Finite Group Databasebeta

← #16947688

Subgroups — #16947688

Order 4352.

262 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 59 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#14531001C212yesmaximal
2#14530364C211yesmaximal, characteristic
3#14526778C212yesmaximal
4#14526737C211yesmaximal, characteristic
5C17×#3261C211yesmaximal, characteristic
6#11762858C2211yescharacteristic
7#11762631—22no—
8#11762625—22no—
9#11762591C2212yes—
10#11762579—21no—
11#11762574—21no—
12#11762567C2211yescharacteristic
13C17×#541—21no—
14C17×#479—22no—
15C17×#470C2212yes—
16C17×#467—21no—
17C17×#462—22no—
18C17×#424C2211yescharacteristic
19C2×Q16×C17—21no—
20C2×Q16×C17D412yes—
21C2×M16×C17C2311yescharacteristic
22C22×C8×C17D411yescharacteristic
23C17×C4⋊Q8—21no—
24C17×#126—42no—
25C17×#125—21no—
26C17×#125—42no—
27C17×C22⋊Q8—22no—
28C4×Q8×C17—22no—
29C17×#117D411yescharacteristic
30C2×#63223—21no—
31C2×#63223—21no—
32C17×#107—21no—
33C17×#106D412yes—
34C17×C4⋊C8—22no—
35C17×#103—22no—
36C17×#103—22no—
37#10587490—22no—
38#10587483—22no—
39C2×Q8×C17—22no—
40C22×C4×C17C2×D411yescharacteristic
41Q16×C17—42no—
42Q16×C17—81no—
43M16×C17—41no—
44C2×C8×C17—21no—
45C2×C8×C17—41no—
46C2×C8×C17C2×D412yes—
47C4⋊C4×C17—21no—
48C4⋊C4×C17—22no—
49C4⋊C4×C17—42no—
50C4⋊C4×C17—42no—
51C4⋊C4×C17—42no—
52C4⋊C4×C17—42no—
53C22⋊C4×C17—42no—
54C22⋊C4×C17SD1612yes—
55C42×C17—21no—
56C42×C17—42no—
57#63223—41no—
58#63223—41no—
59#63223—41no—
60#63223—41no—
61C2×#3622—41no—
62C2×#3622—41no—
63#63214—42no—
64#12305—171nomaximal, Sylow
65C23×C17C2×SD1611yescharacteristic
66Q8×C17—42no—
67Q8×C17—42no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—42no—
72C2×C4×C17—42no—
73C2×C4×C17#12011yescharacteristic
74C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
75C8×C17—22no—
76C8×C17—41no—
77#3622—81no—
78#3622—81no—
79#3261D1711yescharacteristic
80#2239—172no—
81#2103—171no—
82#1342—172no—
83#1328—171no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17#45011yescharacteristic
87C4×C17—21no—
88C4×C17—42no—
89C4×C17—82no—
90C4×C17—82no—
91C4×C17#45411yescharacteristic
92C4×C17#45811yescharacteristic
93#541—21no—
94#479—22no—
95#470C2×D1712yes—
96#467—21no—
97#462—22no—
98#430—171no—
99#424C2×D1711yescharacteristic
100#365—342no—
101#362—342no—
102#349—172no—
103#344—341no—
104#341—341no—
105#338—171no—
106C2×C17—21no—
107C2×C17—41no—
108C2×C17#161611yescharacteristic
109C2×Q16—21no—
110C2×Q16C22⋊D1712yes—
111C2×M16—341no—
112C2×M16—341no—
113C2×M16C22×D1711yescharacteristic
114C22×C8C22⋊D1711yescharacteristic
115C4⋊Q8—21no—
116#126—42no—
117#125—21no—
118#125—42no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117C22⋊D1711yescharacteristic
122M32—342no—
123#108—342no—
124#107—21no—
125#106C22⋊D1712yes—
126C4⋊C8—22no—
127#103—22no—
128#103—22no—
129C17#1230511yescharacteristic, complemented, Sylow
130C2×Q8—22no—
131C22×C4C2×C22⋊D1711yescharacteristic
132Q16—42no—
133Q16—81no—
134M16—41no—
135M16—681no—
136M16—681no—
137M16—681no—
138M16—681no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—681no—
142C2×C8—681no—
143C2×C8C2×C22⋊D1712yes—
144C4⋊C4—21no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—42no—
151C22⋊C4#6322912yes—
152C42—21no—
153C42—42no—
154C16—682no—
155C23C2×#6322911yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#1058761811yescharacteristic
164C2×C4#1058763911yescharacteristic
165C8—22no—
166C8—41no—
167C8—1361no—
168C8—1361no—
169C22—21no—
170C22—41no—
171C22#1176296011yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#1176298211yescharacteristic
177C4#1176299911yescharacteristic
178C2—21no—
179C2—41no—
180C2#1452782111yescharacteristic
subgroupG/H
centerC2#14527821
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
FittingC17×#3261C2
socleC2×C17#1616
prime radicalC23×C17C2×SD16
hypercenter#3261D17
hypocenterC17#12305
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3261

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
#145310012
#145303642
#145267782
#145267372
C17×#32612
#1230517