Finite Group Databasebeta

← #17949350

Subgroups — #17949350

Order 4352.

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

normal subgroups only

This group has 198 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#14543727C211yesmaximal, characteristic
2#14543662C211yesmaximal, characteristic
3#14530126C211yesmaximal, characteristic
4C2×#10587544—21no—
5#11763654—21no—
6#11762852—21no—
7#11762678C2211yescharacteristic
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×#63225—41no—
19C2×C4×Dic17D411yescharacteristic
20C2×#63223—21no—
21C22⋊#3624—41no—
22#10587544—22no—
23#10587544—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—81no—
33C2×#3624—81no—
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—
43#63225—81no—
44#63225—81no—
45C4×Dic17—21no—
46C4×Dic17SD1611yescharacteristic
47C4×Dic17Q1611yescharacteristic
48#63223—22no—
49#63223—41no—
50C2×#3622—41no—
51#7443—171nomaximal, Sylow
52C23×C17#9911yescharacteristic
53Q8×C17—161no—
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—41no—
57C2×C4×C17—41no—
58C2×C4×C17—41no—
59C2×C4×C17—81no—
60C2×C4×C17#10311yescharacteristic
61C2×C4×C17#10411yescharacteristic
62C2×Dic17—21no—
63C2×Dic17—21no—
64C2×Dic17—21no—
65C2×Dic17—21no—
66C2×Dic17—21no—
67C2×Dic17—21no—
68C2×Dic17—41no—
69C2×Dic17—81no—
70#3624—82no—
71#3624—161no—
72#3622—42no—
73#2060—171no—
74#1325—171no—
75#1296—171no—
76C22×C17—21no—
77C22×C17—21no—
78C22×C17#32811yescharacteristic
79C22×C17AΣL(1,𝔽16)11yescharacteristic
80C22×C17#35611yescharacteristic
81C4×C17—21no—
82C4×C17—21no—
83C4×C17—81no—
84C4×C17—81no—
85C4×C17—81no—
86Dic17—21no—
87Dic17—21no—
88Dic17—21no—
89Dic17—21no—
90Dic17—81no—
91#544#59511yescharacteristic
92#428—341no—
93C2×C4⋊C8—341no—
94#384—171no—
95#343—171no—
96#339—341no—
97#324—341no—
98C2×C17—21no—
99C2×C17—21no—
100C2×C17#135411yescharacteristic
101C2×C17#140211yescharacteristic
102C2×C17#140511yescharacteristic
103C2×M16—341no—
104C22×C8—681no—
105C4⋊Q8—41no—
106#125—41no—
107C22⋊Q8—41no—
108#117—21no—
109C2×C4⋊C4—171no—
110C2×C4⋊C4—681no—
111C2×C4⋊C4C2×#59511yescharacteristic
112C2×C42—171no—
113#107—681no—
114#106—681no—
115C4⋊C8—342no—
116C4⋊C8—681no—
117C22⋊C8—681no—
118C17#744311yescharacteristic, complemented, Sylow
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—341no—
122C22×C4—341no—
123C22×C4C22⋊#59511yescharacteristic
124M16—342no—
125M16—681no—
126C2×C8—681no—
127C2×C8—682no—
128C2×C8—1361no—
129C2×C8—1361no—
130C2×C8—1361no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—42no—
136C4⋊C4—681no—
137C4⋊C4—1361no—
138C4⋊C4—1361no—
139C22⋊C4—41no—
140C42—41no—
141C42—171no—
142C42—171no—
143C42—341no—
144C23#1058755111yescharacteristic
145Q8—161no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—81no—
152C2×C4—341no—
153C2×C4—341no—
154C2×C4—341no—
155C2×C4—341no—
156C2×C4—341no—
157C2×C4—341no—
158C2×C4—681no—
159C2×C4—1361no—
160C2×C4#1058754911yescharacteristic
161C2×C4#1058755011yescharacteristic
162C8—2721no—
163C8—682no—
164C8—1362no—
165C22—21no—
166C22—21no—
167C22#1176366311yescharacteristic
168C22#1176370911yescharacteristic
169C22#1176371911yescharacteristic
170C4—21no—
171C4—21no—
172C4—81no—
173C4—81no—
174C4—81no—
175C4—341no—
176C4—341no—
177C4—341no—
178C4—341no—
179C4—1361no—
180C2—21no—
181C2—21no—
182C2#1454378511yescharacteristic
183C2#1454390311yescharacteristic
184C2#1454390911yescharacteristic
subgroupG/H
centerC22#11763709
commutatorC2×C4⋊C4×C17C2×C4
FrattiniC2×C4⋊C4C2×#595
FittingC17×#544C4
socleC22×C17AΣL(1,𝔽16)
prime radicalC23×C17#99
cosocle#11762678C22
hypercenter#544#595
hypocenterC17#7443
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
118. C17#7443semidirect

Maximal subgroups

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

subgroupindex
#145437272
#145436622
#145301262
#744317