Finite Group Databasebeta

← #14541501

Subgroups — #14541501

Order 2176.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763529C211yesmaximal, characteristic, complemented
2#11763474C211yesmaximal, characteristic, complemented
3#11763167C212yesmaximal, complemented
4#11763161C211yesmaximal, characteristic, complemented
5#11763103C212yesmaximal, complemented
6#11763023C212yesmaximal
7#11763015C211yesmaximal, characteristic, complemented
8#11762936C211yesmaximal, characteristic, complemented
9#11762908C212yesmaximal, complemented
10C4×#63228C211yesmaximal, characteristic
11C17×#474C211yesmaximal, characteristic, complemented
12C2×Q8×D17—21no—
13C17×C4⋊Q8C2211yescharacteristic
14C4×D4×C17C2211yescharacteristic
15#10587632—21no—
16#10587622C2212yes—
17C2×#63228C2211yescharacteristic
18#10587612—21no—
19#10587610—21no—
20C2×#63219C2212yes—
21#10587582—22no—
22#10587579C2212yes—
23#10587574C2212yes—
24#10587573C2212yes—
25#10587565—22no—
26C4×D68C2211yescharacteristic
27#10587555C2211yescharacteristic
28C4×Dic34C2211yescharacteristic
29C17×#107C2212yes—
30C17×C4⋊C8C2211yescharacteristic
31C17×#102C2212yes—
32#10587503C2211yescharacteristic
33#10587487C2212yes—
34#10587486C2212yes—
35#10587485C2212yes—
36#10587481C2212yes—
37#10587481C2212yes—
38#10587480C2211yescharacteristic
39#10587478C2211yescharacteristic
40C4×#3622C2211yescharacteristic
41C2×Q8×C17—21no—
42C2×D4×C17C2311yescharacteristic
43C22×C4×C17—21no—
44Q8×D17—44no—
45C2×D68C2311yescharacteristic
46C2×C4×D17—21no—
47C2×C4×D17—22no—
48C2×Dic34—22no—
49C2×Dic34D411yescharacteristic
50C2×Dic34C2312yes—
51C2×C8×C17C2312yes—
52C4⋊C4×C17—21no—
53C4⋊C4×C17C2312yes—
54C4⋊C4×C17C2311yescharacteristic
55C22⋊C4×C17—21no—
56C42×C17C2311yescharacteristic
57C22⋊Dic17—22no—
58C22⋊Dic17—22no—
59#63228—22no—
60#63227—21no—
61#63227—22no—
62C4⋊Dic17—21no—
63C4⋊Dic17—21no—
64C4⋊Dic17D411yescharacteristic
65C4⋊Dic17C2311yescharacteristic
66#63225—22no—
67#63225—22no—
68#63225D412yes—
69C4×Dic17—22no—
70C4×Dic17C2312yes—
71C2×#3622C2311yescharacteristic
72C2×#3622C2311yescharacteristic
73#63219—24no—
74C23×C17—21no—
75C22×D17—21no—
76Q8×C17—42no—
77D4×C17—21no—
78D4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—22no—
81C2×C4×C17—42no—
82C2×C4×C17C2×D411yescharacteristic
83C2×C4×C17C2×D411yescharacteristic
84C2×C4×C17C2411yescharacteristic
85C2×Dic17—22no—
86C2×Dic17—21no—
87C2×Dic17C2×D412yes—
88C2×Dic17C2×D412yes—
89D68—21no—
90D68#4112yes—
91C4×D17—44no—
92C4×D17—42no—
93Dic34—22no—
94Dic34—22no—
95Dic34—22no—
96Dic34—44no—
97C8×C17—22no—
98#3622—21no—
99#3622—21no—
100#3367—171nomaximal, Sylow
101C22×C17—41no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17C22×D411yescharacteristic
105C2×D17—22no—
106C2×D17—41no—
107C2×D17—41no—
108C4×C17—21no—
109C4×C17—42no—
110C4×C17—41no—
111C4×C17AGL(1,ℤ/8)12yes—
112C4×C17C2×#4111yescharacteristic
113C4×C172−1+411yescharacteristic
114Dic17—22no—
115Dic17—22no—
116Dic17—42no—
117Dic17—41no—
118#556—171no—
119D4×Q8—171no—
120#489—172no—
121#487—171no—
122#477—172no—
123#474D1711yescharacteristic, complemented
124#463—172no—
125#461—171no—
126#446—171no—
127#440—172no—
128C4×D8—171no—
129C2×C17—81no—
130C2×C17#54811yescharacteristic
131C2×C17C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C17#57811yescharacteristic
133D17—42no—
134C22×Q8—341no—
135C2×SD16—172no—
136C2×D8—171no—
137C4⋊Q8—172no—
138C4⋊Q8—171no—
139C4⋊Q8C2×D1711yescharacteristic
140#126—342no—
141#124—172no—
142C22⋊Q8—342no—
143C22⋊Q8—341no—
144C22⋊Q8—341no—
145C4×Q8—171no—
146C4×Q8—172no—
147C4×D4—172no—
148C4×D4—171no—
149C4×D4C2×D1711yescharacteristic
150#117—341no—
151#107—171no—
152#107C2×D1712yes—
153C4⋊C8—172no—
154C4⋊C8C2×D1711yescharacteristic
155#103—172no—
156#103—172no—
157#103—172no—
158#102—171no—
159#102—171no—
160#102C2×D1712yes—
161#97—172no—
162C4×C8—171no—
163C17#336711yescharacteristic, complemented, Sylow
164C2×Q8—21no—
165C2×Q8—171no—
166C2×Q8—172no—
167C2×Q8—342no—
168C2×Q8—684no—
169C2×D4—171no—
170C2×D4C22×D1711yescharacteristic
171C22×C4—21no—
172C22×C4—342no—
173C22×C4—341no—
174SD16—344no—
175D8—342no—
176C2×C8—171no—
177C2×C8—171no—
178C2×C8C22×D1712yes—
179C4⋊C4—21no—
180C4⋊C4—171no—
181C4⋊C4—172no—
182C4⋊C4—171no—
183C4⋊C4—342no—
184C4⋊C4—342no—
185C4⋊C4—341no—
186C4⋊C4—341no—
187C4⋊C4C22×D1711yescharacteristic
188C4⋊C4C22×D1712yes—
189C22⋊C4—21no—
190C22⋊C4—342no—
191C22⋊C4—342no—
192C22⋊C4—342no—
193C22⋊C4—341no—
194C42—172no—
195C42—342no—
196C42C22×D1711yescharacteristic
197C23—21no—
198C23—341no—
199Q8—42no—
200Q8—342no—
201Q8—342no—
202Q8—342no—
203Q8—684no—
204D4—21no—
205D4—21no—
206D4—172no—
207D4—341no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—172no—
212C2×C4—172no—
213C2×C4—342no—
214C2×C4—341no—
215C2×C4—684no—
216C2×C4—682no—
217C2×C4D4×D1711yescharacteristic
218C2×C4D4×D1711yescharacteristic
219C2×C4C23×D1711yescharacteristic
220C8—22no—
221C8—341no—
222C8—341no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—342no—
227C22—681no—
228C22—681no—
229C22C2×D4×D1711yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—342no—
234C4—342no—
235C4—682no—
236C4—681no—
237C4#1058759712yes—
238C4#1058769411yescharacteristic
239C4#41×D1711yescharacteristic
240C2—81no—
241C2—682no—
242C2#1176346911yescharacteristic
243C2C2×#1058759711yescharacteristic
244C2#1176362511yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#474C2
socleC22×C17C22×D4
prime radicalC2×#63228C22
hypercenter#474D17
hypocenterC17#3367
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11763529C2semidirect
2. #11763474C2semidirect
3. #11763167C2semidirect
4. #11763161C2semidirect
5. #11763103C2semidirect
7. #11763015C2semidirect
8. #11762936C2semidirect
9. #11762908C2semidirect
11. C17×#474C2semidirect
123. #474D17semidirect
163. C17#3367semidirect

Maximal subgroups

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

subgroupindex
#117635292
#117634742
#117631672
#117631612
#117631032
#117630232
#117630152
#117629362
#117629082
C4×#632282
C17×#4742
#336717