Finite Group Databasebeta

← #17948324

Subgroups — #17948324

Order 4352.

476 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 54 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#14528694C211yesmaximal, characteristic
3C22⋊#63216—22no—
4C2×C22⋊#3622—22no—
5C2×C22⋊#3622C411yescharacteristic
6C2×C22⋊#3622C2211yescharacteristic
7C24×C4×C17C411yescharacteristic
8C25×C17C811yescharacteristic
9C23×C4×C17—21no—
10C23×C4×C17—21no—
11C23×C4×C17—44no—
12C23×C4×C17—41no—
13C23×C4×C17—41no—
14C23×C4×C17C811yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C22×#3622—21no—
17C22×#3622D412yes—
18C2×#63216—42no—
19C22⋊#3622—41no—
20C22⋊#3622—41no—
21C22⋊#3622—44no—
22C24×C17—21no—
23C24×C17—21no—
24C24×C17—42no—
25C24×C17—41no—
26C24×C17—42no—
27C24×C17—41no—
28C24×C17C1612yescomplemented
29C24×C17C2×C811yescharacteristic
30C22×C4×C17—24no—
31C22×C4×C17—21no—
32C22×C4×C17—21no—
33C22×C4×C17—21no—
34C22×C4×C17—42no—
35C22×C4×C17—42no—
36C22×C4×C17—42no—
37C22×C4×C17—42no—
38C22×C4×C17—42no—
39C22×C4×C17—42no—
40C22×C4×C17—44no—
41C22×C4×C17—44no—
42C22×C4×C17—44no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17—41no—
46C22×C4×C17—44no—
47C22×C4×C17C22⋊C411yescharacteristic
48C22×C4×C17M1611yescharacteristic
49C2×#3622—22no—
50C2×#3622—42no—
51C2×#3622—42no—
52C2×#3622—41no—
53#63216—82no—
54#7054—171nomaximal, Sylow
55C23×C17—22no—
56C23×C17—22no—
57C23×C17—21no—
58C23×C17—22no—
59C23×C17—21no—
60C23×C17—41no—
61C23×C17—44no—
62C23×C17—42no—
63C23×C17—41no—
64C23×C17—41no—
65C23×C17—41no—
66C23×C17—44no—
67C23×C17—42no—
68C23×C17—42no—
69C23×C17—42no—
70C23×C17—42no—
71C23×C17—48no—
72C23×C17—42no—
73C23×C17—41no—
74C23×C17—41no—
75C23×C17C22⋊C811yescharacteristic
76C23×C17C2×C1611yescharacteristic
77C23×C17M3211yescharacteristic
78C2×C4×C17—22no—
79C2×C4×C17—22no—
80C2×C4×C17—21no—
81C2×C4×C17—44no—
82C2×C4×C17—42no—
83C2×C4×C17—41no—
84C2×C4×C17—48no—
85C2×C4×C17—42no—
86C2×C4×C17—41no—
87C2×C4×C17—44no—
88C2×C4×C17—42no—
89C2×C4×C17—41no—
90C2×C4×C17—42no—
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#10011yescharacteristic
93#3622—42no—
94#3622—81no—
95#1779—171no—
96#1314—172no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—24no—
100C22×C17—21no—
101C22×C17—21no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17—42no—
105C22×C17—42no—
106C22×C17—42no—
107C22×C17—42no—
108C22×C17—44no—
109C22×C17—44no—
110C22×C17—44no—
111C22×C17—44no—
112C22×C17—42no—
113C22×C17—42no—
114C22×C17—41no—
115C22×C17—42no—
116C22×C17—41no—
117C22×C17#32311yescharacteristic
118C22×C17C22⋊C1611yescharacteristic
119C22×C17#34911yescharacteristic
120C4×C17—21no—
121C4×C17—42no—
122C4×C17—41no—
123C4×C17AΣL(1,𝔽16)12yes—
124C24×C4#59511yescharacteristic
125C2×C22⋊C8—171no—
126C2×C22⋊C8—171no—
127C2×C22⋊C8—342no—
128C22⋊C16—342no—
129C2×C17—21no—
130C2×C17—21no—
131C2×C17—44no—
132C2×C17—41no—
133C2×C17—41no—
134C2×C17#131411yescharacteristic
135C2×C17#131611yescharacteristic
136C2×C17#132011yescharacteristic
137C25#362411yescharacteristic
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—44no—
141C23×C4—41no—
142C23×C4—41no—
143C23×C4#362411yescharacteristic
144C23×C4C2×#59511yescharacteristic
145C22×C8—172no—
146C22×C8—341no—
147C2×C16—682no—
148C22⋊C8—681no—
149C22⋊C8—684no—
150C22⋊C8—681no—
151C17#705411yescharacteristic, complemented, Sylow
152C24—21no—
153C24—21no—
154C24—42no—
155C24—41no—
156C24—42no—
157C24—41no—
158C24#6321612yescomplemented
159C24C2×#362411yescharacteristic
160C22×C4—24no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—44no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—44no—
177C22×C4#6324711yescharacteristic
178C22×C4C22⋊#59511yescharacteristic
179C2×C8—342no—
180C2×C8—682no—
181C2×C8—682no—
182C2×C8—681no—
183C16—1362no—
184C23—22no—
185C23—22no—
186C23—21no—
187C23—22no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23—44no—
192C23—42no—
193C23—41no—
194C23—41no—
195C23—44no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—48no—
201C23—42no—
202C23—41no—
203C23—41no—
204C23C2×#6321611yescharacteristic
205C23#1058753811yescharacteristic
206C23C22⋊#362411yescharacteristic
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4#1058755111yescharacteristic
221C2×C4#1058755311yescharacteristic
222C8—682no—
223C8—1361no—
224C22—21no—
225C22—21no—
226C22—24no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—44no—
236C22—44no—
237C22—44no—
238C22—44no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22#1176365211yescharacteristic
245C22C22⋊#6321611yescharacteristic
246C22#1176370511yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4#1176370912yes—
251C2—21no—
252C2—21no—
253C2—44no—
254C2—41no—
255C2—41no—
256C2#1454370411yescharacteristic
257C2#1454370811yescharacteristic
258C2#1454371611yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC23×C17C2×C16
FrattiniC23×C4C2×#595
FittingC24×C4×C17C4
socleC22×C17#323
prime radicalC25×C17C8
cosocleC2×C22⋊#3622C22
hypercenterC24×C4#595
hypocenterC17#7054
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #14543704C2semidirect
28. C24×C17C16semidirect
151. C17#7054semidirect
158. C24#63216semidirect

Maximal subgroups

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

subgroupindex
#145437042
#145286942
#705417