Finite Group Databasebeta

← #17949332

Subgroups — #17949332

Order 4352.

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

normal subgroups only

This group has 224 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#14543878C211yesmaximal, characteristic
2#14543713C211yesmaximal, characteristic
3#14530313C211yesmaximal, characteristic
4C2×#10587539—21no—
5#11763654—21no—
6C2×#10587478—21no—
7C2×#10587480—21no—
8#11762711C2211yescharacteristic
9#11762564C411yescharacteristic, complemented
10C17×#384C411yescharacteristic, complemented
11C22×D68D411yescharacteristic
12C2×C22⋊#595—41no—
13C2×C4⋊C4×C17—21no—
14C2×C4⋊C4×C17—41no—
15C2×C42×C17C2×C411yescharacteristic
16C2×#63227—41no—
17C2×C4⋊Dic17D411yescharacteristic
18C22×#3622—21no—
19C22⋊#3624—41no—
20#10587539—22no—
21#10587539—41no—
22#10587480—42no—
23#10587478—42no—
24C23×D17—21no—
25C22×#595—81no—
26C22×C4×C17—21no—
27C22×C4×C17—41no—
28C22×C4×C17C22⋊C411yescharacteristic
29C22×Dic17—21no—
30C2×D68—21no—
31C2×D68—41no—
32C2×D68—41no—
33C2×D68SD1611yescharacteristic
34C2×D68Q1611yescharacteristic
35C22⋊#595—42no—
36C22⋊#595—81no—
37C2×#3624—81no—
38C4⋊C4×C17—41no—
39C4⋊C4×C17—41no—
40C4⋊C4×C17—82no—
41C42×C17—41no—
42#63227—82no—
43C4⋊Dic17—41no—
44C2×#3622—22no—
45C2×#3622—41no—
46C2×#3622—41no—
47#7434—171nomaximal, Sylow
48C23×C17#9911yescharacteristic
49C22×D17—21no—
50C22×D17—21no—
51C22×D17—41no—
52C22×D17—41no—
53C22×D17—81no—
54C22×D17—81no—
55C2×#595—82no—
56C2×#595—161no—
57C2×#595—161no—
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—22no—
61C2×C4×C17—41no—
62C2×C4×C17—41no—
63C2×C4×C17—82no—
64C2×C4×C17—81no—
65C2×C4×C17#10311yescharacteristic
66C2×C4×C17#10411yescharacteristic
67C2×Dic17—41no—
68C2×Dic17—81no—
69D68—41no—
70D68—41no—
71D68—81no—
72#3624—161no—
73#3622—42no—
74#2093—171no—
75#1393—171no—
76#1318—171no—
77C22×C17—21no—
78C22×C17—21no—
79C22×C17#32811yescharacteristic
80C22×C17#35211yescharacteristic
81C22×C17#35311yescharacteristic
82C2×D17—41no—
83C2×D17—41no—
84C2×D17—81no—
85C2×D17—81no—
86C2×D17—81no—
87C2×D17—81no—
88C2×D17—161no—
89#595—162no—
90C4×C17—21no—
91C4×C17—21no—
92C4×C17—42no—
93C4×C17—161no—
94Dic17—81no—
95C2×#107—341no—
96C2×#102—341no—
97C2×#99—341no—
98#390—171no—
99#384#59511yescharacteristic, complemented
100#336—171no—
101#324—341no—
102C2×C17—21no—
103C2×C17—21no—
104C2×C17#135211yescharacteristic
105C2×C17#140711yescharacteristic
106C2×C17#140811yescharacteristic
107D17—81no—
108D17—81no—
109C22×D4—171no—
110C22×C8—341no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—171no—
114C2×C22⋊C4—681no—
115C2×C22⋊C4—681no—
116C2×C42C2×#59511yescharacteristic
117#107—682no—
118#102—682no—
119#99—342no—
120#99—681no—
121C22⋊C8—681no—
122C17#743411yescharacteristic, complemented, Sylow
123C24—341no—
124C2×D4—171no—
125C2×D4—171no—
126C2×D4—341no—
127C2×D4—681no—
128C2×D4—681no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—341no—
132C22×C4—1361no—
133C22×C4C22⋊#59511yescharacteristic
134C2×C8—342no—
135C2×C8—681no—
136C2×C8—681no—
137C2×C8—1361no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—82no—
141C4⋊C4—681no—
142C22⋊C4—682no—
143C22⋊C4—1362no—
144C22⋊C4—1361no—
145C42—41no—
146C23—341no—
147C23—341no—
148C23—681no—
149C23—681no—
150C23—1361no—
151C23—1361no—
152C23#1058755111yescharacteristic
153D4—681no—
154D4—681no—
155D4—1361no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—82no—
162C2×C4—81no—
163C2×C4—2721no—
164C2×C4—2721no—
165C2×C4—681no—
166C2×C4—1362no—
167C2×C4—1361no—
168C2×C4#1058754911yescharacteristic
169C2×C4#1058755011yescharacteristic
170C8—2721no—
171C8—682no—
172C22—21no—
173C22—21no—
174C22—2721no—
175C22—681no—
176C22—681no—
177C22—1361no—
178C22—1361no—
179C22—1361no—
180C22—1361no—
181C22#1176366311yescharacteristic
182C22#1176371111yescharacteristic
183C22#1176371311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—161no—
188C4—2722no—
189C4—1361no—
190C2—21no—
191C2—21no—
192C2—1361no—
193C2—1361no—
194C2#1454378111yescharacteristic
195C2#1454391311yescharacteristic
196C2#1454391511yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
FittingC17×#384C4
socleC22×C17#353
prime radicalC22×D68D4
cosocle#11762711C22
hypercenter#384#595
hypocenterC17#7434
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
9. #11762564C4semidirect
10. C17×#384C4semidirect
99. #384#595semidirect
122. C17#7434semidirect

Maximal subgroups

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

subgroupindex
#145438782
#145437132
#145303132
#743417