Finite Group Databasebeta

← #16948726

Subgroups — #16948726

Order 4352.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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#14531025C211yesmaximal, characteristic, complemented
2#14530961C211yesmaximal, characteristic, complemented
3#14530857C211yesmaximal, characteristic
4#14530625C211yesmaximal, characteristic, complemented
5#14526851C211yesmaximal, characteristic, complemented
6#14526846C211yesmaximal, characteristic, complemented
7C17×#1357C211yesmaximal, characteristic, complemented
8#11763245—21no—
9#11763227—21no—
10#11763211C2211yescharacteristic
11#11762927C2211yescharacteristic
12#11762632—21no—
13#11762630C2211yescharacteristic
14#11762622—21no—
15#11762620—21no—
16#11762610—21no—
17#11762610—21no—
18#11762594—21no—
19#11762585C2211yescharacteristic
20C17×#493C2211yescharacteristic
21C17×#364C2211yescharacteristic
22C17×#364C2211yescharacteristic
23C2×D8×C17—21no—
24C2×D8×C17—21no—
25C17×#127—21no—
26#10587590D411yescharacteristic
27#10587587—21no—
28#10587556—21no—
29C17×M32—21no—
30C17×M32—21no—
31C4×C8×C17C2311yescharacteristic
32#10587498—41no—
33#10587497—41no—
34#10587490D411yescharacteristic
35#10587489—21no—
36#10587488—21no—
37#10587483—21no—
38C2×#63214D411yescharacteristic
39C2×#63214D411yescharacteristic
40#10587476—21no—
41#10587469—41no—
42C16×D17—41no—
43C2×D4×C17—41no—
44C2×D4×C17—81no—
45#63252—21no—
46D8×C17—41no—
47D8×C17—41no—
48D8×C17—41no—
49D8×C17—41no—
50C2×C8×C17C2×D411yescharacteristic
51C2×C8×C17C2×D411yescharacteristic
52C42×C17#4111yescharacteristic
53C4⋊Dic17—41no—
54#63225—81no—
55#63223—21no—
56Dic68SD1611yescharacteristic
57D136SD1611yescharacteristic
58#63219—21no—
59#63218—41no—
60C8×D17—41no—
61C16×C17—41no—
62C16×C17—41no—
63#63214—21no—
64#63214—21no—
65#63214—41no—
66#12465—171nomaximal, Sylow
67C23×C17—81no—
68D4×C17—81no—
69D4×C17—81no—
70D4×C17—162no—
71C2×C4×C17—21no—
72C2×C4×C17#12111yescharacteristic
73C22⋊D17—41no—
74C2×Dic17—81no—
75D68—21no—
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#1369—171no—
88#1366—171no—
89#1357D1711yescharacteristic, complemented
90C22×C17—162no—
91C22×C17—161no—
92C22×C17#47211yescharacteristic
93C2×D17—41no—
94C4×C17—41no—
95C4×C17#46311yescharacteristic
96C4×C17#46511yescharacteristic
97Dic17—41no—
98Dic17—161no—
99#509—341no—
100#504—341no—
101#499—171no—
102#493C2×D1711yescharacteristic
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#346—171no—
114C2×C17—21no—
115C2×C17—321no—
116C2×C17#167711yescharacteristic
117D17—81no—
118#135—171no—
119C2×D8—21no—
120C2×D8—21no—
121#131—341no—
122#127—21no—
123#125—341no—
124SD32—681no—
125D16—681no—
126M32—21no—
127M32—21no—
128M32—341no—
129M32—681no—
130C2×C16—171no—
131C2×C16—171no—
132C2×C16—681no—
133#108—171no—
134#107—341no—
135#106—341no—
136#104—341no—
137C4×C8C22×D1711yescharacteristic
138C17#1246511yescharacteristic, complemented, Sylow
139#41—341no—
140C2×D4—41no—
141C2×D4—81no—
142Q16—171no—
143SD16—341no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8—171no—
149M16—341no—
150M16—681no—
151C2×C8—681no—
152C2×C8D4×D1711yescharacteristic
153C2×C8D4×D1711yescharacteristic
154C4⋊C4—681no—
155C4⋊C4—1361no—
156C42#6325211yescharacteristic
157C16—41no—
158C16—41no—
159C16—341no—
160C16—341no—
161C16—681no—
162C23—81no—
163Q8—341no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—341no—
168D4—681no—
169C2×C4—21no—
170C2×C4—681no—
171C2×C4—1361no—
172C2×C4#1058757011yescharacteristic
173C8—681no—
174C8#1058759711yescharacteristic
175C8#1058759811yescharacteristic
176C8SD16×D1711yescharacteristic
177C8#1058760211yescharacteristic
178C22—162no—
179C22—161no—
180C22—681no—
181C22#1176307811yescharacteristic
182C4—41no—
183C4—2721no—
184C4—681no—
185C4#1176302311yescharacteristic
186C4#1176303711yescharacteristic
187C2—21no—
188C2—321no—
189C2—1361no—
190C2#1452819211yescharacteristic
subgroupG/H
centerC2#14528192
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1357C2
socleC2×C17#1677
prime radical#14530857C2
hypercenter#1357D17
hypocenterC17#12465
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #14531025C2semidirect
2. #14530961C2semidirect
4. #14530625C2semidirect
5. #14526851C2semidirect
6. #14526846C2semidirect
7. C17×#1357C2semidirect
89. #1357D17semidirect
138. C17#12465semidirect

Maximal subgroups

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

subgroupindex
#145310252
#145309612
#145308572
#145306252
#145268512
#145268462
C17×#13572
#1246517