Finite Group Databasebeta

← #17948384

Subgroups — #17948384

Order 4352.

316 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 40 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#14543705C211yesmaximal, characteristic, complemented
2#14543656C211yesmaximal, characteristic, complemented
3#14529779C211yesmaximal, characteristic
4#11763780—21no—
5C22⋊#63216—21no—
6C2×#10587624—21no—
7C2×#10587503—21no—
8C2×#10587491C2211yescharacteristic
9#11762572C411yescharacteristic
10C22×D8×C17C411yescharacteristic
11C22×D4×C17—21no—
12C22×C22⋊D17—41no—
13C22×C4×D17D411yescharacteristic
14C2×#63243—41no—
15C2×D8×C17—41no—
16C2×D8×C17—42no—
17C22×C8×C17C2×C411yescharacteristic
18C2×C22⋊Dic17—41no—
19#10587624—42no—
20#10587624—42no—
21C2×C4⋊Dic17—21no—
22C22×#3622D411yescharacteristic
23C22⋊#3624—41no—
24#10587543—22no—
25C2×#63216—41no—
26#10587503—42no—
27#10587491—41no—
28C24×C17—41no—
29C23×D17SD1611yescharacteristic
30C2×D4×C17—22no—
31C2×D4×C17—41no—
32C2×D4×C17—41no—
33C2×D4×C17—41no—
34C2×D4×C17—41no—
35C2×D4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C2×C22⋊D17—44no—
38C2×C22⋊D17—82no—
39C2×C22⋊D17—82no—
40C22×Dic17—41no—
41C22×Dic17D811yescharacteristic
42C2×C4×D17—21no—
43C2×C4×D17—21no—
44C2×C4×D17—41no—
45C2×C4×D17—41no—
46C2×#3624—42no—
47#63243—81no—
48#63243—81no—
49D8×C17—42no—
50D8×C17—42no—
51C2×C8×C17—21no—
52C2×C8×C17—41no—
53C22⋊Dic17—44no—
54C4⋊Dic17—22no—
55C4⋊Dic17—41no—
56C2×#3622—21no—
57C2×#3622—41no—
58#63216—81no—
59#7084—171nomaximal, Sylow
60C23×C17—42no—
61C23×C17—81no—
62C23×C17—81no—
63C23×C17—81no—
64C23×C17—81no—
65C23×C17—81no—
66C23×C17—81no—
67C23×C17#10211yescharacteristic
68C22×D17—21no—
69C22×D17—21no—
70C22×D17—21no—
71C22×D17—41no—
72C22×D17—41no—
73D4×C17—42no—
74D4×C17—42no—
75D4×C17—81no—
76D4×C17—81no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17#9911yescharacteristic
80C2×C4×C17#10411yescharacteristic
81C22⋊D17—88no—
82C2×Dic17—21no—
83C2×Dic17—41no—
84C2×Dic17—42no—
85C2×Dic17—81no—
86C2×Dic17—81no—
87C4×D17—41no—
88C4×D17—41no—
89C4×D17—81no—
90#3624—82no—
91C8×C17—41no—
92#3622—41no—
93#1999—171no—
94#1314—171no—
95#1293—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17—82no—
99C22×C17—82no—
100C22×C17—82no—
101C22×C17—161no—
102C22×C17—161no—
103C22×C17—161no—
104C22×C17—161no—
105C22×C17#32711yescharacteristic
106C22×C17#35911yescharacteristic
107C22×C17#36111yescharacteristic
108C2×D17—42no—
109C2×D17—41no—
110C2×D17—41no—
111C2×D17—41no—
112C2×D17—81no—
113C4×C17—21no—
114C4×C17AΣL(1,𝔽16)11yescharacteristic
115C4×C17#35311yescharacteristic
116Dic17—41no—
117Dic17—82no—
118C22×D8#59511yescharacteristic
119C2×#121—341no—
120C2×#102—341no—
121#407—341no—
122C2×C22⋊C8—171no—
123C22⋊C16—341no—
124#340—171no—
125C2×C17—21no—
126C2×C17—21no—
127C2×C17—162no—
128C2×C17#134111yescharacteristic
129C2×C17#134311yescharacteristic
130C2×C17#134911yescharacteristic
131D17—81no—
132C22×D4—21no—
133C22×D4—681no—
134C23×C4—171no—
135C2×D8—41no—
136C2×D8—42no—
137C2×M16—681no—
138C22×C8—171no—
139C22×C8C2×#59511yescharacteristic
140#121—682no—
141#121—682no—
142C2×C4⋊C4—341no—
143C2×C22⋊C4—681no—
144C2×C16—681no—
145#102—682no—
146C22⋊C8—342no—
147C22⋊C8—681no—
148C22⋊C8—681no—
149C17#708411yescharacteristic, complemented, Sylow
150C24—41no—
151C24—171no—
152C2×D4—22no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—684no—
159C2×D4—1362no—
160C2×D4—1362no—
161C22×C4—171no—
162C22×C4—341no—
163C22×C4—341no—
164C22×C4—681no—
165C22×C4—681no—
166C22×C4—681no—
167C22×C4C22⋊#59511yescharacteristic
168D8—42no—
169D8—42no—
170M16—1361no—
171M16—1361no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8—341no—
175C2×C8—681no—
176C2×C8—682no—
177C4⋊C4—342no—
178C4⋊C4—681no—
179C22⋊C4—684no—
180C16—1361no—
181C23—42no—
182C23—81no—
183C23—81no—
184C23—81no—
185C23—81no—
186C23—81no—
187C23—81no—
188C23—341no—
189C23—341no—
190C23—341no—
191C23—681no—
192C23—681no—
193C23#1058754711yescharacteristic
194D4—42no—
195D4—42no—
196D4—81no—
197D4—81no—
198D4—1368no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—341no—
202C2×C4—681no—
203C2×C4—681no—
204C2×C4—681no—
205C2×C4—682no—
206C2×C4—1361no—
207C2×C4—1361no—
208C2×C4—1361no—
209C2×C4#1058754811yescharacteristic
210C2×C4#1058755111yescharacteristic
211C8—41no—
212C8—681no—
213C8—1362no—
214C22—21no—
215C22—21no—
216C22—82no—
217C22—82no—
218C22—82no—
219C22—161no—
220C22—161no—
221C22—161no—
222C22—161no—
223C22—682no—
224C22—681no—
225C22—681no—
226C22—681no—
227C22—1361no—
228C22#1176366011yescharacteristic
229C22#1176372311yescharacteristic
230C22#1176372711yescharacteristic
231C4—21no—
232C4—681no—
233C4—1362no—
234C4#1176370911yescharacteristic
235C4#1176371311yescharacteristic
236C2—21no—
237C2—21no—
238C2—162no—
239C2—1361no—
240C2#1454375811yescharacteristic
241C2#1454376211yescharacteristic
242C2#1454377411yescharacteristic
subgroupG/H
centerC22#11763660
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×D8×C17C4
socleC22×C17#327
prime radical#14529779C2
cosocleC2×#10587491C22
hypercenterC22×D8#595
hypocenterC17#7084
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. #14543705C2semidirect
2. #14543656C2semidirect
149. C17#7084semidirect

Maximal subgroups

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

subgroupindex
#145437052
#145436562
#145297792
#708417