Finite Group Databasebeta

← #14540984

Subgroups — #14540984

Order 2176.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763512C211yesmaximal, characteristic, complemented
2#11763452C211yesmaximal, characteristic, complemented
3#11763149C211yesmaximal, characteristic, complemented
4#11763121C211yesmaximal, characteristic, complemented
5#11763106C211yesmaximal, characteristic, complemented
6#11763061C211yesmaximal, characteristic, complemented
7#11763058C211yesmaximal, characteristic, complemented
8#11763021C211yesmaximal, characteristic, complemented
9#11762957C211yesmaximal, characteristic, complemented
10#11762944C211yesmaximal, characteristic, complemented
11C4×D136C211yesmaximal, characteristic, complemented
12#11762888C211yesmaximal, characteristic, complemented
13#11762812C211yesmaximal, characteristic, complemented
14#11762809C211yesmaximal, characteristic, complemented
15C17×#488C211yesmaximal, characteristic, complemented
16C2×#63256C2211yescharacteristic
17C2×D4×D17C2211yescharacteristic
18C17×#125C2211yescharacteristic, complemented
19C17×#124C2211yescharacteristic
20#10587632C2211yescharacteristic
21C2×#63230C2211yescharacteristic, complemented
22#10587624C2211yescharacteristic
23C2×#63228C2211yescharacteristic
24C2×D136C2211yescharacteristic
25C2×#63218C2211yescharacteristic
26C2×#63218C2211yescharacteristic, complemented
27#10587584—21no—
28#10587581—21no—
29#10587581C2211yescharacteristic
30#10587581C2211yescharacteristic, complemented
31#10587580—21no—
32#10587579—21no—
33#10587578C2211yescharacteristic
34C4⋊C4×D17C2211yescharacteristic, complemented
35#10587570—21no—
36#10587569—21no—
37#10587568—21no—
38C22⋊C4×D17—21no—
39C4×D68C2211yescharacteristic
40C4×D68C2211yescharacteristic
41C4×D68C2211yescharacteristic, complemented
42C17×#103C2211yescharacteristic, complemented
43C17×#103C2211yescharacteristic, complemented
44C17×#102C2211yescharacteristic
45C17×#102C2211yescharacteristic
46C4×C8×C17C2211yescharacteristic, complemented
47#10587506C2211yescharacteristic, complemented
48#10587503C2211yescharacteristic
49#10587492C2211yescharacteristic
50#10587492C2211yescharacteristic, complemented
51#10587491C2211yescharacteristic
52#10587491C2211yescharacteristic, complemented
53#10587489C2211yescharacteristic, complemented
54#10587480C2211yescharacteristic
55#10587480C2211yescharacteristic
56#10587479C2211yescharacteristic, complemented
57#10587478C2211yescharacteristic, complemented
58C4⋊#3622C2211yescharacteristic, complemented
59C23×D17—21no—
60C2×Q8×C17C2311yescharacteristic
61C2×D4×C17C2311yescharacteristic
62C2×C22⋊D17—21no—
63C2×C22⋊D17—21no—
64#63256—22no—
65#63256—41no—
66D4×D17—22no—
67D4×D17—41no—
68C2×D68—21no—
69C2×D68—21no—
70C2×D68—21no—
71C2×D68D411yescharacteristic
72C2×D68C2311yescharacteristic
73C2×D68C2311yescharacteristic
74C2×C4×D17—21no—
75C2×C4×D17—21no—
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17C2311yescharacteristic
79C2×C4×D17C2311yescharacteristic
80C2×C8×C17C2311yescharacteristic
81C2×C8×C17C2311yescharacteristic
82C4⋊C4×C17—21no—
83C4⋊C4×C17—21no—
84C4⋊C4×C17C2311yescharacteristic
85C4⋊C4×C17C2311yescharacteristic
86C22⋊C4×C17—21no—
87C22⋊C4×C17—21no—
88C42×C17C2311yescharacteristic
89C22⋊Dic17—21no—
90#63230—41no—
91#63228—41no—
92#63227—21no—
93#63227—21no—
94#63227—21no—
95#63227—21no—
96#63227—21no—
97#63227—21no—
98#63227D411yescharacteristic
99#63227D411yescharacteristic
100C4⋊Dic17D411yescharacteristic
101C4⋊Dic17C2311yescharacteristic
102C4⋊Dic17C2311yescharacteristic
103#63225—21no—
104#63225—21no—
105C4×Dic17—21no—
106C2×#3622C2311yescharacteristic
107C2×#3622C2311yescharacteristic
108D136—22no—
109#63218—41no—
110#63218—41no—
111C23×C17—21no—
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—42no—
115C22×D17—42no—
116C22×D17—81no—
117C22×D17C2×D411yescharacteristic
118C22×D17C2×D411yescharacteristic
119Q8×C17—21no—
120Q8×C17—21no—
121D4×C17—21no—
122D4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17C2×D411yescharacteristic
127C2×C4×C17C2×D411yescharacteristic
128C2×C4×C17C2411yescharacteristic
129C22⋊D17—42no—
130C22⋊D17—81no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17C2×D411yescharacteristic
134C2×Dic17C2×D411yescharacteristic
135D68—21no—
136D68—21no—
137D68—21no—
138D68—41no—
139D68—42no—
140D68—42no—
141D68—81no—
142D68#4112yes—
143C4×D17—21no—
144C4×D17—21no—
145C4×D17—21no—
146C4×D17—21no—
147C4×D17—42no—
148C4×D17—81no—
149C4×D17—81no—
150C4×D17—81no—
151C8×C17—21no—
152C8×C17—21no—
153#3622—21no—
154#3622—21no—
155#3322—171nomaximal, Sylow
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17C22×D411yescharacteristic
160C2×D17—21no—
161C2×D17—21no—
162C2×D17—22no—
163C2×D17—21no—
164C2×D17—21no—
165C2×D17—21no—
166C2×D17—21no—
167C2×D17—41no—
168C2×D17—41no—
169C2×D17—41no—
170C2×D17—41no—
171C2×D17—41no—
172C2×D17—84no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—41no—
176C4×C17—41no—
177C4×C17—41no—
178C4×C17C2×#4111yescharacteristic
179C4×C17H(5,𝔽2)11yescharacteristic
180Dic17—21no—
181Dic17—21no—
182Dic17—41no—
183Dic17—41no—
184#553—171no—
185#546—171no—
186#488D1711yescharacteristic, complemented
187#485—171no—
188#480—171no—
189#478—171no—
190#469—171no—
191#468—171no—
192#463—171no—
193#449—171no—
194#447—171no—
195C4×D8—171no—
196#436—171no—
197#418—171no—
198#417—171no—
199C2×C17—81no—
200C2×C17#54611yescharacteristic
201C2×C17#57511yescharacteristic
202C2×C17#57611yescharacteristic
203D17—41no—
204D17—41no—
205D17—42no—
206D17—81no—
207C2×#41—171no—
208C22×D4—171no—
209C2×SD16—171no—
210C2×D8—171no—
211C2×D8—171no—
212C2×M16—171no—
213C2×M16—171no—
214#126—341no—
215#125C2×D1711yescharacteristic, complemented
216#124C2×D1711yescharacteristic
217#123—341no—
218#123—341no—
219C22⋊Q8—171no—
220#121—171no—
221#121—171no—
222#121—171no—
223#121—341no—
224#121—341no—
225#120—341no—
226C4×D4—171no—
227C4×D4—171no—
228C4×D4—171no—
229C4×D4—341no—
230#117—171no—
231C2×C4⋊C4—171no—
232C2×C22⋊C4—341no—
233#107—171no—
234#107—171no—
235#106—171no—
236C4⋊C8—171no—
237#103—171no—
238#103C2×D1711yescharacteristic, complemented
239#103C2×D1711yescharacteristic, complemented
240#102—171no—
241#102—171no—
242#102—171no—
243#102—171no—
244#102—171no—
245#102C2×D1711yescharacteristic
246#102C2×D1711yescharacteristic
247C22⋊C8—171no—
248C22⋊C8—171no—
249C4×C8C2×D1711yescharacteristic, complemented
250C17#332211yescharacteristic, complemented, Sylow
251C24—341no—
252#41—342no—
253#41—681no—
254C2×Q8C22×D1711yescharacteristic
255C2×D4—171no—
256C2×D4—171no—
257C2×D4—171no—
258C2×D4—341no—
259C2×D4—341no—
260C2×D4—341no—
261C2×D4—341no—
262C2×D4—342no—
263C2×D4—341no—
264C2×D4—681no—
265C2×D4C22×D1711yescharacteristic
266C22×C4—171no—
267C22×C4—171no—
268C22×C4—341no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—341no—
272SD16—681no—
273D8—342no—
274D8—681no—
275M16—681no—
276M16—681no—
277C2×C8—171no—
278C2×C8—171no—
279C2×C8C22×D1711yescharacteristic
280C2×C8C22×D1711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—171no—
284C4⋊C4—171no—
285C4⋊C4—171no—
286C4⋊C4—341no—
287C4⋊C4—341no—
288C4⋊C4C22×D1711yescharacteristic
289C4⋊C4C22×D1711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—171no—
293C22⋊C4—171no—
294C22⋊C4—341no—
295C22⋊C4—341no—
296C22⋊C4—341no—
297C22⋊C4—341no—
298C22⋊C4—341no—
299C22⋊C4—341no—
300C22⋊C4—341no—
301C42—341no—
302C42C22×D1711yescharacteristic
303C23—21no—
304C23—171no—
305C23—171no—
306C23—341no—
307C23—341no—
308C23—682no—
309C23—682no—
310C23—1361no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—172no—
316D4—341no—
317D4—341no—
318D4—341no—
319D4—681no—
320D4—682no—
321D4—682no—
322D4—682no—
323D4—1361no—
324D4—1361no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—171no—
329C2×C4—171no—
330C2×C4—341no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—341no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—682no—
337C2×C4—1361no—
338C2×C4—1361no—
339C2×C4—1361no—
340C2×C4D4×D1711yescharacteristic
341C2×C4D4×D1711yescharacteristic
342C2×C4C23×D1711yescharacteristic
343C8—21no—
344C8—21no—
345C8—341no—
346C8—341no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—341no—
351C22—341no—
352C22—341no—
353C22—341no—
354C22—341no—
355C22—341no—
356C22—342no—
357C22—681no—
358C22—681no—
359C22—681no—
360C22—681no—
361C22—681no—
362C22—1364no—
363C22C2×D4×D1711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—341no—
370C4—341no—
371C4—681no—
372C4—681no—
373C4#41×D1711yescharacteristic
374C4#1058769611yescharacteristic
375C2—81no—
376C2—681no—
377C2—681no—
378C2—682no—
379C2—1361no—
380C2#1176345211yescharacteristic
381C2#1176360611yescharacteristic
382C2#1176361111yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#488C2
socleC22×C17C22×D4
hypercenter#488D17
hypocenterC17#3322
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11763512C2semidirect
2. #11763452C2semidirect
3. #11763149C2semidirect
4. #11763121C2semidirect
5. #11763106C2semidirect
6. #11763061C2semidirect
7. #11763058C2semidirect
8. #11763021C2semidirect
9. #11762957C2semidirect
10. #11762944C2semidirect
11. C4×D136C2semidirect
12. #11762888C2semidirect
13. #11762812C2semidirect
14. #11762809C2semidirect
15. C17×#488C2semidirect
18. C17×#125C22semidirect
21. C2×#63230C22semidirect
26. C2×#63218C22semidirect
30. #10587581C22semidirect
34. C4⋊C4×D17C22semidirect
41. C4×D68C22semidirect
42. C17×#103C22semidirect
43. C17×#103C22semidirect
46. C4×C8×C17C22semidirect
47. #10587506C22semidirect
50. #10587492C22semidirect
52. #10587491C22semidirect
53. #10587489C22semidirect
56. #10587479C22semidirect
57. #10587478C22semidirect
58. C4⋊#3622C22semidirect
186. #488D17semidirect
215. #125C2×D17semidirect
238. #103C2×D17semidirect
239. #103C2×D17semidirect
249. C4×C8C2×D17semidirect
250. C17#3322semidirect

Maximal subgroups

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

subgroupindex
#117635122
#117634522
#117631492
#117631212
#117631062
#117630612
#117630582
#117630212
#117629572
#117629442
C4×D1362
#117628882
#117628122
#117628092
C17×#4882
#332217