Finite Group Databasebeta

← #14759787

Subgroups — #14759787

Order 2816.

1306 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 251 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#13083328C211yesmaximal, characteristic, complemented
2#13078008C211yesmaximal, characteristic
3#13077322C213yesmaximal, complemented
4#13069032C213yesmaximal, complemented
5#13068901C213yesmaximal, complemented
6#13068419C213yesmaximal, complemented
7C11×#1791C211yesmaximal, characteristic, complemented
8C11×#585C2211yescharacteristic
9#10623359C2213yes—
10#10623350—26no—
11#10623350C2213yes—
12C2×#67001—26no—
13C2×#67001C2213yes—
14C22×#4313C2211yescharacteristic, complemented
15C11×#413C2213yes—
16C11×#408C2213yes—
17#10622857C414yes—
18#10622856C414yes—
19#10622853C2213yes—
20#10622739C2213yescomplemented
21#10622735C2213yescomplemented
22#10622715C2213yescomplemented
23#10622343—26no—
24#10622342—26no—
25#10622197C2216yescomplemented
26C11×2−1+4—23no—
27C11×H(5,𝔽2)—23no—
28C11×H(5,𝔽2)C2×C414yes—
29C2×C11×#41—26no—
30C2×C11×#41C2313yes—
31C22×C4×D11C2311yescharacteristic
32C2×C11×M16C2313yes—
33C22×C8×C11C2311yescharacteristic
34#67001—24no—
35#67001—212no—
36#67001—26no—
37#67001—212no—
38#67001—26no—
39#66999—23no—
40#66991—23no—
41#66990C2×C416yes—
42#66988C2×C416yes—
43C4×C22⋊D11—26no—
44#66979C2313yes—
45C2×#4318—212no—
46C2×#4318—26no—
47C2×#4318D416yescomplemented
48C2×#4318C2313yes—
49C22×C11⋊C8—24no—
50C22×C11⋊C8D416yescomplemented
51C22×C11⋊C8C2311yescharacteristic
52C2×#4313—23no—
53C2×#4313—23no—
54C11×#101—23no—
55C11×#100—23no—
56C11×C22⋊C8—26no—
57#66898C2×C4112yes—
58(C2×D11)⋊C8—26no—
59#66879—23no—
60Dic11⋊C8—26no—
61C8×Dic11—23no—
62#21484—111nomaximal, Sylow
63C23×D11C22×C411yescharacteristic
64C11×#41—24no—
65C11×#41—212no—
66C11×#41—212no—
67C11×#41—26no—
68C11×#41—26no—
69C2×Q8×C11—26no—
70C2×Q8×C11#4113yes—
71C2×D4×C11—26no—
72C2×D4×C11—212no—
73C2×D4×C11C22×C416yes—
74C2×D4×C11#4113yes—
75C22×C4×C11—24no—
76C22×C4×C11C2×D416yes—
77C22×C4×C11C2411yescharacteristic
78C2×C22⋊D11—26no—
79C22×Dic11C22×C411yescharacteristic
80C2×C4×D11—23no—
81C2×C4×D11—23no—
82C11×M16—26no—
83C2×C8×C11—23no—
84C2×C8×C11—23no—
85C22⋊Dic11—26no—
86C22⋊Dic11C22×C416yes—
87(C2×D11)⋊C4—26no—
88C4⋊Dic11—23no—
89Dic11⋊C4—26no—
90C4×Dic11—23no—
91#4318—212no—
92#4318—212no—
93#4318—26no—
94C2×C11⋊C8—212no—
95C2×C11⋊C8—26no—
96C2×C11⋊C8—26no—
97C2×C11⋊C8C2×D416yes—
98C2×C11⋊C8C2×D413yes—
99C2×C11⋊C8C2×D413yes—
100#4313—41no—
101#4313—43no—
102#3573—111no—
103#3025—111no—
104#2930—113no—
105#1891—113no—
106#1868—113no—
107#1791D1111yescharacteristic, complemented
108#1757—113no—
109C23×C11—24no—
110C23×C11C4×D416yes—
111C23×C11C23×C411yescharacteristic
112C22×D11—23no—
113C22×D11—81no—
114Q8×C11—24no—
115Q8×C11—26no—
116D4×C11—212no—
117D4×C11—212no—
118D4×C11—26no—
119C2×C4×C11—212no—
120C2×C4×C11—26no—
121C2×C4×C11—26no—
122C2×C4×C11C4×D416yes—
123C2×C4×C11C22×D413yes—
124C2×C4×C11C2×#4113yes—
125C22⋊D11—86no—
126C2×Dic11—26no—
127C2×Dic11—23no—
128C4×D11—41no—
129C4×D11—43no—
130C8×C11—41no—
131C8×C11—43no—
132C11⋊C8—26no—
133C11⋊C8#12011yescharacteristic
134C11⋊C8#12013yes—
135#585C2×D1111yescharacteristic
136#568—113no—
137#568—226no—
138C2×#131—113no—
139C2×#131—226no—
140C22×M16—111no—
141#525—113no—
142#458—114no—
143B(4,𝔽2)—114no—
144#436—226no—
145#435—226no—
146#424—113no—
147#413C2×D1113yes—
148#410—113no—
149#408C2×D1113yes—
150#407—113no—
151#405—113no—
152#344—116no—
153C22×C11—26no—
154C22×C11—41no—
155C22×C11—46no—
156C22×C11—84no—
157C22×C11C2×C4×D413yes—
158C2×D11—43no—
159C2×D11—43no—
160C2×D11—41no—
161C4×C11—26no—
162C4×C11C2×#12011yescharacteristic
163C4×C11#52513yes—
164Dic11—46no—
165Dic11—41no—
1662−1+4—23no—
167H(5,𝔽2)—23no—
168H(5,𝔽2)C4×D1114yes—
169C2×#41—26no—
170C2×#41C22×D1113yes—
171C23×C4—111no—
172#131—226no—
173#131—226no—
174#131—2212no—
175#131—224no—
176#131—2212no—
177C2×M16—116no—
178C2×M16—113no—
179C2×M16—223no—
180C2×M16—223no—
181C2×M16—2212no—
182C2×M16—226no—
183C2×M16C22×D1113yes—
184C22×C8—111no—
185C22×C8—116no—
186C22×C8—224no—
187C22×C8C22×D1111yescharacteristic
188#123—116no—
189C22⋊Q8—223no—
190#121—223no—
191#120—116no—
192C4×D4—226no—
193#117—113no—
194C4⋊C8—226no—
195#101—23no—
196#100—23no—
197#99—1112no—
198C22⋊C8—26no—
199C22⋊C8—226no—
200#97—223no—
201C4×C8—223no—
202C2×C11—23no—
203C2×C11—46no—
204C2×C11C4×#12011yescharacteristic
205D11—81no—
206C24—111no—
207#41—24no—
208#41—212no—
209#41—212no—
210#41—26no—
211#41—26no—
212C2×Q8—26no—
213C2×Q8#434113yes—
214C2×D4—26no—
215C2×D4—212no—
216C2×D4—226no—
217C2×D4C2×C4×D1116yes—
218C2×D4#434113yes—
219C22×C4—24no—
220C22×C4—111no—
221C22×C4—223no—
222C22×C4—223no—
223C22×C4D4×D1116yes—
224C22×C4C23×D1111yescharacteristic
225M16—26no—
226M16—2212no—
227M16—2212no—
228M16—226no—
229M16—441no—
230M16—443no—
231C2×C8—23no—
232C2×C8—23no—
233C2×C8—113no—
234C2×C8—113no—
235C2×C8—116no—
236C2×C8—226no—
237C2×C8—226no—
238C2×C8—2212no—
239C4⋊C4—226no—
240C4⋊C4—223no—
241C22⋊C4—116no—
242C22⋊C4—226no—
243C22⋊C4—226no—
244C42—223no—
245C11#2148411yescharacteristic, complemented, Sylow
246C23—24no—
247C23—223no—
248C23—881no—
249C23(C22⋊D11)⋊C416yes—
250C23C22×C4×D1111yescharacteristic
251Q8—24no—
252Q8—26no—
253D4—212no—
254D4—212no—
255D4—26no—
256D4—886no—
257C2×C4—212no—
258C2×C4—26no—
259C2×C4—26no—
260C2×C4—226no—
261C2×C4—223no—
262C2×C4—443no—
263C2×C4—441no—
264C2×C4(C22⋊D11)⋊C416yes—
265C2×C4C2×D4×D1113yes—
266C2×C4C2×#434113yes—
267C8—43no—
268C8—41no—
269C8—111no—
270C8—113no—
271C8—226no—
272C22—26no—
273C22—41no—
274C22—46no—
275C22—84no—
276C22—443no—
277C22—443no—
278C22—441no—
279C22C2×(C22⋊D11)⋊C413yes—
280C4—26no—
281C4—446no—
282C4—441no—
283C4#1062311713yes—
284C4D11×#12011yescharacteristic
285C2—23no—
286C2—46no—
287C2—881no—
288C2#1307111511yescharacteristic
subgroupG/H
centerC4D11×#120
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1791C2
socleC2×C11C4×#120
prime radical#13078008C2
cosocleC22×C4×C11C24
hypercenter#1791D11
hypocenterC11#21484
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1791

Complements

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

NH ≅ G/Ntype
1. #13083328C2semidirect
3. #13077322C2semidirect
4. #13069032C2semidirect
5. #13068901C2semidirect
6. #13068419C2semidirect
7. C11×#1791C2semidirect
14. C22×#4313C22semidirect
20. #10622739C22semidirect
21. #10622735C22semidirect
22. #10622715C22semidirect
25. #10622197C22semidirect
47. C2×#4318D4semidirect
50. C22×C11⋊C8D4semidirect
107. #1791D11semidirect
245. C11#21484semidirect

Maximal subgroups

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

subgroupindex
#130833282
#130780082
#130773222
#130690322
#130689012
#130684192
C11×#17912
#2148411