Finite Group Databasebeta

← #16947704

Subgroups — #16947704

Order 4352.

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

normal subgroups only

This group has 274 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#14540178C211yesmaximal, characteristic
2#14531003C212yesmaximal
3#14526771C212yesmaximal
4#14526735C211yesmaximal, characteristic
5C17×#2102C211yesmaximal, characteristic
6#11763366—21no—
7#11763095—22no—
8#11763067—21no—
9#11763067C2212yes—
10#11763020—22no—
11#11762633—22no—
12#11762624—22no—
13#11762591C2212yes—
14C17×#430C2211yescharacteristic
15C17×#423C2211yescharacteristic
16C17×#344—21no—
17C17×#339—21no—
18C17×H(3,ℤ/4)C2211yescharacteristic
19C2×M16×C17—21no—
20C2×M16×C17D411yescharacteristic
21C2×M16×C17C2311yescharacteristic
22C17×#117—21no—
23C2×C42×C17D411yescharacteristic
24#10587612—41no—
25#10587610—22no—
26#10587610—41no—
27C2×Dic68—21no—
28C2×Dic68D412yes—
29#10587556—41no—
30#10587555—21no—
31#10587555—21no—
32C4×Dic34—22no—
33C4×Dic34—41no—
34C17×#108—22no—
35C17×C4⋊C8—22no—
36#10587488—21no—
37#10587488D412yes—
38#10587487—22no—
39#10587487—22no—
40#10587483—22no—
41C22×C4×C17—21no—
42C22×C4×C17C2×D411yescharacteristic
43C2×Dic34—22no—
44C2×Dic34—41no—
45M16×C17—41no—
46M16×C17—41no—
47M16×C17—41no—
48M16×C17—41no—
49C2×C8×C17—21no—
50C2×C8×C17—41no—
51C2×C8×C17C2×D412yes—
52C4⋊C4×C17—41no—
53C22⋊C4×C17—41no—
54C42×C17—21no—
55C42×C17—41no—
56C42×C17SD1611yescharacteristic
57C42×C17SD1611yescharacteristic
58C22⋊Dic17—42no—
59C4⋊Dic17—22no—
60C4⋊Dic17—41no—
61C4⋊Dic17—41no—
62C4⋊Dic17—41no—
63#63225—42no—
64#63225—42no—
65C4×Dic17—42no—
66Dic68—42no—
67Dic68—81no—
68#63214—42no—
69#12308—171nomaximal, Sylow
70C23×C17AGL(1,ℤ/8)11yescharacteristic
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—42no—
76C2×C4×C17—81no—
77C2×C4×C17#12011yescharacteristic
78C2×C4×C17C2×SD1611yescharacteristic
79C2×Dic17—42no—
80C2×Dic17—42no—
81Dic34—42no—
82Dic34—42no—
83Dic34—82no—
84C8×C17—22no—
85C8×C17—41no—
86C8×C17—81no—
87#3255—171no—
88#2239—172no—
89#2102D1711yescharacteristic
90#1340—172no—
91#1327—171no—
92C22×C17—21no—
93C22×C17—41no—
94C22×C17#45011yescharacteristic
95C4×C17—22no—
96C4×C17—21no—
97C4×C17—41no—
98C4×C17—161no—
99C4×C17#45411yescharacteristic
100C4×C17#45811yescharacteristic
101Dic17—82no—
102Dic17—82no—
103#533—341no—
104#475—342no—
105#470—172no—
106#470—341no—
107#462—342no—
108#430C2×D1711yescharacteristic
109#423C2×D1711yescharacteristic
110#365—342no—
111#362—342no—
112#349—172no—
113#344—21no—
114#339—21no—
115H(3,ℤ/4)C2×D1711yescharacteristic
116C2×C17—21no—
117C2×C17—41no—
118C2×C17#161611yescharacteristic
119C2×Q16—172no—
120C2×Q16—341no—
121C2×M16—21no—
122C2×M16C22⋊D1711yescharacteristic
123C2×M16C22×D1711yescharacteristic
124C4⋊Q8—341no—
125C4⋊Q8—341no—
126#125—681no—
127C22⋊Q8—342no—
128C22⋊Q8—681no—
129C4×Q8—342no—
130C4×Q8—681no—
131#117—21no—
132#117—681no—
133C2×C42C22⋊D1711yescharacteristic
134M32—342no—
135#108—22no—
136#106—172no—
137#106—341no—
138C4⋊C8—22no—
139#103—342no—
140#103—342no—
141C17#1230811yescharacteristic, complemented, Sylow
142C2×Q8—342no—
143C2×Q8—681no—
144C22×C4—21no—
145C22×C4C2×C22⋊D1711yescharacteristic
146Q16—682no—
147Q16—1361no—
148M16—41no—
149M16—41no—
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8D4×D1712yes—
155C4⋊C4—41no—
156C4⋊C4—342no—
157C4⋊C4—681no—
158C4⋊C4—681no—
159C4⋊C4—682no—
160C4⋊C4—681no—
161C4⋊C4—682no—
162C22⋊C4—41no—
163C22⋊C4—682no—
164C42—21no—
165C42—41no—
166C42—682no—
167C42#6323011yescharacteristic
168C42#6323011yescharacteristic
169C16—682no—
170C23#1058763511yescharacteristic
171Q8—682no—
172Q8—682no—
173Q8—1362no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—81no—
180C2×C4—682no—
181C2×C4—682no—
182C2×C4#1058762311yescharacteristic
183C2×C4C2×#6323011yescharacteristic
184C8—22no—
185C8—41no—
186C8—81no—
187C22—21no—
188C22—41no—
189C22#1176295911yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—161no—
194C4—1362no—
195C4—1362no—
196C4#1176298111yescharacteristic
197C4#1176299811yescharacteristic
198C2—21no—
199C2—41no—
200C2#1452782011yescharacteristic
subgroupG/H
centerC2#14527820
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
FittingC17×#2102C2
socleC2×C17#1616
prime radicalC23×C17AGL(1,ℤ/8)
hypercenter#2102D17
hypocenterC17#12308
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2102

Complements

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

NH ≅ G/Ntype
141. C17#12308semidirect

Maximal subgroups

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

subgroupindex
#145401782
#145310032
#145267712
#145267352
C17×#21022
#1230817