Finite Group Databasebeta

← #17958322

Subgroups — #17958322

Order 4352.

440 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544027C212yesmaximal, complemented
2#14543727C212yesmaximal, complemented
3#14543713C212yesmaximal
4#14531498C211yesmaximal, characteristic
5#11763825—22no—
6#11763654—22no—
7#11763654C2214yes—
8C2×#10587633C411yescharacteristic
9C2×Q8×Dic17C2211yescharacteristic
10C2×#10587579C411yescharacteristic
11#11762711C2211yescharacteristic
12#11762698—22no—
13#11762683—22no—
14#11762678C2211yescharacteristic
15#11762655C411yescharacteristic
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C2×C4⋊C4×C17C2×C411yescharacteristic
21C2×C42×C17C2×C411yescharacteristic
22#10587633—22no—
23#10587633C814yescomplemented
24Q8×Dic17—42no—
25C2×#63227—22no—
26C2×#63227—21no—
27C2×#63227—22no—
28C2×C4⋊Dic17D412yes—
29C2×C4⋊Dic17C2311yescharacteristic
30C2×#63225—22no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34#10587579—42no—
35C22⋊#3624—24no—
36C4⋊#3624—42no—
37C4×#3624—42no—
38C17×#95—22no—
39#10587502—21no—
40#10587502—21no—
41C23×D17—21no—
42C2×Q8×C17—41no—
43C2×Q8×C17—41no—
44C2×Q8×C17C2×C812yes—
45C2×Q8×C17M1612yes—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22⋊C412yes—
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—21no—
51C22×Dic17C22⋊C411yescharacteristic
52C22×Dic17C22⋊C411yescharacteristic
53C22×Dic17C2×D412yes—
54C2×D68—21no—
55C2×D68—41no—
56C2×D68—41no—
57C2×D68C2×C812yes—
58C2×C4×D17—42no—
59C2×C4×D17—82no—
60C2×#3624—44no—
61C4⋊C4×C17—41no—
62C42×C17—41no—
63#63227—28no—
64#63227—42no—
65#63227—82no—
66C4⋊Dic17—42no—
67C4⋊Dic17—41no—
68#63225—82no—
69C4×Dic17—21no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—22no—
73C4×Dic17C2×C812yes—
74#11480—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—22no—
77C22×D17—42no—
78C22×D17—42no—
79C22×D17—41no—
80C22×D17—41no—
81Q8×C17—42no—
82Q8×C17—42no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17C22⋊C814yes—
93C2×C4×C17C22×C811yescharacteristic
94C2×C4×C17C2×M1611yescharacteristic
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—21no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—42no—
103C2×Dic17#9912yes—
104D68—42no—
105D68—42no—
106C4×D17—84no—
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—21no—
123C4×C17—21no—
124C4×C17—24no—
125C4×C17—81no—
126C4×C17—81no—
127Dic17—22no—
128Dic17—42no—
129Dic17—42no—
130Dic17—41no—
131C2×#124—171no—
132C2×C4×Q8—171no—
133C2×C4×D4—171no—
134#431—342no—
135#391#59511yescharacteristic
136#390—171no—
137#388—342no—
138#385—342no—
139#384—171no—
140#376—171no—
141#324—174no—
142#324—342no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17#145911yescharacteristic
146C2×C17#212811yescharacteristic
147C2×C17#213311yescharacteristic
148D17—82no—
149C22×Q8C2×#59511yescharacteristic
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—342no—
159C2×C4⋊C4C2×#59511yescharacteristic
160C2×C22⋊C4—342no—
161C2×C22⋊C4—341no—
162C2×C22⋊C4—342no—
163C2×C42—171no—
164C2×C42—172no—
165C2×C42—171no—
166C2×C42C2×#59511yescharacteristic
167C4⋊C8—682no—
168C22⋊C8—344no—
169C4×C8—682no—
170#95—22no—
171#95—341no—
172#95—341no—
173C17#1148011yescharacteristic, complemented, Sylow
174C24—341no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8#6324212yes—
178C2×Q8#6324312yes—
179C2×D4—172no—
180C2×D4—341no—
181C2×D4—681no—
182C2×D4—681no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—171no—
186C22×C4—171no—
187C22×C4—172no—
188C22×C4—341no—
189C22×C4—682no—
190C22×C4—1362no—
191C22×C4C22⋊#59512yes—
192C22×C4C22×#59511yescharacteristic
193C2×C8—684no—
194C4⋊C4—41no—
195C4⋊C4—681no—
196C4⋊C4—682no—
197C4⋊C4—1362no—
198C22⋊C4—348no—
199C22⋊C4—682no—
200C22⋊C4—1362no—
201C42—41no—
202C42—172no—
203C42—342no—
204C42—342no—
205C42—342no—
206C42—341no—
207C23—342no—
208C23—682no—
209C23—682no—
210C23—681no—
211C23—681no—
212C23C2×C22⋊#59511yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—682no—
216D4—682no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—172no—
227C2×C4—342no—
228C2×C4—342no—
229C2×C4—341no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—682no—
234C2×C4—681no—
235C2×C4—1364no—
236C2×C4#1058754314yes—
237C2×C4C2×#6324211yescharacteristic
238C2×C4C2×#6324311yescharacteristic
239C8—1364no—
240C22—21no—
241C22—21no—
242C22—684no—
243C22—682no—
244C22—1362no—
245C22—1361no—
246C22—1361no—
247C22C2×#1058754311yescharacteristic
248C22D17⋊#9911yescharacteristic
249C22#1176379611yescharacteristic
250C4—21no—
251C4—21no—
252C4—24no—
253C4—81no—
254C4—81no—
255C4—342no—
256C4—682no—
257C4—682no—
258C4—681no—
259C2—21no—
260C2—21no—
261C2—1362no—
262C2#1454402211yescharacteristic
263C2#1454506411yescharacteristic
264C2#1454508211yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC2×C4⋊Dic17C23
hypercenter#391#595
hypocenterC17#11480
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #14544027C2semidirect
2. #14543727C2semidirect
23. #10587633C8semidirect
173. C17#11480semidirect

Maximal subgroups

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

subgroupindex
#145440272
#145437272
#145437132
#145314982
#1148017