Finite Group Databasebeta

← #14652891

Subgroups — #14652891

Order 2816.

590 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 147 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#13068733C211yesmaximal, characteristic, complemented
3C2×#10622124C212yesmaximal, complemented
4C2×#10622123C212yesmaximal
5C11×#1767C211yesmaximal, characteristic, complemented
6C2×#66928—22no—
7C2×#66927C2211yescharacteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2212yes—
10C2×C11×#97—21no—
11C43×C11C2211yescharacteristic
12#10622552—21no—
13#10622552—21no—
14#10622552C414yes—
15C2×C4⋊(C11⋊C8)C2212yes—
16C11×#336—21no—
17#10622162—22no—
18#10622124—24no—
19#10622123—24no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44C2×C412yes—
23C22×Dic22—21no—
24C22×C8×C11—22no—
25C2×C42×C11C2×C412yes—
26C2×C42×C11D412yes—
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×(C2×D11)⋊C4—24no—
31C2×(C2×D11)⋊C4—24no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
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⋊C8D414yes—
42C11×#97—42no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45#9710—111nomaximal, Sylow
46C23×D11—22no—
47C22×C4×C11C22⋊C412yes—
48C22×C4×C11C22⋊C412yes—
49C22×C4×C11C22×C411yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×Dic11—22no—
53C2×D44—24no—
54C2×D44—44no—
55C2×D44—42no—
56C2×D44—41no—
57C2×D44—41no—
58C2×D44—42no—
59C2×D44—44no—
60C2×D44—41no—
61C2×D44—41no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×Dic22—44no—
65C2×C8×C11—24no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C42×C11—22no—
69C42×C11—21no—
70C42×C11—24no—
71C42×C11—21no—
72C42×C11—42no—
73C42×C11C2×D412yes—
74C42×C11#4112yes—
75(C2×D11)⋊C4—48no—
76(C2×D11)⋊C4—48no—
77C4⋊Dic11—24no—
78C4⋊Dic11—42no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—44no—
81#2858—111no—
82#1831—111no—
83#1767D1111yescharacteristic, complemented
84C2×#332—112no—
85C2×#331—112no—
86C23×C11C2×C22⋊C411yescharacteristic
87C22×D11—42no—
88C22×D11—44no—
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—44no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11C4×D412yes—
100C2×C4×C11#12112yes—
101C2×C4×C11#12411yescharacteristic
102C2×C4×C11#12711yescharacteristic
103C2×C4×C11#13512yes—
104C2×C4×C11AGL(1,ℤ/8)14yes—
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C11#13711yescharacteristic
107C2×Dic11—42no—
108C2×Dic11—44no—
109D44—84no—
110D44—82no—
111D44—82no—
112D44—82no—
113D44—82no—
114Dic22—82no—
115Dic22—82no—
116C8×C11—44no—
117C11⋊C8—82no—
118C2×C4⋊Q8—111no—
119C2×#127—111no—
120C2×#124—222no—
121C2×C4⋊C8—112no—
122C2×C4⋊C8C2×D1112yes—
123C2×#97—21no—
124#390—114no—
125#390—221no—
126#390—221no—
127C43C2×D1111yescharacteristic
128#336—21no—
129#336—222no—
130#332—224no—
131#331—224no—
132C22×C11#39011yescharacteristic
133C22×C11#41312yes—
134C22×C11#41611yescharacteristic
135C22×C11#41711yescharacteristic
136C22×C11#41812yes—
137C2×D11—84no—
138C2×D11—84no—
139C2×D11—82no—
140C2×D11—82no—
141C2×D11—82no—
142C4×C11—22no—
143C4×C11—42no—
144C4×C11—42no—
145C4×C11#46312yes—
146C4×C11#46412yes—
147C4×C11#49012yes—
148C4×C11#49612yes—
149Dic11—82no—
150C22×Q8—221no—
151C22×D4—112no—
152C22×D4—221no—
153C22×D4—221no—
154C22×C8—22no—
155C22×C8—222no—
156C4⋊Q8—222no—
157C4⋊Q8—222no—
158#127—222no—
159#127—222no—
160#124—448no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4—221no—
163C2×C22⋊C4—224no—
164C2×C22⋊C4—224no—
165C2×C42C4×D1112yes—
166C2×C42D4412yes—
167C2×C42C22⋊D1111yescharacteristic
168C2×C42C22⋊D1111yescharacteristic
169C2×C42C22×D1111yescharacteristic
170C4⋊C8—22no—
171C4⋊C8—222no—
172C4⋊C8—222no—
173C4⋊C8D4414yes—
174#97—42no—
175C2×C11#155312yes—
176C2×C11#155712yes—
177C2×C11#196111yescharacteristic
178C2×C11#196711yescharacteristic
179C2×C11#198311yescharacteristic
180D11—162no—
181C24—222no—
182C2×Q8—441no—
183C2×Q8—441no—
184C2×Q8—444no—
185C2×D4—224no—
186C2×D4—444no—
187C2×D4—441no—
188C2×D4—441no—
189C2×D4—444no—
190C2×D4—442no—
191C2×D4—441no—
192C2×D4—441no—
193C2×D4—442no—
194C22×C4—222no—
195C22×C4(C2×D11)⋊C412yes—
196C22×C4(C2×D11)⋊C412yes—
197C22×C4C2×C4×D1111yescharacteristic
198C22×C4C2×D4411yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200C2×C8—24no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—442no—
204C2×C8—444no—
205C4⋊C4—224no—
206C4⋊C4—442no—
207C22⋊C4—448no—
208C22⋊C4—448no—
209C42—24no—
210C42—21no—
211C42—21no—
212C42—22no—
213C42—42no—
214C42C2×D4412yes—
215C42#433912yes—
216C11#971011yescharacteristic, complemented, Sylow
217C23—444no—
218C23—444no—
219C23—442no—
220C23—442no—
221C23—442no—
222C23C2×(C2×D11)⋊C411yescharacteristic
223Q8—882no—
224Q8—882no—
225D4—884no—
226D4—882no—
227D4—882no—
228D4—882no—
229D4—882no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—444no—
238C2×C4—442no—
239C2×C4C4×D4412yes—
240C2×C4#6692711yescharacteristic
241C2×C4#6692811yescharacteristic
242C2×C4#6696114yes—
243C2×C4#6698312yes—
244C2×C4#6698511yescharacteristic
245C2×C4#6699511yescharacteristic
246C2×C4#6700312yes—
247C8—44no—
248C8—882no—
249C22—884no—
250C22—884no—
251C22—882no—
252C22—882no—
253C22—882no—
254C22#1062255211yescharacteristic
255C22#1062257911yescharacteristic
256C22#1062261511yescharacteristic
257C22#1062274412yes—
258C22#1062274512yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—882no—
263C4#1062232512yes—
264C4#1062232612yes—
265C4#1062262912yes—
266C4#1062264112yes—
267C2—1762no—
268C2#1306732212yes—
269C2#1306733612yes—
270C2#1306944011yescharacteristic
271C2#1306946511yescharacteristic
272C2#1306954811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#9710
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #13068733C2semidirect
3. C2×#10622124C2semidirect
5. C11×#1767C2semidirect
83. #1767D11semidirect
216. C11#9710semidirect

Maximal subgroups

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

subgroupindex
#130769732
#130687332
C2×#106221242
C2×#106221232
C11×#17672
#971011