Finite Group Databasebeta

← #17960876

Subgroups — #17960876

Order 4352.

512 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#11763718C212yesmaximal
2#14544537C212yesmaximal, complemented
3#14543882C212yesmaximal, complemented
4#14531492C211yesmaximal, characteristic
5C2×#10587545C2214yes—
6C4×#63247—22no—
7#11763718C418yescomplemented
8#11763689—22no—
9C2×#10587561C2211yescharacteristic
10C2×#10587573C2211yescharacteristic
11C2×#10587579C411yescharacteristic
12#11762714C2211yescharacteristic
13#11762710C411yescharacteristic
14#11762699—22no—
15#11762680—22no—
16#11762655C411yescharacteristic
17C17×#384C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C22×Dic34C2311yescharacteristic
21C2×#63247—24no—
22C2×C4⋊C4×C17—22no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C42×C17C2×C411yescharacteristic
26C2×#63227—22no—
27C2×#63227—21no—
28C2×#63227—22no—
29C2×#63225D412yes—
30C2×C4×Dic17C2×C411yescharacteristic
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17D412yes—
33#10587579—42no—
34#10587573—42no—
35#10587561—22no—
36#10587561C2×C414yes—
37#10587545—24no—
38#10587545C2×C418yescomplemented
39#10587542—42no—
40C4×#3624—42no—
41#10587502—21no—
42#10587502—21no—
43#10587502—22no—
44C23×D17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17C22⋊C412yes—
48C22×C4×C17C22×C411yescharacteristic
49C22×Dic17—21no—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C22⋊C411yescharacteristic
52C22×Dic17C2×D412yes—
53C2×D68—21no—
54C2×D68—41no—
55C2×D68—41no—
56C2×D68C4212yes—
57C2×C4×D17—42no—
58C2×C4×D17—82no—
59C2×Dic34—41no—
60C2×Dic34—41no—
61C2×Dic34C22×C412yes—
62C2×Dic34#4112yes—
63#63247—28no—
64#63247—44no—
65C2×#3624—44no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—82no—
69C42×C17—21no—
70C42×C17C4212yes—
71#63227—28no—
72#63227—42no—
73#63227—82no—
74#63225—42no—
75C4×Dic17—22no—
76C4×Dic17—22no—
77C4×Dic17—22no—
78C4×Dic17—41no—
79#12632—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81C22×D17—22no—
82C22×D17—42no—
83C22×D17—42no—
84C22×D17—41no—
85C22×D17—41no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—41no—
95C2×C4×C17C2×C4211yescharacteristic
96C2×C4×C17#11711yescharacteristic
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—21no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17#9912yes—
106C2×Dic17C4×D414yes—
107D68—42no—
108D68—42no—
109C4×D17—84no—
110Dic34—42no—
111Dic34—42no—
112#3624—48no—
113#2326—171no—
114C2×#355—172no—
115C4×#101—172no—
116#1394—172no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17C4×C22⋊C411yescharacteristic
120C22×C17C2×#9911yescharacteristic
121C22×C17#41011yescharacteristic
122C2×D17—44no—
123C2×D17—42no—
124C2×D17—82no—
125C2×D17—81no—
126C2×D17—81no—
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—42no—
130C4×C17—42no—
131C4×C17—81no—
132Dic17—22no—
133Dic17—24no—
134Dic17—41no—
135Dic17—81no—
136C2×#124—171no—
137C2×C4×Q8—171no—
138C2×C4×D4—171no—
139C2×#101—174no—
140C4×M16—342no—
141#391—171no—
142#390—171no—
143#388—342no—
144#385—342no—
145#384#59511yescharacteristic
146#376—171no—
147#355—178no—
148#343—342no—
149C2×C17—21no—
150C2×C17—21no—
151C2×C17C4×#9911yescharacteristic
152C2×C17#213311yescharacteristic
153C2×C17#213411yescharacteristic
154D17—82no—
155C22×Q8—171no—
156C22×D4—171no—
157C23×C4—341no—
158C2×M16—344no—
159#124—174no—
160#124—342no—
161C4×Q8—682no—
162C4×D4—682no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—172no—
165C2×C4⋊C4C2×#59511yescharacteristic
166C2×C4⋊C4C2×#59511yescharacteristic
167C2×C22⋊C4—342no—
168C2×C22⋊C4—341no—
169C2×C22⋊C4—342no—
170C2×C42—172no—
171C2×C42—171no—
172C2×C42—171no—
173C2×C42C2×#59511yescharacteristic
174#101—178no—
175#101—344no—
176#97—682no—
177C4×C8—682no—
178#95—341no—
179#95—341no—
180#95—342no—
181C17#1263211yescharacteristic, complemented, Sylow
182C24—341no—
183C2×Q8—172no—
184C2×Q8—172no—
185C2×Q8—681no—
186C2×Q8—681no—
187C2×D4—172no—
188C2×D4—341no—
189C2×D4—681no—
190C2×D4—681no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—172no—
194C22×C4—171no—
195C22×C4—171no—
196C22×C4—341no—
197C22×C4—682no—
198C22×C4—1362no—
199C22×C4C22⋊#59512yes—
200C22×C4C22×#59511yescharacteristic
201M16—348no—
202M16—684no—
203C2×C8—684no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—82no—
207C4⋊C4—682no—
208C22⋊C4—348no—
209C22⋊C4—682no—
210C22⋊C4—1362no—
211C42—21no—
212C42—342no—
213C42—342no—
214C42—342no—
215C42—681no—
216C42C4×#59512yes—
217C23—342no—
218C23—682no—
219C23—682no—
220C23—681no—
221C23—681no—
222C23C2×C22⋊#59511yescharacteristic
223Q8—682no—
224Q8—682no—
225D4—682no—
226D4—682no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—174no—
237C2×C4—172no—
238C2×C4—342no—
239C2×C4—342no—
240C2×C4—341no—
241C2×C4—681no—
242C2×C4—681no—
243C2×C4—681no—
244C2×C4—681no—
245C2×C4—681no—
246C2×C4—1364no—
247C2×C4C2×C4×#59511yescharacteristic
248C2×C4#1058767711yescharacteristic
249C8—688no—
250C22—21no—
251C22—21no—
252C22—684no—
253C22—682no—
254C22—1362no—
255C22—1361no—
256C22—1361no—
257C22C4×C22⋊#59511yescharacteristic
258C22D17⋊#9911yescharacteristic
259C22#1176379011yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4—344no—
266C4—342no—
267C4—681no—
268C4—1361no—
269C2—21no—
270C2—21no—
271C2—1362no—
272C2#1454452911yescharacteristic
273C2#1454508211yescharacteristic
274C2#1454508411yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC22×Dic34C23
hypercenter#384#595
hypocenterC17#12632
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14544537C2semidirect
3. #14543882C2semidirect
7. #11763718C4semidirect
38. #10587545C2×C4semidirect
181. C17#12632semidirect

Maximal subgroups

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

subgroupindex
C2×#117637182
#145445372
#145438822
#145314922
#1263217