Finite Group Databasebeta

← #16947687

Subgroups — #16947687

Order 4352.

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

normal subgroups only

This group has 262 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#14540238C211yesmaximal, characteristic
2#14531003C212yesmaximal
3#14526777C212yesmaximal
4#14526737C211yesmaximal, characteristic
5C17×#2103C211yesmaximal, characteristic
6#11763421—21no—
7#11763117—22no—
8#11763067C2212yes—
9#11763050—21no—
10#11763020—22no—
11#11762633—22no—
12#11762624—22no—
13#11762591C2212yes—
14C17×#430C2211yescharacteristic
15C17×#424C2211yescharacteristic
16C17×#344—21no—
17C17×#341—21no—
18C17×#338C2211yescharacteristic
19C2×M16×C17—21no—
20C2×M16×C17—21no—
21C2×M16×C17C2311yescharacteristic
22C22×C8×C17D411yescharacteristic
23C17×#117D411yescharacteristic
24#10587610—22no—
25C2×Dic68—21no—
26C2×Dic68D412yes—
27#10587575—42no—
28#10587565—42no—
29#10587556—21no—
30#10587555—21no—
31C4×Dic34—22no—
32C17×#108—22no—
33C17×C4⋊C8—22no—
34#10587489—21no—
35#10587488D412yes—
36#10587487—22no—
37#10587487—22no—
38#10587483—22no—
39C22×C4×C17C2×D411yescharacteristic
40C2×Dic34—22no—
41M16×C17—41no—
42M16×C17—41no—
43M16×C17—41no—
44M16×C17—41no—
45M16×C17—41no—
46C2×C8×C17—21no—
47C2×C8×C17—41no—
48C2×C8×C17—41no—
49C2×C8×C17—41no—
50C2×C8×C17C2×D412yes—
51C4⋊C4×C17—21no—
52C22⋊C4×C17SD1612yes—
53C42×C17—21no—
54C22⋊Dic17—42no—
55C4⋊Dic17—22no—
56C4⋊Dic17—42no—
57#63225—42no—
58#63225—42no—
59#63225—42no—
60C4×Dic17—42no—
61Dic68—42no—
62Dic68—81no—
63#63214—42no—
64#12305—171nomaximal, Sylow
65C23×C17C2×SD1611yescharacteristic
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—22no—
69C2×C4×C17#12011yescharacteristic
70C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
71C2×Dic17—42no—
72C2×Dic17—42no—
73Dic34—42no—
74Dic34—42no—
75C8×C17—22no—
76C8×C17—41no—
77C8×C17—81no—
78C8×C17—81no—
79#3261—171no—
80#2239—172no—
81#2103D1711yescharacteristic
82#1342—172no—
83#1328—171no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17#45011yescharacteristic
87C4×C17—21no—
88C4×C17—42no—
89C4×C17#45411yescharacteristic
90C4×C17#45811yescharacteristic
91Dic17—82no—
92Dic17—82no—
93#541—341no—
94#479—342no—
95#470—172no—
96#467—341no—
97#462—342no—
98#430C2×D1711yescharacteristic
99#424C2×D1711yescharacteristic
100#365—342no—
101#362—342no—
102#349—172no—
103#344—21no—
104#341—21no—
105#338C2×D1711yescharacteristic
106C2×C17—21no—
107C2×C17—41no—
108C2×C17#161611yescharacteristic
109C2×Q16—172no—
110C2×Q16—341no—
111C2×M16—21no—
112C2×M16—21no—
113C2×M16C22×D1711yescharacteristic
114C22×C8C22⋊D1711yescharacteristic
115C4⋊Q8—341no—
116#126—682no—
117#125—341no—
118#125—682no—
119C22⋊Q8—342no—
120C4×Q8—342no—
121#117C22⋊D1711yescharacteristic
122M32—342no—
123#108—22no—
124#107—341no—
125#106—172no—
126C4⋊C8—22no—
127#103—342no—
128#103—342no—
129C17#1230511yescharacteristic, complemented, Sylow
130C2×Q8—342no—
131C22×C4C2×C22⋊D1711yescharacteristic
132Q16—682no—
133Q16—1361no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8D4×D1712yes—
144C4⋊C4—21no—
145C4⋊C4—342no—
146C4⋊C4—682no—
147C4⋊C4—682no—
148C4⋊C4—682no—
149C4⋊C4—682no—
150C22⋊C4—682no—
151C22⋊C4#6323012yes—
152C42—21no—
153C42—682no—
154C16—682no—
155C23C2×#6323011yescharacteristic
156Q8—682no—
157Q8—682no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—682no—
162C2×C4—682no—
163C2×C4#1058762311yescharacteristic
164C2×C4#1058763511yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#1176295911yescharacteristic
172C4—21no—
173C4—42no—
174C4—1362no—
175C4—1362no—
176C4#1176298111yescharacteristic
177C4#1176299811yescharacteristic
178C2—21no—
179C2—41no—
180C2#1452782011yescharacteristic
subgroupG/H
centerC2#14527820
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
FittingC17×#2103C2
socleC2×C17#1616
prime radicalC23×C17C2×SD16
hypercenter#2103D17
hypocenterC17#12305
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
129. C17#12305semidirect

Maximal subgroups

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

subgroupindex
#145402382
#145310032
#145267772
#145267372
C17×#21032
#1230517