Finite Group Databasebeta

← #14674453

Subgroups — #14674453

Order 2816.

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

normal subgroups only

This group has 284 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#13081752C211yesmaximal, characteristic
2#13070936C212yesmaximal, complemented
3#13070724C211yesmaximal, characteristic, complemented
4#13066804C212yesmaximal, complemented
5C11×#1400C211yesmaximal, characteristic, complemented
6C2×#66957—21no—
7C2×C11×M32C2211yescharacteristic
8#10622729—21no—
9#10622522—22no—
10#10622521—22no—
11C2×Dic88C2211yescharacteristic, complemented
12#10622517—21no—
13#10622517C2212yes—
14C11×M64C2212yescomplemented
15#10622143C2211yescharacteristic, complemented
16#10622141—21no—
17Dic176—22no—
18#10622087—22no—
19C2×#4339—41no—
20C22×C8×C11D411yescharacteristic
21#66977—41no—
22C2×Dic44—21no—
23C2×Dic44—21no—
24#66957—22no—
25#66957—22no—
26#66957—41no—
27#66957—41no—
28C2×D88—21no—
29C2×#4314—41no—
30C11×M32—22no—
31C2×C11×C16D411yescharacteristic
32C2×C11×C16C2311yescharacteristic
33#66882—21no—
34#66880—41no—
35Dic88—21no—
36Dic88—22no—
37Dic88D412yes—
38#66864—22no—
39#66864—22no—
40D176—21no—
41D176D412yes—
42C11×C32—22no—
43#13668—111nomaximal, Sylow
44C22×C4×C11D811yescharacteristic
45C2×C22⋊D11—81no—
46#4339—42no—
47#4339—42no—
48#4339—81no—
49#4339—81no—
50C2×D44—41no—
51C2×C4×D11—81no—
52C2×Dic22—41no—
53C2×Dic22—41no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11D811yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C22⋊Dic11—81no—
59C4⋊Dic11—41no—
60Dic11⋊C4—81no—
61Dic44—22no—
62Dic44—41no—
63Dic44—41no—
64Dic44—41no—
65D88—22no—
66D88—41no—
67#4314—42no—
68#4314—42no—
69C11×C16—21no—
70C11×C16C2×D412yes—
71#3414—111no—
72#2264—112no—
73#2219—111no—
74#1418—112no—
75#1400D1111yescharacteristic, complemented
76C23×C11D1611yescharacteristic
77C22×D11—81no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11D1611yescharacteristic
81C2×C4×C11C2×D811yescharacteristic
82C22⋊D11—82no—
83C22⋊D11—82no—
84C2×Dic11—81no—
85C2×Dic11—81no—
86C2×Dic11—81no—
87D44—42no—
88D44—81no—
89C4×D11—82no—
90C4×D11—82no—
91Dic22—42no—
92Dic22—81no—
93Dic22—81no—
94Dic22—81no—
95C8×C11—21no—
96C8×C11#12011yescharacteristic
97C8×C11AGL(1,ℤ/8)11yescharacteristic
98C2×#135—221no—
99#510—222no—
100#509—222no—
101#508—112no—
102#508—221no—
103C2×Q32—111no—
104C2×M32C2×D1111yescharacteristic
105#467—221no—
106Q64—222no—
107SD64—222no—
108M64C2×D1112yescomplemented
109#367—111no—
110#358—221no—
111C22×C11—21no—
112C22×C11—41no—
113C22×C11C2×D1611yescharacteristic
114C2×D11—82no—
115C2×D11—162no—
116C4×C11—21no—
117C4×C11#44711yescharacteristic
118C4×C11#50911yescharacteristic
119Dic11—82no—
120Dic11—161no—
121Dic11—161no—
122C2×#41—441no—
123#135—222no—
124#135—222no—
125#135—441no—
126#135—441no—
127C2×Q16—221no—
128C2×Q16—221no—
129C2×SD16—441no—
130C2×D8—221no—
131C22×C8D4411yescharacteristic
132C22⋊Q8—441no—
133Q32—112no—
134Q32—221no—
135Q32—222no—
136SD32—222no—
137SD32—222no—
138D16—112no—
139D16—221no—
140M32—22no—
141C2×C16D4411yescharacteristic
142C2×C16C22×D1111yescharacteristic
143#107—221no—
144#103—441no—
145C32—22no—
146C2×C11—21no—
147C2×C11—41no—
148C2×C11#218411yescharacteristic
149D11—162no—
150#41—442no—
151#41—442no—
152#41—881no—
153#41—881no—
154C2×Q8—441no—
155C2×Q8—441no—
156C2×D4—441no—
157C2×D4—881no—
158C22×C4—881no—
159C22×C4D8811yescharacteristic
160Q16—222no—
161Q16—441no—
162Q16—441no—
163Q16—441no—
164SD16—442no—
165SD16—442no—
166D8—222no—
167D8—441no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8D8811yescharacteristic
171C2×C8C2×D4411yescharacteristic
172C4⋊C4—441no—
173C4⋊C4—881no—
174C22⋊C4—881no—
175C16—21no—
176C16D4×D1112yes—
177C11#1366811yescharacteristic, complemented, Sylow
178C23—881no—
179C23D17611yescharacteristic
180Q8—442no—
181Q8—881no—
182Q8—881no—
183Q8—881no—
184D4—442no—
185D4—881no—
186D4—882no—
187D4—882no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—882no—
191C2×C4—881no—
192C2×C4—882no—
193C2×C4—881no—
194C2×C4—881no—
195C2×C4D17611yescharacteristic
196C2×C4C2×D8811yescharacteristic
197C8—21no—
198C8#6693511yescharacteristic
199C8#6696111yescharacteristic
200C22—21no—
201C22—41no—
202C22—882no—
203C22—1762no—
204C22C2×D17611yescharacteristic
205C4—21no—
206C4—882no—
207C4—1761no—
208C4—1761no—
209C4#1062234511yescharacteristic
210C4#1062252111yescharacteristic
211C2—21no—
212C2—41no—
213C2—1762no—
214C2#1307053011yescharacteristic
subgroupG/H
centerC2#13070530
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1400C2
socleC2×C11#2184
prime radical#13081752C2
hypercenter#1400D11
hypocenterC11#13668
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #1400

Complements

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

NH ≅ G/Ntype
2. #13070936C2semidirect
3. #13070724C2semidirect
4. #13066804C2semidirect
5. C11×#1400C2semidirect
11. C2×Dic88C22semidirect
14. C11×M64C22semidirect
15. #10622143C22semidirect
75. #1400D11semidirect
108. M64C2×D11semidirect
177. C11#13668semidirect

Maximal subgroups

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

subgroupindex
#130817522
#130709362
#130707242
#130668042
C11×#14002
#1366811