Finite Group Databasebeta

← #14540844

Subgroups — #14540844

Order 2176.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763468C211yesmaximal, characteristic
2#11763171C211yesmaximal, characteristic, complemented
3#11763150C211yesmaximal, characteristic, complemented
4#11763133C211yesmaximal, characteristic, complemented
5#11763101C211yesmaximal, characteristic, complemented
6#11763057C211yesmaximal, characteristic, complemented
7#11763048C211yesmaximal, characteristic, complemented
8#11763031C211yesmaximal, characteristic, complemented
9#11762969C211yesmaximal, characteristic, complemented
10#11762964C211yesmaximal, characteristic, complemented
11#11762914C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762817C211yesmaximal, characteristic, complemented
14#11762803C211yesmaximal, characteristic, complemented
15C17×#556C211yesmaximal, characteristic, complemented
16C2×#63252C2211yescharacteristic
17C22×Dic34C2211yescharacteristic
18C17×C4⋊Q8C2211yescharacteristic
19C17×#126—21no—
20C17×#126—21no—
21C17×#124—21no—
22C17×C22⋊Q8C2211yescharacteristic
23C17×C22⋊Q8C2211yescharacteristic
24C4×Q8×C17—21no—
25C4×Q8×C17C2211yescharacteristic
26C4×D4×C17C2211yescharacteristic
27C17×#117C2211yescharacteristic
28C17×#117C2211yescharacteristic
29C2×#63231C2211yescharacteristic
30C2×#63231C2211yescharacteristic
31C2×#63230C2211yescharacteristic
32#10587625—21no—
33#10587616C2211yescharacteristic
34#10587610C2211yescharacteristic
35C2×#63223C2211yescharacteristic
36C22×#3622C2211yescharacteristic
37#10587582—21no—
38#10587571—21no—
39#10587567—21no—
40#10587561C2211yescharacteristic
41C4×Dic34C2211yescharacteristic
42#10587506C2211yescharacteristic
43C22⋊#3622C2211yescharacteristic
44C22⋊#3622C2211yescharacteristic
45#10587481C2211yescharacteristic
46#10587481C2211yescharacteristic
47#10587481C2211yescharacteristic
48#10587481C2211yescharacteristic
49#10587481C2211yescharacteristic
50#10587481C2211yescharacteristic
51#10587480C2211yescharacteristic
52#10587480C2211yescharacteristic
53#10587480C2211yescharacteristic
54#10587479C2211yescharacteristic
55#10587478C2211yescharacteristic
56#10587478C2211yescharacteristic
57C4⋊#3622C2211yescharacteristic
58#10587474C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×Q8×C17C2311yescharacteristic
61C2×D4×C17D411yescharacteristic
62C22×C4×C17C2311yescharacteristic
63C22×C4×C17C2311yescharacteristic
64C2×C22⋊D17—21no—
65C2×C22⋊D17—21no—
66C22×Dic17—21no—
67#63252—22no—
68#63252—41no—
69C2×D68C2311yescharacteristic
70C2×C4×D17—21no—
71C2×Dic34—22no—
72C2×Dic34—21no—
73C2×Dic34—41no—
74C2×Dic34C2311yescharacteristic
75C2×Dic34C2311yescharacteristic
76C4⋊C4×C17—21no—
77C4⋊C4×C17—21no—
78C4⋊C4×C17—21no—
79C4⋊C4×C17—21no—
80C4⋊C4×C17D411yescharacteristic
81C4⋊C4×C17C2311yescharacteristic
82C4⋊C4×C17C2311yescharacteristic
83C4⋊C4×C17C2311yescharacteristic
84C22⋊C4×C17—21no—
85C22⋊C4×C17—21no—
86C22⋊C4×C17—21no—
87C22⋊C4×C17—21no—
88C22⋊C4×C17D411yescharacteristic
89C22⋊C4×C17D411yescharacteristic
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17C2311yescharacteristic
94C22⋊Dic17—21no—
95#63231—22no—
96#63231—41no—
97#63230—41no—
98#63227—21no—
99#63227—21no—
100#63227—21no—
101C4⋊Dic17C2311yescharacteristic
102#63225—21no—
103#63225—21no—
104C4×Dic17—21no—
105#63223—41no—
106C2×#3622—41no—
107C2×#3622C2311yescharacteristic
108C2×#3622C2311yescharacteristic
109C2×#3622C2311yescharacteristic
110C2×#3622C2311yescharacteristic
111C23×C17C2×D411yescharacteristic
112C23×C17C2×D411yescharacteristic
113C22×D17—21no—
114Q8×C17—21no—
115Q8×C17—21no—
116Q8×C17—42no—
117D4×C17—41no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17C2×D411yescharacteristic
127C2×C4×C17C2×D411yescharacteristic
128C2×C4×C17C2×D411yescharacteristic
129C2×C4×C17C2×D411yescharacteristic
130C2×C4×C17C2411yescharacteristic
131C22⋊D17—42no—
132C22⋊D17—42no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—42no—
137D68—21no—
138D68—21no—
139C4×D17—42no—
140Dic34—21no—
141Dic34—21no—
142Dic34—21no—
143Dic34—42no—
144Dic34#4112yes—
145#3622—21no—
146#3622—21no—
147#3622—21no—
148#3622—21no—
149#3313—171nomaximal, Sylow
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17C22×D411yescharacteristic
157C2×D17—41no—
158C2×D17—41no—
159C2×D17—41no—
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17C2×#4111yescharacteristic
169C4×C17H(5,𝔽2)11yescharacteristic
170Dic17—22no—
171Dic17—41no—
172Dic17—41no—
173#556D1711yescharacteristic, complemented
174#548—171no—
175#489—171no—
176#485—171no—
177#482—171no—
178#477—171no—
179#468—171no—
180#467—171no—
181#464—171no—
182#452—171no—
183#451—171no—
184#441—171no—
185#435—171no—
186#419—171no—
187#416—171no—
188C2×C17—41no—
189C2×C17—41no—
190C2×C17#54611yescharacteristic
191C2×C17#57511yescharacteristic
192C2×C17#57811yescharacteristic
193D17—81no—
194C2×#41—171no—
195C22×Q8—171no—
196C2×Q16—171no—
197C2×Q16—171no—
198C2×SD16—171no—
199C2×M16—171no—
200C22×C8—171no—
201C4⋊Q8C2×D1711yescharacteristic
202#126—21no—
203#126—21no—
204#124—21no—
205#124—171no—
206#124—341no—
207C22⋊Q8—171no—
208C22⋊Q8—341no—
209C22⋊Q8C2×D1711yescharacteristic
210C22⋊Q8C2×D1711yescharacteristic
211#121—171no—
212#121—341no—
213C4×Q8—21no—
214C4×Q8—171no—
215C4×Q8C2×D1711yescharacteristic
216C4×D4—341no—
217C4×D4C2×D1711yescharacteristic
218#117C2×D1711yescharacteristic
219#117C2×D1711yescharacteristic
220#107—171no—
221#107—171no—
222#106—171no—
223C4⋊C8—171no—
224#103—171no—
225#103—171no—
226#103—171no—
227#103—171no—
228#103—171no—
229#103—171no—
230#103—171no—
231#102—171no—
232#102—171no—
233#102—171no—
234C22⋊C8—171no—
235C22⋊C8—171no—
236#97—171no—
237C17#331311yescharacteristic, complemented, Sylow
238#41—342no—
239#41—681no—
240C2×Q8—21no—
241C2×Q8—171no—
242C2×Q8—171no—
243C2×Q8—342no—
244C2×Q8—341no—
245C2×Q8—681no—
246C2×Q8C22×D1711yescharacteristic
247C2×D4—171no—
248C2×D4—341no—
249C2×D4—341no—
250C2×D4C22⋊D1711yescharacteristic
251C22×C4—341no—
252C22×C4—341no—
253C22×C4C22×D1711yescharacteristic
254C22×C4C22×D1711yescharacteristic
255Q16—342no—
256Q16—681no—
257SD16—681no—
258M16—681no—
259C2×C8—171no—
260C2×C8—171no—
261C2×C8—171no—
262C2×C8—171no—
263C2×C8—681no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—171no—
269C4⋊C4—341no—
270C4⋊C4—341no—
271C4⋊C4C22⋊D1711yescharacteristic
272C4⋊C4C22×D1711yescharacteristic
273C4⋊C4C22×D1711yescharacteristic
274C4⋊C4C22×D1711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—341no—
280C22⋊C4—341no—
281C22⋊C4—341no—
282C22⋊C4—341no—
283C22⋊C4C22⋊D1711yescharacteristic
284C22⋊C4C22⋊D1711yescharacteristic
285C42—21no—
286C42—21no—
287C42—21no—
288C42—341no—
289C42C22×D1711yescharacteristic
290C23—341no—
291C23C2×C22⋊D1711yescharacteristic
292C23C2×C22⋊D1711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—172no—
297Q8—341no—
298Q8—341no—
299Q8—341no—
300Q8—682no—
301D4—41no—
302D4—341no—
303D4—341no—
304D4—682no—
305D4—682no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—682no—
318C2×C4—682no—
319C2×C4C2×C22⋊D1711yescharacteristic
320C2×C4C2×C22⋊D1711yescharacteristic
321C2×C4C2×C22⋊D1711yescharacteristic
322C2×C4C2×C22⋊D1711yescharacteristic
323C2×C4C23×D1711yescharacteristic
324C8—341no—
325C8—341no—
326C8—341no—
327C8—341no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—681no—
335C22—681no—
336C22—681no—
337C22C22×C22⋊D1711yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—342no—
347C4—681no—
348C4—681no—
349C4#41×D1711yescharacteristic
350C4#1058769611yescharacteristic
351C2—41no—
352C2—41no—
353C2—1361no—
354C2#1176344711yescharacteristic
355C2#1176360711yescharacteristic
356C2#1176362411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#556C2
socleC22×C17C22×D4
prime radical#11763468C2
hypercenter#556D17
hypocenterC17#3313
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #11763171C2semidirect
3. #11763150C2semidirect
4. #11763133C2semidirect
5. #11763101C2semidirect
6. #11763057C2semidirect
7. #11763048C2semidirect
8. #11763031C2semidirect
9. #11762969C2semidirect
10. #11762964C2semidirect
11. #11762914C2semidirect
12. #11762881C2semidirect
13. #11762817C2semidirect
14. #11762803C2semidirect
15. C17×#556C2semidirect
173. #556D17semidirect
237. C17#3313semidirect

Maximal subgroups

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

subgroupindex
#117634682
#117631712
#117631502
#117631332
#117631012
#117630572
#117630482
#117630312
#117629692
#117629642
#117629142
#117628812
#117628172
#117628032
C17×#5562
#331317