Finite Group Databasebeta

← #14645166

Subgroups — #14645166

Order 2816.

1118 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 207 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#13068909C213yesmaximal, complemented
2#13066934C213yesmaximal, complemented
3C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
4C2×C11×H(5,𝔽2)C411yescharacteristic
5C11×#520—23no—
6C11×#518—23no—
7C11×#518C413yes—
8C4×C11×#41—23no—
9C2×C4×D4×C11—23no—
10C2×C4×D4×C11C2213yes—
11C23×C11⋊C8C2211yescharacteristic, complemented
12C2×C22⋊(C11⋊C8)—23no—
13C2×C22⋊(C11⋊C8)C2213yescomplemented
14#10622166—23no—
15#10622163—23no—
16#10622162—23no—
17C11×H(5,𝔽2)—26no—
18C11×H(5,𝔽2)C814yescomplemented
19C2×C11×#41—23no—
20C22×D4×C11—23no—
21C22×D4×C11C2×C413yes—
22C23×C4×C11—21no—
23C23×C4×C11D413yes—
24C23×C4×C11C2311yescharacteristic
25C4×Q8×C11—21no—
26C4×Q8×C11—23no—
27C4×D4×C11—23no—
28C4×D4×C11—26no—
29C4×D4×C11—23no—
30C4×D4×C11—26no—
31C4×D4×C11—26no—
32C4×D4×C11—26no—
33C4×D4×C11—26no—
34C11×#117—26no—
35C11×#117—23no—
36C2×C11×C4⋊C4—23no—
37C2×C11×C4⋊C4D413yes—
38C2×C11×C22⋊C4—23no—
39C2×C11×C22⋊C4—23no—
40C2×C11×C22⋊C4C2×C413yes—
41C2×C11×C22⋊C4D413yes—
42C2×C42×C11—23no—
43C2×C42×C11D413yes—
44C22×C11⋊C8—23no—
45C22×C11⋊C8—23no—
46C22×C11⋊C8—42no—
47C22⋊(C11⋊C8)—26no—
48C22⋊(C11⋊C8)—46no—
49#8316—111nomaximal, Sylow
50C24×C11—21no—
51C24×C11C22⋊C413yes—
52C24×C11C22×C411yescharacteristic
53C11×#41—212no—
54C11×#41—212no—
55C2×Q8×C11—21no—
56C2×D4×C11—23no—
57C2×D4×C11—212no—
58C2×D4×C11—212no—
59C2×D4×C11—26no—
60C2×D4×C11—26no—
61C2×D4×C11C2×C816yes—
62C2×D4×C11M1616yes—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—43no—
71C22×C4×C11—43no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C413yes—
75C22×C4×C11C22⋊C413yes—
76C22×C4×C11C22⋊C413yes—
77C22×C4×C11C2×D413yes—
78C22×C4×C11C2×D413yes—
79C11×C4⋊C4—23no—
80C11×C4⋊C4—23no—
81C11×C4⋊C4—26no—
82C11×C22⋊C4—26no—
83C11×C22⋊C4—26no—
84C11×C22⋊C4—26no—
85C42×C11—26no—
86C42×C11—23no—
87C42×C11—23no—
88C2×C11⋊C8—26no—
89C2×C11⋊C8—43no—
90C2×C11⋊C8—43no—
91C2×C11⋊C8—43no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—43no—
94C4×H(5,𝔽2)D1111yescharacteristic
95#1869—113no—
96#1459—113no—
97C23×C11—24no—
98C23×C11—23no—
99C23×C11—23no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—43no—
103C23×C11—43no—
104C23×C11—81no—
105C23×C11—81no—
106C23×C11C22⋊C816yescomplemented
107C23×C11C2×C22⋊C413yes—
108C23×C11C22×C811yescharacteristic
109C23×C11C2×M1613yes—
110Q8×C11—24no—
111D4×C11—212no—
112D4×C11—212no—
113D4×C11—212no—
114C2×C4×C11—212no—
115C2×C4×C11—23no—
116C2×C4×C11—23no—
117C2×C4×C11—23no—
118C2×C4×C11—23no—
119C2×C4×C11—23no—
120C2×C4×C11—23no—
121C2×C4×C11—43no—
122C2×C4×C11—43no—
123C2×C4×C11—43no—
124C2×C4×C11—43no—
125C2×C4×C11—43no—
126C2×C4×C11—83no—
127C2×C4×C11—83no—
128C2×C4×C11—83no—
129C2×C4×C11C22⋊C816yescomplemented
130C2×C4×C11#12013yes—
131C2×C4×C11#12011yescharacteristic
132C11⋊C8—42no—
133C11⋊C8—83no—
134C2×H(5,𝔽2)Dic1111yescharacteristic
135C23×C8—111no—
136#520—23no—
137#518—23no—
138#518Dic1113yes—
139C4×#41—23no—
140C2×C4×D4—23no—
141C2×C4×D4C2×D1113yes—
142C2×C22⋊C8—113no—
143C2×C22⋊C8—223no—
144#336—223no—
145#324—223no—
146#323—223no—
147C22×C11—23no—
148C22×C11—23no—
149C22×C11—26no—
150C22×C11—41no—
151C22×C11—43no—
152C22×C11—46no—
153C22×C11—43no—
154C22×C11—43no—
155C22×C11—83no—
156C22×C11—84no—
157C22×C11#37911yescharacteristic
158C22×C11C2×C22⋊C813yes—
159C22×C11#40713yes—
160C4×C11—26no—
161C4×C11—23no—
162C4×C11—43no—
163C4×C11—43no—
164C4×C11B(4,𝔽2)11yescharacteristic
165C4×C11#45811yescharacteristic
166H(5,𝔽2)—26no—
167H(5,𝔽2)C11⋊C814yescomplemented
168C2×#41—23no—
169C22×D4—23no—
170C22×D4C2×Dic1113yes—
171C23×C4—21no—
172C23×C4C22⋊D1113yes—
173C23×C4C22×D1111yescharacteristic
174C22×C8—223no—
175C22×C8—223no—
176C22×C8—442no—
177C4×Q8—21no—
178C4×Q8—23no—
179C4×D4—23no—
180C4×D4—26no—
181C4×D4—23no—
182C4×D4—26no—
183C4×D4—26no—
184C4×D4—26no—
185C4×D4—26no—
186#117—26no—
187#117—23no—
188C2×C4⋊C4—23no—
189C2×C4⋊C4C22⋊D1113yes—
190C2×C22⋊C4—23no—
191C2×C22⋊C4—23no—
192C2×C22⋊C4C2×Dic1113yes—
193C2×C22⋊C4C22⋊D1113yes—
194C2×C42—23no—
195C2×C42C22⋊D1113yes—
196C22⋊C8—226no—
197C22⋊C8—446no—
198C2×C11—23no—
199C2×C11—23no—
200C2×C11—46no—
201C2×C11#177911yescharacteristic
202C2×C11#179011yescharacteristic
203C2×C11#179111yescharacteristic
204C24—21no—
205C24C22⋊Dic1113yes—
206C24C22×Dic1111yescharacteristic
207#41—212no—
208#41—212no—
209C2×Q8—21no—
210C2×D4—23no—
211C2×D4—212no—
212C2×D4—212no—
213C2×D4—26no—
214C2×D4—26no—
215C2×D4C2×C11⋊C816yes—
216C2×D4#431816yes—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—23no—
221C22×C4—23no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—43no—
225C22×C4—43no—
226C22×C4—81no—
227C22×C4—81no—
228C22×C4C22⋊Dic1113yes—
229C22×C4C22⋊Dic1113yes—
230C22×C4C22⋊Dic1113yes—
231C22×C4C2×C22⋊D1113yes—
232C22×C4C2×C22⋊D1113yes—
233C2×C8—226no—
234C2×C8—443no—
235C2×C8—441no—
236C2×C8—443no—
237C2×C8—443no—
238C2×C8—443no—
239C4⋊C4—23no—
240C4⋊C4—23no—
241C4⋊C4—26no—
242C22⋊C4—26no—
243C22⋊C4—26no—
244C22⋊C4—26no—
245C42—26no—
246C42—23no—
247C42—23no—
248C11#831611yescharacteristic, complemented, Sylow
249C23—24no—
250C23—23no—
251C23—23no—
252C23—41no—
253C23—41no—
254C23—43no—
255C23—43no—
256C23—81no—
257C23—81no—
258C23C22⋊(C11⋊C8)16yescomplemented
259C23C22×C11⋊C811yescharacteristic
260C23C2×#431813yes—
261C23C2×C22⋊Dic1113yes—
262Q8—24no—
263D4—212no—
264D4—212no—
265D4—212no—
266C2×C4—212no—
267C2×C4—23no—
268C2×C4—23no—
269C2×C4—23no—
270C2×C4—23no—
271C2×C4—23no—
272C2×C4—23no—
273C2×C4—43no—
274C2×C4—43no—
275C2×C4—43no—
276C2×C4—43no—
277C2×C4—43no—
278C2×C4—83no—
279C2×C4—83no—
280C2×C4—83no—
281C2×C4C22⋊(C11⋊C8)16yescomplemented
282C2×C4#6700613yes—
283C2×C4#6700611yescharacteristic
284C8—442no—
285C8—883no—
286C22—23no—
287C22—23no—
288C22—26no—
289C22—41no—
290C22—43no—
291C22—46no—
292C22—43no—
293C22—43no—
294C22—83no—
295C22—84no—
296C22C2×C22⋊(C11⋊C8)13yes—
297C22#1062282013yes—
298C22#1062286011yescharacteristic
299C4—23no—
300C4—26no—
301C4—43no—
302C4—43no—
303C4#1062285611yescharacteristic
304C4#1062285711yescharacteristic
305C2—23no—
306C2—23no—
307C2—46no—
308C2#1306852611yescharacteristic
309C2#1306856411yescharacteristic
310C2#1306856711yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC23×C11C22×C8
FrattiniC23×C4C22×D11
FittingC4×C11×H(5,𝔽2)C2
socleC22×C11#379
prime radicalC2×C11×H(5,𝔽2)C4
cosocleC23×C4×C11C23
hypercenterC4×H(5,𝔽2)D11
hypocenterC11#8316
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13068909C2semidirect
2. #13066934C2semidirect
11. C23×C11⋊C8C22semidirect
13. C2×C22⋊(C11⋊C8)C22semidirect
18. C11×H(5,𝔽2)C8semidirect
106. C23×C11C22⋊C8semidirect
129. C2×C4×C11C22⋊C8semidirect
167. H(5,𝔽2)C11⋊C8semidirect
248. C11#8316semidirect
258. C23C22⋊(C11⋊C8)semidirect
281. C2×C4C22⋊(C11⋊C8)semidirect

Maximal subgroups

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

subgroupindex
#130689092
#130669342
C4×C11×H(5,𝔽2)2
#831611