Finite Group Databasebeta

← #17949790

Subgroups — #17949790

Order 4352.

492 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544700C212yesmaximal, complemented
2#14543604C212yesmaximal, complemented
3#14543601C212yesmaximal
4C4×#10587633C211yesmaximal, characteristic
5C2×#10587544—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587633C411yescharacteristic
9C2×C4×D68C411yescharacteristic
10#11762716C2211yescharacteristic
11#11762710C2211yescharacteristic
12#11762699—22no—
13#11762674C411yescharacteristic
14C4×#63227—22no—
15C42×Dic17C2211yescharacteristic
16C2×C4×Q8×C17C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C22×#3624—24no—
21C4×Q8×C17—42no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26#10587633—22no—
27#10587633C814yescomplemented
28C2×#63227—21no—
29C2×#63227—22no—
30C2×#63227—22no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C4×D68—42no—
37#10587544—44no—
38#10587502—22no—
39#10587502—22no—
40C23×D17—21no—
41C2×Q8×C17—21no—
42C2×Q8×C17—41no—
43C2×Q8×C17—41no—
44C2×Q8×C17C2×C812yes—
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17C22⋊C411yescharacteristic
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—21no—
51C22×Dic17C22⋊C412yes—
52C22×Dic17C2×D412yes—
53C2×D68—21no—
54C2×D68—41no—
55C2×D68—41no—
56C2×D68C2×C812yes—
57C2×C4×D17—44no—
58C2×C4×D17—42no—
59C2×#3624—44no—
60C2×#3624—44no—
61C2×#3624—44no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—42no—
64C42×C17—22no—
65C42×C17—42no—
66#63227—28no—
67#63227—42no—
68#63227—42no—
69#63227—42no—
70C4⋊Dic17—41no—
71C4×Dic17—22no—
72C4×Dic17—22no—
73C4×Dic17—42no—
74C4×Dic17—41no—
75C4×Dic17C2×C812yes—
76C4×Dic17M1612yes—
77#7601—171nomaximal, Sylow
78C23×C17C2×C22⋊C411yescharacteristic
79C22×D17—22no—
80C22×D17—41no—
81C22×D17—41no—
82C22×D17—42no—
83C22×D17—42no—
84Q8×C17—42no—
85Q8×C17—42no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17#10012yes—
97C2×C4×C17C22×C811yescharacteristic
98C2×C4×C17C2×M1611yescharacteristic
99C2×Dic17—22no—
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17C22⋊C814yes—
106C2×Dic17AGL(1,ℤ/8)12yes—
107C2×Dic17#13712yes—
108D68—42no—
109D68—42no—
110C4×D17—84no—
111#3624—84no—
112C4×#124—171no—
113#1831—172no—
114#1272—172no—
115#1270—172no—
116C22×C17C2×C22⋊C811yescharacteristic
117C22×C17#41011yescharacteristic
118C22×C17C2×#10011yescharacteristic
119C22×C17#41712yes—
120C22×C17#42112yes—
121C2×D17—42no—
122C2×D17—44no—
123C2×D17—81no—
124C2×D17—82no—
125C2×D17—81no—
126C4×C17—21no—
127C4×C17—21no—
128C4×C17—22no—
129C4×C17—41no—
130C4×C17—42no—
131C4×C17—81no—
132Dic17—24no—
133Dic17—22no—
134Dic17—22no—
135Dic17—81no—
136C2×#124—171no—
137C2×C4×Q8#59511yescharacteristic
138C2×C4×D4—171no—
139C2×C4⋊C8—342no—
140#391—171no—
141#390—171no—
142#388—342no—
143#382—171no—
144C4×C22⋊C4—342no—
145C43—171no—
146#336—174no—
147#336—342no—
148C2×C17#146011yescharacteristic
149C2×C17#147712yes—
150C2×C17#151212yes—
151C2×C17#153311yescharacteristic
152C2×C17#156011yescharacteristic
153D17—82no—
154C22×Q8C2×#59511yescharacteristic
155C22×D4—171no—
156C23×C4—341no—
157C22×C8—344no—
158#124—174no—
159#124—342no—
160C4×Q8—42no—
161C4×D4—682no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4C2×#59511yescharacteristic
165C2×C22⋊C4—342no—
166C2×C22⋊C4—342no—
167C2×C22⋊C4—341no—
168C2×C42—21no—
169C2×C42—171no—
170C2×C42—172no—
171C2×C42—172no—
172C2×C42—171no—
173C2×C42C2×#59511yescharacteristic
174C4⋊C8—684no—
175#95—342no—
176#95—342no—
177C17#760111yescharacteristic, complemented, Sylow
178C24—341no—
179C2×Q8—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8#6324212yes—
183C2×D4—172no—
184C2×D4—341no—
185C2×D4—681no—
186C2×D4—681no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—172no—
190C22×C4—172no—
191C22×C4—341no—
192C22×C4—684no—
193C22×C4—682no—
194C22×C4C22⋊#59511yescharacteristic
195C22×C4C22⋊#59511yescharacteristic
196C22×C4C22×#59511yescharacteristic
197C2×C8—684no—
198C2×C8—684no—
199C2×C8—684no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—681no—
203C22⋊C4—348no—
204C22⋊C4—682no—
205C22⋊C4—682no—
206C22⋊C4—682no—
207C42—22no—
208C42—42no—
209C42—172no—
210C42—172no—
211C42—342no—
212C42—342no—
213C42—681no—
214C42—682no—
215C23—342no—
216C23—681no—
217C23—681no—
218C23—682no—
219C23—682no—
220C23C2×C22⋊#59511yescharacteristic
221Q8—42no—
222Q8—42no—
223D4—682no—
224D4—682no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—174no—
236C2×C4—172no—
237C2×C4—172no—
238C2×C4—342no—
239C2×C4—342no—
240C2×C4—342no—
241C2×C4—342no—
242C2×C4—681no—
243C2×C4—682no—
244C2×C4—1364no—
245C2×C4#1058755312yes—
246C2×C4C2×#6324211yescharacteristic
247C2×C4D17⋊M1611yescharacteristic
248C8—1364no—
249C22—682no—
250C22—684no—
251C22—1362no—
252C22—1361no—
253C22—1361no—
254C22#1176377711yescharacteristic
255C22#1176378811yescharacteristic
256C22C2×#1058755311yescharacteristic
257C22#1176380012yes—
258C22#1176380812yes—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—42no—
263C4—41no—
264C4—81no—
265C4—342no—
266C4—342no—
267C4—344no—
268C4—1361no—
269C2—1362no—
270C2#1454402311yescharacteristic
271C2#1454408212yes—
272C2#1454419712yes—
273C2#1454426511yescharacteristic
274C2#1454432111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7601
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14544700C2semidirect
2. #14543604C2semidirect
27. #10587633C8semidirect
177. C17#7601semidirect

Maximal subgroups

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

subgroupindex
#145447002
#145436042
#145436012
C4×#105876332
#760117