Finite Group Databasebeta

← #17958442

Subgroups — #17958442

Order 4352.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544035C212yesmaximal
2#14543727C214yesmaximal, complemented
3#14531408C211yesmaximal, characteristic
4#11763829—22no—
5#11763654C2214yes—
6#11763652—22no—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762705—22no—
10#11762682—22no—
11#11762678C2212yes—
12#11762674C412yes—
13C22×C4⋊C4×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C2×C4⋊C4×C17—21no—
17C2×C4⋊C4×C17—42no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C22⋊Dic17—21no—
20C2×C22⋊Dic17D412yes—
21#10587612—24no—
22#10587612—42no—
23C2×C4⋊Dic17—21no—
24C2×C4⋊Dic17C2×C411yescharacteristic
25C2×C4⋊Dic17C2311yescharacteristic
26C2×#63225—24no—
27C2×C4×Dic17C2×C412yes—
28C2×C4×Dic17D412yes—
29C22⋊#3624—24no—
30#10587544—42no—
31#10587542—42no—
32#10587502—24no—
33C24×C17C22⋊C411yescharacteristic
34C22×C4×C17—22no—
35C22×C4×C17—22no—
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—42no—
39C22×C4×C17—82no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C22×C411yescharacteristic
42C22×Dic17—22no—
43C22×Dic17C22⋊C412yes—
44C22×Dic17C2×D412yes—
45C2×#3624—44no—
46C4⋊C4×C17—42no—
47C4⋊C4×C17—42no—
48C22⋊Dic17—24no—
49C22⋊Dic17—42no—
50C4⋊Dic17—24no—
51C4⋊Dic17—41no—
52C4⋊Dic17—41no—
53#63225—84no—
54C4×Dic17—22no—
55C4×Dic17—22no—
56C4×Dic17—22no—
57C4×Dic17M1614yes—
58#11516—171nomaximal, Sylow
59C23×C17—21no—
60C23×C17—21no—
61C23×C17—41no—
62C23×C17—41no—
63C23×C17#10112yes—
64C23×C17C2×C22⋊C411yescharacteristic
65C2×C4×C17—28no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—44no—
71C2×C4×C17—42no—
72C2×C4×C17—84no—
73C2×C4×C17#9912yes—
74C2×C4×C17C2×M1612yes—
75C2×Dic17—24no—
76C2×Dic17—22no—
77C2×Dic17—22no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80C2×Dic17—42no—
81C2×Dic17—42no—
82#3624—84no—
83#2317—171no—
84#1464—172no—
85#1325—174no—
86C22×C17—21no—
87C22×C17—21no—
88C22×C17—22no—
89C22×C17—42no—
90C22×C17—42no—
91C22×C17—41no—
92C22×C17—41no—
93C22×C17#40711yescharacteristic
94C22×C17C2×#9911yescharacteristic
95C22×C17C2×#10111yescharacteristic
96C4×C17—22no—
97C4×C17—22no—
98C4×C17—82no—
99Dic17—44no—
100Dic17—42no—
101Dic17—42no—
102C2×#117—171no—
103C2×#117—171no—
104C22×C4⋊C4#59511yescharacteristic
105#432—342no—
106#389—342no—
107#385—342no—
108#384—172no—
109#382—172no—
110#324—174no—
111#323—342no—
112C2×C17—21no—
113C2×C17—21no—
114C2×C17—42no—
115C2×C17#146311yescharacteristic
116C2×C17#212811yescharacteristic
117C2×C17#213511yescharacteristic
118C23×C4—21no—
119C23×C4C2×#59511yescharacteristic
120#117—344no—
121#117—682no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—171no—
125C2×C4⋊C4—171no—
126C2×C4⋊C4—341no—
127C2×C4⋊C4—344no—
128C2×C4⋊C4C2×#59512yes—
129C2×C22⋊C4—172no—
130C2×C22⋊C4—341no—
131C2×C42—172no—
132C2×C42—172no—
133C4⋊C8—682no—
134C22⋊C8—344no—
135#97—682no—
136#95—344no—
137C17#1151611yescharacteristic, complemented, Sylow
138C24C22⋊#59511yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—82no—
145C22×C4—172no—
146C22×C4—172no—
147C22×C4—342no—
148C22×C4C22⋊#59511yescharacteristic
149C22×C4C22×#59511yescharacteristic
150C2×C8—684no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—344no—
154C4⋊C4—681no—
155C4⋊C4—681no—
156C4⋊C4—1364no—
157C22⋊C4—344no—
158C22⋊C4—682no—
159C42—174no—
160C42—342no—
161C42—342no—
162C42—342no—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#1058754512yes—
168C23C2×C22⋊#59511yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4—84no—
177C2×C4—344no—
178C2×C4—342no—
179C2×C4—342no—
180C2×C4—682no—
181C2×C4—682no—
182C2×C4—682no—
183C2×C4—682no—
184C2×C4#1058755112yes—
185C2×C4D17⋊M1612yes—
186C8—1364no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22#1176378111yescharacteristic
195C22C2×#1058755111yescharacteristic
196C22C2×#1058754511yescharacteristic
197C4—22no—
198C4—22no—
199C4—82no—
200C4—684no—
201C4—682no—
202C4—682no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2#1454403411yescharacteristic
207C2#1454506311yescharacteristic
208C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11516
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543727C2semidirect
137. C17#11516semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437272
#145314082
#1151617