Finite Group Databasebeta

← #16921862

Subgroups — #16921862

Order 4352.

208 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 41 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#14530197C211yesmaximal, characteristic
2#14526909C211yesmaximal, characteristic
3C17×#1318C211yesmaximal, characteristic
4C2×#10587503—21no—
5C2×#10587505—21no—
6#11762675C411yescharacteristic, complemented
7#11762571—21no—
8#11762564C411yescharacteristic, complemented
9C17×#390C2211yescharacteristic
10C17×#324—21no—
11C22×D4×C17D411yescharacteristic
12C2×C4⋊C4×C17D411yescharacteristic
13C2×C22⋊C4×C17—41no—
14C2×C42×C17C2×C411yescharacteristic
15C2×C22⋊Dic17—41no—
16C2×C4⋊Dic17—21no—
17C22×#3622—21no—
18C17×C22⋊C8—41no—
19#10587505—22no—
20#10587505—41no—
21#10587503—41no—
22#10587503—41no—
23#10587502—41no—
24C24×C17—21no—
25C2×D4×C17—21no—
26C2×D4×C17—41no—
27C2×D4×C17—41no—
28C2×D4×C17D811yescharacteristic
29C2×D4×C17SD1611yescharacteristic
30C22×C4×C17—21no—
31C22×C4×C17—21no—
32C22×C4×C17C22⋊C411yescharacteristic
33C22×Dic17—41no—
34C22×Dic17—81no—
35C2×C8×C17—81no—
36C4⋊C4×C17—41no—
37C22⋊C4×C17—82no—
38C42×C17—41no—
39C22⋊Dic17—42no—
40C22⋊Dic17—81no—
41C4⋊Dic17—41no—
42C4⋊Dic17—41no—
43C2×#3622—41no—
44C2×#3622—41no—
45C2×#3622—41no—
46#7412—171nomaximal, Sylow
47C23×C17—21no—
48C23×C17—21no—
49C23×C17—41no—
50C23×C17—41no—
51C23×C17—81no—
52C23×C17—81no—
53C23×C17#9911yescharacteristic
54D4×C17—41no—
55D4×C17—41no—
56D4×C17—81no—
57C2×C4×C17—21no—
58C2×C4×C17—21no—
59C2×C4×C17—41no—
60C2×C4×C17—41no—
61C2×C4×C17—41no—
62C2×C4×C17—41no—
63C2×C4×C17—81no—
64C2×C4×C17#10211yescharacteristic
65C2×C4×C17#10411yescharacteristic
66C2×Dic17—81no—
67C2×Dic17—81no—
68C2×Dic17—82no—
69C2×Dic17—81no—
70C2×Dic17—161no—
71C2×Dic17—161no—
72C8×C17—161no—
73#3622—81no—
74#2073—171no—
75#1393—171no—
76#1318D1711yescharacteristic
77C22×C17—21no—
78C22×C17—21no—
79C22×C17—41no—
80C22×C17—41no—
81C22×C17—81no—
82C22×C17—81no—
83C22×C17—81no—
84C22×C17—81no—
85C22×C17—161no—
86C22×C17#32711yescharacteristic
87C22×C17#35211yescharacteristic
88C22×C17#35411yescharacteristic
89C4×C17—21no—
90C4×C17—21no—
91C4×C17—81no—
92C4×C17—81no—
93Dic17—161no—
94Dic17—162no—
95C2×#102—341no—
96C2×#99—341no—
97#390C2×D1711yescharacteristic
98#382—171no—
99#340—341no—
100#336—171no—
101#324—21no—
102C2×C17—21no—
103C2×C17—21no—
104C2×C17—81no—
105C2×C17—81no—
106C2×C17#134411yescharacteristic
107C2×C17#141211yescharacteristic
108C2×C17#141411yescharacteristic
109C22×D4D6811yescharacteristic
110C22×C8—341no—
111C2×C4⋊C4—341no—
112C2×C4⋊C4C22⋊D1711yescharacteristic
113C2×C22⋊C4—41no—
114C2×C22⋊C4—681no—
115C2×C42C4×D1711yescharacteristic
116#102—681no—
117#102—681no—
118#99—342no—
119#99—681no—
120C22⋊C8—41no—
121#95—681no—
122C17#741211yescharacteristic, complemented, Sylow
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4#6321911yescharacteristic
128C2×D4D13611yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—681no—
132C22×C4—1361no—
133C22×C4#6322711yescharacteristic
134C2×C8—81no—
135C2×C8—681no—
136C2×C8—681no—
137C2×C8—681no—
138C4⋊C4—41no—
139C4⋊C4—681no—
140C4⋊C4—681no—
141C22⋊C4—82no—
142C22⋊C4—682no—
143C22⋊C4—1361no—
144C42—41no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—81no—
150C23—81no—
151C23#1058747711yescharacteristic
152D4—41no—
153D4—41no—
154D4—81no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—81no—
162C2×C4—2721no—
163C2×C4—2721no—
164C2×C4—1361no—
165C2×C4—1361no—
166C2×C4—1362no—
167C2×C4—1361no—
168C2×C4#1058749211yescharacteristic
169C2×C4#1058749611yescharacteristic
170C8—161no—
171C8—1361no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1176254411yescharacteristic
182C22#1176260011yescharacteristic
183C22#1176260311yescharacteristic
184C4—21no—
185C4—21no—
186C4—81no—
187C4—81no—
188C4—2721no—
189C4—2722no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1452678511yescharacteristic
195C2#1452695411yescharacteristic
196C2#1452696011yescharacteristic
subgroupG/H
centerC22#11762603
commutatorC2×C42×C17C2×C4
Frattini#390C2×D17
FittingC17×#1318C2
socleC22×C17#354
prime radicalC22×D4×C17D4
cosocleC17×#390C22
hypercenter#1318D17
hypocenterC17#7412
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
6. #11762675C4semidirect
8. #11762564C4semidirect
122. C17#7412semidirect

Maximal subgroups

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

subgroupindex
#145301972
#145269092
C17×#13182
#741217