Finite Group Databasebeta

← #14530733

Subgroups — #14530733

Order 2176.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#11763606C211yesmaximal, characteristic
2#11763250C211yesmaximal, characteristic, complemented
3#11763064C211yesmaximal, characteristic, complemented
4#11762620C211yesmaximal, characteristic, complemented
5#11762619C211yesmaximal, characteristic, complemented
6#11762590C211yesmaximal, characteristic, complemented
7C17×#510C211yesmaximal, characteristic, complemented
8#41×D17—21no—
9C17×#135C2211yescharacteristic
10C2×Q16×C17C2211yescharacteristic, complemented
11#10587636—21no—
12#10587632—21no—
13#10587604—21no—
14#10587601—21no—
15#10587600—21no—
16#10587597—21no—
17#10587590C2211yescharacteristic
18C2×#63218C2211yescharacteristic
19C17×Q32—21no—
20C17×SD32—21no—
21C17×M32C2211yescharacteristic, complemented
22#10587506—21no—
23#10587500—21no—
24#10587499—21no—
25#10587488C2211yescharacteristic, complemented
26#10587483C2211yescharacteristic, complemented
27#41×C17—21no—
28C2×Q8×C17—21no—
29#63256—21no—
30Q8×D17—21no—
31#63254—21no—
32#63254—41no—
33D4×D17—21no—
34D4×D17—41no—
35#63252—21no—
36#63252—41no—
37C2×C4×D17—41no—
38C2×C4×D17D411yescharacteristic
39Q16×C17—21no—
40Q16×C17—21no—
41Q16×C17D411yescharacteristic
42SD16×C17—21no—
43D8×C17D411yescharacteristic
44C2×C8×C17C2311yescharacteristic
45#63231—21no—
46#63230—21no—
47#63229—21no—
48#63228—21no—
49#63227—41no—
50C4⋊Dic17—21no—
51#63225—41no—
52C2×#3622D411yescharacteristic
53Dic68D411yescharacteristic
54D136D411yescharacteristic
55#63219—21no—
56#63218—21no—
57#63218—21no—
58C16×C17—21no—
59#63214—21no—
60C22×D17—41no—
61C22×D17D811yescharacteristic
62Q8×C17—21no—
63Q8×C17—41no—
64Q8×C17—41no—
65D4×C17—21no—
66D4×C17—41no—
67C2×C4×C17—41no—
68C2×C4×C17—41no—
69C2×C4×C17C2×D411yescharacteristic
70C22⋊D17—41no—
71C22⋊D17—41no—
72C22⋊D17—41no—
73C2×Dic17—41no—
74C2×Dic17—41no—
75C2×Dic17D811yescharacteristic
76D68—21no—
77D68—41no—
78C4×D17—21no—
79C4×D17—21no—
80C4×D17—41no—
81C4×D17—41no—
82C4×D17—41no—
83Dic34—21no—
84Dic34—41no—
85C8×C17C2×D411yescharacteristic
86C8×C17C2×D411yescharacteristic
87#3622—21no—
88#2191—171nomaximal, Sylow
89C22×C17—41no—
90C22×C17C2×D811yescharacteristic
91C2×D17—21no—
92C2×D17—41no—
93C2×D17—41no—
94C2×D17—82no—
95C4×C17—41no—
96C4×C17—81no—
97C4×C17#12011yescharacteristic
98C4×C17AGL(1,ℤ/8)11yescharacteristic
99Dic17—21no—
100Dic17—41no—
101Dic17—81no—
102#575—171no—
103#510—171no—
104#510D1711yescharacteristic, complemented
105#470—171no—
106#360—171no—
107#360—171no—
108#349—171no—
109C2×C17—21no—
110C2×C17—81no—
111C2×C17#44711yescharacteristic
112D17—41no—
113D17—81no—
114C2×#41—341no—
115#137—341no—
116#137—341no—
117AGL(1,ℤ/8)—341no—
118AGL(1,ℤ/8)—341no—
119#135—171no—
120#135—341no—
121#135C2×D1711yescharacteristic
122C2×Q16C2×D1711yescharacteristic, complemented
123C2×M16—171no—
124C22⋊Q8—341no—
125Q32—21no—
126Q32—341no—
127SD32—21no—
128SD32—341no—
129M32—171no—
130M32C2×D1711yescharacteristic, complemented
131#106—171no—
132#103—341no—
133C17#219111yescharacteristic, complemented, Sylow
134#41—21no—
135#41—341no—
136#41—341no—
137#41—341no—
138#41—681no—
139#41—681no—
140C2×Q8—21no—
141C2×Q8—341no—
142C2×D4—341no—
143C2×D4—681no—
144C22×C4—171no—
145C22×C4—681no—
146Q16—21no—
147Q16—21no—
148Q16—171no—
149Q16—341no—
150Q16C22⋊D1711yescharacteristic
151SD16—21no—
152SD16—341no—
153SD16—341no—
154SD16—341no—
155D8—171no—
156D8—341no—
157D8C22⋊D1711yescharacteristic
158M16—341no—
159M16—341no—
160C2×C8—171no—
161C2×C8C22×D1711yescharacteristic
162C4⋊C4—341no—
163C4⋊C4—681no—
164C22⋊C4—681no—
165C16—21no—
166C16—341no—
167C23—171no—
168C23—681no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—341no—
173Q8—681no—
174D4—21no—
175D4—41no—
176D4—341no—
177D4—681no—
178D4—681no—
179D4—681no—
180D4—681no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—171no—
184C2×C4—341no—
185C2×C4—341no—
186C2×C4—681no—
187C2×C4—681no—
188C2×C4—681no—
189C2×C4—681no—
190C2×C4—681no—
191C2×C4D4×D1711yescharacteristic
192C8—341no—
193C8D4×D1711yescharacteristic
194C8C2×C22⋊D1711yescharacteristic
195C22—41no—
196C22—341no—
197C22—681no—
198C22—681no—
199C22—1362no—
200C22D8×D1711yescharacteristic
201C4—41no—
202C4—81no—
203C4—341no—
204C4—681no—
205C4—1361no—
206C4#1058759711yescharacteristic
207C4#1058762311yescharacteristic
208C2—21no—
209C2—81no—
210C2—681no—
211C2—1361no—
212C2#1176294111yescharacteristic
subgroupG/H
centerC2#11762941
commutator, cosocleC2×C8×C17C23
FrattiniC2×C8C22×D17
FittingC17×#510C2
socleC2×C17#447
prime radical#11763606C2
hypercenter#510D17
hypocenterC17#2191
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #11763250C2semidirect
3. #11763064C2semidirect
4. #11762620C2semidirect
5. #11762619C2semidirect
6. #11762590C2semidirect
7. C17×#510C2semidirect
10. C2×Q16×C17C22semidirect
21. C17×M32C22semidirect
25. #10587488C22semidirect
26. #10587483C22semidirect
104. #510D17semidirect
122. C2×Q16C2×D17semidirect
130. M32C2×D17semidirect
133. C17#2191semidirect

Maximal subgroups

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

subgroupindex
#117636062
#117632502
#117630642
#117626202
#117626192
#117625902
C17×#5102
#219117