Finite Group Databasebeta

← #16955137

Subgroups — #16955137

Order 4352.

200 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 51 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#14531104C211yesmaximal, characteristic, complemented
2#14531097C211yesmaximal, characteristic
3#14531042C211yesmaximal, characteristic, complemented
4#14530664C211yesmaximal, characteristic, complemented
5#14526981C211yesmaximal, characteristic, complemented
6#14526976C211yesmaximal, characteristic, complemented
7C17×#1419C211yesmaximal, characteristic, complemented
8#11763241C2211yescharacteristic
9C2×Dic136C2211yescharacteristic
10C2×#10587498—21no—
11#11763192—21no—
12#11762925—21no—
13Dic272—21no—
14#11762648—21no—
15#11762647—21no—
16#11762644—21no—
17#11762643C2211yescharacteristic
18#11762615—21no—
19C16×Dic17C2211yescharacteristic
20C2×C17×D16C2211yescharacteristic
21C17×M64C2211yescharacteristic
22C17×#368C2211yescharacteristic
23C2×D8×C17—21no—
24#10587622—41no—
25C2×#63229—41no—
26#10587593—41no—
27C2×Dic68—21no—
28#10587590—21no—
29C17×D16—21no—
30C17×D16—21no—
31C2×C16×C17C2311yescharacteristic
32C17×#108—21no—
33#10587498—42no—
34#10587496—41no—
35C8×Dic17D411yescharacteristic
36C2×#63214D411yescharacteristic
37Dic136—21no—
38Dic136—21no—
39Dic136D411yescharacteristic
40#10587471—21no—
41D272D411yescharacteristic
42C17×C32—21no—
43#10587465—21no—
44C2×D4×C17—41no—
45#63252—41no—
46C2×Dic34—41no—
47D8×C17—41no—
48D8×C17—41no—
49M16×C17—41no—
50C2×C8×C17C2×D411yescharacteristic
51C22⋊Dic17—82no—
52#63229—81no—
53#63229—81no—
54C4×Dic17D811yescharacteristic
55C2×#3622D811yescharacteristic
56Dic68—21no—
57Dic68—41no—
58Dic68—41no—
59D136—21no—
60#63219—41no—
61#63218—81no—
62C8×D17—81no—
63C16×C17C2×D411yescharacteristic
64C16×C17#4111yescharacteristic
65#63214—21no—
66#13691—171nomaximal, Sylow
67C23×C17—81no—
68D4×C17—81no—
69D4×C17—81no—
70C2×C4×C17C2×D811yescharacteristic
71C22⋊D17—81no—
72C2×Dic17—21no—
73C2×Dic17—81no—
74D68—41no—
75C4×D17—81no—
76Dic34—41no—
77Dic34—81no—
78Dic34—81no—
79C8×C17—81no—
80C8×C17#12111yescharacteristic
81C8×C17AGL(1,ℤ/8)11yescharacteristic
82#3622D1611yescharacteristic
83#3622D1611yescharacteristic
84#2264—171no—
85#2263—171no—
86#2249—171no—
87#2178—171no—
88#1422—171no—
89#1420—171no—
90#1419D1711yescharacteristic, complemented
91C22×C17—162no—
92C22×C17—161no—
93C22×C17#50911yescharacteristic
94C2×D17—81no—
95C4×C17#45911yescharacteristic
96C4×C17C2×D1611yescharacteristic
97Dic17—41no—
98Dic17—81no—
99Dic17—161no—
100#508—171no—
101C2×Q32—171no—
102C2×SD32—341no—
103C2×D16C2×D1711yescharacteristic
104#495—341no—
105#443—341no—
106Q64—341no—
107SD64—341no—
108SD64—341no—
109D32—341no—
110M64—171no—
111M64C2×D1711yescharacteristic
112#368C2×D1711yescharacteristic
113#359—341no—
114C4×C16—171no—
115C2×C17—21no—
116C2×C17—321no—
117C2×C17#220611yescharacteristic
118D17—161no—
119#135—341no—
120C2×Q16—341no—
121C2×SD16—681no—
122C2×D8—21no—
123#131—681no—
124#124—681no—
125Q32—171no—
126Q32—341no—
127Q32—341no—
128SD32—341no—
129SD32—682no—
130D16—21no—
131D16—21no—
132D16—171no—
133C2×C16—171no—
134C2×C16C22×D1711yescharacteristic
135#108—21no—
136#104—681no—
137C4×C8—171no—
138C32—21no—
139C32—341no—
140C17#1369111yescharacteristic, complemented, Sylow
141#41—681no—
142C2×Q8—681no—
143C2×D4—41no—
144Q16—341no—
145Q16—681no—
146Q16—681no—
147SD16—681no—
148SD16—1361no—
149SD16—1361no—
150D8—41no—
151D8—41no—
152D8—341no—
153M16—41no—
154M16—1361no—
155C2×C8—171no—
156C2×C8—1361no—
157C2×C8D4×D1711yescharacteristic
158C22⋊C4—1362no—
159C42—171no—
160C16—341no—
161C16#6325211yescharacteristic
162C16D4×D1711yescharacteristic
163C23—81no—
164Q8—681no—
165Q8—1361no—
166Q8—1361no—
167D4—81no—
168D4—81no—
169D4—681no—
170D4—1361no—
171C2×C4—341no—
172C2×C4—1361no—
173C2×C4—1361no—
174C2×C4D8×D1711yescharacteristic
175C8—81no—
176C8—171no—
177C8—171no—
178C8#1058757011yescharacteristic
179C8#1058760011yescharacteristic
180C22—162no—
181C22—161no—
182C22—1361no—
183C22#1176324611yescharacteristic
184C4—2721no—
185C4—681no—
186C4—1361no—
187C4#1176300311yescharacteristic
188C4D16×D1711yescharacteristic
189C2—21no—
190C2—2721no—
191C2—321no—
192C2#1453081811yescharacteristic
subgroupG/H
centerC2#14530818
commutator, cosocleC2×C16×C17C23
FrattiniC2×C16C22×D17
FittingC17×#1419C2
socleC2×C17#2206
prime radical#14531097C2
hypercenter#1419D17
hypocenterC17#13691
LCSG ▷ C2×C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #14531104C2semidirect
3. #14531042C2semidirect
4. #14530664C2semidirect
5. #14526981C2semidirect
6. #14526976C2semidirect
7. C17×#1419C2semidirect
90. #1419D17semidirect
140. C17#13691semidirect

Maximal subgroups

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

subgroupindex
#145311042
#145310972
#145310422
#145306642
#145269812
#145269762
C17×#14192
#1369117