Finite Group Databasebeta

← #17949348

Subgroups — #17949348

Order 4352.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543725C211yesmaximal, characteristic
2#14543660C211yesmaximal, characteristic
3#14530131C211yesmaximal, characteristic
4C2×#10587542—21no—
5#11763654—21no—
6#11762852—21no—
7#11762674C2211yescharacteristic
8#11762578C411yescharacteristic
9#11762568—21no—
10C17×#544C411yescharacteristic
11C22×#3624—41no—
12C17×C4⋊Q8—41no—
13C17×#125—41no—
14C17×C22⋊Q8—41no—
15C17×#117—21no—
16C2×C4⋊C4×C17C2×C411yescharacteristic
17C2×C4⋊Dic17D411yescharacteristic
18C2×C4×Dic17D411yescharacteristic
19C2×#63223—21no—
20C22⋊#3624—41no—
21#10587542—22no—
22#10587542—41no—
23#10587502—41no—
24#10587479—41no—
25#10587478—41no—
26C2×Q8×C17—41no—
27C22×C4×C17—21no—
28C22×C4×C17C22⋊C411yescharacteristic
29C22×Dic17—21no—
30C22×Dic17—21no—
31C2×#3624—42no—
32C2×#3624—42no—
33C2×#3624—42no—
34C2×#3624—81no—
35C4⋊C4×C17—21no—
36C4⋊C4×C17—21no—
37C4⋊C4×C17—41no—
38C4⋊C4×C17—41no—
39C4⋊C4×C17—42no—
40C22⋊C4×C17—41no—
41C42×C17—41no—
42C4⋊Dic17—41no—
43C4×Dic17—21no—
44C4×Dic17SD1611yescharacteristic
45C4×Dic17Q1611yescharacteristic
46#63223—22no—
47#63223—41no—
48C2×#3622—41no—
49#7442—171nomaximal, Sylow
50C23×C17#9911yescharacteristic
51Q8×C17—161no—
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—41no—
55C2×C4×C17—41no—
56C2×C4×C17—41no—
57C2×C4×C17—81no—
58C2×C4×C17#10311yescharacteristic
59C2×C4×C17#10411yescharacteristic
60C2×Dic17—21no—
61C2×Dic17—21no—
62C2×Dic17—41no—
63C2×Dic17—41no—
64C2×Dic17—41no—
65C2×Dic17—81no—
66#3624—44no—
67#3624—161no—
68#3622—42no—
69#2061—171no—
70#1324—171no—
71#1295—171no—
72C22×C17—21no—
73C22×C17—21no—
74C22×C17#32811yescharacteristic
75C22×C17AΣL(1,𝔽16)11yescharacteristic
76C22×C17#35611yescharacteristic
77C4×C17—21no—
78C4×C17—21no—
79C4×C17—81no—
80C4×C17—81no—
81C4×C17—81no—
82Dic17—41no—
83Dic17—41no—
84Dic17—81no—
85#544#59511yescharacteristic
86#428—341no—
87C2×#97—341no—
88#382—171no—
89#343—171no—
90#339—341no—
91#324—341no—
92C2×C17—21no—
93C2×C17—21no—
94C2×C17#135411yescharacteristic
95C2×C17#140311yescharacteristic
96C2×C17#140411yescharacteristic
97C2×M16—341no—
98C22×C8—681no—
99C4⋊Q8—41no—
100#125—41no—
101C22⋊Q8—41no—
102#117—21no—
103C2×C4⋊C4—171no—
104C2×C4⋊C4C2×#59511yescharacteristic
105C2×C42—171no—
106#107—681no—
107#106—681no—
108C22⋊C8—681no—
109#97—342no—
110#97—681no—
111#95—681no—
112C17#744211yescharacteristic, complemented, Sylow
113C2×Q8—41no—
114C22×C4—21no—
115C22×C4—341no—
116C22×C4—341no—
117C22×C4C22⋊#59511yescharacteristic
118M16—342no—
119M16—681no—
120C2×C8—681no—
121C2×C8—682no—
122C2×C8—682no—
123C2×C8—682no—
124C2×C8—1361no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—42no—
130C4⋊C4—681no—
131C22⋊C4—41no—
132C42—41no—
133C42—171no—
134C42—171no—
135C42—341no—
136C23#1058755111yescharacteristic
137Q8—161no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—341no—
145C2×C4—341no—
146C2×C4—681no—
147C2×C4—681no—
148C2×C4—681no—
149C2×C4—1361no—
150C2×C4#1058754911yescharacteristic
151C2×C4#1058755011yescharacteristic
152C8—2721no—
153C8—682no—
154C8—684no—
155C22—21no—
156C22—21no—
157C22#1176366311yescharacteristic
158C22#1176370911yescharacteristic
159C22#1176371911yescharacteristic
160C4—21no—
161C4—21no—
162C4—81no—
163C4—81no—
164C4—81no—
165C4—681no—
166C4—681no—
167C4—1361no—
168C2—21no—
169C2—21no—
170C2#1454378511yescharacteristic
171C2#1454390511yescharacteristic
172C2#1454390711yescharacteristic
subgroupG/H
centerC22#11763709
commutatorC2×C4⋊C4×C17C2×C4
FrattiniC2×C4⋊C4C2×#595
FittingC17×#544C4
socleC22×C17AΣL(1,𝔽16)
prime radicalC23×C17#99
cosocle#11762674C22
hypercenter#544#595
hypocenterC17#7442
LCSG ▷ C2×C4⋊C4×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #544

Complements

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

NH ≅ G/Ntype
112. C17#7442semidirect

Maximal subgroups

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

subgroupindex
#145437252
#145436602
#145301312
#744217