Finite Group Databasebeta

← #17961559

Subgroups — #17961559

Order 4352.

670 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544613C212yesmaximal
2#14543878C214yesmaximal, complemented
3#14531274C211yesmaximal, characteristic
4C2×#10587539C2214yes—
5C2×#10587551—22no—
6#11763752—22no—
7C22×#63252C2211yescharacteristic
8C2×#10587612C411yescharacteristic, complemented
9#11762715C412yescomplemented
10#11762711C2212yes—
11#11762688—22no—
12C4×#63227—22no—
13C22×C42×C17C411yescharacteristic, complemented
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17D412yes—
17C2×#63252—24no—
18C2×#63252—42no—
19C2×#63252—42no—
20C22×D68C2311yescharacteristic
21C22×C4×D17D412yes—
22C22×Dic34C2×C411yescharacteristic
23C2×C22⋊#595—24no—
24C2×C42×C17—21no—
25C2×C42×C17—42no—
26C2×C42×C17C2×C412yes—
27C2×C22⋊Dic17—21no—
28C2×#63227—24no—
29#10587612—42no—
30C2×C4⋊Dic17C2×C412yes—
31C2×C4×Dic17—21no—
32#10587551—44no—
33(C2×#595)⋊C4—44no—
34#10587539—28no—
35#10587502—24no—
36C24×C17C22⋊C411yescharacteristic
37C23×D17C2×D412yes—
38C22×#595—44no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—44no—
44C22×C4×C17—42no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C2×C22⋊D17—24no—
48C2×C22⋊D17—24no—
49C2×C22⋊D17—42no—
50C22×Dic17—22no—
51C22×Dic17C22⋊C412yes—
52#63252—416no—
53C2×D68—41no—
54C2×D68—41no—
55C2×D68#4114yes—
56C2×C4×D17—24no—
57C2×C4×D17—24no—
58C2×C4×D17—42no—
59C2×Dic34—22no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C22⋊#595—44no—
63C22⋊#595—44no—
64C42×C17—42no—
65C42×C17—42no—
66C22⋊Dic17—42no—
67#63227—48no—
68C4⋊Dic17—42no—
69C4×Dic17—42no—
70#12857—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17#9912yes—
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—22no—
77C22×D17—22no—
78C22×D17—44no—
79C22×D17#12314yes—
80C2×#595—84no—
81C2×#595—88no—
82C2×C4×C17—28no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—24no—
88C2×C4×C17—42no—
89C2×C4×C17—48no—
90C2×C4×C17—42no—
91C2×C4×C17#9912yes—
92C2×C4×C17#11712yes—
93C22⋊D17—48no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—44no—
98C2×Dic17—42no—
99D68—44no—
100C4×D17—48no—
101Dic34—44no—
102#2297—171no—
103#1782—172no—
104#1393—174no—
105C22×C17—22no—
106C22×C17—22no—
107C22×C17—42no—
108C22×C17—42no—
109C22×C17—42no—
110C22×C17#38111yescharacteristic
111C22×C17C2×#9911yescharacteristic
112C22×C17C2×#9911yescharacteristic
113C2×D17—24no—
114C2×D17—44no—
115C2×D17—44no—
116C2×D17—82no—
117#595—164no—
118C4×C17—22no—
119C4×C17—22no—
120C4×C17—44no—
121Dic17—42no—
122Dic17—82no—
123C22×#41—171no—
124C2×#117—171no—
125C22×C42#59511yescharacteristic, complemented
126C2×#99—174no—
127C2×#99—342no—
128#391—172no—
129#390—172no—
130#386—342no—
131#381—342no—
132C4×C22⋊C4—342no—
133C2×C17—21no—
134C2×C17—21no—
135C2×C17—42no—
136C2×C17#181911yescharacteristic
137C2×C17#212612yes—
138D17—44no—
139C2×#41—344no—
140C2×#41—682no—
141C2×#41—682no—
142C22×Q8—171no—
143C22×D4—172no—
144C22×D4—171no—
145C23×C4—21no—
146C23×C4—172no—
147C23×C4C2×#59511yescharacteristic
148#117—682no—
149C2×C4⋊C4—172no—
150C2×C22⋊C4—344no—
151C2×C22⋊C4—341no—
152C2×C22⋊C4—344no—
153C2×C42—21no—
154C2×C42—42no—
155C2×C42—341no—
156C2×C42C2×#59512yes—
157#99—348no—
158#99—684no—
159#95—344no—
160#95—684no—
161C17#1285711yescharacteristic, complemented, Sylow
162C24—172no—
163C24C22⋊#59511yescharacteristic
164#41—6816no—
165C2×Q8—342no—
166C2×Q8—681no—
167C2×Q8—681no—
168C2×D4—174no—
169C2×D4—344no—
170C2×D4—344no—
171C2×D4—681no—
172C2×D4—681no—
173C2×D4—682no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—44no—
179C22×C4—42no—
180C22×C4—172no—
181C22×C4—344no—
182C22×C4—344no—
183C22×C4—342no—
184C22×C4—682no—
185C22×C4—684no—
186C22×C4C22⋊#59511yescharacteristic
187C22×C4C22×#59511yescharacteristic
188C4⋊C4—682no—
189C22⋊C4—688no—
190C22⋊C4—682no—
191C22⋊C4—684no—
192C22⋊C4—684no—
193C42—42no—
194C42—42no—
195C42—682no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—174no—
200C23—342no—
201C23—342no—
202C23—684no—
203C23#1058755112yes—
204C23C2×C22⋊#59511yescharacteristic
205Q8—684no—
206D4—684no—
207D4—688no—
208C2×C4—28no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—42no—
215C2×C4—48no—
216C2×C4—42no—
217C2×C4—342no—
218C2×C4—342no—
219C2×C4—342no—
220C2×C4—688no—
221C2×C4—684no—
222C2×C4—682no—
223C2×C4—1364no—
224C2×C4—1368no—
225C2×C4#1058753912yes—
226C2×C4#1058767712yes—
227C22—22no—
228C22—22no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—344no—
233C22—684no—
234C22—684no—
235C22—1362no—
236C22#1176375211yescharacteristic
237C22C2×#1058755111yescharacteristic
238C22C2×#1058753911yescharacteristic
239C4—22no—
240C4—22no—
241C4—44no—
242C4—2724no—
243C4—682no—
244C4—1362no—
245C2—21no—
246C2—21no—
247C2—42no—
248C2—684no—
249C2#1454467911yescharacteristic
250C2#1454505712yes—
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC22×#63252C22
cosocleC22×D68C23
hypercenterC22×C42#595
hypocenterC17#12857
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #14543878C2semidirect
8. C2×#10587612C4semidirect
9. #11762715C4semidirect
13. C22×C42×C17C4semidirect
125. C22×C42#595semidirect
161. C17#12857semidirect

Maximal subgroups

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

subgroupindex
#145446132
#145438782
#145312742
#1285717