Finite Group Databasebeta

← #14539633

Subgroups — #14539633

Order 2176.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763387C211yesmaximal, characteristic, complemented
2#11763375C211yesmaximal, characteristic, complemented
3#11763149C211yesmaximal, characteristic, complemented
4#11763131C211yesmaximal, characteristic, complemented
5#11763125C211yesmaximal, characteristic, complemented
6#11763123C211yesmaximal, characteristic, complemented
7#11763061C211yesmaximal, characteristic, complemented
8#11763052C211yesmaximal, characteristic, complemented
9#11763042C211yesmaximal, characteristic, complemented
10#11763041C211yesmaximal, characteristic, complemented
11#11762958C211yesmaximal, characteristic, complemented
12#11762954C211yesmaximal, characteristic, complemented
13#11762941C211yesmaximal, characteristic, complemented
14#11762774C211yesmaximal, characteristic, complemented
15C17×#449C211yesmaximal, characteristic, complemented
16C2×#41×C17C2211yescharacteristic, complemented
17C2×D4×D17C2211yescharacteristic
18C2×#63252C2211yescharacteristic
19C2×SD16×C17C2211yescharacteristic
20C2×D8×C17C2211yescharacteristic
21C17×#121C2211yescharacteristic
22#10587632C2211yescharacteristic
23#10587632C2211yescharacteristic, complemented
24C2×#63230C2211yescharacteristic
25#10587626—21no—
26#10587625—21no—
27#10587625—21no—
28#10587624C2211yescharacteristic
29#10587624C2211yescharacteristic
30#10587624C2211yescharacteristic, complemented
31#10587623—21no—
32C2×#63228C2211yescharacteristic
33#10587616—21no—
34#10587616C2211yescharacteristic
35C2×C4⋊Dic17C2211yescharacteristic, complemented
36#10587610—21no—
37C2×#63218C2211yescharacteristic, complemented
38C2×C8×D17C2211yescharacteristic, complemented
39#10587581C2211yescharacteristic
40#10587578C2211yescharacteristic
41#10587571—21no—
42#10587568—21no—
43C17×#103C2211yescharacteristic, complemented
44C17×#102C2211yescharacteristic, complemented
45C17×C22⋊C8C2211yescharacteristic, complemented
46#10587506C2211yescharacteristic, complemented
47#10587503C2211yescharacteristic
48#10587503C2211yescharacteristic
49#10587503C2211yescharacteristic, complemented
50C22⋊#3622C2211yescharacteristic, complemented
51#10587492C2211yescharacteristic
52#10587492C2211yescharacteristic
53#10587491C2211yescharacteristic
54#10587491C2211yescharacteristic
55#10587489C2211yescharacteristic, complemented
56#10587489C2211yescharacteristic, complemented
57#10587479C2211yescharacteristic, complemented
58#10587479C2211yescharacteristic, complemented
59C23×D17—21no—
60#41×C17—41no—
61#41×C17—41no—
62C2×Q8×C17C2311yescharacteristic
63C2×D4×C17—21no—
64C2×D4×C17—21no—
65C2×D4×C17C2311yescharacteristic
66C2×D4×C17C2311yescharacteristic
67C22×C4×C17—21no—
68C22×C4×C17C2311yescharacteristic
69C2×C22⋊D17—21no—
70C2×C22⋊D17—21no—
71C2×C22⋊D17—21no—
72C2×C22⋊D17—21no—
73C2×C22⋊D17—21no—
74C2×C22⋊D17D411yescharacteristic
75C2×C22⋊D17D411yescharacteristic
76C22×Dic17—21no—
77D4×D17—41no—
78D4×D17—41no—
79#63252—41no—
80#63252—41no—
81C2×D68—21no—
82C2×D68D411yescharacteristic
83C2×D68C2311yescharacteristic
84C2×C4×D17C2311yescharacteristic
85C2×C4×D17C2311yescharacteristic
86C2×Dic34D411yescharacteristic
87SD16×C17—41no—
88D8×C17—41no—
89C2×C8×C17C2311yescharacteristic
90C2×C8×C17C2311yescharacteristic
91C4⋊C4×C17C2311yescharacteristic
92C22⋊C4×C17—21no—
93C22⋊Dic17—21no—
94C22⋊Dic17—21no—
95C22⋊Dic17—21no—
96#63230—41no—
97#63228—41no—
98#63227—21no—
99#63227—21no—
100#63227—21no—
101#63227—21no—
102#63227—21no—
103C4⋊Dic17—21no—
104C4⋊Dic17C2311yescharacteristic
105C4⋊Dic17C2311yescharacteristic
106C4⋊Dic17C2311yescharacteristic
107#63225—21no—
108#63225—21no—
109C4×Dic17—21no—
110C2×#3622C2311yescharacteristic
111C2×#3622C2311yescharacteristic
112#63218—41no—
113C8×D17—41no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17C2×D411yescharacteristic
117C22×D17—21no—
118C22×D17—42no—
119C22×D17—81no—
120C22×D17—81no—
121C22×D17C2×D411yescharacteristic
122C22×D17C2×D411yescharacteristic
123Q8×C17—21no—
124Q8×C17—21no—
125D4×C17—21no—
126D4×C17—21no—
127D4×C17—21no—
128D4×C17—21no—
129D4×C17—42no—
130D4×C17—81no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—42no—
136C2×C4×C17C2×D411yescharacteristic
137C2×C4×C17C2411yescharacteristic
138C22⋊D17—41no—
139C22⋊D17—41no—
140C22⋊D17—42no—
141C22⋊D17—81no—
142C22⋊D17—81no—
143C22⋊D17—81no—
144C22⋊D17—81no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—81no—
149C2×Dic17C2×D411yescharacteristic
150C2×Dic17C2×D411yescharacteristic
151D68—21no—
152D68—21no—
153D68—41no—
154D68—81no—
155C4×D17—21no—
156C4×D17—21no—
157C4×D17—21no—
158C4×D17—21no—
159Dic34—41no—
160C8×C17—21no—
161C8×C17—21no—
162#3622—21no—
163#3622—21no—
164#3198—171nomaximal, Sylow
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17C22×D411yescharacteristic
175C2×D17—21no—
176C2×D17—21no—
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—41no—
184C2×D17—84no—
185C4×C17—21no—
186C4×C17—41no—
187C4×C17—41no—
188C4×C17H(5,𝔽2)11yescharacteristic
189C4×C17H(5,𝔽2)11yescharacteristic
190Dic17—21no—
191Dic17—21no—
192Dic17—41no—
193Dic17—41no—
194Dic17—41no—
195#537—171no—
196#535—171no—
197#485—171no—
198#482—171no—
199#481—171no—
200#480—171no—
201#469—171no—
202#468—171no—
203#466—171no—
204#465—171no—
205#450—171no—
206#449—171no—
207#449D1711yescharacteristic, complemented
208#447—171no—
209#408—171no—
210C2×C17—41no—
211C2×C17—81no—
212C2×C17—81no—
213C2×C17#53411yescharacteristic
214C2×C17#57611yescharacteristic
215C2×C17#57711yescharacteristic
216D17—41no—
217D17—41no—
218D17—81no—
219C2×#41—171no—
220C2×#41C2×D1711yescharacteristic, complemented
221C22×D4—171no—
222C2×SD16—171no—
223C2×SD16C2×D1711yescharacteristic
224C2×D8—171no—
225C2×D8C2×D1711yescharacteristic
226C2×M16—171no—
227C22×C8—171no—
228#127—341no—
229#124—341no—
230C22⋊Q8—171no—
231C22⋊Q8—171no—
232C22⋊Q8—341no—
233#121—171no—
234#121—171no—
235#121—171no—
236#121—171no—
237#121—171no—
238#121—341no—
239#121—341no—
240#121—341no—
241#121C2×D1711yescharacteristic
242#120—341no—
243#120—341no—
244#117—171no—
245C2×C4⋊C4—171no—
246#107—171no—
247#107—171no—
248#106—171no—
249#106—171no—
250#103—171no—
251#103C2×D1711yescharacteristic, complemented
252#102—171no—
253#102—171no—
254#102—171no—
255#102—171no—
256#102—171no—
257#102C2×D1711yescharacteristic, complemented
258C22⋊C8—171no—
259C22⋊C8—171no—
260C22⋊C8—171no—
261C22⋊C8C2×D1711yescharacteristic, complemented
262C17#319811yescharacteristic, complemented, Sylow
263C24—341no—
264#41—41no—
265#41—41no—
266#41—681no—
267#41—681no—
268C2×Q8—171no—
269C2×Q8C22×D1711yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—171no—
273C2×D4—171no—
274C2×D4—171no—
275C2×D4—171no—
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×D4C22×D1711yescharacteristic
285C2×D4C22×D1711yescharacteristic
286C22×C4—21no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—341no—
290C22×C4C22×D1711yescharacteristic
291SD16—41no—
292SD16—681no—
293D8—41no—
294D8—681no—
295M16—681no—
296C2×C8—171no—
297C2×C8—171no—
298C2×C8—681no—
299C2×C8C22×D1711yescharacteristic
300C2×C8C22×D1711yescharacteristic
301C4⋊C4—171no—
302C4⋊C4—171no—
303C4⋊C4—171no—
304C4⋊C4—341no—
305C4⋊C4—341no—
306C4⋊C4—341no—
307C4⋊C4C22×D1711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—341no—
310C22⋊C4—341no—
311C22⋊C4—341no—
312C22⋊C4—341no—
313C22⋊C4—341no—
314C22⋊C4—341no—
315C22⋊C4—341no—
316C22⋊C4—341no—
317C42—341no—
318C23—21no—
319C23—21no—
320C23—171no—
321C23—171no—
322C23—341no—
323C23—682no—
324C23—1361no—
325C23—1361no—
326C23D4×D1711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—681no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—341no—
337D4—341no—
338D4—681no—
339D4—681no—
340D4—681no—
341D4—682no—
342D4—1361no—
343D4—1361no—
344D4—1361no—
345D4—1361no—
346D4—1361no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—171no—
353C2×C4—171no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—1361no—
362C2×C4D4×D1711yescharacteristic
363C2×C4C23×D1711yescharacteristic
364C8—21no—
365C8—21no—
366C8—341no—
367C8—341no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—341no—
378C22—341no—
379C22—341no—
380C22—341no—
381C22—341no—
382C22—341no—
383C22—681no—
384C22—681no—
385C22—681no—
386C22—1364no—
387C22C2×D4×D1711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—341no—
392C4—341no—
393C4—681no—
394C4—681no—
395C4—681no—
396C4#1058769111yescharacteristic
397C4#1058769111yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—681no—
402C2—681no—
403C2—1361no—
404C2#1176336911yescharacteristic
405C2#1176361111yescharacteristic
406C2#1176361911yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#449C2
socleC22×C17C22×D4
hypercenter#449D17
hypocenterC17#3198
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11763387C2semidirect
2. #11763375C2semidirect
3. #11763149C2semidirect
4. #11763131C2semidirect
5. #11763125C2semidirect
6. #11763123C2semidirect
7. #11763061C2semidirect
8. #11763052C2semidirect
9. #11763042C2semidirect
10. #11763041C2semidirect
11. #11762958C2semidirect
12. #11762954C2semidirect
13. #11762941C2semidirect
14. #11762774C2semidirect
15. C17×#449C2semidirect
16. C2×#41×C17C22semidirect
23. #10587632C22semidirect
30. #10587624C22semidirect
35. C2×C4⋊Dic17C22semidirect
37. C2×#63218C22semidirect
38. C2×C8×D17C22semidirect
43. C17×#103C22semidirect
44. C17×#102C22semidirect
45. C17×C22⋊C8C22semidirect
46. #10587506C22semidirect
49. #10587503C22semidirect
50. C22⋊#3622C22semidirect
55. #10587489C22semidirect
56. #10587489C22semidirect
57. #10587479C22semidirect
58. #10587479C22semidirect
207. #449D17semidirect
220. C2×#41C2×D17semidirect
251. #103C2×D17semidirect
257. #102C2×D17semidirect
261. C22⋊C8C2×D17semidirect
262. C17#3198semidirect

Maximal subgroups

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

subgroupindex
#117633872
#117633752
#117631492
#117631312
#117631252
#117631232
#117630612
#117630522
#117630422
#117630412
#117629582
#117629542
#117629412
#117627742
C17×#4492
#319817