Finite Group Databasebeta

← #17192096

Subgroups — #17192096

Order 4352.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14541676C211yesmaximal, characteristic, complemented
2#14531025C211yesmaximal, characteristic
3#14531020C211yesmaximal, characteristic, complemented
4#14531015C211yesmaximal, characteristic, complemented
5#14530948C211yesmaximal, characteristic, complemented
6#14530941C211yesmaximal, characteristic, complemented
7#14530931C211yesmaximal, characteristic, complemented
8#14530843C211yesmaximal, characteristic, complemented
9#14530843C211yesmaximal, characteristic, complemented
10#14530821C211yesmaximal, characteristic
11#14530693C211yesmaximal, characteristic, complemented
12#14530653C211yesmaximal, characteristic, complemented
13#14530648C211yesmaximal, characteristic, complemented
14C4×#10587498C211yesmaximal, characteristic, complemented
15C17×#3396C211yesmaximal, characteristic
16#11763537—21no—
17C2×#10587500C2211yescharacteristic
18C2×#10587498C2211yescharacteristic
19C2×#10587498C2211yescharacteristic
20#11763214C2211yescharacteristic
21#11763211C2211yescharacteristic
22#11763211C2211yescharacteristic
23#11763117—21no—
24#11763117—21no—
25#11763095—21no—
26C4×Dic68C2211yescharacteristic
27C4×Dic68C2211yescharacteristic
28C4×Dic68C2211yescharacteristic
29#11762636C2211yescharacteristic
30#11762636C2211yescharacteristic
31#11762634C2211yescharacteristic
32C4⋊#63214C2211yescharacteristic
33C4⋊#63214C2211yescharacteristic
34C4⋊#63214C2211yescharacteristic
35#11762613C2211yescharacteristic
36#11762613C2211yescharacteristic
37#11762613C2211yescharacteristic
38#11762612C2211yescharacteristic
39#11762610C2211yescharacteristic
40#11762610C2211yescharacteristic
41#11762610C2211yescharacteristic
42#11762610C2211yescharacteristic
43#11762610C2211yescharacteristic
44#11762610C2211yescharacteristic
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#10587630—41no—
77C2×Dic68C2311yescharacteristic
78#10587575—41no—
79#10587575—41no—
80#10587573—41no—
81#10587556—21no—
82#10587556—21no—
83#10587555—21no—
84C4×Dic34—21no—
85C4×Dic34—21no—
86C4×Dic34—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#10587500—22no—
98#10587498—22no—
99#10587498—22no—
100#10587489—21no—
101#10587489C2311yescharacteristic
102#10587489C2311yescharacteristic
103#10587489C2311yescharacteristic
104#10587488—21no—
105#10587488—21no—
106#10587487—21no—
107#10587487—21no—
108#10587487—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×Dic34—21no—
122C2×Dic34—41no—
123Q16×C17—21no—
124Q16×C17—21no—
125SD16×C17—81no—
126SD16×C17—81no—
127D8×C17—21no—
128D8×C17—21no—
129D8×C17—21no—
130D8×C17—21no—
131D8×C17—81no—
132C2×C8×C17C2×D411yescharacteristic
133C2×C8×C17C2×D411yescharacteristic
134C2×C8×C17C2×D411yescharacteristic
135C2×C8×C17C2411yescharacteristic
136C4⋊C4×C17—21no—
137C4⋊C4×C17—41no—
138C4⋊C4×C17D811yescharacteristic
139C4⋊C4×C17D811yescharacteristic
140C4⋊C4×C17D811yescharacteristic
141C22⋊C4×C17—41no—
142C22⋊C4×C17—41no—
143C22⋊C4×C17—41no—
144C22⋊C4×C17—41no—
145C22⋊C4×C17—41no—
146C22⋊C4×C17—41no—
147C42×C17—41no—
148C42×C17C2×D411yescharacteristic
149C42×C17C2×D411yescharacteristic
150C42×C17C2×D411yescharacteristic
151C4⋊Dic17—21no—
152C4⋊Dic17—21no—
153C4⋊Dic17—21no—
154C4⋊Dic17—41no—
155#63225—41no—
156#63225—41no—
157#63225—41no—
158#63225—41no—
159#63225—41no—
160#63225—41no—
161#63225—41no—
162C4×Dic17—41no—
163C4×Dic17—41no—
164C4×Dic17—41no—
165Dic68—21no—
166Dic68#4112yes—
167#63214—21no—
168#63214—21no—
169#63214—21no—
170#63214—21no—
171#33938—171nomaximal, Sylow
172C23×C17—41no—
173C23×C17—41no—
174Q8×C17—41no—
175Q8×C17—41no—
176Q8×C17—41no—
177D4×C17—41no—
178D4×C17—41no—
179D4×C17—41no—
180D4×C17—41no—
181D4×C17—82no—
182D4×C17—161no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—161no—
186C2×C4×C17—161no—
187C2×C4×C17C2×D811yescharacteristic
188C2×C4×C17C2×D811yescharacteristic
189C2×C4×C17C2×D811yescharacteristic
190C2×C4×C17C2×D811yescharacteristic
191C2×C4×C17C2×D811yescharacteristic
192C2×C4×C17C2×D811yescharacteristic
193C2×C4×C17C22×D411yescharacteristic
194C2×Dic17—41no—
195C2×Dic17—41no—
196C2×Dic17—41no—
197C2×Dic17—41no—
198Dic34—22no—
199Dic34—41no—
200Dic34—82no—
201C8×C17—21no—
202C8×C17—21no—
203C8×C17—21no—
204C8×C17C2×#4111yescharacteristic
205C8×C172−1+411yescharacteristic
206#3396D1711yescharacteristic
207#3383—171no—
208#2244—171no—
209#2243—171no—
210#2242—171no—
211#2229—171no—
212#2228—171no—
213#2226—171no—
214#2211—171no—
215#2211—171no—
216#2207—171no—
217#2183—171no—
218#2176—171no—
219#2175—171no—
220C4×SD32—171no—
221C22×C17—81no—
222C22×C17—81no—
223C22×C17—81no—
224C22×C17—81no—
225C22×C17—81no—
226C22×C17—81no—
227C22×C17C22×D811yescharacteristic
228C4×C17—21no—
229C4×C17—21no—
230C4×C17—21no—
231C4×C17—21no—
232C4×C17—21no—
233C4×C17—21no—
234C4×C17—81no—
235C4×C17—81no—
236C4×C17#54811yescharacteristic
237C4×C17#57711yescharacteristic
238Dic17—42no—
239Dic17—81no—
240Dic17—81no—
241Dic17—81no—
242#559—21no—
243#557—341no—
244C2×Q32—171no—
245C2×SD32—171no—
246C2×SD32—171no—
247#500—171no—
248#499—171no—
249#499—171no—
250#495C2×D1711yescharacteristic
251#495C2×D1711yescharacteristic
252#493C2×D1711yescharacteristic
253#479—341no—
254#479—341no—
255#475—341no—
256#463—21no—
257#463—21no—
258#460—21no—
259C8×Q8C2×D1711yescharacteristic
260C4×Q16—171no—
261C4×Q16—171no—
262C4×Q16—171no—
263C4×Q16C2×D1711yescharacteristic
264C4×D8C2×D1711yescharacteristic
265C4×D8C2×D1711yescharacteristic
266#367—171no—
267#367—171no—
268#366—171no—
269C4⋊C16—171no—
270C4⋊C16—171no—
271C4⋊C16—171no—
272#358—171no—
273#358—171no—
274#358—171no—
275#358—171no—
276#357—171no—
277#357—171no—
278#357—171no—
279#357—171no—
280#357—171no—
281#357—171no—
282#346—171no—
283#346—171no—
284C4×C16—171no—
285C2×C17—161no—
286C2×C17—161no—
287C2×C17#335811yescharacteristic
288C2×C17#341411yescharacteristic
289C2×C17#341611yescharacteristic
290C2×Q16—171no—
291C2×Q16C22×D1711yescharacteristic
292C2×SD16—21no—
293C2×SD16—21no—
294C2×D8—21no—
295C2×D8C22×D1711yescharacteristic
296C2×D8C22×D1711yescharacteristic
297C4⋊Q8—341no—
298C4⋊Q8—681no—
299#127—21no—
300#125—341no—
301#125—341no—
302#125—681no—
303#125—681no—
304#124—21no—
305#124—21no—
306#124—41no—
307#123—41no—
308#123—41no—
309C4×Q8—21no—
310C4×Q8—341no—
311C4×Q8—341no—
312C4×Q8—341no—
313C4×Q8—681no—
314C4×Q8C22⋊D1711yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—41no—
318Q32—342no—
319SD32—342no—
320SD32—342no—
321C2×C16—171no—
322C2×C16—171no—
323C2×C16—171no—
324C2×C16—171no—
325#107—171no—
326#107—171no—
327#107—171no—
328#107—341no—
329#107C22×D1711yescharacteristic
330#106—341no—
331#106—341no—
332C4⋊C8C22⋊D1711yescharacteristic
333C4⋊C8C22⋊D1711yescharacteristic
334C4⋊C8C22⋊D1711yescharacteristic
335#103—21no—
336#103—341no—
337#103—341no—
338#103—341no—
339#102—21no—
340#102—21no—
341C4×C8C22×D1711yescharacteristic
342C4×C8C22×D1711yescharacteristic
343C4×C8C22×D1711yescharacteristic
344C17#3393811yescharacteristic, complemented, Sylow
345C2×Q8—21no—
346C2×Q8—341no—
347C2×Q8—681no—
348C2×Q8#6322811yescharacteristic
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—41no—
354C22×C4—41no—
355Q16—21no—
356Q16—21no—
357Q16—172no—
358Q16—341no—
359SD16—81no—
360SD16—81no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—21no—
365D8—81no—
366C2×C8C2×C22⋊D1711yescharacteristic
367C2×C8C2×C22⋊D1711yescharacteristic
368C2×C8C2×C22⋊D1711yescharacteristic
369C2×C8C23×D1711yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—341no—
373C4⋊C4—341no—
374C4⋊C4—341no—
375C4⋊C4—681no—
376C4⋊C4—681no—
377C4⋊C4—681no—
378C4⋊C4—681no—
379C4⋊C4—681no—
380C4⋊C4—681no—
381C4⋊C4—681no—
382C4⋊C4—681no—
383C4⋊C4#6322811yescharacteristic
384C4⋊C4#6322811yescharacteristic
385C4⋊C4#6322811yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C42—41no—
393C42—681no—
394C42—681no—
395C42—681no—
396C42C2×C22⋊D1711yescharacteristic
397C42C2×C22⋊D1711yescharacteristic
398C42C2×C22⋊D1711yescharacteristic
399C16—341no—
400C16—341no—
401C16—341no—
402C16—341no—
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—342no—
409Q8—681no—
410Q8—1362no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—161no—
420C2×C4—161no—
421C2×C4—681no—
422C2×C4—681no—
423C2×C4—681no—
424C2×C4—681no—
425C2×C4C2×#6322811yescharacteristic
426C2×C4C2×#6322811yescharacteristic
427C2×C4C2×#6322811yescharacteristic
428C2×C4C2×#6322811yescharacteristic
429C2×C4C2×#6322811yescharacteristic
430C2×C4C2×#6322811yescharacteristic
431C2×C4C22×C22⋊D1711yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#41×D1711yescharacteristic
436C8#1058769711yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×#6322811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—682no—
453C4—1361no—
454C4—1361no—
455C4—1361no—
456C4#1176346611yescharacteristic
457C4#1176362011yescharacteristic
458C2—161no—
459C2—161no—
460C2#1454141511yescharacteristic
461C2#1454191811yescharacteristic
462C2#1454193111yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3396C2
socleC22×C17C22×D8
prime radicalC17×#493C22
hypercenter#3396D17
hypocenterC17#33938
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. #14541676C2semidirect
3. #14531020C2semidirect
4. #14531015C2semidirect
5. #14530948C2semidirect
6. #14530941C2semidirect
7. #14530931C2semidirect
8. #14530843C2semidirect
9. #14530843C2semidirect
11. #14530693C2semidirect
12. #14530653C2semidirect
13. #14530648C2semidirect
14. C4×#10587498C2semidirect
344. C17#33938semidirect

Maximal subgroups

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

subgroupindex
#145416762
#145310252
#145310202
#145310152
#145309482
#145309412
#145309312
#145308432
#145308212
#145306932
#145306532
#145306482
C4×#105874982
C17×#33962
#3393817