Finite Group Databasebeta

← #14540593

Subgroups — #14540593

Order 2176.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763460C211yesmaximal, characteristic, complemented
2D4×C22⋊D17C211yesmaximal, characteristic, complemented
3#11763154C211yesmaximal, characteristic, complemented
4#11763122C211yesmaximal, characteristic, complemented
5#11763121C211yesmaximal, characteristic, complemented
6#11763087C211yesmaximal, characteristic, complemented
7#11763045C211yesmaximal, characteristic, complemented
8#11763044C211yesmaximal, characteristic, complemented
9#11763003C211yesmaximal, characteristic, complemented
10#11762944C211yesmaximal, characteristic, complemented
11#11762943C211yesmaximal, characteristic, complemented
12#11762889C211yesmaximal, characteristic, complemented
13C8×C22⋊D17C211yesmaximal, characteristic, complemented
14#102×D17C211yesmaximal, characteristic, complemented
15C2×C17×#102C211yesmaximal, characteristic, complemented
16C22×D4×C17C2211yescharacteristic
17C22×C22⋊D17—21no—
18C2×D4×D17C2211yescharacteristic
19C2×#63252—21no—
20C22×C8×C17C2211yescharacteristic, complemented
21C2×C4⋊C4×C17C2211yescharacteristic, complemented
22#10587639—21no—
23#10587626C2211yescharacteristic
24#10587625—21no—
25#10587624C2211yescharacteristic
26#10587623—21no—
27D4×Dic17C2211yescharacteristic
28C2×#63228C2211yescharacteristic
29C2×#63228C2211yescharacteristic, complemented
30#10587616C2211yescharacteristic
31#10587616C2211yescharacteristic, complemented
32#10587615—21no—
33C4×C22⋊D17C2211yescharacteristic
34C2×D136C2211yescharacteristic, complemented
35C2×C8×D17C2211yescharacteristic, complemented
36#10587582—21no—
37#10587581C2211yescharacteristic, complemented
38#10587580—21no—
39#10587579C2211yescharacteristic, complemented
40C4⋊C4×D17C2211yescharacteristic, complemented
41#10587574C2211yescharacteristic, complemented
42C17×#102C2211yescharacteristic
43C17×#102C2211yescharacteristic
44C17×#102C2211yescharacteristic, complemented
45C17×#102C2211yescharacteristic, complemented
46#10587503C2211yescharacteristic
47#10587503C2211yescharacteristic, complemented
48C22⋊#3622C2211yescharacteristic, complemented
49#10587492C2211yescharacteristic, complemented
50#10587492C2211yescharacteristic, complemented
51#10587491C2211yescharacteristic, complemented
52#10587489C2211yescharacteristic, complemented
53#10587485C2211yescharacteristic, complemented
54C8×Dic17C2211yescharacteristic, complemented
55#10587480C2211yescharacteristic, complemented
56#10587480C2211yescharacteristic, complemented
57#10587478C2211yescharacteristic, complemented
58#10587478C2211yescharacteristic, complemented
59C24×C17—21no—
60C23×D17—21no—
61C2×D4×C17—22no—
62C2×D4×C17—21no—
63C2×D4×C17—41no—
64C2×D4×C17C2311yescharacteristic
65C2×D4×C17C2311yescharacteristic
66C22×C4×C17—21no—
67C22×C4×C17C2311yescharacteristic
68C2×C22⋊D17—21no—
69C2×C22⋊D17—21no—
70C2×C22⋊D17—21no—
71C2×C22⋊D17—21no—
72C2×C22⋊D17—21no—
73C2×C22⋊D17—21no—
74C2×C22⋊D17—44no—
75C2×C22⋊D17D411yescharacteristic
76C22×Dic17—21no—
77D4×D17—22no—
78D4×D17—41no—
79#63252—44no—
80C2×D68—21no—
81C2×D68C2311yescharacteristic
82C2×D68C2311yescharacteristic
83C2×C4×D17—21no—
84C2×C4×D17—21no—
85C2×C4×D17C2311yescharacteristic
86C2×Dic34—21no—
87C2×C8×C17—41no—
88C2×C8×C17C2311yescharacteristic
89C2×C8×C17C2311yescharacteristic
90C4⋊C4×C17—21no—
91C4⋊C4×C17C2311yescharacteristic
92C4⋊C4×C17C2311yescharacteristic
93C22⋊Dic17—21no—
94C22⋊Dic17—21no—
95C22⋊Dic17D411yescharacteristic
96#63228—22no—
97#63228—41no—
98#63227—21no—
99#63227—21no—
100#63227—21no—
101#63227—21no—
102#63227D411yescharacteristic
103C4⋊Dic17C2311yescharacteristic
104C4⋊Dic17C2311yescharacteristic
105#63225—21no—
106#63225—21no—
107#63225D411yescharacteristic
108C4×Dic17C2311yescharacteristic
109C2×#3622C2311yescharacteristic
110C2×#3622C2311yescharacteristic
111D136—41no—
112C8×D17—41no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—42no—
116C23×C17—42no—
117C23×C17—81no—
118C23×C17C2×D411yescharacteristic
119C22×D17—21no—
120C22×D17—21no—
121C22×D17—42no—
122C22×D17—42no—
123C22×D17—81no—
124C22×D17C2×D411yescharacteristic
125D4×C17—21no—
126D4×C17—21no—
127D4×C17—21no—
128D4×C17—42no—
129D4×C17#4112yescomplemented
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—42no—
135C2×C4×C17C2×D411yescharacteristic
136C2×C4×C17C2411yescharacteristic
137C22⋊D17—42no—
138C22⋊D17—42no—
139C22⋊D17—42no—
140C22⋊D17—42no—
141C22⋊D17—42no—
142C22⋊D17—81no—
143C22⋊D17D814yescomplemented
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—42no—
147C2×Dic17C2×D411yescharacteristic
148C2×Dic17C2×D411yescharacteristic
149C2×Dic17C2×D411yescharacteristic
150D68—21no—
151D68—21no—
152D68—21no—
153D68—21no—
154D68—42no—
155C4×D17—21no—
156C4×D17—21no—
157C4×D17—42no—
158C4×D17—42no—
159Dic34—42no—
160C8×C17—21no—
161C8×C17—21no—
162#3622—21no—
163#3622—21no—
164#3294—171nomaximal, Sylow
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—22no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—84no—
174C22×C17C2×D812yes—
175C22×C17C22×D411yescharacteristic
176C2×D17—21no—
177C2×D17—21no—
178C2×D17—41no—
179C2×D17—41no—
180C2×D17—41no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—41no—
184C2×D17—84no—
185C2×D17C2×D812yes—
186C4×C17—21no—
187C4×C17—41no—
188C4×C17—41no—
189C4×C17C2×#4111yescharacteristic
190C4×C17H(5,𝔽2)11yescharacteristic
191Dic17—21no—
192Dic17—21no—
193Dic17—41no—
194Dic17—41no—
195Dic17C2×D812yes—
196#547—171no—
197D42—171no—
198#486—171no—
199#480—171no—
200#480—171no—
201#474—171no—
202#466—171no—
203#466—171no—
204#459—171no—
205#447—171no—
206#447—171no—
207C4×D8—171no—
208C8×D4—171no—
209C2×#102—171no—
210C2×#102D1711yescharacteristic, complemented
211C2×C17—22no—
212C2×C17—42no—
213C2×C17—81no—
214C2×C17#54611yescharacteristic
215C2×C17C22×D811yescharacteristic
216C2×C17#57711yescharacteristic
217D17—22no—
218D17—81no—
219D17—81no—
220C2×#41—341no—
221C22×D4—171no—
222C22×D4—341no—
223C22×D4C2×D1711yescharacteristic
224C2×D8—171no—
225C2×D8—171no—
226C2×D8—171no—
227C22×C8—171no—
228C22×C8C2×D1711yescharacteristic, complemented
229C4⋊Q8—171no—
230#127—171no—
231#123—341no—
232#123—341no—
233C22⋊Q8—341no—
234#121—171no—
235#121—171no—
236#121—171no—
237#121—171no—
238#121—341no—
239#120—341no—
240#120—341no—
241C4×D4—171no—
242C4×D4—171no—
243C4×D4—171no—
244C2×C4⋊C4—171no—
245C2×C4⋊C4C2×D1711yescharacteristic, complemented
246#107—171no—
247#107—171no—
248#107—171no—
249C4⋊C8—171no—
250#102—171no—
251#102—171no—
252#102—171no—
253#102—171no—
254#102—171no—
255#102—171no—
256#102C2×D1711yescharacteristic
257#102C2×D1711yescharacteristic
258#102C2×D1711yescharacteristic, complemented
259#102C2×D1711yescharacteristic, complemented
260C22⋊C8—171no—
261C22⋊C8—171no—
262C4×C8—171no—
263C17#329411yescharacteristic, complemented, Sylow
264C24—21no—
265C24—341no—
266#41—684no—
267C2×Q8—341no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—171no—
272C2×D4—171no—
273C2×D4—171no—
274C2×D4—341no—
275C2×D4—341no—
276C2×D4—341no—
277C2×D4—341no—
278C2×D4—342no—
279C2×D4—341no—
280C2×D4—341no—
281C2×D4—341no—
282C2×D4—681no—
283C2×D4—684no—
284C2×D4C22×D1711yescharacteristic
285C2×D4C22×D1711yescharacteristic
286C22×C4—21no—
287C22×C4—171no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—341no—
291C22×C4C22×D1711yescharacteristic
292D8—342no—
293D8—681no—
294D8—681no—
295C2×C8—41no—
296C2×C8—171no—
297C2×C8—171no—
298C2×C8—681no—
299C2×C8C22×D1711yescharacteristic
300C2×C8C22×D1711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—171no—
303C4⋊C4—171no—
304C4⋊C4—171no—
305C4⋊C4—341no—
306C4⋊C4—341no—
307C4⋊C4C22×D1711yescharacteristic
308C4⋊C4C22×D1711yescharacteristic
309C22⋊C4—171no—
310C22⋊C4—171no—
311C22⋊C4—341no—
312C22⋊C4—341no—
313C22⋊C4—341no—
314C22⋊C4—341no—
315C22⋊C4—341no—
316C22⋊C4—341no—
317C42—171no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—171no—
324C23—341no—
325C23—341no—
326C23—682no—
327C23—682no—
328C23—1361no—
329C23D4×D1711yescharacteristic
330Q8—682no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—174no—
336D4—341no—
337D4—341no—
338D4—341no—
339D4—341no—
340D4—682no—
341D4—682no—
342D4—682no—
343D4—682no—
344D4—682no—
345D4—682no—
346D4—1361no—
347D4#6325212yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—171no—
354C2×C4—171no—
355C2×C4—171no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—682no—
361C2×C4—682no—
362C2×C4—682no—
363C2×C4D4×D1711yescharacteristic
364C2×C4C23×D1711yescharacteristic
365C8—21no—
366C8—21no—
367C8—341no—
368C8—341no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—172no—
379C22—341no—
380C22—341no—
381C22—681no—
382C22—681no—
383C22—681no—
384C22—681no—
385C22—681no—
386C22—681no—
387C22—1364no—
388C22D8×D1712yes—
389C22C2×D4×D1711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—172no—
394C4—341no—
395C4—341no—
396C4—681no—
397C4—681no—
398C4C2×#6325211yescharacteristic
399C4#1058769111yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—342no—
404C2—1361no—
405C2—1361no—
406C2#1176344911yescharacteristic
407C2C2×D8×D1711yescharacteristic
408C2#1176361511yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC2×C17×#102C2
socleC22×C17C22×D4
hypercenterC2×#102D17
hypocenterC17#3294
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #11763460C2semidirect
2. D4×C22⋊D17C2semidirect
3. #11763154C2semidirect
4. #11763122C2semidirect
5. #11763121C2semidirect
6. #11763087C2semidirect
7. #11763045C2semidirect
8. #11763044C2semidirect
9. #11763003C2semidirect
10. #11762944C2semidirect
11. #11762943C2semidirect
12. #11762889C2semidirect
13. C8×C22⋊D17C2semidirect
14. #102×D17C2semidirect
15. C2×C17×#102C2semidirect
20. C22×C8×C17C22semidirect
21. C2×C4⋊C4×C17C22semidirect
29. C2×#63228C22semidirect
31. #10587616C22semidirect
34. C2×D136C22semidirect
35. C2×C8×D17C22semidirect
37. #10587581C22semidirect
39. #10587579C22semidirect
40. C4⋊C4×D17C22semidirect
41. #10587574C22semidirect
44. C17×#102C22semidirect
45. C17×#102C22semidirect
47. #10587503C22semidirect
48. C22⋊#3622C22semidirect
49. #10587492C22semidirect
50. #10587492C22semidirect
51. #10587491C22semidirect
52. #10587489C22semidirect
53. #10587485C22semidirect
54. C8×Dic17C22semidirect
55. #10587480C22semidirect
56. #10587480C22semidirect
57. #10587478C22semidirect
58. #10587478C22semidirect
129. D4×C17#41semidirect
143. C22⋊D17D8semidirect
210. C2×#102D17semidirect
228. C22×C8C2×D17semidirect
245. C2×C4⋊C4C2×D17semidirect
258. #102C2×D17semidirect
259. #102C2×D17semidirect
263. C17#3294semidirect
347. D4#63252semidirect

Maximal subgroups

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

subgroupindex
#117634602
D4×C22⋊D172
#117631542
#117631222
#117631212
#117630872
#117630452
#117630442
#117630032
#117629442
#117629432
#117628892
C8×C22⋊D172
#102×D172
C2×C17×#1022
#329417