Finite Group Databasebeta

← #14647276

Subgroups — #14647276

Order 2816.

786 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071198C211yesmaximal, characteristic
2#13068531C211yesmaximal, characteristic
3C11⋊#1304C214yesmaximal, complemented
4C11×#1781C211yesmaximal, characteristic
5C23×D4×C11C2211yescharacteristic
6C2×#66979C412yescomplemented
7C2×C11×#99—22no—
8C11×#379C2212yes—
9#10622860C412yescomplemented
10#10622860C2212yes—
11#10622860C2212yes—
12#10622834—22no—
13#10622834—22no—
14C2×#66898—22no—
15C25×C11C2×C411yescharacteristic
16C25×C11C2311yescharacteristic
17C22×D4×C11—24no—
18C22×D4×C11—44no—
19C22×D4×C11D412yes—
20C22×D4×C11D412yes—
21C23×C4×C11C2×C411yescharacteristic
22C2×C11×C22⋊C4—22no—
23C2×C11×C22⋊C4—24no—
24C2×C22⋊Dic11—22no—
25C2×C22⋊Dic11—24no—
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11—24no—
29C2×C22⋊Dic11C2×C414yes—
30#66979—44no—
31C2×C4⋊Dic11—22no—
32C2×C4×Dic11—22no—
33C11×#99—44no—
34#66898—44no—
35#8748—111nomaximal, Sylow
36C24×C11—22no—
37C24×C11—42no—
38C24×C11—42no—
39C24×C11—82no—
40C24×C11—82no—
41C24×C11C22⋊C412yes—
42C24×C11C22×C411yescharacteristic
43C24×C11C2×D411yescharacteristic
44C24×C11C2×D411yescharacteristic
45C24×C11#4114yes—
46C2×D4×C11—24no—
47C2×D4×C11—24no—
48C2×D4×C11—24no—
49C2×D4×C11—24no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—416no—
53C22×C4×C11—22no—
54C22×C4×C11—24no—
55C22×C4×C11—42no—
56C22×C4×C11C22⋊C412yes—
57C22×Dic11—24no—
58C22×Dic11—42no—
59C11×C22⋊C4—44no—
60C11×C22⋊C4—84no—
61C22⋊Dic11—44no—
62C22⋊Dic11—44no—
63C22⋊Dic11—82no—
64C22⋊Dic11—82no—
65C22⋊Dic11—84no—
66C22⋊Dic11—84no—
67C4⋊Dic11—44no—
68C4×Dic11—44no—
69#2309—111no—
70#1781—111no—
71#1781D1111yescharacteristic
72#1304—114no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—42no—
81C23×C11—42no—
82C23×C11—44no—
83C23×C11—44no—
84C23×C11—44no—
85C23×C11—44no—
86C23×C11—44no—
87C23×C11—82no—
88C23×C11—82no—
89C23×C11—88no—
90C23×C11—88no—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11#11712yes—
93C23×C11#12312yes—
94C23×C11#12312yes—
95D4×C11—48no—
96D4×C11—48no—
97C2×C4×C11—28no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—82no—
101C2×C4×C11—84no—
102C2×C4×C11#9914yes—
103C2×Dic11—44no—
104C2×Dic11—44no—
105C2×Dic11—44no—
106C2×Dic11—82no—
107C2×Dic11—84no—
108C23×D4C2×D1111yescharacteristic
109C2×#117—112no—
110C2×#99—22no—
111C2×#99—222no—
112#390—222no—
113#390—222no—
114#379—112no—
115#379—112no—
116#379—112no—
117#379C2×D1112yes—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—24no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—24no—
126C22×C11—44no—
127C22×C11—42no—
128C22×C11—44no—
129C22×C11—82no—
130C22×C11—82no—
131C22×C11—82no—
132C22×C11—82no—
133C22×C11—88no—
134C22×C11—88no—
135C22×C11#38111yescharacteristic
136C22×C11C2×#9912yes—
137C4×C11—24no—
138C4×C11—162no—
139Dic11—84no—
140Dic11—162no—
141C25C4×D1111yescharacteristic
142C25C22×D1111yescharacteristic
143C22×D4—24no—
144C22×D4—44no—
145C22×D4D4412yes—
146C22×D4C22⋊D1112yes—
147C23×C4C4×D1111yescharacteristic
148#117—444no—
149C2×C4⋊C4—222no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—24no—
152C2×C22⋊C4—114no—
153C2×C22⋊C4—222no—
154C2×C22⋊C4—224no—
155C2×C22⋊C4—222no—
156C2×C22⋊C4—222no—
157C2×C22⋊C4—224no—
158C2×C42—222no—
159#99—44no—
160#99—444no—
161C2×C11—22no—
162C2×C11—42no—
163C2×C11—42no—
164C2×C11—42no—
165C2×C11—82no—
166C2×C11#181911yescharacteristic
167C2×C11#182812yes—
168C24—22no—
169C24—42no—
170C24—42no—
171C24—82no—
172C24—82no—
173C24(C2×D11)⋊C412yes—
174C24C2×C4×D1111yescharacteristic
175C24C2×D4411yescharacteristic
176C24#434114yes—
177C24C2×C22⋊D1111yescharacteristic
178C2×D4—24no—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—42no—
183C2×D4—42no—
184C2×D4—416no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—42no—
188C22×C4—224no—
189C22×C4—442no—
190C22×C4(C2×D11)⋊C412yes—
191C4⋊C4—444no—
192C22⋊C4—44no—
193C22⋊C4—84no—
194C22⋊C4—444no—
195C22⋊C4—444no—
196C22⋊C4—882no—
197C22⋊C4—882no—
198C22⋊C4—884no—
199C22⋊C4—884no—
200C42—444no—
201C11#874811yescharacteristic, complemented, Sylow
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—42no—
209C23—44no—
210C23—42no—
211C23—44no—
212C23—42no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—82no—
217C23—82no—
218C23—88no—
219C23—88no—
220C23#6693012yes—
221C23#6693912yes—
222C23C2×(C2×D11)⋊C411yescharacteristic
223C23#6698812yes—
224D4—48no—
225D4—48no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—82no—
230C2×C4—84no—
231C2×C4—444no—
232C2×C4—444no—
233C2×C4—444no—
234C2×C4—882no—
235C2×C4—884no—
236C2×C4#6687014yes—
237C22—22no—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—24no—
242C22—24no—
243C22—22no—
244C22—22no—
245C22—44no—
246C22—42no—
247C22—44no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—82no—
252C22—88no—
253C22—88no—
254C22#1062255611yescharacteristic
255C22C2×#6687012yes—
256C4—24no—
257C4—162no—
258C4—884no—
259C4—1762no—
260C2—22no—
261C2—42no—
262C2—42no—
263C2—42no—
264C2—82no—
265C2#1306868811yescharacteristic
266C2#1306872212yes—
subgroupG/H
centerC22#10622556
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1781C2
socleC22×C11#381
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenter#1781D11
hypocenterC11#8748
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
3. C11⋊#1304C2semidirect
6. C2×#66979C4semidirect
9. #10622860C4semidirect
201. C11#8748semidirect

Maximal subgroups

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

subgroupindex
#130711982
#130685312
C11⋊#13042
C11×#17812
#874811