Finite Group Databasebeta

← #17949668

Subgroups — #17949668

Order 4352.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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#14544499C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543600C212yesmaximal
4C4×#10587622C211yesmaximal, characteristic
5C2×C4×#3624—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587622C411yescharacteristic
9C2×C4×Dic34C411yescharacteristic
10#11762714C2211yescharacteristic
11#11762712C2211yescharacteristic
12#11762703—22no—
13#11762674C411yescharacteristic
14C4×C22⋊Dic17—22no—
15C42×Dic17C2211yescharacteristic
16C2×C4×D4×C17C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C23×C4×C17—21no—
19C22×Dic34C2×C411yescharacteristic
20C22×#3624—24no—
21C4×D4×C17—42no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C22⋊C4×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25C2×C22⋊Dic17—22no—
26C2×C22⋊Dic17—22no—
27#10587622—22no—
28#10587622C814yescomplemented
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×#63225—21no—
31C2×C4×Dic17—21no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C4×Dic34—42no—
37C4×#3624—28no—
38#10587502—22no—
39#10587502—22no—
40C24×C17—21no—
41C2×D4×C17—21no—
42C2×D4×C17—41no—
43C2×D4×C17—41no—
44C2×D4×C17C2×C812yes—
45C22×C4×C17—21no—
46C22×C4×C17—42no—
47C22×C4×C17—44no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17—21no—
53C22×Dic17C22⋊C412yes—
54C22×Dic17C2×D412yes—
55C2×Dic34—21no—
56C2×Dic34—41no—
57C2×Dic34—41no—
58C2×Dic34C2×C812yes—
59C2×#3624—28no—
60C2×#3624—44no—
61C2×#3624—44no—
62C4⋊C4×C17—41no—
63C22⋊C4×C17—42no—
64C42×C17—22no—
65C22⋊Dic17—28no—
66C22⋊Dic17—44no—
67C4⋊Dic17—41no—
68#63225—42no—
69C4×Dic17—24no—
70C4×Dic17—24no—
71C4×Dic17—41no—
72C4×Dic17—42no—
73C4×Dic17C2×C812yes—
74C4×Dic17M1612yes—
75#7567—171nomaximal, Sylow
76C23×C17—22no—
77C23×C17—41no—
78C23×C17—41no—
79C23×C17—42no—
80C23×C17—42no—
81C23×C17C2×C22⋊C411yescharacteristic
82D4×C17—42no—
83D4×C17—42no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17—84no—
91C2×C4×C17#10012yes—
92C2×C4×C17#10414yes—
93C2×C4×C17C22×C811yescharacteristic
94C2×C4×C17C2×M1611yescharacteristic
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—22no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—42no—
104C2×Dic17C22⋊C814yes—
105C2×Dic17#13514yes—
106Dic34—42no—
107Dic34—42no—
108#3624—48no—
109C4×#124—171no—
110#1744—172no—
111#1272—172no—
112#1270—172no—
113C22×C17—42no—
114C22×C17—44no—
115C22×C17—81no—
116C22×C17—82no—
117C22×C17—81no—
118C22×C17C2×C22⋊C811yescharacteristic
119C22×C17#41011yescharacteristic
120C22×C17C2×#10011yescharacteristic
121C22×C17#41612yes—
122C22×C17C2×#10412yes—
123C4×C17—21no—
124C4×C17—21no—
125C4×C17—41no—
126C4×C17—81no—
127C4×C17#32914yes—
128Dic17—24no—
129Dic17—24no—
130Dic17—42no—
131Dic17—81no—
132C2×#124—171no—
133C2×C4×Q8—171no—
134C2×C4×D4#59511yescharacteristic
135C2×C4×C8—342no—
136#391—171no—
137#390—171no—
138#388—342no—
139#382—171no—
140C4×C22⋊C4—342no—
141C43—171no—
142#336—174no—
143#336—342no—
144C2×C17—82no—
145C2×C17#146011yescharacteristic
146C2×C17#147612yes—
147C2×C17#150012yes—
148C2×C17C2×#32911yescharacteristic
149C2×C17#154311yescharacteristic
150C22×Q8—171no—
151C22×D4C2×#59511yescharacteristic
152C23×C4—21no—
153C22×C8—344no—
154#124—174no—
155#124—342no—
156C4×Q8—682no—
157C4×D4—42no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—341no—
160C2×C4⋊C4C2×#59511yescharacteristic
161C2×C22⋊C4—21no—
162C2×C22⋊C4—342no—
163C2×C22⋊C4—342no—
164C2×C42—171no—
165C2×C42—172no—
166C2×C42—172no—
167C2×C42—171no—
168C2×C42—341no—
169C2×C42C2×#59511yescharacteristic
170C4×C8—348no—
171#95—342no—
172#95—342no—
173C17#756711yescharacteristic, complemented, Sylow
174C24—21no—
175C2×Q8—172no—
176C2×Q8—341no—
177C2×Q8—681no—
178C2×Q8—681no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#6324212yes—
183C22×C4—21no—
184C22×C4—44no—
185C22×C4—42no—
186C22×C4—172no—
187C22×C4—172no—
188C22×C4—341no—
189C22×C4—341no—
190C22×C4C22⋊#59511yescharacteristic
191C22×C4C22⋊#59511yescharacteristic
192C22×C4C22×#59511yescharacteristic
193C2×C8—348no—
194C2×C8—684no—
195C2×C8—684no—
196C4⋊C4—41no—
197C4⋊C4—681no—
198C4⋊C4—682no—
199C22⋊C4—42no—
200C22⋊C4—348no—
201C22⋊C4—684no—
202C42—22no—
203C42—172no—
204C42—172no—
205C42—344no—
206C42—344no—
207C42—681no—
208C42—682no—
209C23—22no—
210C23—41no—
211C23—41no—
212C23—42no—
213C23—42no—
214C23C2×C22⋊#59511yescharacteristic
215Q8—682no—
216Q8—682no—
217D4—42no—
218D4—42no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—84no—
226C2×C4—174no—
227C2×C4—174no—
228C2×C4—342no—
229C2×C4—342no—
230C2×C4—342no—
231C2×C4—342no—
232C2×C4—342no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—681no—
236C2×C4—682no—
237C2×C4#1058754814yes—
238C2×C4#1058755312yes—
239C2×C4C2×#6324211yescharacteristic
240C2×C4D17⋊M1611yescharacteristic
241C8—688no—
242C22—42no—
243C22—44no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22#1176377711yescharacteristic
248C22#1176378811yescharacteristic
249C22C2×#1058755311yescharacteristic
250C22#1176379912yes—
251C22C2×#1058754812yes—
252C4—21no—
253C4—21no—
254C4—41no—
255C4—81no—
256C4—344no—
257C4—344no—
258C4—682no—
259C4—1361no—
260C4#1176366414yes—
261C2—82no—
262C2#1454402311yescharacteristic
263C2#1454407612yes—
264C2#1454415512yes—
265C2C2×#1176366411yescharacteristic
266C2#1454428711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7567
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544499C2semidirect
2. #14543605C2semidirect
28. #10587622C8semidirect
173. C17#7567semidirect

Maximal subgroups

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

subgroupindex
#145444992
#145436052
#145436002
C4×#105876222
#756717