Finite Group Databasebeta

← #17960873

Subgroups — #17960873

Order 4352.

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

normal subgroups only

This group has 464 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×#11763719C212yesmaximal
2#14544537C212yesmaximal
3#14543881C212yesmaximal
4#14531502C211yesmaximal, characteristic
5C2×#10587545C2214yes—
6C4×#63247—22no—
7#11763719C418yescomplemented
8#11763689—22no—
9C2×#10587630C2211yescharacteristic
10C2×Q8×Dic17C411yescharacteristic
11C2×#10587573C2211yescharacteristic
12#11762715C2211yescharacteristic
13#11762696—22no—
14#11762691—22no—
15#11762674C411yescharacteristic
16#11762655C411yescharacteristic
17C17×#391C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C22×Dic34C2311yescharacteristic
20C2×#63247—24no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23Q8×Dic17—42no—
24#10587630—22no—
25#10587630C2×C414yes—
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×#63225—22no—
29C2×#63225D412yes—
30C2×C4×Dic17—21no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34#10587573—42no—
35#10587545—24no—
36#10587545C2×C418yes—
37#10587542—42no—
38C4×#3624—42no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—21no—
42#10587502—21no—
43#10587502—22no—
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17C4212yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C412yes—
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D412yes—
57C2×Dic34—41no—
58C2×Dic34—41no—
59C2×Dic34C22×C412yes—
60C2×Dic34#4112yes—
61#63247—28no—
62#63247—44no—
63C2×#3624—44no—
64C4⋊C4×C17—41no—
65C42×C17—41no—
66C4⋊Dic17—42no—
67C4⋊Dic17—41no—
68#63225—28no—
69#63225—42no—
70C4×Dic17—21no—
71C4×Dic17—22no—
72C4×Dic17—22no—
73C4×Dic17—22no—
74C4×Dic17—42no—
75C4×Dic17C4212yes—
76#12631—171nomaximal, Sylow
77C23×C17C2×C22⋊C411yescharacteristic
78Q8×C17—42no—
79Q8×C17—42no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—42no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17C2×C4211yescharacteristic
91C2×C4×C17#11711yescharacteristic
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—21no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17—42no—
101C2×Dic17—41no—
102C2×Dic17#9912yes—
103C2×Dic17C4×D414yes—
104Dic34—42no—
105Dic34—42no—
106#3624—48no—
107#2327—171no—
108C2×#356—172no—
109C4×#101—172no—
110#1394—172no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17C4×C22⋊C411yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17#41011yescharacteristic
116C4×C17—21no—
117C4×C17—21no—
118C4×C17—42no—
119C4×C17—42no—
120C4×C17—81no—
121Dic17—22no—
122Dic17—24no—
123Dic17—42no—
124Dic17—41no—
125Dic17—81no—
126C2×C4⋊Q8—171no—
127C2×C4×Q8—171no—
128C2×C4×Q8—171no—
129C2×#101—174no—
130C4×M16—342no—
131#391—171no—
132#391#59511yescharacteristic
133#387—342no—
134#387—342no—
135#382—171no—
136#376—171no—
137#356—178no—
138#343—342no—
139C2×C17—21no—
140C2×C17—21no—
141C2×C17C4×#9911yescharacteristic
142C2×C17#213311yescharacteristic
143C2×C17#213511yescharacteristic
144C22×Q8—171no—
145C22×Q8C2×#59511yescharacteristic
146C2×M16—344no—
147C4⋊Q8—174no—
148C4⋊Q8—342no—
149C4×Q8—682no—
150C4×Q8—682no—
151C2×C4⋊C4—172no—
152C2×C4⋊C4—171no—
153C2×C4⋊C4—342no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4C2×#59511yescharacteristic
156C2×C42—171no—
157C2×C42—172no—
158C2×C42—171no—
159C2×C42—341no—
160C2×C42C2×#59511yescharacteristic
161#101—178no—
162#101—344no—
163#97—682no—
164C4×C8—682no—
165#95—22no—
166#95—341no—
167#95—341no—
168#95—342no—
169#95—342no—
170C17#1263111yescharacteristic, complemented, Sylow
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—172no—
175C2×Q8—172no—
176C2×Q8—681no—
177C2×Q8—681no—
178C2×Q8C4×#59512yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—172no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—341no—
185C22×C4—341no—
186C22×C4C22⋊#59512yes—
187C22×C4C22×#59511yescharacteristic
188M16—348no—
189M16—684no—
190C2×C8—684no—
191C4⋊C4—41no—
192C4⋊C4—348no—
193C4⋊C4—682no—
194C4⋊C4—681no—
195C4⋊C4—682no—
196C42—41no—
197C42—172no—
198C42—342no—
199C42—342no—
200C42—342no—
201C42—341no—
202C42—682no—
203C23C2×C22⋊#59511yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—682no—
207Q8—682no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—174no—
219C2×C4—172no—
220C2×C4—342no—
221C2×C4—342no—
222C2×C4—342no—
223C2×C4—341no—
224C2×C4—681no—
225C2×C4—681no—
226C2×C4—681no—
227C2×C4—681no—
228C2×C4—682no—
229C2×C4—681no—
230C2×C4C2×C4×#59511yescharacteristic
231C2×C4#1058767711yescharacteristic
232C8—688no—
233C22—21no—
234C22—21no—
235C22C4×C22⋊#59511yescharacteristic
236C22D17⋊#9911yescharacteristic
237C22#1176378911yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—344no—
244C4—342no—
245C4—682no—
246C4—681no—
247C4—1361no—
248C2—21no—
249C2—21no—
250C2#1454453111yescharacteristic
251C2#1454508211yescharacteristic
252C2#1454508711yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenter#391#595
hypocenterC17#12631
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
7. #11763719C4semidirect
170. C17#12631semidirect

Maximal subgroups

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

subgroupindex
C2×#117637192
#145445372
#145438812
#145315022
#1263117