Finite Group Databasebeta

← #14539398

Subgroups — #14539398

Order 2176.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#11763428C212yesmaximal, complemented
2#11763207C211yesmaximal, characteristic, complemented
3#11763168C212yesmaximal, complemented
4#11763064C211yesmaximal, characteristic, complemented
5#11763059C211yesmaximal, characteristic
6#11763035C212yesmaximal, complemented
7#11762921C211yesmaximal, characteristic, complemented
8#11762916C211yesmaximal, characteristic, complemented
9SD16×Dic17C212yesmaximal, complemented
10#11762763C211yesmaximal, characteristic, complemented
11C17×#495C211yesmaximal, characteristic, complemented
12C2×Q16×C17C2211yescharacteristic
13C2×SD16×C17C2212yes—
14C2×D8×C17C2211yescharacteristic
15C17×#124C2212yes—
16#10587632C2212yes—
17Q8×Dic17C2212yes—
18#10587624C2212yes—
19D4×Dic17C2212yes—
20C2×#63218C2211yescharacteristic
21C2×C8×D17C2211yescharacteristic
22#10587572—22no—
23#10587571—22no—
24#10587565—22no—
25#10587564—22no—
26#10587558C2211yescharacteristic
27#10587555C2212yes—
28C4×C8×C17C2211yescharacteristic
29#10587506C2212yes—
30#10587506C2212yes—
31#10587503C2212yes—
32#10587503C2212yes—
33#10587488C2212yes—
34#10587488C2211yescharacteristic
35#10587488C2211yescharacteristic
36#10587486C2211yescharacteristic
37C8×Dic17C2211yescharacteristic
38#10587474C2211yescharacteristic
39C2×Q8×C17C2312yes—
40C2×D4×C17C2312yes—
41C2×C22⋊D17—22no—
42C22×Dic17—22no—
43C2×C4×D17C2311yescharacteristic
44C2×Dic34—22no—
45Q16×C17—22no—
46SD16×C17—24no—
47D8×C17—22no—
48C2×C8×C17C2311yescharacteristic
49C2×C8×C17C2311yescharacteristic
50C22⋊C4×C17—22no—
51C22⋊C4×C17—22no—
52C42×C17C2311yescharacteristic
53C22⋊Dic17—22no—
54C22⋊Dic17—22no—
55#63227—22no—
56#63227D412yes—
57C4⋊Dic17—22no—
58C4⋊Dic17—22no—
59C4⋊Dic17C2312yes—
60C4⋊Dic17C2312yes—
61#63225—22no—
62#63225D412yes—
63C4×Dic17—22no—
64C4×Dic17C2311yescharacteristic
65C2×#3622C2311yescharacteristic
66C2×#3622C2311yescharacteristic
67#63218—22no—
68C8×D17—22no—
69C23×C17—22no—
70C22×D17C2×D411yescharacteristic
71Q8×C17—22no—
72Q8×C17—22no—
73D4×C17—22no—
74D4×C17—22no—
75C2×C4×C17—22no—
76C2×C4×C17C2×D412yes—
77C2×C4×C17C2411yescharacteristic
78C22⋊D17—82no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—82no—
82C2×Dic17C2×D411yescharacteristic
83C2×Dic17C2×D412yes—
84C4×D17—21no—
85C4×D17—21no—
86Dic34—82no—
87C8×C17#4112yes—
88C8×C17#4112yes—
89#3622—21no—
90#3622—21no—
91#3173—171nomaximal, Sylow
92C22×C17—42no—
93C22×C17—42no—
94C22×C17—42no—
95C22×C17C22×D411yescharacteristic
96C2×D17—21no—
97C2×D17—22no—
98C4×C17—22no—
99C4×C17—42no—
100C4×C17C2×#4111yescharacteristic
101C4×C17C2×#4111yescharacteristic
102Dic17—21no—
103Dic17—22no—
104Dic17—42no—
105Dic17—42no—
106#542—172no—
107#498—171no—
108#495D1711yescharacteristic, complemented
109#489—172no—
110#470—171no—
111#469—171no—
112#465—172no—
113#442—171no—
114#441—171no—
115C4×SD16—172no—
116#405—171no—
117C2×C17—82no—
118C2×C17#53211yescharacteristic
119C2×C17#57712yes—
120D17—41no—
121C2×Q16C2×D1711yescharacteristic
122C2×SD16C2×D1712yes—
123C2×D8C2×D1711yescharacteristic
124C2×M16—171no—
125C22×C8—171no—
126C4⋊Q8—172no—
127#126—342no—
128#124—342no—
129#124C2×D1712yes—
130#123—342no—
131C22⋊Q8—172no—
132C22⋊Q8—342no—
133#121—172no—
134C4×Q8—172no—
135C4×D4—172no—
136#117—171no—
137#106—172no—
138#106—171no—
139#106—171no—
140#103—172no—
141#103—172no—
142#102—172no—
143#102—172no—
144#97—171no—
145#97—171no—
146C4×C8—171no—
147C4×C8C2×D1711yescharacteristic
148C17#317311yescharacteristic, complemented, Sylow
149C2×Q8—342no—
150C2×Q8C22×D1712yes—
151C2×D4—342no—
152C2×D4C22×D1712yes—
153C22×C4—171no—
154C22×C4—342no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—342no—
159C2×C8—171no—
160C2×C8—171no—
161C2×C8—342no—
162C2×C8C22×D1711yescharacteristic
163C2×C8C22×D1711yescharacteristic
164C4⋊C4—172no—
165C4⋊C4—172no—
166C4⋊C4—172no—
167C4⋊C4—342no—
168C4⋊C4—342no—
169C4⋊C4—342no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—172no—
173C22⋊C4—342no—
174C22⋊C4—342no—
175C22⋊C4—342no—
176C42—171no—
177C42—342no—
178C42C22×D1711yescharacteristic
179C23—22no—
180C23—171no—
181Q8—22no—
182Q8—22no—
183Q8—1362no—
184D4—22no—
185D4—22no—
186D4—1362no—
187C2×C4—22no—
188C2×C4—172no—
189C2×C4—171no—
190C2×C4—341no—
191C2×C4—341no—
192C2×C4—342no—
193C2×C4—342no—
194C2×C4—1362no—
195C2×C4D4×D1712yes—
196C2×C4C23×D1711yescharacteristic
197C8—341no—
198C8—341no—
199C8#6325412yes—
200C8#6325412yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—341no—
205C22—342no—
206C22C2×D4×D1711yescharacteristic
207C4—22no—
208C4—42no—
209C4—341no—
210C4—342no—
211C4—682no—
212C4—682no—
213C4C2×#6325411yescharacteristic
214C4C2×#6325411yescharacteristic
215C2—82no—
216C2—681no—
217C2#1176335711yescharacteristic
218C2#1176361612yes—
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#495C2
socleC22×C17C22×D4
prime radical#11763059C2
hypercenter#495D17
hypocenterC17#3173
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #11763428C2semidirect
2. #11763207C2semidirect
3. #11763168C2semidirect
4. #11763064C2semidirect
6. #11763035C2semidirect
7. #11762921C2semidirect
8. #11762916C2semidirect
9. SD16×Dic17C2semidirect
10. #11762763C2semidirect
11. C17×#495C2semidirect
108. #495D17semidirect
148. C17#3173semidirect

Maximal subgroups

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

subgroupindex
#117634282
#117632072
#117631682
#117630642
#117630592
#117630352
#117629212
#117629162
SD16×Dic172
#117627632
C17×#4952
#317317