Finite Group Databasebeta

← #14674432

Subgroups — #14674432

Order 2816.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×D11×Q32C211yesmaximal, characteristic
2C2×#10622160C211yesmaximal, characteristic, complemented
3#13070704C211yesmaximal, characteristic
4#13066798C211yesmaximal, characteristic, complemented
5#13066797C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic
7C2×C11×Q64C211yesmaximal, characteristic, complemented
8C2×Q16×D11—21no—
9C2×C11×Q32C2211yescharacteristic
10C2×C11×Q32C2211yescharacteristic
11#10622801—21no—
12C2×#66893—21no—
13D11×Q32—22no—
14D11×Q32—22no—
15C2×Dic88C2211yescharacteristic
16C2×C16×D11C2211yescharacteristic
17C11×Q64—22no—
18C2×C11×C32C2211yescharacteristic
19#10622202—21no—
20#10622160—22no—
21#10622142C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×Q8×D11—41no—
24C2×C11×Q16—21no—
25C2×C11×Q16—21no—
26#66999—41no—
27C2×#4326—41no—
28Q16×D11—24no—
29Q16×D11—42no—
30C2×Dic44—21no—
31C2×C8×D11D411yescharacteristic
32C11×Q32—21no—
33C11×Q32—21no—
34C11×Q32—21no—
35C11×Q32D412yes—
36C2×C11×C16C2311yescharacteristic
37#66899—41no—
38#66893—24no—
39#66882—21no—
40C2×C11⋊C16D411yescharacteristic
41Dic88—21no—
42Dic88D412yes—
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13665—111nomaximal, Sylow
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50Q8×D11—44no—
51Q8×D11—82no—
52C2×C4×D11—81no—
53C2×C4×D11D811yescharacteristic
54C2×Dic22—41no—
55C2×Dic22—81no—
56C11×Q16—22no—
57C11×Q16—41no—
58C11×Q16—41no—
59C11×Q16—41no—
60C2×C8×C11C2×D411yescharacteristic
61#4326—44no—
62(C2×D11)⋊C4—81no—
63C4⋊Dic11—41no—
64Dic11⋊C4—81no—
65C2×C11⋊C8D811yescharacteristic
66Dic44—22no—
67Dic44—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C22×Q32—111no—
74C2×Q64—111no—
75C2×Q64D1111yescharacteristic, complemented
76#2216—111no—
77#1416—111no—
78#1416—111no—
79C22⋊C32—111no—
80C22×D11D1611yescharacteristic
81Q8×C11—42no—
82Q8×C11—81no—
83Q8×C11—81no—
84Q8×C11—81no—
85C2×C4×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11C2×D811yescharacteristic
88C2×Dic11—81no—
89C2×Dic11—81no—
90C2×Dic11D1611yescharacteristic
91C4×D11—21no—
92C4×D11—21no—
93C4×D11—84no—
94Dic22—42no—
95Dic22—84no—
96Dic22—81no—
97C8×C11#12011yescharacteristic
98C8×C11AGL(1,ℤ/8)11yescharacteristic
99C11⋊C8—21no—
100C22×Q16—221no—
101C2×Q32—111no—
102C2×Q32—221no—
103C2×Q32—222no—
104C2×Q32—222no—
105C2×Q32C2×D1111yescharacteristic
106C2×Q32C2×D1111yescharacteristic
107C22×C16—111no—
108#467—221no—
109Q64—22no—
110Q64—222no—
111C2×C32—111no—
112C2×C32C2×D1111yescharacteristic
113#366—111no—
114#358—221no—
115C22×C11C2×D1611yescharacteristic
116C2×D11—21no—
117C2×D11—21no—
118C2×D11Q6412yescomplemented
119C4×C11—82no—
120C4×C11—161no—
121C4×C11#44711yescharacteristic
122C4×C11#50911yescharacteristic
123Dic11—21no—
124Dic11—82no—
125Dic11—161no—
126C22×Q8—441no—
127C2×Q16—21no—
128C2×Q16—21no—
129C2×Q16—224no—
130C2×Q16—221no—
131C2×Q16—441no—
132C2×Q16—442no—
133C22×C8—111no—
134C22⋊Q8—441no—
135Q32—21no—
136Q32—21no—
137Q32—21no—
138Q32—112no—
139Q32—224no—
140Q32—221no—
141Q32C22⋊D1112yes—
142C2×C16—111no—
143C2×C16—221no—
144C2×C16—221no—
145C2×C16C22×D1111yescharacteristic
146#107—221no—
147#103—441no—
148C32—21no—
149C32—221no—
150C2×C11#218411yescharacteristic
151C2×C11C2×Q6411yescharacteristic
152C2×C11#226411yescharacteristic
153D11—22no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—444no—
157C2×Q8—441no—
158C2×Q8—881no—
159C2×Q8—882no—
160C22×C4—111no—
161C22×C4—881no—
162Q16—22no—
163Q16—41no—
164Q16—41no—
165Q16—41no—
166Q16—222no—
167Q16—444no—
168Q16—441no—
169C2×C8—111no—
170C2×C8—221no—
171C2×C8—221no—
172C2×C8D4×D1111yescharacteristic
173C4⋊C4—441no—
174C4⋊C4—881no—
175C22⋊C4—881no—
176C16—221no—
177C16D4×D1111yescharacteristic
178C16C2×C22⋊D1111yescharacteristic
179C11#1366511yescharacteristic, complemented, Sylow
180C23—111no—
181Q8—42no—
182Q8—81no—
183Q8—81no—
184Q8—81no—
185Q8—442no—
186Q8—884no—
187Q8—881no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—111no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—884no—
194C2×C4—881no—
195C2×C4—881no—
196C2×C4D8×D1111yescharacteristic
197C8—221no—
198C8#6696411yescharacteristic
199C8#6699011yescharacteristic
200C22—112no—
201C22—221no—
202C22—221no—
203C22D11×D1611yescharacteristic
204C4—82no—
205C4—161no—
206C4—221no—
207C4—882no—
208C4—1761no—
209C4#1062252411yescharacteristic
210C4#1062276911yescharacteristic
211C2—222no—
212C2#1307052611yescharacteristic
213C2D11×Q6411yescharacteristic
214C2#1307093511yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×Q64C2
socleC22×C11C2×D16
prime radicalC22×D11D16
hypercenterC2×Q64D11
hypocenterC11#13665
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q64

Complements

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

NH ≅ G/Ntype
2. C2×#10622160C2semidirect
4. #13066798C2semidirect
5. #13066797C2semidirect
7. C2×C11×Q64C2semidirect
75. C2×Q64D11semidirect
118. C2×D11Q64semidirect
179. C11#13665semidirect

Maximal subgroups

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

subgroupindex
C2×D11×Q322
C2×#106221602
#130707042
#130667982
#130667972
(C2×D11)⋊C322
C2×C11×Q642
#1366511