Finite Group Databasebeta

← #17958448

Subgroups — #17958448

Order 4352.

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

normal subgroups only

This group has 446 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#14543729C214yesmaximal
3#14531267C211yesmaximal, characteristic
4#11763829—22no—
5#11763654—22no—
6#11763652C2214yes—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762707—22no—
10#11762682C412yes—
11#11762682C2212yes—
12C4×#63225—22no—
13C22×C42×C17C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×C4×C17C2×C412yes—
16C2×C42×C17—21no—
17C2×C42×C17—21no—
18C2×C42×C17—42no—
19C2×C22⋊Dic17C2×C412yes—
20C2×C22⋊Dic17C2×C411yescharacteristic
21C2×C22⋊Dic17C2311yescharacteristic
22#10587612—24no—
23#10587612—42no—
24C2×C4⋊Dic17—21no—
25C2×C4⋊Dic17D412yes—
26C2×#63225—22no—
27C2×#63225—22no—
28C2×C4×Dic17—21no—
29C2×C4×Dic17D412yes—
30C22⋊#3624—24no—
31#10587544—42no—
32#10587542—42no—
33#10587502—22no—
34#10587502—22no—
35C24×C17C22×C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—44no—
41C22×C4×C17—42no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C22⋊C411yescharacteristic
44C22×Dic17—22no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C2×D412yes—
47C2×#3624—44no—
48C42×C17—42no—
49C42×C17—42no—
50C22⋊Dic17—22no—
51C22⋊Dic17—41no—
52C22⋊Dic17—41no—
53C22⋊Dic17M1614yes—
54C4⋊Dic17—24no—
55C4⋊Dic17—42no—
56#63225—44no—
57#63225—44no—
58C4×Dic17—24no—
59C4×Dic17—22no—
60C4×Dic17—22no—
61#11518—171nomaximal, Sylow
62C23×C17—21no—
63C23×C17—21no—
64C23×C17—42no—
65C23×C17C2×C22⋊C411yescharacteristic
66C23×C17C2×M1612yes—
67C2×C4×C17—28no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—24no—
73C2×C4×C17—42no—
74C2×C4×C17—44no—
75C2×C4×C17—42no—
76C2×C4×C17—44no—
77C2×C4×C17#9912yes—
78C2×C4×C17#10112yes—
79C2×Dic17—24no—
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17—42no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86#3624—84no—
87#2296—171no—
88#1464—172no—
89#1326—174no—
90C22×C17—22no—
91C22×C17—22no—
92C22×C17—42no—
93C22×C17—42no—
94C22×C17—42no—
95C22×C17#40711yescharacteristic
96C22×C17C2×#9911yescharacteristic
97C22×C17C2×#10111yescharacteristic
98C4×C17—22no—
99C4×C17—22no—
100C4×C17—44no—
101Dic17—44no—
102Dic17—42no—
103Dic17—42no—
104C2×#117—171no—
105C2×#117—171no—
106C22×C42#59511yescharacteristic
107#432—342no—
108#389—342no—
109#385—172no—
110#385—172no—
111C4×C4⋊C4—342no—
112#324—342no—
113#323—174no—
114C2×C17—21no—
115C2×C17—21no—
116C2×C17—42no—
117C2×C17#146311yescharacteristic
118C2×C17#212012yes—
119C23×C4C2×#59512yes—
120C23×C4C2×#59511yescharacteristic
121#117—344no—
122#117—682no—
123C2×C4⋊C4—172no—
124C2×C4⋊C4—341no—
125C2×C4⋊C4—342no—
126C2×C4⋊C4—342no—
127C2×C22⋊C4—172no—
128C2×C22⋊C4—171no—
129C2×C22⋊C4—171no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—42no—
133C2×C42—172no—
134C2×C42—341no—
135C4⋊C8—682no—
136C22⋊C8—344no—
137#97—682no—
138#95—342no—
139#95—342no—
140C17#1151811yescharacteristic, complemented, Sylow
141C24C22×#59511yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—44no—
147C22×C4—42no—
148C22×C4—172no—
149C22×C4—172no—
150C22×C4—342no—
151C22×C4C22⋊#59511yescharacteristic
152C22×C4C22⋊#59511yescharacteristic
153C2×C8—684no—
154C4⋊C4—344no—
155C4⋊C4—682no—
156C4⋊C4—684no—
157C4⋊C4—684no—
158C22⋊C4—174no—
159C22⋊C4—342no—
160C22⋊C4—681no—
161C22⋊C4—681no—
162C42—42no—
163C42—42no—
164C42—344no—
165C42—342no—
166C42—342no—
167C23—21no—
168C23—21no—
169C23—42no—
170C23D17⋊M1612yes—
171C23C2×C22⋊#59511yescharacteristic
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—44no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—344no—
183C2×C4—342no—
184C2×C4—342no—
185C2×C4—682no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—682no—
189C2×C4#1058754512yes—
190C2×C4#1058755112yes—
191C8—1364no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22#1176378111yescharacteristic
198C22C2×#1058755111yescharacteristic
199C22C2×#1058754511yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—684no—
204C4—682no—
205C4—682no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2#1454403411yescharacteristic
210C2#1454503512yes—
subgroupG/H
centerC22C2×#10587551
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11518
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
140. C17#11518semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437292
#145312672
#1151817