Finite Group Databasebeta

← #14665299

Subgroups — #14665299

Order 2816.

280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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#13079246C211yesmaximal, characteristic
2#13070431C211yesmaximal, characteristic, complemented
3#13070380C211yesmaximal, characteristic, complemented
4#13066677C211yesmaximal, characteristic, complemented
5#13066656C211yesmaximal, characteristic, complemented
6#13066656C211yesmaximal, characteristic, complemented
7C11×#1366C211yesmaximal, characteristic, complemented
8#10623229C411yescharacteristic
9#10623228C411yescharacteristic
10C11×#499C2211yescharacteristic
11#10622682C411yescharacteristic
12#10622680C411yescharacteristic
13D11×M32—21no—
14#10622502—21no—
15#10622499—21no—
16#10622477—21no—
17#10622465—21no—
18#10622306C2211yescharacteristic
19#10622302C2211yescharacteristic
20C11×#364C2211yescharacteristic
21C11×#364C2211yescharacteristic
22#10622152—21no—
23#10622150—21no—
24#10622149—21no—
25#10622101C2211yescharacteristic
26#10622101C2211yescharacteristic
27C11×#125C2×C411yescharacteristic
28C11×#125C2×C411yescharacteristic
29C2×#4314—21no—
30C2×#4314—21no—
31C2×#4313D411yescharacteristic
32C2×C8×D11D411yescharacteristic
33#66951—41no—
34#66950—21no—
35#66948—21no—
36#66948—41no—
37#66947—41no—
38#66946—21no—
39#66943—41no—
40#66940—21no—
41#66927C2×C411yescharacteristic
42#66925C2×C411yescharacteristic
43#66922C2×C411yescharacteristic
44C11×M32—21no—
45C11×M32—21no—
46C11×#107—21no—
47C11×#106—21no—
48C4×C8×C11C2311yescharacteristic
49#66879D411yescharacteristic
50C8×Dic11D411yescharacteristic
51#66876—21no—
52#66876—21no—
53#66874—21no—
54#66874—21no—
55#66873—21no—
56#66873—21no—
57#66867C2×C411yescharacteristic
58#66862—41no—
59C16×D11—41no—
60#11991—111nomaximal, Sylow
61C2×D44—21no—
62C2×D44—41no—
63C2×D44—41no—
64C2×C4×D11—41no—
65C2×C4×D11C22⋊C411yescharacteristic
66C2×Dic22—21no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C42×C11C22×C411yescharacteristic
74(C2×D11)⋊C4—21no—
75(C2×D11)⋊C4—41no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—21no—
81Dic11⋊C4—41no—
82C4×Dic11—41no—
83C4×Dic11C22⋊C411yescharacteristic
84C2×C11⋊C8C22⋊C411yescharacteristic
85C2×C11⋊C8C22⋊C411yescharacteristic
86#4314—41no—
87#4314—41no—
88#4314—41no—
89#4314—41no—
90#4313—21no—
91#4313—21no—
92C8×D11—21no—
93C8×D11—21no—
94C11×C16—41no—
95C11×C16—41no—
96C11⋊C16—41no—
97C11⋊C16—41no—
98#3174—111no—
99#2166—111no—
100#2153—111no—
101#1366—111no—
102#1366D1111yescharacteristic, complemented
103#1359—111no—
104#1359—111no—
105C22×D11—41no—
106C22×D11#10011yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11C2×C22⋊C411yescharacteristic
111C2×Dic11—21no—
112C2×Dic11—41no—
113C2×Dic11#10011yescharacteristic
114D44—41no—
115D44—41no—
116D44—161no—
117D44—161no—
118C4×D11—21no—
119C4×D11—21no—
120C4×D11—161no—
121Dic22—41no—
122Dic22—41no—
123C8×C11#13511yescharacteristic
124C8×C11#13511yescharacteristic
125C8×C11AGL(1,ℤ/8)11yescharacteristic
126C8×C11#13711yescharacteristic
127C11⋊C8—21no—
128C11⋊C8—21no—
129#541—111no—
130#540—111no—
131C2×M32—221no—
132#499C2×D1111yescharacteristic
133#492—111no—
134#491—111no—
135#490—111no—
136#468—221no—
137#465—221no—
138#440—221no—
139C4×SD16—221no—
140#405—111no—
141#364—111no—
142#364—111no—
143#364—221no—
144#364C2×D1111yescharacteristic
145#364C2×D1111yescharacteristic
146#349—221no—
147#347—221no—
148C22×C11C2×#10011yescharacteristic
149C2×D11—21no—
150C2×D11—41no—
151C2×D11—81no—
152C2×D11—81no—
153C2×D11—81no—
154C4×C11—41no—
155C4×C11—81no—
156C4×C11—81no—
157C4×C11#41611yescharacteristic
158C4×C11#41711yescharacteristic
159Dic11—21no—
160Dic11—41no—
161Dic11—81no—
162C2×SD16—221no—
163C2×SD16—221no—
164C2×M16—111no—
165C22×C8—111no—
166C4⋊Q8—111no—
167#127—111no—
168#126—441no—
169#125—441no—
170#125C4×D1111yescharacteristic
171#125C4×D1111yescharacteristic
172#123—441no—
173C22⋊Q8—221no—
174#121—221no—
175#121—441no—
176C4×Q8—221no—
177C4×D4—221no—
178#117—111no—
179M32—21no—
180M32—21no—
181M32—221no—
182M32—221no—
183M32—441no—
184C2×C16—441no—
185#107—21no—
186#106—21no—
187#103—221no—
188#103—221no—
189#102—221no—
190#102—221no—
191#97—111no—
192#97—111no—
193C4×C8—111no—
194C4×C8C22×D1111yescharacteristic
195C2×C11—21no—
196C2×C11#155111yescharacteristic
197D11—41no—
198D11—161no—
199C2×Q8—221no—
200C2×D4—221no—
201C2×D4—441no—
202C2×D4—441no—
203C22×C4—111no—
204C22×C4—441no—
205SD16—441no—
206SD16—441no—
207SD16—441no—
208SD16—441no—
209M16—221no—
210M16—221no—
211C2×C8—111no—
212C2×C8—111no—
213C2×C8—221no—
214C2×C8—221no—
215C2×C8D4×D1111yescharacteristic
216C2×C8D4×D1111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—221no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C22⋊C4—221no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C22⋊C4—441no—
229C42—111no—
230C42—441no—
231C42C2×C4×D1111yescharacteristic
232C16—41no—
233C16—41no—
234C16—441no—
235C16—441no—
236C11#1199111yescharacteristic, complemented, Sylow
237C23—111no—
238C23—441no—
239Q8—441no—
240Q8—441no—
241D4—441no—
242D4—441no—
243D4—1761no—
244D4—1761no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—111no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—441no—
253C2×C4—1761no—
254C2×C4C22⋊C4×D1111yescharacteristic
255C8—221no—
256C8—221no—
257C8#6696711yescharacteristic
258C8#6696911yescharacteristic
259C8#6697111yescharacteristic
260C8#6697211yescharacteristic
261C22—221no—
262C22—441no—
263C22—881no—
264C22—881no—
265C22—881no—
266C22D11×#10011yescharacteristic
267C4—41no—
268C4—81no—
269C4—81no—
270C4—221no—
271C4—441no—
272C4—881no—
273C4#1062241611yescharacteristic
274C4#1062241711yescharacteristic
275C2—21no—
276C2—441no—
277C2—1761no—
278C2#1306731011yescharacteristic
subgroupG/H
centerC2#13067310
commutatorC42×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1366C2
socleC2×C11#1551
prime radical#10623229C4
cosocleC4×C8×C11C23
hypercenter#1366D11
hypocenterC11#11991
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
2. #13070431C2semidirect
3. #13070380C2semidirect
4. #13066677C2semidirect
5. #13066656C2semidirect
6. #13066656C2semidirect
7. C11×#1366C2semidirect
102. #1366D11semidirect
236. C11#11991semidirect

Maximal subgroups

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

subgroupindex
#130792462
#130704312
#130703802
#130666772
#130666562
C11×#13662
#1199111