Finite Group Databasebeta

← #14667537

Subgroups — #14667537

Order 2816.

346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070787C212yesmaximal, complemented
2#13068215C211yesmaximal, characteristic, complemented
3#13066657C211yesmaximal, characteristic, complemented
4#13066589C212yesmaximal, complemented
5C11×#3291C211yesmaximal, characteristic
6C11×#577—22no—
7C11×#492C2211yescharacteristic
8C11×#471—22no—
9C11×#456—21no—
10C11×#453—21no—
11C11×#443C2212yes—
12#10622706—21no—
13#10622683—21no—
14#10622293C2211yescharacteristic, complemented
15#10622204—22no—
16#10622132—22no—
17#10622101C2212yescomplemented
18C8×C11⋊C8C2211yescharacteristic, complemented
19C11×2−1+4—21no—
20C11×H(5,𝔽2)—21no—
21C11×#137—22no—
22C11×#137—42no—
23C11×AGL(1,ℤ/8)—22no—
24C11×AGL(1,ℤ/8)—42no—
25C11×#135—42no—
26C11×#135D412yes—
27C2×C11×SD16—22no—
28C2×C11×SD16—42no—
29C11×#131—22no—
30C11×C4⋊Q8D411yescharacteristic
31C11×#127D411yescharacteristic
32#66922—21no—
33C11×#108D412yes—
34C11×#104—22no—
35C11×#101—21no—
36C11×#100—21no—
37C4×C8×C11C2311yescharacteristic
38#66896—42no—
39#66881—22no—
40#66876—22no—
41#66874—42no—
42C4×C11⋊C8—21no—
43#12365—111nomaximal, Sylow
44C11×#41—22no—
45C11×#41—42no—
46C11×#41—42no—
47C11×#41—81no—
48C2×Q8×C11—21no—
49C2×Q8×C11—42no—
50C2×D4×C11—21no—
51C2×D4×C11—41no—
52C2×D4×C11—42no—
53C2×D4×C11—81no—
54C2×Dic22—41no—
55C11×Q16—42no—
56C11×Q16SD1612yes—
57C11×SD16—22no—
58C11×SD16—42no—
59C11×SD16—42no—
60C11×SD16—42no—
61C11×SD16—42no—
62C11×D8—42no—
63C11×D8SD1612yes—
64C11×M16—22no—
65C11×M16—42no—
66C2×C8×C11—42no—
67C2×C8×C11C2×D412yes—
68C11×C4⋊C4—41no—
69C42×C11C2×D411yescharacteristic
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C2×C11⋊C8—22no—
73C11⋊C16—42no—
74#3291D1111yescharacteristic
75#2230—112no—
76#1708—111no—
77#1359—111no—
78#1335—112no—
79C23×C11—41no—
80C23×C11—81no—
81Q8×C11—22no—
82Q8×C11—42no—
83Q8×C11—81no—
84D4×C11—22no—
85D4×C11—42no—
86D4×C11—42no—
87D4×C11—82no—
88D4×C11—82no—
89D4×C11—81no—
90C2×C4×C11—21no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—81no—
94C2×C4×C11—82no—
95C2×C4×C11#12011yescharacteristic
96C2×Dic11—81no—
97Dic22—82no—
98C8×C11—42no—
99C8×C11C2×SD1612yes—
100C8×C11AGL(1,ℤ/8)12yes—
101C11⋊C8—42no—
102#577—22no—
103#498—111no—
104#492C2×D1111yescharacteristic
105#487—221no—
106#486—221no—
107#471—22no—
108#456—21no—
109#453—21no—
110#443C2×D1112yes—
111#365—222no—
112#364—112no—
113#360—222no—
114C82—111no—
115C22×C11—42no—
116C22×C11—81no—
117C22×C11—161no—
118C22×C11—321no—
119C22×C11#45311yescharacteristic
120C4×C11—22no—
121C4×C11—42no—
122C4×C11—81no—
123C4×C11#45012yes—
124Dic11—161no—
1252−1+4—21no—
126H(5,𝔽2)—21no—
127#137—22no—
128#137—42no—
129AGL(1,ℤ/8)—22no—
130AGL(1,ℤ/8)—42no—
131#135—42no—
132#135C22⋊D1112yes—
133C2×SD16—22no—
134C2×SD16—42no—
135#131—22no—
136C4⋊Q8—221no—
137C4⋊Q8C22⋊D1111yescharacteristic
138#127C22⋊D1111yescharacteristic
139M32—222no—
140#108C22⋊D1112yes—
141#106—222no—
142#104—22no—
143#103—442no—
144#102—442no—
145#101—21no—
146#100—21no—
147C4×C8—221no—
148C4×C8C22×D1111yescharacteristic
149C2×C11—21no—
150C2×C11—82no—
151C2×C11—161no—
152C2×C11#162911yescharacteristic
153#41—22no—
154#41—42no—
155#41—42no—
156#41—81no—
157C2×Q8—21no—
158C2×Q8—42no—
159C2×Q8—441no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—42no—
163C2×D4—81no—
164Q16—42no—
165Q16#432412yes—
166SD16—22no—
167SD16—42no—
168SD16—42no—
169SD16—42no—
170SD16—42no—
171D8—42no—
172D8#432412yes—
173M16—22no—
174M16—42no—
175C2×C8—42no—
176C2×C8—222no—
177C2×C8C2×C22⋊D1112yes—
178C4⋊C4—41no—
179C4⋊C4—441no—
180C4⋊C4—441no—
181C42C2×C22⋊D1111yescharacteristic
182C16—442no—
183C11#1236511yescharacteristic, complemented, Sylow
184C23—41no—
185C23—81no—
186Q8—22no—
187Q8—42no—
188Q8—81no—
189Q8—882no—
190D4—22no—
191D4—42no—
192D4—42no—
193D4—82no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—81no—
200C2×C4—82no—
201C2×C4—881no—
202C2×C4#6700611yescharacteristic
203C8—42no—
204C8—442no—
205C8#6698512yes—
206C8C2×#432412yes—
207C22—42no—
208C22—81no—
209C22—161no—
210C22—321no—
211C22#1062285411yescharacteristic
212C4—22no—
213C4—42no—
214C4—81no—
215C4—1761no—
216C4#1062283112yes—
217C2—21no—
218C2—82no—
219C2—161no—
220C2#1306773211yescharacteristic
subgroupG/H
centerC2#13067732
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#3291C2
socleC2×C11#1629
hypercenter#3291D11
hypocenterC11#12365
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3291

Complements

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

NH ≅ G/Ntype
1. #13070787C2semidirect
2. #13068215C2semidirect
3. #13066657C2semidirect
4. #13066589C2semidirect
14. #10622293C22semidirect
17. #10622101C22semidirect
18. C8×C11⋊C8C22semidirect
183. C11#12365semidirect

Maximal subgroups

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

subgroupindex
#130707872
#130682152
#130666572
#130665892
C11×#32912
#1236511