Finite Group Databasebeta

← #14759791

Subgroups — #14759791

Order 2816.

1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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#13077320C213yesmaximal, complemented
3#13069035C213yesmaximal, complemented
4#13068904C213yesmaximal, complemented
5#13068567C211yesmaximal, characteristic, complemented
6#13068418C213yesmaximal, complemented
7C11×#3025C211yesmaximal, characteristic
8C11×#585C2211yescharacteristic
9C11×#525C2213yes—
10#10623350—26no—
11#10623350C2213yes—
12C2×#67001—26no—
13C2×#67001C2213yes—
14C22×#4318C2211yescharacteristic, complemented
15C11×#458C414yes—
16C11×B(4,𝔽2)C414yes—
17C11×#410C2213yes—
18#10622850C2213yes—
19#10622847C2213yes—
20#10622820C2213yescomplemented
21#10622625—26no—
22#10622624—26no—
23#10622612C2213yescomplemented
24#10622610C2213yescomplemented
25#10622171C2216yescomplemented
26C11×2−1+4—23no—
27C11×H(5,𝔽2)—23no—
28C11×H(5,𝔽2)C2×C414yes—
29C2×C11×#41—26no—
30C2×C11×#41C2313yes—
31C23×C4×C11C2311yescharacteristic
32C11×#123C2×C416yes—
33C11×C22⋊Q8—23no—
34C11×#121—23no—
35C11×#120C2×C416yes—
36C4×D4×C11—26no—
37C11×#117C2313yes—
38#67001—24no—
39#67001—212no—
40#67001—26no—
41#67001—212no—
42#67001—26no—
43C2×#4318—212no—
44C2×#4318—26no—
45C2×#4318—23no—
46C2×#4318—23no—
47C2×#4318D416yescomplemented
48C2×#4318C2313yes—
49C2×#4318C2313yes—
50C22×C11⋊C8—24no—
51C22×C11⋊C8D416yescomplemented
52C22×C11⋊C8C2311yescharacteristic
53C22×C11⋊C8C2311yescharacteristic
54C11×#99C2×C4112yes—
55#66900—23no—
56#66897—23no—
57C22⋊(C11⋊C8)—26no—
58C22⋊(C11⋊C8)—26no—
59C4⋊(C11⋊C8)—26no—
60#66867—23no—
61C4×C11⋊C8—23no—
62#21484—111nomaximal, Sylow
63C24×C11C22×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×C11—26no—
74C2×D4×C11C22×C416yes—
75C2×D4×C11#4113yes—
76C22×C4×C11—24no—
77C22×C4×C11—23no—
78C22×C4×C11—23no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D416yes—
81C22×C4×C11C2411yescharacteristic
82C11×C4⋊C4—26no—
83C11×C4⋊C4—23no—
84C11×C22⋊C4—26no—
85C11×C22⋊C4—26no—
86C11×C22⋊C4C22×C416yes—
87C42×C11—23no—
88#4318—212no—
89#4318—212no—
90#4318—26no—
91#4318—26no—
92#4318—41no—
93#4318—43no—
94C2×C11⋊C8—212no—
95C2×C11⋊C8—26no—
96C2×C11⋊C8—26no—
97C2×C11⋊C8—23no—
98C2×C11⋊C8—23no—
99C2×C11⋊C8C2×D416yes—
100C2×C11⋊C8C2×D413yes—
101C2×C11⋊C8C2×D413yes—
102#3573—111no—
103#3025D1111yescharacteristic
104#2930—113no—
105#1891—113no—
106#1868—113no—
107#1791—111no—
108#1757—113no—
109C23×C11—24no—
110C23×C11—23no—
111C23×C11—81no—
112C23×C11C4×D416yes—
113C23×C11C23×C411yescharacteristic
114Q8×C11—24no—
115Q8×C11—26no—
116D4×C11—212no—
117D4×C11—212no—
118D4×C11—26no—
119D4×C11—86no—
120C2×C4×C11—212no—
121C2×C4×C11—26no—
122C2×C4×C11—26no—
123C2×C4×C11—26no—
124C2×C4×C11—23no—
125C2×C4×C11—41no—
126C2×C4×C11—43no—
127C2×C4×C11C4×D416yes—
128C2×C4×C11C22×D413yes—
129C2×C4×C11C2×#4113yes—
130C11⋊C8—26no—
131C11⋊C8—41no—
132C11⋊C8—43no—
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#525C2×D1113yes—
142#458Dic1114yes—
143B(4,𝔽2)Dic1114yes—
144#436—226no—
145#435—226no—
146#424—113no—
147#413—113no—
148#410C2×D1113yes—
149#408—113no—
150#407—113no—
151#405—113no—
152#344—116no—
153C22×C11—26no—
154C22×C11—41no—
155C22×C11—46no—
156C22×C11—43no—
157C22×C11—43no—
158C22×C11—41no—
159C22×C11—84no—
160C22×C11C2×C4×D413yes—
161C4×C11—26no—
162C4×C11—46no—
163C4×C11—41no—
164C4×C11C2×#12011yescharacteristic
165C4×C11#52513yes—
1662−1+4—23no—
167H(5,𝔽2)—23no—
168H(5,𝔽2)C2×Dic1114yes—
169C2×#41—26no—
170C2×#41C22×D1113yes—
171C23×C4C22×D1111yescharacteristic
172#131—226no—
173#131—226no—
174#131—2212no—
175#131—224no—
176#131—2212no—
177C2×M16—116no—
178C2×M16—113no—
179C2×M16—113no—
180C2×M16—223no—
181C2×M16—223no—
182C2×M16—2212no—
183C2×M16—226no—
184C22×C8—111no—
185C22×C8—116no—
186C22×C8—111no—
187C22×C8—224no—
188#123C2×Dic1116yes—
189C22⋊Q8—23no—
190#121—23no—
191#120C2×Dic1116yes—
192C4×D4—26no—
193#117C22×D1113yes—
194C4⋊C8—226no—
195#101—223no—
196#100—223no—
197#99C2×Dic11112yes—
198C22⋊C8—226no—
199C22⋊C8—226no—
200#97—223no—
201C4×C8—223no—
202C2×C11—23no—
203C2×C11—46no—
204C2×C11—81no—
205C2×C11C4×#12011yescharacteristic
206C24C22×Dic1111yescharacteristic
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—26no—
217C2×D4#434113yes—
218C2×D4C22×Dic1116yes—
219C22×C4—24no—
220C22×C4—23no—
221C22×C4—23no—
222C22×C4D4×D1116yes—
223C22×C4C22×Dic1111yescharacteristic
224C22×C4C23×D1111yescharacteristic
225M16—2212no—
226M16—2212no—
227M16—226no—
228M16—226no—
229M16—441no—
230M16—443no—
231C2×C8—113no—
232C2×C8—113no—
233C2×C8—116no—
234C2×C8—226no—
235C2×C8—226no—
236C2×C8—2212no—
237C2×C8—223no—
238C2×C8—223no—
239C4⋊C4—26no—
240C4⋊C4—23no—
241C22⋊C4—26no—
242C22⋊C4—26no—
243C22⋊C4C22×Dic1116yes—
244C42—23no—
245C11#2148411yescharacteristic, complemented, Sylow
246C23—24no—
247C23—23no—
248C23—81no—
249C23D4×Dic1116yes—
250C23C23×Dic1111yescharacteristic
251Q8—24no—
252Q8—26no—
253D4—212no—
254D4—212no—
255D4—26no—
256D4—86no—
257C2×C4—212no—
258C2×C4—26no—
259C2×C4—26no—
260C2×C4—26no—
261C2×C4—23no—
262C2×C4—43no—
263C2×C4—41no—
264C2×C4D4×Dic1116yes—
265C2×C4C2×D4×D1113yes—
266C2×C4C2×#434113yes—
267C8—111no—
268C8—113no—
269C8—226no—
270C8—443no—
271C8—441no—
272C22—26no—
273C22—41no—
274C22—46no—
275C22—43no—
276C22—43no—
277C22—41no—
278C22—84no—
279C22C2×D4×Dic1113yes—
280C4—26no—
281C4—46no—
282C4—41no—
283C4#1062311713yes—
284C4D11×#12011yescharacteristic
285C2—23no—
286C2—46no—
287C2—81no—
288C2#120×Dic1111yescharacteristic
subgroupG/H
centerC4D11×#120
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3025C2
socleC2×C11C4×#120
cosocleC22×C4×C11C24
hypercenter#3025D11
hypocenterC11#21484
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #3025

Complements

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

NH ≅ G/Ntype
1. #13083328C2semidirect
2. #13077320C2semidirect
3. #13069035C2semidirect
4. #13068904C2semidirect
5. #13068567C2semidirect
6. #13068418C2semidirect
14. C22×#4318C22semidirect
20. #10622820C22semidirect
23. #10622612C22semidirect
24. #10622610C22semidirect
25. #10622171C22semidirect
47. C2×#4318D4semidirect
51. C22×C11⋊C8D4semidirect
245. C11#21484semidirect

Maximal subgroups

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

subgroupindex
#130833282
#130773202
#130690352
#130689042
#130685672
#130684182
C11×#30252
#2148411