Finite Group Databasebeta

← D17⋊#2920 #17979581

Subgroups — D17⋊#2920 #17979581

Order 4352.

2806 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545463C214yesmaximal, complemented
2#14545462C214yesmaximal, complemented
3#14545461C214yesmaximal, complemented
4#14545460C214yesmaximal, complemented
5D17⋊#432C214yesmaximal, complemented
6#14545448C214yesmaximal, complemented
7D17⋊#423C212yesmaximal, complemented
8D17⋊#407C212yesmaximal
9C4×D17⋊M16C212yesmaximal, complemented
10C22×C42×D17C211yesmaximal, characteristic
11C2×D17⋊M16C2214yes—
12#11763832C2218yescomplemented
13#11763831C2218yescomplemented
14#11763830C2218yescomplemented
15#11763829C2218yescomplemented
16#11763828C2218yescomplemented
17#11763827C2218yescomplemented
18#11763826C2218yescomplemented
19#11763825C2218yescomplemented
20#11763814C2214yescomplemented
21#11763813C2214yescomplemented
22#11763812C2218yescomplemented
23#11763810C2218yescomplemented
24#11763781C2214yes—
25#11763780C2218yes—
26#11763779C2214yes—
27#11763777C2218yes—
28C4×#63243C2218yescomplemented
29C4×#63247C2218yescomplemented
30#11763768C2214yescomplemented
31C4×#63242C2214yescomplemented
32C23×C4×D17C412yes—
33C23×C4×D17C2211yescharacteristic
34C22×C4×Dic17C411yescharacteristic
35C22×C4×Dic17C2212yes—
36C2×C42×D17C412yes—
37C2×C42×D17C411yescharacteristic
38C2×C42×D17C411yescharacteristic
39C2×C42×D17C412yes—
40C2×C42×D17C412yes—
41C2×C42×D17C412yes—
42C2×C42×D17C412yes—
43C2×C42×D17C2211yescharacteristic
44C2×C42×D17C2212yes—
45C2×C42×D17C2212yes—
46C2×C42×D17C2212yes—
47C2×C42×D17C2212yes—
48C2×C42×D17C2212yes—
49C2×C42×D17C2211yescharacteristic
50C22×C42×C17C411yescharacteristic
51C24×D17C2×C411yescharacteristic
52C23×C4×C17C2×C411yescharacteristic
53C23×C4×C17C2×C412yes—
54C23×Dic17C2×C412yes—
55C23×Dic17C2311yescharacteristic
56C22×C4×D17—216no—
57C22×C4×D17—28no—
58C22×C4×D17C2×C411yescharacteristic
59C22×C4×D17C2×C411yescharacteristic
60C22×C4×D17C2×C412yes—
61C22×C4×D17C2×C412yes—
62C22×C4×D17C2×C412yes—
63C22×C4×D17C2×C412yes—
64C22×C4×D17C2×C412yes—
65C22×C4×D17C2×C412yes—
66C22×C4×D17C2×C412yes—
67C22×C4×D17C2×C412yes—
68C22×C4×D17C2×C412yes—
69C22×C4×D17C2×C412yes—
70C22×C4×D17C2×C412yes—
71C22×C4×D17C2×C412yes—
72C22×C4×D17C2×C412yes—
73C22×C4×D17C2×C412yes—
74C22×C4×D17C2312yes—
75C22×C4×D17C2312yes—
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C2×#63247C2318yes—
79D17⋊M16—216no—
80C2×#63243C2318yes—
81C2×#63242C2318yes—
82C2×C42×C17C2×C412yes—
83C2×C42×C17C2×C412yes—
84C2×C42×C17C2×C412yes—
85C2×C42×C17C2×C411yescharacteristic
86C2×C42×C17C2×C412yes—
87C2×C42×C17C2×C411yescharacteristic
88C2×C42×C17C2×C412yes—
89C2×C4×Dic17C2×C412yes—
90C2×C4×Dic17C2×C412yes—
91C2×C4×Dic17C2×C412yes—
92C2×C4×Dic17C2×C412yes—
93C2×C4×Dic17C2×C412yes—
94C2×C4×Dic17C2×C412yes—
95C2×C4×Dic17C2×C412yes—
96C2×C4×Dic17C2×C412yes—
97C2×C4×Dic17C2×C412yes—
98C2×C4×Dic17C2×C411yescharacteristic
99C2×C4×Dic17C2×C411yescharacteristic
100C2×C4×Dic17C2×C412yes—
101C2×C4×Dic17C2×C412yes—
102C2×C4×Dic17C2312yes—
103C2×C4×Dic17C2312yes—
104C2×C4×Dic17C2312yes—
105C2×C4×Dic17C2312yes—
106C2×C4×Dic17C2312yes—
107C2×C4×Dic17C2312yes—
108C42×D17C2×C412yes—
109C42×D17C2×C412yes—
110C42×D17C2×C412yes—
111C42×D17C2×C412yes—
112C42×D17C2×C412yes—
113C42×D17C2×C412yes—
114C42×D17C2×C412yes—
115C42×D17C2×C412yes—
116C42×D17C2×C412yes—
117C42×D17C2×C412yes—
118C42×D17C2×C412yes—
119C42×D17C2×C411yescharacteristic
120C42×D17C2×C412yes—
121C42×D17C2×C411yescharacteristic
122C42×D17C2×C412yes—
123C42×D17C2×C412yes—
124C42×D17C2×C412yes—
125C42×D17C2×C412yes—
126C42×D17C2×C412yes—
127C42×D17C2×C412yes—
128C42×D17C2×C412yes—
129C42×D17C2×C412yes—
130C42×D17C2×C412yes—
131C42×D17C2×C411yescharacteristic
132C42×D17C2×C411yescharacteristic
133C42×D17C2×C412yes—
134C42×D17C2311yescharacteristic
135C42×D17C2311yescharacteristic
136C42×D17C2312yes—
137C42×D17C2312yes—
138C42×D17C2311yescharacteristic
139C42×D17C2311yescharacteristic
140C42×D17C2312yes—
141C42×D17C2312yes—
142C42×D17C2312yes—
143C42×D17C2312yes—
144C22⋊#3624C23116yes—
145#10587544C23116yescomplemented
146#10587543C23116yes—
147#10587542C23116yescomplemented
148C4⋊#3624C23116yescomplemented
149C4×#3624C23116yescomplemented
150C24×C17C22×C411yescharacteristic
151C23×D17—24no—
152C23×D17—28no—
153C23×D17C22×C411yescharacteristic
154C23×D17C22×C412yes—
155C23×D17C22×C411yescharacteristic
156C23×D17C22×C412yes—
157C22×C4×C17—24no—
158C22×C4×C17—28no—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C22×C412yes—
161C22×C4×C17C22×C412yes—
162C22×C4×C17C22×C412yes—
163C22×C4×C17C22×C412yes—
164C22×C4×C17C22×C411yescharacteristic
165C22×C4×C17C22×C412yes—
166C22×C4×C17C22×C412yes—
167C22×C4×C17C22×C411yescharacteristic
168C22×C4×C17C22×C412yes—
169C22×Dic17—28no—
170C22×Dic17—24no—
171C22×Dic17C22×C412yes—
172C22×Dic17C22×C412yes—
173C22×Dic17C22×C412yes—
174C22×Dic17C22×C412yes—
175C22×Dic17C22×C412yes—
176C22×Dic17C22×C411yescharacteristic
177C22×Dic17C22×C412yes—
178C22×Dic17C22×C412yes—
179C22×Dic17C2412yes—
180C22×Dic17C2411yescharacteristic
181C2×C4×D17—24no—
182C2×C4×D17—28no—
183C2×C4×D17—24no—
184C2×C4×D17—28no—
185C2×C4×D17—28no—
186C2×C4×D17—24no—
187C2×C4×D17—28no—
188C2×C4×D17—28no—
189C2×C4×D17—28no—
190C2×C4×D17—28no—
191C2×C4×D17—28no—
192C2×C4×D17—28no—
193C2×C4×D17—28no—
194C2×C4×D17—28no—
195C2×C4×D17—28no—
196C2×C4×D17—28no—
197C2×C4×D17—28no—
198C2×C4×D17—28no—
199C2×C4×D17M16116yescomplemented
200C2×C4×D17C22×C412yes—
201C2×C4×D17C22×C412yes—
202C2×C4×D17C22×C412yes—
203C2×C4×D17C22×C412yes—
204C2×C4×D17C22×C412yes—
205C2×C4×D17C22×C412yes—
206C2×C4×D17C22×C412yes—
207C2×C4×D17C22×C412yes—
208C2×C4×D17C22×C412yes—
209C2×C4×D17C22×C412yes—
210C2×C4×D17C22×C412yes—
211C2×C4×D17C22×C412yes—
212C2×C4×D17C22×C412yes—
213C2×C4×D17C22×C412yes—
214C2×C4×D17C22×C412yes—
215C2×C4×D17C22×C412yes—
216C2×C4×D17C22×C412yes—
217C2×C4×D17C22×C411yescharacteristic
218C2×C4×D17C22×C411yescharacteristic
219C2×C4×D17C22×C412yes—
220C2×C4×D17C22×C412yes—
221C2×C4×D17C22×C412yes—
222C2×C4×D17C22×C412yes—
223C2×C4×D17#4118yes—
224C2×C4×D17C2412yes—
225C2×C4×D17C2411yescharacteristic
226C2×C4×D17C2411yescharacteristic
227#63247—216no—
228C2×#3624C24116yes—
229#63243—216no—
230#63242—216no—
231C42×C17C22×C412yes—
232C42×C17C22×C411yescharacteristic
233C42×C17C22×C411yescharacteristic
234C42×C17C22×C412yes—
235C42×C17C22×C412yes—
236C42×C17C22×C412yes—
237C42×C17C22×C412yes—
238C42×C17C22×C412yes—
239C42×C17C22×C411yescharacteristic
240C42×C17C22×C411yescharacteristic
241C4×Dic17C22×C412yes—
242C4×Dic17C22×C412yes—
243C4×Dic17C22×C412yes—
244C4×Dic17C22×C412yes—
245C4×Dic17C22×C412yes—
246C4×Dic17C22×C412yes—
247C4×Dic17C22×C412yes—
248C4×Dic17C22×C412yes—
249C4×Dic17C22×C412yes—
250C4×Dic17C22×C412yes—
251C4×Dic17C22×C412yes—
252C4×Dic17C22×C412yes—
253C4×Dic17C22×C412yes—
254C4×Dic17C22×C411yescharacteristic
255C4×Dic17C22×C411yescharacteristic
256C4×Dic17C22×C412yes—
257C4×Dic17C22×C412yes—
258C4×Dic17C22×C412yes—
259C4×Dic17C22×C412yes—
260C4×Dic17C22×C412yes—
261C4×Dic17C22×C411yescharacteristic
262C4×Dic17C22×C411yescharacteristic
263C4×Dic17C2412yes—
264C4×Dic17C2412yes—
265C4×Dic17C2412yes—
266C4×Dic17C2412yes—
267C2×#2920—171nomaximal, Sylow
268C23×C17—22no—
269C23×C17—24no—
270C23×C17C23×C411yescharacteristic
271C23×C17C23×C412yes—
272C22×D17—232no—
273C22×D17—22no—
274C22×D17—24no—
275C22×D17—24no—
276C22×D17—24no—
277C22×D17—24no—
278C22×D17—24no—
279C22×D17—24no—
280C22×D17—24no—
281C22×D17#11714yes—
282C22×D17C2×M1618yes—
283C22×D17C23×C411yescharacteristic
284C22×D17C23×C412yes—
285C22×D17C23×C411yescharacteristic
286C2×C4×C17—22no—
287C2×C4×C17—24no—
288C2×C4×C17—24no—
289C2×C4×C17—24no—
290C2×C4×C17—24no—
291C2×C4×C17—24no—
292C2×C4×C17—24no—
293C2×C4×C17—24no—
294C2×C4×C17#11714yes—
295C2×C4×C17C2×M1618yescomplemented
296C2×C4×C17C23×C412yes—
297C2×C4×C17C23×C412yes—
298C2×C4×C17C23×C412yes—
299C2×C4×C17C23×C411yescharacteristic
300C2×C4×C17C23×C411yescharacteristic
301C2×C4×C17C23×C412yes—
302C2×C4×C17C23×C412yes—
303C2×Dic17—22no—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—24no—
308C2×Dic17—24no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17C2×M1618yescomplemented
312C2×Dic17C23×C412yes—
313C2×Dic17C23×C412yes—
314C2×Dic17C23×C412yes—
315C2×Dic17C23×C411yescharacteristic
316C2×Dic17C23×C412yes—
317C2×Dic17C23×C412yes—
318C2×Dic17C2×#4114yes—
319C2×Dic17C2511yescharacteristic
320C4×D17—24no—
321C4×D17—24no—
322C4×D17—24no—
323C4×D17—24no—
324C4×D17—24no—
325C4×D17—24no—
326C4×D17—24no—
327C4×D17—24no—
328C4×D17—24no—
329C4×D17—24no—
330C4×D17—24no—
331C4×D17—24no—
332C4×D17—24no—
333C4×D17—24no—
334C4×D17—24no—
335C4×D17—24no—
336C4×D17—24no—
337C4×D17—24no—
338C4×D17#11714yes—
339C4×D17#11714yes—
340C4×D17C2×M1618yes—
341C4×D17C2×M1618yes—
342C4×D17C2×M1618yescomplemented
343C4×D17C2×M1618yescomplemented
344C4×D17C2×#4114yes—
345C4×D17C2×#4114yes—
346#3624—216no—
347C23×C42—171no—
348#2920—174no—
349#2920—174no—
350#2920—174no—
351#2920—174no—
352C2×#432—174no—
353C2×#431—174no—
354C2×#423—172no—
355C2×#407—172no—
356C2×C4×M16—172no—
357C22×C17—28no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17C2×#11712yes—
362C22×C17C22×M1614yes—
363C22×C17C24×C411yescharacteristic
364C2×D17—216no—
365C2×D17—28no—
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—22no—
369C2×D17—28no—
370C2×D17—216no—
371C2×D17C2×#11712yes—
372C2×D17C2×#11712yes—
373C2×D17C22×M1614yes—
374C2×D17C22×M1614yes—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17C2×#11712yes—
379C4×C17C2×#11712yes—
380C4×C17C22×M1614yes—
381C4×C17C22×M1614yes—
382Dic17—22no—
383Dic17—22no—
384Dic17—22no—
385Dic17C2×#11712yes—
386Dic17C22×M1614yes—
387Dic17C22×M1614yes—
388Dic17C22×#4112yes—
389C24×C4—171no—
390C24×C4—172no—
391C22×M16—174no—
392C22×C42—171no—
393C22×C42—172no—
394C22×C42—172no—
395C22×C42—172no—
396C22×C42—172no—
397C22×C42—172no—
398C22×C42—171no—
399C22×C42—171no—
400C22×C42—172no—
401C22×C42—171no—
402C22×C42—171no—
403C22×C42—172no—
404C22×C42—172no—
405C22×C42—172no—
406C22×C42—172no—
407C22×C42—172no—
408C22×C42#59511yescharacteristic
409#432—178no—
410#432—178no—
411#432—178no—
412#432—178no—
413#431—178no—
414#431—178no—
415#431—178no—
416#431—178no—
417#423—178no—
418#423—174no—
419#423—174no—
420C2×C4⋊C8—178no—
421#407—174no—
422#407—178no—
423#407—174no—
424C2×C22⋊C8—178no—
425C4×M16—178no—
426C4×M16—178no—
427C2×#97—174no—
428C2×C4×C8—174no—
429C2×C17—22no—
430C2×C17—24no—
431C2×C17C22×#11711yescharacteristic
432C2×C17C23×M1612yes—
433D17—22no—
434D17—24no—
435D17#292014yescomplemented
436C25—171no—
437C23×C4—172no—
438C23×C4—171no—
439C23×C4—172no—
440C23×C4—171no—
441C23×C4—172no—
442C23×C4—172no—
443C23×C4—172no—
444C23×C4—172no—
445C23×C4—172no—
446C23×C4—172no—
447C23×C4—172no—
448C23×C4—172no—
449C23×C4—172no—
450C23×C4—172no—
451C23×C4—172no—
452C23×C4—171no—
453C23×C4—172no—
454C23×C4—172no—
455C23×C4—171no—
456C23×C4—172no—
457C23×C4—171no—
458C23×C4—172no—
459C23×C4—3416no—
460C23×C4—348no—
461C23×C4C2×#59512yes—
462C23×C4C2×#59511yescharacteristic
463C2×M16—178no—
464C2×M16—178no—
465C2×M16—3416no—
466C22×C8—178no—
467C2×C42—172no—
468C2×C42—172no—
469C2×C42—172no—
470C2×C42—172no—
471C2×C42—172no—
472C2×C42—172no—
473C2×C42—172no—
474C2×C42—172no—
475C2×C42—172no—
476C2×C42—172no—
477C2×C42—172no—
478C2×C42—172no—
479C2×C42—172no—
480C2×C42—172no—
481C2×C42—172no—
482C2×C42—172no—
483C2×C42—172no—
484C2×C42—171no—
485C2×C42—171no—
486C2×C42—171no—
487C2×C42—172no—
488C2×C42—171no—
489C2×C42—172no—
490C2×C42—172no—
491C2×C42—171no—
492C2×C42—172no—
493C2×C42—171no—
494C2×C42—172no—
495C2×C42—172no—
496C2×C42—172no—
497C2×C42—172no—
498C2×C42—172no—
499C2×C42—172no—
500C2×C42—172no—
501C2×C42—172no—
502C2×C42—172no—
503C2×C42—172no—
504C2×C42—172no—
505C2×C42—172no—
506C2×C42—172no—
507C2×C42—172no—
508C2×C42—172no—
509C2×C42—172no—
510C2×C42—172no—
511C2×C42—172no—
512C2×C42—172no—
513C2×C42—171no—
514C2×C42—171no—
515C2×C42—172no—
516C2×C42—172no—
517C2×C42—172no—
518C2×C42—172no—
519C2×C42—171no—
520C2×C42—171no—
521C2×C42—172no—
522C2×C42C2×#59512yes—
523C2×C42C2×#59512yes—
524C2×C42C2×#59512yes—
525C2×C42C2×#59512yes—
526C2×C42C2×#59511yescharacteristic
527C2×C42C2×#59512yes—
528C2×C42C2×#59511yescharacteristic
529C4⋊C8—1716no—
530C4⋊C8—1716no—
531C22⋊C8—1716no—
532C22⋊C8—1716no—
533#97—1716no—
534C4×C8—1716no—
535C17C2×#292011yescharacteristic, complemented, Sylow
536C24—171no—
537C24—172no—
538C24—171no—
539C24—172no—
540C24—344no—
541C24—348no—
542C24C22×#59511yescharacteristic
543C22×C4—28no—
544C22×C4—24no—
545C22×C4—172no—
546C22×C4—171no—
547C22×C4—1716no—
548C22×C4—178no—
549C22×C4—171no—
550C22×C4—171no—
551C22×C4—172no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—172no—
555C22×C4—171no—
556C22×C4—171no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—172no—
561C22×C4—172no—
562C22×C4—171no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—172no—
567C22×C4—172no—
568C22×C4—172no—
569C22×C4—172no—
570C22×C4—172no—
571C22×C4—172no—
572C22×C4—172no—
573C22×C4—172no—
574C22×C4—172no—
575C22×C4—172no—
576C22×C4—172no—
577C22×C4—172no—
578C22×C4—172no—
579C22×C4—172no—
580C22×C4—172no—
581C22×C4—172no—
582C22×C4—172no—
583C22×C4—344no—
584C22×C4—348no—
585C22×C4—348no—
586C22×C4—348no—
587C22×C4—348no—
588C22×C4—348no—
589C22×C4—348no—
590C22×C4—348no—
591C22×C4—348no—
592C22×C4—348no—
593C22×C4—348no—
594C22×C4—348no—
595C22×C4—348no—
596C22×C4—348no—
597C22×C4—344no—
598C22×C4—348no—
599C22×C4—344no—
600C22×C4—348no—
601C22×C4—348no—
602C22×C4—344no—
603C22×C4C22×#59511yescharacteristic
604C22×C4C22×#59512yes—
605C22×C4C22×#59512yes—
606C22×C4C22×#59512yes—
607C22×C4C22×#59512yes—
608C22×C4C22×#59512yes—
609C22×C4C22×#59512yes—
610C22×C4C22×#59512yes—
611C22×C4C22×#59512yes—
612C22×C4C22×#59511yescharacteristic
613M16—3416no—
614M16—3416no—
615C2×C8—1716no—
616C2×C8—3416no—
617C42—172no—
618C42—172no—
619C42—172no—
620C42—172no—
621C42—172no—
622C42—172no—
623C42—171no—
624C42—171no—
625C42—172no—
626C42—172no—
627C42—172no—
628C42—172no—
629C42—172no—
630C42—172no—
631C42—172no—
632C42—172no—
633C42—172no—
634C42—172no—
635C42—172no—
636C42—172no—
637C42—172no—
638C42—172no—
639C42—171no—
640C42—171no—
641C42—172no—
642C42—172no—
643C42C22×#59512yes—
644C42C22×#59511yescharacteristic
645C42C22×#59511yescharacteristic
646C42C22×#59512yes—
647C42C22×#59512yes—
648C42C22×#59512yes—
649C42C22×#59512yes—
650C42C22×#59512yes—
651C42C22×#59511yescharacteristic
652C42C22×#59511yescharacteristic
653C23—22no—
654C23—24no—
655C23—171no—
656C23—174no—
657C23—178no—
658C23—171no—
659C23—172no—
660C23—344no—
661C23—344no—
662C23—344no—
663C23—344no—
664C23—344no—
665C23—344no—
666C23—3432no—
667C23—342no—
668C23—344no—
669C23C23×#59511yescharacteristic
670C23C23×#59512yes—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—174no—
680C2×C4—178no—
681C2×C4—171no—
682C2×C4—171no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—174no—
686C2×C4—174no—
687C2×C4—174no—
688C2×C4—174no—
689C2×C4—178no—
690C2×C4—178no—
691C2×C4—178no—
692C2×C4—178no—
693C2×C4—172no—
694C2×C4—172no—
695C2×C4—172no—
696C2×C4—344no—
697C2×C4—344no—
698C2×C4—344no—
699C2×C4—344no—
700C2×C4—344no—
701C2×C4—344no—
702C2×C4—344no—
703C2×C4—344no—
704C2×C4—344no—
705C2×C4—344no—
706C2×C4—344no—
707C2×C4—344no—
708C2×C4—344no—
709C2×C4—344no—
710C2×C4—344no—
711C2×C4—344no—
712C2×C4—344no—
713C2×C4—344no—
714C2×C4—342no—
715C2×C4—344no—
716C2×C4—344no—
717C2×C4—344no—
718C2×C4—344no—
719C2×C4—344no—
720C2×C4—344no—
721C2×C4—344no—
722C2×C4D17⋊M1618yescomplemented
723C2×C4#1058767714yes—
724C2×C4C23×#59512yes—
725C2×C4C23×#59512yes—
726C2×C4C23×#59512yes—
727C2×C4C23×#59511yescharacteristic
728C2×C4C23×#59511yescharacteristic
729C2×C4C23×#59512yes—
730C2×C4C23×#59512yes—
731C8—3416no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—172no—
737C22—174no—
738C22—172no—
739C22—174no—
740C22—348no—
741C22—3416no—
742C22—348no—
743C22—3416no—
744C22—342no—
745C22—342no—
746C22—342no—
747C22C2×#1058767712yes—
748C22C2×D17⋊M1614yes—
749C22C24×#59511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—172no—
754C4—172no—
755C4—174no—
756C4—174no—
757C4—342no—
758C4—342no—
759C4—342no—
760C4C2×#1058767712yes—
761C4C2×#1058767712yes—
762C4C2×D17⋊M1614yes—
763C4C2×D17⋊M1614yes—
764C2—22no—
765C2—24no—
766C2—174no—
767C2—342no—
768C2—344no—
769C2C22×#1058767711yescharacteristic
770C2C22×D17⋊M1612yes—
subgroupG/H
centerC42C22×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×C42×C17C4
prime radicalC24×D17C2×C4
cosocleC2×Dic17C25
hypercenterC22×C42#595
hypocenterC17C2×#2920
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14545463C2semidirect
2. #14545462C2semidirect
3. #14545461C2semidirect
4. #14545460C2semidirect
5. D17⋊#432C2semidirect
6. #14545448C2semidirect
7. D17⋊#423C2semidirect
9. C4×D17⋊M16C2semidirect
12. #11763832C22semidirect
13. #11763831C22semidirect
14. #11763830C22semidirect
15. #11763829C22semidirect
16. #11763828C22semidirect
17. #11763827C22semidirect
18. #11763826C22semidirect
19. #11763825C22semidirect
20. #11763814C22semidirect
21. #11763813C22semidirect
22. #11763812C22semidirect
23. #11763810C22semidirect
28. C4×#63243C22semidirect
29. C4×#63247C22semidirect
30. #11763768C22semidirect
31. C4×#63242C22semidirect
145. #10587544C23semidirect
147. #10587542C23semidirect
148. C4⋊#3624C23semidirect
149. C4×#3624C23semidirect
199. C2×C4×D17M16semidirect
295. C2×C4×C17C2×M16semidirect
311. C2×Dic17C2×M16semidirect
342. C4×D17C2×M16semidirect
343. C4×D17C2×M16semidirect
435. D17#2920semidirect
535. C17C2×#2920semidirect
722. C2×C4D17⋊M16semidirect

Maximal subgroups

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

subgroupindex
#145454632
#145454622
#145454612
#145454602
D17⋊#4322
#145454482
D17⋊#4232
D17⋊#4072
C4×D17⋊M162
C22×C42×D172
C2×#292017