Finite Group Databasebeta

← #17958422

Subgroups — #17958422

Order 4352.

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

normal subgroups only

This group has 510 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#14543715C214yesmaximal, complemented
3#14531368C211yesmaximal, characteristic
4#11763829—22no—
5#11763654C2214yes—
6#11763652—22no—
7C23×Dic34C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762715C412yes—
10#11762715C2212yes—
11#11762714—22no—
12#11762670—22no—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17—21no—
16C22×Dic34—21no—
17C22×Dic34—24no—
18C22×Dic34—42no—
19C22×Dic34—42no—
20C22×Dic34C2×C412yes—
21C17×#117—42no—
22C2×C4⋊C4×C17—21no—
23C2×C22⋊C4×C17—21no—
24C2×C42×C17C2×C412yes—
25C2×C22⋊Dic17D412yes—
26#10587612—42no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×C4⋊Dic17C2311yescharacteristic
29C2×C4×Dic17D412yes—
30C22⋊#3624—24no—
31#10587544—42no—
32#10587542—42no—
33#10587502—24no—
34#10587502—24no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C22×C411yescharacteristic
42C22×Dic17—24no—
43C22×Dic17—22no—
44C22×Dic17—42no—
45C22×Dic17—42no—
46C22×Dic17C22⋊C412yes—
47C22×Dic17C2×D412yes—
48C2×Dic34—24no—
49C2×Dic34—22no—
50C2×Dic34—42no—
51C2×Dic34—416no—
52C2×Dic34—42no—
53C2×Dic34—42no—
54C2×Dic34—42no—
55C2×Dic34M1614yes—
56C2×#3624—44no—
57C4⋊C4×C17—42no—
58C22⋊C4×C17—42no—
59C42×C17—42no—
60C22⋊Dic17—42no—
61C4⋊Dic17—41no—
62C4⋊Dic17—41no—
63C4×Dic17—22no—
64C4×Dic17—22no—
65#11510—171nomaximal, Sylow
66C23×C17—21no—
67C23×C17—21no—
68C23×C17—41no—
69C23×C17—41no—
70C23×C17#10012yes—
71C23×C17C2×C22⋊C411yescharacteristic
72C2×C4×C17—28no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17#9912yes—
81C2×C4×C17C2×M1612yes—
82C2×Dic17—24no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—48no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90Dic34—48no—
91Dic34—44no—
92Dic34—44no—
93#3624—84no—
94#2310—171no—
95#1464—172no—
96#1319—174no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—22no—
100C22×C17—42no—
101C22×C17—42no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17#40711yescharacteristic
105C22×C17C2×#9911yescharacteristic
106C22×C17C2×#10011yescharacteristic
107C4×C17—22no—
108C4×C17—22no—
109C4×C17—82no—
110Dic17—42no—
111Dic17—42no—
112Dic17—44no—
113C23×Q8—171no—
114C2×#117—171no—
115C2×#117#59511yescharacteristic
116#432—342no—
117#391—172no—
118#391—172no—
119#391—342no—
120#381—342no—
121#324—174no—
122#323—342no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17—42no—
126C2×C17#146211yescharacteristic
127C2×C17#212911yescharacteristic
128C2×C17#213511yescharacteristic
129C22×Q8—172no—
130C22×Q8—344no—
131C22×Q8—341no—
132C22×Q8—682no—
133C22×Q8—682no—
134C23×C4—341no—
135C23×C4C2×#59511yescharacteristic
136#117—42no—
137#117—682no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—171no—
140C2×C4⋊C4—171no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—172no—
143C2×C42—172no—
144C2×C42C2×#59512yes—
145C4⋊C8—682no—
146C22⋊C8—344no—
147#97—682no—
148#95—344no—
149#95—344no—
150C17#1151011yescharacteristic, complemented, Sylow
151C24C22⋊#59511yescharacteristic
152C2×Q8—174no—
153C2×Q8—344no—
154C2×Q8—342no—
155C2×Q8—6816no—
156C2×Q8—682no—
157C2×Q8—682no—
158C2×Q8—682no—
159C2×Q8—682no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—172no—
165C22×C4—172no—
166C22×C4—344no—
167C22×C4—342no—
168C22×C4—682no—
169C22×C4—682no—
170C22×C4C22⋊#59511yescharacteristic
171C22×C4C22×#59511yescharacteristic
172C2×C8—684no—
173C4⋊C4—42no—
174C4⋊C4—681no—
175C4⋊C4—681no—
176C22⋊C4—42no—
177C22⋊C4—682no—
178C42—42no—
179C42—342no—
180C42—342no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#1058755312yes—
186C23C2×C22⋊#59511yescharacteristic
187Q8—684no—
188Q8—684no—
189Q8—688no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—344no—
199C2×C4—342no—
200C2×C4—342no—
201C2×C4—688no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4—682no—
206C2×C4#1058753912yes—
207C2×C4D17⋊M1612yes—
208C8—1364no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22#1176378111yescharacteristic
217C22C2×#1058753911yescharacteristic
218C22C2×#1058755311yescharacteristic
219C4—22no—
220C4—22no—
221C4—82no—
222C4—684no—
223C4—682no—
224C4—682no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#1454403111yescharacteristic
229C2#1454506811yescharacteristic
230C2#1454508811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11510
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543715C2semidirect
150. C17#11510semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437152
#145313682
#1151017