Finite Group Databasebeta

← #11990660

Subgroups — #11990660

Order 1280.

1174 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 179 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
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2#10602919C212yesmaximal
3C2×#64748C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C24×C4×C5C2211yescharacteristic
6C2×C5×C22⋊Q8—24no—
7C2×C5×C22⋊Q8—28no—
8C22×C5×C4⋊C4C411yescharacteristic
9C22×C5×C4⋊C4C2212yes—
10C22×C5×C22⋊C4C412yes—
11C2×C22⋊#168—24no—
12C2×C22⋊#168C2214yes—
13#64748—28no—
14#8308—51nomaximal, Sylow
15C25×C5C2×C411yescharacteristic
16C22×C5×Q8—24no—
17C22×C5×Q8—22no—
18C22×C5×Q8—44no—
19C23×C4×C5—24no—
20C23×C4×C5—44no—
21C23×C4×C5C2×C412yes—
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5C2×C412yes—
24C23×C4×C5D414yes—
25C23×C4×C5C2311yescharacteristic
26C5×C22⋊Q8—232no—
27C2×C5×C4⋊C4—24no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—24no—
30C2×C5×C4⋊C4—24no—
31C2×C5×C4⋊C4D418yes—
32C2×C5×C22⋊C4—24no—
33C2×C5×C22⋊C4—24no—
34C2×C5×C22⋊C4—24no—
35C22×#168—24no—
36C22⋊#168—28no—
37C22⋊#168—48no—
38C22×C22⋊Q8D511yescharacteristic
39#1779—52no—
40C2×#324—54no—
41C24×C5—24no—
42C24×C5—22no—
43C24×C5—24no—
44C24×C5—42no—
45C24×C5C22⋊C412yes—
46C24×C5C22×C411yescharacteristic
47C2×C5×Q8—28no—
48C2×C5×Q8—416no—
49C2×C5×Q8—44no—
50C2×C5×Q8—44no—
51C22×C4×C5—22no—
52C22×C4×C5—24no—
53C22×C4×C5—22no—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—28no—
58C22×C4×C5—28no—
59C22×C4×C5—28no—
60C22×C4×C5—44no—
61C22×C4×C5—42no—
62C22×C4×C5—416no—
63C22×C4×C5—44no—
64C22×C4×C5C22⋊C414yes—
65C22×C4×C5C22⋊C412yes—
66C22×C4×C5C22⋊C414yes—
67C22×C4×C5C2×D412yes—
68C22×C4×C5C2×D414yes—
69C5×C4⋊C4—28no—
70C5×C4⋊C4—216no—
71C5×C22⋊C4—216no—
72C2×#168—48no—
73C2×#168—44no—
74C23×Q8Dic511yescharacteristic
75C24×C4C2×D511yescharacteristic
76C2×C22⋊Q8—24no—
77C2×C22⋊Q8—28no—
78C22×C4⋊C4Dic511yescharacteristic
79C22×C4⋊C4C2×D512yes—
80C22×C22⋊C4Dic512yes—
81C2×C22⋊C8—54no—
82C2×C22⋊C8—104no—
83#324—108no—
84C23×C5—22no—
85C23×C5—22no—
86C23×C5—28no—
87C23×C5—22no—
88C23×C5—24no—
89C23×C5—24no—
90C23×C5—22no—
91C23×C5—416no—
92C23×C5—44no—
93C23×C5—44no—
94C23×C5#10114yes—
95C23×C5C2×C22⋊C412yes—
96C23×C5C2×C22⋊C411yescharacteristic
97C23×C5#13114yes—
98C5×Q8—416no—
99C2×C4×C5—28no—
100C2×C4×C5—22no—
101C2×C4×C5—24no—
102C2×C4×C5—22no—
103C2×C4×C5—24no—
104C2×C4×C5—24no—
105C2×C4×C5—28no—
106C2×C4×C5—44no—
107C2×C4×C5—416no—
108C2×C4×C5—44no—
109C2×C4×C5—44no—
110C2×C4×C5—44no—
111C2×C4×C5—44no—
112C2×C4×C5—44no—
113C2×C4×C5#9914yes—
114C2×C4×C5#12014yes—
115#168—84no—
116C25C2×Dic511yescharacteristic
117C22×Q8—24no—
118C22×Q8—22no—
119C22×Q8—44no—
120C23×C4—24no—
121C23×C4—44no—
122C23×C4C2×Dic512yes—
123C23×C4C2×Dic511yescharacteristic
124C23×C4C2×Dic512yes—
125C23×C4C22⋊D514yes—
126C23×C4C22×D511yescharacteristic
127C22×C8—104no—
128C22⋊Q8—232no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4C22⋊D518yes—
134C2×C22⋊C4—24no—
135C2×C22⋊C4—24no—
136C2×C22⋊C4—24no—
137C22⋊C8—108no—
138C22⋊C8—208no—
139C22×C5—28no—
140C22×C5—22no—
141C22×C5—22no—
142C22×C5—28no—
143C22×C5—24no—
144C22×C5—416no—
145C22×C5—44no—
146C22×C5—42no—
147C22×C5—42no—
148C22×C5#37911yescharacteristic
149C22×C5#40814yes—
150C22×C5#40812yes—
151C22×C5C2×#9912yes—
152C22×C5C2×#10112yes—
153C4×C5—24no—
154C4×C5—24no—
155C4×C5—44no—
156C4×C5—44no—
157C24—22no—
158C24—24no—
159C24—24no—
160C24—42no—
161C24C22⋊Dic512yes—
162C24C22×Dic511yescharacteristic
163C2×Q8—28no—
164C2×Q8—416no—
165C2×Q8—44no—
166C2×Q8—44no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—28no—
174C22×C4—28no—
175C22×C4—28no—
176C22×C4—44no—
177C22×C4—42no—
178C22×C4—416no—
179C22×C4—44no—
180C22×C4C22⋊Dic514yes—
181C22×C4C22⋊Dic512yes—
182C22×C4C22⋊Dic514yes—
183C22×C4C2×C22⋊D512yes—
184C22×C4C2×C22⋊D514yes—
185C2×C8—208no—
186C2×C8—204no—
187C4⋊C4—28no—
188C4⋊C4—216no—
189C22⋊C4—216no—
190C2×C5—24no—
191C2×C5—44no—
192C2×C5#147214yes—
193C2×C5#178011yescharacteristic
194C2×C5#178111yescharacteristic
195C2×C5#178411yescharacteristic
196C23—22no—
197C23—22no—
198C23—28no—
199C23—22no—
200C23—24no—
201C23—22no—
202C23—24no—
203C23—416no—
204C23—44no—
205C23—44no—
206C23#396814yes—
207C23#409414yes—
208C23C2×C22⋊Dic512yes—
209C23C2×C22⋊Dic511yescharacteristic
210Q8—416no—
211C2×C4—28no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—24no—
217C2×C4—28no—
218C2×C4—44no—
219C2×C4—416no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4#396614yes—
226C2×C4#409914yes—
227C8—404no—
228C5#830811yescharacteristic, complemented, Sylow
229C22—22no—
230C22—22no—
231C22—28no—
232C22—24no—
233C22—28no—
234C22—416no—
235C22—42no—
236C22—42no—
237C22—44no—
238C22C2×#396612yes—
239C22C2×#396812yes—
240C22#6552314yes—
241C22#6552312yes—
242C22#6553611yescharacteristic
243C4—24no—
244C4—24no—
245C4—44no—
246C4—44no—
247C2—24no—
248C2—44no—
249C2#1060248414yes—
250C2#1060292311yescharacteristic
251C2#1060292611yescharacteristic
252C2#1060292911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC22×C5×C22⋊Q8C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenterC22×C22⋊Q8D5
hypocenterC5#8308
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#64748C2semidirect
228. C5#8308semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
#106029192
C2×#647482
#83085