Finite Group Databasebeta

← #16948728

Subgroups — #16948728

Order 4352.

196 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 55 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#14531026C211yesmaximal, characteristic, complemented
2#14530961C211yesmaximal, characteristic, complemented
3#14530861C211yesmaximal, characteristic
4#14530627C211yesmaximal, characteristic, complemented
5#14526844C211yesmaximal, characteristic, complemented
6#14526820C211yesmaximal, characteristic, complemented
7C17×#1369C211yesmaximal, characteristic, complemented
8#11763247—21no—
9#11763225—21no—
10#11763211C2211yescharacteristic
11#11763186C2211yescharacteristic
12#11762927C2211yescharacteristic
13#11762632—21no—
14#11762630C2211yescharacteristic
15#11762623—21no—
16#11762620—21no—
17#11762611—21no—
18#11762611—21no—
19#11762592—21no—
20C17×#364C2211yescharacteristic
21C17×#364C2211yescharacteristic
22C17×#346C2211yescharacteristic
23#10587590D411yescharacteristic
24C2×D136—21no—
25C2×D136—21no—
26#10587587—21no—
27#10587560—21no—
28#10587556—21no—
29C17×M32—21no—
30C17×M32—21no—
31C2×C16×C17D411yescharacteristic
32C2×C16×C17D411yescharacteristic
33C4×C8×C17C2311yescharacteristic
34#10587490D411yescharacteristic
35#10587489—21no—
36#10587488—21no—
37#10587483—21no—
38#10587476—21no—
39#10587471—41no—
40D272—41no—
41#10587469—41no—
42C16×D17—41no—
43#63252—21no—
44C2×D68—41no—
45C2×D68—81no—
46C2×C8×C17C2×D411yescharacteristic
47C2×C8×C17C2×D411yescharacteristic
48C42×C17#4111yescharacteristic
49C4⋊Dic17—41no—
50#63225—81no—
51#63223—21no—
52Dic68SD1611yescharacteristic
53D136—41no—
54D136—41no—
55D136—41no—
56D136—41no—
57D136SD1611yescharacteristic
58#63219—21no—
59#63218—41no—
60C8×D17—41no—
61C16×C17—21no—
62C16×C17—21no—
63C16×C17—41no—
64C16×C17—41no—
65#63214—41no—
66#12465—171nomaximal, Sylow
67C22×D17—81no—
68C2×C4×C17—21no—
69C2×C4×C17#12111yescharacteristic
70C22⋊D17—41no—
71C2×Dic17—81no—
72D68—21no—
73D68—81no—
74D68—81no—
75D68—162no—
76C4×D17—41no—
77Dic34—21no—
78C8×C17C2×SD1611yescharacteristic
79C8×C17#13511yescharacteristic
80C8×C17#13511yescharacteristic
81C8×C17AGL(1,ℤ/8)11yescharacteristic
82#3622—41no—
83#2244—171no—
84#2231—171no—
85#2213—171no—
86#2171—171no—
87#1369D1711yescharacteristic, complemented
88#1366—171no—
89#1357—171no—
90C22×C17#47211yescharacteristic
91C2×D17—41no—
92C2×D17—162no—
93C2×D17—161no—
94C4×C17—41no—
95C4×C17#46311yescharacteristic
96C4×C17#46511yescharacteristic
97Dic17—41no—
98Dic17—161no—
99#509—341no—
100#504—341no—
101#499—171no—
102#493—171no—
103#443—171no—
104#365—341no—
105#364—171no—
106#364C2×D1711yescharacteristic
107#364C2×D1711yescharacteristic
108#361—341no—
109#360—341no—
110#357—341no—
111#357—341no—
112#350—341no—
113#346C2×D1711yescharacteristic
114C2×C17—21no—
115C2×C17#167711yescharacteristic
116D17—81no—
117D17—321no—
118#135—171no—
119C2×D8—341no—
120C2×D8—341no—
121#131—341no—
122#127—341no—
123#125—341no—
124SD32—681no—
125D16—681no—
126M32—21no—
127M32—21no—
128M32—341no—
129M32—681no—
130C2×C16—681no—
131C2×C16D6811yescharacteristic
132C2×C16D6811yescharacteristic
133#108—171no—
134#107—341no—
135#106—341no—
136#104—341no—
137C4×C8C22×D1711yescharacteristic
138C17#1246511yescharacteristic, complemented, Sylow
139#41—341no—
140C2×D4—681no—
141C2×D4—1361no—
142Q16—171no—
143SD16—341no—
144D8—171no—
145D8—681no—
146D8—681no—
147D8—681no—
148D8—681no—
149M16—341no—
150M16—681no—
151C2×C8—681no—
152C2×C8C2×D6811yescharacteristic
153C2×C8D4×D1711yescharacteristic
154C4⋊C4—681no—
155C4⋊C4—1361no—
156C42#6325611yescharacteristic
157C16—21no—
158C16—21no—
159C16—41no—
160C16—41no—
161C16—681no—
162C23—1361no—
163Q8—341no—
164D4—2722no—
165D4—341no—
166D4—681no—
167D4—1361no—
168D4—1361no—
169C2×C4—21no—
170C2×C4—681no—
171C2×C4—1361no—
172C2×C4#1058758111yescharacteristic
173C8—681no—
174C8#1058759011yescharacteristic
175C8#1058759411yescharacteristic
176C8SD16×D1711yescharacteristic
177C8#1058760211yescharacteristic
178C22—2722no—
179C22—2721no—
180C22—681no—
181C22#1176308011yescharacteristic
182C4—41no—
183C4—2721no—
184C4—681no—
185C4#1176302511yescharacteristic
186C4#1176303911yescharacteristic
187C2—21no—
188C2—5441no—
189C2—1361no—
190C2#1452819411yescharacteristic
subgroupG/H
centerC2#14528194
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1369C2
socleC2×C17#1677
prime radical#14530861C2
hypercenter#1369D17
hypocenterC17#12465
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1369

Complements

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

NH ≅ G/Ntype
1. #14531026C2semidirect
2. #14530961C2semidirect
4. #14530627C2semidirect
5. #14526844C2semidirect
6. #14526820C2semidirect
7. C17×#1369C2semidirect
87. #1369D17semidirect
138. C17#12465semidirect

Maximal subgroups

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

subgroupindex
#145310262
#145309612
#145308612
#145306272
#145268442
#145268202
C17×#13692
#1246517