Finite Group Databasebeta

← #17948745

Subgroups — #17948745

Order 4352.

290 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 52 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#14544514C211yesmaximal, characteristic
2#14544036C211yesmaximal, characteristic
3#14528860C211yesmaximal, characteristic
4#11763830—21no—
5C2×C22⋊#3624—21no—
6C2×#10587542C411yescharacteristic, complemented
7C2×C4×#3624C411yescharacteristic, complemented
8#11763675—21no—
9#11763655C412yescomplemented
10#11763652—21no—
11C2×#10587563C2211yescharacteristic
12#11762670—21no—
13#11762576C411yescharacteristic
14#11762575—21no—
15C17×#342C411yescharacteristic
16C23×Dic17D411yescharacteristic
17C22×#3624—21no—
18C22×#3624—21no—
19C2×C22⋊C4×C17—21no—
20C2×C22⋊C4×C17C2×C411yescharacteristic
21C2×C22⋊Dic17—21no—
22C2×C22⋊Dic17D411yescharacteristic
23C2×#63225C2×C411yescharacteristic
24C2×#63225Q811yescharacteristic
25C2×C4×Dic17C2×C411yescharacteristic
26C2×C4×Dic17D411yescharacteristic
27#10587563—41no—
28#10587563—41no—
29C22⋊#3624—22no—
30C22⋊#3624—22no—
31C22⋊#3624—22no—
32#10587542—41no—
33#10587542—41no—
34C4⋊#3624—41no—
35C4×#3624—41no—
36#10587502—41no—
37#10587502—41no—
38C24×C17C22⋊C411yescharacteristic
39C22×C4×C17—41no—
40C22×C4×C17C4211yescharacteristic
41C22×C4×C17C4⋊C411yescharacteristic
42C22×Dic17—21no—
43C22×Dic17—21no—
44C22×Dic17—21no—
45C22×Dic17—21no—
46C22×Dic17—41no—
47C22×Dic17—41no—
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C22⋊C411yescharacteristic
50C22×Dic17C4⋊C411yescharacteristic
51C22×Dic17C4⋊C411yescharacteristic
52C2×#3624—22no—
53C2×#3624—22no—
54C2×#3624—41no—
55C2×#3624—41no—
56C2×#3624—41no—
57C2×#3624—41no—
58C2×#3624—42no—
59C22⋊C4×C17—41no—
60C22⋊C4×C17—41no—
61C22⋊C4×C17—41no—
62C22⋊Dic17—41no—
63C22⋊Dic17—41no—
64C22⋊Dic17—41no—
65#63225—41no—
66#63225—41no—
67C4×Dic17—21no—
68C4×Dic17—21no—
69C4×Dic17—21no—
70C4×Dic17—21no—
71#7214—171nomaximal, Sylow
72C23×C17—21no—
73C23×C17—21no—
74C23×C17—41no—
75C23×C17—41no—
76C23×C17#9511yescharacteristic
77C23×C17#10411yescharacteristic
78C23×C17#10411yescharacteristic
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—41no—
82C2×C4×C17—41no—
83C2×C4×C17—81no—
84C2×C4×C17—81no—
85C2×C4×C17—81no—
86C2×Dic17—21no—
87C2×Dic17—21no—
88C2×Dic17—21no—
89C2×Dic17—21no—
90C2×Dic17—21no—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—41no—
94C2×Dic17—41no—
95C2×Dic17—41no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—81no—
100C2×Dic17—81no—
101C2×Dic17—81no—
102C2×Dic17#9911yescharacteristic
103C2×Dic17#9911yescharacteristic
104#3624—42no—
105#3624—42no—
106#3624—82no—
107#1820—171no—
108#1750—171no—
109#1464—171no—
110C22×C17—21no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17—21no—
114C22×C17—41no—
115C22×C17—41no—
116C22×C17—41no—
117C22×C17—41no—
118C22×C17—81no—
119C22×C17H(3,ℤ/4)11yescharacteristic
120C22×C17#33911yescharacteristic
121C22×C17#34211yescharacteristic
122C4×C17—41no—
123C4×C17—41no—
124C4×C17—161no—
125Dic17—21no—
126Dic17—21no—
127Dic17—41no—
128Dic17—41no—
129Dic17—41no—
130Dic17—161no—
131C2×#117—171no—
132#432—341no—
133C2×C22⋊C8—341no—
134C2×#97—171no—
135C2×C4×C8—171no—
136#381—341no—
137#342—171no—
138#342—341no—
139#342#59511yescharacteristic
140#336—341no—
141#324—172no—
142#323—341no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17—41no—
146C2×C17—41no—
147C2×C17#128411yescharacteristic
148C2×C17#139111yescharacteristic
149C2×C17#139511yescharacteristic
150C23×C4—171no—
151C22×C8—341no—
152C22×C8—341no—
153#117—681no—
154#117—681no—
155C2×C4⋊C4—171no—
156C2×C4⋊C4—171no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—171no—
159C2×C22⋊C4—341no—
160C2×C22⋊C4C2×#59511yescharacteristic
161C2×C42—171no—
162C2×C42—171no—
163C4⋊C8—681no—
164C22⋊C8—342no—
165C22⋊C8—342no—
166C22⋊C8—342no—
167#97—681no—
168#97—681no—
169C4×C8—681no—
170#95—681no—
171#95—681no—
172C17#721411yescharacteristic, complemented, Sylow
173C24C22⋊#59511yescharacteristic
174C22×C4—41no—
175C22×C4—171no—
176C22×C4—171no—
177C22×C4—171no—
178C22×C4—171no—
179C22×C4—341no—
180C22×C4—341no—
181C22×C4—341no—
182C22×C4—341no—
183C22×C4—681no—
184C22×C4—681no—
185C22×C4C4×#59511yescharacteristic
186C22×C4C4⋊#59511yescharacteristic
187C2×C8—342no—
188C2×C8—342no—
189C2×C8—681no—
190C2×C8—681no—
191C2×C8—681no—
192C2×C8—681no—
193C2×C8—682no—
194C4⋊C4—681no—
195C4⋊C4—681no—
196C22⋊C4—41no—
197C22⋊C4—41no—
198C22⋊C4—41no—
199C22⋊C4—681no—
200C22⋊C4—681no—
201C22⋊C4—681no—
202C42—341no—
203C42—341no—
204C42—341no—
205C42—341no—
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23(C2×#595)⋊C411yescharacteristic
211C23#1058754811yescharacteristic
212C23#1058755011yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—171no—
221C2×C4—171no—
222C2×C4—341no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—681no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—1361no—
236C2×C4—1361no—
237C2×C4—1361no—
238C8—682no—
239C8—682no—
240C8—1362no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—81no—
250C22#1176367611yescharacteristic
251C22#1176367911yescharacteristic
252C22#1176368611yescharacteristic
253C4—41no—
254C4—41no—
255C4—161no—
256C4—2721no—
257C4—341no—
258C4—341no—
259C4—681no—
260C4—681no—
261C4—681no—
262C2—21no—
263C2—21no—
264C2—41no—
265C2—41no—
266C2#1454363111yescharacteristic
267C2#1454387111yescharacteristic
268C2#1454388311yescharacteristic
subgroupG/H
centerC22#11763686
commutatorC22×C4×C17C42
FrattiniC2×C22⋊C4C2×#595
FittingC17×#342C4
socleC22×C17#342
prime radicalC24×C17C22⋊C4
cosocleC2×#10587563C22
hypercenter#342#595
hypocenterC17#7214
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
6. C2×#10587542C4semidirect
7. C2×C4×#3624C4semidirect
9. #11763655C4semidirect
172. C17#7214semidirect

Maximal subgroups

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

subgroupindex
#145445142
#145440362
#145288602
#721417