Finite Group Databasebeta

← #17950651

Subgroups — #17950651

Order 4352.

1058 conjugacy classes of subgroups.

The subgroup lattice has 574 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#14543626C214yesmaximal, complemented
4C2×#11762772C211yesmaximal, characteristic
5C2×D17⋊M16—21no—
6C22×C22⋊#595C412yes—
7C22×C4×#595—21no—
8#11763781—21no—
9#11763780—21no—
10#11763780C412yescomplemented
11#11763779C412yescomplemented
12#11763777—21no—
13#11763777C2212yes—
14C4×C22⋊#595—21no—
15C4×C22⋊#595—21no—
16C4×C22⋊#595C412yes—
17C4×C22⋊#595C2212yes—
18C2×(C2×#595)⋊C4—21no—
19C23×C4×D17C2211yescharacteristic
20C22×#63223C411yescharacteristic, complemented
21#11762772—21no—
22#11762772—21no—
23#11762772—21no—
24#11762772—21no—
25C2×#10587491C412yescomplemented
26C2×#10587491C2212yes—
27C22×M16×C17C411yescharacteristic, complemented
28C24×D17C2×C411yescharacteristic
29C23×#595—22no—
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17C2×C411yescharacteristic
32C22×C4×D17—42no—
33C22×C4×D17—42no—
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17D411yescharacteristic
38C22×C4×D17D411yescharacteristic
39C22×C4×D17D411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17Q811yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C2×C22⋊#595—22no—
47C2×C22⋊#595—28no—
48C2×C22⋊#595C2×C414yes—
49C2×#63247—22no—
50C2×C4×#595—22no—
51C2×C4×#595—22no—
52C2×C4×#595—42no—
53C2×C4×#595—42no—
54D17⋊M16—42no—
55D17⋊M16—42no—
56C2×#63243—22no—
57C2×#63242—22no—
58C2×M16×C17—21no—
59C2×M16×C17—21no—
60C2×M16×C17—42no—
61C22×C8×C17C2×C412yescomplemented
62C2×#63223—21no—
63C2×#63223—21no—
64C2×#63223—42no—
65C22×#3622C2×C412yescomplemented
66C22⋊#3624—22no—
67C22⋊#3624C2×C414yescomplemented
68(C2×#595)⋊C4—22no—
69(C2×#595)⋊C4—22no—
70#10587543—22no—
71#10587543—22no—
72#10587491—22no—
73#10587491—22no—
74#10587491—22no—
75#10587491—22no—
76C24×C17C4211yescharacteristic
77C23×D17—24no—
78C23×D17—42no—
79C23×D17—42no—
80C23×D17C4211yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C4⋊C411yescharacteristic
84C23×D17C4⋊C411yescharacteristic
85C23×D17C22×C411yescharacteristic
86C22×#595—28no—
87C22×#595—24no—
88C22×#595—44no—
89C22×#595—44no—
90C22×C4×C17—22no—
91C22×C4×C17—22no—
92C22×C4×C17C4211yescharacteristic
93C22×C4×C17C22⋊C411yescharacteristic
94C22×C4×C17C22⋊C411yescharacteristic
95C22×C4×C17C4⋊C411yescharacteristic
96C22×C4×C17C4⋊C411yescharacteristic
97C22×C4×C17C22×C411yescharacteristic
98C22×Dic17—42no—
99C22×Dic17C4211yescharacteristic
100C22×Dic17C22⋊C411yescharacteristic
101C22×Dic17C22⋊C411yescharacteristic
102C22×Dic17C4⋊C411yescharacteristic
103C22×Dic17C4⋊C411yescharacteristic
104C22×Dic17C22×C411yescharacteristic
105C2×C4×D17—22no—
106C2×C4×D17—22no—
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—42no—
110C2×C4×D17—42no—
111C2×C4×D17—41no—
112C2×C4×D17—41no—
113C2×C4×D17—42no—
114C2×C4×D17—41no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—42no—
119C2×C4×D17—41no—
120C2×C4×D17—41no—
121C2×C4×D17—42no—
122C2×C4×D17—42no—
123C2×C4×D17C22⋊C411yescharacteristic
124C2×C4×D17C22⋊C411yescharacteristic
125C2×C4×D17C22⋊C411yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C4⋊C411yescharacteristic
130C2×C4×D17C4⋊C411yescharacteristic
131C2×C4×D17C4⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C2×D411yescharacteristic
136C2×C4×D17C2×D411yescharacteristic
137C2×C4×D17C2×D411yescharacteristic
138C2×C4×D17C2×Q811yescharacteristic
139C22⋊#595—28no—
140C22⋊#595—24no—
141C22⋊#595M1618yescomplemented
142#63247—44no—
143C2×#3624—24no—
144C4×#595—44no—
145C4×#595—42no—
146C4×#595—42no—
147#63243—44no—
148#63242—42no—
149#63242—42no—
150M16×C17—42no—
151M16×C17—42no—
152C2×C8×C17—22no—
153C2×C8×C17—42no—
154#63223—42no—
155#63223—42no—
156C2×#3622—22no—
157C2×#3622—42no—
158#7929—171nomaximal, Sylow
159C23×C17—22no—
160C23×C17—22no—
161C23×C17—41no—
162C23×C17#9511yescharacteristic
163C23×C17#9511yescharacteristic
164C23×C17C2×C4211yescharacteristic
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—416no—
183C22×D17#9511yescharacteristic
184C22×D17#9511yescharacteristic
185C22×D17C2×C22⋊C411yescharacteristic
186C22×D17C2×C4⋊C411yescharacteristic
187C22×D17C2×M1614yes—
188C2×#595—28no—
189C2×#595—44no—
190C2×#595—416no—
191C2×#595—44no—
192C2×C4×C17—22no—
193C2×C4×C17—22no—
194C2×C4×C17—22no—
195C2×C4×C17—21no—
196C2×C4×C17—21no—
197C2×C4×C17—21no—
198C2×C4×C17—21no—
199C2×C4×C17#9511yescharacteristic
200C2×C4×C17#9511yescharacteristic
201C2×C4×C17#9912yes—
202C2×C4×C17#9912yes—
203C2×C4×C17C2×C22⋊C411yescharacteristic
204C2×C4×C17C2×C4⋊C411yescharacteristic
205C2×Dic17—22no—
206C2×Dic17—22no—
207C2×Dic17—41no—
208C2×Dic17—41no—
209C2×Dic17—41no—
210C2×Dic17—41no—
211C2×Dic17#9511yescharacteristic
212C2×Dic17#9511yescharacteristic
213C2×Dic17C2×C22⋊C411yescharacteristic
214C2×Dic17C2×C4⋊C411yescharacteristic
215C4×D17—22no—
216C4×D17—22no—
217C4×D17—22no—
218C4×D17—22no—
219C4×D17—21no—
220C4×D17—21no—
221C4×D17—21no—
222C4×D17—21no—
223C4×D17—21no—
224C4×D17—21no—
225C4×D17—21no—
226C4×D17—21no—
227C4×D17—41no—
228C4×D17—41no—
229C4×D17—41no—
230C4×D17—41no—
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235#3624—44no—
236C8×C17—42no—
237#3622—42no—
238C2×#407—171no—
239C2×#407—171no—
240C2×C4×C22⋊C4—171no—
241#1282—174no—
242C22×C17—21no—
243C22×C17—21no—
244C22×C17—21no—
245C22×C17—21no—
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—44no—
250C22×C17#34212yes—
251C22×C17C2×#9511yescharacteristic
252C22×C17C4×M1612yes—
253C2×D17—28no—
254C2×D17—21no—
255C2×D17—21no—
256C2×D17—21no—
257C2×D17—21no—
258C2×D17—21no—
259C2×D17—21no—
260C2×D17—21no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—44no—
264C2×D17—44no—
265C2×D17—44no—
266C2×D17—44no—
267C2×D17—44no—
268C2×D17#34412yes—
269C2×D17#40712yes—
270C2×D17#42312yes—
271#595—48no—
272C4×C17—21no—
273C4×C17—21no—
274C4×C17#34212yes—
275C4×C17C2×#9911yescharacteristic
276C4×C17C2×#9911yescharacteristic
277Dic17—21no—
278Dic17—21no—
279Dic17—21no—
280Dic17—21no—
281C24×C4—171no—
282C22×M16—171no—
283C22×M16—341no—
284C22×M16#59511yescharacteristic, complemented
285C22×C22⋊C4—172no—
286C22×C42—341no—
287#407—172no—
288#407—172no—
289#407—341no—
290#407—341no—
291#407—341no—
292#407—341no—
293#407—341no—
294#407—341no—
295C2×C22⋊C8—172no—
296C2×C22⋊C8—172no—
297C2×C22⋊C8—172no—
298C2×C22⋊C8—341no—
299C4×C22⋊C4—172no—
300C4×C22⋊C4—172no—
301C4×C22⋊C4—341no—
302C4×C22⋊C4—341no—
303C2×#95—341no—
304C2×C17—22no—
305C2×C17—22no—
306C2×C17—41no—
307C2×C17#172811yescharacteristic
308C2×C17C2×#34211yescharacteristic
309C2×C17C2×#34411yescharacteristic
310D17—22no—
311D17—22no—
312D17—22no—
313D17—41no—
314C25—171no—
315C23×C4—171no—
316C23×C4—171no—
317C23×C4—171no—
318C23×C4—171no—
319C23×C4—171no—
320C23×C4—171no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—171no—
324C23×C4—171no—
325C23×C4—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—342no—
329C23×C4—682no—
330C23×C4—682no—
331C23×C4C2×#59511yescharacteristic
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—42no—
335C2×M16—342no—
336C2×M16—342no—
337C2×M16—341no—
338C2×M16—341no—
339C2×M16—682no—
340C2×M16—682no—
341C2×M16—682no—
342C22×C8—172no—
343C22×C8—342no—
344C22×C8C2×#59512yescomplemented
345C2×C22⋊C4—174no—
346C2×C22⋊C4—348no—
347C2×C22⋊C4—342no—
348C2×C42—342no—
349C2×C42—342no—
350C2×C42—682no—
351C2×C42—682no—
352C22⋊C8—174no—
353C22⋊C8—342no—
354C22⋊C8—342no—
355C22⋊C8—342no—
356C22⋊C8—342no—
357C22⋊C8—342no—
358C22⋊C8—342no—
359C22⋊C8—342no—
360#95—342no—
361#95—342no—
362C17#792911yescharacteristic, complemented, Sylow
363C24—171no—
364C24—171no—
365C24—171no—
366C24—171no—
367C24—171no—
368C24—171no—
369C24—344no—
370C24—682no—
371C24—682no—
372C24C4×#59511yescharacteristic
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—171no—
376C22×C4—171no—
377C22×C4—171no—
378C22×C4—171no—
379C22×C4—171no—
380C22×C4—171no—
381C22×C4—171no—
382C22×C4—171no—
383C22×C4—171no—
384C22×C4—171no—
385C22×C4—171no—
386C22×C4—171no—
387C22×C4—171no—
388C22×C4—171no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—342no—
398C22×C4—342no—
399C22×C4—342no—
400C22×C4—342no—
401C22×C4—344no—
402C22×C4—348no—
403C22×C4—681no—
404C22×C4—681no—
405C22×C4—681no—
406C22×C4—681no—
407C22×C4—681no—
408C22×C4—681no—
409C22×C4—681no—
410C22×C4—681no—
411C22×C4—682no—
412C22×C4—682no—
413C22×C4—682no—
414C22×C4—682no—
415C22×C4—682no—
416C22×C4—682no—
417C22×C4—682no—
418C22×C4—684no—
419C22×C4—684no—
420C22×C4C4×#59511yescharacteristic
421C22×C4C4⋊#59511yescharacteristic
422C22×C4C4⋊#59511yescharacteristic
423C22×C4C22⋊#59511yescharacteristic
424C22×C4C22⋊#59511yescharacteristic
425C22×C4C22×#59511yescharacteristic
426M16—42no—
427M16—42no—
428M16—682no—
429M16—684no—
430M16—684no—
431M16—682no—
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—344no—
435C2×C8—342no—
436C2×C8—682no—
437C2×C8—682no—
438C2×C8—682no—
439C22⋊C4—178no—
440C22⋊C4—344no—
441C22⋊C4—348no—
442C42—682no—
443C42—682no—
444C42—684no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—171no—
449C23—171no—
450C23—171no—
451C23—174no—
452C23—171no—
453C23—342no—
454C23—342no—
455C23—342no—
456C23—342no—
457C23—342no—
458C23—342no—
459C23—342no—
460C23—342no—
461C23—342no—
462C23—342no—
463C23—681no—
464C23—681no—
465C23—681no—
466C23—681no—
467C23—681no—
468C23—681no—
469C23—681no—
470C23—6816no—
471C23(C2×#595)⋊C411yescharacteristic
472C23(C2×#595)⋊C411yescharacteristic
473C23C2×C4×#59511yescharacteristic
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—171no—
482C2×C4—171no—
483C2×C4—171no—
484C2×C4—171no—
485C2×C4—342no—
486C2×C4—342no—
487C2×C4—341no—
488C2×C4—341no—
489C2×C4—341no—
490C2×C4—341no—
491C2×C4—341no—
492C2×C4—341no—
493C2×C4—341no—
494C2×C4—341no—
495C2×C4—342no—
496C2×C4—342no—
497C2×C4—342no—
498C2×C4—342no—
499C2×C4—348no—
500C2×C4—681no—
501C2×C4—681no—
502C2×C4—681no—
503C2×C4—681no—
504C2×C4—681no—
505C2×C4—681no—
506C2×C4—681no—
507C2×C4—681no—
508C2×C4—681no—
509C2×C4—681no—
510C2×C4—681no—
511C2×C4—681no—
512C2×C4—684no—
513C2×C4—6816no—
514C2×C4—684no—
515C2×C4#1058753912yes—
516C2×C4(C2×#595)⋊C411yescharacteristic
517C2×C4(C2×#595)⋊C411yescharacteristic
518C2×C4#1058755112yes—
519C2×C4C2×C4⋊#59511yescharacteristic
520C2×C4C2×C22⋊#59511yescharacteristic
521C8—42no—
522C8—684no—
523C8—682no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—44no—
532C22—172no—
533C22—172no—
534C22—172no—
535C22—348no—
536C22—341no—
537C22—341no—
538C22—341no—
539C22—341no—
540C22—341no—
541C22—341no—
542C22—341no—
543C22—341no—
544C22—341no—
545C22—684no—
546C22—684no—
547C22—684no—
548C22—684no—
549C22—684no—
550C22#1176368712yes—
551C22C2×(C2×#595)⋊C411yescharacteristic
552C22M16×#59512yes—
553C4—21no—
554C4—21no—
555C4—341no—
556C4—341no—
557C4—341no—
558C4—341no—
559C4—688no—
560C4#1176368712yes—
561C4C2×#1058755111yescharacteristic
562C4C2×#1058753911yescharacteristic
563C2—22no—
564C2—22no—
565C2—41no—
566C2—342no—
567C2—342no—
568C2—342no—
569C2—681no—
570C2#1454444611yescharacteristic
571C2C2×#1176368711yescharacteristic
572C2#1454449411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC22×C17C2×#95
prime radicalC24×D17C2×C4
cosocleC22×C4×D17C23
hypercenterC22×M16#595
hypocenterC17#7929
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #14543626C2semidirect
10. #11763780C4semidirect
11. #11763779C4semidirect
20. C22×#63223C4semidirect
25. C2×#10587491C4semidirect
27. C22×M16×C17C4semidirect
61. C22×C8×C17C2×C4semidirect
65. C22×#3622C2×C4semidirect
67. C22⋊#3624C2×C4semidirect
141. C22⋊#595M16semidirect
284. C22×M16#595semidirect
344. C22×C8C2×#595semidirect
362. C17#7929semidirect

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
#145436262
C2×#117627722
#792917