22no—
229#63227—22no—
230#63227—22no—
231#63227—22no—
232C4⋊Dic17—21no—
233C4⋊Dic17—22no—
234C4⋊Dic17—22no—
235C4⋊Dic17C22×C412yes—
236#63225—22no—
237#63225—22no—
238#63225—22no—
239#63225—22no—
240#63225—22no—
241#63225—22no—
242C2×#1508—171nomaximal, Sylow
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—41no—
246C23×C17C2×C22⋊C411yescharacteristic
247C23×C17C2×C22⋊C411yescharacteristic
248C23×C17C2×C22⋊C411yescharacteristic
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—22no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—416no—
266C22×D17#10414yes—
267C22×D17C2×C22⋊C411yescharacteristic
268C22×D17C2×C22⋊C411yescharacteristic
269C22×D17C2×C22⋊C411yescharacteristic
270C22×D17#13714yes—
271C22×D17C22×D411yescharacteristic
272C2×#595—28no—
273C2×#595—44no—
274C2×#595—416no—
275C2×#595—44no—
276Q8×C17—42no—
277Q8×C17—42no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—42no—
287C2×C4×C17—42no—
288C2×C4×C17C2×C22⋊C411yescharacteristic
289C2×C4×C17C2×C22⋊C411yescharacteristic
290C2×C4×C17C2×C22⋊C411yescharacteristic
291C2×C4×C17C23×C411yescharacteristic
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—42no—
301C2×Dic17—42no—
302C2×Dic17C2×C22⋊C411yescharacteristic
303C2×Dic17C2×C22⋊C411yescharacteristic
304C2×Dic17C2×C22⋊C411yescharacteristic
305C2×Dic17C22×D411yescharacteristic
306C4×D17—22no—
307C4×D17—22no—
308C4×D17—22no—
309C4×D17—22no—
310C4×D17—22no—
311C4×D17—22no—
312C4×D17—22no—
313C4×D17—22no—
314C4×D17—22no—
315C4×D17—41no—
316C4×D17—41no—
317C4×D17—41no—
318C4×D17—41no—
319C4×D17—41no—
320C4×D17—41no—
321C4×D17—44no—
322C4×D17—44no—
323C4×D17—44no—
324C4×D17—44no—
325C4×D17#9914yes—
326Dic34—44no—
327Dic34—42no—
328Dic34—44no—
329Dic34—42no—
330#3624—44no—
331C22×C22⋊Q8—171no—
332C2×#407—171no—
333C2×C4×C22⋊C4—171no—
334#1508—174no—
335#1508—172no—
336#1508—172no—
337C2×#328—174no—
338C22×C17—21no—
339C22×C17—21no—
340C22×C17—21no—
341C22×C17—21no—
342C22×C17—21no—
343C22×C17—21no—
344C22×C17—21no—
345C22×C17—44no—
346C22×C17#41912yes—
347C22×C17C2×#10412yes—
348C22×C17C22×C22⋊C411yescharacteristic
349C2×D17—21no—
350C2×D17—21no—
351C2×D17—21no—
352C2×D17—21no—
353C2×D17—28no—
354C2×D17—28no—
355C2×D17—21no—
356C2×D17—21no—
357C2×D17—21no—
358C2×D17—44no—
359C2×D17—44no—
360C2×D17—44no—
361C2×D17—44no—
362C2×D17C2×#9912yes—
363C2×D17#41912yes—
364C2×D17C2×#10412yes—
365C2×D17C2×#10412yes—
366C2×D17C2×#13712yes—
367#595—48no—
368C4×C17—21no—
369C4×C17—21no—
370C4×C17—21no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17C2×#9912yes—
374Dic17—21no—
375Dic17—21no—
376Dic17—21no—
377Dic17—42no—
378Dic17—42no—
379Dic17C2×#9912yes—
380C23×Q8—171no—
381C24×C4—171no—
382C22×M16—341no—
383C2×C22⋊Q8—171no—
384C2×C22⋊Q8—171no—
385C2×C22⋊Q8—172no—
386C2×C22⋊Q8—172no—
387C2×C22⋊Q8—172no—
388C2×C22⋊Q8—172no—
389C2×C22⋊Q8—171no—
390C2×C22⋊Q8—341no—
391C2×C22⋊Q8—341no—
392C2×C22⋊Q8—341no—
393C2×C22⋊Q8—341no—
394C2×C22⋊Q8—341no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8#59511yescharacteristic, complemented
397C22×C4⋊C4—171no—
398C22×C4⋊C4—341no—
399C22×C22⋊C4—341no—
400C22×C22⋊C4—341no—
401C22×C42—341no—
402#407—172no—
403#407—172no—
404#407—341no—
405#407—341no—
406C2×C22⋊C8—172no—
407C2×C22⋊C8—341no—
408C4×C22⋊C4—172no—
409C4×C22⋊C4—172no—
410C4×C22⋊C4—341no—
411C4×C22⋊C4—341no—
412C2×#95—172no—
413#328—178no—
414#328—178no—
415C2×C17—22no—
416C2×C17—22no—
417C2×C17—41no—
418C2×C17C22×#9911yescharacteristic
419C2×C17C2×#41911yescharacteristic
420C2×C17C22×#10411yescharacteristic
421D17—22no—
422D17—22no—
423D17—41no—
424D17#150814yescomplemented
425C25—171no—
426C22×Q8—172no—
427C22×Q8—172no—
428C22×Q8—171no—
429C22×Q8—341no—
430C22×Q8—341no—
431C22×Q8—341no—
432C22×Q8—684no—
433C22×Q8C2×#59511yescharacteristic, complemented
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—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—342no—
450C23×C4—684no—
451C23×C4C2×#59511yescharacteristic
452C2×M16—342no—
453C2×M16—342no—
454C2×M16—684no—
455C22×C8—342no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—172no—
459C22⋊Q8—172no—
460C22⋊Q8—172no—
461C22⋊Q8—172no—
462C22⋊Q8—172no—
463C22⋊Q8—172no—
464C22⋊Q8—342no—
465C22⋊Q8—342no—
466C22⋊Q8—342no—
467C22⋊Q8—342no—
468C22⋊Q8—342no—
469C22⋊Q8—342no—
470C22⋊Q8—342no—
471C22⋊Q8—342no—
472C22⋊Q8—341no—
473C22⋊Q8—341no—
474C22⋊Q8—341no—
475C22⋊Q8—341no—
476C22⋊Q8—341no—
477C22⋊Q8—341no—
478C22⋊Q8C2×#59512yes—
479C22⋊Q8C2×#59512yescomplemented
480C2×C4⋊C4—21no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—172no—
483C2×C4⋊C4—172no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—341no—
486C2×C4⋊C4—342no—
487C2×C4⋊C4—342no—
488C2×C4⋊C4—342no—
489C2×C4⋊C4—342no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4C2×#59511yescharacteristic, complemented
495C2×C22⋊C4—21no—
496C2×C22⋊C4—342no—
497C2×C22⋊C4—342no—
498C2×C22⋊C4—342no—
499C2×C22⋊C4—342no—
500C2×C22⋊C4—341no—
501C2×C22⋊C4—341no—
502C2×C22⋊C4—342no—
503C2×C22⋊C4—342no—
504C2×C22⋊C4—348no—
505C2×C22⋊C4—341no—
506C2×C42—342no—
507C2×C42—342no—
508C2×C42—684no—
509C22⋊C8—174no—
510C22⋊C8—342no—
511C22⋊C8—342no—
512C22⋊C8—342no—
513#95—174no—
514#95—342no—
515C17C2×#150811yescharacteristic, complemented, Sylow
516C24—171no—
517C24—171no—
518C24—171no—
519C24—171no—
520C24—171no—
521C24—171no—
522C24—344no—
523C24—344no—
524C24—682no—
525C24C22⋊#59511yescharacteristic
526C2×Q8—21no—
527C2×Q8—42no—
528C2×Q8—172no—
529C2×Q8—342no—
530C2×Q8—342no—
531C2×Q8—341no—
532C2×Q8—682no—
533C2×Q8—684no—
534C2×Q8—684no—
535C2×Q8—684no—
536C2×Q8—684no—
537C2×Q8—684no—
538C2×Q8C22×#59512yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
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—171no—
561C22×C4—171no—
562C22×C4—171no—
563C22×C4—171no—
564C22×C4—344no—
565C22×C4—344no—
566C22×C4—344no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—344no—
572C22×C4—348no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—682no—
579C22×C4—682no—
580C22×C4—682no—
581C22×C4—682no—
582C22×C4—682no—
583C22×C4—682no—
584C22×C4—684no—
585C22×C4—684no—
586C22×C4—682no—
587C22×C4—684no—
588C22×C4—684no—
589C22×C4C22⋊#59511yescharacteristic
590C22×C4C22⋊#59511yescharacteristic
591C22×C4C22⋊#59511yescharacteristic
592C22×C4C22×#59511yescharacteristic
593C22×C4C22×#59511yescharacteristic
594C22×C4C22×#59511yescharacteristic
595M16—684no—
596M16—684no—
597C2×C8—344no—
598C2×C8—684no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—172no—
603C4⋊C4—342no—
604C4⋊C4—342no—
605C4⋊C4—342no—
606C4⋊C4—342no—
607C4⋊C4—342no—
608C4⋊C4—342no—
609C4⋊C4—341no—
610C4⋊C4—342no—
611C4⋊C4—342no—
612C4⋊C4C22×#59512yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—342no—
616C22⋊C4—342no—
617C22⋊C4—342no—
618C22⋊C4—342no—
619C22⋊C4—348no—
620C22⋊C4—348no—
621C22⋊C4—342no—
622C22⋊C4—342no—
623C42—684no—
624C42—684no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—171no—
629C23—174no—
630C23—174no—
631C23—171no—
632C23—171no—
633C23—171no—
634C23—342no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23—342no—
644C23—342no—
645C23—342no—
646C23—342no—
647C23—681no—
648C23—681no—
649C23—681no—
650C23—6816no—
651C23C2×C22⋊#59511yescharacteristic
652C23C2×C22⋊#59511yescharacteristic
653C23C2×C22⋊#59511yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—682no—
657Q8—684no—
658Q8—684no—
659Q8—682no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—171no—
671C2×C4—174no—
672C2×C4—171no—
673C2×C4—171no—
674C2×C4—171no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—348no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—684no—
697C2×C4—684no—
698C2×C4—684no—
699C2×C4—684no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—682no—
704C2×C4—684no—
705C2×C4—684no—
706C2×C4—6816no—
707C2×C4—682no—
708C2×C4C2×C22⋊#59511yescharacteristic
709C2×C4C2×C22⋊#59511yescharacteristic
710C2×C4C2×C22⋊#59511yescharacteristic
711C2×C4C23×#59511yescharacteristic
712C8—684no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—44no—
721C22—172no—
722C22—172no—
723C22—172no—
724C22—172no—
725C22—172no—
726C22—348no—
727C22—348no—
728C22—341no—
729C22—341no—
730C22—341no—
731C22—341no—
732C22—341no—
733C22—341no—
734C22—341no—
735C22—684no—
736C22—684no—
737C22—684no—
738C22—684no—
739C22#1176380212yes—
740C22D17⋊#10412yes—
741C22C22×C22⋊#59511yescharacteristic
742C4—21no—
743C4—21no—
744C4—21no—
745C4—42no—
746C4—42no—
747C4—172no—
748C4—341no—
749C4—341no—
750C4—341no—
751C4—688no—
752C4—682no—
753C4—682no—
754C4D17⋊#9912yes—
755C2—22no—
756C2—22no—
757C2—41no—
758C2—174no—
759C2—342no—
760C2—342no—
761C2—681no—
762C2C2×D17⋊#9911yescharacteristic
763C2C2×#1176380211yescharacteristic
764C2C2×D17⋊#10411yescharacteristic
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×#1508
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. #14544184C2semidirect
4. #14544183C2semidirect
5. #14544182C2semidirect
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
83. C17×C22⋊Q8C2×C4semidirect
85. C2×C4⋊C4×C17C2×C4semidirect
90. #10587632C2×C4semidirect
95. C2×C4⋊Dic17C2×C4semidirect
99. #10587610C2×C4semidirect
105. #10587583C2×C4semidirect
118. C4⋊C4×D17C2×C4semidirect
396. C2×C22⋊Q8#595semidirect
424. D17#1508semidirect
433. C22×Q8C2×#595semidirect
479. C22⋊Q8C2×#595semidirect
494. C2×C4⋊C4C2×#595semidirect
515. C17C2×#1508semidirect

Maximal subgroups

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

subgroupindex
D17⋊#4072
C2×C4×C22⋊#5952
#145441842
#145441832
#145441822
D17⋊#3282
C2×C22⋊Q8×D172
C2×#150817