Finite Group Databasebeta

← #17949313

Subgroups — #17949313

Order 4352.

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

normal subgroups only

This group has 214 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#14543711C211yesmaximal, characteristic
2#14543687C211yesmaximal, characteristic
3#14529952C211yesmaximal, characteristic
4#11763779—21no—
5#11763652—21no—
6#11763435C411yescharacteristic
7#11762670—21no—
8#11762670C2211yescharacteristic
9#11762575—21no—
10C17×#342C411yescharacteristic
11C23×Dic17D411yescharacteristic
12C2×#63247—41no—
13C2×C22⋊C4×C17—21no—
14C2×C22⋊C4×C17C2×C411yescharacteristic
15C2×C22⋊Dic17—21no—
16C2×C22⋊Dic17D411yescharacteristic
17#10587610—41no—
18#10587564—42no—
19C22⋊#3624—22no—
20C22⋊#3624—41no—
21C22⋊#3624—41no—
22#10587502—41no—
23#10587502—42no—
24C24×C17C22⋊C411yescharacteristic
25C22×C4×C17—21no—
26C22×C4×C17—41no—
27C22×Dic17—21no—
28C22×Dic17—21no—
29C22×Dic17—22no—
30C22×Dic17—21no—
31C22×Dic17—41no—
32C22×Dic17—41no—
33C22×Dic17SD1611yescharacteristic
34C22×Dic17Q1611yescharacteristic
35C2×Dic34—41no—
36#63247—81no—
37#63247—81no—
38C2×#3624—42no—
39C2×#3624—81no—
40C22⋊C4×C17—41no—
41C22⋊C4×C17—41no—
42C22⋊C4×C17—41no—
43C22⋊Dic17—41no—
44C22⋊Dic17—41no—
45C22⋊Dic17—41no—
46C4⋊Dic17—41no—
47#63225—42no—
48#7427—171nomaximal, Sylow
49C23×C17—21no—
50C23×C17—21no—
51C23×C17—81no—
52C23×C17#9911yescharacteristic
53C23×C17#10311yescharacteristic
54C23×C17#10411yescharacteristic
55C2×C4×C17—41no—
56C2×C4×C17—81no—
57C2×C4×C17—81no—
58C2×C4×C17—82no—
59C2×Dic17—21no—
60C2×Dic17—21no—
61C2×Dic17—41no—
62C2×Dic17—41no—
63C2×Dic17—41no—
64C2×Dic17—41no—
65C2×Dic17—42no—
66C2×Dic17—41no—
67C2×Dic17—81no—
68C2×Dic17—81no—
69C2×Dic17—82no—
70Dic34—161no—
71#3624—82no—
72#3624—161no—
73#2030—171no—
74#1317—171no—
75#1306—171no—
76C22×C17—21no—
77C22×C17—21no—
78C22×C17—41no—
79C22×C17—41no—
80C22×C17—41no—
81C22×C17—42no—
82C22×C17—81no—
83C22×C17#32811yescharacteristic
84C22×C17AΣL(1,𝔽16)11yescharacteristic
85C22×C17#35411yescharacteristic
86C4×C17—81no—
87C4×C17—161no—
88Dic17—41no—
89Dic17—41no—
90Dic17—81no—
91Dic17—82no—
92#543—171no—
93#407—341no—
94#381—171no—
95#381—341no—
96#342—341no—
97#342#59511yescharacteristic
98#323—341no—
99C2×C17—21no—
100C2×C17—21no—
101C2×C17—21no—
102C2×C17—41no—
103C2×C17—41no—
104C2×C17#135111yescharacteristic
105C23×C4—171no—
106C2×M16—681no—
107C22⋊Q8—682no—
108C22⋊Q8—681no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—171no—
111C2×C22⋊C4—341no—
112C2×C22⋊C4C2×#59511yescharacteristic
113C22⋊C8—342no—
114C22⋊C8—681no—
115C22⋊C8—681no—
116#95—681no—
117#95—682no—
118C17#742711yescharacteristic, complemented, Sylow
119C24C22⋊#59511yescharacteristic
120C2×Q8—681no—
121C22×C4—21no—
122C22×C4—41no—
123C22×C4—171no—
124C22×C4—171no—
125C22×C4—341no—
126C22×C4—341no—
127C22×C4—342no—
128C22×C4—341no—
129C22×C4—681no—
130C22×C4—681no—
131M16—1361no—
132M16—1361no—
133C2×C8—682no—
134C2×C8—1361no—
135C4⋊C4—682no—
136C4⋊C4—681no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—681no—
141C22⋊C4—681no—
142C22⋊C4—681no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1058753911yescharacteristic
147C23#1058754811yescharacteristic
148C23#1058754911yescharacteristic
149Q8—2721no—
150C2×C4—41no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4—82no—
154C2×C4—341no—
155C2×C4—341no—
156C2×C4—681no—
157C2×C4—681no—
158C2×C4—681no—
159C2×C4—681no—
160C2×C4—681no—
161C2×C4—682no—
162C2×C4—1361no—
163C2×C4—1361no—
164C2×C4—1362no—
165C8—2721no—
166C8—1362no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1176366211yescharacteristic
175C22#1176371011yescharacteristic
176C22#1176371611yescharacteristic
177C4—81no—
178C4—161no—
179C4—681no—
180C4—681no—
181C4—1361no—
182C4—1362no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1454377811yescharacteristic
subgroupG/H
centerC2#14543778
commutatorC2×C22⋊C4×C17C2×C4
FrattiniC2×C22⋊C4C2×#595
FittingC17×#342C4
socleC2×C17#1351
prime radicalC24×C17C22⋊C4
cosocle#11762670C22
hypercenter#342#595
hypocenterC17#7427
LCSG ▷ C2×C22⋊C4×C17 ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
118. C17#7427semidirect

Maximal subgroups

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

subgroupindex
#145437112
#145436872
#145299522
#742717