Finite Group Databasebeta

← #14539550

Subgroups — #14539550

Order 2176.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763322C211yesmaximal, characteristic, complemented
2#121×D17C211yesmaximal, characteristic, complemented
3#11763143C211yesmaximal, characteristic, complemented
4#11763135C211yesmaximal, characteristic, complemented
5#11763131C211yesmaximal, characteristic, complemented
6#11763129C211yesmaximal, characteristic, complemented
7#11763045C211yesmaximal, characteristic, complemented
8#11763043C211yesmaximal, characteristic, complemented
9#11763040C211yesmaximal, characteristic, complemented
10#11762958C211yesmaximal, characteristic, complemented
11#11762957C211yesmaximal, characteristic, complemented
12#11762953C211yesmaximal, characteristic, complemented
13#11762944C211yesmaximal, characteristic, complemented
14C2×#10587491C211yesmaximal, characteristic, complemented
15C17×#465C211yesmaximal, characteristic, complemented
16C2×#63256C2211yescharacteristic, complemented
17C2×D4×D17—21no—
18C2×D4×D17C2211yescharacteristic
19C22×C4×D17C2211yescharacteristic
20C2×SD16×C17C2211yescharacteristic, complemented
21C22×C8×C17C2211yescharacteristic, complemented
22C17×C22⋊Q8C2211yescharacteristic, complemented
23C17×#121C2211yescharacteristic
24#10587632C2211yescharacteristic
25C2×#63230C2211yescharacteristic, complemented
26#10587625—21no—
27#10587624C2211yescharacteristic
28C2×#63228C2211yescharacteristic, complemented
29#10587616C2211yescharacteristic
30#10587616C2211yescharacteristic, complemented
31C22×#3622C2211yescharacteristic, complemented
32C2×D136C2211yescharacteristic, complemented
33#10587581C2211yescharacteristic
34#10587581C2211yescharacteristic
35#10587580—21no—
36#10587579—21no—
37#10587578C2211yescharacteristic, complemented
38C4⋊C4×D17C2211yescharacteristic
39#10587570—21no—
40#10587568—21no—
41#10587567—21no—
42C22⋊C4×D17—21no—
43C17×#106C2211yescharacteristic, complemented
44C17×#103C2211yescharacteristic, complemented
45C17×#102C2211yescharacteristic, complemented
46#10587506C2211yescharacteristic, complemented
47#10587503C2211yescharacteristic, complemented
48#10587492C2211yescharacteristic, complemented
49#10587492C2211yescharacteristic, complemented
50#10587491C2211yescharacteristic
51#10587491C2211yescharacteristic
52#10587491C2211yescharacteristic, complemented
53#10587491C2211yescharacteristic, complemented
54#10587489C2211yescharacteristic, complemented
55#10587480C2211yescharacteristic, complemented
56#10587480C2211yescharacteristic, complemented
57#10587479C2211yescharacteristic, complemented
58#10587478C2211yescharacteristic, complemented
59C23×D17—21no—
60C23×D17D411yescharacteristic
61C2×Q8×C17C2311yescharacteristic
62C2×D4×C17—21no—
63C2×D4×C17C2311yescharacteristic
64C22×C4×C17C2311yescharacteristic
65C2×C22⋊D17—21no—
66C2×C22⋊D17—21no—
67C2×C22⋊D17—21no—
68C2×C22⋊D17—21no—
69C22×Dic17D411yescharacteristic
70#63256—41no—
71#63256—41no—
72D4×D17—41no—
73D4×D17—41no—
74D4×D17—44no—
75C2×D68—21no—
76C2×D68—21no—
77C2×D68—21no—
78C2×D68C2311yescharacteristic
79C2×D68C2311yescharacteristic
80C2×C4×D17—21no—
81C2×C4×D17—21no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17D411yescharacteristic
85C2×C4×D17D411yescharacteristic
86C2×C4×D17C2311yescharacteristic
87C2×C4×D17C2311yescharacteristic
88SD16×C17—41no—
89C2×C8×C17—41no—
90C2×C8×C17C2311yescharacteristic
91C2×C8×C17C2311yescharacteristic
92C4⋊C4×C17—21no—
93C4⋊C4×C17C2311yescharacteristic
94C4⋊C4×C17C2311yescharacteristic
95C22⋊C4×C17—21no—
96C22⋊C4×C17—21no—
97C22⋊Dic17—21no—
98#63230—41no—
99#63228—41no—
100#63227—21no—
101#63227—21no—
102#63227—21no—
103#63227—21no—
104#63227—21no—
105#63227—21no—
106C4⋊Dic17C2311yescharacteristic
107C4⋊Dic17C2311yescharacteristic
108#63225—21no—
109#63225—21no—
110C4×Dic17—21no—
111C2×#3622—41no—
112C2×#3622C2311yescharacteristic
113C2×#3622C2311yescharacteristic
114D136—41no—
115C23×C17—21no—
116C23×C17C2×D411yescharacteristic
117C22×D17—22no—
118C22×D17—22no—
119C22×D17—21no—
120C22×D17—21no—
121C22×D17—41no—
122C22×D17—42no—
123C22×D17—42no—
124C22×D17—42no—
125C22×D17C2×D411yescharacteristic
126C22×D17C2×D411yescharacteristic
127Q8×C17—21no—
128Q8×C17—21no—
129D4×C17—21no—
130D4×C17—21no—
131D4×C17—42no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17C2×D411yescharacteristic
138C2×C4×C17C2411yescharacteristic
139C22⋊D17—42no—
140C22⋊D17—42no—
141C22⋊D17—42no—
142C22⋊D17—42no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—41no—
146C2×Dic17C2×D411yescharacteristic
147C2×Dic17C2×D411yescharacteristic
148D68—21no—
149D68—21no—
150D68—21no—
151D68—21no—
152D68—42no—
153D68—42no—
154D68—42no—
155C4×D17—21no—
156C4×D17—21no—
157C4×D17—21no—
158C4×D17—21no—
159C4×D17—41no—
160C4×D17—41no—
161C4×D17—42no—
162C4×D17—42no—
163C8×C17—21no—
164C8×C17—21no—
165#3622—21no—
166#3622—21no—
167#3188—171nomaximal, Sylow
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17AGL(1,ℤ/8)12yes—
174C22×C17C22×D411yescharacteristic
175C2×D17—21no—
176C2×D17—21no—
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—44no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—41no—
184C2×D17—41no—
185C2×D17—41no—
186C2×D17—41no—
187C2×D17—84no—
188C2×D17#13512yes—
189C4×C17—21no—
190C4×C17—41no—
191C4×C17—41no—
192C4×C17—41no—
193C4×C17H(5,𝔽2)11yescharacteristic
194C4×C17H(5,𝔽2)11yescharacteristic
195Dic17—21no—
196Dic17—21no—
197Dic17—41no—
198Dic17—41no—
199#525—171no—
200C2×#121—171no—
201#484—171no—
202#482—171no—
203#482—171no—
204#481—171no—
205#466—171no—
206#466—171no—
207#465—171no—
208#465D1711yescharacteristic, complemented
209#450—171no—
210#449—171no—
211#449—171no—
212#447—171no—
213C2×C22⋊C8—171no—
214C2×C17—22no—
215C2×C17—81no—
216C2×C17#53411yescharacteristic
217C2×C17C2×#13511yescharacteristic
218C2×C17C2×AGL(1,ℤ/8)11yescharacteristic
219D17—22no—
220D17—41no—
221D17—81no—
222D17—81no—
223C2×#41—171no—
224C22×D4—171no—
225C22×D4—341no—
226C23×C4—171no—
227C2×SD16—171no—
228C2×SD16C2×D1711yescharacteristic, complemented
229C2×D8—171no—
230C2×D8—171no—
231C22×C8—171no—
232C22×C8C2×D1711yescharacteristic, complemented
233#123—341no—
234C22⋊Q8—171no—
235C22⋊Q8C2×D1711yescharacteristic, complemented
236#121—171no—
237#121—171no—
238#121—171no—
239#121—171no—
240#121—171no—
241#121—341no—
242#121—341no—
243#121C2×D1711yescharacteristic
244#120—341no—
245C4×D4—341no—
246C4×D4—341no—
247#117—171no—
248C2×C4⋊C4—171no—
249C2×C22⋊C4—341no—
250#107—171no—
251#107—171no—
252#106—171no—
253#106C2×D1711yescharacteristic, complemented
254#103—171no—
255#103C2×D1711yescharacteristic, complemented
256#102—171no—
257#102—171no—
258#102—171no—
259#102—171no—
260#102—171no—
261#102C2×D1711yescharacteristic, complemented
262C22⋊C8—171no—
263C22⋊C8—171no—
264C22⋊C8—171no—
265C22⋊C8—171no—
266C17#318811yescharacteristic, complemented, Sylow
267C24—171no—
268C24—341no—
269#41—681no—
270#41—681no—
271C2×Q8C22×D1711yescharacteristic
272C2×D4—21no—
273C2×D4—171no—
274C2×D4—171no—
275C2×D4—341no—
276C2×D4—341no—
277C2×D4—341no—
278C2×D4—341no—
279C2×D4—341no—
280C2×D4—341no—
281C2×D4—341no—
282C2×D4—681no—
283C2×D4—681no—
284C2×D4—684no—
285C2×D4C22×D1711yescharacteristic
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—341no—
292C22×C4—341no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4C22×D1711yescharacteristic
296SD16—41no—
297SD16—681no—
298D8—681no—
299D8—681no—
300C2×C8—41no—
301C2×C8—171no—
302C2×C8—171no—
303C2×C8—681no—
304C2×C8C22×D1711yescharacteristic
305C2×C8C22×D1711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—171no—
308C4⋊C4—171no—
309C4⋊C4—341no—
310C4⋊C4—341no—
311C4⋊C4C22×D1711yescharacteristic
312C4⋊C4C22×D1711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—341no—
316C22⋊C4—341no—
317C22⋊C4—341no—
318C22⋊C4—341no—
319C22⋊C4—341no—
320C22⋊C4—341no—
321C22⋊C4—341no—
322C42—341no—
323C23—21no—
324C23—171no—
325C23—171no—
326C23—342no—
327C23—342no—
328C23—341no—
329C23—341no—
330C23—681no—
331C23—682no—
332C23—682no—
333C23—682no—
334C23D4×D1711yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—341no—
341D4—341no—
342D4—341no—
343D4—341no—
344D4—682no—
345D4—682no—
346D4—682no—
347D4—682no—
348D4—682no—
349D4—682no—
350D4—682no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—171no—
357C2×C4—171no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—341no—
362C2×C4—341no—
363C2×C4—341no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—682no—
367C2×C4—682no—
368C2×C4—681no—
369C2×C4D4×D1711yescharacteristic
370C2×C4C23×D1711yescharacteristic
371C8—21no—
372C8—21no—
373C8—341no—
374C8—341no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—172no—
381C22—341no—
382C22—341no—
383C22—341no—
384C22—341no—
385C22—341no—
386C22—684no—
387C22—681no—
388C22—681no—
389C22—681no—
390C22—681no—
391C22—681no—
392C22—681no—
393C22—1364no—
394C22#1058760012yes—
395C22C2×D4×D1711yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—341no—
401C4—341no—
402C4—681no—
403C4—681no—
404C4#1058769111yescharacteristic
405C4#1058769611yescharacteristic
406C2—22no—
407C2—81no—
408C2—342no—
409C2—681no—
410C2—1361no—
411C2—1361no—
412C2#1176336711yescharacteristic
413C2#135×D1711yescharacteristic
414C2C2×#1058760011yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#465C2
socleC22×C17C22×D4
hypercenter#465D17
hypocenterC17#3188
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11763322C2semidirect
2. #121×D17C2semidirect
3. #11763143C2semidirect
4. #11763135C2semidirect
5. #11763131C2semidirect
6. #11763129C2semidirect
7. #11763045C2semidirect
8. #11763043C2semidirect
9. #11763040C2semidirect
10. #11762958C2semidirect
11. #11762957C2semidirect
12. #11762953C2semidirect
13. #11762944C2semidirect
14. C2×#10587491C2semidirect
15. C17×#465C2semidirect
16. C2×#63256C22semidirect
20. C2×SD16×C17C22semidirect
21. C22×C8×C17C22semidirect
22. C17×C22⋊Q8C22semidirect
25. C2×#63230C22semidirect
28. C2×#63228C22semidirect
30. #10587616C22semidirect
31. C22×#3622C22semidirect
32. C2×D136C22semidirect
37. #10587578C22semidirect
43. C17×#106C22semidirect
44. C17×#103C22semidirect
45. C17×#102C22semidirect
46. #10587506C22semidirect
47. #10587503C22semidirect
48. #10587492C22semidirect
49. #10587492C22semidirect
52. #10587491C22semidirect
53. #10587491C22semidirect
54. #10587489C22semidirect
55. #10587480C22semidirect
56. #10587480C22semidirect
57. #10587479C22semidirect
58. #10587478C22semidirect
208. #465D17semidirect
228. C2×SD16C2×D17semidirect
232. C22×C8C2×D17semidirect
235. C22⋊Q8C2×D17semidirect
253. #106C2×D17semidirect
255. #103C2×D17semidirect
261. #102C2×D17semidirect
266. C17#3188semidirect

Maximal subgroups

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

subgroupindex
#117633222
#121×D172
#117631432
#117631352
#117631312
#117631292
#117630452
#117630432
#117630402
#117629582
#117629572
#117629532
#117629442
C2×#105874912
C17×#4652
#318817