Finite Group Databasebeta

← #14656289

Subgroups — #14656289

Order 2816.

742 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#10622688C212yesmaximal, complemented
2#13069552C211yesmaximal, characteristic, complemented
3C2×#10622182C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C2×C11×#493C211yesmaximal, characteristic
6C22×C11×D8—22no—
7C2×C11×#127C2212yes—
8C22×#4324—22no—
9C2×C4×Dic22C2211yescharacteristic
10C11×#493—24no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66896—22no—
13#10622688—24no—
14#10622688—24no—
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622188—22no—
18#10622182—24no—
19C22×D4×C11—22no—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×Dic22D411yescharacteristic
23C2×C11×D8—28no—
24C2×C11×D8—44no—
25C2×C11×D8—44no—
26C22×C8×C11D412yes—
27C11×#127—22no—
28C11×#127—22no—
29C11×#127—22no—
30C11×#127D414yes—
31C2×C42×C11C2311yescharacteristic
32C2×#4324—28no—
33C2×#4324—44no—
34C2×#4324—44no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C22×C11⋊C8—22no—
39C22×C11⋊C8—21no—
40C4×Dic22—22no—
41C4×Dic22—22no—
42C4×C8×C11—22no—
43#66896—28no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)D414yes—
47#10262—111nomaximal, Sylow
48C24×C11—42no—
49C2×D4×C11—24no—
50C2×D4×C11—24no—
51C2×D4×C11—24no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—44no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—44no—
60C2×D4×C11—42no—
61C2×D4×C11—84no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×Dic22—22no—
68C2×Dic22—21no—
69C2×Dic22—22no—
70C2×Dic22D812yescomplemented
71C11×D8—416no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11SD1614yescomplemented
75C42×C11C2×D412yes—
76C42×C11C2×D412yes—
77#4324—416no—
78C4⋊Dic11—22no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81C4×Dic11—41no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87C2×#493D1111yescharacteristic
88C2×#460—112no—
89#1984—111no—
90C2×#331—112no—
91#1277—111no—
92C23×C11—44no—
93C23×C11—84no—
94C23×C11—82no—
95C23×C11—82no—
96C23×C11—84no—
97C23×C11#12111yescharacteristic
98D4×C11—44no—
99D4×C11—44no—
100D4×C11—48no—
101D4×C11—84no—
102D4×C11—84no—
103D4×C11—82no—
104D4×C11—82no—
105D4×C11—82no—
106D4×C11—82no—
107C2×C4×C11—22no—
108C2×C4×C11#12012yes—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11#12112yes—
111C2×C4×C11#12711yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11C2×SD1612yes—
114C2×C4×C11#13511yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)12yes—
116C2×C4×C11AGL(1,ℤ/8)12yes—
117C2×Dic11—22no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—42no—
122Dic22—24no—
123Dic22—42no—
124C8×C11—24no—
125C11⋊C8—44no—
126C11⋊C8—81no—
127C22×SD16—222no—
128C22×D8—22no—
129C2×#127C2×D1112yes—
130C2×C4×Q8—111no—
131#493—24no—
132#460—224no—
133#460—224no—
134C2×C4⋊C8—112no—
135C2×C4⋊C8—111no—
136C2×#102—222no—
137C2×C4×C8C2×D1111yescharacteristic
138#336—222no—
139#331—224no—
140C22×C11—84no—
141C22×C11—84no—
142C22×C11—84no—
143C22×C11—164no—
144C22×C11—164no—
145C22×C11#39211yescharacteristic
146C22×C11#46012yes—
147C22×C11#46611yescharacteristic
148C22×C11#46911yescharacteristic
149C22×C11#47212yes—
150C4×C11—22no—
151C4×C11#44712yes—
152C4×C11#44912yes—
153C4×C11#45012yes—
154C4×C11#49211yescharacteristic
155C4×C11#49611yescharacteristic
156Dic11—42no—
157Dic11—81no—
158C22×Q8—111no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—22no—
162C2×SD16—228no—
163C2×SD16—444no—
164C2×SD16—444no—
165C2×D8—28no—
166C2×D8—44no—
167C2×D8—44no—
168C22×C8—222no—
169C22×C8—221no—
170C22×C8C22⋊D1112yes—
171#127—22no—
172#127—22no—
173#127—22no—
174#127C22⋊D1114yes—
175C4×Q8—222no—
176C4×Q8—222no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—221no—
179C2×C42—221no—
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—114no—
182C4⋊C8—222no—
183C4⋊C8—222no—
184#102—228no—
185C4×C8—22no—
186C2×C11—164no—
187C2×C11#166812yes—
188C2×C11#168812yes—
189C2×C11#199911yescharacteristic
190C2×C11#201411yescharacteristic
191C2×C11#201811yescharacteristic
192C24—42no—
193C2×Q8—112no—
194C2×Q8—221no—
195C2×Q8—222no—
196C2×Q8—222no—
197C2×D4—24no—
198C2×D4—24no—
199C2×D4—24no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—44no—
205C2×D4—44no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—84no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4D4×D1111yescharacteristic
213C22×C4#434111yescharacteristic
214C22×C4C2×C22⋊D1111yescharacteristic
215SD16—4416no—
216D8—416no—
217C2×C8—22no—
218C2×C8—22no—
219C2×C8—224no—
220C2×C8—442no—
221C2×C8—442no—
222C2×C8—442no—
223C2×C8—441no—
224C2×C8#432414yescomplemented
225C4⋊C4—222no—
226C4⋊C4—442no—
227C42—441no—
228C42—441no—
229C42D4×D1112yes—
230C42C2×C22⋊D1112yes—
231C11#1026211yescharacteristic, complemented, Sylow
232C23—44no—
233C23—82no—
234C23—82no—
235C23—84no—
236C23—84no—
237C23#6699111yescharacteristic
238Q8—224no—
239Q8—442no—
240D4—44no—
241D4—44no—
242D4—48no—
243D4—84no—
244D4—84no—
245D4—82no—
246D4—82no—
247D4—82no—
248D4—82no—
249C2×C4—22no—
250C2×C4—222no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—442no—
254C2×C4—441no—
255C2×C4D8×D1111yescharacteristic
256C2×C4#6696412yes—
257C2×C4#6696511yescharacteristic
258C2×C4#6698512yes—
259C2×C4C2×#432412yes—
260C2×C4#6699012yes—
261C2×C4#6699212yes—
262C2×C4#6699311yescharacteristic
263C2×C4#6700611yescharacteristic
264C8—24no—
265C8—444no—
266C8—881no—
267C22—84no—
268C22—84no—
269C22—84no—
270C22—164no—
271C22—164no—
272C22#1062268812yes—
273C22#1062277011yescharacteristic
274C22#1062277211yescharacteristic
275C22#1062277312yes—
276C22#1062283611yescharacteristic
277C4—22no—
278C4—442no—
279C4—881no—
280C4#1062268711yescharacteristic
281C4#1062268911yescharacteristic
282C4#1062276912yes—
283C4#1062277112yes—
284C4#1062283112yes—
285C2—164no—
286C2#1306797312yes—
287C2#1306809712yes—
288C2#1306961111yescharacteristic
289C2#1306970411yescharacteristic
290C2#1306972311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#493C2
socleC23×C11#121
hypercenterC2×#493D11
hypocenterC11#10262
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10622688C2semidirect
2. #13069552C2semidirect
3. C2×#10622182C2semidirect
4. #13066451C2semidirect
70. C2×Dic22D8semidirect
74. C2×C8×C11SD16semidirect
224. C2×C8#4324semidirect
231. C11#10262semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
#130695522
C2×#106221822
#130664512
C2×C11×#4932
#1026211