Finite Group Databasebeta

← #17953662

Subgroups — #17953662

Order 4352.

538 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 72 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#14544679C212yesmaximal
2#14543683C214yesmaximal
3#14531379C211yesmaximal, characteristic
4#11763750C2214yes—
5#11763687—22no—
6#11763687—22no—
7C22×#63227C2211yescharacteristic
8#11762700—22no—
9#11762698—22no—
10#11762667C412yescomplemented
11#11762664C2212yes—
12C4×C22⋊Dic17C411yescharacteristic, complemented
13C4×C22⋊C4×C17C411yescharacteristic, complemented
14C24×D17C2311yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17C2×C411yescharacteristic
17C2×C22⋊#595—24no—
18C2×C22⋊#595—24no—
19C2×C22⋊#595—24no—
20C2×C22⋊C4×C17C2×C412yes—
21C2×C42×C17—21no—
22C2×C22⋊Dic17C2×C412yes—
23C2×#63227—22no—
24C2×#63227—22no—
25C2×#63227—24no—
26C2×#63227D412yes—
27C2×#63227D412yes—
28C2×#63225—22no—
29C2×C4×Dic17—21no—
30C17×#95—21no—
31#10587502—21no—
32#10587502—22no—
33C24×C17C22×C411yescharacteristic
34C23×D17—42no—
35C23×D17—81no—
36C23×D17—81no—
37C23×D17C2×D412yes—
38C23×D17#4114yes—
39C22×#595—44no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—81no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×C4×C17C22⋊C411yescharacteristic
45C22×Dic17—22no—
46C22×Dic17—22no—
47C22×Dic17—81no—
48C22×Dic17C22⋊C412yes—
49C22⋊#595—48no—
50C22⋊#595—84no—
51C22⋊#595—84no—
52C22⋊C4×C17—42no—
53C42×C17—81no—
54C22⋊Dic17—42no—
55#63227—24no—
56#63227—24no—
57#63227—82no—
58#63227—82no—
59#63225—82no—
60C4×Dic17—81no—
61#8750—171nomaximal, Sylow
62C23×C17—22no—
63C23×C17—41no—
64C23×C17—41no—
65C23×C17C2×C22⋊C411yescharacteristic
66C23×C17#11712yes—
67C22×D17—24no—
68C22×D17—44no—
69C22×D17—44no—
70C22×D17—44no—
71C22×D17—42no—
72C22×D17—42no—
73C22×D17—88no—
74C22×D17#12314yes—
75C2×#595—84no—
76C2×#595—84no—
77C2×#595—84no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—41no—
81C2×C4×C17—41no—
82C2×C4×C17—42no—
83C2×C4×C17—42no—
84C2×C4×C17—42no—
85C2×C4×C17—82no—
86C2×Dic17—22no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—82no—
92#2312—171no—
93#1819—172no—
94#1304—174no—
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—22no—
98C22×C17—22no—
99C22×C17—22no—
100C22×C17—44no—
101C22×C17#38111yescharacteristic
102C22×C17#41012yes—
103C2×D17—24no—
104C2×D17—24no—
105C2×D17—24no—
106C2×D17—84no—
107C2×D17—88no—
108#595—164no—
109C4×C17—41no—
110C4×C17—41no—
111C4×C17—82no—
112Dic17—42no—
113Dic17—82no—
114C22×C22⋊C4—171no—
115#388—342no—
116#388—342no—
117#380—172no—
118#379—172no—
119#379—174no—
120C4×C22⋊C4—171no—
121C4×C22⋊C4#59511yescharacteristic, complemented
122#342—342no—
123#342—342no—
124C2×C17—22no—
125C2×C17—42no—
126C2×C17#182011yescharacteristic
127C2×C17#182811yescharacteristic
128C2×C17#182811yescharacteristic
129D17—44no—
130C25—171no—
131C23×C4—171no—
132C23×C4C2×#59511yescharacteristic
133C2×C4⋊C4—342no—
134C2×C22⋊C4—172no—
135C2×C22⋊C4—172no—
136C2×C22⋊C4—172no—
137C2×C22⋊C4—344no—
138C2×C22⋊C4—344no—
139C2×C22⋊C4—342no—
140C2×C22⋊C4—342no—
141C2×C22⋊C4—344no—
142C2×C22⋊C4—344no—
143C2×C22⋊C4C2×#59512yes—
144C2×C42—21no—
145C2×C42—341no—
146#95—21no—
147#95—342no—
148#95—341no—
149C17#875011yescharacteristic, complemented, Sylow
150C24—172no—
151C24—174no—
152C24—682no—
153C24—1361no—
154C24—1361no—
155C24C22×#59511yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—81no—
159C22×C4—172no—
160C22×C4—342no—
161C22×C4—342no—
162C22×C4—684no—
163C22×C4—1361no—
164C22×C4C22⋊#59511yescharacteristic
165C22×C4C22⋊#59511yescharacteristic
166C4⋊C4—1362no—
167C22⋊C4—42no—
168C22⋊C4—344no—
169C22⋊C4—344no—
170C22⋊C4—682no—
171C22⋊C4—688no—
172C22⋊C4—1362no—
173C22⋊C4—1362no—
174C22⋊C4—1364no—
175C22⋊C4—1364no—
176C42—81no—
177C42—1361no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—174no—
182C23—344no—
183C23—682no—
184C23—682no—
185C23—684no—
186C23—684no—
187C23—684no—
188C23—1368no—
189C23#1058767712yes—
190C23C2×C22⋊#59511yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—82no—
199C2×C4—342no—
200C2×C4—682no—
201C2×C4—682no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—1364no—
205C2×C4—1364no—
206C2×C4—1364no—
207C2×C4—1362no—
208C22—21no—
209C22—21no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—44no—
214C22—344no—
215C22—344no—
216C22—344no—
217C22—1364no—
218C22—1368no—
219C22#1176375211yescharacteristic
220C22#1176378812yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—2724no—
225C4—682no—
226C4—1362no—
227C2—22no—
228C2—42no—
229C2—684no—
230C2#1454468111yescharacteristic
231C2#1454469511yescharacteristic
232C2#1454469611yescharacteristic
subgroupG/H
centerC22#11763752
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17#381
prime radical, cosocleC24×D17C23
hypercenterC4×C22⋊C4#595
hypocenterC17#8750
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
10. #11762667C4semidirect
12. C4×C22⋊Dic17C4semidirect
13. C4×C22⋊C4×C17C4semidirect
121. C4×C22⋊C4#595semidirect
149. C17#8750semidirect

Maximal subgroups

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

subgroupindex
#145446792
#145436832
#145313792
#875017