Finite Group Databasebeta

← #14541284

Subgroups — #14541284

Order 2176.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763505C211yesmaximal, characteristic, complemented
2#11763215C211yesmaximal, characteristic, complemented
3#11763133C211yesmaximal, characteristic, complemented
4#11763133C211yesmaximal, characteristic, complemented
5#11763130C211yesmaximal, characteristic, complemented
6#11763120C211yesmaximal, characteristic, complemented
7#11763109C211yesmaximal, characteristic, complemented
8#11763086C211yesmaximal, characteristic, complemented
9#11763060C211yesmaximal, characteristic, complemented
10#11763043C211yesmaximal, characteristic, complemented
11#11762919C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762852C211yesmaximal, characteristic, complemented
14#11762845C211yesmaximal, characteristic, complemented
15C17×#555C211yesmaximal, characteristic, complemented
16C17×C4⋊Q8C2211yescharacteristic
17C17×#124—21no—
18C17×#124—21no—
19C17×#121—21no—
20C17×#121C2211yescharacteristic
21C17×#121C2211yescharacteristic
22C4×D4×C17C2211yescharacteristic
23C4×D4×C17C2211yescharacteristic
24C17×#117—21no—
25C17×#117C2211yescharacteristic
26C17×#117C2211yescharacteristic
27#10587625—21no—
28C2×#63228C2211yescharacteristic
29#10587616C2211yescharacteristic
30#10587616C2211yescharacteristic
31#10587612C2211yescharacteristic
32C2×C4⋊Dic17C2211yescharacteristic
33C2×#63223C2211yescharacteristic
34C22×#3622C2211yescharacteristic
35#10587584—21no—
36#10587569—21no—
37#10587567—21no—
38C4×D68C2211yescharacteristic
39#10587556C2211yescharacteristic
40#10587503C2211yescharacteristic
41#10587503C2211yescharacteristic
42#10587503C2211yescharacteristic
43C22⋊#3622C2211yescharacteristic
44C22⋊#3622C2211yescharacteristic
45#10587480C2211yescharacteristic
46#10587480C2211yescharacteristic
47#10587480C2211yescharacteristic
48#10587479C2211yescharacteristic
49#10587479C2211yescharacteristic
50#10587479C2211yescharacteristic
51#10587479C2211yescharacteristic
52#10587478C2211yescharacteristic
53#10587478C2211yescharacteristic
54#10587478C2211yescharacteristic
55#10587478C2211yescharacteristic
56#10587478C2211yescharacteristic
57C4⋊#3622C2211yescharacteristic
58#10587474C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×D4×C17—21no—
61C2×D4×C17—21no—
62C2×D4×C17D411yescharacteristic
63C2×D4×C17C2311yescharacteristic
64C22×C4×C17—21no—
65C22×C4×C17C2311yescharacteristic
66C22×C4×C17C2311yescharacteristic
67C2×C22⋊D17—21no—
68C2×C22⋊D17—21no—
69C22×Dic17—21no—
70C2×D68C2311yescharacteristic
71C2×C4×D17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17D411yescharacteristic
74C4⋊C4×C17C2311yescharacteristic
75C4⋊C4×C17C2311yescharacteristic
76C4⋊C4×C17C2311yescharacteristic
77C22⋊C4×C17—21no—
78C22⋊C4×C17—21no—
79C22⋊C4×C17—21no—
80C22⋊C4×C17—21no—
81C22⋊C4×C17—21no—
82C22⋊C4×C17D411yescharacteristic
83C22⋊C4×C17D411yescharacteristic
84C42×C17—21no—
85C42×C17—21no—
86C42×C17C2311yescharacteristic
87C22⋊Dic17—21no—
88#63228—22no—
89#63227—21no—
90#63227—21no—
91#63227—21no—
92C4⋊Dic17—21no—
93C4⋊Dic17C2311yescharacteristic
94C4⋊Dic17C2311yescharacteristic
95C4⋊Dic17C2311yescharacteristic
96#63225—21no—
97#63225—21no—
98C4×Dic17—21no—
99#63223—22no—
100C2×#3622—22no—
101C2×#3622C2311yescharacteristic
102C2×#3622C2311yescharacteristic
103C2×#3622C2311yescharacteristic
104C2×#3622C2311yescharacteristic
105C23×C17—21no—
106C23×C17C2×D411yescharacteristic
107C23×C17C2×D411yescharacteristic
108C22×D17—21no—
109Q8×C17—81no—
110D4×C17—21no—
111D4×C17—21no—
112D4×C17—41no—
113D4×C17—81no—
114D4×C17—81no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—42no—
123C2×C4×C17C2×D411yescharacteristic
124C2×C4×C17C2×D411yescharacteristic
125C2×C4×C17C2×D411yescharacteristic
126C2×C4×C17C2×D411yescharacteristic
127C2×C4×C17C2411yescharacteristic
128C22⋊D17—42no—
129C22⋊D17—81no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—81no—
134D68—21no—
135D68—21no—
136C4×D17—81no—
137#3622—21no—
138#3622—21no—
139#3622—21no—
140#3622#4112yes—
141#3347—171nomaximal, Sylow
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—21no—
145C22×C17—21no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—41no—
151C22×C17C22×D411yescharacteristic
152C2×D17—41no—
153C2×D17—41no—
154C2×D17—41no—
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—41no—
160C4×C17—41no—
161C4×C17—41no—
162C4×C17C2×#4111yescharacteristic
163C4×C172−1+411yescharacteristic
164Dic17—41no—
165Dic17—41no—
166Dic17—41no—
167#555D1711yescharacteristic, complemented
168#553—171no—
169#501—171no—
170#482—171no—
171#482—171no—
172#482—171no—
173#480—171no—
174#478—171no—
175#474—171no—
176#469—171no—
177#466—171no—
178#442—171no—
179#435—171no—
180#428—171no—
181#427—171no—
182C2×C17—41no—
183C2×C17—41no—
184C2×C17—81no—
185C2×C17#54711yescharacteristic
186C2×C17#57511yescharacteristic
187C2×C17#57611yescharacteristic
188D17—81no—
189C2×D8—171no—
190C2×M16—171no—
191C22×C8—171no—
192C4⋊Q8C2×D1711yescharacteristic
193#126—341no—
194#125—171no—
195#124—21no—
196#124—21no—
197#123—341no—
198#121—21no—
199#121—171no—
200#121—171no—
201#121—341no—
202#121C2×D1711yescharacteristic
203#121C2×D1711yescharacteristic
204C4×D4—171no—
205C4×D4—341no—
206C4×D4C2×D1711yescharacteristic
207C4×D4C2×D1711yescharacteristic
208#117—21no—
209#117—171no—
210#117C2×D1711yescharacteristic
211#117C2×D1711yescharacteristic
212C2×C4⋊C4—171no—
213#107—171no—
214#107—171no—
215#107—171no—
216#107—171no—
217#107—171no—
218#106—171no—
219#106—171no—
220#106—171no—
221#106—171no—
222C4⋊C8—171no—
223#102—171no—
224#102—171no—
225#102—171no—
226#102—171no—
227#102—171no—
228#102—171no—
229C22⋊C8—171no—
230C22⋊C8—171no—
231#97—171no—
232C17#334711yescharacteristic, complemented, Sylow
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—171no—
237C2×D4—341no—
238C2×D4—341no—
239C2×D4C22⋊D1711yescharacteristic
240C2×D4C22×D1711yescharacteristic
241C22×C4—21no—
242C22×C4—341no—
243C22×C4—341no—
244C22×C4C22×D1711yescharacteristic
245C22×C4C22×D1711yescharacteristic
246D8—342no—
247M16—342no—
248C2×C8—171no—
249C2×C8—171no—
250C2×C8—171no—
251C2×C8—171no—
252C2×C8—342no—
253C4⋊C4—21no—
254C4⋊C4—171no—
255C4⋊C4—171no—
256C4⋊C4—171no—
257C4⋊C4—341no—
258C4⋊C4—341no—
259C4⋊C4—341no—
260C4⋊C4C22⋊D1711yescharacteristic
261C4⋊C4C22×D1711yescharacteristic
262C4⋊C4C22×D1711yescharacteristic
263C4⋊C4C22×D1711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—341no—
270C22⋊C4—341no—
271C22⋊C4—341no—
272C22⋊C4—341no—
273C22⋊C4C22⋊D1711yescharacteristic
274C22⋊C4C22⋊D1711yescharacteristic
275C42—21no—
276C42—21no—
277C42—341no—
278C42C22×D1711yescharacteristic
279C23—21no—
280C23—341no—
281C23C2×C22⋊D1711yescharacteristic
282C23C2×C22⋊D1711yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—341no—
290D4—341no—
291D4—682no—
292D4—1361no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—341no—
302C2×C4—341no—
303C2×C4—341no—
304C2×C4—1361no—
305C2×C4—1361no—
306C2×C4C2×C22⋊D1711yescharacteristic
307C2×C4C2×C22⋊D1711yescharacteristic
308C2×C4C2×C22⋊D1711yescharacteristic
309C2×C4C2×C22⋊D1711yescharacteristic
310C2×C4C23×D1711yescharacteristic
311C8—172no—
312C8—341no—
313C8—341no—
314C8—341no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—681no—
325C22—681no—
326C22—681no—
327C22C22×C22⋊D1711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—681no—
336C4—681no—
337C4—681no—
338C4#41×D1711yescharacteristic
339C4#1058769711yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—1361no—
344C2#1176345811yescharacteristic
345C2#1176360711yescharacteristic
346C2#1176361211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#555C2
socleC22×C17C22×D4
hypercenter#555D17
hypocenterC17#3347
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #11763505C2semidirect
2. #11763215C2semidirect
3. #11763133C2semidirect
4. #11763133C2semidirect
5. #11763130C2semidirect
6. #11763120C2semidirect
7. #11763109C2semidirect
8. #11763086C2semidirect
9. #11763060C2semidirect
10. #11763043C2semidirect
11. #11762919C2semidirect
12. #11762881C2semidirect
13. #11762852C2semidirect
14. #11762845C2semidirect
15. C17×#555C2semidirect
167. #555D17semidirect
232. C17#3347semidirect

Maximal subgroups

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

subgroupindex
#117635052
#117632152
#117631332
#117631302
#117631202
#117631092
#117630862
#117630602
#117630432
#117629192
#117628812
#117628522
#117628452
C17×#5552
#334717