Finite Group Databasebeta

← #14540046

Subgroups — #14540046

Order 2176.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763437C211yesmaximal, characteristic
2#11763219C211yesmaximal, characteristic, complemented
3#11763208C211yesmaximal, characteristic, complemented
4#11763177C211yesmaximal, characteristic, complemented
5#11763159C211yesmaximal, characteristic, complemented
6#11763147C211yesmaximal, characteristic
7#11763147C211yesmaximal, characteristic
8#11763142C211yesmaximal, characteristic
9#11763137C211yesmaximal, characteristic
10#11763116C211yesmaximal, characteristic, complemented
11#11763116C211yesmaximal, characteristic, complemented
12#11763104C211yesmaximal, characteristic, complemented
13#11763094C211yesmaximal, characteristic, complemented
14#11762870C211yesmaximal, characteristic
15C17×#541C211yesmaximal, characteristic
16C17×C4⋊Q8C2211yescharacteristic
17C17×#126—21no—
18C17×#126—21no—
19C17×#125—21no—
20C17×#125—21no—
21C17×#125C2211yescharacteristic
22C17×C22⋊Q8C2211yescharacteristic
23C17×C22⋊Q8C2211yescharacteristic
24C4×Q8×C17C2211yescharacteristic
25C4×Q8×C17C2211yescharacteristic
26C17×#117C2211yescharacteristic
27#10587612C2211yescharacteristic
28C2×C4⋊Dic17C2211yescharacteristic
29#10587576—21no—
30#10587574—21no—
31#10587564—21no—
32#10587564—21no—
33#10587556C2211yescharacteristic
34#10587556C2211yescharacteristic
35#10587555C2211yescharacteristic
36#10587555C2211yescharacteristic
37#10587506C2211yescharacteristic
38#10587506C2211yescharacteristic
39#10587506C2211yescharacteristic
40#10587506C2211yescharacteristic
41#10587506C2211yescharacteristic
42#10587506C2211yescharacteristic
43#10587506C2211yescharacteristic
44#10587506C2211yescharacteristic
45C22⋊#3622C2211yescharacteristic
46C22⋊#3622C2211yescharacteristic
47#10587479C2211yescharacteristic
48#10587479C2211yescharacteristic
49#10587479C2211yescharacteristic
50#10587479C2211yescharacteristic
51#10587478C2211yescharacteristic
52#10587478C2211yescharacteristic
53#10587478C2211yescharacteristic
54#10587478C2211yescharacteristic
55C4⋊#3622C2211yescharacteristic
56C4⋊#3622C2211yescharacteristic
57#10587474C2211yescharacteristic
58C4×#3622C2211yescharacteristic
59C2×Q8×C17C2311yescharacteristic
60C2×Q8×C17C2311yescharacteristic
61C22×C4×C17C2311yescharacteristic
62C22×Dic17—21no—
63C2×Dic34—21no—
64C2×Dic34—21no—
65C4⋊C4×C17—21no—
66C4⋊C4×C17—21no—
67C4⋊C4×C17—21no—
68C4⋊C4×C17—21no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17D411yescharacteristic
74C4⋊C4×C17D411yescharacteristic
75C4⋊C4×C17C2311yescharacteristic
76C4⋊C4×C17C2311yescharacteristic
77C22⋊C4×C17—21no—
78C22⋊C4×C17—21no—
79C22⋊C4×C17D411yescharacteristic
80C22⋊C4×C17D411yescharacteristic
81C42×C17—21no—
82C42×C17—21no—
83C42×C17C2311yescharacteristic
84C42×C17C2311yescharacteristic
85C22⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17C2311yescharacteristic
90C4⋊Dic17C2311yescharacteristic
91C4⋊Dic17C2311yescharacteristic
92C4⋊Dic17C2311yescharacteristic
93#63225—21no—
94#63225—21no—
95#63225—21no—
96#63225—21no—
97C4×Dic17—21no—
98C2×#3622C2311yescharacteristic
99C2×#3622C2311yescharacteristic
100C2×#3622C2311yescharacteristic
101C2×#3622C2311yescharacteristic
102C23×C17C2×D411yescharacteristic
103Q8×C17—21no—
104Q8×C17—21no—
105Q8×C17—21no—
106Q8×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17C2×D411yescharacteristic
114C2×C4×C17C2×D411yescharacteristic
115C2×C4×C17C2×D411yescharacteristic
116C2×C4×C17C2×D411yescharacteristic
117C2×C4×C17C2×D411yescharacteristic
118C2×C4×C17C2411yescharacteristic
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—81no—
124Dic34—81no—
125Dic34—81no—
126#3622—21no—
127#3622—21no—
128#3622—21no—
129#3622—21no—
130#3242—171nomaximal, Sylow
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17C22×D411yescharacteristic
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—21no—
139C4×C17—21no—
140C4×C17—41no—
141C4×C17—41no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C172−1+411yescharacteristic
145C4×C172−1+411yescharacteristic
146Dic17—41no—
147Dic17—41no—
148Dic17—41no—
149Dic17—41no—
150#544—171no—
151#541D1711yescharacteristic
152#501—171no—
153#499—171no—
154#491—171no—
155#487—171no—
156#485—171no—
157#485—171no—
158#484—171no—
159#483—171no—
160#479—171no—
161#479—171no—
162#477—171no—
163#475—171no—
164#433—171no—
165C2×C17—41no—
166C2×C17#53611yescharacteristic
167C2×C17#57711yescharacteristic
168C2×C17#57811yescharacteristic
169C4⋊Q8—171no—
170C4⋊Q8—171no—
171C4⋊Q8—341no—
172C4⋊Q8C2×D1711yescharacteristic
173#126—21no—
174#126—21no—
175#125—21no—
176#125—21no—
177#125—171no—
178#125—171no—
179#125—341no—
180#125C2×D1711yescharacteristic
181C22⋊Q8—341no—
182C22⋊Q8—341no—
183C22⋊Q8C2×D1711yescharacteristic
184C22⋊Q8C2×D1711yescharacteristic
185C4×Q8C2×D1711yescharacteristic
186C4×Q8C2×D1711yescharacteristic
187#117—171no—
188#117C2×D1711yescharacteristic
189C2×C4⋊C4—171no—
190#107—171no—
191#107—171no—
192#107—171no—
193#107—171no—
194#106—171no—
195#106—171no—
196#106—171no—
197#106—171no—
198C4⋊C8—171no—
199C4⋊C8—171no—
200#103—171no—
201#103—171no—
202#103—171no—
203#103—171no—
204#103—171no—
205#103—171no—
206#103—171no—
207#103—171no—
208C22⋊C8—171no—
209C22⋊C8—171no—
210#97—171no—
211C4×C8—171no—
212C17#324211yescharacteristic, complemented, Sylow
213C2×Q8—341no—
214C2×Q8—341no—
215C2×Q8C22×D1711yescharacteristic
216C2×Q8C22×D1711yescharacteristic
217C22×C4—341no—
218C22×C4C22×D1711yescharacteristic
219C2×C8—171no—
220C2×C8—171no—
221C2×C8—171no—
222C2×C8—171no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—171no—
232C4⋊C4—171no—
233C4⋊C4—171no—
234C4⋊C4—171no—
235C4⋊C4—341no—
236C4⋊C4—341no—
237C4⋊C4—341no—
238C4⋊C4—341no—
239C4⋊C4—341no—
240C4⋊C4—341no—
241C4⋊C4—341no—
242C4⋊C4C22⋊D1711yescharacteristic
243C4⋊C4C22⋊D1711yescharacteristic
244C4⋊C4C22×D1711yescharacteristic
245C4⋊C4C22×D1711yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—341no—
249C22⋊C4C22⋊D1711yescharacteristic
250C22⋊C4C22⋊D1711yescharacteristic
251C42—21no—
252C42—21no—
253C42—341no—
254C42C22×D1711yescharacteristic
255C42C22×D1711yescharacteristic
256C23C2×C22⋊D1711yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—21no—
260Q8—21no—
261Q8—1361no—
262Q8—1361no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—1361no—
274C2×C4C2×C22⋊D1711yescharacteristic
275C2×C4C2×C22⋊D1711yescharacteristic
276C2×C4C2×C22⋊D1711yescharacteristic
277C2×C4C2×C22⋊D1711yescharacteristic
278C2×C4C2×C22⋊D1711yescharacteristic
279C2×C4C23×D1711yescharacteristic
280C8—341no—
281C8—341no—
282C8—341no—
283C8—341no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×C22⋊D1711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—681no—
298C4—681no—
299C4—681no—
300C4—681no—
301C4#1058769711yescharacteristic
302C4#1058769711yescharacteristic
303C2—41no—
304C2#1176338011yescharacteristic
305C2#1176361711yescharacteristic
306C2#1176362411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#541C2
socleC22×C17C22×D4
prime radicalC23×C17C2×D4
hypercenter#541D17
hypocenterC17#3242
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #11763219C2semidirect
3. #11763208C2semidirect
4. #11763177C2semidirect
5. #11763159C2semidirect
10. #11763116C2semidirect
11. #11763116C2semidirect
12. #11763104C2semidirect
13. #11763094C2semidirect
212. C17#3242semidirect

Maximal subgroups

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

subgroupindex
#117634372
#117632192
#117632082
#117631772
#117631592
#117631472
#117631422
#117631372
#117631162
#117631042
#117630942
#117628702
C17×#5412
#324217