Finite Group Databasebeta

← #17953587

Subgroups — #17953587

Order 4352.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544510C212yesmaximal
2#14543660C212yesmaximal, complemented
3#14543660C212yesmaximal, complemented
4#14531187C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6C2×#10587542C2214yes—
7#11763675—22no—
8C2×#10587612C411yescharacteristic
9C22×C4×Dic17C2211yescharacteristic
10#11762678C411yescharacteristic
11#11762678C411yescharacteristic
12#11762674C2211yescharacteristic
13#11762674C2211yescharacteristic
14#11762667—22no—
15C4×#63225—22no—
16C2×C17×#117C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17D412yes—
19C22×#3624—24no—
20C17×#117—42no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C22⋊C4×C17—21no—
24C2×C42×C17—21no—
25C2×C22⋊Dic17—21no—
26#10587612—42no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×C4⋊Dic17C2×C411yescharacteristic
29C2×#63225—22no—
30C2×#63225—22no—
31C2×C4×Dic17—24no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C22⋊#3624—28no—
37#10587542—28no—
38#10587502—22no—
39#10587502—22no—
40C24×C17C22⋊C411yescharacteristic
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—24no—
49C22×Dic17—24no—
50C22×Dic17—21no—
51C22×Dic17—21no—
52C22×Dic17—42no—
53C22×Dic17C22⋊C412yes—
54C22×Dic17C2×D412yes—
55C2×#3624—28no—
56C2×#3624—44no—
57C2×#3624—44no—
58C4⋊C4×C17—41no—
59C4⋊C4×C17—41no—
60C22⋊C4×C17—42no—
61C42×C17—42no—
62C22⋊Dic17—42no—
63C4⋊Dic17—41no—
64C4⋊Dic17—41no—
65#63225—44no—
66#63225—44no—
67C4×Dic17—22no—
68C4×Dic17—24no—
69C4×Dic17—42no—
70C4×Dic17#4114yes—
71#8721—171nomaximal, Sylow
72C23×C17—21no—
73C23×C17—21no—
74C23×C17—22no—
75C23×C17—22no—
76C23×C17#10112yes—
77C23×C17C2×C22⋊C411yescharacteristic
78C2×C4×C17—28no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17#10012yes—
88C2×C4×C17#11712yes—
89C2×Dic17—22no—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—22no—
93C2×Dic17—48no—
94C2×Dic17—41no—
95C2×Dic17—41no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17#10414yes—
99C2×Dic17#12314yes—
100#3624—48no—
101#2285—171no—
102#1749—172no—
103#1295—172no—
104#1295—172no—
105C22×C17—22no—
106C22×C17—24no—
107C22×C17—41no—
108C22×C17—42no—
109C22×C17—41no—
110C22×C17#38111yescharacteristic
111C22×C17C2×#10011yescharacteristic
112C22×C17C2×#10111yescharacteristic
113C22×C17C2×#10412yes—
114C22×C17#42112yes—
115C4×C17—22no—
116C4×C17—22no—
117C4×C17—81no—
118C4×C17—81no—
119Dic17—24no—
120Dic17—24no—
121Dic17—81no—
122Dic17—81no—
123C2×#117—171no—
124C2×#117#59511yescharacteristic
125C22×C42—171no—
126C2×C22⋊C8—342no—
127C2×#97—174no—
128#384—171no—
129#384—171no—
130#382—171no—
131#382—171no—
132#380—342no—
133C4×C4⋊C4—342no—
134#336—342no—
135C2×C17—42no—
136C2×C17#152511yescharacteristic
137C2×C17#153112yes—
138C2×C17#153611yescharacteristic
139C2×C17#182111yescharacteristic
140C2×C17#182612yes—
141C23×C4—172no—
142C23×C4C2×#59511yescharacteristic
143C22×C8—344no—
144#117—42no—
145#117—682no—
146C2×C4⋊C4—171no—
147C2×C4⋊C4—171no—
148C2×C4⋊C4—342no—
149C2×C4⋊C4—342no—
150C2×C4⋊C4C2×#59511yescharacteristic
151C2×C4⋊C4C2×#59511yescharacteristic
152C2×C22⋊C4—21no—
153C2×C22⋊C4—341no—
154C2×C42—21no—
155C2×C42—171no—
156C2×C42—172no—
157C2×C42—171no—
158C2×C42—344no—
159C2×C42—341no—
160C22⋊C8—348no—
161#97—348no—
162#95—342no—
163#95—342no—
164C17#872111yescharacteristic, complemented, Sylow
165C24C22⋊#59511yescharacteristic
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—172no—
172C22×C4—172no—
173C22×C4—344no—
174C22×C4—344no—
175C22×C4—341no—
176C22×C4—341no—
177C22×C4—682no—
178C22×C4C22⋊#59511yescharacteristic
179C22×C4C22×#59511yescharacteristic
180C2×C8—348no—
181C2×C8—684no—
182C2×C8—684no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—681no—
186C4⋊C4—681no—
187C4⋊C4—684no—
188C4⋊C4—684no—
189C22⋊C4—42no—
190C22⋊C4—682no—
191C42—42no—
192C42—174no—
193C42—344no—
194C42—342no—
195C42—682no—
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23#1058754512yes—
201C23C2×C22⋊#59511yescharacteristic
202C2×C4—28no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—174no—
212C2×C4—174no—
213C2×C4—342no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—342no—
217C2×C4—688no—
218C2×C4—681no—
219C2×C4—681no—
220C2×C4—682no—
221C2×C4—682no—
222C2×C4#1058755312yes—
223C2×C4#1058767712yes—
224C8—688no—
225C22—22no—
226C22—24no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22#1176375211yescharacteristic
231C22C2×#1058755311yescharacteristic
232C22C2×#1058754511yescharacteristic
233C22D17⋊#10412yes—
234C22#1176380612yes—
235C4—22no—
236C4—22no—
237C4—81no—
238C4—81no—
239C4—344no—
240C4—344no—
241C4—1361no—
242C4—1361no—
243C2—42no—
244C2#1454423811yescharacteristic
245C2#1454425612yes—
246C2#1454427211yescharacteristic
247C2#1454468311yescharacteristic
248C2#1454469212yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#8721
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543660C2semidirect
3. #14543660C2semidirect
164. C17#8721semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436602
#145311872
#872117