Finite Group Databasebeta

← #17949327

Subgroups — #17949327

Order 4352.

210 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 32 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#14543717C211yesmaximal, characteristic
2#14543664C211yesmaximal, characteristic
3#14530301C211yesmaximal, characteristic
4C4×C22⋊#595—21no—
5#11763705—21no—
6#11762858—21no—
7#11762858C411yescharacteristic, complemented
8#11762772—21no—
9#11762772C2211yescharacteristic
10C17×#338C411yescharacteristic, complemented
11C22×C4×D17D411yescharacteristic
12C2×C22⋊#595—41no—
13C2×C4×#595—41no—
14C2×M16×C17—21no—
15C2×M16×C17C2×C411yescharacteristic
16C2×#63223—21no—
17C2×#63223D411yescharacteristic
18(C2×#595)⋊C4—22no—
19#10587538—41no—
20#10587491—41no—
21#10587491—42no—
22#10587490—41no—
23#10587490—42no—
24C23×D17SD1611yescharacteristic
25C22×#595—42no—
26C22×C4×C17C22⋊C411yescharacteristic
27C22×Dic17Q1611yescharacteristic
28C2×C4×D17—21no—
29C2×C4×D17—21no—
30C2×C4×D17—41no—
31C2×C4×D17—41no—
32C22⋊#595—44no—
33C4×#595—81no—
34C4×#595—81no—
35M16×C17—41no—
36M16×C17—41no—
37M16×C17—41no—
38C2×C8×C17—22no—
39C2×C8×C17—21no—
40#63223—41no—
41#63223—41no—
42#63223—41no—
43C2×#3622—21no—
44C2×#3622—41no—
45#63216—81no—
46#7432—171nomaximal, Sylow
47C23×C17#10311yescharacteristic
48C22×D17—21no—
49C22×D17—42no—
50C22×D17—41no—
51C2×#595—44no—
52C2×#595—82no—
53C2×#595—82no—
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17#9911yescharacteristic
57C2×C4×C17#10411yescharacteristic
58C2×Dic17—21no—
59C2×Dic17—41no—
60C4×D17—41no—
61C4×D17—41no—
62C4×D17—81no—
63C8×C17—42no—
64C8×C17—41no—
65#3622—41no—
66#3622—81no—
67#2091—171no—
68#1320—171no—
69#1297—171no—
70C22×C17—21no—
71C22×C17—41no—
72C22×C17#32811yescharacteristic
73C2×D17—22no—
74C2×D17—41no—
75C2×D17—41no—
76C2×D17—42no—
77C2×D17—81no—
78#595—84no—
79C4×C17—21no—
80C4×C17#35211yescharacteristic
81C4×C17#35311yescharacteristic
82Dic17—41no—
83#430—171no—
84#430—341no—
85#407—171no—
86#407—341no—
87C4×C22⋊C4—341no—
88#349—341no—
89#338#59511yescharacteristic, complemented
90C2×C17—21no—
91C2×C17—41no—
92C2×C17#135211yescharacteristic
93D17—42no—
94C23×C4—171no—
95C2×M16—21no—
96C2×M16—171no—
97C2×M16—341no—
98C2×M16C2×#59511yescharacteristic
99C2×C22⋊C4—681no—
100C2×C42—681no—
101M32—681no—
102#108—681no—
103#108—682no—
104C22⋊C8—681no—
105C22⋊C8—682no—
106#95—342no—
107C17#743211yescharacteristic, complemented, Sylow
108C24—171no—
109C22×C4—171no—
110C22×C4—341no—
111C22×C4—341no—
112C22×C4—681no—
113C22×C4—681no—
114C22×C4—682no—
115C22×C4C22⋊#59511yescharacteristic
116M16—41no—
117M16—41no—
118M16—41no—
119M16—681no—
120M16—681no—
121M16—681no—
122C2×C8—22no—
123C2×C8—21no—
124C2×C8—341no—
125C2×C8—681no—
126C22⋊C4—684no—
127C42—1361no—
128C42—1361no—
129C16—1361no—
130C23—341no—
131C23—681no—
132C23—682no—
133C23#1058754911yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—341no—
137C2×C4—681no—
138C2×C4—681no—
139C2×C4—681no—
140C2×C4—684no—
141C2×C4—1361no—
142C2×C4—1362no—
143C2×C4—1362no—
144C2×C4#1058753911yescharacteristic
145C2×C4#1058754811yescharacteristic
146C8—42no—
147C8—41no—
148C8—681no—
149C8—1361no—
150C22—21no—
151C22—41no—
152C22—342no—
153C22—681no—
154C22—682no—
155C22—681no—
156C22—1361no—
157C22#1176366211yescharacteristic
158C4—21no—
159C4—681no—
160C4—1364no—
161C4#1176371211yescharacteristic
162C4#1176371411yescharacteristic
163C2—21no—
164C2—41no—
165C2—682no—
166C2#1454378011yescharacteristic
subgroupG/H
centerC4#11763714
commutatorC2×M16×C17C2×C4
FrattiniC2×M16C2×#595
FittingC17×#338C4
socleC2×C17#1352
prime radicalC23×D17SD16
cosocle#11762772C22
hypercenter#338#595
hypocenterC17#7432
LCSG ▷ C2×M16×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
7. #11762858C4semidirect
10. C17×#338C4semidirect
89. #338#595semidirect
107. C17#7432semidirect

Maximal subgroups

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

subgroupindex
#145437172
#145436642
#145303012
#743217