Finite Group Databasebeta

← #17958321

Subgroups — #17958321

Order 4352.

440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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#14544026C212yesmaximal, complemented
2#14543726C212yesmaximal, complemented
3#14543713C212yesmaximal
4#14531495C211yesmaximal, characteristic
5#11763826—22no—
6#11763655—22no—
7#11763654C2214yes—
8C2×#10587561C411yescharacteristic
9C2×C4×Dic34C2211yescharacteristic
10C2×C4×D68C411yescharacteristic
11#11762715C411yescharacteristic
12#11762711C2211yescharacteristic
13#11762701—22no—
14#11762683—22no—
15#11762679C2211yescharacteristic
16C17×#376C411yescharacteristic
17C22×D68C2×C411yescharacteristic
18C22×C4×D17—21no—
19C22×Dic34C2×C411yescharacteristic
20C2×C42×C17C2×C411yescharacteristic
21C2×C42×C17C2×C411yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23C2×#63227—21no—
24C2×#63227—22no—
25C2×#63227—22no—
26C2×C4⋊Dic17—22no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×C4⋊Dic17C2311yescharacteristic
29C2×#63225D412yes—
30C2×C4×Dic17D412yes—
31#10587561—22no—
32#10587561C814yescomplemented
33C4×D68—42no—
34C4×Dic34—42no—
35C22⋊#3624—24no—
36#10587544—42no—
37C4×#3624—42no—
38C17×#95—21no—
39C17×#95—21no—
40#10587502—22no—
41C23×D17—21no—
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C22×Dic17—21no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17C2×D412yes—
50C2×D68—21no—
51C2×D68—41no—
52C2×D68—41no—
53C2×D68C2×C812yes—
54C2×C4×D17—42no—
55C2×C4×D17—82no—
56C2×Dic34—41no—
57C2×Dic34—41no—
58C2×Dic34C2×C812yes—
59C2×Dic34M1612yes—
60C2×#3624—44no—
61C42×C17—22no—
62C42×C17—21no—
63C42×C17—41no—
64C42×C17C2×C812yes—
65#63227—28no—
66#63227—42no—
67#63227—82no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70C4⋊Dic17—82no—
71#63225—42no—
72C4×Dic17—22no—
73C4×Dic17—22no—
74#11480—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—22no—
77C22×D17—42no—
78C22×D17—42no—
79C22×D17—41no—
80C22×D17—41no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—21no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17#9912yes—
93C2×C4×C17C22×C811yescharacteristic
94C2×C4×C17C2×M1611yescharacteristic
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—41no—
101C2×Dic17C22⋊C814yes—
102D68—42no—
103D68—42no—
104C4×D17—84no—
105Dic34—42no—
106Dic34—42no—
107#3624—84no—
108#2326—171no—
109#1461—172no—
110#1325—172no—
111#1318—172no—
112C22×C17—21no—
113C22×C17—21no—
114C22×C17C2×C22⋊C811yescharacteristic
115C22×C17C2×#9911yescharacteristic
116C22×C17#41311yescharacteristic
117C2×D17—44no—
118C2×D17—42no—
119C2×D17—82no—
120C2×D17—81no—
121C2×D17—81no—
122C4×C17—22no—
123C4×C17—21no—
124C4×C17—21no—
125C4×C17—42no—
126C4×C17—41no—
127C4×C17—81no—
128Dic17—24no—
129Dic17—42no—
130Dic17—81no—
131C2×#124—171no—
132C2×C4×Q8—171no—
133C2×C4×D4—171no—
134#431—342no—
135#391—171no—
136#390—171no—
137#388—342no—
138#385—342no—
139#384—171no—
140#376#59511yescharacteristic
141#324—174no—
142#324—342no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17#145911yescharacteristic
146C2×C17#212811yescharacteristic
147C2×C17#213311yescharacteristic
148D17—82no—
149C22×Q8—171no—
150C22×D4—171no—
151C23×C4—341no—
152#124—174no—
153#124—342no—
154C4×Q8—682no—
155C4×D4—682no—
156C2×C4⋊C4—172no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—342no—
160C2×C22⋊C4—342no—
161C2×C22⋊C4—341no—
162C2×C22⋊C4—342no—
163C2×C42—172no—
164C2×C42C2×#59511yescharacteristic
165C2×C42C2×#59511yescharacteristic
166C2×C42C2×#59511yescharacteristic
167C4⋊C8—682no—
168C22⋊C8—344no—
169C4×C8—682no—
170#95—21no—
171#95—21no—
172#95—342no—
173C17#1148011yescharacteristic, complemented, Sylow
174C24—341no—
175C2×Q8—172no—
176C2×Q8—172no—
177C2×Q8—681no—
178C2×Q8—681no—
179C2×D4—172no—
180C2×D4—341no—
181C2×D4—681no—
182C2×D4—681no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—172no—
186C22×C4—172no—
187C22×C4—341no—
188C22×C4—682no—
189C22×C4—1362no—
190C22×C4C22⋊#59511yescharacteristic
191C22×C4C22⋊#59511yescharacteristic
192C22×C4C22×#59511yescharacteristic
193C2×C8—684no—
194C4⋊C4—682no—
195C4⋊C4—681no—
196C4⋊C4—681no—
197C4⋊C4—1362no—
198C22⋊C4—348no—
199C22⋊C4—682no—
200C22⋊C4—1362no—
201C42—21no—
202C42—22no—
203C42—41no—
204C42—342no—
205C42—342no—
206C42#6324212yes—
207C23—342no—
208C23—682no—
209C23—682no—
210C23—681no—
211C23—681no—
212C23C2×C22⋊#59511yescharacteristic
213Q8—682no—
214Q8—682no—
215D4—682no—
216D4—682no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—174no—
229C2×C4—342no—
230C2×C4—342no—
231C2×C4—342no—
232C2×C4—682no—
233C2×C4—682no—
234C2×C4—681no—
235C2×C4—1364no—
236C2×C4#1058753912yes—
237C2×C4C2×#6324211yescharacteristic
238C2×C4D17⋊M1611yescharacteristic
239C8—1364no—
240C22—21no—
241C22—21no—
242C22—684no—
243C22—682no—
244C22—1362no—
245C22—1361no—
246C22—1361no—
247C22#1176377711yescharacteristic
248C22C2×#1058753911yescharacteristic
249C22#1176379511yescharacteristic
250C4—21no—
251C4—21no—
252C4—22no—
253C4—42no—
254C4—41no—
255C4—81no—
256C4—344no—
257C4—682no—
258C4—1361no—
259C2—21no—
260C2—21no—
261C2—1362no—
262C2#1454402111yescharacteristic
263C2#1454506511yescharacteristic
264C2#1454508111yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#376C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC2×C4⋊Dic17C23
hypercenter#376#595
hypocenterC17#11480
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #14544026C2semidirect
2. #14543726C2semidirect
32. #10587561C8semidirect
173. C17#11480semidirect

Maximal subgroups

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

subgroupindex
#145440262
#145437262
#145437132
#145314952
#1148017