Finite Group Databasebeta

← #17192087

Subgroups — #17192087

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#14541797C211yesmaximal, characteristic, complemented
2#14531027C211yesmaximal, characteristic, complemented
3#14531023C211yesmaximal, characteristic, complemented
4#14531018C211yesmaximal, characteristic, complemented
5#14530945C211yesmaximal, characteristic, complemented
6#14530938C211yesmaximal, characteristic, complemented
7#14530918C211yesmaximal, characteristic, complemented
8#14530839C211yesmaximal, characteristic, complemented
9#14530839C211yesmaximal, characteristic, complemented
10#14530819C211yesmaximal, characteristic
11#14530693C211yesmaximal, characteristic, complemented
12#14530658C211yesmaximal, characteristic, complemented
13#14530648C211yesmaximal, characteristic, complemented
14C4×#10587497C211yesmaximal, characteristic, complemented
15C17×#3380C211yesmaximal, characteristic, complemented
16#11763544—21no—
17C2×#10587498C2211yescharacteristic
18C2×#10587497C2211yescharacteristic
19C2×#10587497C2211yescharacteristic
20#11763193C2211yescharacteristic
21#11763193C2211yescharacteristic
22#11763186C2211yescharacteristic
23#11763025—21no—
24#11763025—21no—
25#11763010—21no—
26C4×Dic68C2211yescharacteristic
27C4×D136C2211yescharacteristic
28C4×D136C2211yescharacteristic
29#11762636C2211yescharacteristic
30#11762634C2211yescharacteristic
31#11762634C2211yescharacteristic
32C4⋊#63214C2211yescharacteristic
33C4⋊#63214C2211yescharacteristic
34C4⋊#63214C2211yescharacteristic
35#11762612C2211yescharacteristic
36#11762612C2211yescharacteristic
37#11762612C2211yescharacteristic
38#11762610C2211yescharacteristic
39#11762609C2211yescharacteristic
40#11762609C2211yescharacteristic
41#11762609C2211yescharacteristic
42#11762609C2211yescharacteristic
43#11762609C2211yescharacteristic
44#11762609C2211yescharacteristic
45#11762585C2211yescharacteristic
46#11762585C2211yescharacteristic
47C4×#63214C2211yescharacteristic
48C17×#554—21no—
49C17×#500C2211yescharacteristic
50C17×#499C2211yescharacteristic
51C17×#499C2211yescharacteristic
52C17×#478—21no—
53C17×#478—21no—
54C17×#476—21no—
55C8×Q8×C17C2211yescharacteristic
56C4×D8×C17C2211yescharacteristic
57C4×D8×C17C2211yescharacteristic
58C4×D8×C17C2211yescharacteristic
59C2×D8×C17C2311yescharacteristic
60C17×C4⋊Q8—21no—
61C17×#125—21no—
62C17×#125—21no—
63C17×C22⋊Q8—41no—
64C17×C22⋊Q8—41no—
65C17×C22⋊Q8—41no—
66C4×Q8×C17D411yescharacteristic
67C4×D4×C17—21no—
68C4×D4×C17—21no—
69C4×D4×C17—21no—
70C2×C4⋊C4×C17—41no—
71#10587633—41no—
72C2×Dic68C2311yescharacteristic
73C2×D136—21no—
74C2×D136C2311yescharacteristic
75C2×D136C2311yescharacteristic
76C2×#63219—21no—
77C2×#63219—21no—
78#10587580—41no—
79#10587580—41no—
80#10587579—41no—
81#10587561—21no—
82#10587561—21no—
83#10587560—21no—
84C4×D68—21no—
85C4×D68—21no—
86C4×Dic34—21no—
87C17×#107—21no—
88C17×#107C2311yescharacteristic
89C17×#107C2311yescharacteristic
90C17×#107C2311yescharacteristic
91C17×#106—21no—
92C17×#106—21no—
93C17×C4⋊C8D411yescharacteristic
94C17×C4⋊C8D411yescharacteristic
95C17×C4⋊C8D411yescharacteristic
96C17×#102—21no—
97C17×#102—21no—
98C17×#102—21no—
99C4×C8×C17C2311yescharacteristic
100C4×C8×C17C2311yescharacteristic
101C4×C8×C17C2311yescharacteristic
102#10587498—22no—
103#10587497—22no—
104#10587497—22no—
105#10587492—21no—
106#10587492—21no—
107#10587489C2311yescharacteristic
108#10587487—21no—
109C2×#63214C2311yescharacteristic
110C2×#63214C2311yescharacteristic
111C2×#63214C2311yescharacteristic
112C2×#63214C2311yescharacteristic
113C2×Q8×C17—41no—
114C2×Q8×C17D811yescharacteristic
115C2×D4×C17—21no—
116C22×C4×C17—41no—
117C22×C4×C17—41no—
118C22×C4×C17—41no—
119C2×D68—21no—
120C2×D68—21no—
121C2×D68—41no—
122C2×D68—41no—
123C2×C4×D17—41no—
124C2×C4×D17—41no—
125C2×Dic34—21no—
126D8×C17—21no—
127D8×C17#4112yes—
128C2×C8×C17C2×D411yescharacteristic
129C2×C8×C17C2×D411yescharacteristic
130C2×C8×C17C2×D411yescharacteristic
131C2×C8×C17C2411yescharacteristic
132C4⋊C4×C17—21no—
133C4⋊C4×C17—21no—
134C4⋊C4×C17—21no—
135C4⋊C4×C17—41no—
136C4⋊C4×C17—41no—
137C4⋊C4×C17—41no—
138C4⋊C4×C17—41no—
139C4⋊C4×C17—41no—
140C4⋊C4×C17D811yescharacteristic
141C4⋊C4×C17D811yescharacteristic
142C4⋊C4×C17D811yescharacteristic
143C22⋊C4×C17—41no—
144C22⋊C4×C17—41no—
145C22⋊C4×C17—41no—
146C42×C17C2×D411yescharacteristic
147C42×C17C2×D411yescharacteristic
148C42×C17C2×D411yescharacteristic
149#63227—41no—
150#63227—41no—
151#63227—41no—
152#63227—41no—
153#63227—41no—
154#63227—41no—
155C4⋊Dic17—21no—
156#63225—41no—
157C4×Dic17—41no—
158Dic68—21no—
159Dic68—21no—
160D136—21no—
161D136—21no—
162D136—21no—
163D136—21no—
164D136—81no—
165#63219—81no—
166#63219—81no—
167#63214—21no—
168#63214—21no—
169#63214—21no—
170#63214—21no—
171#33937—171nomaximal, Sylow
172C23×C17—41no—
173C22×D17—41no—
174C22×D17—41no—
175Q8×C17—41no—
176Q8×C17—161no—
177D4×C17—22no—
178D4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—41no—
182C2×C4×C17—82no—
183C2×C4×C17—161no—
184C2×C4×C17—161no—
185C2×C4×C17C2×D811yescharacteristic
186C2×C4×C17C2×D811yescharacteristic
187C2×C4×C17C2×D811yescharacteristic
188C2×C4×C17C2×D811yescharacteristic
189C2×C4×C17C2×D811yescharacteristic
190C2×C4×C17C2×D811yescharacteristic
191C2×C4×C17C22×D411yescharacteristic
192C2×Dic17—41no—
193C2×Dic17—41no—
194D68—41no—
195D68—41no—
196D68—41no—
197D68—41no—
198D68—82no—
199D68—161no—
200C4×D17—161no—
201C4×D17—161no—
202Dic34—41no—
203Dic34—41no—
204C8×C17—21no—
205C8×C17—21no—
206C8×C17—21no—
207C8×C17C2×#4111yescharacteristic
208C8×C172−1+411yescharacteristic
209#3396—171no—
210#3380D1711yescharacteristic, complemented
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—42no—
225C22×C17—81no—
226C22×C17—81no—
227C22×C17C22×D811yescharacteristic
228C2×D17—81no—
229C2×D17—81no—
230C2×D17—81no—
231C2×D17—81no—
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—81no—
243C4×C17#54811yescharacteristic
244C4×C17#57711yescharacteristic
245Dic17—81no—
246Dic17—81no—
247#559—341no—
248#554—21no—
249C2×SD32—171no—
250C2×D16—171no—
251C2×D16—171no—
252#500C2×D1711yescharacteristic
253#499C2×D1711yescharacteristic
254#499C2×D1711yescharacteristic
255#495—171no—
256#495—171no—
257#493—171no—
258#478—21no—
259#478—21no—
260#476—21no—
261#463—341no—
262#463—341no—
263#460—341no—
264C8×Q8C2×D1711yescharacteristic
265C4×Q16—171no—
266C4×D8—171no—
267C4×D8—171no—
268C4×D8C2×D1711yescharacteristic
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—82no—
291C2×C17#335811yescharacteristic
292C2×C17#341411yescharacteristic
293C2×C17#341511yescharacteristic
294D17—161no—
295D17—161no—
296C2×Q16—171no—
297C2×SD16—341no—
298C2×SD16—341no—
299C2×D8—171no—
300C2×D8—171no—
301C2×D8—341no—
302C2×D8C22×D1711yescharacteristic
303C4⋊Q8—21no—
304#127—341no—
305#125—21no—
306#125—21no—
307#124—341no—
308#124—341no—
309#124—681no—
310#123—681no—
311#123—681no—
312C22⋊Q8—41no—
313C22⋊Q8—41no—
314C22⋊Q8—41no—
315C4×Q8—341no—
316C4×Q8C22⋊D1711yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—341no—
321C4×D4—341no—
322C4×D4—681no—
323C2×C4⋊C4—41no—
324SD32—342no—
325D16—342no—
326D16—342no—
327C2×C16—171no—
328C2×C16—171no—
329C2×C16—171no—
330C2×C16—171no—
331#107—21no—
332#107—171no—
333#107C22×D1711yescharacteristic
334#107C22×D1711yescharacteristic
335#107C22×D1711yescharacteristic
336#106—21no—
337#106—21no—
338C4⋊C8C22⋊D1711yescharacteristic
339C4⋊C8C22⋊D1711yescharacteristic
340C4⋊C8C22⋊D1711yescharacteristic
341#103—341no—
342#102—21no—
343#102—21no—
344#102—21no—
345#102—341no—
346#102—341no—
347C4×C8C22×D1711yescharacteristic
348C4×C8C22×D1711yescharacteristic
349C4×C8C22×D1711yescharacteristic
350C17#3393711yescharacteristic, complemented, Sylow
351C2×Q8—41no—
352C2×Q8—341no—
353C2×Q8#6322811yescharacteristic
354C2×D4—21no—
355C2×D4—341no—
356C2×D4—341no—
357C2×D4—681no—
358C2×D4—681no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—681no—
363C22×C4—681no—
364Q16—341no—
365Q16—341no—
366SD16—1361no—
367SD16—1361no—
368D8—21no—
369D8—341no—
370D8—341no—
371D8—341no—
372D8—341no—
373D8—1361no—
374D8#6325612yes—
375C2×C8C2×C22⋊D1711yescharacteristic
376C2×C8C2×C22⋊D1711yescharacteristic
377C2×C8C2×C22⋊D1711yescharacteristic
378C2×C8C23×D1711yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—341no—
388C4⋊C4—681no—
389C4⋊C4#6322811yescharacteristic
390C4⋊C4#6322811yescharacteristic
391C4⋊C4#6322811yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—681no—
396C22⋊C4—681no—
397C22⋊C4—681no—
398C22⋊C4—681no—
399C22⋊C4—681no—
400C22⋊C4—681no—
401C42—681no—
402C42C2×C22⋊D1711yescharacteristic
403C42C2×C22⋊D1711yescharacteristic
404C42C2×C22⋊D1711yescharacteristic
405C16—341no—
406C16—341no—
407C16—341no—
408C16—341no—
409C23—41no—
410C23—681no—
411C23—681no—
412Q8—41no—
413Q8—161no—
414Q8—681no—
415Q8—681no—
416D4—22no—
417D4—41no—
418D4—2721no—
419D4—681no—
420D4—681no—
421D4—681no—
422D4—681no—
423D4—1362no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—161no—
429C2×C4—161no—
430C2×C4—2721no—
431C2×C4—2721no—
432C2×C4—681no—
433C2×C4—681no—
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—
444C8C2×#6325611yescharacteristic
445C8#1058769411yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—1361no—
450C22—1361no—
451C22—1361no—
452C22—1361no—
453C22—1361no—
454C22—1361no—
455C22C22×#6322811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—1361no—
466C4—1361no—
467C4#1176347011yescharacteristic
468C4#1176361711yescharacteristic
469C2—82no—
470C2—2721no—
471C2—2721no—
472C2#1454141911yescharacteristic
473C2#1454191811yescharacteristic
474C2#1454192311yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3380C2
socleC22×C17C22×D8
prime radical#14530819C2
hypercenter#3380D17
hypocenterC17#33937
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #14541797C2semidirect
2. #14531027C2semidirect
3. #14531023C2semidirect
4. #14531018C2semidirect
5. #14530945C2semidirect
6. #14530938C2semidirect
7. #14530918C2semidirect
8. #14530839C2semidirect
9. #14530839C2semidirect
11. #14530693C2semidirect
12. #14530658C2semidirect
13. #14530648C2semidirect
14. C4×#10587497C2semidirect
15. C17×#3380C2semidirect
210. #3380D17semidirect
350. C17#33937semidirect

Maximal subgroups

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

subgroupindex
#145417972
#145310272
#145310232
#145310182
#145309452
#145309382
#145309182
#145308392
#145308192
#145306932
#145306582
#145306482
C4×#105874972
C17×#33802
#3393717