Finite Group Databasebeta

← #17949137

Subgroups — #17949137

Order 4352.

302 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 38 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#14543708C212yesmaximal
2#14528858C211yesmaximal, characteristic
3#11763652—22no—
4#11762665C411yescharacteristic
5#11762665C2211yescharacteristic
6#11762576—22no—
7C22×C22⋊C4×C17C411yescharacteristic
8C25×C17C2×C411yescharacteristic
9C23×C4×C17—21no—
10C2×C22⋊C4×C17—21no—
11C2×C22⋊C4×C17—41no—
12C2×C22⋊C4×C17—41no—
13C2×C22⋊C4×C17C812yescomplemented
14C2×C22⋊Dic17—21no—
15C2×C22⋊Dic17—41no—
16C2×C22⋊Dic17—41no—
17C2×C22⋊Dic17D412yes—
18C22⋊#3624—42no—
19C24×C17—21no—
20C24×C17—21no—
21C24×C17—42no—
22C24×C17—82no—
23C24×C17C22⋊C411yescharacteristic
24C24×C17C2×C811yescharacteristic
25C24×C17M1611yescharacteristic
26C22×C4×C17—22no—
27C22×C4×C17—41no—
28C22×C4×C17—41no—
29C22×C4×C17—82no—
30C22×Dic17—22no—
31C22×Dic17—41no—
32C2×#3624—82no—
33C22⋊C4×C17—41no—
34C22⋊C4×C17—41no—
35C22⋊C4×C17—42no—
36C22⋊Dic17—42no—
37C22⋊Dic17—42no—
38C22⋊Dic17—82no—
39C22⋊Dic17—82no—
40#7349—171nomaximal, Sylow
41C23×C17—21no—
42C23×C17—22no—
43C23×C17—21no—
44C23×C17—42no—
45C23×C17—41no—
46C23×C17—42no—
47C23×C17—42no—
48C23×C17—42no—
49C23×C17—41no—
50C23×C17—42no—
51C23×C17—81no—
52C23×C17—81no—
53C23×C17—81no—
54C23×C17—81no—
55C23×C17—84no—
56C23×C17—84no—
57C23×C17C22⋊C811yescharacteristic
58C23×C17#9911yescharacteristic
59C23×C17#10011yescharacteristic
60C2×C4×C17—42no—
61C2×C4×C17—82no—
62C2×C4×C17—82no—
63C2×C4×C17—82no—
64C2×Dic17—42no—
65C2×Dic17—82no—
66C2×Dic17—81no—
67C2×Dic17—82no—
68#3624—162no—
69#1819—171no—
70#1316—172no—
71C22×C17—22no—
72C22×C17—21no—
73C22×C17—21no—
74C22×C17—41no—
75C22×C17—41no—
76C22×C17—41no—
77C22×C17—41no—
78C22×C17—41no—
79C22×C17—41no—
80C22×C17—42no—
81C22×C17—42no—
82C22×C17—41no—
83C22×C17—41no—
84C22×C17—82no—
85C22×C17—84no—
86C22×C17—84no—
87C22×C17—82no—
88C22×C17#32311yescharacteristic
89C22×C17#35212yes—
90C4×C17—82no—
91Dic17—82no—
92Dic17—161no—
93C22×C22⋊C4#59511yescharacteristic
94#379—171no—
95#379—171no—
96#342—342no—
97#323—342no—
98C2×C17—22no—
99C2×C17—21no—
100C2×C17—41no—
101C2×C17—42no—
102C2×C17—41no—
103C2×C17—81no—
104C2×C17#131711yescharacteristic
105C25C2×#59511yescharacteristic
106C23×C4—21no—
107C2×C22⋊C4—21no—
108C2×C22⋊C4—41no—
109C2×C22⋊C4—41no—
110C2×C22⋊C4—172no—
111C2×C22⋊C4—341no—
112C2×C22⋊C4—681no—
113C2×C22⋊C4—681no—
114C2×C22⋊C4#362412yescomplemented
115C22⋊C8—682no—
116C17#734911yescharacteristic, complemented, Sylow
117C24—21no—
118C24—21no—
119C24—42no—
120C24—82no—
121C24C2×#362411yescharacteristic
122C24#6324711yescharacteristic
123C24C22⋊#59511yescharacteristic
124C22×C4—22no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—82no—
128C22×C4—342no—
129C22×C4—681no—
130C2×C8—1362no—
131C22⋊C4—41no—
132C22⋊C4—41no—
133C22⋊C4—42no—
134C22⋊C4—682no—
135C22⋊C4—682no—
136C22⋊C4—1362no—
137C22⋊C4—1362no—
138C23—21no—
139C23—22no—
140C23—21no—
141C23—42no—
142C23—41no—
143C23—42no—
144C23—42no—
145C23—42no—
146C23—41no—
147C23—42no—
148C23—81no—
149C23—81no—
150C23—81no—
151C23—81no—
152C23—84no—
153C23—84no—
154C23#1058755111yescharacteristic
155C23C22⋊#362411yescharacteristic
156C23#1058755311yescharacteristic
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—82no—
161C2×C4—682no—
162C2×C4—1361no—
163C2×C4—1362no—
164C2×C4—1362no—
165C8—2722no—
166C22—22no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22—82no—
180C22—84no—
181C22—84no—
182C22—82no—
183C22#1176365211yescharacteristic
184C22#1176371112yes—
185C4—82no—
186C4—2721no—
187C4—1362no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—42no—
192C2—41no—
193C2—81no—
194C2#1454371011yescharacteristic
subgroupG/H
centerC2#14543710
commutatorC24×C17C2×C8
FrattiniC25C2×#595
FittingC22×C22⋊C4×C17C4
socleC2×C17#1317
prime radicalC25×C17C2×C4
cosocle#11762665C22
hypercenterC22×C22⋊C4#595
hypocenterC17#7349
LCSG ▷ C24×C17 ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
13. C2×C22⋊C4×C17C8semidirect
114. C2×C22⋊C4#3624semidirect
116. C17#7349semidirect

Maximal subgroups

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

subgroupindex
#145437082
#145288582
#734917