Finite Group Databasebeta

← #17949965

Subgroups — #17949965

Order 4352.

624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 114 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#14544700C212yesmaximal, complemented
2#14543601C214yesmaximal, complemented
3#14531346C211yesmaximal, characteristic
4C2×#10587544—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×#10587560C411yescharacteristic
8C2×#10587579—22no—
9C2×#10587579C412yes—
10#11762710—22no—
11#11762710C2212yes—
12C42×Dic17C2211yescharacteristic
13C17×#384C411yescharacteristic
14C22×D68—22no—
15C22×D68C2×C412yes—
16C22×C4×D17—22no—
17C22×#3624—24no—
18C2×C4⋊C4×C17—22no—
19C2×C4⋊C4×C17C2×C412yes—
20C2×C42×C17C2×C411yescharacteristic
21C2×#63227—22no—
22C2×#63227—24no—
23C2×C4×Dic17C2×C411yescharacteristic
24C2×C4×Dic17D412yes—
25C2×C4×Dic17D412yes—
26C2×C4×Dic17C2311yescharacteristic
27#10587579—44no—
28#10587579—44no—
29#10587579—44no—
30#10587560—24no—
31#10587544—44no—
32C23×D17—22no—
33C22×C4×C17—22no—
34C22×C4×C17C22⋊C412yes—
35C22×C4×C17C22×C411yescharacteristic
36C22×Dic17C22⋊C411yescharacteristic
37C22×Dic17C22⋊C411yescharacteristic
38C22×Dic17C2×D412yes—
39C2×D68—28no—
40C2×D68—22no—
41C2×D68—42no—
42C2×D68—42no—
43C2×D68—44no—
44C2×D68—44no—
45C2×D68M1614yes—
46C2×C4×D17—44no—
47C2×C4×D17—48no—
48C2×#3624—44no—
49C2×#3624—44no—
50C2×#3624—44no—
51C4⋊C4×C17—42no—
52C4⋊C4×C17—44no—
53C42×C17—22no—
54#63227—44no—
55#63227—44no—
56#63227—44no—
57C4×Dic17—22no—
58C4×Dic17—42no—
59C4×Dic17—41no—
60C4×Dic17D814yes—
61C4×Dic17SD1614yes—
62#7651—171nomaximal, Sylow
63C23×C17C2×C22⋊C411yescharacteristic
64C22×D17—24no—
65C22×D17—42no—
66C22×D17—42no—
67C22×D17—44no—
68C22×D17—44no—
69C2×C4×C17—22no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—42no—
74C2×C4×C17—44no—
75C2×C4×C17#10214yes—
76C2×C4×C17C2×M1612yes—
77C2×Dic17—22no—
78C2×Dic17—22no—
79C2×Dic17—21no—
80C2×Dic17—22no—
81C2×Dic17#10012yes—
82C2×Dic17#10214yes—
83C2×Dic17C2×D812yes—
84C2×Dic17C2×SD1612yes—
85D68—44no—
86D68—44no—
87D68—416no—
88C4×D17—88no—
89#3624—84no—
90C4×#127—171no—
91#1831—172no—
92#1270—174no—
93C22×C17#40711yescharacteristic
94C22×C17#41011yescharacteristic
95C22×C17C2×#10011yescharacteristic
96C22×C17C2×#10212yes—
97C22×C17#42112yes—
98C2×D17—44no—
99C2×D17—48no—
100C2×D17—82no—
101C2×D17—82no—
102C2×D17—84no—
103C4×C17—22no—
104C4×C17—24no—
105C4×C17—82no—
106Dic17—22no—
107Dic17—22no—
108Dic17—41no—
109Dic17#33114yes—
110C2×#127—171no—
111C2×C4×D4—172no—
112C2×C4×D4—342no—
113C2×C4⋊C8—342no—
114#390—172no—
115#390—342no—
116#384#59511yescharacteristic
117C43—171no—
118#336—174no—
119#336—342no—
120C2×C17#146611yescharacteristic
121C2×C17#148612yes—
122C2×C17#151712yes—
123C2×C17#153611yescharacteristic
124C2×C17C2×#33111yescharacteristic
125D17—84no—
126C22×D4—172no—
127C22×D4—342no—
128C23×C4—342no—
129C22×C8—344no—
130#127—344no—
131C4×D4—684no—
132C4×D4—684no—
133C4×D4—684no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4C2×#59512yes—
136C2×C22⋊C4—342no—
137C2×C22⋊C4—344no—
138C2×C42—172no—
139C2×C42—171no—
140C2×C42—172no—
141C2×C42—171no—
142C2×C42C2×#59511yescharacteristic
143C4⋊C8—684no—
144C17#765111yescharacteristic, complemented, Sylow
145C24—342no—
146C2×D4—174no—
147C2×D4—348no—
148C2×D4—342no—
149C2×D4—682no—
150C2×D4—682no—
151C2×D4—684no—
152C2×D4—684no—
153C22×C4—22no—
154C22×C4—171no—
155C22×C4—172no—
156C22×C4—171no—
157C22×C4—688no—
158C22×C4—684no—
159C22×C4C22⋊#59512yes—
160C22×C4C22×#59511yescharacteristic
161C2×C8—684no—
162C2×C8—684no—
163C2×C8—684no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C22⋊C4—684no—
167C22⋊C4—684no—
168C22⋊C4—684no—
169C42—22no—
170C42—174no—
171C42—174no—
172C42—342no—
173C42—681no—
174C42—682no—
175C23—344no—
176C23—682no—
177C23—682no—
178C23—684no—
179C23—684no—
180C23C2×C22⋊#59511yescharacteristic
181D4—684no—
182D4—684no—
183D4—6816no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—172no—
191C2×C4—174no—
192C2×C4—172no—
193C2×C4—172no—
194C2×C4—342no—
195C2×C4—342no—
196C2×C4—341no—
197C2×C4—342no—
198C2×C4—1368no—
199C2×C4#1058754714yes—
200C2×C4D17⋊M1612yes—
201C8—1364no—
202C22—684no—
203C22—688no—
204C22—1364no—
205C22—1362no—
206C22—1362no—
207C22#1176378111yescharacteristic
208C22#1176379011yescharacteristic
209C22D17⋊#10011yescharacteristic
210C22C2×#1058754712yes—
211C22#1176380812yes—
212C4—22no—
213C4—24no—
214C4—82no—
215C4—174no—
216C4—342no—
217C4—342no—
218C4—681no—
219C2—1364no—
220C2#1454404511yescharacteristic
221C2#1454411112yes—
222C2#1454421512yes—
223C2#1454427411yescharacteristic
224C2D17⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587560C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#7651
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #14544700C2semidirect
2. #14543601C2semidirect
144. C17#7651semidirect

Maximal subgroups

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

subgroupindex
#145447002
#145436012
#145313462
#765117