Finite Group Databasebeta

← #14658168

Subgroups — #14658168

Order 2816.

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

normal subgroups only

This group has 490 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#13069602C212yesmaximal
2#13069040C212yesmaximal
3#13068793C211yesmaximal, characteristic
4#13066484C211yesmaximal, characteristic
5C11×#3189C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2212yes—
7C23×C11⋊C8C2211yescharacteristic
8C11×#484—22no—
9C11×#467—21no—
10C11×#467—21no—
11C11×#451—22no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×#66899—22no—
14#10622825C2212yes—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C8—21no—
17#10622188—21no—
18#10622167—22no—
19#10622164—22no—
20#10622164—22no—
21C22×Q8×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—22no—
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C22⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11—22no—
38C2×C4×Dic11—21no—
39C22×C11⋊C8—22no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—42no—
42C11×#107—21no—
43C11×#107—21no—
44C11×#103—22no—
45C11×#103—22no—
46C11×C22⋊C8—22no—
47#66899—44no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50Dic11⋊C8—42no—
51#10566—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×C4×C11#4112yes—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—42no—
68C11×Q16—81no—
69C11×Q16—81no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C22⋊Dic11—21no—
81C22⋊Dic11—22no—
82C22⋊Dic11—42no—
83C22⋊Dic11—42no—
84C22⋊Dic11Q1612yescomplemented
85C4⋊Dic11—42no—
86C4⋊Dic11—42no—
87C4×Dic11—41no—
88C4×Dic11—41no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—24no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—41no—
94#3189D1111yescharacteristic
95#1996—112no—
96#1892—112no—
97#1850—111no—
98#1289—111no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11#12111yescharacteristic
102C23×C11#12112yes—
103C23×C11C2×Q1611yescharacteristic
104C23×C11#13511yescharacteristic
105C23×C11#13712yes—
106Q8×C11—44no—
107Q8×C11—42no—
108Q8×C11—42no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11—82no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12312yes—
121C2×C4×C11#12411yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131C8×C11—41no—
132C8×C11—41no—
133C11⋊C8—42no—
134C23×C8—111no—
135C2×C22⋊Q8C2×D1112yes—
136#484—22no—
137#467—21no—
138#467—21no—
139#451—22no—
140C2×C4⋊C8—221no—
141C2×#103—222no—
142C2×C22⋊C8C2×D1111yescharacteristic
143#380—112no—
144C4×C22⋊C4—111no—
145#342—222no—
146#342—222no—
147#340—222no—
148#336—221no—
149C22×C11—22no—
150C22×C11—21no—
151C22×C11—22no—
152C22×C11—21no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11#39411yescharacteristic
157C22×C11#46212yes—
158C22×C11#46412yes—
159C22×C11#46711yescharacteristic
160C22×C11#47011yescharacteristic
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—82no—
164C4×C11—82no—
165C4×C11B(4,𝔽2)11yescharacteristic
166C4×C11#45811yescharacteristic
167Dic11—42no—
168Dic11—81no—
169Dic11—162no—
170C22×Q8C22⋊D1112yes—
171C23×C4C22×D1111yescharacteristic
172C2×Q16—21no—
173C2×Q16—21no—
174C22×C8—221no—
175C22×C8—222no—
176C22×C8—442no—
177C22×C8C22⋊D1111yescharacteristic
178C22×C8C22⋊D1111yescharacteristic
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—222no—
185C2×C4⋊C4C22⋊D1112yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—111no—
188C2×C22⋊C4—111no—
189C2×C22⋊C4—222no—
190C2×C42—221no—
191#107—21no—
192#107—21no—
193C4⋊C8—442no—
194#103—22no—
195#103—22no—
196#103—444no—
197C22⋊C8—22no—
198#95—221no—
199#95—222no—
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11#204411yescharacteristic
205C2×C11#205311yescharacteristic
206C2×C11#205611yescharacteristic
207C24D4×D1111yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—42no—
211C2×Q8—42no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—442no—
219C22×C4#434111yescharacteristic
220C22×C4#434112yes—
221C22×C4C2×C22⋊D1112yes—
222C22×C4C2×C22⋊D1111yescharacteristic
223Q16—81no—
224Q16—81no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—224no—
230C2×C8—222no—
231C2×C8—441no—
232C2×C8—442no—
233C2×C8—441no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—442no—
239C4⋊C4—442no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—112no—
243C22⋊C4—221no—
244C22⋊C4—222no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C42—441no—
248C42—441no—
249C11#1056611yescharacteristic, complemented, Sylow
250C23—41no—
251C23—41no—
252C23Q16×D1111yescharacteristic
253C23#6697112yes—
254C23#6697211yescharacteristic
255C23#6699111yescharacteristic
256C23#6699212yes—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—222no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—882no—
277C2×C4—882no—
278C2×C4—882no—
279C2×C4#6698812yes—
280C2×C4#6698911yescharacteristic
281C2×C4#6700611yescharacteristic
282C8—41no—
283C8—41no—
284C8—442no—
285C22—22no—
286C22—21no—
287C22—22no—
288C22—21no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22#1062279512yes—
293C22#1062279812yes—
294C22#1062280111yescharacteristic
295C22#1062280211yescharacteristic
296C22#1062283511yescharacteristic
297C4—22no—
298C4—21no—
299C4—82no—
300C4—82no—
301C4—442no—
302C4—881no—
303C4—1762no—
304C4#1062285611yescharacteristic
305C4#1062285711yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2#1306986411yescharacteristic
311C2#1306991911yescharacteristic
312C2#1306993611yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3189C2
socleC22×C11#394
prime radicalC24×C11C2×D4
hypercenter#3189D11
hypocenterC11#10566
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
84. C22⋊Dic11Q16semidirect
249. C11#10566semidirect

Maximal subgroups

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

subgroupindex
#130696022
#130690402
#130687932
#130664842
C11×#31892
#1056611