Finite Group Databasebeta

← #14674451

Subgroups — #14674451

Order 2816.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070933C212yesmaximal, complemented
2#13070724C211yesmaximal, characteristic, complemented
3#13066803C212yesmaximal, complemented
4#13066756C211yesmaximal, characteristic, complemented
5C11×#3414C211yesmaximal, characteristic
6C2×C11×#135—21no—
7C11×#510—22no—
8C11×#509—22no—
9C11×#508—21no—
10C11×#508C2212yes—
11C2×C11×M32C2211yescharacteristic
12#10622729—21no—
13C2×Dic88C2211yescharacteristic, complemented
14#10622160—22no—
15#10622158—22no—
16#10622143C2211yescharacteristic, complemented
17#10622141—21no—
18#10622137C2212yescomplemented
19C2×C11×#41—41no—
20C11×#135—22no—
21C11×#135—22no—
22C11×#135—41no—
23C11×#135—41no—
24C2×C11×Q16—21no—
25C2×C11×SD16—41no—
26C2×C11×D8—21no—
27C22×C8×C11D411yescharacteristic
28#66977—41no—
29C2×Dic44—21no—
30C11×Q32—21no—
31C11×Q32D412yes—
32C11×SD32—22no—
33C11×SD32—22no—
34C11×D16—21no—
35C11×D16D412yes—
36C11×M32—22no—
37C2×C11×C16D411yescharacteristic
38C2×C11×C16C2311yescharacteristic
39#66882—21no—
40#66880—41no—
41Dic88—22no—
42C11⋊C32—22no—
43#13668—111nomaximal, Sylow
44C11×#41—42no—
45C11×#41—42no—
46C11×#41—81no—
47C11×#41—81no—
48C2×Q8×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11—81no—
51C22×C4×C11—81no—
52C22×C4×C11D811yescharacteristic
53C2×Dic22—41no—
54C11×Q16—22no—
55C11×Q16—41no—
56C11×SD16—42no—
57C11×SD16—42no—
58C11×D8—22no—
59C11×D8—41no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11D811yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C22⋊Dic11—81no—
65C4⋊Dic11—41no—
66Dic11⋊C4—81no—
67Dic44—41no—
68Dic44—41no—
69C11×C16—21no—
70C11×C16C2×D412yes—
71#3414D1111yescharacteristic
72#2264—112no—
73#2219—111no—
74#1418—112no—
75#1400—111no—
76C23×C11—81no—
77C23×C11D1611yescharacteristic
78Q8×C11—42no—
79Q8×C11—81no—
80D4×C11—42no—
81D4×C11—81no—
82D4×C11—82no—
83D4×C11—82no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—82no—
87C2×C4×C11—81no—
88C2×C4×C11—82no—
89C2×C4×C11D1611yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×Dic11—81no—
92C2×Dic11—81no—
93Dic22—81no—
94Dic22—81no—
95C8×C11—21no—
96C8×C11#12011yescharacteristic
97C8×C11AGL(1,ℤ/8)11yescharacteristic
98C2×#135—21no—
99#510—22no—
100#509—22no—
101#508—21no—
102#508C2×D1112yes—
103C2×Q32—111no—
104C2×M32C2×D1111yescharacteristic
105#467—221no—
106Q64—222no—
107SD64—222no—
108M64—112no—
109#367—111no—
110#358—221no—
111C22×C11—21no—
112C22×C11—41no—
113C22×C11—82no—
114C22×C11—162no—
115C22×C11C2×D1611yescharacteristic
116C4×C11—21no—
117C4×C11—82no—
118C4×C11#44711yescharacteristic
119C4×C11#50911yescharacteristic
120Dic11—161no—
121Dic11—161no—
122C2×#41—41no—
123#135—22no—
124#135—22no—
125#135—41no—
126#135—41no—
127C2×Q16—21no—
128C2×Q16—221no—
129C2×SD16—41no—
130C2×D8—21no—
131C22×C8C22⋊D1111yescharacteristic
132C22⋊Q8—441no—
133Q32—21no—
134Q32—222no—
135Q32C22⋊D1112yes—
136SD32—22no—
137SD32—22no—
138D16—21no—
139D16C22⋊D1112yes—
140M32—22no—
141C2×C16C22⋊D1111yescharacteristic
142C2×C16C22×D1111yescharacteristic
143#107—221no—
144#103—441no—
145C32—222no—
146C2×C11—21no—
147C2×C11—41no—
148C2×C11—162no—
149C2×C11#218411yescharacteristic
150#41—42no—
151#41—42no—
152#41—81no—
153#41—81no—
154C2×Q8—41no—
155C2×Q8—441no—
156C2×D4—41no—
157C2×D4—81no—
158C22×C4—81no—
159C22×C4#432311yescharacteristic
160Q16—22no—
161Q16—41no—
162Q16—441no—
163Q16—441no—
164SD16—42no—
165SD16—42no—
166D8—22no—
167D8—41no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8#432311yescharacteristic
171C2×C8C2×C22⋊D1111yescharacteristic
172C4⋊C4—441no—
173C4⋊C4—881no—
174C22⋊C4—881no—
175C16—21no—
176C16C2×C22⋊D1112yes—
177C11#1366811yescharacteristic, complemented, Sylow
178C23—81no—
179C23#6689011yescharacteristic
180Q8—42no—
181Q8—81no—
182Q8—881no—
183Q8—881no—
184D4—42no—
185D4—81no—
186D4—82no—
187D4—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—82no—
191C2×C4—81no—
192C2×C4—82no—
193C2×C4—881no—
194C2×C4—881no—
195C2×C4#6689011yescharacteristic
196C2×C4C2×#432311yescharacteristic
197C8—21no—
198C8#6698511yescharacteristic
199C8#6700611yescharacteristic
200C22—21no—
201C22—41no—
202C22—82no—
203C22—162no—
204C22C2×#6689011yescharacteristic
205C4—21no—
206C4—82no—
207C4—1761no—
208C4—1761no—
209C4#1062276011yescharacteristic
210C4#1062283011yescharacteristic
211C2—21no—
212C2—41no—
213C2—162no—
214C2#1307052811yescharacteristic
subgroupG/H
centerC2#13070528
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
Fitting, prime radicalC11×#3414C2
socleC2×C11#2184
hypercenter#3414D11
hypocenterC11#13668
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #13070933C2semidirect
2. #13070724C2semidirect
3. #13066803C2semidirect
4. #13066756C2semidirect
13. C2×Dic88C22semidirect
16. #10622143C22semidirect
18. #10622137C22semidirect
177. C11#13668semidirect

Maximal subgroups

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

subgroupindex
#130709332
#130707242
#130668032
#130667562
C11×#34142
#1366811