Finite Group Databasebeta

← #14646019

Subgroups — #14646019

Order 2816.

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

normal subgroups only

This group has 682 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
1#13069606C212yesmaximal, complemented
2#13067354C211yesmaximal, characteristic, complemented
3#13067211C211yesmaximal, characteristic, complemented
4#13067055C212yesmaximal
5C11×#3509C211yesmaximal, characteristic
6C11×#557—22no—
7C11×#556—22no—
8C11×#552—24no—
9C11×#541—22no—
10C11×#536C412yes—
11C11×#533—22no—
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C11×#519C412yes—
15C4×C11×#41C2211yescharacteristic
16#10622537C2212yes—
17C4×#4318C2212yes—
18#10622185—22no—
19#10622181—22no—
20Q8⋊(C11⋊C8)—22no—
21D4⋊(C11⋊C8)—22no—
22#10622168—24no—
23C2×C11×#41C2×C411yescharacteristic
24C22×Q8×C11C2×C412yes—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—22no—
29C11×C4⋊Q8D412yes—
30C11×#126—28no—
31C11×#125—24no—
32C11×#125—28no—
33C11×#125D412yes—
34C11×#124—22no—
35C11×#123—24no—
36C11×C22⋊Q8—24no—
37C11×C22⋊Q8—22no—
38C11×C22⋊Q8—24no—
39C4×Q8×C11—24no—
40C4×Q8×C11—24no—
41C4×Q8×C11—24no—
42C4×Q8×C11—22no—
43C4×Q8×C11D412yes—
44C4×D4×C11—22no—
45C4×D4×C11D412yes—
46C11×#117—24no—
47C11×#117—24no—
48C11×#117—21no—
49C11×#117C2×C411yescharacteristic
50C11×#117C2×C412yes—
51C2×C11×C4⋊C4D414yes—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4318—22no—
55C2×#4318—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58#66867—22no—
59C4×C11⋊C8—22no—
60#8474—111nomaximal, Sylow
61C11×#41—42no—
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C2×Q8×C11—22no—
65C2×Q8×C11—44no—
66C2×Q8×C11C22⋊C411yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11C22⋊C411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11C22⋊C414yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D412yes—
74C11×C4⋊C4—28no—
75C11×C4⋊C4—28no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4—24no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—24no—
81C11×C4⋊C4C22⋊C412yes—
82C11×C4⋊C4C22⋊C414yes—
83C11×C22⋊C4—28no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C42×C11—28no—
88C42×C11—21no—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11C2×D412yes—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94#4318—24no—
95#4318—42no—
96#4318—44no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#3509D1111yescharacteristic
100#1997—112no—
101#1561—111no—
102#1526—111no—
103#1489—112no—
104C23×C11—21no—
105C23×C11C2×C22⋊C411yescharacteristic
106Q8×C11—22no—
107Q8×C11—44no—
108Q8×C11—44no—
109Q8×C11—42no—
110Q8×C11—42no—
111D4×C11—22no—
112D4×C11—42no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—44no—
124C2×C4×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11C2×C22⋊C411yescharacteristic
126C2×C4×C11#12012yes—
127C2×C4×C11#12012yes—
128C11⋊C8—44no—
129C11⋊C8—82no—
130#557—22no—
131#556—22no—
132#552—24no—
133#541—22no—
134#536Dic1112yes—
135#533—22no—
136#533C2×D1111yescharacteristic
137C2×C4⋊Q8C2×D1111yescharacteristic
138#519Dic1112yes—
139C4×#41C2×D1111yescharacteristic
140#423—112no—
141C4×M16—112no—
142#343—224no—
143#332—222no—
144#330—222no—
145Q8⋊C8—222no—
146D4⋊C8—222no—
147C22×C11—22no—
148C22×C11—21no—
149C22×C11—42no—
150C22×C11—41no—
151C22×C11#37911yescharacteristic
152C4×C11—22no—
153C4×C11—21no—
154C4×C11—42no—
155C4×C11—44no—
156C4×C11—41no—
157C4×C11—44no—
158C4×C11#41312yes—
159C4×C11#45412yes—
160C4×C11#45612yes—
161C2×#41C2×Dic1111yescharacteristic
162C22×Q8C2×Dic1112yes—
163C2×M16—222no—
164C2×M16—222no—
165C4⋊Q8—22no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—22no—
169C4⋊Q8C22⋊D1112yes—
170#126—28no—
171#125—24no—
172#125—28no—
173#125C22⋊D1112yes—
174#124—22no—
175#123—24no—
176C22⋊Q8—24no—
177C22⋊Q8—22no—
178C22⋊Q8—24no—
179C4×Q8—24no—
180C4×Q8—24no—
181C4×Q8—24no—
182C4×Q8—22no—
183C4×Q8C22⋊D1112yes—
184C4×D4—22no—
185C4×D4C22⋊D1112yes—
186#117—24no—
187#117—24no—
188#117—21no—
189#117C2×Dic1111yescharacteristic
190#117C2×Dic1112yes—
191C2×C4⋊C4C22⋊D1114yes—
192C2×C42—21no—
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—222no—
195C4⋊C8—222no—
196#97—222no—
197C4×C8—222no—
198C2×C11—41no—
199C2×C11—81no—
200C2×C11#178511yescharacteristic
201C2×C11#179312yes—
202#41—42no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—44no—
207C2×Q8C22⋊Dic1111yescharacteristic
208C2×D4—21no—
209C2×D4C22⋊Dic1111yescharacteristic
210C22×C4—21no—
211C22×C4—22no—
212C22×C4C22⋊Dic1114yes—
213C22×C4C22×Dic1111yescharacteristic
214C22×C4C2×C22⋊D1112yes—
215M16—224no—
216M16—442no—
217M16—444no—
218C2×C8—442no—
219C2×C8—442no—
220C4⋊C4—28no—
221C4⋊C4—28no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—24no—
227C4⋊C4C22⋊Dic1112yes—
228C4⋊C4C22⋊Dic1114yes—
229C22⋊C4—28no—
230C22⋊C4—21no—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C42—28no—
234C42—21no—
235C42—22no—
236C42—22no—
237C42C2×C22⋊D1112yes—
238C42C2×C22⋊D1111yescharacteristic
239C42C2×C22⋊D1111yescharacteristic
240C11#847411yescharacteristic, complemented, Sylow
241C23—21no—
242C23C2×C22⋊Dic1111yescharacteristic
243Q8—22no—
244Q8—44no—
245Q8—44no—
246Q8—42no—
247Q8—42no—
248D4—22no—
249D4—42no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4C2×C22⋊Dic1111yescharacteristic
262C2×C4C2×C22⋊Dic1111yescharacteristic
263C2×C4#6700612yes—
264C2×C4#6700612yes—
265C8—444no—
266C8—882no—
267C22—21no—
268C22—22no—
269C22—41no—
270C22—42no—
271C22#1062286011yescharacteristic
272C4—21no—
273C4—22no—
274C4—41no—
275C4—44no—
276C4—42no—
277C4—44no—
278C4#1062285012yes—
279C4#1062285812yes—
280C4#1062285912yes—
281C2—41no—
282C2—81no—
283C2#1306854411yescharacteristic
284C2#1306857512yes—
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3509C2
socleC22×C11#379
prime radicalC2×C11×#41C2×C4
cosocleC2×C42×C11C23
hypercenter#3509D11
hypocenterC11#8474
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13069606C2semidirect
2. #13067354C2semidirect
3. #13067211C2semidirect
240. C11#8474semidirect

Maximal subgroups

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

subgroupindex
#130696062
#130673542
#130672112
#130670552
C11×#35092
#847411