Finite Group Databasebeta

← #17948325

Subgroups — #17948325

Order 4352.

476 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 50 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#14543704C212yesmaximal, complemented
2#14528693C211yesmaximal, characteristic
3C22⋊#63216—22no—
4C23×C4×D17C411yescharacteristic
5C2×C22⋊#3622C2211yescharacteristic
6C2×#10587491—22no—
7C2×C17×C22⋊C8C411yescharacteristic
8C24×D17C811yescharacteristic
9C23×C4×C17C2×C411yescharacteristic
10C23×Dic17C811yescharacteristic
11C22×C4×D17—21no—
12C22×C4×D17—21no—
13C22×C4×D17—44no—
14C22×C4×D17—41no—
15C22×C4×D17—41no—
16C22×C8×C17—21no—
17C22×#3622D412yes—
18C2×#63216—42no—
19C17×C22⋊C8—41no—
20C22⋊#3622—41no—
21#10587491—44no—
22C24×C17C2×C811yescharacteristic
23C23×D17—21no—
24C23×D17—21no—
25C23×D17—42no—
26C23×D17—42no—
27C23×D17—41no—
28C23×D17—41no—
29C23×D17C1612yescomplemented
30C22×C4×C17—21no—
31C22×C4×C17—21no—
32C22×C4×C17—42no—
33C22×C4×C17C22⋊C411yescharacteristic
34C22×C4×C17M1611yescharacteristic
35C22×Dic17—21no—
36C22×Dic17—42no—
37C22×Dic17—41no—
38C2×C4×D17—24no—
39C2×C4×D17—42no—
40C2×C4×D17—42no—
41C2×C4×D17—42no—
42C2×C4×D17—42no—
43C2×C4×D17—44no—
44C2×C4×D17—44no—
45C2×C4×D17—44no—
46C2×C4×D17—41no—
47C2×C4×D17—41no—
48C2×C4×D17—44no—
49C2×C8×C17—42no—
50C2×C8×C17—41no—
51C2×#3622—22no—
52C2×#3622—42no—
53#63216—82no—
54#7054—171nomaximal, Sylow
55C23×C17—21no—
56C23×C17—21no—
57C23×C17—41no—
58C23×C17—41no—
59C23×C17C22⋊C811yescharacteristic
60C23×C17C2×C1611yescharacteristic
61C23×C17M3211yescharacteristic
62C22×D17—22no—
63C22×D17—22no—
64C22×D17—22no—
65C22×D17—44no—
66C22×D17—44no—
67C22×D17—41no—
68C22×D17—41no—
69C22×D17—42no—
70C22×D17—42no—
71C22×D17—48no—
72C22×D17—42no—
73C22×D17—41no—
74C22×D17—41no—
75C22×D17—42no—
76C22×D17—42no—
77C22×D17—42no—
78C2×C4×C17—22no—
79C2×C4×C17—21no—
80C2×C4×C17—42no—
81C2×C4×C17—42no—
82C2×C4×C17—41no—
83C2×C4×C17#9911yescharacteristic
84C2×C4×C17#10011yescharacteristic
85C2×Dic17—22no—
86C2×Dic17—41no—
87C2×Dic17—42no—
88C2×Dic17—41no—
89C2×Dic17—42no—
90C4×D17—44no—
91C4×D17—48no—
92C4×D17—44no—
93C8×C17—81no—
94#3622—42no—
95#1779—171no—
96#1314—172no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—21no—
100C22×C17—21no—
101C22×C17—41no—
102C22×C17—41no—
103C22×C17—42no—
104C22×C17—41no—
105C22×C17—41no—
106C22×C17#32311yescharacteristic
107C22×C17C22⋊C1611yescharacteristic
108C22×C17#34911yescharacteristic
109C2×D17—24no—
110C2×D17—42no—
111C2×D17—42no—
112C2×D17—42no—
113C2×D17—44no—
114C2×D17—44no—
115C2×D17—44no—
116C2×D17—42no—
117C2×D17—42no—
118C2×D17—42no—
119C2×D17—44no—
120C4×C17—21no—
121C4×C17—41no—
122C4×C17AΣL(1,𝔽16)12yes—
123Dic17—42no—
124C24×C4—171no—
125C2×C22⋊C8—171no—
126C2×C22⋊C8—342no—
127C2×C22⋊C8#59511yescharacteristic
128C22⋊C16—342no—
129C2×C17—21no—
130C2×C17—21no—
131C2×C17—41no—
132C2×C17—41no—
133C2×C17#131411yescharacteristic
134C2×C17#131611yescharacteristic
135C2×C17#132011yescharacteristic
136D17—44no—
137C25—171no—
138C23×C4—171no—
139C23×C4—341no—
140C23×C4—341no—
141C23×C4—681no—
142C23×C4—681no—
143C23×C4—684no—
144C23×C4C2×#59511yescharacteristic
145C22×C8—21no—
146C22×C8—172no—
147C2×C16—682no—
148C22⋊C8—41no—
149C22⋊C8—684no—
150C22⋊C8—681no—
151C17#705411yescharacteristic, complemented, Sylow
152C24—172no—
153C24—341no—
154C24—341no—
155C24—681no—
156C24—681no—
157C24—682no—
158C24—682no—
159C24#6324211yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4—344no—
164C22×C4—341no—
165C22×C4—682no—
166C22×C4—682no—
167C22×C4—682no—
168C22×C4—682no—
169C22×C4—684no—
170C22×C4—684no—
171C22×C4—684no—
172C22×C4—684no—
173C22×C4—682no—
174C22×C4—681no—
175C22×C4—681no—
176C22×C4—681no—
177C22×C4#6324311yescharacteristic
178C22×C4C22⋊#59511yescharacteristic
179C2×C8—42no—
180C2×C8—41no—
181C2×C8—342no—
182C2×C8—682no—
183C16—1362no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—41no—
188C23—342no—
189C23—342no—
190C23—342no—
191C23—682no—
192C23—681no—
193C23—681no—
194C23—682no—
195C23—684no—
196C23—684no—
197C23—682no—
198C23—682no—
199C23—682no—
200C23—688no—
201C23—682no—
202C23—681no—
203C23—681no—
204C23#1058752911yescharacteristic
205C23#1058753011yescharacteristic
206C23#1058754311yescharacteristic
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—342no—
213C2×C4—684no—
214C2×C4—688no—
215C2×C4—681no—
216C2×C4—682no—
217C2×C4—681no—
218C2×C4—684no—
219C2×C4—682no—
220C2×C4#1058753911yescharacteristic
221C2×C4#1058755311yescharacteristic
222C8—81no—
223C8—682no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—344no—
234C22—682no—
235C22—682no—
236C22—682no—
237C22—684no—
238C22—684no—
239C22—684no—
240C22—684no—
241C22—682no—
242C22—682no—
243C22—682no—
244C22#1176365311yescharacteristic
245C22#1176370411yescharacteristic
246C22#1176370611yescharacteristic
247C4—21no—
248C4—41no—
249C4—682no—
250C4#1176371012yes—
251C2—21no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—684no—
256C2#1454370511yescharacteristic
257C2#1454370911yescharacteristic
258C2#1454371711yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC23×C17C2×C16
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#323
prime radicalC24×D17C8
cosocleC2×C22⋊#3622C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7054
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #14543704C2semidirect
29. C23×D17C16semidirect
151. C17#7054semidirect

Maximal subgroups

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

subgroupindex
#145437042
#145286932
#705417