Finite Group Databasebeta

← #17192081

Subgroups — #17192081

Order 4352.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14541652C211yesmaximal, characteristic, complemented
2#14531025C211yesmaximal, characteristic, complemented
3#14531020C211yesmaximal, characteristic, complemented
4#14531015C211yesmaximal, characteristic, complemented
5#14530948C211yesmaximal, characteristic, complemented
6#14530941C211yesmaximal, characteristic, complemented
7#14530921C211yesmaximal, characteristic, complemented
8#14530836C211yesmaximal, characteristic, complemented
9#14530836C211yesmaximal, characteristic, complemented
10#14530816C211yesmaximal, characteristic
11#14530693C211yesmaximal, characteristic, complemented
12#14530658C211yesmaximal, characteristic, complemented
13#14530646C211yesmaximal, characteristic, complemented
14C4×#10587497C211yesmaximal, characteristic, complemented
15C17×#3396C211yesmaximal, characteristic, complemented
16#11763519—21no—
17C2×#10587499C2211yescharacteristic
18C2×#10587497C2211yescharacteristic
19C2×#10587497C2211yescharacteristic
20#11763214C2211yescharacteristic
21#11763211C2211yescharacteristic
22#11763211C2211yescharacteristic
23#11763110—21no—
24#11763110—21no—
25#11763100—21no—
26C4×D136C2211yescharacteristic
27C4×D136C2211yescharacteristic
28C4×D136C2211yescharacteristic
29#11762636C2211yescharacteristic
30#11762634C2211yescharacteristic
31#11762634C2211yescharacteristic
32C4⋊#63214C2211yescharacteristic
33C4⋊#63214C2211yescharacteristic
34C4⋊#63214C2211yescharacteristic
35#11762613C2211yescharacteristic
36#11762613C2211yescharacteristic
37#11762613C2211yescharacteristic
38#11762610C2211yescharacteristic
39#11762610C2211yescharacteristic
40#11762610C2211yescharacteristic
41#11762610C2211yescharacteristic
42#11762610C2211yescharacteristic
43#11762610C2211yescharacteristic
44#11762609C2211yescharacteristic
45#11762585C2211yescharacteristic
46#11762585C2211yescharacteristic
47C4×#63214C2211yescharacteristic
48C17×#559—21no—
49C17×#495C2211yescharacteristic
50C17×#495C2211yescharacteristic
51C17×#493C2211yescharacteristic
52C17×#463—21no—
53C17×#463—21no—
54C17×#460—21no—
55C8×Q8×C17C2211yescharacteristic
56C4×Q16×C17C2211yescharacteristic
57C4×D8×C17C2211yescharacteristic
58C4×D8×C17C2211yescharacteristic
59C2×Q16×C17C2311yescharacteristic
60C2×SD16×C17—21no—
61C2×SD16×C17—21no—
62C2×D8×C17—21no—
63C2×D8×C17C2311yescharacteristic
64C2×D8×C17C2311yescharacteristic
65C17×#127—21no—
66C17×#124—21no—
67C17×#124—21no—
68C17×#124—41no—
69C17×#123—41no—
70C17×#123—41no—
71C4×Q8×C17—21no—
72C4×Q8×C17D411yescharacteristic
73C4×D4×C17—21no—
74C4×D4×C17—21no—
75C4×D4×C17—41no—
76#10587632—41no—
77C2×D136C2311yescharacteristic
78#10587582—41no—
79#10587582—41no—
80C4⋊C4×D17—41no—
81C4×D68—21no—
82C4×D68—21no—
83C4×D68—21no—
84#10587556—21no—
85#10587556—21no—
86#10587555—21no—
87C17×#107C2311yescharacteristic
88C17×C4⋊C8D411yescharacteristic
89C17×C4⋊C8D411yescharacteristic
90C17×C4⋊C8D411yescharacteristic
91C17×#103—21no—
92C17×#102—21no—
93C17×#102—21no—
94C4×C8×C17C2311yescharacteristic
95C4×C8×C17C2311yescharacteristic
96C4×C8×C17C2311yescharacteristic
97#10587499—22no—
98#10587497—22no—
99#10587497—22no—
100#10587492—21no—
101#10587492—21no—
102#10587492—21no—
103#10587489—21no—
104#10587489C2311yescharacteristic
105#10587489C2311yescharacteristic
106#10587489C2311yescharacteristic
107#10587488—21no—
108#10587488—21no—
109C2×#63214C2311yescharacteristic
110C2×#63214C2311yescharacteristic
111C2×#63214C2311yescharacteristic
112C2×#63214C2311yescharacteristic
113C2×Q8×C17—21no—
114C2×Q8×C17D811yescharacteristic
115C2×D4×C17—21no—
116C2×D4×C17—21no—
117C2×D4×C17—41no—
118C2×D4×C17—41no—
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C2×D68—21no—
122C2×C4×D17—41no—
123C2×C4×D17—41no—
124C2×C4×D17—41no—
125C2×Dic34—41no—
126Q16×C17—21no—
127Q16×C17—21no—
128SD16×C17—81no—
129SD16×C17—81no—
130D8×C17—21no—
131D8×C17—21no—
132D8×C17—21no—
133D8×C17—21no—
134D8×C17—81no—
135C2×C8×C17C2×D411yescharacteristic
136C2×C8×C17C2×D411yescharacteristic
137C2×C8×C17C2×D411yescharacteristic
138C2×C8×C17C2411yescharacteristic
139C4⋊C4×C17—21no—
140C4⋊C4×C17—41no—
141C4⋊C4×C17D811yescharacteristic
142C4⋊C4×C17D811yescharacteristic
143C4⋊C4×C17D811yescharacteristic
144C22⋊C4×C17—41no—
145C22⋊C4×C17—41no—
146C22⋊C4×C17—41no—
147C22⋊C4×C17—41no—
148C22⋊C4×C17—41no—
149C22⋊C4×C17—41no—
150C42×C17—41no—
151C42×C17C2×D411yescharacteristic
152C42×C17C2×D411yescharacteristic
153C42×C17C2×D411yescharacteristic
154#63227—41no—
155#63227—41no—
156#63227—41no—
157C4⋊Dic17—21no—
158C4⋊Dic17—21no—
159C4⋊Dic17—21no—
160C4⋊Dic17—41no—
161#63225—41no—
162#63225—41no—
163#63225—41no—
164#63225—41no—
165D136—21no—
166D136#4112yes—
167#63214—21no—
168#63214—21no—
169#63214—21no—
170#63214—21no—
171#33937—171nomaximal, Sylow
172C23×C17—41no—
173C23×C17—41no—
174C22×D17—41no—
175Q8×C17—41no—
176Q8×C17—41no—
177Q8×C17—41no—
178D4×C17—41no—
179D4×C17—41no—
180D4×C17—41no—
181D4×C17—41no—
182D4×C17—82no—
183D4×C17—161no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—161no—
187C2×C4×C17—161no—
188C2×C4×C17C2×D811yescharacteristic
189C2×C4×C17C2×D811yescharacteristic
190C2×C4×C17C2×D811yescharacteristic
191C2×C4×C17C2×D811yescharacteristic
192C2×C4×C17C2×D811yescharacteristic
193C2×C4×C17C2×D811yescharacteristic
194C2×C4×C17C22×D411yescharacteristic
195C2×Dic17—41no—
196C2×Dic17—41no—
197C2×Dic17—41no—
198D68—22no—
199D68—41no—
200C4×D17—82no—
201C4×D17—161no—
202C4×D17—161no—
203Dic34—161no—
204C8×C17—21no—
205C8×C17—21no—
206C8×C17—21no—
207C8×C17C2×#4111yescharacteristic
208C8×C172−1+411yescharacteristic
209#3396D1711yescharacteristic, complemented
210#3380—171no—
211#2244—171no—
212#2243—171no—
213#2242—171no—
214#2229—171no—
215#2228—171no—
216#2224—171no—
217#2210—171no—
218#2210—171no—
219#2206—171no—
220#2183—171no—
221#2177—171no—
222#2175—171no—
223C4×D16—171no—
224C22×C17—81no—
225C22×C17—81no—
226C22×C17—81no—
227C22×C17—81no—
228C22×C17—81no—
229C22×C17—81no—
230C22×C17C22×D811yescharacteristic
231C2×D17—42no—
232C2×D17—81no—
233C2×D17—81no—
234C4×C17—21no—
235C4×C17—21no—
236C4×C17—21no—
237C4×C17—21no—
238C4×C17—21no—
239C4×C17—21no—
240C4×C17—81no—
241C4×C17—81no—
242C4×C17#54811yescharacteristic
243C4×C17#57711yescharacteristic
244Dic17—81no—
245Dic17—81no—
246Dic17—81no—
247#559—21no—
248#554—341no—
249C2×SD32—171no—
250C2×D16—171no—
251C2×D16—171no—
252#500—171no—
253#499—171no—
254#499—171no—
255#495C2×D1711yescharacteristic
256#495C2×D1711yescharacteristic
257#493C2×D1711yescharacteristic
258#478—341no—
259#478—341no—
260#476—341no—
261#463—21no—
262#463—21no—
263#460—21no—
264C8×Q8C2×D1711yescharacteristic
265C4×Q16C2×D1711yescharacteristic
266C4×D8—171no—
267C4×D8—171no—
268C4×D8—171no—
269C4×D8C2×D1711yescharacteristic
270C4×D8C2×D1711yescharacteristic
271#367—171no—
272#366—171no—
273#366—171no—
274C4⋊C16—171no—
275C4⋊C16—171no—
276C4⋊C16—171no—
277#358—171no—
278#358—171no—
279#358—171no—
280#357—171no—
281#357—171no—
282#357—171no—
283#357—171no—
284#357—171no—
285#357—171no—
286#357—171no—
287#346—171no—
288#346—171no—
289C4×C16—171no—
290C2×C17—161no—
291C2×C17—161no—
292C2×C17#335811yescharacteristic
293C2×C17#341411yescharacteristic
294C2×C17#341511yescharacteristic
295D17—82no—
296C2×Q16C22×D1711yescharacteristic
297C2×SD16—21no—
298C2×SD16—21no—
299C2×D8—21no—
300C2×D8—171no—
301C2×D8C22×D1711yescharacteristic
302C2×D8C22×D1711yescharacteristic
303C4⋊Q8—341no—
304#127—21no—
305#125—341no—
306#125—341no—
307#124—21no—
308#124—21no—
309#124—41no—
310#123—41no—
311#123—41no—
312C22⋊Q8—681no—
313C22⋊Q8—681no—
314C22⋊Q8—681no—
315C4×Q8—21no—
316C4×Q8C22⋊D1711yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—41no—
320C4×D4—341no—
321C4×D4—341no—
322C4×D4—341no—
323C2×C4⋊C4—681no—
324SD32—342no—
325D16—342no—
326D16—342no—
327C2×C16—171no—
328C2×C16—171no—
329C2×C16—171no—
330C2×C16—171no—
331#107—171no—
332#107—171no—
333#107—171no—
334#107—341no—
335#107C22×D1711yescharacteristic
336#106—341no—
337#106—341no—
338C4⋊C8C22⋊D1711yescharacteristic
339C4⋊C8C22⋊D1711yescharacteristic
340C4⋊C8C22⋊D1711yescharacteristic
341#103—21no—
342#102—21no—
343#102—21no—
344#102—341no—
345#102—341no—
346#102—341no—
347C4×C8C22×D1711yescharacteristic
348C4×C8C22×D1711yescharacteristic
349C4×C8C22×D1711yescharacteristic
350C17#3393711yescharacteristic, complemented, Sylow
351C2×Q8—21no—
352C2×Q8—681no—
353C2×Q8#6322811yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—341no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—681no—
362C22×C4—681no—
363C22×C4—681no—
364Q16—21no—
365Q16—21no—
366SD16—81no—
367SD16—81no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—21no—
372D8—81no—
373D8—172no—
374D8—341no—
375C2×C8C2×C22⋊D1711yescharacteristic
376C2×C8C2×C22⋊D1711yescharacteristic
377C2×C8C2×C22⋊D1711yescharacteristic
378C2×C8C23×D1711yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—341no—
382C4⋊C4—341no—
383C4⋊C4—341no—
384C4⋊C4—681no—
385C4⋊C4—681no—
386C4⋊C4—681no—
387C4⋊C4—681no—
388C4⋊C4—681no—
389C4⋊C4#6322811yescharacteristic
390C4⋊C4#6322811yescharacteristic
391C4⋊C4#6322811yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—681no—
399C22⋊C4—681no—
400C22⋊C4—681no—
401C42—41no—
402C42C2×C22⋊D1711yescharacteristic
403C42C2×C22⋊D1711yescharacteristic
404C42C2×C22⋊D1711yescharacteristic
405C16—341no—
406C16—341no—
407C16—341no—
408C16—341no—
409C23—41no—
410C23—41no—
411C23—681no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—2721no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—342no—
423D4—681no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—2721no—
429C2×C4—2721no—
430C2×C4—681no—
431C2×C4—681no—
432C2×C4—681no—
433C2×C4—1362no—
434C2×C4C2×#6322811yescharacteristic
435C2×C4C2×#6322811yescharacteristic
436C2×C4C2×#6322811yescharacteristic
437C2×C4C2×#6322811yescharacteristic
438C2×C4C2×#6322811yescharacteristic
439C2×C4C2×#6322811yescharacteristic
440C2×C4C22×C22⋊D1711yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8#41×D1711yescharacteristic
445C8#1058769711yescharacteristic
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—682no—
453C22—1361no—
454C22—1361no—
455C22C22×#6322811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—1361no—
465C4—1361no—
466C4—1361no—
467C4#1176346611yescharacteristic
468C4#1176362011yescharacteristic
469C2—161no—
470C2—161no—
471C2—1362no—
472C2#1454141511yescharacteristic
473C2#1454191811yescharacteristic
474C2#1454192311yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3396C2
socleC22×C17C22×D8
prime radical#14530816C2
hypercenter#3396D17
hypocenterC17#33937
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #14541652C2semidirect
2. #14531025C2semidirect
3. #14531020C2semidirect
4. #14531015C2semidirect
5. #14530948C2semidirect
6. #14530941C2semidirect
7. #14530921C2semidirect
8. #14530836C2semidirect
9. #14530836C2semidirect
11. #14530693C2semidirect
12. #14530658C2semidirect
13. #14530646C2semidirect
14. C4×#10587497C2semidirect
15. C17×#3396C2semidirect
209. #3396D17semidirect
350. C17#33937semidirect

Maximal subgroups

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

subgroupindex
#145416522
#145310252
#145310202
#145310152
#145309482
#145309412
#145309212
#145308362
#145308162
#145306932
#145306582
#145306462
C4×#105874972
C17×#33962
#3393717