Finite Group Databasebeta

← #14666299

Subgroups — #14666299

Order 2816.

384 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070561C212yesmaximal, complemented
2#13069903C211yesmaximal, characteristic, complemented
3#13066607C212yesmaximal, complemented
4#13066567C211yesmaximal, characteristic, complemented
5C11×#3253C211yesmaximal, characteristic, complemented
6C11×#532—21no—
7#10623279C2211yescharacteristic
8C11×#476—22no—
9C11×#469—21no—
10C11×#469C2212yes—
11C11×#459—22no—
12C11×#423C2211yescharacteristic
13#10622760—22no—
14#10622745—21no—
15C2×#66869—21no—
16C11⋊#338C2211yescharacteristic
17#10622191C2212yes—
18#10622126—22no—
19C2×C11×#41—41no—
20C2×#4339—21no—
21C2×C11×D8—21no—
22C2×C11×D8D412yes—
23C2×C11×M16D411yescharacteristic
24C2×C11×M16C2311yescharacteristic
25C11×C4⋊Q8—21no—
26C11×#127—21no—
27C11×#124—41no—
28C11×#121—22no—
29C11×#121—41no—
30C4×D4×C11—22no—
31C4×D4×C11—41no—
32C2×C42×C11D411yescharacteristic
33C2×#4318—21no—
34#66962—41no—
35#66961—41no—
36#66957—22no—
37C11×#106—21no—
38C11×#106D412yes—
39C11×C4⋊C8—22no—
40C11×#102—22no—
41C11×#102—22no—
42#66891—42no—
43#66890—42no—
44#66888—41no—
45#66887—41no—
46#66876—22no—
47#66869—41no—
48#66869—41no—
49#12173—111nomaximal, Sylow
50C11×#41—84no—
51C2×Q8×C11—41no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—42no—
56C22×C4×C11—21no—
57C22×C4×C11—42no—
58C22×C4×C11C2×D411yescharacteristic
59C2×C22⋊D11—41no—
60#4339—41no—
61#4339—41no—
62#4339—41no—
63#4339—41no—
64C2×D44—21no—
65C2×C4×D11—41no—
66C2×Dic22—21no—
67C11×D8—42no—
68C11×D8—81no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D412yes—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—41no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C42×C11—21no—
78C42×C11D811yescharacteristic
79C42×C11D811yescharacteristic
80#4318—41no—
81#4318—41no—
82C2×C11⋊C8—41no—
83Dic44—22no—
84D88—22no—
85#4314—42no—
86C11⋊C16—42no—
87#3253D1111yescharacteristic, complemented
88#2190—112no—
89#2050—111no—
90#1341—112no—
91#1327—111no—
92C23×C11—42no—
93C23×C11AGL(1,ℤ/8)11yescharacteristic
94C22×D11—41no—
95Q8×C11—82no—
96D4×C11—42no—
97D4×C11—42no—
98D4×C11—82no—
99D4×C11—82no—
100D4×C11—84no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—84no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C22⋊D11—81no—
111C22⋊D11—81no—
112C2×Dic11—41no—
113D44—41no—
114D44—41no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—41no—
118Dic22—41no—
119C8×C11—22no—
120C8×C11—41no—
121C11⋊C8—81no—
122#575—111no—
123#532—21no—
124#509—222no—
125#476—22no—
126#469—21no—
127#469C2×D1112yes—
128#459—22no—
129#423C2×D1111yescharacteristic
130C2×#104—221no—
131#413—221no—
132#360—222no—
133#349—112no—
134#338—111no—
135C22×C11—21no—
136C22×C11—41no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11#44711yescharacteristic
141C2×D11—81no—
142C2×D11—161no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11—82no—
147C4×C11#45411yescharacteristic
148C4×C11B(4,𝔽2)11yescharacteristic
149Dic11—81no—
150C2×#41—41no—
151C2×#41—221no—
152#137—441no—
153AGL(1,ℤ/8)—441no—
154#135—222no—
155C2×D8—21no—
156C2×D8C22⋊D1112yes—
157C2×M16—221no—
158C2×M16C22⋊D1111yescharacteristic
159C2×M16C22×D1111yescharacteristic
160C4⋊Q8—21no—
161#127—21no—
162#124—41no—
163#121—22no—
164#121—41no—
165C4×D4—22no—
166C4×D4—41no—
167C2×C42C22⋊D1111yescharacteristic
168SD32—442no—
169D16—442no—
170M32—222no—
171#106—21no—
172#106C22⋊D1112yes—
173C4⋊C8—22no—
174#104—441no—
175#104—441no—
176#102—22no—
177#102—22no—
178#101—441no—
179#100—441no—
180C2×C11—21no—
181C2×C11—41no—
182C2×C11—162no—
183C2×C11#159811yescharacteristic
184D11—161no—
185#41—84no—
186#41—441no—
187#41—441no—
188#41—441no—
189#41—441no—
190C2×Q8—41no—
191C2×Q8—221no—
192C2×D4—22no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—42no—
196C2×D4—221no—
197C2×D4—441no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—441no—
201C22×C4C2×C22⋊D1111yescharacteristic
202Q16—222no—
203SD16—442no—
204D8—42no—
205D8—81no—
206D8—222no—
207M16—41no—
208M16—41no—
209M16—441no—
210M16—441no—
211C2×C8—21no—
212C2×C8—441no—
213C2×C8C2×C22⋊D1112yes—
214C4⋊C4—22no—
215C4⋊C4—41no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C42—21no—
219C42#432311yescharacteristic
220C42#432311yescharacteristic
221C16—442no—
222C11#1217311yescharacteristic, complemented, Sylow
223C23—42no—
224C23—441no—
225C23#6698511yescharacteristic
226Q8—82no—
227Q8—441no—
228Q8—441no—
229D4—42no—
230D4—42no—
231D4—82no—
232D4—82no—
233D4—84no—
234D4—441no—
235D4—441no—
236D4—881no—
237D4—881no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—84no—
245C2×C4—441no—
246C2×C4—881no—
247C2×C4—881no—
248C2×C4C2×#432311yescharacteristic
249C2×C4#6700611yescharacteristic
250C8—22no—
251C8—41no—
252C8—881no—
253C22—21no—
254C22—41no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—881no—
259C22—1761no—
260C22#1062283011yescharacteristic
261C4—22no—
262C4—21no—
263C4—41no—
264C4—82no—
265C4—881no—
266C4#1062285711yescharacteristic
267C4#1062285811yescharacteristic
268C2—21no—
269C2—41no—
270C2—162no—
271C2—1761no—
272C2#1306755111yescharacteristic
subgroupG/H
centerC2#13067551
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3253C2
socleC2×C11#1598
hypercenter#3253D11
hypocenterC11#12173
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #13070561C2semidirect
2. #13069903C2semidirect
3. #13066607C2semidirect
4. #13066567C2semidirect
5. C11×#3253C2semidirect
87. #3253D11semidirect
222. C11#12173semidirect

Maximal subgroups

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

subgroupindex
#130705612
#130699032
#130666072
#130665672
C11×#32532
#1217311