Finite Group Databasebeta

← #16955200

Subgroups — #16955200

Order 4352.

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

normal subgroups only

This group has 184 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
1C2×#11762648C211yesmaximal, characteristic, complemented
2#14531077C211yesmaximal, characteristic, complemented
3#14530910C211yesmaximal, characteristic, complemented
4#14530905C211yesmaximal, characteristic
5#14526976C211yesmaximal, characteristic, complemented
6#14526973C211yesmaximal, characteristic, complemented
7C17×#1425C211yesmaximal, characteristic, complemented
8C2×Dic136C2211yescharacteristic
9C2×D272C2211yescharacteristic
10#11763225C2211yescharacteristic
11#11763085—21no—
12#11763080—21no—
13#11762648—21no—
14#11762648—21no—
15#11762643C2211yescharacteristic
16#11762642—21no—
17C32×D17—21no—
18#11762624—21no—
19#11762621—21no—
20C2×C17×C32C2211yescharacteristic
21C17×#368C2211yescharacteristic
22C17×#368C2211yescharacteristic
23#10587595—41no—
24#10587594—41no—
25C2×Dic68—21no—
26C2×D136—21no—
27#10587587D411yescharacteristic
28C2×C16×C17C2311yescharacteristic
29C17×#108—21no—
30C17×#108—21no—
31#10587495—41no—
32#10587494—41no—
33#10587483D411yescharacteristic
34Dic136—21no—
35Dic136—21no—
36D272—21no—
37D272—21no—
38#10587469—21no—
39C16×D17—21no—
40C17×C32D411yescharacteristic
41C17×C32D411yescharacteristic
42#10587465—21no—
43#63252D811yescharacteristic
44C2×D68—41no—
45C2×Dic34—41no—
46M16×C17—41no—
47M16×C17—41no—
48C2×C8×C17C2×D411yescharacteristic
49#63223D811yescharacteristic
50Dic68—41no—
51Dic68—41no—
52Dic68—81no—
53D136—41no—
54D136—41no—
55D136—81no—
56#63219—81no—
57#63219—81no—
58#63218—21no—
59C8×D17—21no—
60C16×C17C2×D411yescharacteristic
61C16×C17#4111yescharacteristic
62#63214—21no—
63#13702—171nomaximal, Sylow
64C22×D17—81no—
65C2×C4×C17C2×D811yescharacteristic
66C22⋊D17—21no—
67C2×Dic17—81no—
68D68—81no—
69D68—81no—
70D68D1611yescharacteristic
71C4×D17—21no—
72Dic34—81no—
73Dic34—81no—
74Dic34D1611yescharacteristic
75C8×C17—81no—
76C8×C17—81no—
77C8×C17#12111yescharacteristic
78C8×C17#13511yescharacteristic
79#3622—21no—
80C2×SD64—171no—
81#2258—171no—
82#2222—171no—
83#2221—171no—
84#1425D1711yescharacteristic, complemented
85#1420—171no—
86#1419—171no—
87C22×C17#50811yescharacteristic
88C2×D17—21no—
89C2×D17—161no—
90C2×D17—321no—
91C4×C17#46611yescharacteristic
92C4×C17C2×D1611yescharacteristic
93Dic17—21no—
94Dic17—161no—
95C2×Q32—171no—
96C2×D16—171no—
97#504—171no—
98#473—341no—
99#472—341no—
100SD64—341no—
101SD64—341no—
102M64—171no—
103M64—341no—
104C2×C32—341no—
105C2×C32C2×D1711yescharacteristic
106#368C2×D1711yescharacteristic
107#368C2×D1711yescharacteristic
108#362—341no—
109#361—341no—
110C2×C17—21no—
111C2×C17#221511yescharacteristic
112D17—41no—
113D17—321no—
114#137—681no—
115AGL(1,ℤ/8)—681no—
116C2×Q16—341no—
117C2×D8—341no—
118#131—171no—
119Q32—341no—
120Q32—341no—
121D16—341no—
122D16—341no—
123M32—171no—
124M32—341no—
125C2×C16—341no—
126C2×C16C22×D1711yescharacteristic
127#108—21no—
128#108—21no—
129#101—681no—
130#100—681no—
131C32—341no—
132C32D6811yescharacteristic
133C32D6811yescharacteristic
134C17#1370211yescharacteristic, complemented, Sylow
135#41—171no—
136C2×Q8—681no—
137C2×D4—681no—
138Q16—681no—
139Q16—681no—
140Q16—1361no—
141SD16—1361no—
142SD16—1361no—
143D8—681no—
144D8—681no—
145D8—1361no—
146M16—41no—
147M16—41no—
148M16—171no—
149M16—341no—
150C2×C8—341no—
151C2×C8D4×D1711yescharacteristic
152C16—341no—
153C16C2×D6811yescharacteristic
154C16#6325611yescharacteristic
155C23—1361no—
156Q8—171no—
157Q8—1361no—
158Q8—1361no—
159D4—171no—
160D4—341no—
161D4—1361no—
162D4—1361no—
163C2×C4—341no—
164C2×C4—1361no—
165C2×C4D8×D1711yescharacteristic
166C8—81no—
167C8—81no—
168C8—341no—
169C8#1058758111yescharacteristic
170C8#1058760511yescharacteristic
171C22—2721no—
172C22—5441no—
173C22—341no—
174C22#1176324211yescharacteristic
175C4—2721no—
176C4—341no—
177C4#1176304611yescharacteristic
178C4D16×D1711yescharacteristic
179C2—21no—
180C2—5441no—
181C2—681no—
182C2#1453087111yescharacteristic
subgroupG/H
centerC2#14530871
commutator, cosocleC2×C16×C17C23
FrattiniC2×C16C22×D17
FittingC17×#1425C2
socleC2×C17#2215
prime radical#14530905C2
hypercenter#1425D17
hypocenterC17#13702
LCSG ▷ C2×C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1425

Complements

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

NH ≅ G/Ntype
1. C2×#11762648C2semidirect
2. #14531077C2semidirect
3. #14530910C2semidirect
5. #14526976C2semidirect
6. #14526973C2semidirect
7. C17×#1425C2semidirect
84. #1425D17semidirect
134. C17#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#117626482
#145310772
#145309102
#145309052
#145269762
#145269732
C17×#14252
#1370217