Finite Group Databasebeta

← #14652874

Subgroups — #14652874

Order 2816.

610 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 151 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#13076973C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic, complemented
3C2×#10622119C212yesmaximal, complemented
4C2×#10622123C212yesmaximal
5C11×#1842C211yesmaximal, characteristic, complemented
6C2×#66928C414yes—
7C2×#66927C2211yescharacteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8—22no—
10C2×C11×C4⋊C8C2212yes—
11C43×C11C2211yescharacteristic
12#10622552—21no—
13#10622552—21no—
14#10622552—22no—
15C2×C4⋊(C11⋊C8)C2212yes—
16C2×#66867—21no—
17#10622162—21no—
18#10622123—24no—
19#10622119—24no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44C2×C412yes—
23C22×Dic22C2×C412yes—
24C22×C8×C11—22no—
25C2×C42×C11C2×C412yes—
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×(C2×D11)⋊C4—24no—
31C2×(C2×D11)⋊C4—24no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C22×C11⋊C8—22no—
35#66928—48no—
36#66927—22no—
37#66927—22no—
38#66922—22no—
39#66922—22no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8—22no—
42C11×C4⋊C8—44no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45#66867—42no—
46#9707—111nomaximal, Sylow
47C23×D11—22no—
48C22×C4×C11C22⋊C412yes—
49C22×C4×C11C22⋊C412yes—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×Dic11—22no—
54C2×D44—24no—
55C2×D44—44no—
56C2×D44—42no—
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—42no—
60C2×D44—41no—
61C2×D44—42no—
62C2×D44—41no—
63C2×D44—42no—
64C2×Dic22—24no—
65C2×Dic22—44no—
66C2×C8×C11—42no—
67C2×C8×C11—44no—
68C42×C11—24no—
69C42×C11—22no—
70C42×C11—21no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11—21no—
74C42×C11C2×D412yes—
75C42×C11#4112yes—
76(C2×D11)⋊C4—48no—
77(C2×D11)⋊C4—48no—
78C4⋊Dic11—42no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2858—111no—
85#1842D1111yescharacteristic, complemented
86#1767—111no—
87C2×#333—112no—
88C2×#331—112no—
89C23×C11C2×C22⋊C411yescharacteristic
90C22×D11—42no—
91C22×D11—44no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—44no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11#10014yes—
102C2×C4×C11C4×D412yes—
103C2×C4×C11#12112yes—
104C2×C4×C11#12411yescharacteristic
105C2×C4×C11#12711yescharacteristic
106C2×C4×C11#13512yes—
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×C4×C11#13711yescharacteristic
110C2×C4×C11#13712yes—
111C2×Dic11—42no—
112C2×Dic11—44no—
113D44—84no—
114D44—82no—
115D44—82no—
116D44—82no—
117D44—81no—
118D44—81no—
119Dic22—84no—
120C8×C11—82no—
121C11⋊C8—44no—
122C2×C4⋊Q8—111no—
123C2×#127—111no—
124C2×#124—114no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—112no—
127C2×C4⋊C8C2×D1112yes—
128C2×#97—221no—
129#390—221no—
130#390—221no—
131#390—222no—
132C43C2×D1111yescharacteristic
133#336—221no—
134#333—224no—
135#331—224no—
136C22×C11#39011yescharacteristic
137C22×C11C2×#10012yes—
138C22×C11#41611yescharacteristic
139C22×C11#41711yescharacteristic
140C22×C11#41712yes—
141C2×D11—84no—
142C2×D11—84no—
143C2×D11—82no—
144C2×D11—82no—
145C2×D11—82no—
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11#46312yes—
150C4×C11#46412yes—
151C4×C11#48912yes—
152C4×C11#49611yescharacteristic
153C4×C11#49711yescharacteristic
154Dic11—82no—
155C22×Q8—112no—
156C22×D4—112no—
157C22×D4—221no—
158C22×D4—221no—
159C22×C8—22no—
160C22×C8—222no—
161C4⋊Q8—222no—
162C4⋊Q8—222no—
163#127—222no—
164#127—222no—
165#124—448no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4—221no—
168C2×C22⋊C4—224no—
169C2×C22⋊C4—224no—
170C2×C42C4×D1112yes—
171C2×C42D4411yescharacteristic
172C2×C42D4411yescharacteristic
173C2×C42C22⋊D1112yes—
174C2×C42C22×D1111yescharacteristic
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—44no—
178C4⋊C8—114no—
179C4⋊C8—222no—
180#97—442no—
181C2×C11#155112yes—
182C2×C11#156012yes—
183C2×C11#195911yescharacteristic
184C2×C11#196511yescharacteristic
185C2×C11#198311yescharacteristic
186D11—162no—
187C24—222no—
188C2×Q8—224no—
189C2×Q8—444no—
190C2×D4—224no—
191C2×D4—444no—
192C2×D4—442no—
193C2×D4—442no—
194C2×D4—441no—
195C2×D4—441no—
196C2×D4—442no—
197C2×D4—441no—
198C2×D4—442no—
199C2×D4—441no—
200C22×C4—222no—
201C22×C4(C2×D11)⋊C412yes—
202C22×C4(C2×D11)⋊C412yes—
203C22×C4C2×C4×D1111yescharacteristic
204C22×C4C2×D4411yescharacteristic
205C22×C4C2×C22⋊D1111yescharacteristic
206C2×C8—44no—
207C2×C8—42no—
208C2×C8—224no—
209C2×C8—442no—
210C2×C8—442no—
211C4⋊C4—442no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C22⋊C4—448no—
215C22⋊C4—448no—
216C42—24no—
217C42—22no—
218C42—21no—
219C42—21no—
220C42—22no—
221C42—22no—
222C42D4×D1112yes—
223C42#434312yes—
224C11#970711yescharacteristic, complemented, Sylow
225C23—442no—
226C23—444no—
227C23—442no—
228C23—444no—
229C23—442no—
230C23C2×(C2×D11)⋊C411yescharacteristic
231Q8—884no—
232D4—884no—
233D4—881no—
234D4—881no—
235D4—882no—
236D4—882no—
237D4—882no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—444no—
245C2×C4—442no—
246C2×C4#6688714yes—
247C2×C4#6694612yes—
248C2×C4#6694812yes—
249C2×C4#6695712yes—
250C2×C4#6696111yescharacteristic
251C2×C4#6696211yescharacteristic
252C2×C4#6698512yes—
253C2×C4#6699311yescharacteristic
254C2×C4#6699512yes—
255C2×C4#6700011yescharacteristic
256C8—82no—
257C8—444no—
258C22—884no—
259C22—884no—
260C22—882no—
261C22—882no—
262C22—882no—
263C22#1062257912yes—
264C22#1062260111yescharacteristic
265C22#1062272611yescharacteristic
266C22C2×#6688712yes—
267C22#1062274611yescharacteristic
268C4—24no—
269C4—22no—
270C4—42no—
271C4—882no—
272C4#1062245712yes—
273C4#1062245812yes—
274C4#1062268711yescharacteristic
275C4#1062269911yescharacteristic
276C4#1062270212yes—
277C2—1762no—
278C2#1306730912yes—
279C2#1306734912yes—
280C2#1306943011yescharacteristic
281C2#1306945511yescharacteristic
282C2#1306954611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1842C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1842D11
hypocenterC11#9707
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1842

Complements

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

NH ≅ G/Ntype
2. #13068469C2semidirect
3. C2×#10622119C2semidirect
5. C11×#1842C2semidirect
85. #1842D11semidirect
224. C11#9707semidirect

Maximal subgroups

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

subgroupindex
#130769732
#130684692
C2×#106221192
C2×#106221232
C11×#18422
#970711