Finite Group Databasebeta

← #17949964

Subgroups — #17949964

Order 4352.

624 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 118 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#14543600C214yesmaximal, complemented
3#127×Dic17C211yesmaximal, characteristic
4C2×#10587544—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×D4×Dic17—22no—
8C2×D4×Dic17C412yes—
9#11762712—22no—
10#11762712C2212yes—
11#11762679C411yescharacteristic
12C42×Dic17C2211yescharacteristic
13C2×C17×#127C411yescharacteristic
14C22×D4×C17—22no—
15C22×D4×C17C2×C412yes—
16C23×Dic17—22no—
17C22×#3624—24no—
18C17×#127—24no—
19C2×C42×C17C2×C411yescharacteristic
20C2×C22⋊Dic17—22no—
21C2×C22⋊Dic17—24no—
22D4×Dic17—44no—
23D4×Dic17—44no—
24D4×Dic17—44no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17C2×C412yes—
27C2×C4×Dic17C2×C411yescharacteristic
28C2×C4×Dic17D412yes—
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31#10587544—44no—
32C24×C17—22no—
33C2×D4×C17—28no—
34C2×D4×C17—22no—
35C2×D4×C17—42no—
36C2×D4×C17—42no—
37C2×D4×C17—44no—
38C2×D4×C17—44no—
39C2×D4×C17M1614yes—
40C22×C4×C17C22⋊C412yes—
41C22×C4×C17C22×C411yescharacteristic
42C22×Dic17—22no—
43C22×Dic17—44no—
44C22×Dic17—48no—
45C22×Dic17C22⋊C411yescharacteristic
46C22×Dic17C22⋊C411yescharacteristic
47C22×Dic17C2×D412yes—
48C2×#3624—44no—
49C2×#3624—44no—
50C2×#3624—44no—
51C42×C17—22no—
52C22⋊Dic17—44no—
53C22⋊Dic17—44no—
54C22⋊Dic17—44no—
55C4⋊Dic17—44no—
56C4⋊Dic17—42no—
57C4×Dic17—22no—
58C4×Dic17—42no—
59C4×Dic17—41no—
60C4×Dic17D814yes—
61C4×Dic17SD1614yes—
62#7651—171nomaximal, Sylow
63C23×C17—24no—
64C23×C17—42no—
65C23×C17—42no—
66C23×C17—44no—
67C23×C17—44no—
68C23×C17C2×C22⋊C411yescharacteristic
69D4×C17—44no—
70D4×C17—44no—
71D4×C17—416no—
72C2×C4×C17—22no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—22no—
76C2×C4×C17#10214yes—
77C2×C4×C17C2×M1612yes—
78C2×Dic17—22no—
79C2×Dic17—22no—
80C2×Dic17—21no—
81C2×Dic17—22no—
82C2×Dic17—42no—
83C2×Dic17—44no—
84C2×Dic17—88no—
85C2×Dic17#10012yes—
86C2×Dic17#10214yes—
87C2×Dic17C2×D812yes—
88C2×Dic17C2×SD1612yes—
89#3624—84no—
90C4×#127—171no—
91#1831—172no—
92#1270—174no—
93C22×C17—44no—
94C22×C17—48no—
95C22×C17—82no—
96C22×C17—82no—
97C22×C17—84no—
98C22×C17#40711yescharacteristic
99C22×C17#41011yescharacteristic
100C22×C17C2×#10011yescharacteristic
101C22×C17C2×#10212yes—
102C22×C17#42112yes—
103C4×C17—22no—
104C4×C17—24no—
105Dic17—22no—
106Dic17—22no—
107Dic17—41no—
108Dic17—82no—
109Dic17#33114yes—
110C2×#127#59511yescharacteristic
111C2×C4×D4—172no—
112C2×C4×D4—342no—
113C2×C4⋊C8—342no—
114#390—172no—
115#390—342no—
116#384—171no—
117C43—171no—
118#336—174no—
119#336—342no—
120C2×C17—84no—
121C2×C17#146611yescharacteristic
122C2×C17#148612yes—
123C2×C17#151712yes—
124C2×C17#153611yescharacteristic
125C2×C17C2×#33111yescharacteristic
126C22×D4—22no—
127C22×D4C2×#59512yes—
128C23×C4—342no—
129C22×C8—344no—
130#127—24no—
131C4×D4—684no—
132C4×D4—684no—
133C4×D4—684no—
134C2×C4⋊C4—172no—
135C2×C4⋊C4—342no—
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—22no—
146C2×D4—28no—
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—42no—
150C2×D4—44no—
151C2×D4—44no—
152C2×D4#6324714yes—
153C22×C4—171no—
154C22×C4—172no—
155C22×C4—171no—
156C22×C4—342no—
157C22×C4—688no—
158C22×C4—684no—
159C22×C4C22⋊#59512yes—
160C22×C4C22×#59511yescharacteristic
161C2×C8—684no—
162C2×C8—684no—
163C2×C8—684no—
164C4⋊C4—682no—
165C4⋊C4—684no—
166C22⋊C4—684no—
167C22⋊C4—684no—
168C22⋊C4—684no—
169C42—22no—
170C42—174no—
171C42—174no—
172C42—342no—
173C42—681no—
174C42—682no—
175C23—24no—
176C23—42no—
177C23—42no—
178C23—44no—
179C23—44no—
180C23C2×C22⋊#59511yescharacteristic
181D4—44no—
182D4—44no—
183D4—416no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—172no—
189C2×C4—174no—
190C2×C4—172no—
191C2×C4—172no—
192C2×C4—342no—
193C2×C4—342no—
194C2×C4—341no—
195C2×C4—342no—
196C2×C4—682no—
197C2×C4—684no—
198C2×C4—1368no—
199C2×C4#1058754714yes—
200C2×C4C2×#6324712yes—
201C8—1364no—
202C22—44no—
203C22—48no—
204C22—84no—
205C22—82no—
206C22—82no—
207C22#1176377911yescharacteristic
208C22#1176378911yescharacteristic
209C22D17⋊#10011yescharacteristic
210C22C2×#1058754712yes—
211C22#1176380712yes—
212C4—22no—
213C4—24no—
214C4—174no—
215C4—342no—
216C4—342no—
217C4—681no—
218C4—1362no—
219C2—84no—
220C2#1454404411yescharacteristic
221C2#1454410912yes—
222C2#1454421312yes—
223C2#1454427311yescharacteristic
224C2D17⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#127C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#127#595
hypocenterC17#7651
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14544700C2semidirect
2. #14543600C2semidirect
144. C17#7651semidirect

Maximal subgroups

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

subgroupindex
#145447002
#145436002
#127×Dic172
#765117