Finite Group Databasebeta

← #14642351

Subgroups — #14642351

Order 2816.

500 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 119 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#13068684C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066439C214yesmaximal, complemented
4C11×#2857C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11C2211yescharacteristic
8C11×#391—21no—
9C11×#389—21no—
10C11×#389C2212yes—
11C11×#384C411yescharacteristic
12C11×#380—21no—
13C11×#380C412yes—
14C2×C22⋊(C11⋊C8)—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×#66867—21no—
17#10622162—21no—
18#10622162C2212yes—
19#10622162C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—42no—
25C11×C22⋊Q8—44no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C22⋊C4—22no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—22no—
40C11×#95—22no—
41C11×#95—22no—
42C22⋊(C11⋊C8)—24no—
43C22⋊(C11⋊C8)—42no—
44#66867—42no—
45#7708—111nomaximal, Sylow
46C24×C11C22⋊C411yescharacteristic
47C2×Q8×C11—42no—
48C2×Q8×C11—42no—
49C2×Q8×C11—42no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C11×C4⋊C4—24no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—44no—
73C11×C22⋊C4—44no—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—41no—
77C42×C11—41no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2857D1111yescharacteristic
85#1817—111no—
86#1749—111no—
87#1271—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11#10112yes—
95C23×C11C2×C22⋊C411yescharacteristic
96Q8×C11—84no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—44no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11#9912yes—
120C2×C4×C11#10412yes—
121C2×C4×C11#13112yes—
122C2×C4×C11AGL(1,ℤ/8)12yes—
123C2×C4×C11#13712yes—
124C11⋊C8—44no—
125C11⋊C8—82no—
126C2×C4⋊Q8Dic1111yescharacteristic
127C2×C22⋊Q8—21no—
128C22×C42C2×D1111yescharacteristic
129C2×C22⋊C8—221no—
130C2×C22⋊C8—221no—
131C2×#97—221no—
132#391—21no—
133#389—21no—
134#389C2×D1112yes—
135#384Dic1111yescharacteristic
136#380—21no—
137#380Dic1112yes—
138#336—112no—
139#336—112no—
140#336—221no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11#40811yescharacteristic
149C22×C11C2×#9911yescharacteristic
150C22×C11C2×#10111yescharacteristic
151C22×C11#41811yescharacteristic
152C22×C11#41911yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C22×C11#42111yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—82no—
162C4×C11—82no—
163C22×Q8—21no—
164C23×C4C2×Dic1111yescharacteristic
165C23×C4C22⋊D1111yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C22×C8—222no—
168C22×C8—222no—
169C4⋊Q8—42no—
170C22⋊Q8—44no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C2×Dic1112yes—
176C2×C4⋊C4C2×Dic1112yes—
177C2×C22⋊C4—22no—
178C2×C42—42no—
179C2×C42C2×Dic1111yescharacteristic
180C2×C42C22⋊D1111yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22×D1111yescharacteristic
183C22⋊C8—224no—
184C22⋊C8—442no—
185#97—442no—
186#95—22no—
187#95—22no—
188C2×C11—42no—
189C2×C11#147211yescharacteristic
190C2×C11#148411yescharacteristic
191C2×C11#149711yescharacteristic
192C2×C11#150811yescharacteristic
193C2×C11#151011yescharacteristic
194C2×C11#153111yescharacteristic
195C2×C11#155611yescharacteristic
196C24C22⋊Dic1111yescharacteristic
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C22⋊Dic1111yescharacteristic
212C22×C4C22⋊Dic1111yescharacteristic
213C22×C4C22⋊Dic1111yescharacteristic
214C22×C4C22×Dic1111yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217C2×C8—224no—
218C2×C8—442no—
219C2×C8—442no—
220C2×C8—442no—
221C2×C8—442no—
222C2×C8—442no—
223C4⋊C4—24no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—44no—
229C22⋊C4—44no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C11#770811yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#6690012yes—
242C23C2×C22⋊Dic1111yescharacteristic
243Q8—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#6689812yes—
267C2×C4#6690112yes—
268C2×C4#6698512yes—
269C2×C4#6699512yes—
270C2×C4#6700112yes—
271C8—444no—
272C8—882no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22#1062282811yescharacteristic
281C22C2×#6689811yescharacteristic
282C22#1062283811yescharacteristic
283C22C2×#6690011yescharacteristic
284C22#1062284711yescharacteristic
285C22C2×#6690111yescharacteristic
286C22#1062284911yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—82no—
294C4—82no—
295C2—42no—
296C2#1306698011yescharacteristic
297C2#1306703311yescharacteristic
298C2#1306708911yescharacteristic
299C2#1306713611yescharacteristic
300C2#1306714511yescharacteristic
301C2#1306723111yescharacteristic
302C2#1306733311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2857D11
hypocenterC11#7708
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. #13066439C2semidirect
234. C11#7708semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130683782
#130664392
C11×#28572
#770811